  We analyze the symmetries and other invariant qualities of the
$\mathcal{D}$-metrics (type D aligned Einstein Maxwell solutions with
cosmological constant whose Debever null principal directions determine
shear-free geodesic null congruences). We recover some properties and deduce
new ones about their isometry group and about their quadratic first integrals
of the geodesic equation, and we analyze when these invariant symmetries
characterize the family of metrics. We show that the subfamily of the Kerr-NUT
solutions are those admitting a Papapetrou field aligned with the Weyl tensor.
