  We study the unflavored Schur indices in the $\mathcal{N}=4$ super-Yang-Mills
theory for the $B_n,C_n,D_n, G_2$ gauge groups. We explore two methods, namely
the character expansion method and the Fermi gas method, to efficiently compute
the $q$-series expansion of the Schur indices to some high orders. Using the
available data and the modular properties, we are able to fix the exact
formulas for the general gauge groups up to some high ranks and discover some
interesting new features. We also identify some empirical modular anomaly
equations, but unlike the case of $A_n$ groups, they are quite complicated and
not sufficiently useful to fix exact formulas for gauge groups of arbitrary
rank.
