Subgroup order question

[brain]

If G is a group of order 12, then G must have a subgroup of all the following orders except

A 1 B 2 C 4 D 6 E 12

Is it evident that subgroup of order 4 always exists?

[johnnybegoog]

Yeah by one of the Sylow theorems (http://planetmath.org/encyclopedia/SylowTheorems.html) G must have a 2-subgroup (ie here a subgroup of order 4), so the correct answer is D.

[aaaaa]

This is just their way of asking you to identify the fact that A_4 (which has 12 elements) has no subgroup of order 6, so if you were to interpret a potential "converse" to Lagrange's theorem in this way, it would be false.

[bobn]

then G must have a subgroup

so, there might a subgroup of order 6, but its not true that there must be a subgroup of order 6.

[brain]

OK, thanks everybody.