By Lagrange's theorem the possible order of the subgroups of the group will be 1 or 3 or 37 or 111
Now by Sylow's 1st theorem this group must have a subgroup of order 3 and as well as 37.
Then we can prove that every abelian group of order 111 is cyclic.
Now my question is:
Is there be any non-abelian group of order 111?
If there be a non abelian group of order 111 then the given statement is False otherwise the statement is True .