The American government is divided into different departments. These include the most powerful people who hold office. Obviously, the president is probably considered the most powerful person in the American government. So, his department which is the Executive cabinet is probably the most powerful. The list of powerful people are listed based on who is next in line to become the president.
These include the vice president, speaker of the house, senate pro tempore, secretary of state, secretary of the treasury, secretary of defense and the attorney general. Depending on the person, that would depend on the department. For example, the Department of Defense would include the secretary of defense. However, this would merely be an opinion. The most powerful department would depend upon what you value.