We present studies on the low-temperature magnetization of a two-dimensional electron system (2DES) in the integer quantum Hall-effect regime. The 2DES was formed in a modulation-doped AlGaAs/GaAs heterojunction. Using molecular-beam epitaxy it has been integrated into a highly sensitive micromechanical cantilever magnetometer. We observe de Haas–van Alphen oscillations at even filling factors up to ν=40 which for ν