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Is the abelian scheme you consider a fixed one?

If the base is of characteristic $p$, and $l = p$ then the Lie algebra of $A[l]$ is isomorphic to $Lie(A)$, so you get a dimension condition.

For example, $\alpha_p \oplus \alpha_p$ cannot be embedded in an elliptic curve.

There are also more general condition your group scheme $G$ should satisfy. Assume that $S$ is the spectrum of an Artinian algebra and that $G$ is $p$-torsion with a trivial bi-nilpotent part. We have an exact sequence: $$0 \to G^{mult} \to G \to G^{et} \to 0$$

then the orders of $G^{mult}$ and $G^{et}$ must be equal if $G$ is the $p$-torsion of an abelian scheme.

On the other hand, in section (15.4) of the book "Commutative group schemes" of F. Oort, there is the following result:

Every finite flat commutative group scheme is a subgroup scheme of some abelian variety $A$.

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Is the abelian scheme you consider a fixed one?

If the base is of characteristic $p$, and $l = p$ then the Lie algebra of $A[l]$ is isomorphic to $Lie(A)$, so you get a dimension condition.

For example, $\alpha_p \oplus \alpha_p$ cannot be embedded in an elliptic curve.

There are also more general condition your group scheme $G$ should satisfy. Assume that $S$ is the spectrum of an Artinian algebra and that $G$ is $p$-torsion with a trivial bi-nilpotent part. We have an exact sequence: $$0 \to G^{mult} \to G \to G^{et} \to 0$$

then the orders of $G^{mult}$ and $G^{et}$ must be equal if $G$ is the $p$-torsion of an abelian scheme.

On the other hand, in the book "Commutative group schemes" of F. Oort, there is the following result:

Every finite flat commutative group scheme is a subgroup scheme of some abelian variety $A$.