Subgroups — C₂×C₁₃⋊C₉×D₇₇ #49114453

Order 36036.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₉×D₇₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₁×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₃×D₇₇	C₃	1	1	yes	maximal, characteristic
4	C₇×C₁₁×C₁₃⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×D₇₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic
7	C₂×D₁₁×C₁₃⋊C₉	—	7	1	no	maximal, Hall
8	C₂×C₁₃×D₇₇	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×D₇×C₁₃⋊C₉	—	11	1	no	maximal, Hall
10	C₃×C₇×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic
11	C₂×C₉×D₇₇	—	13	1	no	maximal, Hall
12	C₂×C₁₁×C₁₃⋊C₉	D₇	1	1	yes	characteristic, complemented
13	D₁₁×C₁₃⋊C₉	—	7	2	no	—
14	C₁₃×D₇₇	C₂×C₉	1	2	yes	complemented
15	C₂×C₇×C₁₁×C₁₃	C₂×C₉	1	1	yes	characteristic, complemented
16	C₂×C₃×C₁₃×D₁₁	—	7	1	no	—
17	C₂×C₇×C₁₃⋊C₉	D₁₁	1	1	yes	characteristic, complemented
18	D₇×C₁₃⋊C₉	—	11	2	no	—
19	C₂×C₇×C₉×C₁₁	—	13	1	no	—
20	C₉×D₇₇	—	13	2	no	—
21	C₁₁×C₁₃⋊C₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₁₃×D₇	—	11	1	no	—
23	C₇×C₁₁×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×D₇₇	C₁₃⋊C₃	1	1	yes	characteristic
25	C₂×C₃×C₁₁×C₁₃	C₃×D₇	1	1	yes	characteristic
26	C₃×C₁₃×D₁₁	—	7	2	no	—
27	C₇×C₁₃⋊C₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₇×C₉×C₁₁	—	13	1	no	Hall
29	C₂×C₁₃×D₁₁	—	7	1	no	Hall
30	C₂×C₃×C₇×C₁₃	C₃×D₁₁	1	1	yes	characteristic
31	C₃×C₁₃×D₇	—	11	2	no	—
32	C₂²×C₁₃⋊C₉	—	77	1	no	Hall
33	C₂×C₃×C₇×C₁₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
34	C₃×D₇₇	C₂×C₁₃⋊C₃	1	2	yes	—
35	C₃×C₁₁×C₁₃	C₂×C₃×D₇	1	1	yes	characteristic
36	C₂×C₉×D₁₁	—	91	1	no	Hall
37	C₂×C₁₃×D₇	—	11	1	no	Hall
38	C₂×D₇₇	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₁₁×C₁₃	C₉×D₇	1	1	yes	characteristic, complemented
40	C₁₃×D₁₁	—	7	2	no	—
41	C₃×C₇×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic
42	C₂×C₉×D₇	—	143	1	no	Hall
43	C₂×C₁₃⋊C₉	—	77	2	no	—
44	C₂×C₁₃⋊C₉	D₇₇	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	C₉×D₁₁	—	91	2	no	—
48	C₂×C₇×C₁₃	C₉×D₁₁	1	1	yes	characteristic, complemented
49	C₁₃×D₇	—	11	2	no	—
50	C₂²×C₃×C₁₃	—	77	1	no	—
51	C₂×C₇×C₁₁	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented
52	D₇₇	C₂×C₁₃⋊C₉	1	2	yes	direct product factor
53	C₁₁×C₁₃	C₂×C₉×D₇	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×D₁₁	—	7	1	no	—
55	C₂×C₇×C₉	—	13	1	no	—
56	C₉×D₇	—	143	2	no	—
57	C₁₃⋊C₉	C₂×D₇₇	1	1	yes	characteristic, direct product factor, Hall
58	C₉×C₁₁	—	13	1	no	Hall
59	C₇×C₁₃	C₂×C₉×D₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂×C₃×D₇	—	11	1	no	—
61	C₂×C₃×C₁₃	—	77	2	no	—
62	C₂×C₃×C₁₃	C₃×D₇₇	1	1	yes	characteristic
