The best way to answer this question is to look at the social theory of Peter Berger.
Berger argues that people have an innate desire to create order in the world. So, they create culture. Objectivation is the world that people create. The world is seen to have a life of its own. The irony is that people have created it. So, people accept it. They even create what he calls institutions. And these institutions seek to shape and control people. Again the important point to keep in mind is that people create it.
Finally, he talks about plausibility structures. Plausibility structures are those things in society that seem "right." What is plausible is what is compatible with a society.
To go back to the main question, those in power (the dominant group) create society in their image and create plausibility structures. They make it seem like the ways things are done are self-evident, when, in fact, they created it. This is how they exert power.
Those who do not have power (the subordinate group) have two options. They can play their roles, or challenge the system. Most of the time, they play a certain role in society, and often they do not even see that society is created. This is partially why they are the subordinate group.
The dominant group is the group who is in charge of leading the subordinate group. Subordinates follow the direction of a dominant leader.
I disagree that subordinate necessarily means "weaker and less respected." In a working situation (the military works well as an example here), everyone reports to someone higher (all the way up to the president).
To me, these terms do not have to define power. They can simply define responsibility.
The dominant group is the one that has the power in a given society. The subordinate group is the one that does not have the power and is therefore generally weaker and less respected than the dominant group. The dominant group is able to shape society and its values, generally in ways that help it remain dominant.