Subgroups — C₃₁×(C₃⋊D₃)⋊D₂₃ #38787342

Order 25668.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×D₆₉	C₂	1	2	yes	maximal, complemented
2	C₃⋊D₃×C₂₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₃₁×D₂₃	—	3	2	no	maximal
4	C₃²×C₂₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃₁×D₆₉	D₃	1	2	yes	complemented
6	D₃×C₂₃×C₃₁	—	3	2	no	—
7	D₃×C₂₃×C₃₁	—	6	1	no	—
8	C₃×C₃₁×D₂₃	—	3	2	no	—
9	C₂×C₃₁×D₂₃	—	9	1	no	Hall
10	C₃×C₂₃×C₃₁	—	2	1	no	—
11	C₃×C₂₃×C₃₁	C₂×D₃	1	2	yes	complemented
12	C₂×C₂₃×C₃₁	—	9	1	no	—
13	C₃₁×D₂₃	—	3	2	no	—
14	D₃²×C₃₁	—	23	1	no	maximal, Hall
15	(C₃⋊D₃)⋊D₂₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂₃×C₃₁	D₃²	1	1	yes	characteristic, complemented, Hall
17	C₃⋊D₃×C₃₁	D₂₃	1	1	yes	characteristic, complemented
18	C₃×D₃×C₃₁	—	23	2	no	—
19	C₃⋊D₃×C₂₃	C₂×C₃₁	1	1	yes	characteristic, complemented
20	C₃×D₆₉	C₂×C₃₁	1	2	yes	complemented
21	C₂×D₃×C₃₁	—	69	2	no	—
22	C₃²×C₃₁	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
23	D₃×D₂₃	—	3	2	no	—
24	C₃²×C₂₃	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₃₁	—	69	2	no	—
26	D₃×C₃₁	—	3	2	no	—
27	D₃×C₃₁	—	6	1	no	—
28	D₃×C₃₁	—	23	2	no	—
29	D₆₉	D₃×C₃₁	1	2	yes	complemented
30	C₃×D₂₃	—	3	2	no	—
31	D₃×C₂₃	—	3	2	no	—
32	D₃×C₂₃	—	6	1	no	—
33	C₂²×C₃₁	—	207	1	no	Hall
34	C₃×C₃₁	—	2	1	no	—
35	C₃×C₃₁	D₃×D₂₃	1	2	yes	complemented
36	C₂×D₂₃	—	9	1	no	Hall
37	C₃×C₂₃	—	2	1	no	—
38	C₃×C₂₃	C₂×D₃×C₃₁	1	2	yes	complemented
39	C₂×C₃₁	—	9	1	no	—
40	C₂×C₃₁	—	69	2	no	—
41	C₂×C₂₃	—	9	1	no	—
42	D₂₃	—	3	2	no	—
43	D₃²	—	23	1	no	Hall
44	C₃₁	(C₃⋊D₃)⋊D₂₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₂₃	D₃²×C₃₁	1	1	yes	characteristic, complemented, Sylow
46	C₃⋊D₃	C₃₁×D₂₃	1	1	yes	characteristic, complemented
47	C₃×D₃	—	23	2	no	—
48	C₂×D₃	—	69	2	no	—
49	C₃²	C₂×C₃₁×D₂₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	69	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	23	2	no	—
54	C₂²	—	207	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×C₃₁×D₂₃	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	69	2	no	—

	subgroup	G/H
center, hypercenter	C₃₁	(C₃⋊D₃)⋊D₂₃
commutator, cosocle, hypocenter	C₃²×C₂₃	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃×C₃₁	C₂²
LCS	G ▷ C₃²×C₂₃
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×D₆₉	C₂	semidirect
2. C₃⋊D₃×C₂₃×C₃₁	C₂	semidirect
4. C₃²×C₂₃×C₃₁	C₂²	semidirect
5. C₃₁×D₆₉	D₃	semidirect
11. C₃×C₂₃×C₃₁	C₂×D₃	semidirect
15. (C₃⋊D₃)⋊D₂₃	C₃₁	direct (N × H)
16. C₂₃×C₃₁	D₃²	semidirect
17. C₃⋊D₃×C₃₁	D₂₃	semidirect
19. C₃⋊D₃×C₂₃	C₂×C₃₁	semidirect
20. C₃×D₆₉	C₂×C₃₁	semidirect
22. C₃²×C₃₁	C₂×D₂₃	semidirect
24. C₃²×C₂₃	C₂²×C₃₁	semidirect
29. D₆₉	D₃×C₃₁	semidirect
35. C₃×C₃₁	D₃×D₂₃	semidirect
38. C₃×C₂₃	C₂×D₃×C₃₁	semidirect
44. C₃₁	(C₃⋊D₃)⋊D₂₃	direct (N × H)
45. C₂₃	D₃²×C₃₁	semidirect
46. C₃⋊D₃	C₃₁×D₂₃	semidirect
49. C₃²	C₂×C₃₁×D₂₃	semidirect
56. C₃	D₃×C₃₁×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃₁×D₆₉	2
C₃⋊D₃×C₂₃×C₃₁	2
D₃×C₃₁×D₂₃	3
D₃²×C₃₁	23
(C₃⋊D₃)⋊D₂₃	31

Subgroups — C31×(C3⋊D3)⋊D23 #38787342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×(C₃⋊D₃)⋊D₂₃ #38787342