Which of the following is a subgroup of the group $G = \{2^n \mid n \in \mathbb{Z}\}$ under multiplication?
$\{4^n \mid n \in \mathbb{N}\}$
$\{3^n \mid n \in \mathbb{Z}\}$
$\{6^n \mid n \in \mathbb{N}\}$
$\{4^n \mid n \in \mathbb{Z}\}$
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