Group #46809937 — subgroups

Subgroups — #46809937

Order 34432.

336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 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	#31771240	C₂	1	1	yes	maximal, characteristic, complemented
2	#31770797	C₂	1	2	yes	maximal, complemented
3	#31770349	C₂	1	1	yes	maximal, characteristic, complemented
4	#31770334	C₂	1	2	yes	maximal, complemented
5	#493×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×D₂₆₉	—	2	2	no	—
7	C₂×#16864387	—	2	2	no	—
8	#22575424	—	2	2	no	—
9	#22575421	—	2	2	no	—
10	C₄×D₁₀₇₆	C₂²	1	2	yes	—
11	C₄⋊#14524130	C₂²	1	2	yes	complemented
12	#22575374	—	2	2	no	—
13	C₂×D₈×C₂₆₉	—	2	2	no	—
14	#127×C₂₆₉	C₂²	1	1	yes	characteristic
15	#127×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
16	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₂₆₉	—	2	2	no	—
18	C₂×D₁₀₇₆	D₄	1	2	yes	—
19	C₂×C₂²⋊D₂₆₉	—	2	4	no	—
20	D₄×D₂₆₉	—	4	4	no	—
21	D₄×D₂₆₉	—	4	4	no	—
22	C₂×C₄×D₂₆₉	—	2	2	no	—
23	#16864387	—	4	4	no	—
24	C₂×#14524130	—	2	2	no	—
25	C₄⋊Dic₂₆₉	D₄	1	2	yes	—
26	C₂²⋊Dic₂₆₉	—	2	2	no	—
27	#16864379	—	2	2	no	—
28	C₂×D₄×C₂₆₉	—	2	2	no	—
29	C₂×D₄×C₂₆₉	—	2	2	no	—
30	C₂×D₄×C₂₆₉	—	2	1	no	—
31	C₂×D₄×C₂₆₉	D₄	1	2	yes	—
32	D₈×C₂₆₉	—	4	4	no	—
33	C₂×C₈×C₂₆₉	—	2	1	no	—
34	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
35	C₂²×D₂₆₉	—	2	2	no	—
36	C₂²×D₂₆₉	—	4	8	no	—
37	C₂²×D₂₆₉	—	8	2	no	—
38	D₁₀₇₆	—	2	2	no	—
39	D₁₀₇₆	D₈	1	4	yes	complemented
40	C₂²⋊D₂₆₉	—	4	8	no	—
41	C₂×Dic₂₆₉	—	2	2	no	—
42	C₄×D₂₆₉	—	4	2	no	—
43	C₄×D₂₆₉	—	4	2	no	—
44	#14524130	—	4	2	no	—
45	C₂³×C₂₆₉	—	2	2	no	—
46	C₂³×C₂₆₉	—	4	1	no	—
47	D₄×C₂₆₉	—	4	2	no	—
48	D₄×C₂₆₉	—	4	2	no	—
49	D₄×C₂₆₉	—	4	2	no	—
50	D₄×C₂₆₉	—	4	2	no	—
51	D₄×C₂₆₉	—	4	2	no	—
52	D₄×C₂₆₉	—	4	2	no	—
53	C₂×C₄×C₂₆₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
55	C₈×C₂₆₉	—	2	2	no	—
56	C₂²×C₂₆₉	—	4	4	no	—
57	C₂²×C₂₆₉	—	4	2	no	—
58	C₂²×C₂₆₉	—	8	2	no	—
59	C₂²×C₂₆₉	—	8	1	no	—
60	C₂²×C₂₆₉	#120	1	1	yes	characteristic
61	C₂×D₂₆₉	—	2	4	no	—
62	C₂×D₂₆₉	—	4	2	no	—
63	C₂×D₂₆₉	—	4	2	no	—
64	C₂×D₂₆₉	—	8	8	no	—
65	C₄×C₂₆₉	—	2	1	no	—
66	C₄×C₂₆₉	C₂×D₈	1	2	yes	—
67	C₄×C₂₆₉	AGL(1,ℤ/8)	1	2	yes	—
