Which of the following is a subgroup of the group \(G=\left\{2^{n} \mid n \in Z\right\}\) under multiplication?

Since, \(\quad\left\{4^{\mathrm{n}} \mid \mathrm{n} \in \mathrm{N}\right\},\left\{3^{\mathrm{n}} \mid \mathrm{n} \in \mathrm{Z}\right\} \quad\) and \(\left\{6^{n} \mid n \in N\right\}\) are not subset of the group \(\mathrm{G}=\left\{2^{\mathrm{n}} \mid \mathrm{n} \in \mathrm{Z}\right\}\) and not satisfy all the properties of group axiom but \(\left\{4^{n} \mid n \in Z\right\}\) is a subset of \(\mathrm{G}=\left\{2^{\mathrm{n}} \mid \mathrm{n} \in \mathrm{Z}\right\}\) and satisfy all the properties, i.e., closure, associative, multiplicative inverse, multiplicative identity exist with respect to multiplication. So, \(\left\{4^{\mathrm{n}} \mid \mathrm{n} \in \mathrm{Z}\right\}\) is a subgroup.