Group #46810391 — subgroups

Subgroups — #46810391

Order 34432.

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

normal subgroups only

This group has 146 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	#31771003	C₂	1	1	yes	maximal, characteristic
2	#31770900	C₂	1	1	yes	maximal, characteristic
3	#31770815	C₂	1	1	yes	maximal, characteristic
4	#31770358	C₂	1	1	yes	maximal, characteristic
5	#31770353	C₂	1	1	yes	maximal, characteristic
6	#31770350	C₂	1	1	yes	maximal, characteristic
7	#446×C₂₆₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#16864392	—	2	1	no	—
9	#22575453	C₂²	1	1	yes	characteristic
10	#22575453	C₂²	1	1	yes	characteristic
11	#22575386	—	2	1	no	—
12	#22575385	—	2	1	no	—
13	#22575385	—	2	1	no	—
14	C₄⋊#14524130	C₂²	1	1	yes	characteristic
15	C₄⋊#14524130	C₂²	1	1	yes	characteristic
16	#22575377	—	2	1	no	—
17	#22575376	—	2	1	no	—
18	C₄×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic
19	C₄⋊C₈×C₂₆₉	—	2	1	no	—
20	C₄⋊C₈×C₂₆₉	C₂²	1	1	yes	characteristic
21	#97×C₂₆₉	—	2	1	no	—
22	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
23	C₂×Dic₅₃₈	—	2	1	no	—
24	C₂×Dic₅₃₈	—	2	1	no	—
25	#16864392	—	4	2	no	—
26	C₂×#14524130	—	2	1	no	—
27	C₂×#14524130	—	2	1	no	—
28	C₄⋊Dic₂₆₉	—	2	1	no	—
29	C₄⋊Dic₂₆₉	—	2	1	no	—
30	C₄⋊Dic₂₆₉	—	2	1	no	—
31	C₄⋊Dic₂₆₉	—	2	1	no	—
32	C₂×Q₈×C₂₆₉	D₄	1	1	yes	characteristic
33	C₂×C₈×C₂₆₉	—	2	1	no	—
34	C₂×C₈×C₂₆₉	D₄	1	1	yes	characteristic
35	C₂×C₈×C₂₆₉	D₄	1	1	yes	characteristic
36	C₄⋊C₄×C₂₆₉	—	2	1	no	—
37	C₄⋊C₄×C₂₆₉	D₄	1	1	yes	characteristic
38	C₄²×C₂₆₉	—	2	1	no	—
39	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
40	Dic₅₃₈	—	4	1	no	—
41	Dic₅₃₈	—	4	1	no	—
42	Dic₅₃₈	—	8	1	no	—
43	C₂×Dic₂₆₉	—	4	1	no	—
44	C₂×Dic₂₆₉	—	4	1	no	—
45	#14524130	—	4	1	no	—
46	#14524130	—	4	1	no	—
47	Q₈×C₂₆₉	—	2	1	no	—
48	Q₈×C₂₆₉	—	2	1	no	—
49	C₂×C₄×C₂₆₉	—	2	1	no	—
50	C₂×C₄×C₂₆₉	—	2	1	no	—
51	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₂₆₉	#41	1	1	yes	characteristic
54	C₈×C₂₆₉	—	2	1	no	—
55	C₈×C₂₆₉	—	4	1	no	—
56	C₈×C₂₆₉	Q₁₆	1	2	yes	complemented
57	C₂²×C₂₆₉	#121	1	1	yes	characteristic
58	C₄×C₂₆₉	—	2	1	no	—
59	C₄×C₂₆₉	—	4	1	no	—
60	C₄×C₂₆₉	—	4	1	no	—
61	C₄×C₂₆₉	C₂×Q₁₆	1	1	yes	characteristic
62	C₄×C₂₆₉	AGL(1,ℤ/8)	1	1	yes	characteristic
63	C₄×C₂₆₉	#137	1	1	yes	characteristic
