Group #14647535 — subgroups

Subgroups — #14647535

Order 2816.

382 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 163 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	#13068733	C₂	1	1	yes	maximal, characteristic
2	#13068362	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622117	C₂	1	2	yes	maximal
4	C₂×#10622118	C₂	1	2	yes	maximal
5	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
7	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
8	C₄³×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
12	#10622162	—	2	2	no	—
13	#10622162	C₄	1	2	yes	—
14	#10622162	C₄	1	2	yes	—
15	#10622118	—	2	4	no	—
16	#10622117	—	2	4	no	—
17	C₂²×C₈×C₁₁	—	2	2	no	—
18	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₁	D₄	1	2	yes	—
21	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
22	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
23	C₂²×C₁₁⋊C₈	—	2	1	no	—
24	C₂²×C₁₁⋊C₈	—	2	1	no	—
25	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
26	C₁₁×C₄⋊C₈	—	2	2	no	—
27	C₁₁×C₄⋊C₈	—	2	2	no	—
28	C₁₁×C₄⋊C₈	—	4	4	no	—
29	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
31	C₄×C₁₁⋊C₈	D₄	1	4	yes	—
32	C₄×C₁₁⋊C₈	Q₈	1	4	yes	—
33	#8812	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
35	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
36	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₈×C₁₁	—	4	2	no	—
40	C₂×C₈×C₁₁	—	4	4	no	—
41	C₄²×C₁₁	—	2	4	no	—
42	C₄²×C₁₁	—	2	2	no	—
43	C₄²×C₁₁	—	2	2	no	—
44	C₄²×C₁₁	—	2	2	no	—
45	C₄²×C₁₁	—	2	2	no	—
46	C₄²×C₁₁	C₂×D₄	1	2	yes	—
47	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
48	C₂×C₁₁⋊C₈	—	2	4	no	—
49	C₂×C₁₁⋊C₈	—	2	4	no	—
50	C₂×C₁₁⋊C₈	—	4	1	no	—
51	C₂×C₁₁⋊C₈	—	4	1	no	—
52	C₂×C₁₁⋊C₈	—	4	2	no	—
53	C₂×C₁₁⋊C₈	—	4	2	no	—
54	C₂×C₁₁⋊C₈	C₄⋊C₄	1	8	yes	—
55	#1842	D₁₁	1	1	yes	characteristic
56	#1831	—	11	1	no	—
57	#1744	—	11	1	no	—
58	C₂×#335	—	11	2	no	—
59	C₂×#334	—	11	2	no	—
60	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₁	—	2	2	no	—
62	C₂×C₄×C₁₁	—	2	2	no	—
63	C₂×C₄×C₁₁	—	2	2	no	—
64	C₂×C₄×C₁₁	—	2	2	no	—
65	C₂×C₄×C₁₁	—	2	2	no	—
66	C₂×C₄×C₁₁	—	2	2	no	—
67	C₂×C₄×C₁₁	#108	1	4	yes	—
68	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
69	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
71	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₁	#131	1	2	yes	—
73	C₂×C₄×C₁₁	#131	1	2	yes	—
74	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
75	C₂×C₄×C₁₁	#137	1	2	yes	—
76	C₈×C₁₁	—	8	2	no	—
77	C₁₁⋊C₈	—	2	8	no	—
78	C₁₁⋊C₈	—	8	1	no	—
79	C₁₁⋊C₈	—	8	1	no	—
80	C₂×C₄⋊C₈	—	2	2	no	—
81	C₂×C₄⋊C₈	—	11	1	no	—
82	C₂×C₄⋊C₈	—	11	1	no	—
83	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
84	C₂×C₄×C₈	—	11	2	no	—
85	C₄³	C₂×D₁₁	1	1	yes	characteristic
86	#336	—	11	2	no	—
87	#336	—	11	2	no	—
88	#336	—	22	2	no	—
89	#335	—	22	4	no	—
