Group #49114460 — subgroups

Subgroups — C₉×D₁₃×D₇₇ #49114460

Order 36036.

120 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₁₀₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×C₁₃×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₉×C₁₁×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₃×D₇₇	C₃	1	1	yes	maximal, characteristic
5	C₇×C₉×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₁₀₀₁	C₂×C₃	1	1	yes	characteristic
7	C₃×C₁₃×D₇₇	C₂×C₃	1	1	yes	characteristic
8	C₃×C₇×C₁₁×D₁₃	C₂×C₃	1	1	yes	characteristic
9	C₉×D₁₁×D₁₃	—	7	1	no	maximal, Hall
10	D₁₃×D₇₇	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₉×D₇×D₁₃	—	11	1	no	maximal, Hall
12	C₃×C₇×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₉×D₇₇	—	13	1	no	maximal, Hall
14	C₉×D₁₄₃	—	7	1	no	—
15	C₉×C₁₃×D₁₁	—	7	1	no	—
16	C₉×C₁₁×D₁₃	D₇	1	1	yes	characteristic, complemented
17	D₁₀₀₁	C₂×C₉	1	1	yes	characteristic, complemented
18	C₁₃×D₇₇	C₂×C₉	1	1	yes	characteristic, complemented
19	C₇×C₁₁×D₁₃	C₂×C₉	1	1	yes	characteristic, complemented
20	C₃×D₁₁×D₁₃	—	7	1	no	—
21	C₉×D₉₁	—	11	1	no	—
22	C₉×C₁₃×D₇	—	11	1	no	—
23	C₇×C₉×D₁₃	D₁₁	1	1	yes	characteristic, complemented
24	C₂×C₇×C₉×C₁₁	—	13	1	no	—
25	C₉×D₇₇	—	13	1	no	—
26	C₉×D₇₇	D₁₃	1	1	yes	characteristic, direct product factor
27	C₉×C₁₁×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	C₃×D₇×D₁₃	—	11	1	no	—
29	C₇×C₁₁×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×D₇₇	—	13	1	no	—
31	C₃×D₁₄₃	—	7	1	no	—
32	C₃×C₁₃×D₁₁	—	7	1	no	—
33	C₃×C₁₁×D₁₃	C₃×D₇	1	1	yes	characteristic
34	C₇×C₉×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
35	C₇×C₉×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
36	D₁₁×D₁₃	—	7	1	no	Hall
37	C₃×D₉₁	—	11	1	no	—
38	C₃×C₁₃×D₇	—	11	1	no	—
39	C₃×C₇×D₁₃	C₃×D₁₁	1	1	yes	characteristic
40	C₂×C₉×D₁₃	—	77	1	no	Hall
41	C₂×C₃×C₇×C₁₁	—	13	1	no	—
42	C₃×D₇₇	—	13	1	no	—
43	C₃×D₇₇	C₃×D₁₃	1	1	yes	characteristic
44	C₃×C₁₁×C₁₃	C₂×C₃×D₇	1	1	yes	characteristic
45	C₂×C₉×D₁₁	—	91	1	no	Hall
46	D₇×D₁₃	—	11	1	no	Hall
47	C₂×D₇₇	—	13	1	no	Hall
48	D₁₄₃	—	7	1	no	—
49	C₁₁×D₁₃	C₉×D₇	1	1	yes	characteristic, complemented
50	C₁₃×D₁₁	—	7	1	no	—
51	C₃×C₇×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic
52	C₂×C₉×D₇	—	143	1	no	Hall
