On the torsion of rational elliptic curves over quartic fields

Let E be an elliptic curve defined over Q and let G = E(Q)ₜₒᵣₛ be the associated torsion subgroup. We study, for a given G, which possible groups G ⊆ H could appear such that H=E(K)ₜₒᵣₛ, for [K:Q]=4 and H is one of the possible torsion structures that occur infinitely often as torsion structures of elliptic curves defined over quartic number fields.