Subgroups — C₂×C₁₃×D₁₁×C₇⋊C₉ #49114444

Order 36036.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₁×C₇⋊C₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₁₃×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₇×C₁₃×D₁₁	C₃	1	1	yes	maximal, characteristic
4	C₁₁×C₁₃×C₇⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₁₃×D₁₁	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic
7	C₂×C₉×C₁₃×D₁₁	—	7	1	no	maximal, Hall
8	C₂×C₇×C₁₃×D₁₁	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₁₃×C₇⋊C₉	—	11	1	no	maximal, Hall
10	C₃×C₇×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic
11	C₂×D₁₁×C₇⋊C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₉×C₁₃×D₁₁	—	7	2	no	—
13	C₂×C₉×C₁₁×C₁₃	—	7	1	no	—
14	C₇×C₁₃×D₁₁	C₂×C₉	1	2	yes	complemented
15	C₂×C₇×C₁₁×C₁₃	C₂×C₉	1	1	yes	characteristic, complemented
16	C₂×C₃×C₁₃×D₁₁	ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₂×C₁₃×C₇⋊C₉	—	11	2	no	—
18	C₂×C₁₃×C₇⋊C₉	D₁₁	1	1	yes	characteristic, direct product factor
19	C₂×C₁₁×C₇⋊C₉	C₂×C₁₃	1	1	yes	characteristic, complemented
20	D₁₁×C₇⋊C₉	C₂×C₁₃	1	2	yes	direct product factor
21	C₉×C₁₁×C₁₃	—	7	1	no	Hall
22	C₂²×C₃×C₇×C₁₃	—	11	1	no	—
23	C₇×C₁₁×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₇×D₁₁	C₃×C₁₃	1	1	yes	characteristic
25	C₂×C₃×C₁₁×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
26	C₃×C₁₃×D₁₁	C₂×ΓL(1,𝔽₈)	1	2	yes	—
27	C₁₃×C₇⋊C₉	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
28	C₁₁×C₇⋊C₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₁₃×D₁₁	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₇×C₁₃	—	11	2	no	—
31	C₂×C₃×C₇×C₁₃	C₃×D₁₁	1	1	yes	characteristic
32	C₂²×C₉×C₁₃	—	77	1	no	Hall
33	C₂×C₃×C₇×C₁₁	C₂×C₃×C₁₃	1	1	yes	characteristic
34	C₃×C₇×D₁₁	C₂×C₃×C₁₃	1	2	yes	—
35	C₃×C₁₁×C₁₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
36	C₂×C₉×D₁₁	—	7	1	no	Hall
37	C₂²×C₇×C₁₃	—	11	1	no	Hall
38	C₂×C₇×D₁₁	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₁₁×C₁₃	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
40	C₁₃×D₁₁	C₂×C₇⋊C₉	1	2	yes	direct product factor
41	C₃×C₇×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic
42	C₂²×C₇⋊C₉	—	11	1	no	Hall
43	C₂×C₉×C₁₃	—	7	1	no	—
44	C₂×C₉×C₁₃	—	77	2	no	—
45	C₃×C₇×C₁₁	C₂²×C₃×C₁₃	1	1	yes	characteristic
46	C₂×C₉×C₁₁	—	7	1	no	—
47	C₉×D₁₁	—	7	2	no	—
48	C₂×C₇×C₁₃	—	11	2	no	—
49	C₂×C₇×C₁₃	C₉×D₁₁	1	1	yes	characteristic, complemented
50	C₂²×C₃×C₁₃	—	11	1	no	—
51	C₂×C₇×C₁₁	C₂×C₉×C₁₃	1	1	yes	characteristic, complemented
52	C₇×D₁₁	C₂×C₉×C₁₃	1	2	yes	complemented
53	C₁₁×C₁₃	C₂²×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×D₁₁	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
55	C₂×C₇⋊C₉	—	11	2	no	—
56	C₂×C₇⋊C₉	C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
57	C₉×C₁₃	—	7	1	no	Hall
58	C₉×C₁₁	—	7	1	no	Hall
59	C₇×C₁₃	C₂×C₉×D₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃×C₇	—	11	1	no	—
61	C₂×C₃×C₁₃	—	11	2	no	—
62	C₂×C₃×C₁₃	ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic
63	C₇×C₁₁	C₂²×C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
64	C₂×C₃×C₁₁	C₂×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
