49. If the finite group G contains a subgroup of order seven but no element (other than the identity) is its own inverse, then the order of G could be

A.27 B.28 C.35 D.37 E.42

I'm new to group theory so I'm not sure what is the proper approach to this question. I know from Lagrange's Th that 7 divides the order of G. And since no element in the subgroup is its own inverse, I guess it indicates that the subgroup is a cyclic subgroup. And then I'm stuck in the process.

Would anyone be willing to offer a tip or help me correct my approach? Thanks.