How to spell PATIRARCY correctly?

If someone misspells "patirarcy" instead of "patriarchy", here are a few correct suggestions to offer: 1) "patriarchy" - the correct spelling of the word; 2) "patriarchal" - an adjective to describe the patriarchal system; 3) "patriarchs" - the plural form of the word, referring to male leaders in a society; 4) "paternalistic" - a related term describing a system