noun, noun which may take the genitive case particle 'no'
under the control of; under the dominion of
Used to indicate that someone or something is under the control, influence, or jurisdiction of another. Often followed by に置く, にある, or に入る.
その地域は敵の支配下に置かれた。
The area was placed under enemy control.
会社は外資系企業の支配下にある。
The company is under the control of a foreign-affiliated firm.
占領下 specifically means under military occupation, while 支配下 more broadly means under someone's control or rule, not necessarily through military occupation.
支配下 emphasizes being under direct control or domination, whereas 傘下 more neutrally describes organizational affiliation.
Compound of 支配 (control, domination) and 下 (under).