A fundamental question related to any Lie algebra is to know its subalgebras. This is particularly true in the case of E 6 , an algebra which seems just large enough to contain the algebras which describe the fundamental forces in the Standard Model of particle physics. In this situation, the question is not just to know which subalgebras exist in E 6 but to know how the subalgebras fit inside the larger algebra and how they are related to each other.