I am wondering if there is any literature on general formula of the Moebius function of subgroup lattices of any finite abelian group $G$? What I know is

When $G$ is cyclic, the Moebius function is simply the classical number theoretic one.

When $G=(\mathbb Z/p\mathbb Z)^r$, the formula involves the number of $k$-dimensional linear subspace of $G$.

But is there some formula for any finite abelian group?