Subgroups — C₃×D₃×C₂₃×D₄₁ #46800425

Order 33948.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₃×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₂₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₃×D₁₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₂₃×D₄₁	—	3	1	no	maximal
5	D₃×C₂₃×D₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₂₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂₃×D₁₂₃	C₂×C₃	1	1	yes	characteristic, complemented
8	D₃×C₂₃×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₂₃×D₄₁	—	2	1	no	—
10	C₃×C₂₃×D₄₁	—	3	1	no	—
11	C₃×C₂₃×D₄₁	D₃	1	1	yes	characteristic, direct product factor
12	C₃×C₂₃×D₄₁	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₃×C₂₃×C₄₁	—	3	1	no	—
14	C₂×C₂₃×D₄₁	—	3	1	no	Hall
15	C₃×C₂₃×C₄₁	—	2	1	no	—
16	C₃×C₂₃×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₂₃×C₄₁	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×C₂₃×C₄₁	—	3	1	no	—
19	C₂₃×D₄₁	—	3	1	no	—
20	C₂₃×D₄₁	C₃×D₃	1	1	yes	characteristic, direct product factor
21	C₃×D₃×D₄₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂₃×C₄₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×D₃×C₂₃	—	41	1	no	maximal, Hall
24	C₃×D₁₂₃	C₂×C₂₃	1	1	yes	characteristic, complemented
25	C₃×D₃×C₄₁	C₂×C₂₃	1	1	yes	characteristic, complemented
26	C₃²×D₄₁	C₂×C₂₃	1	1	yes	characteristic, complemented
27	C₂×C₃×D₄₁	—	3	1	no	—
28	D₃×D₄₁	C₃×C₂₃	1	1	yes	characteristic, direct product factor
29	C₂×C₃²×C₂₃	—	41	1	no	—
30	C₃×D₃×C₂₃	—	41	1	no	—
31	C₃×D₃×C₂₃	D₄₁	1	1	yes	characteristic, direct product factor
32	C₃²×C₄₁	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₃×C₂₃	—	123	1	no	—
34	C₂×D₃×C₂₃	—	41	1	no	—
35	C₂×C₃×C₄₁	—	3	1	no	—
36	D₁₂₃	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
37	C₃×D₄₁	—	2	1	no	—
38	C₃×D₄₁	—	3	1	no	—
39	C₃×D₄₁	D₃×C₂₃	1	1	yes	characteristic, direct product factor
40	C₃×D₄₁	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
41	D₃×C₄₁	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
42	C₃²×C₂₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
43	C₂×D₄₁	—	3	1	no	Hall
44	C₂×C₃×C₂₃	—	3	1	no	—
45	C₂×C₃×C₂₃	—	41	1	no	—
46	C₂×C₃×C₂₃	—	41	1	no	—
47	C₂×C₃×C₂₃	—	82	1	no	—
48	C₂×C₃×C₂₃	—	123	1	no	—
49	D₃×C₂₃	—	41	1	no	—
50	D₃×C₂₃	C₃×D₄₁	1	1	yes	characteristic, direct product factor
51	C₃×C₄₁	—	2	1	no	—
52	C₃×C₄₁	C₂×D₃×C₂₃	1	1	yes	characteristic, complemented
53	C₃×C₄₁	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented
54	C₂²×C₂₃	—	123	1	no	Hall
55	C₂×C₄₁	—	3	1	no	—
56	D₄₁	—	3	1	no	—
57	D₄₁	C₃×D₃×C₂₃	1	1	yes	characteristic, direct product factor
58	C₃×C₂₃	—	2	1	no	—
