The OED on 'Shogun'

shogun Sou.gun. Now only Hist. Forms: 7 shongo, 8-9 seogun, (9 djogoun), s(h)iogoon, sjogun, 9 ziogoon, 9- shogun. [Jap. shogun, short for sei-i-tai shogun, `barbarian-subduing great general', bestowed on the first holder of the office in 1192. Shogun is a Japanese sound-substitution for Chinese chiang chiin (chiang to lead, chiin army).] The hereditary commander-in-chief of the Japanese army, until 1867 the virtual ruler of Japan. Also called tycoon. By successive usurpations of power, the Shogun or Tycoon had become the real ruler of Japan, though nominally the subject of the Mikado, and acting in his name. This state of things was misunderstood by Europeans, and it was erroneously supposed that there were two emperors in Japan, the Mikado (who was the object of a loyalty of the nature of religious devotion) being called `the spiritual emperor', and the Shogun `the temporal emperor'. In 1867, with the abolition of the feudal system, the Mikado assumed the actual sovereignty, and the reign of the Shoguns came to an end.

1615 R. Cocks Diary (Hakl. Soc.) I. 5 His wife is sent back to her father Shongo Samme, King of Edo and to succeed in the Empire.
1727 Scheuchzer tr. Kæmpfer's Japan App. i. 65 It was thought expedient, that the Seogun, or Crown-General, should be sent against them at the head of the imperial army.
1863 Alcock Capital of Tycoon II. 233 The Seogun, or Dai-Seogun.
1875 N. Amer. Rev. CXX. 281 The fall of the shogun's (tycoon's) government.
1879 Audsley & Bowes Keramic Art Japan I. Pref., The difficulty which modern writers have found in deciding upon the correct mode of spelling the single word Shôgun; in the Japanese Government Reports we find it written Shogun; Mr. F. Ottwell Adams..writes it..Shôgun; Mr. Dickson, Shiogoon; Mr. Mossman, Siogoon; Mr. Mitford, Shogun; Dr. Siebold, Sjôgun; and Mr. Satow..Shôgun;
b. attrib. as designating fashions or art belonging to the Japanese feudal period.

1889 Sir E. Arnold Seas & Lands xiv. (1895) 226 A seated figure, which might have been taken at first for the chief triumph of the Shogun carvers' work.
1904 D. Sladen Playing the Game i. vi, Tied in the elegant and fantastic Shogun knots which are the formal way of fastening up presents in Dai Nippon.
Hence

'shogunal a., pertaining to a shogun, the shoguns, or the shogunate;

'shogunate, the office or dignity of a shogun or the shoguns;

'shogunite (rare), a partisan of the shogunate;

'shogunship = shogunate.

1841 Mann. & Cust; Japanese 357 The Annals begin to tell..of rival heirs contending for the ziogoonship.
1871 A. B. Mitford Tales Old Japan I. 99 After..the abolition of the Shogunate, he accompanied the last of the Shoguns in his retirement.
1873 Mossman New Japan 333 The despotic rule of the Mikados before the Siogoonate was established.
1883 E. M. Thompson R. Cocks' Diary (Hakl. Soc.) I. 5 note, Iyéyasu held the Shogunate only two years;
1890 Sir E. Arnold Seas & Lands xxii. (1895) 364 The rebels, or Shogunites, were defeated.
1899 C. J. Holmes Hokusai 14 His artistic reputation had even spread to the Shogunal court.