Patriarchy refers to a social system or government where Men are the primary figures of authority while Women hold subservient positions. Paternalism means something similar. A patriarchy and paternalism are found in many traditional societies and traditional Religions including Christian fundamentalism. Conservatives being traditional almost invariably support some degree of patriarchy. Liberal Christianity isn't paternalist and liberal Christian denominations allow women to be priests, ministers, religious leaders.
In a traditional hierarchical partiarchy a Lady frequently has power over lowly manservants or even her sons but the lady derives her limited authority from Gentlemen higher up the social scale, her husband, her father etc.