Hopf orders via Breuil modules

Let R be a discrete valuation ring with quotient field K and residue field k of characteristic p>2. Each finite flat abelian R-Hopf algebra of rank pn has a corresponding Breuil module. We determine the Breuil modules for the Hopf algebras which are generically isomorphic to KG where G is an elementary abelian p-group, and give an explicit classification for p>3, n⩽2.