The depth of subgroups of PSL(2,q)

Let G:=PSL(2,q) with q a prime power. The depth of each subgroup H of G, which is the depth of the inclusion of group algebras kH⊆kG for a field k of characteristic 0, is determined. It turns out that for q⩾13 almost every proper nontrivial subgroup has depth 3 in G. The exceptions are the dihedral subgroups of order 2(q+1) for q even and the semidirect products with a Sylow p-subgroup of G as normal subgroup for q odd respectively which have depth 5 in G. If q⩽11 the values of the depths range between 2 and 5.