We theoretically investigate the effects of inclusions on the domain formation in mixed lipid bilayers supported on a geometrically patterned substrate. It is found that the inclusions may distribute quite differently with varying volume fraction and size of inclusions. The distribution of inclusions will effectively change the spontaneous curvature of the inclusion-rich lipid domains, and consequently can sort the lipid domains in the supported bilayers. By varying the volume fraction and size of inclusions, we obtain a rich variety of laterally organized lipid bilayers and reveal some interesting transitions between these structures. The present model provides a possible strategy to control the domain formation in the supported membranes, and may yield some theoretical insight into the design of biosensors by the reorganization of lipids and inclusions.