mischief vs hooliganism

mischief and hooliganism both are nouns.

Word	Noun	Adjective	Verb	Adverb
mischief	Yes	No	No	No
hooliganism	Yes	No	No	No

As nouns, hooliganism is a hyponym of mischief; that is, hooliganism is a word with a more specific, narrower meaning than mischief:

mischief: reckless or malicious behavior that causes discomfort or annoyance in others
hooliganism: willful wanton and malicious destruction of the property of others

Other hyponyms of mischief include blaze, hell, monkey business, malicious mischief, vandalism.

mischief (noun)	hooliganism (noun)
reckless or malicious behavior that causes discomfort or annoyance in others	willful wanton and malicious destruction of the property of others
the quality or nature of being harmful or evil