  The (real) GraviGUT algebra is an extension of the $\mathfrak{spin}(11,3)$
algebra by a $64$-dimensional Lie algebra, but there is some ambiguity in the
literature about its definition. Recently, Lisi constructed an embedding of the
GraviGUT algebra into the quaternionic real form of $E_8$. We clarify the
definition, showing that there is only one possibility, and then prove that the
GraviGUT algebra cannot be embedded into any real form of $E_8$. We then modify
Lisi's construction to create true Lie algebra embeddings of the extended
GraviGUT algebra into $E_8$. We classify these embeddings up to inner
automorphism.
