Group #49114494 — subgroups

Subgroups — D₇₇⋊D₁₁₇ #49114494

Order 36036.

120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 35 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	C₁₁×D₈₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₁₂₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₃×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇₇⋊D₃₉	—	3	1	no	maximal
5	C₇×C₉×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁×D₂₇₃	—	3	1	no	—
7	C₇×D₄₂₉	—	3	1	no	—
8	C₃×C₁₃×D₇₇	D₃	1	1	yes	characteristic
9	D₁₁×D₁₁₇	—	7	1	no	maximal, Hall
10	D₇₇⋊D₁₃	—	9	1	no	Hall
11	D₇×D₁₁₇	—	11	1	no	maximal, Hall
12	C₃×C₇×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic
13	D₆₃⋊D₁₁	—	13	1	no	maximal, Hall
14	D₁₂₈₇	D₇	1	1	yes	characteristic, complemented
15	C₁₁×D₁₁₇	—	7	1	no	—
16	C₉×C₁₃×D₁₁	—	7	1	no	—
17	C₁₃×D₇₇	D₉	1	1	yes	characteristic, complemented
18	C₁₁×D₉₁	—	9	1	no	—
19	C₇×D₁₄₃	—	9	1	no	—
20	D₁₁×D₃₉	—	21	1	no	—
21	D₈₁₉	D₁₁	1	1	yes	characteristic, complemented
22	C₇×D₁₁₇	—	11	1	no	—
23	C₉×C₁₃×D₇	—	11	1	no	—
24	C₁₁×D₆₃	—	13	1	no	—
25	C₇×D₉₉	—	13	1	no	—
26	C₉×D₇₇	D₁₃	1	1	yes	characteristic, complemented
27	C₉×C₁₁×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	D₇×D₃₉	—	33	1	no	—
29	C₇×C₁₁×C₁₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
30	D₂₁⋊D₁₁	—	39	1	no	—
31	D₄₂₉	—	3	1	no	—
32	C₁₁×D₃₉	—	21	1	no	—
33	C₃×C₁₃×D₁₁	—	7	1	no	—
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	—	63	1	no	Hall
37	D₂₇₃	—	3	1	no	—
38	C₇×D₃₉	—	33	1	no	—
39	C₃×C₁₃×D₇	—	11	1	no	—
40	C₂×D₁₁₇	—	77	1	no	Hall
41	C₁₁×D₂₁	—	39	1	no	—
42	C₇×D₃₃	—	39	1	no	—
43	C₃×D₇₇	D₃₉	1	1	yes	characteristic
44	C₃×C₁₁×C₁₃	D₃×D₇	1	1	yes	characteristic
45	D₉×D₁₁	—	91	1	no	Hall
46	D₇×D₁₃	—	99	1	no	Hall
47	D₇×D₁₁	—	117	1	no	Hall
48	D₁₄₃	—	9	1	no	—
49	C₁₁×D₁₃	—	63	1	no	—
50	C₁₃×D₁₁	—	7	1	no	—
51	C₃×C₇×C₁₃	D₃×D₁₁	1	1	yes	characteristic
52	D₇×D₉	—	143	1	no	Hall
53	C₂×C₉×C₁₃	—	77	1	no	—
54	D₁₁₇	—	7	1	no	—
55	D₁₁₇	—	11	1	no	—
