Group #14653207 — subgroups

Subgroups — #14653207

Order 2816.

414 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 155 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	C₂×#10622293	C₂	1	1	yes	maximal, characteristic
2	#13068788	C₂	1	1	yes	maximal, characteristic
3	#13067300	C₂	1	2	yes	maximal
4	#13067296	C₂	1	2	yes	maximal
5	C₁₁×#1450	C₂	1	1	yes	maximal, characteristic
6	C₂×#66922	C₂²	1	2	yes	—
7	C₁₁×#431	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×#66883	—	2	2	no	—
10	C₂×#66881	—	2	2	no	—
11	#10622537	C₂²	1	1	yes	characteristic
12	#10622537	C₂²	1	1	yes	characteristic
13	#10622293	—	2	1	no	—
14	#10622293	—	2	1	no	—
15	#10622293	C₄	1	4	yes	—
16	C₁₁×#322	—	2	1	no	—
17	C₈²×C₁₁	—	2	1	no	—
18	#10622120	—	2	4	no	—
19	#10622119	—	2	4	no	—
20	C₂²×Dic₂₂	—	2	2	no	—
21	C₂²×C₈×C₁₁	D₄	1	2	yes	—
22	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₁	—	2	2	no	—
24	C₂×C₄⋊Dic₁₁	—	2	2	no	—
25	C₂×#4318	—	2	1	no	—
26	C₂×#4318	—	2	1	no	—
27	#66922	—	2	2	no	—
28	#66922	—	2	2	no	—
29	#66922	—	2	2	no	—
30	#66922	C₂×C₄	1	4	yes	—
31	C₁₁×C₄⋊C₈	D₄	1	4	yes	—
32	C₁₁×C₂²⋊C₈	—	2	2	no	—
33	C₄×C₈×C₁₁	—	2	2	no	—
34	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
36	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
37	#66883	—	4	4	no	—
38	#66881	—	2	4	no	—
39	#66881	—	2	4	no	—
40	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
42	#9767	—	11	1	no	maximal, Sylow
43	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₁	#41	1	2	yes	—
45	C₂²×Dic₁₁	—	4	2	no	—
46	C₂×Dic₂₂	—	2	4	no	—
47	C₂×Dic₂₂	—	4	2	no	—
48	C₂×Dic₂₂	—	8	4	no	—
49	C₂×C₈×C₁₁	—	2	4	no	—
50	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
51	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
52	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
53	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
54	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
55	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₄²×C₁₁	C₂×D₄	1	2	yes	—
57	C₄⋊Dic₁₁	—	2	4	no	—
58	C₄⋊Dic₁₁	—	2	4	no	—
59	C₄⋊Dic₁₁	—	4	2	no	—
60	C₄⋊Dic₁₁	—	4	2	no	—
61	#4318	—	4	2	no	—
62	#4318	—	4	2	no	—
63	C₂×C₁₁⋊C₈	—	4	1	no	—
64	C₂×C₁₁⋊C₈	—	4	1	no	—
65	C₂×#498	—	11	1	no	—
66	#1848	—	11	1	no	—
67	#1549	—	11	2	no	—
68	#1548	—	11	2	no	—
69	#1450	D₁₁	1	1	yes	characteristic
70	C₂³×C₁₁	#124	1	1	yes	characteristic
71	C₂×C₄×C₁₁	—	2	4	no	—
72	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
74	C₂×C₄×C₁₁	#121	1	2	yes	—
75	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
76	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
77	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
78	C₂×Dic₁₁	—	4	4	no	—
79	C₂×Dic₁₁	—	8	4	no	—
80	Dic₂₂	—	8	4	no	—
81	Dic₂₂	—	8	4	no	—
82	C₈×C₁₁	—	4	4	no	—
83	C₈×C₁₁	#103	1	4	yes	—
84	C₈×C₁₁	#103	1	4	yes	—
85	C₁₁⋊C₈	—	8	1	no	—
86	C₁₁⋊C₈	—	8	1	no	—
87	C₂×C₄⋊Q₈	—	11	2	no	—
88	#498	—	11	4	no	—
89	#498	—	22	1	no	—
90	#498	—	22	1	no	—
