  We study degree 2 and 4 elliptic subcovers of hyperelliptic curves of genus 3
defined over $\mathbb C$. The family of genus 3 hyperelliptic curves which have
a degree 2 cover to an elliptic curve $E$ and degree 4 covers to elliptic
curves $E_1$ and $E_2$ is a 2-dimensional subvariety of the hyperelliptic
moduli $\mathcal H_3$. We determine this subvariety explicitly. For any given
moduli point $\mathfrak p \in \mathcal H_3$ we determine explicitly if the
corresponding genus 3 curve $\mathcal X$ belongs or not to such family. When it
does, we can determine elliptic subcovers $E$, $E_1$, and $E_2$ in terms of the
absolute invariants $t_1, \dots, t_6$ as in \cite{hyp_mod_3}. This variety
provides a new family of hyperelliptic curves of genus 3 for which the
Jacobians completely split. The sublocus of such family when $E_1$ is
isomorphic to $E_2$ is a 1-dimensional variety which we determine explicitly.
We can also determine $\mathcal X$ and $E$ starting form the $j$-invariant of
$E_1$.
