Why didn't the Permian Extinction kill all the cockroaches?, does anybody else wish cockroaches were extinct?

C-ckroaches were a diverse and successful terrestrial insect group back then, and still are today.  Enough of them were hardy enough to survive the close-of-Permian events, apparently, to continue to thrive into the Triassic and beyond. 

Plenty of insects had the advantage of being small, able to live in what we would consider restricted oxygen conditions, preference for sheltering under fallen logs, ability to eat decaying / decayed material.  Those are the kind of things that make for a survivor of mass extinctions.