Group #11799126 — subgroups

Subgroups — #11799126

Order 1152.

225 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 225 conjugacy classes of subgroups — too many to draw. Only its 64 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×#494	C₂	1	1	yes	maximal, characteristic, complemented
2	#10588859	C₂	1	2	yes	maximal
3	#10588380	C₂	1	1	yes	maximal, characteristic
4	#10588242	C₂	1	2	yes	maximal, complemented
5	#10588140	C₂	1	1	yes	maximal, characteristic, complemented
6	#71317	—	3	1	no	maximal
7	C₂×C₉×Q₁₆	—	2	1	no	—
8	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
9	C₉×C₄⋊Q₈	—	2	1	no	—
10	#63467	C₂²	1	1	yes	characteristic
11	#63464	—	2	1	no	—
12	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
13	#63388	—	2	2	no	—
14	#63387	—	2	2	no	—
15	#63372	C₂²	1	1	yes	characteristic
16	#63371	C₂²	1	2	yes	—
17	#63364	—	2	1	no	—
18	C₃×#494	D₃	1	1	yes	characteristic
19	#5179	—	3	2	no	—
20	#4700	—	3	1	no	—
21	#4565	—	3	2	no	—
22	#4463	—	3	1	no	—
23	C₂×Q₈×C₉	—	2	2	no	—
24	#3697	—	2	1	no	—
25	C₉×Q₁₆	—	2	2	no	—
26	C₉×Q₁₆	—	2	2	no	—
27	C₉×Q₁₆	—	4	1	no	—
28	C₉×Q₁₆	—	4	1	no	—
29	C₂×C₈×C₉	D₄	1	1	yes	characteristic
30	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
31	C₉×C₄⋊C₄	—	4	2	no	—
32	C₄²×C₉	D₄	1	1	yes	characteristic
33	#3667	—	2	1	no	—
34	D₇₂	D₄	1	1	yes	characteristic
35	#3664	—	2	1	no	—
36	#3663	—	4	1	no	—
37	C₈×D₉	—	4	1	no	—
38	Dic₃₆	D₄	1	1	yes	characteristic
39	C₉⋊C₁₆	—	2	2	no	—
40	#2214	—	9	1	no	Sylow
41	C₂×C₃×Q₁₆	—	2	1	no	—
42	C₂×C₃×Q₁₆	C₂×D₃	1	2	yes	—
43	C₃×C₄⋊Q₈	—	2	1	no	—
44	#904	—	3	1	no	—
45	#901	—	6	1	no	—
46	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
47	#829	—	6	2	no	—
48	#828	—	6	2	no	—
49	#819	—	3	1	no	—
50	#812	—	3	2	no	—
51	#805	—	6	1	no	—
52	Q₈×C₉	—	4	2	no	—
53	Q₈×C₉	—	4	2	no	—
54	C₂×C₄×C₉	—	2	1	no	—
55	C₂×C₄×C₉	—	4	2	no	—
56	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
57	#611	—	4	1	no	—
58	D₃₆	—	2	1	no	—
59	C₄×D₉	—	4	1	no	—
60	Dic₁₈	—	2	1	no	—
61	C₈×C₉	D₈	1	1	yes	characteristic
62	C₈×C₉	D₈	1	1	yes	characteristic
63	C₈×C₉	C₂×D₄	1	1	yes	characteristic
64	C₈×C₉	#41	1	1	yes	characteristic
65	C₉⋊C₈	—	4	1	no	—
66	#510	—	9	2	no	—
67	#494	D₉	1	1	yes	characteristic, complemented
68	#443	—	9	1	no	—
69	#364	—	9	1	no	—
70	#362	—	9	2	no	—
71	C₂×C₃×Q₈	—	2	2	no	—
72	#235	—	6	1	no	—
73	C₃×Q₁₆	—	2	2	no	—
74	C₃×Q₁₆	—	2	2	no	—
75	C₃×Q₁₆	—	4	1	no	—
76	C₃×Q₁₆	—	4	1	no	—
77	C₂×C₃×C₈	#67	1	1	yes	characteristic
78	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
79	C₃×C₄⋊C₄	—	4	2	no	—
80	C₃×C₄²	#67	1	1	yes	characteristic
81	#208	—	6	1	no	—
