Non-abelian composition factors of ℓ-Brauer m-rational groups

It is known that sporadic groups, alternating groups, and only finitely many groups of Lie type may occur as non-abelian composition factors of non-solvable m-rational groups. In this paper, we prove a similar statement for ℓ-Brauer m-rational groups, and give an explicit list of the possible non-abelian composition factors of ℓ-Brauer rational groups.