91	#431	C₂×D₁₁	1	2	yes	—
92	C₂×#108	—	22	2	no	—
93	C₂×#106	—	22	2	no	—
94	#423	—	11	1	no	—
95	#423	—	11	1	no	—
96	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
97	#333	—	22	4	no	—
98	#332	—	22	4	no	—
99	#322	—	2	1	no	—
100	C₈²	—	2	1	no	—
101	C₂²×C₁₁	—	2	2	no	—
102	C₂²×C₁₁	#390	1	1	yes	characteristic
103	C₂²×C₁₁	#487	1	2	yes	—
104	C₄×C₁₁	—	2	2	no	—
105	C₄×C₁₁	C₂×#103	1	2	yes	—
106	C₄×C₁₁	#471	1	4	yes	—
107	C₄×C₁₁	#492	1	1	yes	characteristic
108	C₄×C₁₁	#494	1	1	yes	characteristic
109	Dic₁₁	—	8	4	no	—
110	C₂²×Q₈	—	22	2	no	—
111	C₂×M₁₆	—	22	1	no	—
112	C₂×M₁₆	—	22	1	no	—
113	C₂²×C₈	D₄₄	1	2	yes	—
114	C₄⋊Q₈	—	11	4	no	—
115	C₄⋊Q₈	—	22	2	no	—
116	C₄⋊Q₈	—	22	2	no	—
117	C₄⋊Q₈	—	22	2	no	—
118	C₂×C₄⋊C₄	—	22	2	no	—
119	C₂×C₄⋊C₄	—	22	2	no	—
120	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
121	#108	—	44	4	no	—
122	#106	—	22	4	no	—
123	#106	—	22	4	no	—
124	C₄⋊C₈	—	22	2	no	—
125	C₄⋊C₈	—	22	2	no	—
126	C₄⋊C₈	D₄₄	1	4	yes	—
127	C₂²⋊C₈	—	2	2	no	—
128	C₄×C₈	—	2	2	no	—
129	C₄×C₈	C₄×D₁₁	1	2	yes	—
130	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
131	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
132	C₂×C₁₁	—	2	2	no	—
133	C₂×C₁₁	#1956	1	1	yes	characteristic
134	C₂×C₁₁	#1977	1	2	yes	—
135	C₂×Q₈	—	22	4	no	—
136	C₂×Q₈	—	44	2	no	—
137	C₂×Q₈	—	88	4	no	—
138	C₂²×C₄	—	44	2	no	—
139	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
140	C₂²×C₄	#4339	1	2	yes	—
141	M₁₆	—	44	2	no	—
142	M₁₆	—	44	2	no	—
143	C₂×C₈	—	2	4	no	—
144	C₂×C₈	—	44	1	no	—
145	C₂×C₈	—	44	1	no	—
146	C₂×C₈	#4314	1	4	yes	—
147	C₂×C₈	Dic₄₄	1	4	yes	—
148	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
149	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
150	C₄⋊C₄	—	22	4	no	—
151	C₄⋊C₄	—	22	4	no	—
152	C₄⋊C₄	—	44	2	no	—
153	C₄⋊C₄	—	44	2	no	—
154	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
155	C₄²	C₂×D₄₄	1	2	yes	—
156	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
157	C₁₁	#9767	1	1	yes	characteristic, complemented, Sylow
158	C₂³	#66928	1	1	yes	characteristic
159	Q₈	—	88	4	no	—
160	Q₈	—	88	4	no	—
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	44	4	no	—
163	C₂×C₄	—	88	4	no	—
164	C₂×C₄	C₄×D₄₄	1	2	yes	—
165	C₂×C₄	#66927	1	1	yes	characteristic
166	C₂×C₄	C₂×#4314	1	2	yes	—
167	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
168	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
169	C₂×C₄	#66983	1	2	yes	—
170	C₈	—	4	4	no	—
171	C₈	—	88	1	no	—
172	C₈	—	88	1	no	—
173	C₈	#66880	1	4	yes	—
174	C₈	#66880	1	4	yes	—
175	C₂²	—	2	2	no	—
176	C₂²	#10622294	1	2	yes	—
177	C₂²	#10622552	1	1	yes	characteristic
178	C₄	—	2	2	no	—
179	C₄	—	88	4	no	—
180	C₄	#10622306	1	1	yes	characteristic
181	C₄	#10622312	1	1	yes	characteristic
182	C₄	C₂×#66880	1	2	yes	—
183	C₄	#10622754	1	4	yes	—
184	C₂	—	2	2	no	—
185	C₂	#13069418	1	1	yes	characteristic
186	C₂	#13069519	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622293

