  We consider an Abelian gauge field coupled to a particular truncation of
Horndeski theory. The Galileon field has translation symmetry and couples non
minimally both to the metric and the gauge field. When the gauge-scalar
coupling is zero the gauge field reduces to a standard Maxwell field. By taking
into account the symmetries of the action, we construct charged black hole
solutions. Allowing the scalar field to softly break symmetries of spacetime we
construct black holes where the scalar field is regular on the black hole event
horizon. Some of these solutions can be interpreted as the equivalent of
Reissner-Nordstrom black holes of scalar tensor theories with a non trivial
scalar field. A self tuning black hole solution found previously is extended to
the presence of dyonic charge without affecting whatsoever the self tuning of a
large positive cosmological constant. Finally, for a general shift invariant
scalar tensor theory we demonstrate that the scalar field Ansatz and method we
employ are mathematically compatible with the field equations. This opens up
the possibility for novel searches of hairy black holes in a far more general
setting of Horndeski theory.
