Moderate# To What Extent Does the Converse of Lagrange's Theorem Fail?

ABSALG-I1NBAB

Consider the direct product $G=A_4\times \mathbb{Z}_3$, which is a group of order 36. Note that 36 has for divisors 1, 2, 3 , 4, 6, 9, 12, 18, 36.

Which of the following statements is **FALSE** about existence of subgroups of $G$ and the given order?