The Bianchi classification of maximal D = 8 gauged supergravities

We perform the generalized dimensional reduction of D = 11 supergravity over three-dimensional group manifolds as classified by Bianchi. Thus, we construct 11 different maximal D = 8 gauged supergravities, two of which have an additional parameter. One class of group manifolds (class B) leads to supergravities that are defined by a set of equations of motion that cannot be integrated to an action. All 1/2 BPS domain wall solutions are given. We also find a non-supersymmetric domain wall solution where the single transverse direction is time. This solution describes an expanding universe and upon reduction gives the Einstein-de Sitter universe in D = 4. The uplifting of the different solutions to M-theory and the isometries of the corresponding group manifold are discussed.