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We investigate the superconformal indices for the Chern-Simons-mattertheories proposed for M2-branes probing the cones over N^{010}/Z_k, Q^{111},M^{32} with N=2,3 supersymmetries and compare them with the corresponding dualgravity indices. For N^{010}, we find perfect agreements. In addition, forN^{010}/Z_k, we also find an agreement with the gravity index including thecontributions from two types of D6-branes wrapping RP^3. For Q^{111}, we findthat the model obtained by adding fundamental flavors to the N=6 theory has theright structure to be the correct model. For M^{32}, we find the matching withthe gravity index modulo contributions from peculiar saddle points.

Refined test of AdS4/CFT3 correspondence for N=2,3 theories