Prove that there is no homomorphism from $\mathbb{Z}_{8} \oplus \mathbb{Z}_{2}$ ont0 $\mathbb{Z}_{4} \oplus \mathbb{Z}_{4}$

Prove that there is no homomorphism from $\mathbb{Z}_{8} \oplus \mathbb{Z}_{2}$ ont0 $\mathbb{Z}_{4} \oplus \mathbb{Z}_{4}$.

My idea for the proof : Let $\phi$ be such homomorphism. Since Ker $\phi$ is a subgroup of $\mathbb{Z}_{8} \oplus \mathbb{Z}_{2}$ , then i must find all possible subgroups of it and then prove that $(\mathbb{Z}_{8} \oplus \mathbb{Z}_{2})/$Ker$\:\phi $ is not isomorphic with $\mathbb{Z}_{4} \oplus \mathbb{Z}_{4}$ where Ker $\phi$ can be any of the subgroup. To prove it isnt isomorphic is by finding elements in $\mathbb{Z}_{8} \oplus \mathbb{Z}_{2}$ that has order such that no elements in $\mathbb{Z}_{4} \oplus \mathbb{Z}_{4}$ have that order.

Is there any better way..?

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