Subgroups — C₂×C₉×C₁₁×C₁₃×D₇ #49114517

Order 36036.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

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

Maximal subgroups

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

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

Subgroups — C2×C9×C11×C13×D7 #49114517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₁×C₁₃×D₇ #49114517