This will follow a list and talk about details step by step.

Firstly, lets talk about the Bear Infantry.

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1. It is not "Bear Infantry", it is Bear Officer

Most people learn about the Bear Infantry from Shogun 2 FOTS, but it is not a real units in Boshin War, bear infantry never existed, it is simply a creation in the game.

However, Bear Hat does exist. The Imperial sides officers will wear these hats.

Satsuma officer wear the Black Bear Hats. The "Black Bear" in Japanese "Koguma", 黒熊.
Choshu officer wear the White Bear Hats. The "White Bear" in Japanese "Haguma", 白熊.
Tosa officer wear the Red Bear Hats. The "Red Bear" in Japanese "Shaguma", 赤熊.

So the officers wear the bear hats, and the colour difference is an identify to which clan you belong to.
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Here is a wiki page about the vear hats:
https://en.wikipedia.org/wiki/Shaguma

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2. Imagination of the Jinshotai Bear Hats

The only units wear bear hats, maybe the Tosa (土佐藩) Jinshotai (迅衝隊), the artwork about the Battle of Ueno showed it. (Links below)

Surly, the game can add in a infantry called " Jinshotai" as the red bear infantry (Seriously, it is a suggestion, we can create some imaginations, but at least it can be more historical)

However history did not work in that way.

According to official documents, no Tosa soldiers fought during the Battle of Ueno. Hence, this artwork is more an imagination instead of facts.

In fact, we can assume bear hats works the same way for Tosa, officers wear them. And the Jinshotai wear the normal uniform and hats.
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Here is the artwork about the Tosa Jinshotai in the Battle of Ueno:
https://ja.wikipedia.org/wiki/%E8%BF%85%E8%A1%9D%E9%9A%8A#/media/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Battle_of_Ueno_at_Ueno_temple.JPG

The men in black western uniforms and red bear hats are members from Jinshotai, but remember what I said before, this artwork is unreliable, since Tosa soldiers did not appear during the battle.
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3. Closest to the "Bear Infantry", Yamaguni-tai

In fact, there is a Bear Infantry... well, something pretty close to it. They wear a different kind of Bear Hat, different from the Tosa, Choshu, or Satsuma ones.

Tottori Domain (鳥取藩) Yamaguni-tai (山国隊) is a militia units during the Boshin War, and they fought in the Imperial Army.
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Photos about modern parade:
http://kntryk.blog.fc2.com/blog-entry-1244.html?sp
https://www.sankei.com/article/20181020-MY2IF6NSXZL35OOSHTIPRWPHYY/photo/R4CSH7BLW5JTBGXLQQQ6JHBAUM/

Anime Artwork:
https://blog.goo.ne.jp/sieg1945/e/0167213f46943040a0897d1820fc621d

Check the detail about their hats, it is totally different from what the normal bear hats.

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4. No Bear Hats for Shogun units

Simply because only Imperial officers wear them, no shogun soldiers wear them.

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5. Cadets and Graduates

Another artwork may tell another story, it looks like some Army Cadets may wear the Bear Hats.

The artwork below is about an exercise in 1870, the soldiers are cadets.
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Artwork:
https://blogimg.goo.ne.jp/user_image/5c/5e/7cb4f0d4520b74a8a9931a0a6747d683.jpg

By the way, if you like the post, please support me by post your ideas, I may also do more researches on Victorian Era army.

Personal, I learn about the Japanese and Italy history during the Victorian Era, and their military as well.

Big Two, second topic

Flags.

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I know it is kinda awful to do the flags, when the creator does not have much information about the war factions.

But talking about flags, I must talk about clans, or domains.

Remember, this focus mainly on domains, alliance and their flags, I will talk about the units later, in the unit focus post.
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1. The flag in the mod

The shogun flag is Aizu clan, and the Imperial is the Satsuma clan.