53	C₂×C₉×C₁₃	—	77	1	no	—
54	C₉×D₁₃	—	77	1	no	—
55	C₉×D₁₃	D₇₇	1	1	yes	characteristic, direct product factor
56	C₃×C₇×C₁₁	C₂×C₃×D₁₃	1	1	yes	characteristic
57	C₂×C₉×C₁₁	—	13	1	no	—
58	C₉×D₁₁	—	7	1	no	—
59	C₉×D₁₁	—	91	1	no	—
60	D₉₁	—	11	1	no	—
61	C₇×D₁₃	C₉×D₁₁	1	1	yes	characteristic, complemented
62	C₁₃×D₇	—	11	1	no	—
63	C₂×C₃×D₁₃	—	77	1	no	—
64	C₂×C₇×C₁₁	—	13	1	no	—
65	D₇₇	—	13	1	no	—
66	D₇₇	C₉×D₁₃	1	1	yes	characteristic, direct product factor
67	C₁₁×C₁₃	C₂×C₉×D₇	1	1	yes	characteristic, complemented, Hall
68	C₂×C₃×D₁₁	—	91	1	no	—
69	C₂×C₇×C₉	—	13	1	no	—
70	C₉×D₇	—	11	1	no	—
71	C₉×D₇	—	143	1	no	—
72	C₉×C₁₃	C₂×D₇₇	1	1	yes	characteristic, complemented, Hall
73	C₉×C₁₁	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
74	C₇×C₁₃	C₂×C₉×D₁₁	1	1	yes	characteristic, complemented, Hall
75	C₂×C₃×D₇	—	143	1	no	—
76	C₂×C₃×C₁₃	—	77	1	no	—
77	C₃×D₁₃	—	77	1	no	—
78	C₃×D₁₃	C₃×D₇₇	1	1	yes	characteristic
79	C₇×C₁₁	C₂×C₉×D₁₃	1	1	yes	characteristic, complemented, Hall
80	C₂×C₃×C₁₁	—	13	1	no	—
81	C₃×D₁₁	—	7	1	no	—
82	C₃×D₁₁	—	91	1	no	—
83	C₇×C₉	D₁₁×D₁₃	1	1	yes	characteristic, complemented, Hall
84	C₂×D₁₃	—	77	1	no	Hall
85	C₂×D₁₁	—	91	1	no	Hall
86	C₂×C₃×C₇	—	13	1	no	—
87	C₃×D₇	—	11	1	no	—
88	C₃×D₇	—	143	1	no	—
89	C₃×C₁₃	C₂×C₃×D₇₇	1	1	yes	characteristic
90	C₂²×C₉	—	1001	1	no	Hall
91	C₃×C₁₁	C₃×D₇×D₁₃	1	1	yes	characteristic
92	C₂×D₇	—	143	1	no	Hall
93	C₂×C₁₃	—	77	1	no	—
94	D₁₃	—	77	1	no	—
95	D₁₃	C₉×D₇₇	1	1	yes	characteristic, direct product factor
96	C₂×C₁₁	—	13	1	no	—
97	D₁₁	—	7	1	no	—
98	D₁₁	—	91	1	no	—
99	C₃×C₇	C₃×D₁₁×D₁₃	1	1	yes	characteristic
100	C₂×C₉	—	13	1	no	—
101	C₂×C₉	—	77	1	no	—
102	C₂×C₉	—	1001	1	no	—
103	C₂×C₇	—	13	1	no	—
104	D₇	—	11	1	no	—
105	D₇	—	143	1	no	—
106	C₁₃	C₂×C₉×D₇₇	1	1	yes	characteristic, complemented, Sylow
107	C₂²×C₃	—	1001	1	no	—
108	C₁₁	C₉×D₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
109	C₉	D₁₃×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
110	C₇	C₉×D₁₁×D₁₃	1	1	yes	characteristic, complemented, Sylow
111	C₂×C₃	—	13	1	no	—
112	C₂×C₃	—	77	1	no	—
113	C₂×C₃	—	1001	1	no	—
114	C₂²	—	1001	1	no	Sylow
115	C₃	C₃×D₁₃×D₇₇	1	1	yes	characteristic
116	C₂	—	13	1	no	—
117	C₂	—	77	1	no	—
118	C₂	—	1001	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×D₁₀₀₁

