Imperial Mum Crest
The Imperial family has two main crests, the chrysanthemum and the paulonia leaves.
The former is the main crest, and it has been in use for centuries. However, it was first
designated as an official Imperial crest in Meiji 2 [1869].

The symbol is a 16-petal mum with another 16 petals in the background. There is also
a plain 16-petal mum and a 14-petal mum as well. There are other variations, too, since
the mum crest is integrated in other family crests. One count places the number at
over 150 versions. The official crest, though, is used exclusively by the Imperial family.

As far as military sake cups are concerned, the mum itself is often stylized,
naturalized, and painted in a variety of colors. Its presence on a cup symbolized not
only the emperor but also the country of Japan.

Here are some examples I have found, but there are almost endless variations.
Official Imperial crest
16 petals
10 petals
Inscribed in gold 'Conquer China, Victorious Return.'
The blue kanji around the rim say 'Army Infantry 1st Class
Sergeant Ishikawa Gentaro, Dispatch Soldier.'
The kanji used for 'China' here is the old one, which dates this cup
to the First Sino-Japan War (1894-5).
Medic cup with Red Cross and mums.
Inscribed 'Army Medic Unit, Discharge Commemorative, Fujimoto.'
The poem says something like 'Your body is lighter than a feather, but duty
is heavier than a mountain. Do your duty and you can return home and
enjoy the blossoms.'
Inscribed 'Infantry 6th Regiment, Discharge Commemorative.'