Group #14653237 — subgroups

Subgroups — #14653237

Order 2816.

478 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 159 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	#13068788	C₂	1	1	yes	maximal, characteristic
2	#13067288	C₂	1	4	yes	maximal
3	#13066899	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₁×Q₁₆	—	2	2	no	—
6	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₁₁×#494	—	2	1	no	—
8	C₁₁×#494	—	2	1	no	—
9	C₁₁×#494	C₄	1	4	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×#66883	—	2	2	no	—
12	#10622538	C₂²	1	2	yes	—
13	#10622537	C₂²	1	2	yes	—
14	#10622185	—	2	8	no	—
15	#10622093	—	2	1	no	—
16	C₈×C₁₁⋊C₈	—	2	1	no	—
17	C₂²×Q₈×C₁₁	—	2	2	no	—
18	C₂×C₁₁×Q₁₆	—	2	4	no	—
19	C₂×C₁₁×Q₁₆	—	2	4	no	—
20	C₂×C₁₁×Q₁₆	—	4	4	no	—
21	C₂×C₁₁×Q₁₆	—	4	4	no	—
22	C₂²×C₈×C₁₁	D₄	1	2	yes	—
23	C₁₁×C₄⋊Q₈	—	2	4	no	—
24	C₁₁×C₄⋊Q₈	—	2	2	no	—
25	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
26	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
27	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
28	C₂×#4318	—	2	2	no	—
29	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
31	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
32	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
33	#66883	—	4	4	no	—
34	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
35	C₄⋊(C₁₁⋊C₈)	D₄	1	4	yes	—
36	C₄×C₁₁⋊C₈	—	2	2	no	—
37	#9772	—	11	1	no	maximal, Sylow
38	C₂×Q₈×C₁₁	—	2	4	no	—
39	C₂×Q₈×C₁₁	—	4	2	no	—
40	C₂×Q₈×C₁₁	—	4	4	no	—
41	C₂×Q₈×C₁₁	—	4	4	no	—
42	C₂²×C₄×C₁₁	—	4	2	no	—
43	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₁	#41	1	2	yes	—
45	C₁₁×Q₁₆	—	4	8	no	—
46	C₁₁×Q₁₆	—	4	8	no	—
47	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
48	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
49	C₂×C₈×C₁₁	D₈	1	4	yes	—
50	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
51	C₁₁×C₄⋊C₄	—	2	8	no	—
52	C₁₁×C₄⋊C₄	—	4	4	no	—
53	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
54	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₄²×C₁₁	C₂×D₄	1	2	yes	—
56	#4318	—	4	4	no	—
57	C₂×C₁₁⋊C₈	—	2	4	no	—
58	C₂×C₁₁⋊C₈	—	4	2	no	—
59	C₂×#494	D₁₁	1	1	yes	characteristic
60	#1848	—	11	1	no	—
61	#1546	—	11	4	no	—
62	#1450	—	11	1	no	—
63	C₂³×C₁₁	#124	1	1	yes	characteristic
64	Q₈×C₁₁	—	4	8	no	—
65	Q₈×C₁₁	—	8	2	no	—
66	Q₈×C₁₁	—	8	2	no	—
67	C₂×C₄×C₁₁	—	2	4	no	—
68	C₂×C₄×C₁₁	—	4	4	no	—
69	C₂×C₄×C₁₁	—	8	4	no	—
70	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
72	C₂×C₄×C₁₁	#121	1	2	yes	—
73	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
75	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
76	C₈×C₁₁	#102	1	4	yes	—
77	C₈×C₁₁	#102	1	4	yes	—
78	C₁₁⋊C₈	—	4	4	no	—
79	C₁₁⋊C₈	—	8	2	no	—
80	C₂²×Q₁₆	—	2	2	no	—
81	C₂×C₄⋊Q₈	C₂×D₁₁	1	2	yes	—
82	#494	—	2	1	no	—
83	#494	—	2	1	no	—
