Group #37524587 — subgroups

Subgroups — D₉₁⋊D₆₃ #37524587

Order 22932.

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

normal subgroups only

This group has 156 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	C₁₃×C₇⋊D₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₈₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₉×D₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₉₁⋊D₂₁	—	3	1	no	maximal
5	C₇²×C₉×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×C₃⋊(C₇⋊D₇)	—	3	1	no	—
7	C₇×D₂₇₃	—	3	1	no	—
8	C₃×C₇×D₉₁	D₃	1	1	yes	characteristic
9	D₆₃⋊D₁₃	—	7	1	no	maximal
10	D₁₃×D₆₃	—	7	1	no	maximal
11	(C₇⋊D₇)⋊D₁₃	—	9	1	no	Hall
12	C₃×C₇²×C₁₃	C₂×D₃	1	1	yes	characteristic
13	D₇×D₆₃	—	13	1	no	maximal, Hall
14	D₈₁₉	D₇	1	1	yes	characteristic, complemented
15	C₁₃×D₆₃	—	7	1	no	—
16	C₁₃×D₆₃	—	7	1	no	—
17	C₁₃×D₆₃	—	14	3	no	—
18	C₇×D₁₁₇	—	7	1	no	—
19	C₉×D₉₁	D₇	1	1	yes	characteristic, complemented
20	C₇×C₉×D₁₃	—	7	1	no	—
21	C₁₃×C₇⋊D₇	—	9	1	no	—
22	C₇×D₉₁	—	9	1	no	—
23	C₇×D₉₁	D₉	1	1	yes	characteristic, complemented
24	D₂₁⋊D₁₃	—	21	1	no	—
25	D₁₃×D₂₁	—	21	1	no	—
26	C₇⋊D₆₃	D₁₃	1	1	yes	characteristic, complemented
27	C₇×D₆₃	—	13	1	no	—
28	C₇×C₉×D₇	—	13	1	no	—
29	C₇×C₉×C₁₃	—	2	3	no	—
30	C₇×C₉×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented
31	C₇×C₉×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented
32	C₇²×C₁₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
33	D₇×D₂₁	—	39	1	no	—
34	D₂₇₃	—	3	1	no	—
35	C₁₃×D₂₁	—	21	1	no	—
36	C₁₃×D₂₁	—	21	1	no	—
37	C₁₃×D₂₁	—	42	3	no	—
38	C₇×D₃₉	—	21	1	no	—
39	C₃×D₉₁	D₂₁	1	1	yes	characteristic
40	C₃×C₇×D₁₃	—	7	1	no	—
41	D₉×D₁₃	—	49	1	no	Hall
42	C₇²×C₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
43	D₇×D₁₃	—	63	1	no	—
44	D₇×D₁₃	—	63	1	no	—
45	C₃⋊(C₇⋊D₇)	—	3	1	no	—
46	C₇×D₂₁	—	39	1	no	—
47	C₃×C₇×D₇	—	13	1	no	—
48	C₃×C₇×C₁₃	—	2	3	no	—
49	C₃×C₇×C₁₃	D₃×D₇	1	1	yes	characteristic
50	C₃×C₇×C₁₃	C₂×D₂₁	1	1	yes	characteristic
51	C₂×D₆₃	—	91	1	no	—
52	D₇×D₉	—	91	1	no	—
53	D₁₁₇	—	7	1	no	—
54	C₉×D₁₃	—	7	1	no	—
55	C₁₃×D₉	—	49	1	no	—
56	D₇²	—	117	1	no	Hall
57	D₉₁	—	9	1	no	—
