Subgroups — C₂×C₃×C₇×D₁₂₃ #23780243

Order 10332.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₁₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₁₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₇×D₄₁	—	3	1	no	maximal
5	C₃²×C₇×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₇×C₄₁	—	2	1	no	—
7	C₂×C₃×C₇×C₄₁	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₇×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₇×D₁₂₃	C₂×C₃	1	2	yes	direct product factor
10	C₃×C₇×D₄₁	—	3	2	no	—
11	C₂×C₃×D₁₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₇×D₄₁	—	3	1	no	Hall
13	C₃×C₇×C₄₁	—	2	1	no	—
14	C₃×C₇×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented
15	C₃×C₇×C₄₁	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃²×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented
17	C₃×D₁₂₃	C₂×C₇	1	2	yes	direct product factor
18	C₂×C₇×C₄₁	C₃×D₃	1	1	yes	characteristic, complemented
19	C₇×D₄₁	—	3	2	no	—
20	C₂×D₁₂₃	C₃×C₇	1	1	yes	characteristic, direct product factor
21	C₂×C₃×D₄₁	—	3	1	no	—
22	C₃²×C₄₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
23	C₇×C₄₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×D₃×C₇	—	41	1	no	maximal, Hall
25	C₂×C₃×C₄₁	—	2	1	no	—
26	C₂×C₃×C₄₁	D₃×C₇	1	1	yes	characteristic, complemented
27	C₂×C₃×C₄₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented
28	D₁₂₃	C₂×C₃×C₇	1	2	yes	direct product factor
29	C₃×D₄₁	—	3	2	no	—
30	C₂×D₄₁	—	3	1	no	Hall
31	C₂×C₃²×C₇	D₄₁	1	1	yes	characteristic, complemented
32	C₃×D₃×C₇	—	41	2	no	—
33	C₃×C₄₁	—	2	1	no	—
34	C₃×C₄₁	C₂×D₃×C₇	1	1	yes	characteristic, complemented
35	C₃×C₄₁	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
36	C₂²×C₃×C₇	—	123	1	no	—
37	C₂×D₃×C₇	—	41	1	no	—
38	C₂×C₄₁	C₃×D₃×C₇	1	1	yes	characteristic, complemented
39	D₄₁	—	3	2	no	—
40	C₃²×C₇	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₇	—	2	1	no	—
42	C₂×C₃×C₇	—	123	2	no	—
43	C₂×C₃×C₇	C₃×D₄₁	1	1	yes	characteristic, complemented
44	C₂×C₃×C₇	D₁₂₃	1	1	yes	characteristic, direct product factor
45	D₃×C₇	—	41	2	no	—
46	C₄₁	C₂×C₃×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃×D₃	—	41	1	no	Hall
48	C₂²×C₇	—	123	1	no	Hall
49	C₃×C₇	—	2	1	no	—
50	C₃×C₇	C₂×C₃×D₄₁	1	1	yes	characteristic, complemented
51	C₃×C₇	C₂×D₁₂₃	1	1	yes	characteristic, direct product factor
52	C₂×C₃²	C₇×D₄₁	1	1	yes	characteristic, complemented
53	C₃×D₃	—	41	2	no	—
54	C₂×C₇	—	123	2	no	—
55	C₂×C₇	C₃×D₁₂₃	1	1	yes	characteristic, direct product factor
56	C₂²×C₃	—	123	1	no	—
57	C₂×D₃	—	41	1	no	—
58	C₃²	C₂×C₇×D₄₁	1	1	yes	characteristic, complemented, Sylow
59	C₇	C₂×C₃×D₁₂₃	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	123	2	no	—
62	C₂×C₃	C₃×C₇×D₄₁	1	1	yes	characteristic, complemented
63	C₂×C₃	C₇×D₁₂₃	1	1	yes	characteristic, direct product factor
64	D₃	—	41	2	no	—
65	C₂²	—	123	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₃×C₇×D₄₁	1	1	yes	characteristic, complemented
68	C₃	C₂×C₇×D₁₂₃	1	1	yes	characteristic, direct product factor
69	C₂	—	123	2	no	—
70	C₂	C₃×C₇×D₁₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	D₁₂₃
commutator, cosocle, hypocenter	C₃×C₄₁	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₄₁	C₂
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₁₂₃	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₄₁	C₂	semidirect
3. C₂×C₇×D₁₂₃	C₃	direct (N × H)
5. C₃²×C₇×C₄₁	C₂²	semidirect
7. C₂×C₃×C₇×C₄₁	D₃	semidirect
8. C₂×C₃×C₇×C₄₁	C₂×C₃	semidirect
9. C₇×D₁₂₃	C₂×C₃	direct (N × H)
11. C₂×C₃×D₁₂₃	C₇	direct (N × H)
14. C₃×C₇×C₄₁	C₂×D₃	semidirect
15. C₃×C₇×C₄₁	C₂²×C₃	semidirect
16. C₂×C₃²×C₄₁	C₂×C₇	semidirect
17. C₃×D₁₂₃	C₂×C₇	direct (N × H)
18. C₂×C₇×C₄₁	C₃×D₃	semidirect
20. C₂×D₁₂₃	C₃×C₇	direct (N × H)
22. C₃²×C₄₁	C₂²×C₇	semidirect
23. C₇×C₄₁	C₂×C₃×D₃	semidirect
26. C₂×C₃×C₄₁	D₃×C₇	semidirect
27. C₂×C₃×C₄₁	C₂×C₃×C₇	semidirect
28. D₁₂₃	C₂×C₃×C₇	direct (N × H)
31. C₂×C₃²×C₇	D₄₁	semidirect
34. C₃×C₄₁	C₂×D₃×C₇	semidirect
35. C₃×C₄₁	C₂²×C₃×C₇	semidirect
38. C₂×C₄₁	C₃×D₃×C₇	semidirect
40. C₃²×C₇	C₂×D₄₁	semidirect
43. C₂×C₃×C₇	C₃×D₄₁	semidirect
44. C₂×C₃×C₇	D₁₂₃	direct (N × H)
46. C₄₁	C₂×C₃×D₃×C₇	semidirect
50. C₃×C₇	C₂×C₃×D₄₁	semidirect
51. C₃×C₇	C₂×D₁₂₃	direct (N × H)
52. C₂×C₃²	C₇×D₄₁	semidirect
55. C₂×C₇	C₃×D₁₂₃	direct (N × H)
58. C₃²	C₂×C₇×D₄₁	semidirect
59. C₇	C₂×C₃×D₁₂₃	direct (N × H)
62. C₂×C₃	C₃×C₇×D₄₁	semidirect
63. C₂×C₃	C₇×D₁₂₃	direct (N × H)
67. C₃	C₂×C₃×C₇×D₄₁	semidirect
68. C₃	C₂×C₇×D₁₂₃	direct (N × H)
70. C₂	C₃×C₇×D₁₂₃	direct (N × H)

Subgroups — C2×C3×C7×D123 #23780243

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₇×D₁₂₃ #23780243