Group #14656382 — subgroups

Subgroups — #14656382

Order 2816.

574 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10622312	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622464	C₂	1	2	yes	maximal
3	#13069552	C₂	1	1	yes	maximal, characteristic
4	C₂×#10622124	C₂	1	2	yes	maximal
5	C₁₁×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₄₄	—	2	2	no	—
7	C₂×#66922	C₂²	1	2	yes	—
8	C₂×C₄×Dic₂₂	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×#66881	—	2	2	no	—
12	C₂×#66880	—	2	2	no	—
13	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
14	#10622464	—	2	4	no	—
15	#10622464	—	2	4	no	—
16	#10622312	—	2	4	no	—
17	#10622188	—	2	2	no	—
18	#10622124	—	2	4	no	—
19	C₂²×Dic₂₂	—	2	2	no	—
20	C₂²×Dic₂₂	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	—	2	2	no	—
22	C₂²×C₈×C₁₁	D₄	1	2	yes	—
23	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₁	—	2	2	no	—
25	C₂×C₄⋊Dic₁₁	—	2	2	no	—
26	C₂×C₄⋊Dic₁₁	D₄	1	1	yes	characteristic
27	C₂×Dic₁₁⋊C₄	—	2	1	no	—
28	C₂×C₄×Dic₁₁	—	2	1	no	—
29	C₂²×C₁₁⋊C₈	—	2	1	no	—
30	C₂×Dic₄₄	—	2	8	no	—
31	C₂×Dic₄₄	—	4	4	no	—
32	C₂×Dic₄₄	—	4	4	no	—
33	#66922	—	2	2	no	—
34	#66922	—	2	2	no	—
35	#66922	—	2	2	no	—
36	#66922	D₄	1	4	yes	—
37	C₄×Dic₂₂	—	2	2	no	—
38	C₄×Dic₂₂	—	2	2	no	—
39	C₁₁×C₄⋊C₈	—	2	2	no	—
40	C₁₁×C₄⋊C₈	D₄	1	4	yes	—
41	C₄×C₈×C₁₁	—	2	2	no	—
42	#66881	—	2	8	no	—
43	#66880	—	2	8	no	—
44	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
45	#10276	—	11	1	no	maximal, Sylow
46	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
49	C₂²×Dic₁₁	—	2	1	no	—
50	C₂²×Dic₁₁	—	2	1	no	—
51	C₂²×Dic₁₁	—	4	2	no	—
52	C₂×Dic₂₂	—	2	2	no	—
53	C₂×Dic₂₂	—	2	4	no	—
54	C₂×Dic₂₂	—	2	1	no	—
55	C₂×Dic₂₂	—	2	2	no	—
56	C₂×Dic₂₂	—	4	2	no	—
57	C₂×Dic₂₂	—	4	4	no	—
58	C₂×Dic₂₂	—	4	4	no	—
59	C₂×Dic₂₂	Q₁₆	1	2	yes	complemented
60	C₂×C₈×C₁₁	—	2	2	no	—
61	C₂×C₈×C₁₁	—	2	4	no	—
62	C₂×C₈×C₁₁	—	2	2	no	—
63	C₂×C₈×C₁₁	—	4	2	no	—
64	C₂×C₈×C₁₁	—	4	2	no	—
65	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
66	C₄²×C₁₁	C₂×D₄	1	2	yes	—
67	C₄²×C₁₁	C₂×D₄	1	2	yes	—
68	C₄⋊Dic₁₁	—	2	4	no	—
69	C₄⋊Dic₁₁	—	2	2	no	—
70	C₄⋊Dic₁₁	—	2	4	no	—
71	C₄⋊Dic₁₁	—	4	2	no	—
72	C₄⋊Dic₁₁	—	4	2	no	—
73	Dic₁₁⋊C₄	—	4	2	no	—
74	C₄×Dic₁₁	—	4	1	no	—
75	C₄×Dic₁₁	—	4	1	no	—
76	C₂×C₁₁⋊C₈	—	4	1	no	—
77	C₂×C₁₁⋊C₈	—	4	2	no	—
78	Dic₄₄	—	4	16	no	—
79	C₂×#494	—	11	1	no	—
80	C₂×#475	—	11	2	no	—
81	#1984	—	11	1	no	—
