is s3 abelian or non abelian ?

[Jeffrey]

Is S3 abelian or non Abelian?
The group S3 is non abelian (for example (12)(23) 6= (23)(12)) but all its proper subgroups have order 1, 2, and 3, and you've see that all such groups are cyclic (hence abelian). The group D4 also works.