  It is a classical result that any complex analytic Lie supergroup
$\mathcal{G}$ is split \cite{kosz}, that is its structure sheaf is isomorphic
to the structure sheaf of a certain vector bundle. However, there do exist
non-split complex analytic homogeneous supermanifolds.
  We study the question how to find out whether a complex analytic homogeneous
supermanifold is split or non-split. Our main result is a description of left
invariant gradings on a complex analytic homogeneous supermanifold
$\mathcal{G}/\mathcal{H}$ in the terms of $\mathcal{H}$-invariants. As a
corollary to our investigations we get some simple sufficient conditions for a
complex analytic homogeneous supermanifold to be split in terms of Lie
algebras.
