Suborder (Animalia): Incirrina

Incirrata (or Incirrina) is a suborder of the order Octopoda. The suborder contains the classic "benthic octopuses," as well as many pelagic octopus families, including the paper nautiluses. The incirrate octopuses are distinguished from the cirrate octopuses by the absence in the former of the "cirri" filaments (found with the suckers) for which the cirrates are named, as well as by the lack of paired swimming fins on the head, and lack of a small internal shell (the "shell" of Argonauta species is not a true shell, but a thin calcite egg case).

Reference: Wikipedia