Predictions for superheavy elements beyond Z=126

We study energy landscapes for selected superheavy even-even systems with Z = 128-148 using both the microscopic-macroscopic Woods-Saxon and Skyrme SLy6 Hartree-Fock plus BCS models. Including nonaxial shapes proves crucial, as many apparent minima obtained when studying only axially symmetric shapes turn out to be saddle points, and triaxiality can drastically reduce fission barriers. Although both models often predict similar equilibria, only the SLy6 model predicts moderate stability in the N greater than or similar to 228 region, with barriers up to 4.5 MeV. A rough estimate suggests fission half-lives in the mu s range; this would mean similar to ms halflives of odd and odd-odd systems. Nuclei from the N approximate to 180 region with predicted approximate to 4 MeV fission barriers have short alpha half-lives. There is no sign of stability for intermediate neutron numbers. As the SLy6 interaction is known to overestimate fission barriers, no long-lived nuclei are to be expected in the whole studied region. The shell corrections obtained in two models suggest a probable doubly magic system Z = 164, N = 308, with the half-life of 100 s estimated in the Woods-Saxon model.