C₂

yes

maximal, characteristic, complemented

C₉×C₁₃×D₇₇

C₂

yes

maximal, characteristic, complemented

C₇×C₉×C₁₁×D₁₃

C₂

yes

maximal, characteristic, complemented

C₃×D₁₃×D₇₇

C₃

yes

maximal, characteristic

C₇×C₉×C₁₁×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₃×D₁₀₀₁

C₂×C₃

yes

characteristic

C₃×C₁₃×D₇₇

C₂×C₃

yes

characteristic

C₃×C₇×C₁₁×D₁₃

C₂×C₃

yes

characteristic

C₉×D₁₁×D₁₃

—

maximal, Hall

D₁₃×D₇₇

C₉

yes

characteristic, direct product factor, Hall

C₉×D₇×D₁₃

—

maximal, Hall

C₃×C₇×C₁₁×C₁₃

C₂²×C₃

yes

characteristic

C₂×C₉×D₇₇

—

maximal, Hall

C₉×D₁₄₃

—

C₉×C₁₃×D₁₁

—

C₉×C₁₁×D₁₃

D₇

yes

characteristic, complemented

D₁₀₀₁

C₂×C₉

yes

characteristic, complemented

C₁₃×D₇₇

C₂×C₉

yes

characteristic, complemented

C₇×C₁₁×D₁₃

C₂×C₉

yes

characteristic, complemented

C₃×D₁₁×D₁₃

—

C₉×D₉₁

—

C₉×C₁₃×D₇

—

C₇×C₉×D₁₃

D₁₁

yes

characteristic, complemented

C₂×C₇×C₉×C₁₁

—

C₉×D₇₇

—

C₉×D₇₇

D₁₃

yes

characteristic, direct product factor

C₉×C₁₁×C₁₃

C₂×D₇

yes

characteristic, complemented, Hall

C₃×D₇×D₁₃

—

C₇×C₁₁×C₁₃

C₂²×C₉

yes

characteristic, complemented, Hall

C₂×C₃×D₇₇

—

C₃×D₁₄₃

—

C₃×C₁₃×D₁₁

—

C₃×C₁₁×D₁₃

C₃×D₇

yes

characteristic

C₇×C₉×C₁₃

C₂×D₁₁

yes

characteristic, complemented, Hall

C₇×C₉×C₁₁

C₂×D₁₃

yes

characteristic, complemented, Hall

D₁₁×D₁₃

—

Hall

C₃×D₉₁

—

C₃×C₁₃×D₇

—

C₃×C₇×D₁₃

C₃×D₁₁

yes

characteristic

C₂×C₉×D₁₃

—

Hall

C₂×C₃×C₇×C₁₁

—

C₃×D₇₇

—

C₃×D₇₇

C₃×D₁₃

yes

characteristic

C₃×C₁₁×C₁₃

C₂×C₃×D₇

yes

characteristic

C₂×C₉×D₁₁

—

Hall

D₇×D₁₃

—

Hall

C₂×D₇₇

—

Hall

D₁₄₃

—

C₁₁×D₁₃

C₉×D₇

yes

characteristic, complemented

C₁₃×D₁₁

—

C₃×C₇×C₁₃

C₂×C₃×D₁₁

yes

characteristic

C₂×C₉×D₇

—

143

Hall

C₂×C₉×C₁₃

—

C₉×D₁₃

—

C₉×D₁₃

D₇₇

yes

characteristic, direct product factor

C₃×C₇×C₁₁

C₂×C₃×D₁₃

yes

