This paper investigates subspace-based target detection in OFDM integrated sensing and communications (ISAC) systems, considering the impact of various constellations. To meet diverse communication demands, different constellation schemes with varying modulation orders (e.g., PSK, QAM) can be employed, which in turn leads to variations in peak sidelobe levels (PSLs) within the radar functionality. These PSL fluctuations pose a significant challenge in the context of multi-target detection, particularly in scenarios where strong sidelobe masking effects manifest. To tackle this challenge, we have devised a subspace-based approach for a step-by-step target detection process, systematically eliminating interference stemming from detected targets. Simulation results corroborate the effectiveness of the proposed method in achieving consistently high target detection performance under a wide range of constellation options in OFDM ISAC systems.