We demonstrate silicon-organic hybrid (SOH) electro-optic modulators that enable quadrature phase-shift keying (QPSK) and 16-state quadrature amplitude modulation (16QAM) with high signal quality and record-low energy consumption. SOH integration combines highly efficient electro-optic organic materials with conventional silicon-on-insulator (SOI) slot waveguides, and allows to overcome the intrinsic limitations of silicon as an optical integration platform. We demonstrate QPSK and 16QAM signaling at symbol rates of 28 GBd with peak-to-peak drive voltages of 0.6 V(pp). For the 16QAM experiment at 112 Gbit/s, we measure a bit-error ratio of 5.1 × 10⁻⁵ and a record-low energy consumption of only 19 fJ/bit.