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A bstract We study the superconformal index of 4d    $$ \mathcal{N} $$  N = 4 USp(2 N   c  ) and SO( N   c  ) SYM from a matrix model perspective. We focus on the Cardy-like limit of the index. Both in the symplectic and orthogonal case the index is dominated by a saddle point solution which we identify, reducing the calculation to a matrix integral of a pure Chern-Simons theory on the three-sphere. We further compute the subleading logarithmic corrections, which are of the order of the center of the gauge group. In the USp(2 N   c  ) case we also study other subleading saddles of the matrix integral. Finally we discuss the case of the Leigh-Strassler fixed point with SU( N   c  ) gauge group, and we compute the entropy of the dual black hole from the Legendre transform of the entropy function.

The SCI of $$ \mathcal{N} $$ = 4 USp(2Nc) and SO(Nc) SYM as a matrix integral