  We find solutions of the bosonic sector of gauged N=4, D=4 SU(2) $\times$
SU(2) supergravity, which represent dilaton black holes with toroidal or
spherical event horizons. The axion is consistently truncated, and the gauge
group is broken to U(1) $\times$ U(1). The spherical black holes carry two
electric and two magnetic abelian charges, whereas the toroidal holes have
vanishing magnetic charges. The spacetime metrics are warped products, and the
manifolds turn out to be globally hyperbolic, in contrast to standard gauged
supergravity ground states. It is shown that in the toroidal case, there are
solutions preserving one quarter or one half of the supersymmetries, while for
spherical topologies all supersymmetries are broken. In general, the toroidal
BPS states represent naked singularities, but there is also a supersymmetric
black hole with vanishing Hawking temperature. The 1/2 supersymmetric case
arises for vanishing charges and mass, and represents the known domain wall
solution of the Freedman-Schwarz model. It provides the background in which the
black holes live. Finally, we use Chamseddine's and Volkov's Kaluza-Klein
interpretation of gauged N=4, D=4 SU(2) $\times$ SU(2) supergravity to lift our
solutions to ten and eleven dimensions and to consider them as solutions to the
leading order equations of motion of the string-/M-theory effective action.