56	C₃×C₇×C₁₁	C₂×D₃₉	1	1	yes	characteristic
57	D₉₉	—	13	1	no	—
58	C₉×D₁₁	—	7	1	no	—
59	C₁₁×D₉	—	91	1	no	—
60	D₉₁	—	9	1	no	—
61	C₇×D₁₃	—	99	1	no	—
62	C₁₃×D₇	—	11	1	no	—
63	C₂×D₃₉	—	231	1	no	—
64	D₇₇	D₁₁₇	1	1	yes	characteristic, complemented
65	C₇×D₁₁	—	117	1	no	—
66	C₁₁×D₇	—	117	1	no	—
67	C₁₁×C₁₃	D₇×D₉	1	1	yes	characteristic, complemented, Hall
68	D₃×D₁₁	—	273	1	no	—
69	D₆₃	—	13	1	no	—
70	C₉×D₇	—	11	1	no	—
71	C₇×D₉	—	143	1	no	—
72	C₉×C₁₃	D₇×D₁₁	1	1	yes	characteristic, complemented, Hall
73	C₉×C₁₁	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
74	C₇×C₁₃	D₉×D₁₁	1	1	yes	characteristic, complemented, Hall
75	D₃×D₇	—	429	1	no	—
76	C₂×C₃×C₁₃	—	77	1	no	—
77	D₃₉	—	21	1	no	—
78	D₃₉	—	33	1	no	—
79	C₇×C₁₁	C₂×D₁₁₇	1	1	yes	characteristic, complemented, Hall
80	D₃₃	—	39	1	no	—
81	C₃×D₁₁	—	7	1	no	—
82	D₃×C₁₁	—	273	1	no	—
83	C₇×C₉	D₁₁×D₁₃	1	1	yes	characteristic, complemented, Hall
84	C₂×D₁₃	—	693	1	no	Hall
85	C₂×D₁₁	—	819	1	no	Hall
86	D₂₁	—	39	1	no	—
87	C₃×D₇	—	11	1	no	—
88	D₃×C₇	—	429	1	no	—
89	C₃×C₁₃	D₂₁⋊D₁₁	1	1	yes	characteristic
90	C₂×D₉	—	1001	1	no	Hall
91	C₃×C₁₁	D₇×D₃₉	1	1	yes	characteristic
92	C₂×D₇	—	1287	1	no	Hall
93	C₂×C₁₃	—	77	1	no	—
94	D₁₃	—	63	1	no	—
95	D₁₃	—	99	1	no	—
96	C₂×C₁₁	—	819	1	no	—
97	D₁₁	—	7	1	no	—
98	D₁₁	—	117	1	no	—
99	C₃×C₇	D₁₁×D₃₉	1	1	yes	characteristic
100	C₂×C₉	—	77	1	no	—
101	D₉	—	91	1	no	—
102	D₉	—	143	1	no	—
103	C₂×C₇	—	1287	1	no	—
104	D₇	—	11	1	no	—
105	D₇	—	117	1	no	—
106	C₁₃	D₆₃⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
107	C₂×D₃	—	3003	1	no	—
108	C₁₁	D₇×D₁₁₇	1	1	yes	characteristic, complemented, Sylow
109	C₉	D₇₇⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
110	C₇	D₁₁×D₁₁₇	1	1	yes	characteristic, complemented, Sylow
111	C₂×C₃	—	77	1	no	—
112	D₃	—	273	1	no	—
113	D₃	—	429	1	no	—
114	C₂²	—	9009	1	no	Sylow
115	C₃	D₇₇⋊D₃₉	1	1	yes	characteristic
116	C₂	—	1287	1	no	—
117	C₂	—	819	1	no	—
118	C₂	—	77	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×D₈₁₉

