Subgroups — C₂×D₃₁×C₂₃⋊C₁₁ #44535880

Order 31372.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₁×C₂₃⋊C₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃₁×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×C₂₃⋊C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₃×D₃₁	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₂₃×C₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented
6	C₂₃×D₃₁	C₂×C₁₁	1	2	yes	complemented
7	C₂×C₁₁×D₃₁	—	23	1	no	maximal, Hall
8	C₂²×C₂₃⋊C₁₁	—	31	1	no	maximal, Hall
9	C₂₃×C₃₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₃₁	—	23	1	no	—
11	C₁₁×D₃₁	—	23	2	no	—
12	C₂×C₂₃⋊C₁₁	—	31	2	no	—
13	C₂×C₂₃⋊C₁₁	D₃₁	1	1	yes	characteristic, direct product factor
14	C₁₁×C₃₁	—	23	1	no	Hall
15	C₂₃⋊C₁₁	C₂×D₃₁	1	1	yes	characteristic, direct product factor, Hall
16	C₂×D₃₁	C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₂₃	—	31	1	no	Hall
18	C₂×C₃₁	C₂×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
19	D₃₁	C₂×C₂₃⋊C₁₁	1	2	yes	direct product factor
20	C₂×C₂₃	—	31	2	no	—
21	C₂×C₂₃	C₁₁×D₃₁	1	1	yes	characteristic, complemented
22	C₂²×C₁₁	—	713	1	no	Hall
23	C₃₁	C₂²×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented, Sylow
24	C₂₃	C₂×C₁₁×D₃₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₁	—	23	1	no	—
26	C₂×C₁₁	—	713	2	no	—
27	C₁₁	—	23	1	no	Sylow
28	C₂²	—	31	1	no	Sylow
29	C₂	—	31	2	no	—
30	C₂	D₃₁×C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃₁×C₂₃⋊C₁₁
commutator, cosocle, hypocenter	C₂₃×C₃₁	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₂₃×C₃₁	C₂×C₁₁
LCS	G ▷ C₂₃×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₃₁×C₂₃⋊C₁₁	C₂	direct (N × H)
2. C₂×C₃₁×C₂₃⋊C₁₁	C₂	semidirect
3. C₃₁×C₂₃⋊C₁₁	C₂²	semidirect
4. C₂×C₂₃×D₃₁	C₁₁	semidirect
5. C₂×C₂₃×C₃₁	C₂×C₁₁	semidirect
6. C₂₃×D₃₁	C₂×C₁₁	semidirect
9. C₂₃×C₃₁	C₂²×C₁₁	semidirect
13. C₂×C₂₃⋊C₁₁	D₃₁	direct (N × H)
15. C₂₃⋊C₁₁	C₂×D₃₁	direct (N × H)
16. C₂×D₃₁	C₂₃⋊C₁₁	direct (N × H)
18. C₂×C₃₁	C₂×C₂₃⋊C₁₁	semidirect
19. D₃₁	C₂×C₂₃⋊C₁₁	direct (N × H)
21. C₂×C₂₃	C₁₁×D₃₁	semidirect
23. C₃₁	C₂²×C₂₃⋊C₁₁	semidirect
24. C₂₃	C₂×C₁₁×D₃₁	semidirect
30. C₂	D₃₁×C₂₃⋊C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃₁×C₂₃⋊C₁₁	2
C₂×C₃₁×C₂₃⋊C₁₁	2
C₂×C₂₃×D₃₁	11
C₂×C₁₁×D₃₁	23
C₂²×C₂₃⋊C₁₁	31

Subgroups — C2×D31×C23⋊C11 #44535880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₁×C₂₃⋊C₁₁ #44535880