characteristic

C₂×C₉×C₁₁

—

C₉×D₁₁

—

C₉×D₁₁

—

D₉₁

—

C₇×D₁₃

C₉×D₁₁

yes

characteristic, complemented

C₁₃×D₇

—

C₂×C₃×D₁₃

—

C₂×C₇×C₁₁

—

D₇₇

—

D₇₇

C₉×D₁₃

yes

characteristic, direct product factor

C₁₁×C₁₃

C₂×C₉×D₇

yes

characteristic, complemented, Hall

C₂×C₃×D₁₁

—

C₂×C₇×C₉

—

C₉×D₇

—

C₉×D₇

—

143

—

C₉×C₁₃

C₂×D₇₇

yes

characteristic, complemented, Hall

C₉×C₁₁

D₇×D₁₃

yes

characteristic, complemented, Hall

C₇×C₁₃

C₂×C₉×D₁₁

yes

characteristic, complemented, Hall

C₂×C₃×D₇

—

143

—

C₂×C₃×C₁₃

—

C₃×D₁₃

—

C₃×D₁₃

C₃×D₇₇

yes

characteristic

C₇×C₁₁

C₂×C₉×D₁₃

yes

characteristic, complemented, Hall

C₂×C₃×C₁₁

—

C₃×D₁₁

—

C₃×D₁₁

—

C₇×C₉

D₁₁×D₁₃

yes

characteristic, complemented, Hall

C₂×D₁₃

—

Hall

C₂×D₁₁

—

Hall

C₂×C₃×C₇

—

C₃×D₇

—

C₃×D₇

—

143

—

C₃×C₁₃

C₂×C₃×D₇₇

yes

characteristic

C₂²×C₉

—

1001

Hall

C₃×C₁₁

C₃×D₇×D₁₃

yes

characteristic

C₂×D₇

—

143

Hall

C₂×C₁₃

—

D₁₃

—

D₁₃

C₉×D₇₇

yes

characteristic, direct product factor

C₂×C₁₁

—

D₁₁

—

D₁₁

—

C₃×C₇

C₃×D₁₁×D₁₃

yes

characteristic

100

C₂×C₉

—

101

C₂×C₉

—

102

C₂×C₉

—

1001

—

103

C₂×C₇

—

104

D₇

—

105

D₇

—

143

—

106

C₁₃

C₂×C₉×D₇₇

yes

characteristic, complemented, Sylow

107

C₂²×C₃

—

1001

—

108

C₁₁

C₉×D₇×D₁₃

yes

characteristic, complemented, Sylow

109

C₉

D₁₃×D₇₇

yes

characteristic, direct product factor, Sylow

110

C₇

C₉×D₁₁×D₁₃

yes

characteristic, complemented, Sylow

111

C₂×C₃

—

112

C₂×C₃

—

113

C₂×C₃

—

1001

—

114

C₂²

—

1001

Sylow

115

C₃

C₃×D₁₃×D₇₇

yes

characteristic

116

C₂

—

117

C₂

—

118

C₂

—

1001

—

	subgroup	G/H
center, hypercenter	C₉	D₁₃×D₇₇
commutator, hypocenter	C₇×C₁₁×C₁₃	C₂²×C₉
Frattini	C₃	C₃×D₁₃×D₇₇
Fitting	C₇×C₉×C₁₁×C₁₃	C₂²
socle, cosocle	C₃×C₇×C₁₁×C₁₃	C₂²×C₃
prime radical	C₃×D₁₃×D₇₇	C₃
LCS	G ▷ C₇×C₁₁×C₁₃
UCS	C₁ ◁ C₉

