Subgroups — C₇×C₁₁×C₃⋊#1039 #37528388

Order 23100.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₇×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁×#1039	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₇×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₁₁×Dic₁₅	—	5	6	no	maximal
5	C₂×C₅²×C₇×C₁₁	D₃	1	1	yes	characteristic
6	C₁₁×C₃⋊#1039	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×C₇×C₁₁	D₅	1	6	yes	—
8	C₇×C₃⋊#1039	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅²×C₇×C₁₁	Dic₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₅²×C₁₁	C₂×C₇	1	1	yes	characteristic
11	C₇×C₁₁×Dic₅	—	15	6	no	—
12	C₃×C₅×C₇×C₁₁	Dic₅	1	6	yes	complemented
13	C₁₁×#1039	—	3	1	no	Hall
14	C₂×C₃×C₅²×C₇	C₂×C₁₁	1	1	yes	characteristic
15	C₇×C₁₁×Dic₃	—	25	1	no	Hall
16	C₃×C₅²×C₁₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₇×C₁₁	D₁₅	1	6	yes	—
18	C₇×#1039	—	3	1	no	Hall
19	C₁₁×Dic₁₅	—	5	6	no	—
20	C₂×C₅²×C₁₁	D₃×C₇	1	1	yes	characteristic
21	C₃×C₅²×C₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₁₁	C₅⋊D₅	1	1	yes	characteristic
23	C₇×Dic₁₅	—	5	6	no	—
24	C₅×C₇×C₁₁	Dic₁₅	1	6	yes	complemented
25	C₂×C₅²×C₇	D₃×C₁₁	1	1	yes	characteristic
26	C₂×C₃×C₅×C₁₁	C₇×D₅	1	6	yes	—
27	C₄×C₇×C₁₁	—	75	1	no	Hall
28	C₃⋊#1039	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
29	C₅²×C₁₁	C₇×Dic₃	1	1	yes	characteristic, complemented, Hall
30	C₃×C₇×C₁₁	#1039	1	1	yes	characteristic, complemented, Hall
31	C₁₁×Dic₅	—	15	6	no	—
32	C₂×C₃×C₅×C₇	D₅×C₁₁	1	6	yes	—
33	C₅²×C₇	C₁₁×Dic₃	1	1	yes	characteristic, complemented, Hall
34	C₃×C₅×C₁₁	C₇×Dic₅	1	6	yes	complemented
35	C₂×C₇×C₁₁	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
36	C₂×C₃×C₅²	C₂×C₇×C₁₁	1	1	yes	characteristic
37	C₇×Dic₅	—	15	6	no	—
38	C₁₁×Dic₃	—	25	1	no	Hall
39	C₂×C₅×C₁₁	C₇×D₁₅	1	6	yes	—
40	C₃×C₅×C₇	C₁₁×Dic₅	1	6	yes	complemented
41	#1039	—	3	1	no	Hall
42	C₇×Dic₃	—	25	1	no	Hall
43	C₇×C₁₁	C₃⋊#1039	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₅²	C₄×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅×C₇	C₁₁×D₁₅	1	6	yes	—
46	C₂×C₃×C₁₁	C₇×C₅⋊D₅	1	1	yes	characteristic
47	Dic₁₅	—	5	6	no	—
48	C₅×C₁₁	C₇×Dic₁₅	1	6	yes	complemented
49	C₂×C₅²	D₃×C₇×C₁₁	1	1	yes	characteristic
50	C₄×C₁₁	—	75	1	no	Hall
51	C₂×C₃×C₇	C₁₁×C₅⋊D₅	1	1	yes	characteristic
52	C₅×C₇	C₁₁×Dic₁₅	1	6	yes	complemented
53	C₃×C₁₁	C₇×#1039	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	C₇×D₅×C₁₁	1	6	yes	—
55	C₄×C₇	—	75	1	no	Hall
56	C₅²	C₇×C₁₁×Dic₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₁₁	C₇×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
58	C₃×C₇	C₁₁×#1039	1	1	yes	characteristic, complemented, Hall
59	Dic₅	—	15	6	no	—
60	C₃×C₅	C₇×C₁₁×Dic₅	1	6	yes	complemented
61	C₂×C₇	C₁₁×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
62	Dic₃	—	25	1	no	Hall
63	C₁₁	C₇×C₃⋊#1039	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₅	C₇×C₁₁×D₁₅	1	6	yes	—
65	C₇	C₁₁×C₃⋊#1039	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₃	C₇×C₁₁×C₅⋊D₅	1	1	yes	characteristic
67	C₅	C₇×C₁₁×Dic₁₅	1	6	yes	complemented
68	C₄	—	75	1	no	Sylow
69	C₃	C₇×C₁₁×#1039	1	1	yes	characteristic, complemented, Sylow
70	C₂	C₇×C₁₁×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₁	C₃⋊(C₅⋊D₅)
commutator, hypocenter	C₃×C₅²	C₄×C₇×C₁₁
Frattini	C₂	C₇×C₁₁×C₃⋊(C₅⋊D₅)
Fitting, socle, prime radical	C₂×C₃×C₅²×C₇×C₁₁	C₂
cosocle	C₂×C₃×C₅²	C₂×C₇×C₁₁
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂×C₇×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₇×C₁₁	C₄	semidirect
6. C₁₁×C₃⋊#1039	C₇	direct (N × H)
8. C₇×C₃⋊#1039	C₁₁	direct (N × H)
9. C₅²×C₇×C₁₁	Dic₃	semidirect
12. C₃×C₅×C₇×C₁₁	Dic₅	semidirect
16. C₃×C₅²×C₁₁	C₄×C₇	semidirect
21. C₃×C₅²×C₇	C₄×C₁₁	semidirect
24. C₅×C₇×C₁₁	Dic₁₅	semidirect
28. C₃⋊#1039	C₇×C₁₁	direct (N × H)
29. C₅²×C₁₁	C₇×Dic₃	semidirect
30. C₃×C₇×C₁₁	#1039	semidirect
33. C₅²×C₇	C₁₁×Dic₃	semidirect
34. C₃×C₅×C₁₁	C₇×Dic₅	semidirect
40. C₃×C₅×C₇	C₁₁×Dic₅	semidirect
43. C₇×C₁₁	C₃⋊#1039	direct (N × H)
44. C₃×C₅²	C₄×C₇×C₁₁	semidirect
48. C₅×C₁₁	C₇×Dic₁₅	semidirect
52. C₅×C₇	C₁₁×Dic₁₅	semidirect
53. C₃×C₁₁	C₇×#1039	semidirect
56. C₅²	C₇×C₁₁×Dic₃	semidirect
58. C₃×C₇	C₁₁×#1039	semidirect
60. C₃×C₅	C₇×C₁₁×Dic₅	semidirect
63. C₁₁	C₇×C₃⋊#1039	direct (N × H)
65. C₇	C₁₁×C₃⋊#1039	direct (N × H)
67. C₅	C₇×C₁₁×Dic₁₅	semidirect
69. C₃	C₇×C₁₁×#1039	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²×C₇×C₁₁	2
C₇×C₁₁×#1039	3
C₇×C₁₁×Dic₁₅	5
C₁₁×C₃⋊#1039	7
C₇×C₃⋊#1039	11

Subgroups — C7×C11×C3⋊#1039 #37528388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁×C₃⋊#1039 #37528388