68	Dic₂₆₉	—	4	2	no	—
69	C₂×C₂₆₉	—	8	2	no	—
70	C₂×C₂₆₉	—	16	1	no	—
71	C₂×C₂₆₉	#447	1	2	yes	—
72	C₂×C₂₆₉	#453	1	1	yes	characteristic
73	D₂₆₉	—	4	4	no	—
74	C₂₆₉	#1619	1	1	yes	characteristic, complemented, Sylow
75	#1619	—	269	1	no	maximal, Sylow
76	D₄²	—	269	1	no	—
77	#493	D₂₆₉	1	1	yes	characteristic, complemented
78	#459	—	269	2	no	—
79	#331	—	269	1	no	—
80	D₄⋊C₈	—	269	2	no	—
81	C₂²×D₄	—	538	2	no	—
82	C₂×D₈	—	2	2	no	—
83	C₂×D₈	—	538	2	no	—
84	#127	C₂×D₂₆₉	1	1	yes	characteristic
85	#127	C₂×D₂₆₉	1	1	yes	characteristic, complemented
86	#121	—	538	2	no	—
87	#120	—	538	2	no	—
88	C₄×D₄	—	269	2	no	—
89	C₄⋊C₈	—	269	2	no	—
90	#102	—	538	2	no	—
91	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
92	C₂⁴	—	538	2	no	—
93	C₂×D₄	—	2	2	no	—
94	C₂×D₄	—	2	2	no	—
95	C₂×D₄	—	2	1	no	—
96	C₂×D₄	—	269	2	no	—
97	C₂×D₄	—	538	4	no	—
98	C₂×D₄	—	1076	4	no	—
99	C₂×D₄	—	1076	4	no	—
100	C₂×D₄	C₂²⋊D₂₆₉	1	2	yes	—
101	C₂²×C₄	—	538	2	no	—
102	D₈	—	4	4	no	—
103	D₈	—	1076	4	no	—
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	538	2	no	—
106	C₄⋊C₄	—	269	2	no	—
107	C₂²⋊C₄	—	538	2	no	—
108	C₂²⋊C₄	—	538	2	no	—
109	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
110	C₂³	—	2	2	no	—
111	C₂³	—	4	1	no	—
112	C₂³	—	538	2	no	—
113	C₂³	—	1076	8	no	—
114	C₂³	—	2152	2	no	—
115	D₄	—	4	2	no	—
116	D₄	—	4	2	no	—
117	D₄	—	4	2	no	—
118	D₄	—	4	2	no	—
119	D₄	—	4	2	no	—
120	D₄	—	4	2	no	—
121	D₄	—	269	4	no	—
122	D₄	—	538	2	no	—
123	D₄	—	1076	8	no	—
124	C₂×C₄	—	538	2	no	—
125	C₂×C₄	—	1076	2	no	—
126	C₂×C₄	—	1076	2	no	—
127	C₂×C₄	D₄×D₂₆₉	1	2	yes	—
128	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
129	C₈	—	2	2	no	—
130	C₈	—	1076	2	no	—
131	C₂²	—	4	4	no	—
132	C₂²	—	4	2	no	—
133	C₂²	—	8	2	no	—
134	C₂²	—	8	1	no	—
135	C₂²	—	538	4	no	—
136	C₂²	—	1076	2	no	—
137	C₂²	—	1076	2	no	—
138	C₂²	—	2152	8	no	—
139	C₂²	#22575421	1	1	yes	characteristic
140	C₄	—	2	1	no	—
141	C₄	—	1076	2	no	—
142	C₄	D₈×D₂₆₉	1	2	yes	—
143	C₄	#22575477	1	2	yes	—
144	C₂	—	8	2	no	—
145	C₂	—	16	1	no	—
146	C₂	—	1076	4	no	—
147	C₂	#31770737	1	2	yes	—
148	C₂	#31770772	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31771240

