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If G is a group and H is a subgroup of G, we write fla(H) for the lattice of overgroups of H in G. It is an open question whether or not every finite lattice is isomorphic to some finite group interval lattice eJG(H), where G is finite. We prove that no DA-(m) , ... ,m,)lattice and few M-Iattices have the form (:a(H) , where G is an alternating or symmetric group of prime degree.doi:10.1515/jgt.2008.065 fatcat:tgvbz7tryfdoxl4mgserallp3y