hagiarchy n.

before vowels hagi-, word-forming element meaning "of a saint, saintly, holy," from Greek hagios "sacred, devoted to the gods" (of things), "holy, pure" (of persons), in Ecclesiastical Greek, "a saint," which is perhaps from PIE *yag- "to worship, reverence" (source also of Greek agnos "chaste," Sanskrit yajati "reveres (a god) with sacrifices, worships," Old Persian ayadana "temple").

word-forming element meaning "rule," from Latin -archia, from Greek -arkhia "rule," from arkhos "leader, chief, ruler," from arkhē "beginning, origin, first place," verbal noun of arkhein "to be the first," hence "to begin" and "to rule" (see archon).

word-forming element forming nouns meaning "rule or government by," from French -cratie or directly from Medieval Latin -cratia, from Greek -kratia "power, might; rule, sway; power over; a power, authority," from kratos "strength," from PIE *kre-tes- "power, strength," suffixed form of root *kar- "hard." The connective -o- has come to be viewed as part of it. Productive in English from c. 1800.