Well, GP didn't mean this, but most thermonuclear bombs derive a large amount of their yield from fission of a U238 "tamper" and "sparkplug", driving by neutrons from D-T fusion.
Technically, there is no pure fusion bomb so I guess in a way you could say everything is fission powered, but that's like saying your gasoline car is battery powered because that's what started the engine.
Nope! Essentially all modern large thermonuclear devices are fission-fusion-fission devices, where the last fission stage (again, driven by fusion neutrons) produces the majority of the yield. You can omit that stage, by using a non-fissile material, for easier testing (...do you really want to test a 100MT device?...) with less fallout, but in actual use, they would all have fissile tampers.
Except that in a thermonuclear bomb, fission also occurs at the end as well as the start... The initial fission explosion starts off a fusion reaction, and then neutrons from the fusion process carry on to start another fission reaction, usually of the LEU 'tamper' encasing the bomb. In fact, a large proportion of the energy output is from this third stage fission reaction.