82	C₂×#332	—	11	2	no	—
83	#1277	D₁₁	1	1	yes	characteristic
84	C₂³×C₁₁	#121	1	1	yes	characteristic
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
87	C₂×C₄×C₁₁	#120	1	2	yes	—
88	C₂×C₄×C₁₁	#121	1	2	yes	—
89	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
90	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
91	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
93	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
94	C₂×C₄×C₁₁	#137	1	2	yes	—
95	C₂×Dic₁₁	—	2	2	no	—
96	C₂×Dic₁₁	—	4	1	no	—
97	C₂×Dic₁₁	—	4	1	no	—
98	C₂×Dic₁₁	—	4	1	no	—
99	C₂×Dic₁₁	—	4	4	no	—
100	C₂×Dic₁₁	—	4	2	no	—
101	C₂×Dic₁₁	—	8	4	no	—
102	Dic₂₂	—	2	4	no	—
103	Dic₂₂	—	4	2	no	—
104	Dic₂₂	—	4	8	no	—
105	Dic₂₂	—	8	2	no	—
106	Dic₂₂	—	8	2	no	—
107	C₈×C₁₁	—	2	4	no	—
108	C₈×C₁₁	—	4	4	no	—
109	C₁₁⋊C₈	—	8	1	no	—
110	C₂²×Q₁₆	—	22	2	no	—
111	C₂×C₄⋊Q₈	—	11	2	no	—
112	C₂×C₄×Q₈	—	11	1	no	—
113	#494	—	22	4	no	—
114	#475	—	22	4	no	—
115	#475	—	22	4	no	—
116	C₂×#106	—	22	2	no	—
117	C₂×C₄⋊C₈	—	11	1	no	—
118	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
119	C₂×#103	—	22	2	no	—
120	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
121	#336	—	22	2	no	—
122	#332	—	22	4	no	—
123	C₂²×C₁₁	#392	1	1	yes	characteristic
124	C₂²×C₁₁	#460	1	2	yes	—
125	C₂²×C₁₁	#467	1	1	yes	characteristic
126	C₂²×C₁₁	#470	1	1	yes	characteristic
127	C₂²×C₁₁	#473	1	2	yes	—
128	C₄×C₁₁	—	2	2	no	—
129	C₄×C₁₁	#450	1	2	yes	—
130	C₄×C₁₁	#451	1	2	yes	—
131	C₄×C₁₁	#452	1	2	yes	—
132	C₄×C₁₁	#492	1	1	yes	characteristic
133	C₄×C₁₁	#496	1	1	yes	characteristic
134	Dic₁₁	—	4	2	no	—
135	Dic₁₁	—	8	4	no	—
136	Dic₁₁	—	8	1	no	—
137	C₂²×Q₈	—	11	1	no	—
138	C₂²×Q₈	—	22	2	no	—
139	C₂×Q₁₆	—	22	8	no	—
140	C₂×Q₁₆	—	44	4	no	—
141	C₂×Q₁₆	—	44	4	no	—
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	—	22	1	no	—
144	C₂²×C₈	D₄₄	1	2	yes	—
145	C₄⋊Q₈	—	11	4	no	—
146	C₄⋊Q₈	—	22	2	no	—
147	C₄⋊Q₈	—	22	2	no	—
148	C₄⋊Q₈	—	22	2	no	—
149	C₄×Q₈	—	22	2	no	—
150	C₄×Q₈	—	22	2	no	—
151	C₂×C₄⋊C₄	—	11	1	no	—
152	C₂×C₄⋊C₄	—	22	2	no	—
153	C₂×C₄⋊C₄	—	22	2	no	—
154	C₂×C₄⋊C₄	—	22	1	no	—
155	C₂×C₄²	—	22	1	no	—
156	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
157	#106	—	22	8	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	22	2	no	—
160	C₄⋊C₈	D₄₄	1	4	yes	—
161	#103	—	22	8	no	—
162	C₄×C₈	—	2	2	no	—
163	C₂×C₁₁	#1670	1	2	yes	—
164	C₂×C₁₁	#1690	1	2	yes	—