84	#494	Dic₁₁	1	4	yes	—
85	#431	—	11	2	no	—
86	C₂×#108	—	22	2	no	—
87	#423	—	11	2	no	—
88	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
89	#332	—	22	8	no	—
90	#322	—	22	1	no	—
91	C₈²	—	22	1	no	—
92	C₂²×C₁₁	—	2	2	no	—
93	C₂²×C₁₁	#390	1	1	yes	characteristic
94	C₂²×C₁₁	#486	1	2	yes	—
95	C₄×C₁₁	—	2	2	no	—
96	C₄×C₁₁	—	8	4	no	—
97	C₄×C₁₁	C₂×#102	1	2	yes	—
98	C₄×C₁₁	#473	1	4	yes	—
99	C₄×C₁₁	#492	1	1	yes	characteristic
100	C₄×C₁₁	#493	1	1	yes	characteristic
101	C₂²×Q₈	—	2	2	no	—
102	C₂×Q₁₆	—	2	4	no	—
103	C₂×Q₁₆	—	2	4	no	—
104	C₂×Q₁₆	—	4	4	no	—
105	C₂×Q₁₆	—	4	4	no	—
106	C₂×M₁₆	—	22	2	no	—
107	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
108	C₄⋊Q₈	—	2	4	no	—
109	C₄⋊Q₈	—	2	2	no	—
110	C₄⋊Q₈	C₂×Dic₁₁	1	4	yes	—
111	C₂×C₄⋊C₄	—	2	4	no	—
112	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
113	#108	—	44	4	no	—
114	C₄⋊C₈	—	11	4	no	—
115	C₄⋊C₈	—	22	4	no	—
116	C₂²⋊C₈	—	22	2	no	—
117	C₄×C₈	—	22	2	no	—
118	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
119	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
120	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
121	C₂×C₁₁	—	2	2	no	—
122	C₂×C₁₁	#1957	1	1	yes	characteristic
123	C₂×C₁₁	#1979	1	2	yes	—
124	C₂×Q₈	—	2	4	no	—
125	C₂×Q₈	—	4	2	no	—
126	C₂×Q₈	—	4	4	no	—
127	C₂×Q₈	—	4	4	no	—
128	C₂²×C₄	—	4	2	no	—
129	C₂²×C₄	#4341	1	2	yes	—
130	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
131	Q₁₆	—	4	8	no	—
132	Q₁₆	—	4	8	no	—
133	M₁₆	—	44	4	no	—
134	C₂×C₈	—	22	4	no	—
135	C₂×C₈	—	44	2	no	—
136	C₂×C₈	#4323	1	4	yes	—
137	C₂×C₈	#4324	1	4	yes	—
138	C₂×C₈	C₂²⋊Dic₁₁	1	2	yes	—
139	C₂×C₈	C₂²⋊Dic₁₁	1	2	yes	—
140	C₄⋊C₄	—	2	8	no	—
141	C₄⋊C₄	—	4	4	no	—
142	C₄²	D₄×D₁₁	1	2	yes	—
143	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
144	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
145	C₁₁	#9772	1	1	yes	characteristic, complemented, Sylow
146	C₂³	#66989	1	1	yes	characteristic
147	Q₈	—	4	8	no	—
148	Q₈	—	8	2	no	—
149	Q₈	—	8	2	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	4	4	no	—
152	C₂×C₄	—	8	4	no	—
153	C₂×C₄	C₂×#4323	1	2	yes	—
154	C₂×C₄	C₂×#4324	1	2	yes	—
155	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
156	C₂×C₄	#66991	1	2	yes	—
157	C₂×C₄	#66993	1	1	yes	characteristic
158	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
159	C₈	—	44	4	no	—
160	C₈	—	88	2	no	—
161	C₈	#66896	1	4	yes	—
162	C₈	#66896	1	4	yes	—
163	C₂²	—	2	2	no	—
164	C₂²	#10622683	1	2	yes	—
165	C₂²	#10622834	1	1	yes	characteristic
166	C₄	—	2	2	no	—
167	C₄	—	8	4	no	—
168	C₄	#10622686	1	1	yes	characteristic
169	C₄	#10622689	1	1	yes	characteristic
170	C₄	#10622805	1	4	yes	—
171	C₄	C₂×#66896	1	2	yes	—
172	C₂	—	2	2	no	—
173	C₂	#13069423	1	1	yes	characteristic
174	C₂	#13069532	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068788