90	#334	—	22	4	no	—
91	C₂²×C₁₁	#384	1	1	yes	characteristic
92	C₂²×C₁₁	#424	1	1	yes	characteristic
93	C₂²×C₁₁	#424	1	1	yes	characteristic
94	C₂²×C₁₁	#428	1	2	yes	—
95	C₂²×C₁₁	C₂×#108	1	2	yes	—
96	C₄×C₁₁	—	2	4	no	—
97	C₄×C₁₁	—	2	2	no	—
98	C₄×C₁₁	—	4	2	no	—
99	C₄×C₁₁	#424	1	4	yes	—
100	C₄×C₁₁	#496	1	1	yes	characteristic
101	C₄×C₁₁	#497	1	1	yes	characteristic
102	C₄×C₁₁	#501	1	2	yes	—
103	C₂²×C₈	—	2	2	no	—
104	C₂²×C₈	—	11	4	no	—
105	C₂²×C₈	—	22	1	no	—
106	C₂²×C₈	—	22	1	no	—
107	C₂×C₄²	Dic₂₂	1	2	yes	—
108	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
109	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
110	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
111	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
112	C₄⋊C₈	—	2	2	no	—
113	C₄⋊C₈	—	2	2	no	—
114	C₄⋊C₈	—	4	4	no	—
115	C₄⋊C₈	—	22	2	no	—
116	C₄⋊C₈	—	22	2	no	—
117	C₄×C₈	—	11	4	no	—
118	C₄×C₈	—	11	4	no	—
119	C₂×C₁₁	#1573	1	2	yes	—
120	C₂×C₁₁	#1574	1	2	yes	—
121	C₂×C₁₁	#1843	1	1	yes	characteristic
122	C₂×C₁₁	#1847	1	1	yes	characteristic
123	C₂×C₁₁	#1848	1	1	yes	characteristic
124	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
125	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
126	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
127	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
128	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
129	C₂×C₈	—	4	4	no	—
130	C₂×C₈	—	4	2	no	—
131	C₂×C₈	—	11	8	no	—
132	C₂×C₈	—	22	4	no	—
133	C₂×C₈	—	22	4	no	—
134	C₂×C₈	—	44	2	no	—
135	C₂×C₈	—	44	1	no	—
136	C₂×C₈	—	44	1	no	—
137	C₂×C₈	—	44	2	no	—
138	C₄²	—	2	4	no	—
139	C₄²	—	2	2	no	—
140	C₄²	—	2	2	no	—
141	C₄²	—	2	2	no	—
142	C₄²	—	2	2	no	—
143	C₄²	D₄×D₁₁	1	2	yes	—
144	C₄²	Q₈×D₁₁	1	2	yes	—
145	C₁₁	#8812	1	1	yes	characteristic, complemented, Sylow
146	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	#66886	1	4	yes	—
154	C₂×C₄	#66941	1	2	yes	—
155	C₂×C₄	C₄⋊C₄×D₁₁	1	2	yes	—
156	C₂×C₄	#66954	1	2	yes	—
157	C₂×C₄	#66960	1	2	yes	—
158	C₂×C₄	#66985	1	2	yes	—
159	C₂×C₄	#66993	1	1	yes	characteristic
160	C₂×C₄	#66995	1	2	yes	—
161	C₂×C₄	#66997	1	1	yes	characteristic
162	C₈	—	8	2	no	—
163	C₈	—	22	8	no	—
164	C₈	—	88	1	no	—
165	C₈	—	88	1	no	—
166	C₂²	#10622577	1	2	yes	—
167	C₂²	#10622589	1	1	yes	characteristic
168	C₂²	#10622715	1	1	yes	characteristic
169	C₂²	#10622732	1	1	yes	characteristic
170	C₂²	C₂×#66886	1	2	yes	—
171	C₄	—	2	4	no	—
172	C₄	—	2	2	no	—
173	C₄	—	4	2	no	—
174	C₄	#10622452	1	4	yes	—
175	C₄	#10622687	1	1	yes	characteristic
176	C₄	#10622693	1	2	yes	—
177	C₄	#10622699	1	1	yes	characteristic
178	C₂	#13067399	1	2	yes	—
179	C₂	#13067407	1	2	yes	—
180	C₂	#13068769	1	1	yes	characteristic
181	C₂	#13068782	1	1	yes	characteristic
182	C₂	#13068787	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13068733

