Subdue does have several uses, but really only one meaning - to bring something under control.
If you were to describe a colour as "subdued" it means that it is muted, not too loud - as if controlled.
Similarly if a person is described as "subdued" they may be sullen, as if controlled by their emotions.
If you want to use it to describe groups or people under sovereignty or control, don't be put off by the other uses - context will make the meaning clear.
However, subdued in this sense also describes that action of bringing people or a country under control, or subjection. Using the word subdued implies that there may have been some military act such as an invasion. If you simply want to state that a group or nation is under the control of another without getting into the history of how that came about, you may want to choose a word other than subdued.
Synonyms of subdued in the sense of a military takeover include:
- conquered
- overpowered
- suppressed
As you can see, these mostly have negative connotations.
To simply show sovereignty you could use:
- ruled
- governed
- controlled