58	D₉₁	D₆₃	1	1	yes	characteristic, complemented
59	C₇×D₁₃	—	7	1	no	—
60	C₇×D₁₃	—	63	1	no	—
61	C₁₃×D₇	—	63	1	no	—
62	C₁₃×D₇	—	63	1	no	—
63	C₁₃×D₇	—	126	3	no	—
64	D₃×D₁₃	—	147	1	no	—
65	C₃×C₇²	D₃×D₁₃	1	1	yes	characteristic
66	C₂×C₇×C₉	—	91	1	no	—
67	D₆₃	—	7	1	no	—
68	D₆₃	—	7	1	no	—
69	D₆₃	—	13	1	no	—
70	D₆₃	—	14	3	no	—
71	C₉×D₇	—	13	1	no	—
72	C₇×D₉	—	91	1	no	—
73	C₉×C₁₃	D₇²	1	1	yes	characteristic, complemented, Hall
74	C₇⋊D₇	—	9	1	no	—
75	C₇×D₇	—	13	1	no	—
76	C₇×D₇	—	117	1	no	—
77	C₇×C₁₃	—	2	3	no	—
78	C₇×C₁₃	D₇×D₉	1	1	yes	characteristic, complemented
79	C₇×C₁₃	C₂×D₆₃	1	1	yes	characteristic, complemented
80	C₂×D₂₁	—	273	1	no	—
81	D₃×D₇	—	273	1	no	—
82	D₃₉	—	21	1	no	—
83	C₃×D₁₃	—	7	1	no	—
84	D₃×C₁₃	—	147	1	no	—
85	C₇×C₉	—	2	3	no	—
86	C₇×C₉	D₇×D₁₃	1	1	yes	characteristic, complemented
87	C₇×C₉	D₇×D₁₃	1	1	yes	characteristic, complemented
88	C₂×D₁₃	—	441	1	no	Hall
89	C₇²	D₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
90	C₂×C₃×C₇	—	91	1	no	—
91	D₂₁	—	21	1	no	—
92	D₂₁	—	21	1	no	—
93	D₂₁	—	39	1	no	—
94	D₂₁	—	42	3	no	—
95	C₃×D₇	—	13	1	no	—
96	D₃×C₇	—	273	1	no	—
97	C₃×C₁₃	D₇×D₂₁	1	1	yes	characteristic
98	C₂×D₉	—	637	1	no	Hall
99	C₂×D₇	—	819	1	no	—
100	C₂×D₇	—	819	1	no	—
101	C₂×C₁₃	—	441	1	no	—
102	D₁₃	—	7	1	no	—
103	D₁₃	—	63	1	no	—
104	C₃×C₇	—	2	3	no	—
105	C₃×C₇	D₁₃×D₂₁	1	1	yes	characteristic
106	C₃×C₇	D₂₁⋊D₁₃	1	1	yes	characteristic
107	C₂×C₉	—	91	1	no	—
108	D₉	—	49	1	no	—
109	D₉	—	91	1	no	—
110	C₂×C₇	—	819	1	no	—
111	C₂×C₇	—	91	1	no	—
112	D₇	—	13	1	no	—
113	D₇	—	63	1	no	—
114	D₇	—	63	1	no	—
115	D₇	—	117	1	no	—
116	D₇	—	126	3	no	—
117	C₁₃	D₇×D₆₃	1	1	yes	characteristic, complemented, Sylow
118	C₂×D₃	—	1911	1	no	—
119	C₉	(C₇⋊D₇)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
120	C₇	—	2	3	no	—
121	C₇	D₁₃×D₆₃	1	1	yes	characteristic, complemented
122	C₇	D₆₃⋊D₁₃	1	1	yes	characteristic, complemented
123	C₂×C₃	—	91	1	no	—
124	D₃	—	273	1	no	—
125	D₃	—	147	1	no	—
126	C₂²	—	5733	1	no	Sylow
127	C₃	D₉₁⋊D₂₁	1	1	yes	characteristic
128	C₂	—	819	1	no	—
129	C₂	—	91	1	no	—
130	C₂	—	441	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×C₇⋊D₆₃

