2-Coverings for exceptional and sporadic simple groups

In this paper we prove that if G is a finite exceptional simple group of Lie type, then G admits a 2-covering if, and only if, it is one of the following groups: G_2(2^a), F_4(3^a), G_2(2)', 3G_2(3)', 2F_4(2)'. Furthermore, if G is a finite sporadic simple group, then G admits a 2-covering if, and only if, G = M_11.