Subgroups — C₂×C₃×C₂₃×D₂₁ #19154016

Order 5796.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×D₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×D₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₇×C₂₃	—	3	1	no	maximal
5	C₃²×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₇×C₂₃	—	2	1	no	—
7	C₂×C₃×C₇×C₂₃	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₇×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂₃×D₂₁	C₂×C₃	1	2	yes	direct product factor
10	C₃×D₇×C₂₃	—	3	2	no	—
11	C₂×C₃×D₃×C₂₃	—	7	1	no	maximal, Hall
12	C₂×D₇×C₂₃	—	3	1	no	Hall
13	C₃×C₇×C₂₃	—	2	1	no	—
14	C₃×C₇×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented
15	C₃×C₇×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃²×C₂₃	D₇	1	1	yes	characteristic, complemented
17	C₃×D₃×C₂₃	—	7	2	no	—
18	C₂×C₇×C₂₃	C₃×D₃	1	1	yes	characteristic, complemented
19	D₇×C₂₃	—	3	2	no	—
20	C₂²×C₃×C₂₃	—	21	1	no	—
21	C₂×D₃×C₂₃	—	7	1	no	—
22	C₂×C₃×D₂₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₃²×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	C₇×C₂₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₂₃	—	2	1	no	—
26	C₂×C₃×C₂₃	—	21	2	no	—
27	C₂×C₃×C₂₃	C₃×D₇	1	1	yes	characteristic, complemented
28	C₂×C₃×C₂₃	D₂₁	1	1	yes	characteristic, direct product factor
29	D₃×C₂₃	—	7	2	no	—
30	C₂×C₃²×C₇	C₂×C₂₃	1	1	yes	characteristic, complemented
31	C₃×D₂₁	C₂×C₂₃	1	2	yes	direct product factor
32	C₂²×C₂₃	—	21	1	no	Hall
33	C₂×D₂₁	C₃×C₂₃	1	1	yes	characteristic, direct product factor
34	C₂×C₃×D₇	—	3	1	no	—
35	C₃×C₂₃	—	2	1	no	—
36	C₃×C₂₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
37	C₃×C₂₃	C₂×D₂₁	1	1	yes	characteristic, direct product factor
38	C₃²×C₇	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₂₃	—	21	2	no	—
40	C₂×C₂₃	C₃×D₂₁	1	1	yes	characteristic, direct product factor
41	C₂×C₃×C₇	—	2	1	no	—
42	C₂×C₃×C₇	D₃×C₂₃	1	1	yes	characteristic, complemented
43	C₂×C₃×C₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
44	D₂₁	C₂×C₃×C₂₃	1	2	yes	direct product factor
45	C₃×D₇	—	3	2	no	—
46	C₂×C₃×D₃	—	7	1	no	Hall
47	C₂×D₇	—	3	1	no	Hall
48	C₂₃	C₂×C₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
49	C₃×C₇	—	2	1	no	—
50	C₃×C₇	C₂×D₃×C₂₃	1	1	yes	characteristic, complemented
51	C₃×C₇	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented
52	C₂×C₃²	D₇×C₂₃	1	1	yes	characteristic, complemented
53	C₃×D₃	—	7	2	no	—
54	C₂×C₇	C₃×D₃×C₂₃	1	1	yes	characteristic, complemented
55	D₇	—	3	2	no	—
56	C₂²×C₃	—	21	1	no	—
57	C₂×D₃	—	7	1	no	—
58	C₃²	C₂×D₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
59	C₇	C₂×C₃×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	21	2	no	—
62	C₂×C₃	C₃×D₇×C₂₃	1	1	yes	characteristic, complemented
63	C₂×C₃	C₂₃×D₂₁	1	1	yes	characteristic, direct product factor
64	D₃	—	7	2	no	—
65	C₂²	—	21	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₃×D₇×C₂₃	1	1	yes	characteristic, complemented
68	C₃	C₂×C₂₃×D₂₁	1	1	yes	characteristic, direct product factor
69	C₂	—	21	2	no	—
70	C₂	C₃×C₂₃×D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₃	D₂₁
commutator, hypocenter	C₃×C₇	C₂²×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₂₃	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₃×D₂₁	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₂₃	C₂	semidirect
3. C₂×C₂₃×D₂₁	C₃	direct (N × H)
5. C₃²×C₇×C₂₃	C₂²	semidirect
7. C₂×C₃×C₇×C₂₃	D₃	semidirect
8. C₂×C₃×C₇×C₂₃	C₂×C₃	semidirect
9. C₂₃×D₂₁	C₂×C₃	direct (N × H)
14. C₃×C₇×C₂₃	C₂×D₃	semidirect
15. C₃×C₇×C₂₃	C₂²×C₃	semidirect
16. C₂×C₃²×C₂₃	D₇	semidirect
18. C₂×C₇×C₂₃	C₃×D₃	semidirect
22. C₂×C₃×D₂₁	C₂₃	direct (N × H)
23. C₃²×C₂₃	C₂×D₇	semidirect
24. C₇×C₂₃	C₂×C₃×D₃	semidirect
27. C₂×C₃×C₂₃	C₃×D₇	semidirect
28. C₂×C₃×C₂₃	D₂₁	direct (N × H)
30. C₂×C₃²×C₇	C₂×C₂₃	semidirect
31. C₃×D₂₁	C₂×C₂₃	direct (N × H)
33. C₂×D₂₁	C₃×C₂₃	direct (N × H)
36. C₃×C₂₃	C₂×C₃×D₇	semidirect
37. C₃×C₂₃	C₂×D₂₁	direct (N × H)
38. C₃²×C₇	C₂²×C₂₃	semidirect
40. C₂×C₂₃	C₃×D₂₁	direct (N × H)
42. C₂×C₃×C₇	D₃×C₂₃	semidirect
43. C₂×C₃×C₇	C₂×C₃×C₂₃	semidirect
44. D₂₁	C₂×C₃×C₂₃	direct (N × H)
48. C₂₃	C₂×C₃×D₂₁	direct (N × H)
50. C₃×C₇	C₂×D₃×C₂₃	semidirect
51. C₃×C₇	C₂²×C₃×C₂₃	semidirect
52. C₂×C₃²	D₇×C₂₃	semidirect
54. C₂×C₇	C₃×D₃×C₂₃	semidirect
58. C₃²	C₂×D₇×C₂₃	semidirect
59. C₇	C₂×C₃×D₃×C₂₃	semidirect
62. C₂×C₃	C₃×D₇×C₂₃	semidirect
63. C₂×C₃	C₂₃×D₂₁	direct (N × H)
67. C₃	C₂×C₃×D₇×C₂₃	semidirect
68. C₃	C₂×C₂₃×D₂₁	direct (N × H)
70. C₂	C₃×C₂₃×D₂₁	direct (N × H)

Subgroups — C2×C3×C23×D21 #19154016

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₂₃×D₂₁ #19154016