Hybrid plasmonic lasers provide deep subwavelength optical confinement, strongly enhanced light-matter interaction and together with nanoscale footprint promise new applications in optical communication, bio-sensing and photolithography. The subwavelength hybrid plasmonic lasers reported so far often use bottom up grown nanowires, nanorods and nanosquares, making it difficult to integrate these devices into industry-relevant high density plasmonic circuits. Here, we report the first experimental demonstration of AlGaInP based, red-emitting hybrid plasmonic lasers at room temperature using lithography based fabrication processes. Resonant cavities with deep subwavelength 2D and 3D mode confinement of lambda square/56 and lambda cube/199, respectively are demonstrated. A range of cavity geometries (waveguides, rings, squares and disks) show very low lasing thresholds of 0.6-1.8 mJ/cm square with wide gain bandwidth (610 nm-685 nm), which are attributed to the heterogeneous geometry of the gain material, the optimized etching technique, and the strong overlap of the gain material with the plasmonic modes. Most importantly, we establish the connection between mode confinements and enhanced absorption and stimulated emission, which play a critical role in maintaining low lasing thresholds at extremely small hybrid plasmonic cavities. Our results pave the way for the further integration of dense arrays of hybrid plasmonic lasers with optical and electronic technology platforms.