82	Dic₁₂	—	3	1	no	—
83	D₂₄	—	3	1	no	—
84	#204	—	6	1	no	—
85	ΓL(1,𝔽₂₅)	—	12	1	no	—
86	D₃×C₈	—	12	1	no	—
87	C₃⋊C₁₆	—	6	2	no	—
88	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
89	C₂×D₉	—	4	1	no	—
90	C₄×C₉	—	2	2	no	—
91	C₄×C₉	—	8	2	no	—
92	C₄×C₉	#121	1	1	yes	characteristic
93	C₄×C₉	C₂×D₈	1	1	yes	characteristic
94	Dic₉	—	4	1	no	—
95	#135	—	9	1	no	—
96	C₂×Q₁₆	—	2	1	no	—
97	C₂×Q₁₆	C₂×D₉	1	2	yes	—
98	#131	—	18	1	no	—
99	C₄⋊Q₈	—	2	1	no	—
100	Q₃₂	—	18	2	no	—
101	SD₃₂	—	18	2	no	—
102	M₃₂	—	9	2	no	—
103	#108	—	9	1	no	—
104	#104	—	18	1	no	—
105	C₄×C₈	C₂×D₉	1	1	yes	characteristic
106	C₃×Q₈	—	4	2	no	—
107	C₃×Q₈	—	4	2	no	—
108	C₂×C₃×C₄	—	2	1	no	—
109	C₂×C₃×C₄	—	4	2	no	—
110	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
111	#67	—	12	1	no	—
112	D₁₂	—	6	1	no	—
113	C₄×D₃	—	12	1	no	—
114	Dic₆	—	6	1	no	—
115	C₃×C₈	#213	1	1	yes	characteristic
116	C₃×C₈	#213	1	1	yes	characteristic
117	C₃×C₈	D₃×D₄	1	1	yes	characteristic
118	C₃×C₈	#237	1	1	yes	characteristic
119	C₃⋊C₈	—	12	1	no	—
120	C₂×C₉	—	2	1	no	—
121	C₂×C₉	#459	1	1	yes	characteristic
122	D₉	—	8	1	no	—
123	#41	—	18	1	no	—
124	C₂×Q₈	—	2	2	no	—
125	Q₁₆	—	2	2	no	—
126	Q₁₆	—	2	2	no	—
127	Q₁₆	—	4	1	no	—
128	Q₁₆	—	4	1	no	—
129	Q₁₆	—	9	1	no	—
130	SD₁₆	—	18	1	no	—
131	D₈	—	9	1	no	—
132	M₁₆	—	18	1	no	—
133	M₁₆	—	36	1	no	—
134	C₂×C₈	—	36	1	no	—
135	C₂×C₈	#611	1	1	yes	characteristic
136	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
137	C₄⋊C₄	—	4	2	no	—
138	C₄²	#611	1	1	yes	characteristic
139	C₁₆	—	18	2	no	—
140	C₂²×C₃	#932	1	1	yes	characteristic
141	C₂×D₃	—	12	1	no	—
142	C₃×C₄	—	2	2	no	—
143	C₃×C₄	—	8	2	no	—
144	C₃×C₄	C₂×#213	1	1	yes	characteristic
145	C₃×C₄	#938	1	1	yes	characteristic
146	Dic₃	—	12	1	no	—
147	C₉	#2214	1	1	yes	characteristic, complemented, Sylow
148	Q₈	—	4	2	no	—
149	Q₈	—	4	2	no	—
150	Q₈	—	18	1	no	—
151	D₄	—	18	1	no	—
152	D₄	—	36	1	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	—	36	1	no	—
156	C₂×C₄	C₂×#611	1	1	yes	characteristic
157	C₈	—	36	1	no	—
158	C₈	#3673	1	1	yes	characteristic
159	C₈	#3673	1	1	yes	characteristic
160	C₈	D₄×D₉	1	1	yes	characteristic
161	C₈	#3699	1	1	yes	characteristic
162	C₂×C₃	—	2	1	no	—
163	C₂×C₃	#5072	1	1	yes	characteristic
164	D₃	—	24	1	no	—
165	C₂²	—	36	1	no	—
166	C₂²	#63495	1	1	yes	characteristic
167	C₄	—	2	2	no	—
168	C₄	—	8	2	no	—
169	C₄	—	36	1	no	—
170	C₄	C₂×#3673	1	1	yes	characteristic
171	C₄	#63500	1	1	yes	characteristic
172	C₃	#71317	1	1	yes	characteristic
173	C₂	—	2	1	no	—
174	C₂	—	72	1	no	—
175	C₂	#10588754	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#494

