Quiz:Subgroup structure of symmetric group:S4

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See subgroup structure of symmetric group:S4 for background information.

Basic stuff

Summary table on the structure of subgroups: [SHOW MORE]

1 What are the possible orders of subgroups of the symmetric group of degree four?

1,2,6,24 only
1,3,8,24 only
1,4,12,24 only
1,2,3,4,12,24 only
1,2,3,4,6,12,24 only
1,2,3,4,8,12,24 only
1,2,3,4,6,8,12,24 only

2 What are the possible orders of normal subgroups of the symmetric group of degree four?

1,2,6,24 only
1,3,8,24 only
1,4,12,24 only
1,2,3,4,12,24 only
1,2,3,4,6,12,24 only
1,2,3,4,8,12,24 only
1,2,3,4,6,8,12,24 only

3 What are the possible orders of quotient groups of the symmetric group of degree four?

1,2,6,24 only
1,3,8,24 only
1,4,12,24 only
1,2,3,4,12,24 only
1,2,3,4,6,12,24 only
1,2,3,4,8,12,24 only
1,2,3,4,6,8,12,24 only

4 For which of the following orders of subgroups do there exist two distinct conjugacy classes of subgroups in the symmetric group of that order for which the subgroups are isomorphic as abstract groups?

2 only
3 only
4 only
6 only
2 and 3 only
3 and 4 only
2 and 4 only
3 and 6 only