Group #14647579 — subgroups

Subgroups — #14647579

Order 2816.

322 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 143 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	#13068753	C₂	1	2	yes	maximal
2	#13067374	C₂	1	2	yes	maximal
3	#13067372	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1566	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#423	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	#10622537	C₂²	1	2	yes	—
9	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
11	C₁₁×#334	—	2	2	no	—
12	#10622196	—	2	4	no	—
13	#10622117	—	2	4	no	—
14	#10622095	—	2	2	no	—
15	C₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
16	C₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
17	C₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
18	C₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
19	C₂×C₁₁×M₁₆	—	2	2	no	—
20	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
21	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
22	C₂×#4318	—	2	2	no	—
23	C₂²×C₁₁⋊C₈	D₄	1	2	yes	—
24	C₂²×C₁₁⋊C₈	Q₈	1	2	yes	—
25	C₁₁×C₄⋊C₈	—	2	2	no	—
26	C₁₁×C₄⋊C₈	—	2	2	no	—
27	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₁₁	D₄	1	2	yes	—
30	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
32	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
33	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
35	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₁₁⋊C₈	D₄	1	2	yes	—
37	C₄×C₁₁⋊C₈	Q₈	1	2	yes	—
38	#8824	—	11	1	no	maximal, Sylow
39	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
42	C₁₁×M₁₆	—	4	4	no	—
43	C₂×C₈×C₁₁	—	2	4	no	—
44	C₂×C₈×C₁₁	—	4	2	no	—
45	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
46	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
47	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
48	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
49	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
50	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
51	#4318	—	4	4	no	—
52	C₂×C₁₁⋊C₈	—	2	4	no	—
53	C₂×C₁₁⋊C₈	—	2	4	no	—
54	C₂×C₁₁⋊C₈	—	4	2	no	—
55	C₂×C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
56	C₂×C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
57	C₂×C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
58	C₂×C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
59	#1837	—	11	2	no	—
60	#1567	—	11	2	no	—
61	#1566	—	11	1	no	—
62	#1566	D₁₁	1	1	yes	characteristic
63	C₂×C₈²	—	11	1	no	—
64	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
65	C₂×C₄×C₁₁	—	2	2	no	—
66	C₂×C₄×C₁₁	—	2	2	no	—
67	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
71	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
73	C₂×C₄×C₁₁	#135	1	4	yes	—
74	C₈×C₁₁	—	2	2	no	—
75	C₈×C₁₁	—	8	2	no	—
76	C₈×C₁₁	#108	1	4	yes	—
77	C₁₁⋊C₈	—	2	2	no	—
78	C₁₁⋊C₈	—	2	2	no	—
79	C₁₁⋊C₈	—	2	2	no	—
80	C₁₁⋊C₈	—	8	2	no	—
81	C₁₁⋊C₈	#108	1	4	yes	—
82	#423	—	11	2	no	—
83	#423	C₂×D₁₁	1	2	yes	—
84	C₂×C₄×C₈	—	11	1	no	—
85	C₂×C₄×C₈	—	11	1	no	—
