Noetherianness is subgroup-closed

Statement
Any subgroup of a Noetherian group is Noetherian group.

Similar facts

 * Noetherianness is quotient-closed
 * Noetherianness is extenion-closed
 * Artinianness is subgroup-closed

Opposite facts

 * Finitely generated not implies Noetherian shows that a subgroup of a finitely generated group need not be finitely generated.