C₂

yes

maximal, characteristic, complemented

#31770797

C₂

yes

maximal, complemented

#31770349

C₂

yes

maximal, characteristic, complemented

#31770334

C₂

yes

maximal, complemented

#493×C₂₆₉

C₂

yes

maximal, characteristic, complemented

C₂×D₄×D₂₆₉

—

C₂×#16864387

—

#22575424

—

#22575421

—

C₄×D₁₀₇₆

C₂²

yes

—

C₄⋊#14524130

C₂²

yes

complemented

#22575374

—

C₂×D₈×C₂₆₉

—

#127×C₂₆₉

C₂²

yes

characteristic

#127×C₂₆₉

C₂²

yes

characteristic, complemented

C₄×C₈×C₂₆₉

C₂²

yes

characteristic, complemented

C₂³×D₂₆₉

—

C₂×D₁₀₇₆

D₄

yes

—

C₂×C₂²⋊D₂₆₉

—

D₄×D₂₆₉

—

D₄×D₂₆₉

—

C₂×C₄×D₂₆₉

—

#16864387

—

C₂×#14524130

—

C₄⋊Dic₂₆₉

D₄

yes

—

C₂²⋊Dic₂₆₉

—

#16864379

—

C₂×D₄×C₂₆₉

—

C₂×D₄×C₂₆₉

—

C₂×D₄×C₂₆₉

—

C₂×D₄×C₂₆₉

D₄

yes

—

D₈×C₂₆₉

—

C₂×C₈×C₂₆₉

—

C₄²×C₂₆₉

C₂³

yes

characteristic

C₂²×D₂₆₉

—

C₂²×D₂₆₉

—

C₂²×D₂₆₉

—

D₁₀₇₆

—

D₁₀₇₆

D₈

yes

complemented

C₂²⋊D₂₆₉

—

C₂×Dic₂₆₉

—

C₄×D₂₆₉

—

C₄×D₂₆₉

—

#14524130

—

C₂³×C₂₆₉

—

C₂³×C₂₆₉

—

D₄×C₂₆₉

—

D₄×C₂₆₉

—

D₄×C₂₆₉

—

D₄×C₂₆₉

—

D₄×C₂₆₉

—

D₄×C₂₆₉

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₈×C₂₆₉

—

C₂²×C₂₆₉

—

C₂²×C₂₆₉

—

C₂²×C₂₆₉

—

C₂²×C₂₆₉

—

C₂²×C₂₆₉

#120

yes

characteristic

C₂×D₂₆₉

—

C₂×D₂₆₉

—

C₂×D₂₆₉

—

C₂×D₂₆₉

—

C₄×C₂₆₉

—

C₄×C₂₆₉

C₂×D₈

yes

—

C₄×C₂₆₉

AGL(1,ℤ/8)