86	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
87	#341	—	22	4	no	—
88	#335	—	22	4	no	—
89	#334	—	2	2	no	—
90	#334	—	22	2	no	—
91	C₈²	—	11	1	no	—
92	C₈²	—	11	1	no	—
93	C₈²	—	11	1	no	—
94	C₈²	—	11	1	no	—
95	C₂²×C₁₁	—	2	1	no	—
96	C₂²×C₁₁	—	2	1	no	—
97	C₂²×C₁₁	#384	1	1	yes	characteristic
98	C₂²×C₁₁	#499	1	2	yes	—
99	C₄×C₁₁	—	2	1	no	—
100	C₄×C₁₁	—	2	1	no	—
101	C₄×C₁₁	#427	1	2	yes	—
102	C₄×C₁₁	C₂×#108	1	2	yes	—
103	C₄×C₁₁	C₂×#108	1	2	yes	—
104	C₄×C₁₁	#495	1	2	yes	—
105	C₂×M₁₆	—	2	2	no	—
106	C₂×M₁₆	—	22	2	no	—
107	C₂²×C₈	—	11	2	no	—
108	C₂²×C₈	—	11	2	no	—
109	C₂²×C₈	Dic₂₂	1	2	yes	—
110	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
111	C₄⋊C₈	—	2	2	no	—
112	C₄⋊C₈	—	2	2	no	—
113	C₄⋊C₈	—	22	2	no	—
114	C₄⋊C₈	—	22	2	no	—
115	C₄×C₈	—	11	1	no	—
116	C₄×C₈	—	11	1	no	—
117	C₄×C₈	—	11	1	no	—
118	C₄×C₈	—	11	1	no	—
119	C₄×C₈	—	11	2	no	—
120	C₄×C₈	—	11	2	no	—
121	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
122	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
123	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
124	C₂×C₁₁	—	2	2	no	—
125	C₂×C₁₁	#1846	1	1	yes	characteristic
126	C₂×C₁₁	#1848	1	1	yes	characteristic
127	C₂×C₁₁	#1848	1	1	yes	characteristic
128	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
129	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
130	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
131	M₁₆	—	4	4	no	—
132	M₁₆	—	44	4	no	—
133	C₂×C₈	—	2	4	no	—
134	C₂×C₈	—	4	2	no	—
135	C₂×C₈	—	11	2	no	—
136	C₂×C₈	—	11	2	no	—
137	C₂×C₈	—	11	2	no	—
138	C₂×C₈	—	11	2	no	—
139	C₂×C₈	—	22	4	no	—
140	C₂×C₈	—	22	4	no	—
141	C₂×C₈	—	44	2	no	—
142	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
143	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
144	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
145	C₄²	D₄×D₁₁	1	1	yes	characteristic
146	C₄²	Q₈×D₁₁	1	1	yes	characteristic
147	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
148	C₁₁	#8824	1	1	yes	characteristic, complemented, Sylow
149	C₂³	#66941	1	1	yes	characteristic
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	#66941	1	1	yes	characteristic
153	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
154	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
155	C₂×C₄	#66969	1	4	yes	—
156	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
157	C₂×C₄	#66993	1	1	yes	characteristic
158	C₂×C₄	#66997	1	1	yes	characteristic
159	C₈	—	2	2	no	—
160	C₈	—	8	2	no	—
161	C₈	—	11	4	no	—
162	C₈	—	22	2	no	—
163	C₈	—	22	2	no	—
164	C₈	—	22	2	no	—
165	C₈	—	88	2	no	—
166	C₈	#66886	1	4	yes	—
167	C₂²	—	2	1	no	—
168	C₂²	—	2	1	no	—
169	C₂²	#10622471	1	2	yes	—
170	C₂²	#10622589	1	1	yes	characteristic
171	C₄	—	2	1	no	—
172	C₄	—	2	1	no	—
173	C₄	#10622473	1	2	yes	—
174	C₄	D₁₁×#108	1	2	yes	—
175	C₄	C₂×#66886	1	2	yes	—
176	C₄	#10622781	1	2	yes	—
177	C₂	—	2	2	no	—
178	C₂	#13068777	1	1	yes	characteristic
179	C₂	#13068786	1	1	yes	characteristic
180	C₂	#13068787	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13068753