C₂

yes

maximal, characteristic, complemented

C₇×D₈₁₉

C₂

yes

maximal, characteristic, complemented

C₇×C₉×D₉₁

C₂

yes

maximal, characteristic, complemented

D₉₁⋊D₂₁

—

maximal

C₇²×C₉×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₁₃×C₃⋊(C₇⋊D₇)

—

C₇×D₂₇₃

—

C₃×C₇×D₉₁

D₃

yes

characteristic

D₆₃⋊D₁₃

—

maximal

D₁₃×D₆₃

—

maximal

(C₇⋊D₇)⋊D₁₃

—

Hall

C₃×C₇²×C₁₃

C₂×D₃

yes

characteristic

D₇×D₆₃

—

maximal, Hall

D₈₁₉

D₇

yes

characteristic, complemented

C₁₃×D₆₃

—

C₁₃×D₆₃

—

C₁₃×D₆₃

—

C₇×D₁₁₇

—

C₉×D₉₁

D₇

yes

characteristic, complemented

C₇×C₉×D₁₃

—

C₁₃×C₇⋊D₇

—

C₇×D₉₁

—

C₇×D₉₁

D₉

yes

characteristic, complemented

D₂₁⋊D₁₃

—

D₁₃×D₂₁

—

C₇⋊D₆₃

D₁₃

yes

characteristic, complemented

C₇×D₆₃

—

C₇×C₉×D₇

—

C₇×C₉×C₁₃

—

C₇×C₉×C₁₃

C₂×D₇

yes

characteristic, complemented

C₇×C₉×C₁₃

C₂×D₇

yes

characteristic, complemented

C₇²×C₁₃

C₂×D₉

yes

characteristic, complemented, Hall

D₇×D₂₁

—

D₂₇₃

—

C₁₃×D₂₁

—

C₁₃×D₂₁

—

C₁₃×D₂₁

—

C₇×D₃₉

—

C₃×D₉₁

D₂₁

yes

characteristic

C₃×C₇×D₁₃

—

D₉×D₁₃

—

Hall

C₇²×C₉

C₂×D₁₃

yes

characteristic, complemented, Hall

D₇×D₁₃

—

D₇×D₁₃

—

C₃⋊(C₇⋊D₇)

—

C₇×D₂₁

—

C₃×C₇×D₇

—

C₃×C₇×C₁₃

—

C₃×C₇×C₁₃

D₃×D₇

yes

characteristic

C₃×C₇×C₁₃

C₂×D₂₁

yes

characteristic

C₂×D₆₃

—

D₇×D₉

—

D₁₁₇

—

C₉×D₁₃

—

C₁₃×D₉

—

D₇²

—

117

Hall

D₉₁

—

D₉₁

D₆₃

yes

characteristic, complemented

C₇×D₁₃

—

C₇×D₁₃

—

C₁₃×D₇

—

C₁₃×D₇

—

C₁₃×D₇

—

126

—

D₃×D₁₃

—

147

—

C₃×C₇²

D₃×D₁₃

yes

characteristic

C₂×C₇×C₉

—

D₆₃

—

D₆₃

—

D₆₃

—

D₆₃

—

C₉×D₇

—

C₇×D₉

—

C₉×C₁₃

D₇²

yes

characteristic, complemented, Hall

C₇⋊D₇

—

C₇×D₇

—

C₇×D₇

—

117

—

C₇×C₁₃

—

C₇×C₁₃

D₇×D₉

yes

characteristic, complemented

C₇×C₁₃

C₂×D₆₃

yes

characteristic, complemented

C₂×D₂₁

—

273

—

D₃×D₇

—

273

—

D₃₉

—

C₃×D₁₃

—

D₃×C₁₃

—

147

—

C₇×C₉

—

C₇×C₉

D₇×D₁₃

yes

characteristic, complemented

C₇×C₉

D₇×D₁₃

yes

characteristic, complemented

C₂×D₁₃

—

441

Hall

C₇²

D₉×D₁₃

yes

characteristic, complemented, Sylow

C₂×C₃×C₇

—

D₂₁

—

D₂₁

—

D₂₁

—

D₂₁

—

C₃×D₇

—

D₃×C₇

—

273

—

C₃×C₁₃

D₇×D₂₁

yes

characteristic

C₂×D₉

—

637

Hall

C₂×D₇

—

819

—

100

C₂×D₇

—

819

—

101

C₂×C₁₃

—

441

—

102

D₁₃

—

103

D₁₃

—

104

C₃×C₇

—

105

C₃×C₇

D₁₃×D₂₁

yes

characteristic

106

C₃×C₇

D₂₁⋊D₁₃

yes

characteristic

107

C₂×C₉

—

108

D₉

—

109

D₉

—

110

C₂×C₇

—

819

—

111

C₂×C₇

—

112

D₇

—

113

D₇

—

114

D₇

—

115

D₇

—

117

—

116

D₇

—

126

—

117

C₁₃

D₇×D₆₃

yes

characteristic, complemented, Sylow

118

C₂×D₃

—

1911

—

119

C₉

(C₇⋊D₇)⋊D₁₃

yes

characteristic, complemented, Sylow

120

C₇

—

121

C₇

D₁₃×D₆₃

yes

characteristic, complemented

122

C₇

D₆₃⋊D₁₃

yes

characteristic, complemented

123

C₂×C₃

—

124

D₃

—

273

—

125

D₃

—

147

—

126

C₂²

—

5733

Sylow

127

C₃

D₉₁⋊D₂₁

yes

characteristic

128

C₂

—

819

—

129

C₂

—

130

C₂

—

441

—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇²×C₉×C₁₃	C₂²
Frattini	C₃	D₉₁⋊D₂₁
socle	C₃×C₇²×C₁₃	C₂×D₃
LCS	G ▷ C₇²×C₉×C₁₃
UCS	C₁

