The Mobius function of PSL (3, 2 p) for any prime p

Let G be the simple group PSL(3, 2p), where p is a prime number. For any subgroup H of G, we compute the Mobius function μ(H) of H in the subgroup lattice of G. To this aim, we describe the intersections of maximal subgroups of G. We point out some connections of the Mobius function with other combinatorial objects, and, in this context, we compute the reduced Euler characteristic of the order complex of the subposet of r-subgroups of PGL(3,q), for any prime r and any prime power q.