  Only two ways to construct non-liftable Calabi-Yau threefolds are currently
known, one example by Hirokado and one method of Schr\"oer. This article
computes some cohomological invariants of these examples of non-liftable
Calabi-Yau threefolds, in particular it computes their mini-versal
deformations. One conclusion is that their mixed characteristic mini-versal
deformation spaces are actually smooth over the characteristic $p$ base field.
Furthermore, a new family, constructed in the spirit of Schr\"oer, is
introduced and the same calculations are performed for it.
