Subgroups — C₄₁×(C₃⋊D₃)⋊D₂₃ #46800439

Order 33948.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×D₆₉	C₂	1	2	yes	maximal, complemented
2	C₃⋊D₃×C₂₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₄₁×D₂₃	—	3	2	no	maximal
4	C₃²×C₂₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₄₁×D₆₉	D₃	1	2	yes	complemented
6	D₃×C₂₃×C₄₁	—	3	2	no	—
7	D₃×C₂₃×C₄₁	—	6	1	no	—
8	C₃×C₄₁×D₂₃	—	3	2	no	—
9	C₂×C₄₁×D₂₃	—	9	1	no	Hall
10	C₃×C₂₃×C₄₁	—	2	1	no	—
11	C₃×C₂₃×C₄₁	C₂×D₃	1	2	yes	complemented
12	C₂×C₂₃×C₄₁	—	9	1	no	—
13	C₄₁×D₂₃	—	3	2	no	—
14	D₃²×C₄₁	—	23	1	no	maximal, Hall
15	C₂₃×C₄₁	D₃²	1	1	yes	characteristic, complemented, Hall
16	(C₃⋊D₃)⋊D₂₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃⋊D₃×C₄₁	D₂₃	1	1	yes	characteristic, complemented
18	C₃×D₃×C₄₁	—	23	2	no	—
19	C₂×D₃×C₄₁	—	69	2	no	—
20	C₃⋊D₃×C₂₃	C₂×C₄₁	1	1	yes	characteristic, complemented
21	C₃×D₆₉	C₂×C₄₁	1	2	yes	complemented
22	C₃²×C₄₁	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
23	D₃×D₂₃	—	3	2	no	—
24	C₂×C₃×C₄₁	—	69	2	no	—
25	D₃×C₄₁	—	3	2	no	—
26	D₃×C₄₁	—	6	1	no	—
27	D₃×C₄₁	—	23	2	no	—
28	C₃²×C₂₃	C₂²×C₄₁	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₄₁	—	207	1	no	Hall
30	D₆₉	D₃×C₄₁	1	2	yes	complemented
31	C₃×D₂₃	—	3	2	no	—
32	D₃×C₂₃	—	3	2	no	—
33	D₃×C₂₃	—	6	1	no	—
34	C₃×C₄₁	—	2	1	no	—
35	C₃×C₄₁	D₃×D₂₃	1	2	yes	complemented
36	C₂×D₂₃	—	9	1	no	Hall
37	C₂×C₄₁	—	9	1	no	—
38	C₂×C₄₁	—	69	2	no	—
39	C₃×C₂₃	—	2	1	no	—
40	C₃×C₂₃	C₂×D₃×C₄₁	1	2	yes	complemented
41	C₂×C₂₃	—	9	1	no	—
42	D₂₃	—	3	2	no	—
43	C₄₁	(C₃⋊D₃)⋊D₂₃	1	1	yes	characteristic, direct product factor, Sylow
44	D₃²	—	23	1	no	Hall
45	C₂₃	D₃²×C₄₁	1	1	yes	characteristic, complemented, Sylow
46	C₃⋊D₃	C₄₁×D₂₃	1	1	yes	characteristic, complemented
47	C₃×D₃	—	23	2	no	—
48	C₂×D₃	—	69	2	no	—
49	C₃²	C₂×C₄₁×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×C₄₁×D₂₃	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	69	2	no	—

	subgroup	G/H
center, hypercenter	C₄₁	(C₃⋊D₃)⋊D₂₃
commutator, cosocle, hypocenter	C₃²×C₂₃	C₂²×C₄₁
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃×C₄₁	C₂²
LCS	G ▷ C₃²×C₂₃
UCS	C₁ ◁ C₄₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₁×D₆₉	C₂	semidirect
2. C₃⋊D₃×C₂₃×C₄₁	C₂	semidirect
4. C₃²×C₂₃×C₄₁	C₂²	semidirect
5. C₄₁×D₆₉	D₃	semidirect
11. C₃×C₂₃×C₄₁	C₂×D₃	semidirect
15. C₂₃×C₄₁	D₃²	semidirect
16. (C₃⋊D₃)⋊D₂₃	C₄₁	direct (N × H)
17. C₃⋊D₃×C₄₁	D₂₃	semidirect
20. C₃⋊D₃×C₂₃	C₂×C₄₁	semidirect
21. C₃×D₆₉	C₂×C₄₁	semidirect
22. C₃²×C₄₁	C₂×D₂₃	semidirect
28. C₃²×C₂₃	C₂²×C₄₁	semidirect
30. D₆₉	D₃×C₄₁	semidirect
35. C₃×C₄₁	D₃×D₂₃	semidirect
40. C₃×C₂₃	C₂×D₃×C₄₁	semidirect
43. C₄₁	(C₃⋊D₃)⋊D₂₃	direct (N × H)
45. C₂₃	D₃²×C₄₁	semidirect
46. C₃⋊D₃	C₄₁×D₂₃	semidirect
49. C₃²	C₂×C₄₁×D₂₃	semidirect
56. C₃	D₃×C₄₁×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄₁×D₆₉	2
C₃⋊D₃×C₂₃×C₄₁	2
D₃×C₄₁×D₂₃	3
D₃²×C₄₁	23
(C₃⋊D₃)⋊D₂₃	41

Subgroups — C41×(C3⋊D3)⋊D23 #46800439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×(C₃⋊D₃)⋊D₂₃ #46800439