Well, quiet nice choice, because they do represent the main clan fighting for their sides. However... other symbols may work much better... since not all soldier fought for the Shogun from Aizu, and not all Imperial soldiers are from Satsuma.

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2. Tokugawa Shogun and Imperial Court, two flowers

Using simply the symbol for Tokugawa and Imperial court maybe much better choice.

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Tokugawa Clan Mon:

https://en.wikipedia.org/wiki/Tokugawa_clan#/media/File:Tokugawa_family_crest.svghttps://en.wikipedia.org/wiki/Tokugawa_clan#/media/File:Tokugawa_family_crest.svg

The tokugawa clan mon is three hollyhock leaves inside a circle.
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Imperial Court Mon:

https://en.wikipedia.org/wiki/Mon_(emblem)#/media/File:Imperial_Seal_of_Japan.svg

Chrysanthemum blossom
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So yes, two mons are all flowers, so it is kinda "flower war".

However, although I suggested using the Tokugawa Mon, not many Shogun forces really used it as a flag during Boshin War, which I will explain later...

The Imperial court flag, did appear during the war, and it appeared a lot. The most famous event is during the Battle of Toba–Fushimi, where the Imperial Court Army showed the flag, and Shogun soldiers just retreated.

In Japanese history, fighting against the Emperor is a huge problem since the Tokugawa Shogun. The shogun force retreated from Toba–Fushimi simply because the Imperial flag means the Emperor himself, fighting against the army which owns the flag, meaning fighting against the Emperor.
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Imperial Court Flag:

http://blog-imgs-43.fc2.com/e/c/o/ecogeo/nisikinomihata.jpg
https://twitter.com/yukin_done/status/758842373086466048/photo/1
https://ameblo.jp/hosizoralove/image-12095065265-13482453386.html
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3. Why not Tokugawa hollyhock Mon?

The story is quiet complex, but I will explain it short.

The Boshin War, is a conflict started by Shogun and the Imperial Court, however, Shogun did not fight a lot.

Japan was divided into clans, or domains, there are two government, Shogun, and Imperial Court. The Boshin War is simply clans who support the Imperial Court fight against who support Shogun, you can learn this from Shogun 2 FOTS easily.

This means Shogun does not own lot of soldiers, in fact, their army are formed by all the clans. When a war start, the Shogun will call different clans, the clan who support the war will donate their troopers.

During the Boshin War, official shogun army only showed in two battles, small or large: Battle of Toba–Fushimi, Battle of Kōshū-Katsunuma.

Then, the Shogun surrendered, but not the remaining soldiers. Many soldiers escaped and continued their fights.

But still, Aizu clan used Tokugawa mon flag.

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4. Then what flag are the "Shogunate Army" use?

As I mentioned, the Shogun army is not simply Shogun soldiers, they are formed by Shogunate soldiers and other clans who supported Shogun.

We ll talk them later.
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Shogunate Army (幕府陸軍)
Shogun reformed its units under the western pattern, and later under French advisors and training.

The shogunate army I will talk about it later, now just focus on the flag:
https://twitter.com/ikkaisai/status/793053835723800576/photo/1

So yes, they use the "Red Ball" flag.

Here is also a Japanese Wiki page if you do not believe:
https://ja.wikipedia.org/wiki/%E5%B9%95%E5%BA%9C%E9%99%B8%E8%BB%8D

Tokugawa Shogun also have their own flag.

Tokugawa Shogunate Flag:
https://en.wikipedia.org/wiki/Tokugawa_shogunate#/media/File:Flag_of_the_Tokugawa_Shogunate.svg

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5. What other "Shogun Force" use?

I said, Shogun are supported by main clans. After the shogun fall, many clans formed their own alliance.

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5-1 top dog, Aizu domain (会津藩)

So yes, the mod captured that. Aizu is a main domain which supports the shogun.

