A subject in the sentence refers to who performs an action. Whereas, a complete subject is also the simple subject or main word in a sentence which may have a modifier to describe it.
To identify a complete subject in the sentence, it answers to the question of "Who performs the action?" or "What performs the action?" A complete subject includes the subject and the words which modify it.
Therefore, in the above sentence, the subject 'Coach Mack's basketball team' is modified by 'from 2011.'
