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The group $(\mathbb{Z}/2\mathbb{Z}) \wr S_{n}$ is finite maximal for $n$ sufficiently large (probably $n>72$ will do, by a theorem of M.Collins on a sharp form of Jordan's theorem on finite complex linear groups, and this is likely more generous than the true bound). I mean here the group of $n \times n$ monomial matrices with all non-zero entries $\pm 1$.