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5-2 Ouetsu Reppan Domei (奥羽越列藩同盟, Alliance of the domains of Mutsu, Dewa, and Echigo)

After Shogun surrendered, the Imperial Army went to the domains of Mutsu, Dewa, and Echigo. They wanted punish Aizu domain, which is the main supporter of the Shogun. However, many domains in the area were unhappy about the decision.

Later, these domains formed an alliance, the Ouetsu Reppan Domei. Meaning: Alliance of the domains of Mutsu, Dewa, and Echigo; or short as coalition of northern domains.

Most members use the flag of Ouetsu Reppan Domei, but there are some domains which also use their own flags. (Aizu used both, others I will talk about them later)

The flag of Ouetsu Reppan Domei:
https://en.wikipedia.org/wiki/%C5%8Cuetsu_Reppan_D%C5%8Dmei#/media/File:Standard-bearer_in_2006_Aizu_parade.JPG
http://www.yae-mottoshiritai.jp/ashiato/reppan.html
https://blog.goo.ne.jp/mearikutiari/e/a8a1e23d7c4b6163cf3f68e0a5e218d8

Aizu was part of the Ouetsu Reppan Domei.
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5-2-1 The leaders of the Alliance, Sendai and Yonezawa

Sendai (仙台) was a main domain, also one of the leader in the Ouetsu Reppan Domei, they have a quiet large army, however, their equipment are old.

https://en.wikipedia.org/wiki/Sendai_Domain

Yonezawa (米沢) was another leader of the Ouetsu Reppan Domei. They also have a large army, mainly old equipment, but some good weapons are bought.

Seems like Sendai and Yonezawa used the flag of Ouetsu Reppan Domei only.

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5-2-2 The Gatling buyer, Nagaoka

Nagaoka (長岡) is a member of the Ouetsu Reppan Domei, they are famous because they bought two out of three Gatling guns during the Bakumatsu period.

The flag of Nagaoka troopers:
https://mo6380392.exblog.jp/22451630/
https://twitter.com/mntmch_warren/status/1292787363547029504/photo/2

Their flag is also called "ladder flag"
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5-2-3 The only winner, Shōnai

Shonai(庄内) is a member of the Ouetsu Reppan Domei, they are famous because they success campaign against the Imperial army. Shonai is the only domain in the Ouetsu Reppan Domei, which do not lose any territory during the Boshin War.

The flag of Shonai army:
https://ameblo.jp/staydream2017/image-12343924083-14110645895.html
https://twitter.com/sugashinobu/status/911871241958461440/photo/1

Their flag is also called "Seven Star Flag"
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5-2-4 Other domains

There are many domains in the alliance, I will not cover all of them.

But I will show few with their own flags.

The flag of Nihonmatsu (二本松):
https://www.kilamek-communication.net/2018/09/25/post-12960/

The flag of Tanagura (棚倉), (The third one, count from the left):
http://nasukougen.web.fc2.com/boshin/bosinimg/DSC_0059.jpg
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5-2-5 Betrayed Domains

Not every domain joined the alliance really fought for the alliance, many of them joined the Imperial Court when the war broke out.

The artwork on Kubota (久保田), which the domain is also known as Akita (秋田):
https://akita.keizai.biz/headline/2822/

The flag of Kubota is Satake clan's mon:
https://en.wikipedia.org/wiki/Satake_clan#/media/File:Satake.jpg
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Next post will come later, which will talk about other powers and their flags

5-3 Republic of Ezo

Shogunate soldier fought all the way to the North, however, Ouetsu Reppan Domei was defeated. Many people who hate the Imperial Army went to Ezo, and in there, they built their new country, the Republic of Ezo (蝦夷共和国)

Their flag:
http://g-nextage.jugem.jp/?eid=40
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5-4 Other Units

Many units during the Bakumatsu period used their own flags, sometimes these flags were designed, sometimes they are simply words indicate what units it is.

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5-4-1 The sword of the Shogun, Shinsengumi

Shinsengumi is a armed police force in the Bakumatsu period. They are Ronin from all over the country, and fight for the Shogun until the end.

