I'm interested in examples of "big" finite subgroups of $G(\mathbb C)$ for $G=\mathrm{Sp}_{2n}, \mathrm{SO}_{2n+1}$. A subgroup $H$ of $G(\mathbb C)$ is said to be **big** if the associated representation of $H$ is irreducible. For example, consider the Weyl group $W\cong N_G(T)/T$, we can take $H$ to be any finite subgroup of $N_G(T)$ for which $H/(H\cap T) \cong W$. Is there any other examples of big finite subgroups of $G(\mathbb C)$?

The work of Griess-Ryba http://www.math.lsa.umich.edu/~rlg/researchandpublications/pdffiles1/qfseag.pdf gives a classification of quasi-simple groups which embed into exceptional algebraic groups. But I don't know of any similar work for classical groups.