C₂

yes

maximal, characteristic, complemented

C₇×D₁₂₈₇

C₂

yes

maximal, characteristic, complemented

C₉×C₁₃×D₇₇

C₂

yes

maximal, characteristic, complemented

D₇₇⋊D₃₉

—

maximal

C₇×C₉×C₁₁×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₁₁×D₂₇₃

—

C₇×D₄₂₉

—

C₃×C₁₃×D₇₇

D₃

yes

characteristic

D₁₁×D₁₁₇

—

maximal, Hall

D₇₇⋊D₁₃

—

Hall

D₇×D₁₁₇

—

maximal, Hall

C₃×C₇×C₁₁×C₁₃

C₂×D₃

yes

characteristic

D₆₃⋊D₁₁

—

maximal, Hall

D₁₂₈₇

D₇

yes

characteristic, complemented

C₁₁×D₁₁₇

—

C₉×C₁₃×D₁₁

—

C₁₃×D₇₇

D₉

yes

characteristic, complemented

C₁₁×D₉₁

—

C₇×D₁₄₃

—

D₁₁×D₃₉

—

D₈₁₉

D₁₁

yes

characteristic, complemented

C₇×D₁₁₇

—

C₉×C₁₃×D₇

—

C₁₁×D₆₃

—

C₇×D₉₉

—

C₉×D₇₇

D₁₃

yes

characteristic, complemented

C₉×C₁₁×C₁₃

C₂×D₇

yes

characteristic, complemented, Hall

D₇×D₃₉

—

C₇×C₁₁×C₁₃

C₂×D₉

yes

characteristic, complemented, Hall

D₂₁⋊D₁₁

—

D₄₂₉

—

C₁₁×D₃₉

—

C₃×C₁₃×D₁₁

—

C₇×C₉×C₁₃

C₂×D₁₁

yes

characteristic, complemented, Hall

C₇×C₉×C₁₁

C₂×D₁₃

yes

characteristic, complemented, Hall

D₁₁×D₁₃

—

Hall

D₂₇₃

—

C₇×D₃₉

—

C₃×C₁₃×D₇

—

C₂×D₁₁₇

—

Hall

C₁₁×D₂₁

—

C₇×D₃₃

—

C₃×D₇₇

D₃₉

yes

characteristic

C₃×C₁₁×C₁₃

D₃×D₇

yes

characteristic

D₉×D₁₁

—

Hall

D₇×D₁₃

—

Hall

D₇×D₁₁

—

117

Hall

D₁₄₃

—

C₁₁×D₁₃

—

C₁₃×D₁₁

—

C₃×C₇×C₁₃

D₃×D₁₁

yes

characteristic

D₇×D₉

—

143

Hall

C₂×C₉×C₁₃

—

D₁₁₇

—

D₁₁₇

—

C₃×C₇×C₁₁

C₂×D₃₉

yes

characteristic

D₉₉

—

C₉×D₁₁

—

C₁₁×D₉

—

D₉₁

—

C₇×D₁₃

—

C₁₃×D₇

—

C₂×D₃₉

—

231

—

D₇₇

D₁₁₇

yes

characteristic, complemented

C₇×D₁₁

—

117

—

C₁₁×D₇

—

117

—

C₁₁×C₁₃

D₇×D₉

yes

characteristic, complemented, Hall

D₃×D₁₁

—

273

—

D₆₃

—

C₉×D₇

—

C₇×D₉

—

143

—

C₉×C₁₃

D₇×D₁₁

yes

characteristic, complemented, Hall

C₉×C₁₁

D₇×D₁₃

yes

characteristic, complemented, Hall

C₇×C₁₃

D₉×D₁₁

yes

characteristic, complemented, Hall

D₃×D₇

—

429

—

C₂×C₃×C₁₃

—

D₃₉

—

D₃₉

—

C₇×C₁₁

C₂×D₁₁₇

yes

characteristic, complemented, Hall

D₃₃

—

C₃×D₁₁

—

D₃×C₁₁

—

273

—

C₇×C₉

D₁₁×D₁₃

yes

characteristic, complemented, Hall

C₂×D₁₃

—

693

Hall

C₂×D₁₁

—

819

Hall

D₂₁

—

C₃×D₇

—

D₃×C₇

—

429

—

C₃×C₁₃

D₂₁⋊D₁₁

yes

characteristic

C₂×D₉

—

1001

Hall

C₃×C₁₁

D₇×D₃₉

yes

characteristic

C₂×D₇

—

1287

Hall

C₂×C₁₃

—

D₁₃

—

D₁₃

—

C₂×C₁₁

—

819

—

D₁₁

—

D₁₁

—

117

—

C₃×C₇

D₁₁×D₃₉

yes

characteristic

100

C₂×C₉

—

101

D₉

—

102

D₉

—

143

—

103

C₂×C₇

—

1287

—

104

D₇

—

105

D₇

—

117

—

106

C₁₃

D₆₃⋊D₁₁

yes

characteristic, complemented, Sylow

107

C₂×D₃

—

3003

—

108

C₁₁

D₇×D₁₁₇

yes

characteristic, complemented, Sylow

109

C₉

D₇₇⋊D₁₃

yes

characteristic, complemented, Sylow

110

C₇

D₁₁×D₁₁₇

yes

characteristic, complemented, Sylow

111

C₂×C₃

—

112

D₃

—

273

—

113

D₃

—

429

—

114

C₂²

—

9009

Sylow

115

C₃

D₇₇⋊D₃₉

yes

characteristic

116

C₂

—

1287

—

117

C₂

—

819

—

118

C₂

—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₉×C₁₁×C₁₃	C₂²
Frattini	C₃	D₇₇⋊D₃₉
socle	C₃×C₇×C₁₁×C₁₃	C₂×D₃
LCS	G ▷ C₇×C₉×C₁₁×C₁₃
UCS	C₁