C₂

yes

maximal, characteristic

#13068788

C₂

yes

maximal, characteristic

#13067300

C₂

yes

maximal

#13067296

C₂

yes

maximal

C₁₁×#1450

C₂

yes

maximal, characteristic

C₂×#66922

C₂²

yes

—

C₁₁×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

—

—

C₂²

yes

characteristic

#10622537

C₂²

yes

—

—

C₄

yes

—

C₁₁×#322

—

C₈²×C₁₁

—

#10622120

—

#10622119

—

C₂²×Dic₂₂

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

—

—

—

—

—

C₂×C₄

yes

—

C₁₁×C₄⋊C₈

D₄

yes

—

C₁₁×C₂²⋊C₈

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

—

—

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#9767

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₂×C₈×C₁₁

Q₁₆

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

#124

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

—

C₂×C₄×C₁₁

#121

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

#103

yes

—

C₈×C₁₁

#103

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₂×C₄⋊Q₈

—

—

—

—

C₂×D₁₁

yes

—

—

—

—

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

100

C₈²

—

101

C₂²×C₁₁

—

102

C₂²×C₁₁

#390

yes

characteristic

103

C₂²×C₁₁

#487

yes

—

104

C₄×C₁₁

—

105

C₄×C₁₁

C₂×#103

yes

—

106

C₄×C₁₁

#471

yes

—

107

C₄×C₁₁

#492

yes

characteristic

108

C₄×C₁₁

#494

yes

characteristic

109

Dic₁₁

—

110

C₂²×Q₈

—

111

C₂×M₁₆

—

112

C₂×M₁₆

—

113

C₂²×C₈

D₄₄

yes

—

114

C₄⋊Q₈

—

115

C₄⋊Q₈

—

116

C₄⋊Q₈

—

117

C₄⋊Q₈

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄²

C₂²×D₁₁

yes

characteristic

121

#108

—

122

#106

—

123

#106

—

124

C₄⋊C₈

—

125

C₄⋊C₈

—

126

C₄⋊C₈

D₄₄

yes

—

127

C₂²⋊C₈

—

128

C₄×C₈

—

129

C₄×C₈

C₄×D₁₁

yes

—

130

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

131

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

132

C₂×C₁₁

—

133

C₂×C₁₁

#1956

yes

characteristic

134

C₂×C₁₁

#1977

yes

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂²×C₄

—

139

C₂²×C₄

C₂×D₄₄

yes

characteristic

140

C₂²×C₄

#4339

yes

—

141

M₁₆

—

142

M₁₆

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

#4314

yes

—

147

C₂×C₈

Dic₄₄

yes

—

148

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

149

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄²

C₂×C₄×D₁₁

yes

characteristic

155

C₄²

C₂×D₄₄

yes

—

156

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

157

C₁₁

#9767

yes

characteristic, complemented, Sylow

158

C₂³

#66928

yes

characteristic

159

Q₈

—

160

Q₈

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

C₄×D₄₄

yes

—

165

C₂×C₄

#66927

yes

characteristic

166

C₂×C₄

C₂×#4314

yes

—

167

C₂×C₄

C₂×Dic₄₄

yes

—

168

C₂×C₄

C₂×(C₂×D₁₁)⋊C₄

yes

characteristic

169

C₂×C₄

#66983

yes

—

170

C₈

—

171

C₈

—

172

C₈

—

173

C₈

#66880

yes

—

174

C₈

#66880

yes

—

175

C₂²

—

176

C₂²

#10622294

yes

—

177

C₂²

#10622552

yes

characteristic

178

C₄

—

179

C₄

—

180

C₄

#10622306

yes

characteristic

181

C₄

#10622312

yes

characteristic

182

C₄

C₂×#66880

yes

—

183

C₄

#10622754

yes

—

184

C₂

—

185

C₂

#13069418

yes

characteristic

186

C₂

#13069519

yes

—

	subgroup	G/H
center	C₂²	#10622552
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1450	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂³×C₁₁	#124
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1450	D₁₁
hypocenter	C₁₁	#9767
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

subgroup

G/H

center

C₂²

#10622552

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1450

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

N	H ≅ G/N	type
157. C₁₁	#9767	semidirect

H ≅ G/N

type

157. C₁₁

#9767

semidirect

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

subgroup	index
C₂×#10622293	2
#13068788	2
#13067300	2
#13067296	2
C₁₁×#1450	2
#9767	11

subgroup

index

C₁₁×#1450

Subgroups — #14653207

Conjugacy classes of subgroups

Complements

Maximal subgroups