Pupae can be classified into three types&colon; obtect, exarate, and coarctate. There are three types of pupae&colon; obtect, exarate or coarctate. The pupae of Diptera can be obtect, exarate or coarctate. Obtect pupae are compact, with the legs and other appendages enclosed. Pupae are obtect in the Nematocera, or coarcate in Brachycera.