165	C₂×C₁₁	#2001	1	1	yes	characteristic
166	C₂×C₁₁	#2014	1	1	yes	characteristic
167	C₂×C₁₁	#2020	1	1	yes	characteristic
168	C₂×Q₈	—	11	2	no	—
169	C₂×Q₈	—	22	1	no	—
170	C₂×Q₈	—	22	2	no	—
171	C₂×Q₈	—	22	4	no	—
172	C₂×Q₈	—	22	2	no	—
173	C₂×Q₈	—	44	2	no	—
174	C₂×Q₈	—	44	4	no	—
175	C₂×Q₈	—	44	4	no	—
176	C₂²×C₄	—	22	1	no	—
177	C₂²×C₄	—	22	1	no	—
178	C₂²×C₄	—	44	2	no	—
179	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
180	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
181	C₂²×C₄	#4343	1	1	yes	characteristic
182	Q₁₆	—	44	16	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	4	no	—
186	C₂×C₈	—	4	2	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	44	1	no	—
189	C₂×C₈	—	44	2	no	—
190	C₂×C₈	#4314	1	4	yes	—
191	C₄⋊C₄	—	22	4	no	—
192	C₄⋊C₄	—	22	2	no	—
193	C₄⋊C₄	—	22	4	no	—
194	C₄⋊C₄	—	44	2	no	—
195	C₄⋊C₄	—	44	2	no	—
196	C₄⋊C₄	—	44	2	no	—
197	C₄²	—	44	1	no	—
198	C₄²	—	44	1	no	—
199	C₄²	C₂×D₄₄	1	2	yes	—
200	C₄²	D₄×D₁₁	1	2	yes	—
201	C₁₁	#10276	1	1	yes	characteristic, complemented, Sylow
202	C₂³	#66948	1	1	yes	characteristic
203	Q₈	—	22	4	no	—
204	Q₈	—	44	2	no	—
205	Q₈	—	44	8	no	—
206	Q₈	—	88	2	no	—
207	Q₈	—	88	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	22	2	no	—
210	C₂×C₄	—	44	1	no	—
211	C₂×C₄	—	44	1	no	—
212	C₂×C₄	—	44	2	no	—
213	C₂×C₄	—	44	1	no	—
214	C₂×C₄	—	44	4	no	—
215	C₂×C₄	—	88	4	no	—
216	C₂×C₄	#66927	1	1	yes	characteristic
217	C₂×C₄	#66935	1	1	yes	characteristic
218	C₂×C₄	#66935	1	2	yes	—
219	C₂×C₄	#66948	1	2	yes	—
220	C₂×C₄	C₂×#4314	1	2	yes	—
221	C₂×C₄	#66961	1	2	yes	—
222	C₂×C₄	#66965	1	1	yes	characteristic
223	C₂×C₄	#66968	1	2	yes	—
224	C₂×C₄	Q₁₆×D₁₁	1	1	yes	characteristic
225	C₈	—	2	4	no	—
226	C₈	—	4	4	no	—
227	C₈	—	88	1	no	—
228	C₂²	#10622284	1	1	yes	characteristic
229	C₂²	#10622461	1	2	yes	—
230	C₂²	#10622481	1	1	yes	characteristic
231	C₂²	#10622500	1	1	yes	characteristic
232	C₂²	#10622509	1	2	yes	—
233	C₄	—	2	2	no	—
234	C₄	—	44	2	no	—
235	C₄	—	88	4	no	—
236	C₄	—	88	1	no	—
237	C₄	#10622306	1	1	yes	characteristic
238	C₄	#10622325	1	1	yes	characteristic
239	C₄	#10622344	1	2	yes	—
240	C₄	#10622396	1	2	yes	—
241	C₄	#10622421	1	2	yes	—
242	C₂	#13067987	1	2	yes	—
243	C₂	#13068111	1	2	yes	—
244	C₂	#13069627	1	1	yes	characteristic
245	C₂	#13069706	1	1	yes	characteristic
246	C₂	#13069738	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622312

