ILLOGIC is a playable word

illogic Scrabble® Dictionary

noun
pl. illogics
absence of logic
17 Playable Words can be made from "ILLOGIC"
   2-Letter Words (5 found)
   3-Letter Words (6 found)
   4-Letter Words (4 found)
   5-Letter Words (1 found)
   7-Letter Words (1 found)