subgroup

G/H

center, hypercenter

C₁

commutator, Fitting, cosocle, hypocenter

C₇²×C₉×C₁₃

C₂²

Frattini

C₃

D₉₁⋊D₂₁

socle

C₃×C₇²×C₁₃

C₂×D₃

LCS

G ▷ C₇²×C₉×C₁₃

UCS

C₁

N	H ≅ G/N	type
1. C₁₃×C₇⋊D₆₃	C₂	semidirect
2. C₇×D₈₁₉	C₂	semidirect
3. C₇×C₉×D₉₁	C₂	semidirect
5. C₇²×C₉×C₁₃	C₂²	semidirect
14. D₈₁₉	D₇	semidirect
19. C₉×D₉₁	D₇	semidirect
23. C₇×D₉₁	D₉	semidirect
26. C₇⋊D₆₃	D₁₃	semidirect
30. C₇×C₉×C₁₃	C₂×D₇	semidirect
31. C₇×C₉×C₁₃	C₂×D₇	semidirect
32. C₇²×C₁₃	C₂×D₉	semidirect
42. C₇²×C₉	C₂×D₁₃	semidirect
58. D₉₁	D₆₃	semidirect
73. C₉×C₁₃	D₇²	semidirect
78. C₇×C₁₃	D₇×D₉	semidirect
79. C₇×C₁₃	C₂×D₆₃	semidirect
86. C₇×C₉	D₇×D₁₃	semidirect
87. C₇×C₉	D₇×D₁₃	semidirect
89. C₇²	D₉×D₁₃	semidirect
117. C₁₃	D₇×D₆₃	semidirect
119. C₉	(C₇⋊D₇)⋊D₁₃	semidirect
121. C₇	D₁₃×D₆₃	semidirect
122. C₇	D₆₃⋊D₁₃	semidirect

H ≅ G/N

type

1. C₁₃×C₇⋊D₆₃

C₂

semidirect

2. C₇×D₈₁₉

C₂

semidirect

3. C₇×C₉×D₉₁

C₂

semidirect

5. C₇²×C₉×C₁₃

C₂²

semidirect

14. D₈₁₉

D₇

semidirect

19. C₉×D₉₁

D₇

semidirect

23. C₇×D₉₁

D₉

semidirect

26. C₇⋊D₆₃

D₁₃

semidirect

30. C₇×C₉×C₁₃

C₂×D₇

semidirect

31. C₇×C₉×C₁₃

C₂×D₇

semidirect

32. C₇²×C₁₃

C₂×D₉

semidirect

42. C₇²×C₉

C₂×D₁₃

semidirect

58. D₉₁

D₆₃

semidirect

73. C₉×C₁₃

D₇²

semidirect

78. C₇×C₁₃

D₇×D₉

semidirect

79. C₇×C₁₃

C₂×D₆₃

semidirect

86. C₇×C₉

D₇×D₁₃

semidirect

87. C₇×C₉

D₇×D₁₃

semidirect

89. C₇²

D₉×D₁₃

semidirect

117. C₁₃

D₇×D₆₃

semidirect

119. C₉

(C₇⋊D₇)⋊D₁₃

semidirect

121. C₇

D₁₃×D₆₃

semidirect

122. C₇

D₆₃⋊D₁₃

semidirect

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

subgroup	index
C₁₃×C₇⋊D₆₃	2
C₇×D₈₁₉	2
C₇×C₉×D₉₁	2
D₉₁⋊D₂₁	3
D₆₃⋊D₁₃	7
D₁₃×D₆₃	7
D₇×D₆₃	13

subgroup

index

C₁₃×C₇⋊D₆₃

C₇×D₈₁₉

C₇×C₉×D₉₁

D₉₁⋊D₂₁

D₆₃⋊D₁₃

D₁₃×D₆₃

D₇×D₆₃

Subgroups — D₉₁⋊D₆₃ #37524587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D91⋊D63 #37524587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉₁⋊D₆₃ #37524587