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.
管理下 emphasizes being under management or supervision, often in administrative or operational contexts, whereas 支配下 can imply broader or more absolute control.
Compound of 支配 (control, domination) and 下 (under).