C₂

yes

maximal, characteristic

#13067288

C₂

yes

maximal

#13066899

C₂

yes

maximal, characteristic

C₂×C₁₁×#494

C₂

yes

maximal, characteristic

C₂²×C₁₁×Q₁₆

—

C₂×C₁₁×C₄⋊Q₈

C₂²

yes

—

C₁₁×#494

—

C₁₁×#494

—

C₁₁×#494

C₄

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

—

#10622538

C₂²

yes

—

#10622537

C₂²

yes

—

#10622185

—

#10622093

—

C₈×C₁₁⋊C₈

—

C₂²×Q₈×C₁₁

—

C₂×C₁₁×Q₁₆

—

C₂×C₁₁×Q₁₆

—

C₂×C₁₁×Q₁₆

—

C₂×C₁₁×Q₁₆

—

C₂²×C₈×C₁₁

D₄

yes

—

C₁₁×C₄⋊Q₈

—

C₁₁×C₄⋊Q₈

—

C₁₁×C₄⋊Q₈

C₂×C₄

yes

—

C₂×C₁₁×C₄⋊C₄

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×#4318

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

characteristic

C₂²⋊(C₁₁⋊C₈)

—

#66883

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

D₄

yes

—

C₄×C₁₁⋊C₈

—

#9772

—

maximal, Sylow

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₁₁×Q₁₆

—

C₁₁×Q₁₆

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×#494

D₁₁

yes

—

—

—

C₂³×C₁₁

#124

yes

characteristic

Q₈×C₁₁

—

Q₈×C₁₁

—

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

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×D₈

yes

—

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₈×C₁₁

#102

yes

—

C₈×C₁₁

#102

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

C₂×D₁₁

yes

—

#494

—

#494

—

#494

Dic₁₁

yes

—

#431

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#332

—

#322

—

C₈²

—

C₂²×C₁₁

—

C₂²×C₁₁

#390

yes

characteristic

C₂²×C₁₁

#486

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

C₂×#102

yes

—

C₄×C₁₁

#473

yes

—

C₄×C₁₁

#492

yes

characteristic

100

C₄×C₁₁

#493

yes

characteristic

101

C₂²×Q₈

—

102

C₂×Q₁₆

—

103

C₂×Q₁₆

—

104

C₂×Q₁₆

—

105

C₂×Q₁₆

—

106

C₂×M₁₆

—

107

C₂²×C₈

C₂²⋊D₁₁

yes

—

108

C₄⋊Q₈

—

109

C₄⋊Q₈

—

110

C₄⋊Q₈

C₂×Dic₁₁

yes

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄²

C₂²×D₁₁

yes

characteristic

113

#108

—

114

C₄⋊C₈

—

115

C₄⋊C₈

—

116

C₂²⋊C₈

—

117

C₄×C₈

—

118

C₄×C₈

C₂×Dic₁₁

yes

—

119

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

120

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

121

C₂×C₁₁

—

122

C₂×C₁₁

#1957

yes

characteristic

123

C₂×C₁₁

#1979

yes

—

124

C₂×Q₈

—

125

C₂×Q₈

—

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂²×C₄

—

129

C₂²×C₄

#4341

yes

—

130

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

131

Q₁₆

—

132

Q₁₆

—

133

M₁₆

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

#4323

yes

—

137

C₂×C₈

#4324

yes

—

138

C₂×C₈

C₂²⋊Dic₁₁

yes

—

139

C₂×C₈

C₂²⋊Dic₁₁

yes

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄²

D₄×D₁₁

yes

—

143

C₄²

C₂²×Dic₁₁

yes

characteristic

144

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

145

C₁₁

#9772

yes

characteristic, complemented, Sylow

146

C₂³

#66989

yes

characteristic

147

Q₈

—

148

Q₈

—

149

Q₈

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

C₂×#4323

yes

—

154

C₂×C₄

C₂×#4324

yes

—

155

C₂×C₄

D₄×Dic₁₁

yes

—

156

C₂×C₄

#66991

yes

—

157

C₂×C₄

#66993

yes

characteristic

158

C₂×C₄

C₂×C₂²⋊Dic₁₁

yes

characteristic

159

C₈

—

160

C₈

—

161

C₈

#66896

yes

—

162

C₈

#66896

yes

—

163

C₂²

—

164

C₂²

#10622683

yes

—

165

C₂²

#10622834

yes

characteristic

166

C₄

—

167

C₄

—

168

C₄

#10622686

yes

characteristic

169

C₄

#10622689

yes

characteristic

170

C₄

#10622805

yes

—

171

C₄

C₂×#66896

yes

—

172

C₂

—

173

C₂

#13069423

yes

characteristic

174

C₂

#13069532

yes

—

	subgroup	G/H
center	C₂²	#10622834
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₁₁×#494	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂³×C₁₁	#124
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#494	D₁₁
hypocenter	C₁₁	#9772
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂²

#10622834

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₂×C₁₁×#494

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
145. C₁₁	#9772	semidirect

H ≅ G/N

type

145. C₁₁

#9772

semidirect

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

subgroup	index
#13068788	2
#13067288	2
#13066899	2
C₂×C₁₁×#494	2
#9772	11

subgroup

index

C₂×C₁₁×#494

Subgroups — #14653237

Conjugacy classes of subgroups

Complements

Maximal subgroups