Group #14673669 — subgroups

Subgroups — #14673669

Order 2816.

276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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	#13070231	C₂	1	1	yes	maximal, characteristic
2	#13068671	C₂	1	2	yes	maximal
3	#13066718	C₂	1	1	yes	maximal, characteristic, complemented
4	#13066713	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2161	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#66954	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
8	C₂×C₁₁×#108	C₂²	1	2	yes	—
9	#10622752	—	2	2	no	—
10	#10622719	C₂²	1	2	yes	—
11	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₁₁×#368	—	2	2	no	—
13	#10622194	—	2	2	no	—
14	(C₂×D₁₁)⋊C₁₆	—	2	2	no	—
15	C₂×#4339	D₄	1	1	yes	characteristic
16	C₂×C₁₁×M₁₆	—	2	2	no	—
17	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
18	#66979	—	2	2	no	—
19	C₂×#4318	D₄	1	1	yes	characteristic
20	#66954	—	2	2	no	—
21	#66954	—	2	2	no	—
22	C₂×#4313	—	2	1	no	—
23	C₂×C₈×D₁₁	—	2	1	no	—
24	C₁₁×M₃₂	—	2	2	no	—
25	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
26	C₁₁×#108	—	2	2	no	—
27	C₁₁×#108	—	2	2	no	—
28	#66889	—	4	4	no	—
29	#66882	—	2	2	no	—
30	#66881	—	2	2	no	—
31	C₂×C₁₁⋊C₁₆	—	2	1	no	—
32	C₂×C₁₁⋊C₁₆	—	2	2	no	—
33	#13499	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₂²⋊D₁₁	—	2	1	no	—
36	#4339	—	2	2	no	—
37	#4339	—	2	2	no	—
38	C₂×D₄₄	Q₁₆	1	1	yes	characteristic
39	C₂×C₄×D₁₁	—	2	1	no	—
40	C₂×Dic₂₂	Q₁₆	1	1	yes	characteristic
41	C₁₁×M₁₆	—	4	2	no	—
42	C₁₁×M₁₆	—	4	2	no	—
43	C₂×C₈×C₁₁	—	4	2	no	—
44	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
46	C₂×C₈×C₁₁	#41	1	2	yes	—
47	C₂×C₈×C₁₁	#41	1	2	yes	—
48	C₂²⋊Dic₁₁	—	4	2	no	—
49	C₄⋊Dic₁₁	—	4	2	no	—
50	C₄×Dic₁₁	—	4	2	no	—
51	#4318	—	2	2	no	—
52	C₂×C₁₁⋊C₈	—	2	1	no	—
53	#4313	—	4	2	no	—
54	C₈×D₁₁	—	4	1	no	—
55	C₈×D₁₁	—	4	1	no	—
56	C₁₁×C₁₆	—	2	2	no	—
57	C₁₁⋊C₁₆	—	4	1	no	—
58	#2161	D₁₁	1	1	yes	characteristic, complemented
59	#2113	—	11	1	no	—
60	#1814	—	11	2	no	—
61	#1384	—	11	1	no	—
62	#1382	—	11	2	no	—
63	C₂³×C₁₁	#135	1	1	yes	characteristic
64	C₂²×D₁₁	—	2	1	no	—
65	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
66	C₂×C₄×C₁₁	#123	1	2	yes	—
67	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
68	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
69	C₂²⋊D₁₁	—	4	2	no	—
70	C₂×Dic₁₁	—	2	1	no	—
71	C₂×Dic₁₁	—	8	2	no	—
72	D₄₄	—	2	2	no	—
73	C₄×D₁₁	—	4	1	no	—
74	C₄×D₁₁	—	4	1	no	—
75	Dic₂₂	—	2	2	no	—
76	C₈×C₁₁	—	8	2	no	—
77	C₈×C₁₁	#123	1	1	yes	characteristic
78	C₈×C₁₁	#124	1	1	yes	characteristic
79	C₈×C₁₁	#126	1	2	yes	—
80	C₁₁⋊C₈	—	4	1	no	—
81	C₂×#131	—	11	1	no	—
82	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
83	C₂²×C₁₆	—	11	1	no	—
84	C₂×#108	C₂×D₁₁	1	2	yes	—
85	#427	—	11	2	no	—
86	#421	—	22	2	no	—
87	#368	—	2	2	no	—
88	C₂²⋊C₁₆	—	22	2	no	—
89	#344	—	22	2	no	—
90	C₂²×C₁₁	—	4	1	no	—
91	C₂²×C₁₁	#467	1	1	yes	characteristic
92	C₂²×C₁₁	#482	1	2	yes	—
93	C₂×D₁₁	—	4	2	no	—
94	C₂×D₁₁	—	4	1	no	—
95	C₄×C₁₁	#397	1	1	yes	characteristic
96	C₄×C₁₁	#469	1	1	yes	characteristic
97	C₄×C₁₁	#484	1	2	yes	—
98	Dic₁₁	—	4	1	no	—
99	Dic₁₁	—	16	2	no	—
100	C₂×#41	—	11	1	no	—
101	#131	—	22	2	no	—
102	#131	—	22	2	no	—
103	C₂×M₁₆	—	2	2	no	—
104	C₂×M₁₆	—	11	1	no	—
105	C₂×M₁₆	—	22	1	no	—
106	C₂²×C₈	—	22	1	no	—
107	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
108	#117	—	22	2	no	—
109	M₃₂	—	2	2	no	—
110	C₂×C₁₆	—	22	2	no	—
111	C₂×C₁₆	—	22	1	no	—
112	C₂×C₁₆	C₂²⋊D₁₁	1	2	yes	—
113	#108	—	2	2	no	—
114	#108	—	2	2	no	—
115	#107	—	22	2	no	—
116	#106	—	22	2	no	—
117	#104	—	44	4	no	—
118	C₂×C₁₁	—	2	2	no	—
119	C₂×C₁₁	—	2	1	no	—
120	C₂×C₁₁	#2076	1	1	yes	characteristic
121	D₁₁	—	8	1	no	—
122	#41	—	22	2	no	—
123	#41	—	22	2	no	—
124	C₂×Q₈	—	11	1	no	—
125	C₂×D₄	—	11	1	no	—
126	C₂×D₄	—	22	1	no	—
127	C₂²×C₄	—	22	1	no	—
128	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
129	M₁₆	—	4	2	no	—
130	M₁₆	—	4	2	no	—
131	M₁₆	—	22	2	no	—
132	M₁₆	—	44	2	no	—
133	C₂×C₈	—	4	2	no	—
134	C₂×C₈	—	22	1	no	—
135	C₂×C₈	—	44	1	no	—
136	C₂×C₈	—	44	1	no	—
137	C₂×C₈	#4339	1	2	yes	—
138	C₂×C₈	#4341	1	1	yes	characteristic
139	C₂×C₈	#4343	1	2	yes	—
140	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
141	C₄⋊C₄	—	44	2	no	—
142	C₂²⋊C₄	—	44	2	no	—
143	C₄²	—	44	2	no	—
144	C₁₆	—	2	2	no	—
145	C₁₆	—	44	1	no	—
146	C₁₁	#13499	1	1	yes	characteristic, complemented, Sylow
147	C₂³	—	22	1	no	—
148	C₂³	#66972	1	1	yes	characteristic
149	Q₈	—	22	2	no	—
150	D₄	—	22	2	no	—
151	D₄	—	44	2	no	—
152	C₂×C₄	—	22	1	no	—
153	C₂×C₄	—	44	1	no	—
154	C₂×C₄	—	44	1	no	—
155	C₂×C₄	—	88	2	no	—
156	C₂×C₄	#66947	1	2	yes	—
157	C₂×C₄	#66964	1	2	yes	—
158	C₂×C₄	Q₁₆×D₁₁	1	1	yes	characteristic
159	C₂×C₄	#66991	1	1	yes	characteristic
160	C₈	—	8	2	no	—
161	C₈	—	44	1	no	—
162	C₈	#66951	1	2	yes	—
163	C₈	#66982	1	1	yes	characteristic
164	C₈	#67000	1	1	yes	characteristic
165	C₂²	—	4	1	no	—
166	C₂²	—	44	2	no	—
167	C₂²	—	44	1	no	—
168	C₂²	#10622498	1	2	yes	—
169	C₂²	#10622801	1	1	yes	characteristic
170	C₄	—	44	1	no	—
171	C₄	—	176	2	no	—
172	C₄	#10622497	1	2	yes	—
173	C₄	#10622606	1	1	yes	characteristic
174	C₄	#10622772	1	1	yes	characteristic
175	C₂	—	2	2	no	—
176	C₂	—	2	1	no	—
177	C₂	—	88	1	no	—
178	C₂	#13070045	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13070231