64	C₄×C₂₆₉	#137	1	1	yes	characteristic
65	Dic₂₆₉	—	8	1	no	—
66	Dic₂₆₉	—	8	1	no	—
67	C₂×C₂₆₉	#462	1	1	yes	characteristic
68	C₂×C₂₆₉	#468	1	1	yes	characteristic
69	C₂×C₂₆₉	#471	1	1	yes	characteristic
70	C₂₆₉	#1692	1	1	yes	characteristic, complemented, Sylow
71	#1692	—	269	1	no	maximal, Sylow
72	#498	—	269	1	no	—
73	#477	—	269	1	no	—
74	#462	—	269	1	no	—
75	#446	D₂₆₉	1	1	yes	characteristic
76	#335	—	269	1	no	—
77	#333	—	269	1	no	—
78	#332	—	269	1	no	—
79	C₂×Q₁₆	—	538	1	no	—
80	C₄⋊Q₈	—	269	1	no	—
81	C₄⋊Q₈	—	269	1	no	—
82	C₄×Q₈	C₂×D₂₆₉	1	1	yes	characteristic
83	#107	—	538	1	no	—
84	#106	—	538	1	no	—
85	#106	—	538	1	no	—
86	C₄⋊C₈	—	2	1	no	—
87	C₄⋊C₈	—	269	1	no	—
88	C₄⋊C₈	—	269	1	no	—
89	C₄⋊C₈	C₂×D₂₆₉	1	1	yes	characteristic
90	#103	—	538	1	no	—
91	#103	—	538	1	no	—
92	#97	—	2	1	no	—
93	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic
94	C₂×Q₈	—	538	1	no	—
95	C₂×Q₈	—	538	1	no	—
96	C₂×Q₈	D₁₀₇₆	1	1	yes	characteristic
97	Q₁₆	—	1076	2	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	538	1	no	—
100	C₂×C₈	—	538	1	no	—
101	C₂×C₈	C₂²⋊D₂₆₉	1	1	yes	characteristic
102	C₂×C₈	C₂²⋊D₂₆₉	1	1	yes	characteristic
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	538	1	no	—
105	C₄⋊C₄	—	538	1	no	—
106	C₄⋊C₄	—	538	1	no	—
107	C₄⋊C₄	—	538	1	no	—
108	C₄⋊C₄	D₁₀₇₆	1	1	yes	characteristic
109	C₄²	—	2	1	no	—
110	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
111	Q₈	—	2	1	no	—
112	Q₈	—	2	1	no	—
113	Q₈	—	1076	1	no	—
114	Q₈	—	1076	1	no	—
115	Q₈	—	2152	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	1076	1	no	—
119	C₂×C₄	—	1076	1	no	—
120	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
121	C₂×C₄	C₂×D₁₀₇₆	1	1	yes	characteristic
122	C₂×C₄	#16864402	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	4	1	no	—
125	C₈	—	1076	1	no	—
126	C₈	—	1076	1	no	—
127	C₈	#16864392	1	2	yes	complemented
128	C₂²	#22575427	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	4	1	no	—
131	C₄	—	4	1	no	—
132	C₄	—	2152	1	no	—
133	C₄	—	2152	1	no	—
134	C₄	C₂×#16864392	1	1	yes	characteristic
135	C₄	#22575481	1	1	yes	characteristic
136	C₄	#22575483	1	1	yes	characteristic
137	C₄	#22575486	1	1	yes	characteristic
138	C₂	#31770815	1	1	yes	characteristic
139	C₂	#31770851	1	1	yes	characteristic
140	C₂	#31770868	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31771003