Their flag:
https://en.wikipedia.org/wiki/Shinsengumi#/media/File:Flag_of_Shinsengumi.svg
https://www.photolibrary.jp/img74/12516_228729.html

The blue version:
https://publicdomainq.net/shinsengumi-flag-0020652/

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5-4-2 The Edo rebels, Shōgitai

Shogitai (彰義隊) was a unit formed by mainly Shogun samurais, and later waged the Battle of Ueno against the Imperial Army.

Their flag:
http://byp.cocolog-nifty.com/.shared/image.html?/photos/uncategorized/2018/04/13/sennin301.jpg
https://twitter.com/monakayoshihiro/status/1146730292117299201/photo/1
https://ameblo.jp/takasugi4039/image-11386872368-12251393680.html

The 一番 and 二番 on the flag means unit one and unit two.

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Later on the Imperial Army flags

6. Imperial Court Domains

Then we ll focus on the Domains on the Imperial Side and their flags.

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6-1 The back bone. Satsuma

Satsuma (薩摩) is a main domain which fight for the Imperial Court. The Imperial flag in the mod is the Satsuma Mon. Satsuma used that kind of flag during the Boshin War.

Satsuma Flag of the "Cross" Mon:

http://www.aizushinsengumi.com/shiryoukan_page/23.jpg

Satsuma, also used a more western style flag during the Boshin War.

Satsuma Army Flag during Boshin War:
https://en.wikipedia.org/wiki/Satsuma_Domain#/media/File:Flag_of_Satsuma_domain.svg

Artillery unit with Satsuma Army Western Pattern Flag:
http://www.pref.kagoshima.jp/ab23/reimeikan/josetsu/theme/gendai/boshin/images/1149.jpg

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6-2 The pioneer, Choshu

Choshu (長州) is a main domain which fight for the Imperial Court.

Choshu Mori Mon:
https://en.wikipedia.org/wiki/M%C5%8Dri_clan#/media/File:Ichimonjimitsuboshi.svg

Choshu Mori Mon flag in artwork (The closet one, Satsuma flag also appear):
https://blog-imgs-121.fc2.com/s/h/i/shibayan1954/2017021921092568f.jpg

Choshu Army Western Pattern Flag:
https://en.wikipedia.org/wiki/Ch%C5%8Dsh%C5%AB_Domain#/media/File:Flag_of_Choshu_domain.svg

Choshu soldier with Choshu Army Western Flag in artwork:
https://blog-imgs-121.fc2.com/s/h/i/shibayan1954/20170219210902cb3.jpg

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6-3 The supporter, Tosa

Tosa (長州) is a main domain which fight for the Imperial Court.

Tosa Army Western Pattern Flag:
https://en.wikipedia.org/wiki/Tosa_Domain#/media/File:Flag_of_Tosa_domain.svg

Tosa Army Western Pattern Flag in artwork (On the right side army):
https://upload.wikimedia.org/wikipedia/commons/thumb/1/1d/TobaFushimiBattle2.jpg/600px-TobaFushimiBattle2.jpg

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6-4 The Armstrong Maker, Saga

Saga (佐賀) is a main domain which fight for the Imperial Court, they are famous because they can make Armstrong cannons.

Saga Army Flag:
http://www.saganet.ne.jp/tunetami/con_16/img/9.jpg
https://www.facebook.com/furusatosagatanbou/photos/pcb.594138217384772/594138087384785/?type=3&theater

Saga Artillery Unit with flag in artwork:
https://img01.sagafan.jp/usr/furusato/UE.jpg

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Well, yes, there are more clans, but I will not go through all of them. I d better stop here.

I introduce most "Special" flags on both sides, if you are interested in more, most domains just used their mon flag. Hence, you can simply google the domain you want and find their mon and just put it on flag.

I will decide to talk about the unit or weapons first...

If you are interested in this topic, you can choose on which goes first.