  We give a classification of compact solitons for the pluriclosed flow on
complex surfaces. First, by exploiting results from the Kodaira classification
of surfaces, we show that the complex surface underlying a soliton must be
K\"ahler except for the possibility of steady solitons on minimal Hopf
surfaces. Then, we construct steady solitons on all class $1$ Hopf surfaces by
exploiting a natural symmetry ansatz.