subgroup

G/H

center, hypercenter

C₁

commutator, Fitting, cosocle, hypocenter

C₇×C₉×C₁₁×C₁₃

C₂²

Frattini

C₃

D₇₇⋊D₃₉

socle

C₃×C₇×C₁₁×C₁₃

C₂×D₃

LCS

G ▷ C₇×C₉×C₁₁×C₁₃

UCS

C₁

N	H ≅ G/N	type
1. C₁₁×D₈₁₉	C₂	semidirect
2. C₇×D₁₂₈₇	C₂	semidirect
3. C₉×C₁₃×D₇₇	C₂	semidirect
5. C₇×C₉×C₁₁×C₁₃	C₂²	semidirect
14. D₁₂₈₇	D₇	semidirect
17. C₁₃×D₇₇	D₉	semidirect
21. D₈₁₉	D₁₁	semidirect
26. C₉×D₇₇	D₁₃	semidirect
27. C₉×C₁₁×C₁₃	C₂×D₇	semidirect
29. C₇×C₁₁×C₁₃	C₂×D₉	semidirect
34. C₇×C₉×C₁₃	C₂×D₁₁	semidirect
35. C₇×C₉×C₁₁	C₂×D₁₃	semidirect
64. D₇₇	D₁₁₇	semidirect
67. C₁₁×C₁₃	D₇×D₉	semidirect
72. C₉×C₁₃	D₇×D₁₁	semidirect
73. C₉×C₁₁	D₇×D₁₃	semidirect
74. C₇×C₁₃	D₉×D₁₁	semidirect
79. C₇×C₁₁	C₂×D₁₁₇	semidirect
83. C₇×C₉	D₁₁×D₁₃	semidirect
106. C₁₃	D₆₃⋊D₁₁	semidirect
108. C₁₁	D₇×D₁₁₇	semidirect
109. C₉	D₇₇⋊D₁₃	semidirect
110. C₇	D₁₁×D₁₁₇	semidirect

H ≅ G/N

type

1. C₁₁×D₈₁₉

C₂

semidirect

2. C₇×D₁₂₈₇

C₂

semidirect

3. C₉×C₁₃×D₇₇

C₂

semidirect

5. C₇×C₉×C₁₁×C₁₃

C₂²

semidirect

14. D₁₂₈₇

D₇

semidirect

17. C₁₃×D₇₇

D₉

semidirect

21. D₈₁₉

D₁₁

semidirect

26. C₉×D₇₇

D₁₃

semidirect

27. C₉×C₁₁×C₁₃

C₂×D₇

semidirect

29. C₇×C₁₁×C₁₃

C₂×D₉

semidirect

34. C₇×C₉×C₁₃

C₂×D₁₁

semidirect

35. C₇×C₉×C₁₁

C₂×D₁₃

semidirect

64. D₇₇

D₁₁₇

semidirect

67. C₁₁×C₁₃

D₇×D₉

semidirect

72. C₉×C₁₃

D₇×D₁₁

semidirect

73. C₉×C₁₁

D₇×D₁₃

semidirect

74. C₇×C₁₃

D₉×D₁₁

semidirect

79. C₇×C₁₁

C₂×D₁₁₇

semidirect

83. C₇×C₉

D₁₁×D₁₃

semidirect

106. C₁₃

D₆₃⋊D₁₁

semidirect

108. C₁₁

D₇×D₁₁₇

semidirect

109. C₉

D₇₇⋊D₁₃

semidirect

110. C₇

D₁₁×D₁₁₇

semidirect

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

subgroup	index
C₁₁×D₈₁₉	2
C₇×D₁₂₈₇	2
C₉×C₁₃×D₇₇	2
D₇₇⋊D₃₉	3
D₁₁×D₁₁₇	7
D₇×D₁₁₇	11
D₆₃⋊D₁₁	13

subgroup

index

C₁₁×D₈₁₉

C₇×D₁₂₈₇

C₉×C₁₃×D₇₇

D₇₇⋊D₃₉

D₁₁×D₁₁₇

D₇×D₁₁₇

D₆₃⋊D₁₁

Subgroups — D₇₇⋊D₁₁₇ #49114494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D77⋊D117 #49114494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₇⋊D₁₁₇ #49114494