  A quadratic form has a one-class spinor genus if its spinor genus consists of
a single equivalence class. In this paper, we determine that there is only one
primitive quaternary genus which has a one-class spinor genus but not a
one-class genus. In all other cases, the genera of primitive quaternary
lattices either have a genus and spinor genus which coincide, or the the genus
splits into multiple spinor genera, which in turn split into multiple
equivalence classes.