C₂

yes

maximal, characteristic

#13068671

C₂

yes

maximal

#13066718

C₂

yes

maximal, characteristic, complemented

#13066713

C₂

yes

maximal, complemented

C₁₁×#2161

C₂

yes

maximal, characteristic, complemented

C₂×#66954

C₂²

yes

characteristic

C₂×C₁₁×M₃₂

C₂²

yes

characteristic

C₂×C₁₁×#108

C₂²

yes

—

#10622752

—

#10622719

C₂²

yes

—

C₂²×C₁₁⋊C₁₆

C₂²

yes

characteristic

C₁₁×#368

—

#10622194

—

(C₂×D₁₁)⋊C₁₆

—

C₂×#4339

D₄

yes

characteristic

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

C₂³

yes

characteristic

#66979

—

C₂×#4318

D₄

yes

—

—

—

C₂×C₈×D₁₁

—

C₁₁×M₃₂

—

C₂×C₁₁×C₁₆

D₄

yes

—

C₁₁×#108

—

C₁₁×#108

—

#66889

—

#66882

—

#66881

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

—

#13499

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₁

—

#4339

—

#4339

—

C₂×D₄₄

Q₁₆

yes

characteristic

C₂×C₄×D₁₁

—

C₂×Dic₂₂

Q₁₆

yes

characteristic

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂×D₄

yes

C₂×C₈×C₁₁

yes

C₂×C₈×C₁₁

yes

—

C₂×C₈×C₁₁

#41

yes

—

C₂²⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄×Dic₁₁

—

#4318

—

C₂×C₁₁⋊C₈

—

#4313

—

C₈×D₁₁

—

C₈×D₁₁

—

C₁₁×C₁₆

—

C₁₁⋊C₁₆

—

#2161

D₁₁

yes

characteristic, complemented

—

—

—

—

C₂³×C₁₁

#135

yes

characteristic

C₂²×D₁₁

—

C₂×C₄×C₁₁

#121

yes

characteristic

C₂×C₄×C₁₁

#123

yes

—

C₂×C₄×C₁₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₁

AGL(1,ℤ/8)

