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We complete the description of semistable models for modular curvesassociated with maximal subgroups of $\mathrm{GL}_2 ({\mathbb F}_p )$ (for $p$any prime, $p>5$). That is, in the new cases of non-split Cartan modular curvesand exceptional subgroups, we identify the irreducible components andsingularities of the reduction mod $p$, and the complete local rings at thesingularities. We review the case of split Cartan modular curves. Thisdescription suffices for computing the group of connected components of thefibre at $p$ of the N\'eron model of the Jacobian.

Semistable reduction of modular curves associated with maximal subgroups in prime level