Non-Abelian composition factors of m-rational groups

Walter Feit and Gary Seitz proved that only finitely many groups of Lie type and alternating groups may occur as non-abelian composition factors of non-solvable rational groups. More recently, John McKay posed the question of classifying the possible non-abelian composition factors of quadratic rational groups. In this paper, we answer the question of McKay, and provide a generalization to m-rational groups.