A class of AdS_2×Σ_2, with Σ_2 being a two-sphere or a hyperbolic space, solutions within four-dimensional N=4 gauged supergravity coupled to three-vector multiplets with dyonic gauging is identified. The gauged supergravity has non-semisimple SO(3) (T^3,T̂^3) gauge group and can be obtained from a consistent truncation of eleven-dimensional supergravity on a tri-sasakian manifold. The maximally symmetric vacua contain AdS_4 geometries with N=1,3 supersymmetry corresponding to N=1 and N=3

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... onformal field theories (SCFTs) in three dimensions. We find supersymmetric solutions of the form AdS_2×Σ_2 preserving two supercharges. These solutions describe twisted compactifications of the dual N=1 and N=3 SCFTs and should arise as near horizon geometries of dyonic black holes in asymptotically AdS_4 space-time. Most solutions have hyperbolic horizons although some of them exhibit spherical horizons. These provide a new class of AdS_2×Σ_2 geometries with known M-theory origin.