This is constructed from VisibLie_E8 and uses the Mathematica package Mathgroup. A comprehensive PowerPoint/PDF that gives an overview of the underlying theory and VisibLie_E8 tool capability is in this post.
Greg Moxness, Tucson AZ
Added visualization of the embeddings of the maximal subgroups with associated projection matrices of Lie Algebras in the Dynkin Diagram pane (#4) of VisibLie_E8