65	C₃×D₁₁	C₂×C₁₃×ΓL(1,𝔽₈)	1	2	yes	—
66	C₇⋊C₉	C₂×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor, Hall
67	C₂²×C₁₃	—	11	1	no	Hall
68	C₂×D₁₁	C₁₃×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
69	C₂×C₃×C₇	—	11	2	no	—
70	C₂×C₃×C₇	C₃×C₁₃×D₁₁	1	1	yes	characteristic
71	C₃×C₁₃	C₂×ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic
72	C₂²×C₉	—	77	1	no	Hall
73	C₃×C₁₁	C₂²×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
74	C₂²×C₇	—	11	1	no	Hall
75	C₂×C₁₃	—	11	2	no	—
76	C₂×C₁₃	D₁₁×C₇⋊C₉	1	1	yes	characteristic, direct product factor
77	C₂×C₁₁	C₂×C₁₃×C₇⋊C₉	1	1	yes	characteristic, complemented
78	D₁₁	C₂×C₁₃×C₇⋊C₉	1	2	yes	direct product factor
79	C₃×C₇	C₂×C₃×C₁₃×D₁₁	1	1	yes	characteristic
80	C₂×C₉	—	7	1	no	—
81	C₂×C₉	—	77	2	no	—
82	C₂×C₇	—	11	2	no	—
83	C₂×C₇	C₉×C₁₃×D₁₁	1	1	yes	characteristic, complemented
84	C₁₃	C₂×D₁₁×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
85	C₂²×C₃	—	11	1	no	—
86	C₁₁	C₂²×C₁₃×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
87	C₉	—	7	1	no	Sylow
88	C₇	C₂×C₉×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
89	C₂×C₃	—	11	2	no	—
90	C₂×C₃	C₁₃×ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic
91	C₂²	—	11	1	no	Sylow
92	C₃	C₂×C₁₃×ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic
93	C₂	—	11	2	no	—
94	C₂	C₁₃×D₁₁×C₇⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	ΓL(1,𝔽₈)×D₁₁
commutator, hypocenter	C₇×C₁₁	C₂²×C₉×C₁₃
Frattini	C₃	C₂×C₁₃×ΓL(1,𝔽₈)×D₁₁
Fitting, socle	C₂×C₃×C₇×C₁₁×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₇×C₁₃×D₁₁	C₃
cosocle	C₃×C₇×C₁₁	C₂²×C₃×C₁₃
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₁₁×C₇⋊C₉	C₂	direct (N × H)
2. C₂×C₁₁×C₁₃×C₇⋊C₉	C₂	semidirect
4. C₁₁×C₁₃×C₇⋊C₉	C₂²	semidirect
8. C₂×C₇×C₁₃×D₁₁	C₉	semidirect
11. C₂×D₁₁×C₇⋊C₉	C₁₃	direct (N × H)
14. C₇×C₁₃×D₁₁	C₂×C₉	semidirect
15. C₂×C₇×C₁₁×C₁₃	C₂×C₉	semidirect
18. C₂×C₁₃×C₇⋊C₉	D₁₁	direct (N × H)
19. C₂×C₁₁×C₇⋊C₉	C₂×C₁₃	semidirect
20. D₁₁×C₇⋊C₉	C₂×C₁₃	direct (N × H)
23. C₇×C₁₁×C₁₃	C₂²×C₉	semidirect
27. C₁₃×C₇⋊C₉	C₂×D₁₁	direct (N × H)
28. C₁₁×C₇⋊C₉	C₂²×C₁₃	semidirect
29. C₂×C₁₃×D₁₁	C₇⋊C₉	direct (N × H)
38. C₂×C₇×D₁₁	C₉×C₁₃	semidirect
39. C₂×C₁₁×C₁₃	C₂×C₇⋊C₉	semidirect
40. C₁₃×D₁₁	C₂×C₇⋊C₉	direct (N × H)
49. C₂×C₇×C₁₃	C₉×D₁₁	semidirect
51. C₂×C₇×C₁₁	C₂×C₉×C₁₃	semidirect
52. C₇×D₁₁	C₂×C₉×C₁₃	semidirect
53. C₁₁×C₁₃	C₂²×C₇⋊C₉	semidirect
56. C₂×C₇⋊C₉	C₁₃×D₁₁	direct (N × H)
59. C₇×C₁₃	C₂×C₉×D₁₁	semidirect
63. C₇×C₁₁	C₂²×C₉×C₁₃	semidirect
66. C₇⋊C₉	C₂×C₁₃×D₁₁	direct (N × H)
68. C₂×D₁₁	C₁₃×C₇⋊C₉	direct (N × H)
76. C₂×C₁₃	D₁₁×C₇⋊C₉	direct (N × H)
77. C₂×C₁₁	C₂×C₁₃×C₇⋊C₉	semidirect
78. D₁₁	C₂×C₁₃×C₇⋊C₉	direct (N × H)
83. C₂×C₇	C₉×C₁₃×D₁₁	semidirect
84. C₁₃	C₂×D₁₁×C₇⋊C₉	direct (N × H)
86. C₁₁	C₂²×C₁₃×C₇⋊C₉	semidirect
88. C₇	C₂×C₉×C₁₃×D₁₁	semidirect
94. C₂	C₁₃×D₁₁×C₇⋊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
C₁₃×D₁₁×C₇⋊C₉	2
C₂×C₁₁×C₁₃×C₇⋊C₉	2
C₂×C₃×C₇×C₁₃×D₁₁	3
C₂×C₉×C₁₃×D₁₁	7
C₂²×C₁₃×C₇⋊C₉	11
C₂×D₁₁×C₇⋊C₉	13

Subgroups — C2×C13×D11×C7⋊C9 #49114444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₁₁×C₇⋊C₉ #49114444