C₂

yes

maximal, characteristic, complemented

#10588859

C₂

yes

maximal

#10588380

C₂

yes

maximal, characteristic

#10588242

C₂

yes

maximal, complemented

#10588140

C₂

yes

maximal, characteristic, complemented

#71317

—

maximal

C₂×C₉×Q₁₆

—

C₂×C₉×Q₁₆

C₂²

yes

—

C₉×C₄⋊Q₈

—

#63467

C₂²

yes

characteristic

#63464

—

C₄×C₈×C₉

C₂²

yes

—

—

C₂²

yes

characteristic

#63371

C₂²

yes

—

#63364

—

C₃×#494

D₃

yes

—

—

—

—

C₂×Q₈×C₉

—

#3697

—

C₉×Q₁₆

—

C₉×Q₁₆

—

C₉×Q₁₆

—

C₉×Q₁₆

—

C₂×C₈×C₉

D₄

yes

characteristic

C₂×C₈×C₉

C₂³

yes

characteristic

C₉×C₄⋊C₄

—

C₄²×C₉

D₄

yes

characteristic

#3667

—

D₇₂

D₄

yes

characteristic

#3664

—

#3663

—

C₈×D₉

—

Dic₃₆

D₄

yes

characteristic

C₉⋊C₁₆

—

#2214

—

Sylow

C₂×C₃×Q₁₆

—

C₂×C₃×Q₁₆

C₂×D₃

yes

—

C₃×C₄⋊Q₈

—

#904

—

#901

—

C₃×C₄×C₈

C₂×D₃

yes

—

—

—

—

—

Q₈×C₉

—

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

#611

—

D₃₆

—

C₄×D₉

—

Dic₁₈

—

C₈×C₉

D₈

yes

characteristic

C₈×C₉

D₈

yes

characteristic

C₈×C₉

C₂×D₄

yes

characteristic

C₈×C₉

#41

yes

characteristic

C₉⋊C₈

—

#510

—

#494

D₉

yes

characteristic, complemented

#443

—

#364

—

#362

—

C₂×C₃×Q₈

—

#235

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₂×C₃×C₈

#67

yes

characteristic

C₂×C₃×C₈

C₂²×D₃

yes

characteristic

C₃×C₄⋊C₄

—

C₃×C₄²

#67

yes

characteristic

#208

—

Dic₁₂

—

D₂₄

—

#204

—

ΓL(1,𝔽₂₅)

