Subgroups — C₃²×C₃₁⋊#1181 #44569102

Order 32364.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃₁⋊#1181	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₂₉×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₃₁×D₂₉	C₂×C₃	1	4	yes	—
5	C₃₁⋊#1181	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₂₉×C₃₁	C₃×C₄	1	4	yes	complemented
7	C₃₁×D₂₉	C₂×C₃²	1	1	yes	characteristic
8	C₃²×Dic₃₁	—	29	1	no	maximal, Hall
9	C₃²×#1181	—	31	1	no	maximal, Hall
10	C₂₉×C₃₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃²×C₃₁	—	29	1	no	—
12	C₃²×D₂₉	D₃₁	1	1	yes	characteristic
13	C₃×Dic₃₁	—	29	4	no	—
14	C₃×#1181	—	31	4	no	—
15	C₃²×C₃₁	#1181	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₂₉	Dic₃₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₃₁	—	29	4	no	—
18	C₃×D₂₉	C₃×D₃₁	1	4	yes	—
19	Dic₃₁	—	29	1	no	Hall
20	#1181	—	31	1	no	Hall
21	C₃×C₃₁	C₃×#1181	1	4	yes	complemented
22	C₃×C₂₉	C₃×Dic₃₁	1	4	yes	complemented
23	C₂×C₃₁	—	29	1	no	—
24	D₂₉	C₃²×D₃₁	1	1	yes	characteristic
25	C₃²×C₄	—	899	1	no	Hall
26	C₃₁	C₃²×#1181	1	1	yes	characteristic, complemented, Sylow
27	C₂₉	C₃²×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃²	—	29	1	no	—
29	C₃×C₄	—	899	4	no	—
30	C₃²	C₃₁⋊#1181	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	29	4	no	—
32	C₄	—	899	1	no	Sylow
33	C₃	C₃×C₃₁⋊#1181	1	4	yes	direct product factor
34	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	C₃₁⋊#1181
commutator, hypocenter	C₂₉×C₃₁	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₂₉×C₃₁	C₄
prime radical	C₃²×C₃₁×D₂₉	C₂
cosocle	C₃₁×D₂₉	C₂×C₃²
LCS	G ▷ C₂₉×C₃₁
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×C₃₁⋊#1181	C₃	direct (N × H)
3. C₃²×C₂₉×C₃₁	C₄	semidirect
5. C₃₁⋊#1181	C₃²	direct (N × H)
6. C₃×C₂₉×C₃₁	C₃×C₄	semidirect
10. C₂₉×C₃₁	C₃²×C₄	semidirect
15. C₃²×C₃₁	#1181	semidirect
16. C₃²×C₂₉	Dic₃₁	semidirect
21. C₃×C₃₁	C₃×#1181	semidirect
22. C₃×C₂₉	C₃×Dic₃₁	semidirect
26. C₃₁	C₃²×#1181	semidirect
27. C₂₉	C₃²×Dic₃₁	semidirect
30. C₃²	C₃₁⋊#1181	direct (N × H)
33. C₃	C₃×C₃₁⋊#1181	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₃₁×D₂₉	2
C₃×C₃₁⋊#1181	3
C₃²×Dic₃₁	29
C₃²×#1181	31

Subgroups — C32×C31⋊#1181 #44569102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₃₁⋊#1181 #44569102