The extremal black holes of N=4 supergravity from so(8, 2+n) nilpotent orbits

We consider the stationary solutions of N = 4 supergravity coupled to n vector multiplets that define linear superpositions of non-interacting extremal black holes. The most general solutions of this type are derived from the graded decompositions of so(8, 2 + n) associated to its nilpotent orbits. We illustrate the formalism by giving explicitly asymptotically Minkowski non-BPS solutions of the most exotic class depending on 6 + n harmonic functions.