subgroup

G/H

center, hypercenter

C₉

D₁₃×D₇₇

commutator, hypocenter

C₇×C₁₁×C₁₃

C₂²×C₉

Frattini

C₃

C₃×D₁₃×D₇₇

Fitting

C₇×C₉×C₁₁×C₁₃

C₂²

socle, cosocle

C₃×C₇×C₁₁×C₁₃

C₂²×C₃

prime radical

C₃×D₁₃×D₇₇

C₃

LCS

G ▷ C₇×C₁₁×C₁₃

UCS

C₁ ◁ C₉

N	H ≅ G/N	type
1. C₉×D₁₀₀₁	C₂	semidirect
2. C₉×C₁₃×D₇₇	C₂	semidirect
3. C₇×C₉×C₁₁×D₁₃	C₂	semidirect
5. C₇×C₉×C₁₁×C₁₃	C₂²	semidirect
10. D₁₃×D₇₇	C₉	direct (N × H)
16. C₉×C₁₁×D₁₃	D₇	semidirect
17. D₁₀₀₁	C₂×C₉	semidirect
18. C₁₃×D₇₇	C₂×C₉	semidirect
19. C₇×C₁₁×D₁₃	C₂×C₉	semidirect
23. C₇×C₉×D₁₃	D₁₁	semidirect
26. C₉×D₇₇	D₁₃	direct (N × H)
27. C₉×C₁₁×C₁₃	C₂×D₇	semidirect
29. C₇×C₁₁×C₁₃	C₂²×C₉	semidirect
34. C₇×C₉×C₁₃	C₂×D₁₁	semidirect
35. C₇×C₉×C₁₁	C₂×D₁₃	semidirect
49. C₁₁×D₁₃	C₉×D₇	semidirect
55. C₉×D₁₃	D₇₇	direct (N × H)
61. C₇×D₁₃	C₉×D₁₁	semidirect
66. D₇₇	C₉×D₁₃	direct (N × H)
67. C₁₁×C₁₃	C₂×C₉×D₇	semidirect
72. C₉×C₁₃	C₂×D₇₇	semidirect
73. C₉×C₁₁	D₇×D₁₃	semidirect
74. C₇×C₁₃	C₂×C₉×D₁₁	semidirect
79. C₇×C₁₁	C₂×C₉×D₁₃	semidirect
83. C₇×C₉	D₁₁×D₁₃	semidirect
95. D₁₃	C₉×D₇₇	direct (N × H)
106. C₁₃	C₂×C₉×D₇₇	semidirect
108. C₁₁	C₉×D₇×D₁₃	semidirect
109. C₉	D₁₃×D₇₇	direct (N × H)
110. C₇	C₉×D₁₁×D₁₃	semidirect

H ≅ G/N

type

1. C₉×D₁₀₀₁

C₂

semidirect

2. C₉×C₁₃×D₇₇

C₂

semidirect

3. C₇×C₉×C₁₁×D₁₃

C₂

semidirect

5. C₇×C₉×C₁₁×C₁₃

C₂²

semidirect

10. D₁₃×D₇₇

C₉

direct (N × H)

16. C₉×C₁₁×D₁₃

D₇

semidirect

17. D₁₀₀₁

C₂×C₉

semidirect

18. C₁₃×D₇₇

C₂×C₉

semidirect

19. C₇×C₁₁×D₁₃

C₂×C₉

semidirect

23. C₇×C₉×D₁₃

D₁₁

semidirect

26. C₉×D₇₇

D₁₃

direct (N × H)

27. C₉×C₁₁×C₁₃

C₂×D₇

semidirect

29. C₇×C₁₁×C₁₃

C₂²×C₉

semidirect

34. C₇×C₉×C₁₃

C₂×D₁₁

semidirect

35. C₇×C₉×C₁₁

C₂×D₁₃

semidirect

49. C₁₁×D₁₃

C₉×D₇

semidirect

55. C₉×D₁₃

D₇₇

direct (N × H)

61. C₇×D₁₃

C₉×D₁₁

semidirect

66. D₇₇

C₉×D₁₃

direct (N × H)

67. C₁₁×C₁₃

C₂×C₉×D₇

semidirect

72. C₉×C₁₃

C₂×D₇₇

semidirect

73. C₉×C₁₁

D₇×D₁₃

semidirect

74. C₇×C₁₃

C₂×C₉×D₁₁

semidirect

79. C₇×C₁₁

C₂×C₉×D₁₃

semidirect

83. C₇×C₉

D₁₁×D₁₃

semidirect

95. D₁₃

C₉×D₇₇

direct (N × H)

106. C₁₃

C₂×C₉×D₇₇

semidirect

108. C₁₁

C₉×D₇×D₁₃

semidirect

109. C₉

D₁₃×D₇₇

direct (N × H)

110. C₇

C₉×D₁₁×D₁₃

semidirect

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

subgroup	index
C₉×D₁₀₀₁	2
C₉×C₁₃×D₇₇	2
C₇×C₉×C₁₁×D₁₃	2
C₃×D₁₃×D₇₇	3
C₉×D₁₁×D₁₃	7
C₉×D₇×D₁₃	11
C₂×C₉×D₇₇	13

subgroup

index

C₉×D₁₀₀₁

C₉×C₁₃×D₇₇

C₇×C₉×C₁₁×D₁₃

C₃×D₁₃×D₇₇

C₉×D₁₁×D₁₃

C₉×D₇×D₁₃

C₂×C₉×D₇₇

Subgroups — C₉×D₁₃×D₇₇ #49114460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×D13×D77 #49114460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₁₃×D₇₇ #49114460