Let $G$ be a non-abelian finite $p$-group. I wonder if $Z(G) \leq \Phi(G)$, where $\Phi(G)$ is the Frattini subgroup of $G$? I'd known that it is true for non-abelian groups of order $p^3$ but I doubt it is true in general or not.
I understand that it isn't true in general. As showed below it isn't true for some group of order $p^4$.