  We analyze K3 surfaces admitting an elliptic fibration $E$ and a finite group
$G$ of symplectic automorphisms preserving this elliptic fibration. We
construct the quotient elliptic fibration $E/G$ comparing its properties to the
ones of $E$. We show that if $E$ admits an $n$-torsion section, its quotient by
the group of automorphisms induced by this section admits again an $n$-torsion
section. Considering automorphisms coming from the base of the fibration, we
can describe the Mordell--Weil lattice of a fibration described by Kloosterman.
We give the isometries between lattices described by the author and Sarti and
lattices described by Shioda and by Griees and Lam. Moreover we show that for
certain groups $H$ of $G$, $H$ subgroups of $G$, a K3 surface which admits $H$
as group of symplectic automorphisms actually admits $G$ as group of symplectic
automorphisms.
