I found in the literature many references on the representability of quotients of group schemes but almost nothing about subgroups. For this reason I hope that my question is a silly one and that what I am asking is well known to experts. Let $G$ be a group algebraic space over a base which is the spectrum of a discrete valuation ring. Let $H\subset G$ be a subgroup functor of $G$ which is also an etale sheaf. Under which conditions is it known that $H$ is a group algebraic space? We can assume that $G$ has a trivial obstruction and deformation theory if it could help. We can also assume that $H$ is the kernel of an homomorphism of group sheaves $G\rightarrow K$ but $K$ is not necessarily represented by an algebraic space.