  Motivated by a recent observation that the LLM geometries admit 1/4-BPS
M5-brane probes with worldvolume AdS3 X \Sigma_2 X S1 preserving the
R-symmetry, we initiate a classification of the most general AdS3 X S2
geometries in M-theory. We retain all field strengths consistent with symmetry
and derive the torsion conditions for M_6 in terms of two linearly independent
spinors. Surprisingly, we identify three Killing directions for M_6, but only
two of these generate isometries of the overall ansatz. We show that the
existence of this third direction depends on the norm of the spinors. Then,
specialising to the case where the spinors define an SU(2)-structure and the
class of solutions is 1/4-BPS, we note that supersymmetry dictates that all
magnetic fluxes necessarily thread the S2. Finally, by assuming that the two
remaining Killing directions are parallel and aligned with one of the two
vectors defining the SU(2)-structure, we derive a general relationship for the
two spinors before extracting a known class of solutions from the torsion
conditions.
