# How many subgroups of order 4 does D_4 have?

How many subgroups of order 4 does ${D}_{4}$ have?
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stuth1
We know that ${D}_{n}$ is a dehedral group of order 2n. It is non-abelian group.
Therefore, the order of ${D}_{4}$ is 8 and the list of elements is given by
${D}_{4}=\left\{e,a,{a}^{2},{a}^{3},b,ba,b{a}^{2},b{a}^{3}\right\}$
There are 3 subgroup of order in ${D}_{4}$ which is given by
${H}_{1}=\left\{e,a,{a}^{2},{a}^{3}\right\},$
${H}_{2}=\left\{e,b,{a}^{2},b{a}^{2}\right\}$
${H}_{3}=\left\{e,ba,{a}^{2},b{a}^{3}\right\}$