Subordination in rank: dismissal must be by an officer of equal or higher rank, not by a lower authority. The text explains that 'officer' denotes a person holding an office of trust or authority, while 'subordinate' denotes an inferior rank or legal subordination and may be subordinate in law despite practical independence. The operative test for an 'officer subordinate' is whether the officer performs duties subject to the direction and control of a superior; disciplinary or removal action must be taken by an authority not lower in rank than the appointing authority.