63	C₇×C₁₁	C₂²×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
64	C₂×C₃×C₁₁	D₇×C₁₃⋊C₃	1	1	yes	characteristic
65	C₃×D₁₁	—	7	2	no	—
66	C₇×C₉	—	13	1	no	Hall
67	C₂²×C₁₃	—	77	1	no	Hall
68	C₂×D₁₁	—	7	1	no	Hall
69	C₂×C₃×C₇	D₁₁×C₁₃⋊C₃	1	1	yes	characteristic
70	C₃×D₇	—	11	2	no	—
71	C₃×C₁₃	C₂×C₃×D₇₇	1	1	yes	characteristic
72	C₂²×C₉	—	1001	1	no	Hall
73	C₃×C₁₁	C₂×D₇×C₁₃⋊C₃	1	1	yes	characteristic
74	C₂×D₇	—	11	1	no	Hall
75	C₂×C₁₃	—	77	2	no	—
76	C₂×C₁₃	C₉×D₇₇	1	1	yes	characteristic, complemented
77	C₂×C₁₁	D₇×C₁₃⋊C₉	1	1	yes	characteristic, complemented
78	D₁₁	—	7	2	no	—
79	C₃×C₇	C₂×D₁₁×C₁₃⋊C₃	1	1	yes	characteristic
80	C₂×C₉	—	13	1	no	—
81	C₂×C₉	—	1001	2	no	—
82	C₂×C₇	D₁₁×C₁₃⋊C₉	1	1	yes	characteristic, complemented
83	D₇	—	11	2	no	—
84	C₁₃	C₂×C₉×D₇₇	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₃	—	77	1	no	—
86	C₁₁	C₂×D₇×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
87	C₉	—	13	1	no	Sylow
88	C₇	C₂×D₁₁×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
89	C₂×C₃	—	77	2	no	—
90	C₂×C₃	C₁₃⋊C₃×D₇₇	1	1	yes	characteristic
91	C₂²	—	77	1	no	Sylow
92	C₃	C₂×C₁₃⋊C₃×D₇₇	1	1	yes	characteristic
93	C₂	—	77	2	no	—
94	C₂	C₁₃⋊C₉×D₇₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₃⋊C₃×D₇₇
commutator, hypocenter	C₇×C₁₁×C₁₃	C₂²×C₉
Frattini	C₃	C₂×C₁₃⋊C₃×D₇₇
Fitting, socle	C₂×C₃×C₇×C₁₁×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₁₃×D₇₇	C₃
cosocle	C₃×C₇×C₁₁×C₁₃	C₂²×C₃
LCS	G ▷ C₇×C₁₁×C₁₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊C₉×D₇₇	C₂	direct (N × H)
2. C₂×C₇×C₁₁×C₁₃⋊C₉	C₂	semidirect
4. C₇×C₁₁×C₁₃⋊C₉	C₂²	semidirect
8. C₂×C₁₃×D₇₇	C₉	semidirect
12. C₂×C₁₁×C₁₃⋊C₉	D₇	semidirect
14. C₁₃×D₇₇	C₂×C₉	semidirect
15. C₂×C₇×C₁₁×C₁₃	C₂×C₉	semidirect
17. C₂×C₇×C₁₃⋊C₉	D₁₁	semidirect
21. C₁₁×C₁₃⋊C₉	C₂×D₇	semidirect
23. C₇×C₁₁×C₁₃	C₂²×C₉	semidirect
27. C₇×C₁₃⋊C₉	C₂×D₁₁	semidirect
38. C₂×D₇₇	C₁₃⋊C₉	direct (N × H)
39. C₂×C₁₁×C₁₃	C₉×D₇	semidirect
44. C₂×C₁₃⋊C₉	D₇₇	direct (N × H)
48. C₂×C₇×C₁₃	C₉×D₁₁	semidirect
51. C₂×C₇×C₁₁	C₂×C₁₃⋊C₉	semidirect
52. D₇₇	C₂×C₁₃⋊C₉	direct (N × H)
53. C₁₁×C₁₃	C₂×C₉×D₇	semidirect
57. C₁₃⋊C₉	C₂×D₇₇	direct (N × H)
59. C₇×C₁₃	C₂×C₉×D₁₁	semidirect
63. C₇×C₁₁	C₂²×C₁₃⋊C₉	semidirect
76. C₂×C₁₃	C₉×D₇₇	semidirect
77. C₂×C₁₁	D₇×C₁₃⋊C₉	semidirect
82. C₂×C₇	D₁₁×C₁₃⋊C₉	semidirect
84. C₁₃	C₂×C₉×D₇₇	semidirect
86. C₁₁	C₂×D₇×C₁₃⋊C₉	semidirect
88. C₇	C₂×D₁₁×C₁₃⋊C₉	semidirect
94. C₂	C₁₃⋊C₉×D₇₇	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⋊C₉×D₇₇	2
C₂×C₇×C₁₁×C₁₃⋊C₉	2
C₂×C₃×C₁₃×D₇₇	3
C₂×D₁₁×C₁₃⋊C₉	7
C₂×D₇×C₁₃⋊C₉	11
C₂×C₉×D₇₇	13

Subgroups — C2×C13⋊C9×D77 #49114453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃⋊C₉×D₇₇ #49114453