Normality of nilpotent varieties in E6

We determine which nilpotent orbits in E6 have closures which are normal varieties and which do not. At the same time we are able to verify a conjecture in [E. Sommers, Comm. Math. Univ. Sancti Pauli 49 (1) (2000) 101–104] concerning functions on non-special nilpotent orbits for E6.