—

D₃×C₈

—

C₃⋊C₁₆

—

C₂²×C₉

AGL(1,ℤ/8)

yes

characteristic

C₂×D₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#121

yes

characteristic

C₄×C₉

C₂×D₈

yes

characteristic

Dic₉

—

#135

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₉

yes

—

#131

—

C₄⋊Q₈

—

100

Q₃₂

—

101

SD₃₂

—

102

M₃₂

—

103

#108

—

104

#104

—

105

C₄×C₈

C₂×D₉

yes

characteristic

106

C₃×Q₈

—

107

C₃×Q₈

—

108

C₂×C₃×C₄

—

109

C₂×C₃×C₄

—

110

C₂×C₃×C₄

C₂×#67

yes

characteristic

111

#67

—

112

D₁₂

—

113

C₄×D₃

—

114

Dic₆

—

115

C₃×C₈

#213

yes

characteristic

116

C₃×C₈

#213

yes

characteristic

117

C₃×C₈

D₃×D₄

yes

characteristic

118

C₃×C₈

#237

yes

characteristic

119

C₃⋊C₈

—

120

C₂×C₉

—

121

C₂×C₉

#459

yes

characteristic

122

D₉

—

123

#41

—

124

C₂×Q₈

—

125

Q₁₆

—

126

Q₁₆

—

127

Q₁₆

—

128

Q₁₆

—

129

Q₁₆

—

130

SD₁₆

—

131

D₈

—

132

M₁₆

—

133

M₁₆

—

134

C₂×C₈

—

135

C₂×C₈

#611

yes

characteristic

136

C₂×C₈

C₂²×D₉

yes

characteristic

137

C₄⋊C₄

—

138

C₄²

#611

yes

characteristic

139

C₁₆

—

140

C₂²×C₃

#932

yes

characteristic

141

C₂×D₃

—

142

C₃×C₄

—

143

C₃×C₄

—

144

C₃×C₄

C₂×#213

yes

characteristic

145

C₃×C₄

#938

yes

characteristic

146

Dic₃

—

147

C₉

#2214

yes

characteristic, complemented, Sylow

148

Q₈

—

149

Q₈

—

150

Q₈

—

151

D₄

—

152

D₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

C₂×#611

yes

characteristic

157

C₈

—

158

C₈

#3673

yes

characteristic

159

C₈

#3673

yes

characteristic

160

C₈

D₄×D₉

yes

characteristic

161

C₈

#3699

yes

characteristic

162

C₂×C₃

—

163

C₂×C₃

#5072

yes

characteristic

164

D₃

—

165

C₂²

—

166

C₂²

#63495

yes

characteristic

167

C₄

—

168

C₄

—

169

C₄

—

170

C₄

C₂×#3673

yes

characteristic

171

C₄

#63500

yes

characteristic

172

C₃

#71317

yes

characteristic

173

C₂

—

174

C₂

—

175

C₂

#10588754

yes

characteristic

	subgroup	G/H
center	C₂	#10588754
commutator, cosocle	C₂×C₈×C₉	C₂³
Frattini	C₂×C₃×C₈	C₂²×D₃
Fitting	C₉×#494	C₂
socle	C₂×C₃	#5072
prime radical	#63467	C₂²
hypercenter	#494	D₉
hypocenter	C₉	#2214
LCS	G ▷ C₂×C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #494

subgroup

G/H

center

C₂

#10588754

commutator, cosocle

C₂×C₈×C₉

C₂³

Frattini

C₂×C₃×C₈

C₂²×D₃

C₂

C₂×C₃

C₂²

D₉

C₉

G ▷ C₂×C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #494

N	H ≅ G/N	type
1. C₉×#494	C₂	semidirect
4. #10588242	C₂	semidirect
5. #10588140	C₂	semidirect
67. #494	D₉	semidirect
147. C₉	#2214	semidirect

H ≅ G/N

type

1. C₉×#494

C₂

semidirect

4. #10588242

C₂

semidirect

5. #10588140

C₂

semidirect

67. #494

D₉

semidirect

147. C₉

#2214

semidirect

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

subgroup	index
C₉×#494	2
#10588859	2
#10588380	2
#10588242	2
#10588140	2
#71317	3

subgroup

index

Subgroups — #11799126

Conjugacy classes of subgroups

Complements

Maximal subgroups