C₂

yes

maximal

#13067374

C₂

yes

maximal

#13067372

C₂

yes

maximal, characteristic

C₂×C₈×C₁₁⋊C₈

C₂

yes

maximal, characteristic

C₁₁×#1566

C₂

yes

maximal, characteristic

C₁₁×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622537

C₂²

yes

—

C₂×C₄×C₁₁⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₁₁⋊C₈

C₂²

yes

characteristic

C₁₁×#334

—

#10622196

—

#10622117

—

#10622095

—

C₈×C₁₁⋊C₈

C₄

yes

characteristic

C₈×C₁₁⋊C₈

C₄

yes

characteristic

C₈×C₁₁⋊C₈

C₄

yes

characteristic

C₈×C₁₁⋊C₈

C₄

yes

characteristic

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×#4318

—

C₂²×C₁₁⋊C₈

D₄

yes

—

C₂²×C₁₁⋊C₈

Q₈

yes

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

C₄×C₁₁⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₁⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₁⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₁⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₁⋊C₈

D₄

yes

—

C₄×C₁₁⋊C₈

Q₈

yes

—

#8824

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×Q₈

yes

characteristic

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

—

—

—

D₁₁

yes

characteristic

C₂×C₈²

—

C₂³×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

#135

yes

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#108

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₁₁⋊C₈

#108

yes

—

#423

—

#423

C₂×D₁₁

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

—

C₈²

—

C₈²

—

C₈²

—

C₈²

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#384

yes

characteristic

C₂²×C₁₁

#499

yes

—

C₄×C₁₁

—

100

C₄×C₁₁

—

101

C₄×C₁₁

#427

yes

—

102

C₄×C₁₁

C₂×#108

yes

—

103

C₄×C₁₁

C₂×#108

yes

—

104

C₄×C₁₁

#495

yes

—

105

C₂×M₁₆

—

106

C₂×M₁₆

—

107

C₂²×C₈

—

108

C₂²×C₈

—

109

C₂²×C₈

Dic₂₂

yes

—

110

C₂×C₄²

C₂²×D₁₁

yes

characteristic

111

C₄⋊C₈

—

112

C₄⋊C₈

—

113

C₄⋊C₈

—

114

C₄⋊C₈

—

115

C₄×C₈

—

116

C₄×C₈

—

117

C₄×C₈

—

118

C₄×C₈

—

119

C₄×C₈

—

120

C₄×C₈

—

121

C₄×C₈

C₄×D₁₁

yes

characteristic

122

C₄×C₈

C₄×D₁₁

yes

characteristic

123

C₄×C₈

C₂²⋊D₁₁

yes

—

124

C₂×C₁₁

—

125

C₂×C₁₁

#1846

yes

characteristic

126

C₂×C₁₁

#1848

yes

characteristic

127

C₂×C₁₁

#1848

yes

characteristic

128

C₂²×C₄

C₂×Dic₂₂

yes

characteristic

129

C₂²×C₄

D₄×D₁₁

yes

characteristic

130

C₂²×C₄

Q₈×D₁₁

yes

characteristic

131

M₁₆

—

132

M₁₆

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

Dic₁₁⋊C₄

yes

—

143

C₂×C₈

Dic₁₁⋊C₄

yes

—

144

C₄²

C₂×C₄×D₁₁

yes

characteristic

145

C₄²

D₄×D₁₁

yes

characteristic

146

C₄²

Q₈×D₁₁

yes

characteristic

147

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

148

C₁₁

#8824

yes

characteristic, complemented, Sylow

149

C₂³

#66941

yes

characteristic

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

#66941

yes

characteristic

153

C₂×C₄

C₄⋊C₄×D₁₁

yes

characteristic

154

C₂×C₄

C₄⋊C₄×D₁₁

yes

characteristic

155

C₂×C₄

#66969

yes

—

156

C₂×C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

157

C₂×C₄

#66993

yes

characteristic

158

C₂×C₄

#66997

yes

characteristic

159

C₈

—

160

C₈

—

161

C₈

—

162

C₈

—

163

C₈

—

164

C₈

—

165

C₈

—

166

C₈

#66886

yes

—

167

C₂²

—

168

C₂²

—

169

C₂²

#10622471

yes

—

170

C₂²

#10622589

yes

characteristic

171

C₄

—

172

C₄

—

173

C₄

#10622473

yes

—

174

C₄

D₁₁×#108

yes

—

175

C₄

C₂×#66886

yes

—

176

C₄

#10622781

yes

—

177

C₂

—

178

C₂

#13068777

yes

characteristic

179

C₂

#13068786

yes

characteristic

180

C₂

#13068787

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#66993
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1566	C₂
socle	C₂²×C₁₁	#384
prime radical	C₂³×C₁₁	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1566	D₁₁
hypocenter	C₁₁	#8824
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂×C₄

#66993

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1566

C₂

socle

C₂²×C₁₁

#384

prime radical

C₂³×C₁₁

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
148. C₁₁	#8824	semidirect

H ≅ G/N

type

148. C₁₁

#8824

semidirect

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

subgroup	index
#13068753	2
#13067374	2
#13067372	2
C₂×C₈×C₁₁⋊C₈	2
C₁₁×#1566	2
#8824	11

subgroup

index

#13068753

#13067374

#13067372

C₂×C₈×C₁₁⋊C₈

C₁₁×#1566

#8824

Subgroups — #14647579

Conjugacy classes of subgroups

Complements

Maximal subgroups