As others have said, that's basically the case. Most of the complexity, though, is at the bottom, in the engines. Absolutely incredible machines designed to withstand—and control—incredible forces. Turbopumps spinning at tens of thousands of revolutions per second. Insane amounts of heat that need to be cooled so the engine bell doesn't melt. Handling cryogenic fuels (liquid oxygen is very, very cold!) at very high pressures, moving them at very high speeds.
One failure mode, out of the many many possible failure modes, that's particularly interesting to me is that if the pressure in the pipes going into the turbopumps (which push the fuel into the combustion chamber fast enough to keep the explosion going) is too low, then you'll get cavitation on the back of the turbopump blades, and the forces from that will destroy the turbopump in under a second. Kaboom.
Oh, also, these pumps have to spin so fast that they themselves are driven by essentially little mini rocket engines.
Turbopumps spinning at tens of thousands of revolutions per second.
This is actually not true. These turbopumps are quite large and spin fairly slowly. The design RPM on the F-1 turbopump appears to have been 5500 RPM, for example. (That's not to say they aren't complicated, because they were using 55,000 horsepower to push the propellants into the engine.)
One failure mode, out of the many many possible failure modes, that's particularly interesting to me is that if the pressure in the pipes going into the turbopumps (which push the fuel into the combustion chamber fast enough to keep the explosion going) is too low, then you'll get cavitation on the back of the turbopump blades, and the forces from that will destroy the turbopump in under a second. Kaboom.
Oh, also, these pumps have to spin so fast that they themselves are driven by essentially little mini rocket engines.
For a visual depiction of the complexity of rocket engines, check out SpaceX's Raptor engine, arguably the most advanced engine being produced right now: https://imgix.bustle.com/uploads/image/2020/4/6/c1349369-162...
I'm no rocket scientist, though, just an interested amateur. Real rocket scientists please correct me if I got anything wrong!