$SL(2, \mathbb F_3)$ does not have a subgroup of order $12$ Using the characteristic polynomial I can prove that $SL(2, \mathbb F_3)$ does not has an element of order $12$, but how can I prove that $SL(2, \mathbb F_3)$ does not has a subgroup of order $12$?

This is Theorem $2$ in George Mackiw's article :http://www.maa.org/sites/default/files/George_Mackiw20823.pdf.
