  We classify the class $S$ theories of type $E_7$. These are four-dimensional
$\mathcal{N}=2$ superconformal field theories arising from the compactification
of the $E_7$ $(2,0)$ theory on a punctured Riemann surface, $C$. The
classification is given by listing all 3-punctured spheres ("fixtures"), and
connecting cylinders, which can arise in a pants-decomposition of $C$. We find
exactly 11,000 fixtures with three regular punctures, and an additional 48 with
one "irregular puncture" (in the sense used in our previous works). To organize
this large number of theories, we have created a web application at
https://golem.ph.utexas.edu/class-S/E7/ . Among these theories, we find 10 new
ones with a simple exceptional global symmetry group, as well as a new rank-2
SCFT and several new rank-3 SCFTs. As an application, we study the
strong-coupling limit of the $E_7$ gauge theory with 3 hypermultiplets in the
$56$. Using our results, we also verify recent conjectures that the $T^2$
compactification of certain $6d$ $(1,0)$ theories can alternatively be realized
in class $S$ as fixtures in the $E_7$ or $E_8$ theories.
