Quasi-reductive supergroups with small even parts

We describe all supergroups with the largest even supersubgroups being isomorphic to ${\mathrm{G}\mathrm{L}}_2,{\mathrm{S}\mathrm{L}}_2$ or ${\mathrm{P}\mathrm{S}\mathrm{L}}_2$. These results are applied to the description of centralizers of certain tori in the quasi-reductive supergroups.