  Extreme near-horizon geometries in D=11 supergravity preserving four
supersymmetries are classified. It is shown that the Killing spinors fall into
three possible orbits, corresponding to pairs of spinors defined on the spatial
cross-sections of the horizon which have isotropy groups SU(3), G2, or SU(4).
In each case, the conditions on the geometry and the 4-form flux are
determined. The integrability conditions obtained from the Killing spinor
equations are also investigated.
