officialdom vs establishment

officialdom and establishment both are nouns.

Word	Noun	Adjective	Verb	Adverb
officialdom	Yes	No	No	No
establishment	Yes	No	No	No

As nouns, establishment is a hypernym of officialdom; that is, establishment is a word with a broader meaning than officialdom:

officialdom: people elected or appointed to administer a government
establishment: the persons (or committees or departments etc.) who make up a body for the purpose of administering something

Other hypernyms of officialdom include administration, brass, governance, governing body, organisation, organization.

officialdom (noun)	establishment (noun)
people elected or appointed to administer a government	the act of forming or establishing something
	a public or private structure (business or governmental or educational) including buildings and equipment for business or residence
	the cognitive process of establishing a valid proof
	an organization founded and united for a specific purpose
	any large organization
	the persons (or committees or departments etc.) who make up a body for the purpose of administering something
	(ecology) the process by which a plant or animal becomes established in a new habitat