What Alex says is correct, but there is another viewpoint, which is a bit easier in some ways. You can consider a finitely generated $\mathbb{Z}_{p}$-free $\mathbb{Z}_{p}G$-modules which have no proper non-zero pure submodules. These are the module modules which are irreducible when the ground ring is extended to $\mathbb{Q}_{p}.$ There are finitely many isomorphism types of such modules. It may be possible to deduce the structure of faithful such modules for teh the dihedral group using Clifford theory( I haven't time to outlne all details, but I think the restriction to a cyclic subgroup of index $2$ may remain irreducible (though not absolutely irreducible).
What Alex says is correct, but there is another viewpoint, which is a bit easier in some ways. You can consider a finitely generated $\mathbb{Z}_{p}$-free $\mathbb{Z}_{p}G$-modules which have no proper non-zero pure submodules. These are the module which are irreducible when the ground ring is extended to $\mathbb{Q}_{p}.$ There are finitely many isomorphism types of such modules. It may be possible to deduce the structure of faithful such modules for teh dihedral group using Clifford theory ( I haven't time to outlne all details, but I think the restriction to a cyclic subgroup of index $2$ may remain irreducible (though not absolutely irreducible).