electromagnetism - One question about sextupole

In multipole expansion, we use monopole, dipole, quadrupole or octupole to describe an electromagnetic field. But I saw someone use sextupole to describe transition states.

If we expand an electromagnetic field by spherical harmonics, $\ell=0,1,2,3$ represent monopole, dipole, quadrupole and octupole. Do we sextupole in electric field? For different $m$ in the expansion, are they also different modes?