Catalyzes the oxidation of primary alcohols including methanol. a primary alcohol + 2 Fe(III)-[cytochrome cL] = an aldehyde + 2 Fe(II)-[cytochrome cL] + 2 H(+) Heterotetramer composed of 2 alpha and 2 beta subunits. Belongs to the methanol dehydrogenase subunit 2 family.