yes

—

Dic₂₆₉

—

C₂×C₂₆₉

—

C₂×C₂₆₉

—

C₂×C₂₆₉

#447

yes

—

C₂×C₂₆₉

#453

yes

characteristic

D₂₆₉

—

C₂₆₉

#1619

yes

characteristic, complemented, Sylow

#1619

—

269

maximal, Sylow

D₄²

—

269

—

#493

D₂₆₉

yes

characteristic, complemented

#459

—

269

—

#331

—

269

—

D₄⋊C₈

—

269

—

C₂²×D₄

—

538

—

C₂×D₈

—

C₂×D₈

—

538

—

#127

C₂×D₂₆₉

yes

characteristic

#127

C₂×D₂₆₉

yes

characteristic, complemented

#121

—

538

—

#120

—

538

—

C₄×D₄

—

269

—

C₄⋊C₈

—

269

—

#102

—

538

—

C₄×C₈

C₂×D₂₆₉

yes

characteristic, complemented

C₂⁴

—

538

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

269

—

C₂×D₄

—

538

—

C₂×D₄

—

1076

—

C₂×D₄

—

1076

—

100

C₂×D₄

C₂²⋊D₂₆₉

yes

—

101

C₂²×C₄

—

538

—

102

D₈

—

103

D₈

—

1076

—

104

C₂×C₈

—

105

C₂×C₈

—

538

—

106

C₄⋊C₄

—

269

—

107

C₂²⋊C₄

—

538

—

108

C₂²⋊C₄

—

538

—

109

C₄²

C₂²×D₂₆₉

yes

characteristic

110

C₂³

—

111

C₂³

—

112

C₂³

—

538

—

113

C₂³

—

1076

—

114

C₂³

—

2152

—

115

D₄

—

116

D₄

—

117

D₄

—

118

D₄

—

119

D₄

—

120

D₄

—

121

D₄

—

269

—

122

D₄

—

538

—

123

D₄

—

1076

—

124

C₂×C₄

—

538

—

125

C₂×C₄

—

1076

—

126

C₂×C₄

—

1076

—

127

C₂×C₄

D₄×D₂₆₉

yes

—

128

C₂×C₄

C₂×C₂²⋊D₂₆₉

yes

characteristic

129

C₈

—

130

C₈

—

1076

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

538

—

136

C₂²

—

1076

—

137

C₂²

—

1076

—

138

C₂²

—

2152

—

139

C₂²

#22575421

yes

characteristic

140

C₄

—

141

C₄

—

1076

—

142

C₄

D₈×D₂₆₉

yes

—

143

C₄

#22575477

yes

—

144

C₂

—

145

C₂

—

146

C₂

—

1076

—

147

C₂

#31770737

yes

—

148

C₂

#31770772

yes

characteristic

	subgroup	G/H
center	C₂²	#22575421
commutator, cosocle	C₄²×C₂₆₉	C₂³
Frattini	C₄²	C₂²×D₂₆₉
Fitting	#493×C₂₆₉	C₂
socle	C₂²×C₂₆₉	#120
hypercenter	#493	D₂₆₉
hypocenter	C₂₆₉	#1619
LCS	G ▷ C₄²×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#22575421

commutator, cosocle

C₄²×C₂₆₉

C₂³

Frattini

C₄²

C₂²×D₂₆₉

Fitting

#493×C₂₆₉

C₂

C₂²×C₂₆₉

D₂₆₉

C₂₆₉

G ▷ C₄²×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂₆₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #31771240	C₂	semidirect
2. #31770797	C₂	semidirect
3. #31770349	C₂	semidirect
4. #31770334	C₂	semidirect
5. #493×C₂₆₉	C₂	semidirect
11. C₄⋊#14524130	C₂²	semidirect
15. #127×C₂₆₉	C₂²	semidirect
16. C₄×C₈×C₂₆₉	C₂²	semidirect
39. D₁₀₇₆	D₈	semidirect
74. C₂₆₉	#1619	semidirect
77. #493	D₂₆₉	semidirect
85. #127	C₂×D₂₆₉	semidirect
91. C₄×C₈	C₂×D₂₆₉	semidirect

H ≅ G/N

type

1. #31771240

C₂

semidirect

2. #31770797

C₂

semidirect

3. #31770349

C₂

semidirect

4. #31770334

C₂

semidirect

5. #493×C₂₆₉

C₂

semidirect

11. C₄⋊#14524130

C₂²

semidirect

15. #127×C₂₆₉

C₂²

semidirect

16. C₄×C₈×C₂₆₉

C₂²

semidirect

39. D₁₀₇₆

D₈

semidirect

74. C₂₆₉

#1619

semidirect

77. #493

D₂₆₉

semidirect

85. #127

C₂×D₂₆₉

semidirect

91. C₄×C₈

C₂×D₂₆₉

semidirect

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

subgroup	index
#31771240	2
#31770797	2
#31770349	2
#31770334	2
#493×C₂₆₉	2
#1619	269

subgroup

index

#493×C₂₆₉

269

Subgroups — #46809937

Conjugacy classes of subgroups

Complements

Maximal subgroups