C₂

yes

maximal, characteristic

#31770900

C₂

yes

maximal, characteristic

#31770815

C₂

yes

maximal, characteristic

#31770358

C₂

yes

maximal, characteristic

#31770353

C₂

yes

maximal, characteristic

#31770350

C₂

yes

maximal, characteristic

#446×C₂₆₉

C₂

yes

maximal, characteristic

C₂×#16864392

—

#22575453

C₂²

yes

characteristic

#22575453

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₄⋊#14524130

C₂²

yes

characteristic

#22575377

—

#22575376

—

C₄×Q₈×C₂₆₉

C₂²

yes

characteristic

C₄⋊C₈×C₂₆₉

—

C₄⋊C₈×C₂₆₉

C₂²

yes

characteristic

#97×C₂₆₉

—

C₄×C₈×C₂₆₉

C₂²

yes

characteristic

C₂×Dic₅₃₈

—

C₂×Dic₅₃₈

—

#16864392

—

C₂×#14524130

—

C₂×#14524130

—

C₄⋊Dic₂₆₉

—

C₄⋊Dic₂₆₉

—

C₄⋊Dic₂₆₉

—

C₄⋊Dic₂₆₉

—

C₂×Q₈×C₂₆₉

D₄

yes

characteristic

C₂×C₈×C₂₆₉

—

C₂×C₈×C₂₆₉

D₄

yes

characteristic

C₂×C₈×C₂₆₉

D₄

yes

characteristic

C₄⋊C₄×C₂₆₉

—

C₄⋊C₄×C₂₆₉

D₄

yes

characteristic

C₄²×C₂₆₉

—

C₄²×C₂₆₉

C₂³

yes

characteristic

Dic₅₃₈

—

Dic₅₃₈

—

Dic₅₃₈

—

C₂×Dic₂₆₉

—

C₂×Dic₂₆₉

—

#14524130

—

#14524130

—

Q₈×C₂₆₉

—

Q₈×C₂₆₉

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₉

#41

yes

characteristic

C₈×C₂₆₉

—

C₈×C₂₆₉

—

C₈×C₂₆₉

Q₁₆

yes

complemented

C₂²×C₂₆₉

#121

yes

characteristic

C₄×C₂₆₉

—

C₄×C₂₆₉

—

C₄×C₂₆₉

—

C₄×C₂₆₉

C₂×Q₁₆

yes

C₄×C₂₆₉

yes

C₄×C₂₆₉

yes

C₄×C₂₆₉

yes

Dic₂₆₉

—

Dic₂₆₉

—

C₂×C₂₆₉

yes

C₂×C₂₆₉

yes

C₂×C₂₆₉

yes

C₂₆₉

yes

characteristic, complemented, Sylow

#1692

—

269

maximal, Sylow

#498

—

269

—

#477

—

269

—

#462

—

269

—

#446

D₂₆₉

yes

characteristic

#335

—

269

—

#333

—

269

—

#332

—

269

—

C₂×Q₁₆

—

538

—

C₄⋊Q₈

—

269

—

C₄⋊Q₈

—

269

—

C₄×Q₈

C₂×D₂₆₉

yes

characteristic

#107

—

538

—

#106

—

538

—

#106

—

538

—

C₄⋊C₈

—

C₄⋊C₈

—

269

—

C₄⋊C₈

—

269

—

C₄⋊C₈

C₂×D₂₆₉

yes

characteristic

#103

—

538

—

#103

—

538

—

#97

—

C₄×C₈

C₂×D₂₆₉

yes

characteristic

C₂×Q₈

—

538

—

C₂×Q₈

—

538

—

C₂×Q₈

D₁₀₇₆

yes

characteristic

Q₁₆

—

1076

—

C₂×C₈

—

C₂×C₈

—

538

—

100

C₂×C₈

—

538

—

101

C₂×C₈

C₂²⋊D₂₆₉

yes

characteristic

102

C₂×C₈

C₂²⋊D₂₆₉

yes

characteristic

103

C₄⋊C₄

—

104

C₄⋊C₄

—

538

—

105

C₄⋊C₄

—

538

—

106

C₄⋊C₄

—

538

—

107

C₄⋊C₄

—

538

—

108

C₄⋊C₄

D₁₀₇₆

yes

characteristic

109

C₄²

—

110

C₄²

C₂²×D₂₆₉

yes

characteristic

111

Q₈

—

112

Q₈

—

113

Q₈

—

1076

—

114

Q₈

—

1076

—

115

Q₈

—

2152

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

1076

—

119

C₂×C₄

—

1076

—

120

C₂×C₄

C₂×C₂²⋊D₂₆₉

yes

characteristic

121

C₂×C₄

C₂×D₁₀₇₆

yes

characteristic

122

C₂×C₄

#16864402

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

1076

—

126

C₈

—

1076

—

127

C₈

#16864392

yes

complemented

128

C₂²

#22575427

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

2152

—

133

C₄

—

2152

—

134

C₄

C₂×#16864392

yes

characteristic

135

C₄

#22575481

yes

characteristic

136

C₄

#22575483

yes

characteristic

137

C₄

#22575486

yes

characteristic

138

C₂

#31770815

yes

characteristic

139

C₂

#31770851

yes

characteristic

140

C₂

#31770868

yes

characteristic

	subgroup	G/H
center	C₂²	#22575427
commutator, cosocle	C₄²×C₂₆₉	C₂³
Frattini	C₄²	C₂²×D₂₆₉
Fitting	#446×C₂₆₉	C₂
socle, prime radical	C₂²×C₂₆₉	#121
hypercenter	#446	D₂₆₉
hypocenter	C₂₆₉	#1692
LCS	G ▷ C₄²×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #446

subgroup

G/H

center

C₂²

#22575427

commutator, cosocle

C₄²×C₂₆₉

C₂³

Frattini

C₄²

C₂²×D₂₆₉

Fitting

#446×C₂₆₉

C₂

C₂²×C₂₆₉

D₂₆₉

C₂₆₉

G ▷ C₄²×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂₆₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #446

N	H ≅ G/N	type
56. C₈×C₂₆₉	Q₁₆	semidirect
70. C₂₆₉	#1692	semidirect
127. C₈	#16864392	semidirect

H ≅ G/N

type

56. C₈×C₂₆₉

Q₁₆

semidirect

70. C₂₆₉

#1692

semidirect

127. C₈

#16864392

semidirect

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

subgroup	index
#31771003	2
#31770900	2
#31770815	2
#31770358	2
#31770353	2
#31770350	2
#446×C₂₆₉	2
#1692	269

subgroup

index

#446×C₂₆₉

269

Subgroups — #46810391

Conjugacy classes of subgroups

Complements

Maximal subgroups