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We investigate a mode gap confined dielectric band laser via a 1-D photonic crystal (PhC) nanobeam (NB) nanocavity with lattice gradually shifted PhC mirror. Owing to different modal symmetries, different zeroth-order dielectric mode properties, including quality (Q) factors, mode volumes, lasing thresholds, and slope efficiencies, in nanocavities with two different cavity sizes are investigated. In experiments, single-mode lasing from dielectric bands with low effective lasing thresholds is obtained. Rising of the high-order modes is also observed when we increase the PhC mirror periods for high Q factor of the zeroth-order dielectric mode. In addition, we observe the bonding and antibonding modes in beamwidth mismatched coupled NB nanocavities and switch the dominant lasing mode via spatially nonuniform carrier injection.