String theory is like evolution, bottom-up QFTs are creationism
Jacques Distler and three co-authors (CDTZ, Austin and Maryland) have published an impressively technical paper "classifying" certain exotic beasts,
Tinkertoys for the \(E_8\) Theory.Their paper is accompanied by a cool interactive website which you should investigate. In particular, if you're asking why they didn't include "all the stuff" from the website in their paper, try this subpage on four punctured spheres. Pick a combination of the four parameters and press "go". What you get are some diagrams of S-duality frames (1,025,438 of them) where you see two circles with some objects and left-right arrows connecting them. You can click at the objects and get additional data on the "fixtures".
If you don't understand what the data means and how to use them, don't worry. 7 billion people don't understand it and my estimate is that 30 people in the world may deal with the data – to the extent that they would have a chance to discover a typo if one were artificially introduced. ;-)