coeducation vs education

coeducation and education both are nouns.

Word	Noun	Adjective	Verb	Adverb
coeducation	Yes	No	No	No
education	Yes	No	No	No

As nouns, education is a hypernym of coeducation; that is, education is a word with a broader meaning than coeducation:

coeducation: education of men and women in the same institutions
education: the activities of educating or instructing; activities that impart knowledge or skill

Other hypernyms of coeducation include didactics, educational activity, instruction, pedagogy, teaching.

coeducation (noun)	education (noun)
education of men and women in the same institutions	the activities of educating or instructing; activities that impart knowledge or skill
	the profession of teaching (especially at a school or college or university)
	the result of good upbringing (especially knowledge of correct social behavior)
	knowledge acquired by learning and instruction
	the gradual process of acquiring knowledge