Subgroups — D₃×C₇×D₁₄₃ #26046549

Order 12012.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₁₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×D₁₄₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₁₄₃	—	3	1	no	—
7	C₇×D₁₄₃	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₇×C₁₁×C₁₃	—	3	1	no	—
9	D₃×D₁₄₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	D₃×C₇×D₁₃	—	11	1	no	maximal, Hall
11	C₇×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	D₃×C₇×D₁₁	—	13	1	no	maximal, Hall
13	D₄₂₉	C₂×C₇	1	1	yes	characteristic, complemented
14	D₃×C₁₁×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
15	C₃×D₁₄₃	C₂×C₇	1	1	yes	characteristic, complemented
16	C₂×D₁₄₃	—	3	1	no	Hall
17	C₇×D₃₉	—	11	1	no	—
18	D₃×C₇×C₁₃	D₁₁	1	1	yes	characteristic, complemented
19	C₃×C₇×D₁₃	—	11	1	no	—
20	C₇×D₃₃	—	13	1	no	—
21	D₃×C₇×C₁₁	D₁₃	1	1	yes	characteristic, complemented
22	C₃×C₇×D₁₁	—	13	1	no	—
23	C₃×C₁₁×C₁₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇×D₁₃	—	33	1	no	Hall
25	C₂×C₇×D₁₁	—	39	1	no	Hall
26	C₂×C₁₁×C₁₃	—	3	1	no	—
27	D₁₄₃	—	3	1	no	—
28	D₁₄₃	D₃×C₇	1	1	yes	characteristic, direct product factor
29	C₃×C₇×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
30	C₃×C₇×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇×C₁₃	—	3	1	no	—
32	C₇×D₁₃	—	11	1	no	—
33	C₇×D₁₃	—	33	1	no	—
34	D₃×D₁₃	—	11	1	no	Hall
35	C₂×C₇×C₁₁	—	3	1	no	—
36	C₇×D₁₁	—	13	1	no	—
37	C₇×D₁₁	—	39	1	no	—
38	C₁₁×C₁₃	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
39	D₃×D₁₁	—	13	1	no	Hall
40	C₇×C₁₃	D₃×D₁₁	1	1	yes	characteristic, complemented, Hall
41	C₂×D₃×C₇	—	143	1	no	Hall
42	D₃₉	—	11	1	no	—
43	C₃×D₁₃	—	11	1	no	—
44	D₃×C₁₃	C₇×D₁₁	1	1	yes	characteristic, complemented
45	C₇×C₁₁	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
46	D₃₃	—	13	1	no	—
47	C₃×D₁₁	—	13	1	no	—
48	D₃×C₁₁	C₇×D₁₃	1	1	yes	characteristic, complemented
49	C₂×D₁₃	—	33	1	no	Hall
50	C₂×D₁₁	—	39	1	no	Hall
51	C₂×C₃×C₇	—	143	1	no	—
52	D₃×C₇	—	143	1	no	—
53	D₃×C₇	D₁₄₃	1	1	yes	characteristic, direct product factor
54	C₃×C₁₃	C₂×C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
55	C₃×C₁₁	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
56	C₂²×C₇	—	429	1	no	Hall
57	C₂×C₁₃	—	3	1	no	—
58	D₁₃	—	11	1	no	—
59	D₁₃	—	33	1	no	—
60	C₂×C₁₁	—	3	1	no	—
61	D₁₁	—	13	1	no	—
62	D₁₁	—	39	1	no	—
63	C₃×C₇	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Hall
64	C₂×C₇	—	3	1	no	—
65	C₂×C₇	—	143	1	no	—
66	C₂×C₇	—	429	1	no	—
67	C₁₃	D₃×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
68	C₂×D₃	—	143	1	no	Hall
69	C₁₁	D₃×C₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
70	C₇	D₃×D₁₄₃	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₃	—	143	1	no	—
72	D₃	—	143	1	no	—
73	D₃	C₇×D₁₄₃	1	1	yes	characteristic, direct product factor
74	C₂²	—	429	1	no	Sylow
75	C₃	C₂×C₇×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	143	1	no	—
78	C₂	—	429	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₃×D₁₄₃
commutator, cosocle, hypocenter	C₃×C₁₁×C₁₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₃	C₂²
LCS	G ▷ C₃×C₁₁×C₁₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₄₂₉	C₂	semidirect
2. D₃×C₇×C₁₁×C₁₃	C₂	semidirect
3. C₃×C₇×D₁₄₃	C₂	semidirect
5. C₃×C₇×C₁₁×C₁₃	C₂²	semidirect
7. C₇×D₁₄₃	D₃	direct (N × H)
9. D₃×D₁₄₃	C₇	direct (N × H)
11. C₇×C₁₁×C₁₃	C₂×D₃	semidirect
13. D₄₂₉	C₂×C₇	semidirect
14. D₃×C₁₁×C₁₃	C₂×C₇	semidirect
15. C₃×D₁₄₃	C₂×C₇	semidirect
18. D₃×C₇×C₁₃	D₁₁	semidirect
21. D₃×C₇×C₁₁	D₁₃	semidirect
23. C₃×C₁₁×C₁₃	C₂²×C₇	semidirect
28. D₁₄₃	D₃×C₇	direct (N × H)
29. C₃×C₇×C₁₃	C₂×D₁₁	semidirect
30. C₃×C₇×C₁₁	C₂×D₁₃	semidirect
38. C₁₁×C₁₃	C₂×D₃×C₇	semidirect
40. C₇×C₁₃	D₃×D₁₁	semidirect
44. D₃×C₁₃	C₇×D₁₁	semidirect
45. C₇×C₁₁	D₃×D₁₃	semidirect
48. D₃×C₁₁	C₇×D₁₃	semidirect
53. D₃×C₇	D₁₄₃	direct (N × H)
54. C₃×C₁₃	C₂×C₇×D₁₁	semidirect
55. C₃×C₁₁	C₂×C₇×D₁₃	semidirect
63. C₃×C₇	C₂×D₁₄₃	semidirect
67. C₁₃	D₃×C₇×D₁₁	semidirect
69. C₁₁	D₃×C₇×D₁₃	semidirect
70. C₇	D₃×D₁₄₃	direct (N × H)
73. D₃	C₇×D₁₄₃	direct (N × H)
75. C₃	C₂×C₇×D₁₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₄₂₉	2
D₃×C₇×C₁₁×C₁₃	2
C₃×C₇×D₁₄₃	2
C₂×C₇×D₁₄₃	3
D₃×D₁₄₃	7
D₃×C₇×D₁₃	11
D₃×C₇×D₁₁	13

Subgroups — D3×C7×D143 #26046549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×D₁₄₃ #26046549