59	C₃×C₂₃	D₃×D₄₁	1	1	yes	characteristic, direct product factor
60	C₃×C₂₃	C₂×C₃×D₄₁	1	1	yes	characteristic, complemented
61	C₂×C₂₃	—	3	1	no	—
62	C₂×C₂₃	—	41	1	no	—
63	C₂×C₂₃	—	123	1	no	—
64	C₄₁	C₂×C₃×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃×D₃	—	41	1	no	Hall
66	C₂₃	C₃×D₃×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×C₃²	—	41	1	no	—
68	C₃×D₃	—	41	1	no	—
69	C₃×D₃	C₂₃×D₄₁	1	1	yes	characteristic, direct product factor
70	C₂²×C₃	—	123	1	no	—
71	C₂×D₃	—	41	1	no	—
72	C₃²	C₂×C₂₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	41	1	no	—
75	C₂×C₃	—	41	1	no	—
76	C₂×C₃	—	82	1	no	—
77	C₂×C₃	—	123	1	no	—
78	D₃	—	41	1	no	—
79	D₃	C₃×C₂₃×D₄₁	1	1	yes	characteristic, direct product factor
80	C₂²	—	123	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×C₂₃×D₄₁	1	1	yes	characteristic, direct product factor
83	C₃	C₂×C₃×C₂₃×D₄₁	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	41	1	no	—
86	C₂	—	123	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₃×D₄₁
commutator, cosocle, hypocenter	C₃×C₄₁	C₂²×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃×C₄₁	C₂²
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₃×D₄₁	C₂	semidirect
2. C₃×D₃×C₂₃×C₄₁	C₂	semidirect
3. C₃×C₂₃×D₁₂₃	C₂	semidirect
5. D₃×C₂₃×D₄₁	C₃	direct (N × H)
6. C₃²×C₂₃×C₄₁	C₂²	semidirect
7. C₂₃×D₁₂₃	C₂×C₃	semidirect
8. D₃×C₂₃×C₄₁	C₂×C₃	semidirect
11. C₃×C₂₃×D₄₁	D₃	direct (N × H)
12. C₃×C₂₃×D₄₁	C₂×C₃	semidirect
16. C₃×C₂₃×C₄₁	C₂×D₃	semidirect
17. C₃×C₂₃×C₄₁	C₂²×C₃	semidirect
20. C₂₃×D₄₁	C₃×D₃	direct (N × H)
21. C₃×D₃×D₄₁	C₂₃	direct (N × H)
22. C₂₃×C₄₁	C₂×C₃×D₃	semidirect
24. C₃×D₁₂₃	C₂×C₂₃	semidirect
25. C₃×D₃×C₄₁	C₂×C₂₃	semidirect
26. C₃²×D₄₁	C₂×C₂₃	semidirect
28. D₃×D₄₁	C₃×C₂₃	direct (N × H)
31. C₃×D₃×C₂₃	D₄₁	direct (N × H)
32. C₃²×C₄₁	C₂²×C₂₃	semidirect
36. D₁₂₃	C₂×C₃×C₂₃	semidirect
39. C₃×D₄₁	D₃×C₂₃	direct (N × H)
40. C₃×D₄₁	C₂×C₃×C₂₃	semidirect
41. D₃×C₄₁	C₂×C₃×C₂₃	semidirect
42. C₃²×C₂₃	C₂×D₄₁	semidirect
50. D₃×C₂₃	C₃×D₄₁	direct (N × H)
52. C₃×C₄₁	C₂×D₃×C₂₃	semidirect
53. C₃×C₄₁	C₂²×C₃×C₂₃	semidirect
57. D₄₁	C₃×D₃×C₂₃	direct (N × H)
59. C₃×C₂₃	D₃×D₄₁	direct (N × H)
60. C₃×C₂₃	C₂×C₃×D₄₁	semidirect
64. C₄₁	C₂×C₃×D₃×C₂₃	semidirect
66. C₂₃	C₃×D₃×D₄₁	direct (N × H)
69. C₃×D₃	C₂₃×D₄₁	direct (N × H)
72. C₃²	C₂×C₂₃×D₄₁	semidirect
79. D₃	C₃×C₂₃×D₄₁	direct (N × H)
82. C₃	D₃×C₂₃×D₄₁	direct (N × H)
83. C₃	C₂×C₃×C₂₃×D₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₂₃×D₄₁	2
C₃×D₃×C₂₃×C₄₁	2
C₃×C₂₃×D₁₂₃	2
C₂×C₃×C₂₃×D₄₁	3
D₃×C₂₃×D₄₁	3
C₃×D₃×D₄₁	23
C₂×C₃×D₃×C₂₃	41

Subgroups — C3×D3×C23×D41 #46800425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₂₃×D₄₁ #46800425