Let $G$ be a $p$-group and $A$ an elementary $p$-group. Suppose that $\sharp G=\sharp A$, where $\sharp (-)$ denotes the order of $(-)$. Write $C_{d}(G)$ (resp. $C_{d}(A)$) for the cardinality of the set of subgroups of $G$ (resp. $A$) whose order are equal to $d$.

My question is that $C_{d}(G) \leq C_{d}(A)$?