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Let G be an exceptional algebraic group defined over an algebraically closedfield k of characteristic p>0 and let H be a subgroup of G. Then followingSerre we say H is G-completely reducible or G-cr if, whenever H is contained ina parabolic subgroup P of G, then H is in a Levi subgroup of that parabolic.Building on work of Liebeck and Seitz, we find all triples (X,G,p) such thatthere exists a closed, connected, simple non-G-cr subgroup H<G with root systemX.

Non-G-completely reducible subgroups of the exceptional algebraic groups