Hegemonical is an adjective that refers to a dominating influence or leadership. Some antonyms or opposite words for hegemonic would be submissive, subordinate, dependent, weak, modest, humble, and meek. These words imply a lack of control, power, and authority over a particular domain. For instance, a subordinate is someone who is secondary to their boss, and they don't play a role in making essential decisions. A meek person, on the other hand, is gentle and submissive, and they don't try to assert their dominance over others. Thus, these antonyms serve to describe a character that is diametrically opposite to one that is hegemonic in nature.