C₂

yes

maximal, characteristic

#13068362

C₂

yes

maximal, characteristic

C₂×#10622117

C₂

yes

maximal

C₂×#10622118

C₂

yes

maximal

C₁₁×#1842

C₂

yes

maximal, characteristic

C₂×C₁₁×C₄⋊C₈

—

C₂×C₁₁×C₄⋊C₈

C₂²

yes

—

C₄³×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊(C₁₁⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₁₁⋊C₈)

C₂²

yes

characteristic

C₂×C₄×C₁₁⋊C₈

C₂²

yes

—

#10622162

—

#10622162

C₄

yes

—

#10622162

C₄

yes

—

#10622118

—

#10622117

—

C₂²×C₈×C₁₁

—

C₂×C₄²×C₁₁

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₁

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂²×C₁₁⋊C₈

—

C₂²×C₁₁⋊C₈

—

C₂²×C₁₁⋊C₈

C₂×C₄

yes

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

C₄×C₁₁⋊C₈

D₄

yes

—

C₄×C₁₁⋊C₈

Q₈

yes

—

#8812

—

maximal, Sylow

C₂²×C₄×C₁₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

#1842

D₁₁

yes

—

—

—

—

C₂³×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#108

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

#131

yes

—

C₂×C₄×C₁₁

#131

yes

—

C₂×C₄×C₁₁

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₁

#137

yes

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₁₁

yes

—

C₂×C₄×C₈

—

C₄³

C₂×D₁₁

yes

—

—

—

—

—

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

—

C₂²×C₁₁

C₂×#108

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#424

yes

—

100

C₄×C₁₁

#496

yes

characteristic

101

C₄×C₁₁

#497

yes

characteristic

102

C₄×C₁₁

#501

yes

—

103

C₂²×C₈

—

104

C₂²×C₈

—

105

C₂²×C₈

—

106

C₂²×C₈

—

107

C₂×C₄²

Dic₂₂

yes

—

108

C₂×C₄²

C₄×D₁₁

yes

characteristic

109

C₂×C₄²

C₄×D₁₁

yes

characteristic

110

C₂×C₄²

C₂²⋊D₁₁

yes

—

111

C₂×C₄²

C₂²×D₁₁

yes

characteristic

112

C₄⋊C₈

—

113

C₄⋊C₈

—

114

C₄⋊C₈

—

115

C₄⋊C₈

—

116

C₄⋊C₈

—

117

C₄×C₈

—

118

C₄×C₈

—

119

C₂×C₁₁

#1573

yes

—

120

C₂×C₁₁

#1574

yes

—

121

C₂×C₁₁

#1843

yes

characteristic

122

C₂×C₁₁

#1847

yes

characteristic

123

C₂×C₁₁

#1848

yes

characteristic

124

C₂²×C₄

Dic₁₁⋊C₄

yes

—

125

C₂²×C₄

Dic₁₁⋊C₄

yes

—

126

C₂²×C₄

C₂×Dic₂₂

yes

characteristic

127

C₂²×C₄

C₂×C₄×D₁₁

yes

characteristic

128

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₄²

—

139

C₄²

—

140

C₄²

—

141

C₄²

—

142

C₄²

—

143

C₄²

D₄×D₁₁

yes

—

144

C₄²

Q₈×D₁₁

yes

—

145

C₁₁

#8812

yes

characteristic, complemented, Sylow

146

C₂³

C₂×Dic₁₁⋊C₄

yes

characteristic

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

#66886

yes

—

154

C₂×C₄

#66941

yes

—

155

C₂×C₄

C₄⋊C₄×D₁₁

yes

—

156

C₂×C₄

#66954

yes

—

157

C₂×C₄

#66960

yes

—

158

C₂×C₄

#66985

yes

—

159

C₂×C₄

#66993

yes

characteristic

160

C₂×C₄

#66995

yes

—

161

C₂×C₄

#66997

yes

characteristic

162

C₈

—

163

C₈

—

164

C₈

—

165

C₈

—

166

C₂²

#10622577

yes

—

167

C₂²

#10622589

yes

characteristic

168

C₂²

#10622715

yes

characteristic

169

C₂²

#10622732

yes

characteristic

170

C₂²

C₂×#66886

yes

—

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

#10622452

yes

—

175

C₄

#10622687

yes

characteristic

176

C₄

#10622693

yes

—

177

C₄

#10622699

yes

characteristic

178

C₂

#13067399

yes

—

179

C₂

#13067407

yes

—

180

C₂

#13068769

yes

characteristic

181

C₂

#13068782

yes

characteristic

182

C₂

#13068787

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₁
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1842	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1842	D₁₁
hypocenter	C₁₁	#8812
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

subgroup

G/H

center

C₂²×C₄

C₂×C₂²⋊D₁₁

commutator

C₂²×C₄×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1842

C₂

socle, prime radical

C₂³×C₁₁

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

N	H ≅ G/N	type
145. C₁₁	#8812	semidirect

H ≅ G/N

type

145. C₁₁

#8812

semidirect

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

subgroup	index
#13068733	2
#13068362	2
C₂×#10622117	2
C₂×#10622118	2
C₁₁×#1842	2
#8812	11

subgroup

index

C₁₁×#1842

Subgroups — #14647535

Conjugacy classes of subgroups

Complements

Maximal subgroups