C₂

yes

maximal, characteristic

C₂×#10622464

C₂

yes

maximal

#13069552

C₂

yes

maximal, characteristic

C₂×#10622124

C₂

yes

maximal

C₁₁×#1277

C₂

yes

maximal, characteristic

C₂²×Dic₄₄

—

C₂×#66922

C₂²

yes

—

C₂×C₄×Dic₂₂

C₂²

yes

characteristic

C₂×C₁₁×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66881

—

C₂×#66880

—

C₂×C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

—

—

—

—

C₂²×Dic₂₂

—

C₂²×Dic₂₂

D₄

yes

characteristic

C₂²×C₈×C₁₁

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

D₄

yes

characteristic

C₂×Dic₁₁⋊C₄

—

C₂×C₄×Dic₁₁

—

C₂²×C₁₁⋊C₈

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

—

—

—

D₄

yes

—

C₄×Dic₂₂

—

C₄×Dic₂₂

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

D₄

yes

—

C₄×C₈×C₁₁

—

#66881

—

#66880

—

C₄⋊(C₁₁⋊C₈)

—

#10276

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

characteristic

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

Q₁₆

yes

complemented

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

Dic₄₄

—

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

#121

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#120

yes

characteristic

C₂×C₄×C₁₁

#120

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×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

—

C₂×C₄×C₁₁

#137

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

100

C₂×Dic₁₁

—

101

C₂×Dic₁₁

—

102

Dic₂₂

—

103

Dic₂₂

—

104

Dic₂₂

—

105

Dic₂₂

—

106

Dic₂₂

—

107

C₈×C₁₁

—

108

C₈×C₁₁

—

109

C₁₁⋊C₈

—

110

C₂²×Q₁₆

—

111

C₂×C₄⋊Q₈

—

112

C₂×C₄×Q₈

—

113

#494

—

114

#475

—

115

#475

—

116

C₂×#106

—

117

C₂×C₄⋊C₈

—

118

C₂×C₄⋊C₈

C₂×D₁₁

yes

—

119

C₂×#103

—

120

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

121

#336

—

122

#332

—

123

C₂²×C₁₁

#392

yes

characteristic

124

C₂²×C₁₁

#460

yes

—

125

C₂²×C₁₁

#467

yes

characteristic

126

C₂²×C₁₁

#470

yes

characteristic

127

C₂²×C₁₁

#473

yes

—

128

C₄×C₁₁

—

129

C₄×C₁₁

#450

yes

—

130

C₄×C₁₁

#451

yes

—

131

C₄×C₁₁

#452

yes

—

132

C₄×C₁₁

#492

yes

characteristic

133

C₄×C₁₁

#496

yes

characteristic

134

Dic₁₁

—

135

Dic₁₁

—

136

Dic₁₁

—

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂×Q₁₆

—

140

C₂×Q₁₆

—

141

C₂×Q₁₆

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₂²×C₈

D₄₄

yes

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂²×D₁₁

yes

characteristic

157

#106

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

D₄₄

yes

—

161

#103

—

162

C₄×C₈

—

163

C₂×C₁₁

#1670

yes

—

164

C₂×C₁₁

#1690

yes

—

165

C₂×C₁₁

#2001

yes

characteristic

166

C₂×C₁₁

#2014

yes

characteristic

167

C₂×C₁₁

#2020

yes

characteristic

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

C₂×D₄₄

yes

characteristic

180

C₂²×C₄

D₄×D₁₁

yes

characteristic

181

C₂²×C₄

#4343

yes

characteristic

182

Q₁₆

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

#4314

yes

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

C₂×D₄₄

yes

—

200

C₄²

D₄×D₁₁

yes

—

201

C₁₁

#10276

yes

characteristic, complemented, Sylow

202

C₂³

#66948

yes

characteristic

203

Q₈

—

204

Q₈

—

205

Q₈

—

206

Q₈

—

207

Q₈

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

#66927

yes

characteristic

217

C₂×C₄

#66935

yes

characteristic

218

C₂×C₄

#66935

yes

—

219

C₂×C₄

#66948

yes

—

220

C₂×C₄

C₂×#4314

yes

—

221

C₂×C₄

#66961

yes

—

222

C₂×C₄

#66965

yes

characteristic

223

C₂×C₄

#66968

yes

—

224

C₂×C₄

Q₁₆×D₁₁

yes

characteristic

225

C₈

—

226

C₈

—

227

C₈

—

228

C₂²

#10622284

yes

characteristic

229

C₂²

#10622461

yes

—

230

C₂²

#10622481

yes

characteristic

231

C₂²

#10622500

yes

characteristic

232

C₂²

#10622509

yes

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

#10622306

yes

characteristic

238

C₄

#10622325

yes

characteristic

239

C₄

#10622344

yes

—

240

C₄

#10622396

yes

—

241

C₄

#10622421

yes

—

242

C₂

#13067987

yes

—

243

C₂

#13068111

yes

—

244

C₂

#13069627

yes

characteristic

245

C₂

#13069706

yes

characteristic

246

C₂

#13069738

yes

characteristic

	subgroup	G/H
center	C₂³	#66948
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1277	C₂
socle, prime radical	C₂³×C₁₁	#121
hypercenter	#1277	D₁₁
hypocenter	C₁₁	#10276
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂³

#66948

commutator, cosocle

C₂×C₄²×C₁₁

C₂³

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1277

C₂

C₂³×C₁₁

D₁₁

C₁₁

G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
59. C₂×Dic₂₂	Q₁₆	semidirect
201. C₁₁	#10276	semidirect

H ≅ G/N

type

59. C₂×Dic₂₂

Q₁₆

semidirect

201. C₁₁

#10276

semidirect

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

subgroup	index
C₂×#10622312	2
C₂×#10622464	2
#13069552	2
C₂×#10622124	2
C₁₁×#1277	2
#10276	11

subgroup

index

C₁₁×#1277

Subgroups — #14656382

Conjugacy classes of subgroups

Complements

Maximal subgroups