The 248-dimensional adjoint representation of E8, when similarly restricted, transforms under E6×SU(3) as: (8,1) + (1,78) + (3,27) + (3,27).
The 248-dimensional adjoint representation of E8, when similarly restricted, transforms under SU(3)×E6 as:: formula_20We may again see the decomposition by looking at the roots together with the generators in the Cartan subalgebra.