A search is presented for a narrow resonance decaying to a pair of oppositely charged muons using $\sqrt{s}=$ 13 TeV proton-proton collision data recorded at the LHC. In the 45-75 and 110-200 GeV resonance mass ranges, the search is based on conventional triggering and event reconstruction techniques. In the 11.5-45 GeV mass range, the search uses data collected with dimuon triggers with low transverse momentum thresholds, recorded at high rate by storing a reduced amount of trigger-level information. The data correspond to integrated luminosities of 137 fb$^{-1}$ and 96.6 fb$^{-1}$ for conventional and high-rate triggering, respectively. No significant resonant peaks are observed in the probed mass ranges. The search sets the most stringent constraints to date on a dark photon in the $\sim$30-75 and 110-200 GeV mass ranges.