Finite Group Databasebeta

← C₃₁⋊C₃² #22575713

Subgroups — C₃₁⋊C₃² #22575713

Order 8649.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668333	C₃	1	1	yes	maximal, characteristic, complemented
2	#15668332	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃₁×C₃₁⋊C₃	C₃	1	2	yes	maximal, complemented
4	C₃₁²	C₃²	1	1	yes	characteristic, complemented, Sylow
5	C₃×C₃₁⋊C₃	—	31	2	no	maximal
6	C₃×C₃₁	—	31	2	no	—
7	C₃₁⋊C₃	—	31	2	no	—
8	C₃₁⋊C₃	—	31	2	no	—
9	C₃₁⋊C₃	—	93	10	no	—
10	C₃₁⋊C₃	C₃₁⋊C₃	1	2	yes	direct product factor
11	C₃₁	—	3	10	no	—
12	C₃₁	C₃×C₃₁⋊C₃	1	2	yes	complemented
13	C₃²	—	961	1	no	Sylow
14	C₃	—	31	2	no	—
15	C₃	—	961	1	no	—
16	C₃	—	961	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃₁²	C₃²
LCS	G ▷ C₃₁²
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #15668333	C₃	semidirect
2. #15668332	C₃	semidirect
3. C₃₁×C₃₁⋊C₃	C₃	semidirect
4. C₃₁²	C₃²	semidirect
10. C₃₁⋊C₃	C₃₁⋊C₃	direct (N × H)
12. C₃₁	C₃×C₃₁⋊C₃	semidirect