Radical 3-subgroups of the finite groups of Lie type E6

We consider the universal version of the finite exceptional group of Lie type G=E6ε(q) with 3|q−ε, where E6+1(q)=E6(q) and E6−1(q)=2E6(q). We classify, up to conjugacy, the radical 3-subgroups of G. As an application, the essential 3-rank of the Frobenius category FD(G) is determined, where D is a Sylow 3-subgroup of G.