Subgroups — C₂×C₁₁×D₇×C₁₃⋊C₉ #49114451

Order 36036.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₇×C₁₃⋊C₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₁×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₁×C₁₃×D₇	C₃	1	1	yes	maximal, characteristic
4	C₇×C₁₁×C₁₃⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₁₃×D₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic
7	C₂²×C₁₁×C₁₃⋊C₉	—	7	1	no	maximal, Hall
8	C₂×C₁₁×C₁₃×D₇	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×D₇×C₁₃⋊C₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₇×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic
11	C₂×C₉×C₁₁×D₇	—	13	1	no	maximal, Hall
12	C₂×C₁₁×C₁₃⋊C₉	—	7	2	no	—
13	C₂×C₁₁×C₁₃⋊C₉	D₇	1	1	yes	characteristic, direct product factor
14	C₁₁×C₁₃×D₇	C₂×C₉	1	2	yes	complemented
15	C₂×C₇×C₁₁×C₁₃	C₂×C₉	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₁₁×C₁₃	—	7	1	no	—
17	C₂×C₇×C₁₃⋊C₉	C₂×C₁₁	1	1	yes	characteristic, complemented
18	D₇×C₁₃⋊C₉	C₂×C₁₁	1	2	yes	direct product factor
19	C₂×C₇×C₉×C₁₁	—	13	1	no	—
20	C₉×C₁₁×D₇	—	13	2	no	—
21	C₁₁×C₁₃⋊C₉	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₁₃×D₇	C₃×C₁₁	1	1	yes	characteristic
23	C₇×C₁₁×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₁₁×D₇	C₁₃⋊C₃	1	1	yes	characteristic
25	C₂×C₃×C₁₁×C₁₃	—	7	2	no	—
26	C₂×C₃×C₁₁×C₁₃	C₃×D₇	1	1	yes	characteristic
27	C₇×C₁₃⋊C₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
28	C₇×C₉×C₁₁	—	13	1	no	Hall
29	C₂²×C₁₁×C₁₃	—	7	1	no	Hall
30	C₂×C₃×C₇×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic
31	C₃×C₁₃×D₇	C₂×C₃×C₁₁	1	2	yes	—
32	C₂²×C₁₃⋊C₉	—	7	1	no	Hall
33	C₂×C₃×C₇×C₁₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
34	C₃×C₁₁×D₇	C₂×C₁₃⋊C₃	1	2	yes	—
35	C₃×C₁₁×C₁₃	C₂×C₃×D₇	1	1	yes	characteristic
36	C₂²×C₉×C₁₁	—	91	1	no	Hall
37	C₂×C₁₃×D₇	C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
38	C₂×C₁₁×D₇	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₁₁×C₁₃	—	7	2	no	—
40	C₂×C₁₁×C₁₃	C₉×D₇	1	1	yes	characteristic, complemented
41	C₃×C₇×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic
42	C₂×C₉×D₇	—	13	1	no	Hall
43	C₂×C₁₃⋊C₉	—	7	2	no	—
44	C₂×C₁₃⋊C₉	C₁₁×D₇	1	1	yes	characteristic, direct product factor
45	C₃×C₇×C₁₁	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
46	C₂×C₉×C₁₁	—	13	1	no	—
47	C₂×C₉×C₁₁	—	91	2	no	—
48	C₂×C₇×C₁₃	C₂×C₉×C₁₁	1	1	yes	characteristic, complemented
49	C₁₃×D₇	C₂×C₉×C₁₁	1	2	yes	complemented
50	C₂²×C₃×C₁₃	—	7	1	no	—
51	C₂×C₇×C₁₁	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented
52	C₁₁×D₇	C₂×C₁₃⋊C₉	1	2	yes	direct product factor
53	C₁₁×C₁₃	C₂×C₉×D₇	1	1	yes	characteristic, complemented, Hall
54	C₂²×C₃×C₁₁	—	7	1	no	—
55	C₂×C₇×C₉	—	13	1	no	—
56	C₉×D₇	—	13	2	no	—
57	C₁₃⋊C₉	C₂×C₁₁×D₇	1	1	yes	characteristic, direct product factor, Hall
58	C₉×C₁₁	—	13	1	no	Hall
59	C₇×C₁₃	C₂²×C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂×C₃×D₇	C₁₁×C₁₃⋊C₃	1	1	yes	characteristic
61	C₂×C₃×C₁₃	—	7	2	no	—
62	C₂×C₃×C₁₃	C₃×C₁₁×D₇	1	1	yes	characteristic