yes

—

C₂²⋊D₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

D₄₄

—

C₄×D₁₁

—

C₄×D₁₁

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

yes

C₈×C₁₁

yes

C₈×C₁₁

yes

—

C₁₁⋊C₈

—

C₂×#131

—

C₂×M₃₂

C₂×D₁₁

yes

characteristic

C₂²×C₁₆

—

C₂×#108

C₂×D₁₁

yes

—

#427

—

#421

—

#368

—

C₂²⋊C₁₆

—

#344

—

C₂²×C₁₁

—

C₂²×C₁₁

#467

yes

characteristic

C₂²×C₁₁

#482

yes

—

C₂×D₁₁

—

C₂×D₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

Dic₁₁

—

Dic₁₁

—

100

C₂×#41

—

101

#131

—

102

#131

—

103

C₂×M₁₆

—

104

C₂×M₁₆

—

105

C₂×M₁₆

—

106

C₂²×C₈

—

107

C₂²×C₈

C₂²×D₁₁

yes

characteristic

108

#117

—

109

M₃₂

—

110

C₂×C₁₆

—

111

C₂×C₁₆

—

112

C₂×C₁₆

C₂²⋊D₁₁

yes

—

113

#108

—

114

#108

—

115

#107

—

116

#106

—

117

#104

—

118

C₂×C₁₁

—

119

C₂×C₁₁

—

120

C₂×C₁₁

#2076

yes

characteristic

121

D₁₁

—

122

#41

—

123

#41

—

124

C₂×Q₈

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂²×C₄

—

128

C₂²×C₄

D₄×D₁₁

yes

characteristic

129

M₁₆

—

130

M₁₆

—

131

M₁₆

—

132

M₁₆

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

#4339

yes

—

138

C₂×C₈

#4341

yes

characteristic

139

C₂×C₈

#4343

yes

—

140

C₂×C₈

C₂×C₂²⋊D₁₁

yes

characteristic

141

C₄⋊C₄

—

142

C₂²⋊C₄

—

143

C₄²

—

144

C₁₆

—

145

C₁₆

—

146

C₁₁

#13499

yes

characteristic, complemented, Sylow

147

C₂³

—

148

C₂³

#66972

yes

characteristic

149

Q₈

—

150

D₄

—

151

D₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

#66947

yes

—

157

C₂×C₄

#66964

yes

—

158

C₂×C₄

Q₁₆×D₁₁

yes

characteristic

159

C₂×C₄

#66991

yes

characteristic

160

C₈

—

161

C₈

—

162

C₈

#66951

yes

—

163

C₈

#66982

yes

characteristic

164

C₈

#67000

yes

characteristic

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

#10622498

yes

—

169

C₂²

#10622801

yes

characteristic

170

C₄

—

171

C₄

—

176

—

172

C₄

#10622497

yes

—

173

C₄

#10622606

yes

characteristic

174

C₄

#10622772

yes

characteristic

175

C₂

—

176

C₂

—

177

C₂

—

178

C₂

#13070045

yes

characteristic

	subgroup	G/H
center	C₄	#10622772
commutator, cosocle	C₂²×C₈×C₁₁	C₂³
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#2161	C₂
socle	C₂×C₁₁	#2076
prime radical	C₂×#4339	D₄
hypercenter	#2161	D₁₁
hypocenter	C₁₁	#13499
LCS	G ▷ C₂²×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2161

subgroup

G/H

center

C₄

#10622772

commutator, cosocle

C₂²×C₈×C₁₁

C₂³

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#2161

C₂

C₂×C₁₁

D₄

D₁₁

C₁₁

G ▷ C₂²×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2161

N	H ≅ G/N	type
3. #13066718	C₂	semidirect
4. #13066713	C₂	semidirect
5. C₁₁×#2161	C₂	semidirect
58. #2161	D₁₁	semidirect
146. C₁₁	#13499	semidirect

H ≅ G/N

type

3. #13066718

C₂

semidirect

4. #13066713

C₂

semidirect

5. C₁₁×#2161

C₂

semidirect

58. #2161

D₁₁

semidirect

146. C₁₁

#13499

semidirect

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

subgroup	index
#13070231	2
#13068671	2
#13066718	2
#13066713	2
C₁₁×#2161	2
#13499	11

subgroup

index

C₁₁×#2161

Subgroups — #14673669

Conjugacy classes of subgroups

Complements

Maximal subgroups