63	C₇×C₁₁	C₂²×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
64	C₂×C₃×C₁₁	—	7	2	no	—
65	C₂×C₃×C₁₁	D₇×C₁₃⋊C₃	1	1	yes	characteristic
66	C₇×C₉	—	13	1	no	Hall
67	C₂²×C₁₃	—	7	1	no	Hall
68	C₂²×C₁₁	—	7	1	no	Hall
69	C₂×C₃×C₇	C₂×C₁₁×C₁₃⋊C₃	1	1	yes	characteristic
70	C₃×D₇	C₂×C₁₁×C₁₃⋊C₃	1	2	yes	—
71	C₃×C₁₃	C₂×C₃×C₁₁×D₇	1	1	yes	characteristic
72	C₂²×C₉	—	91	1	no	Hall
73	C₃×C₁₁	C₂×D₇×C₁₃⋊C₃	1	1	yes	characteristic
74	C₂×D₇	C₁₁×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
75	C₂×C₁₃	—	7	2	no	—
76	C₂×C₁₃	C₉×C₁₁×D₇	1	1	yes	characteristic, complemented
77	C₂×C₁₁	—	7	2	no	—
78	C₂×C₁₁	D₇×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor
79	C₃×C₇	C₂²×C₁₁×C₁₃⋊C₃	1	1	yes	characteristic
80	C₂×C₉	—	13	1	no	—
81	C₂×C₉	—	91	2	no	—
82	C₂×C₇	C₂×C₁₁×C₁₃⋊C₉	1	1	yes	characteristic, complemented
83	D₇	C₂×C₁₁×C₁₃⋊C₉	1	2	yes	direct product factor
84	C₁₃	C₂×C₉×C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₃	—	7	1	no	—
86	C₁₁	C₂×D₇×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
87	C₉	—	13	1	no	Sylow
88	C₇	C₂²×C₁₁×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
89	C₂×C₃	—	7	2	no	—
90	C₂×C₃	C₁₁×D₇×C₁₃⋊C₃	1	1	yes	characteristic
91	C₂²	—	7	1	no	Sylow
92	C₃	C₂×C₁₁×D₇×C₁₃⋊C₃	1	1	yes	characteristic
93	C₂	—	7	2	no	—
94	C₂	C₁₁×D₇×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁	D₇×C₁₃⋊C₃
commutator, hypocenter	C₇×C₁₃	C₂²×C₉×C₁₁
Frattini	C₃	C₂×C₁₁×D₇×C₁₃⋊C₃
Fitting, socle	C₂×C₃×C₇×C₁₁×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₁₁×C₁₃×D₇	C₃
cosocle	C₃×C₇×C₁₃	C₂²×C₃×C₁₁
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₇×C₁₃⋊C₉	C₂	direct (N × H)
2. C₂×C₇×C₁₁×C₁₃⋊C₉	C₂	semidirect
4. C₇×C₁₁×C₁₃⋊C₉	C₂²	semidirect
8. C₂×C₁₁×C₁₃×D₇	C₉	semidirect
9. C₂×D₇×C₁₃⋊C₉	C₁₁	direct (N × H)
13. C₂×C₁₁×C₁₃⋊C₉	D₇	direct (N × H)
14. C₁₁×C₁₃×D₇	C₂×C₉	semidirect
15. C₂×C₇×C₁₁×C₁₃	C₂×C₉	semidirect
17. C₂×C₇×C₁₃⋊C₉	C₂×C₁₁	semidirect
18. D₇×C₁₃⋊C₉	C₂×C₁₁	direct (N × H)
21. C₁₁×C₁₃⋊C₉	C₂×D₇	direct (N × H)
23. C₇×C₁₁×C₁₃	C₂²×C₉	semidirect
27. C₇×C₁₃⋊C₉	C₂²×C₁₁	semidirect
37. C₂×C₁₃×D₇	C₉×C₁₁	semidirect
38. C₂×C₁₁×D₇	C₁₃⋊C₉	direct (N × H)
40. C₂×C₁₁×C₁₃	C₉×D₇	semidirect
44. C₂×C₁₃⋊C₉	C₁₁×D₇	direct (N × H)
48. C₂×C₇×C₁₃	C₂×C₉×C₁₁	semidirect
49. C₁₃×D₇	C₂×C₉×C₁₁	semidirect
51. C₂×C₇×C₁₁	C₂×C₁₃⋊C₉	semidirect
52. C₁₁×D₇	C₂×C₁₃⋊C₉	direct (N × H)
53. C₁₁×C₁₃	C₂×C₉×D₇	semidirect
57. C₁₃⋊C₉	C₂×C₁₁×D₇	direct (N × H)
59. C₇×C₁₃	C₂²×C₉×C₁₁	semidirect
63. C₇×C₁₁	C₂²×C₁₃⋊C₉	semidirect
74. C₂×D₇	C₁₁×C₁₃⋊C₉	direct (N × H)
76. C₂×C₁₃	C₉×C₁₁×D₇	semidirect
78. C₂×C₁₁	D₇×C₁₃⋊C₉	direct (N × H)
82. C₂×C₇	C₂×C₁₁×C₁₃⋊C₉	semidirect
83. D₇	C₂×C₁₁×C₁₃⋊C₉	direct (N × H)
84. C₁₃	C₂×C₉×C₁₁×D₇	semidirect
86. C₁₁	C₂×D₇×C₁₃⋊C₉	direct (N × H)
88. C₇	C₂²×C₁₁×C₁₃⋊C₉	semidirect
94. C₂	C₁₁×D₇×C₁₃⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×D₇×C₁₃⋊C₉	2
C₂×C₇×C₁₁×C₁₃⋊C₉	2
C₂×C₃×C₁₁×C₁₃×D₇	3
C₂²×C₁₁×C₁₃⋊C₉	7
C₂×D₇×C₁₃⋊C₉	11
C₂×C₉×C₁₁×D₇	13

Subgroups — C2×C11×D7×C13⋊C9 #49114451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₇×C₁₃⋊C₉ #49114451