Group #14908273 — subgroups

Subgroups — #14908273

Order 2816.

650 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 171 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×#10622514	C₂	1	1	yes	maximal, characteristic
2	#13078267	C₂	1	2	yes	maximal
3	#13070721	C₂	1	4	yes	maximal, complemented
4	#13070704	C₂	1	4	yes	maximal, complemented
5	#13070400	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070336	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₁×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
9	#10623347	—	2	2	no	—
10	C₂×#66954	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×Q₃₂	—	2	4	no	—
12	C₂×C₁₁×Q₃₂	C₂²	1	2	yes	—
13	C₂×C₁₁×Q₃₂	C₂²	1	2	yes	—
14	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
15	#10622838	—	2	2	no	—
16	#10622802	—	2	4	no	—
17	#10622801	C₂²	1	8	yes	—
18	#10622719	C₂²	1	2	yes	—
19	C₂×#66876	C₂²	1	1	yes	characteristic
20	#10622514	—	2	4	no	—
21	C₂×#66862	C₂²	1	2	yes	—
22	C₂×C₁₆×D₁₁	C₂²	1	2	yes	—
23	#10622202	C₂²	1	8	yes	—
24	#10622143	C₂²	1	2	yes	—
25	#10622142	C₂²	1	2	yes	—
26	C₂²×Q₈×C₁₁	—	2	2	no	—
27	C₂×#4339	D₄	1	1	yes	characteristic
28	C₂×C₁₁×Q₁₆	—	2	4	no	—
29	C₂×C₁₁×Q₁₆	—	2	2	no	—
30	C₂×C₁₁×Q₁₆	—	2	4	no	—
31	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
32	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
33	#67000	—	4	2	no	—
34	#66999	—	2	8	no	—
35	#66997	—	4	2	no	—
36	#66982	—	4	4	no	—
37	#66979	—	2	2	no	—
38	C₂×#4318	D₄	1	1	yes	characteristic
39	#66954	—	2	2	no	—
40	#66954	—	2	2	no	—
41	C₂×#4313	D₄	1	2	yes	—
42	C₂×C₈×D₁₁	C₂³	1	2	yes	—
43	C₁₁×Q₃₂	—	2	4	no	—
44	C₁₁×Q₃₂	—	2	4	no	—
45	C₂×C₁₁×C₁₆	D₄	1	4	yes	—
46	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
47	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
48	#66899	—	2	8	no	—
49	#66882	C₂³	1	4	yes	—
50	#66881	—	2	2	no	—
51	#66876	—	2	2	no	—
52	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
53	#66862	—	2	4	no	—
54	C₁₆×D₁₁	—	2	4	no	—
55	#33608	—	11	1	no	maximal, Sylow
56	C₂×Q₈×C₁₁	—	2	4	no	—
57	C₂×Q₈×C₁₁	—	4	2	no	—
58	C₂×Q₈×C₁₁	—	4	4	no	—
59	C₂×Q₈×C₁₁	—	4	4	no	—
60	C₂²×C₄×C₁₁	—	4	2	no	—
61	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₂×C₂²⋊D₁₁	D₈	1	2	yes	—
63	#4339	—	2	2	no	—
64	#4339	—	2	2	no	—
65	C₂×D₄₄	D₈	1	1	yes	characteristic
66	C₂×C₄×D₁₁	C₂×D₄	1	2	yes	—
67	C₂×Dic₂₂	D₈	1	1	yes	characteristic
68	C₁₁×Q₁₆	—	2	4	no	—
69	C₁₁×Q₁₆	—	2	4	no	—
70	C₁₁×Q₁₆	—	4	4	no	—
71	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	#41	1	2	yes	—
74	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
75	C₂²⋊Dic₁₁	—	4	2	no	—
76	(C₂×D₁₁)⋊C₄	—	4	8	no	—
77	C₄⋊Dic₁₁	—	2	4	no	—
78	Dic₁₁⋊C₄	—	4	8	no	—
79	C₄×Dic₁₁	—	4	2	no	—
80	#4318	—	2	2	no	—
81	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
82	#4313	—	2	4	no	—
83	C₈×D₁₁	—	2	2	no	—
84	C₈×D₁₁	—	2	2	no	—
85	C₁₁×C₁₆	C₂×D₄	1	2	yes	—
86	C₁₁×C₁₆	C₂×D₄	1	2	yes	—
87	C₁₁⋊C₁₆	—	2	2	no	—
88	C₂²×Q₃₂	D₁₁	1	1	yes	characteristic, complemented
89	C₂×#504	—	11	1	no	—
90	#3059	—	11	2	no	—
91	#2219	—	11	4	no	—
92	#2216	—	11	4	no	—
93	#2158	—	11	1	no	—
94	#2141	—	11	2	no	—
95	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
96	C₂²×D₁₁	C₂×D₈	1	2	yes	—
97	Q₈×C₁₁	—	4	4	no	—
98	Q₈×C₁₁	—	4	4	no	—
99	Q₈×C₁₁	—	8	4	no	—
100	C₂×C₄×C₁₁	—	4	4	no	—
101	C₂×C₄×C₁₁	—	8	4	no	—
102	C₂×C₄×C₁₁	#121	1	2	yes	—
103	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
104	C₂×C₄×C₁₁	#135	1	2	yes	—
105	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
106	C₂²⋊D₁₁	—	2	4	no	—
107	C₂×Dic₁₁	—	4	4	no	—
108	C₂×Dic₁₁	C₂×D₈	1	2	yes	—
109	D₄₄	—	2	2	no	—
110	C₄×D₁₁	—	2	2	no	—
111	C₄×D₁₁	—	2	2	no	—
112	Dic₂₂	—	2	2	no	—
113	C₈×C₁₁	#121	1	2	yes	—
114	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
115	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
116	C₁₁⋊C₈	—	2	2	no	—
117	C₂²×Q₁₆	C₂×D₁₁	1	2	yes	—
118	C₂×#131	—	11	1	no	—
119	#536	—	22	2	no	—
120	C₂×Q₃₂	—	2	4	no	—
121	C₂×Q₃₂	C₂×D₁₁	1	2	yes	—
122	C₂×Q₃₂	C₂×D₁₁	1	2	yes	—
123	#504	—	22	4	no	—
124	C₂×M₃₂	—	11	1	no	—
125	C₂×M₃₂	—	11	2	no	—
126	C₂²×C₁₆	—	11	2	no	—
127	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
128	#470	—	22	4	no	—
129	#467	—	11	8	no	—
130	#427	—	11	2	no	—
131	#419	—	22	2	no	—
132	#367	—	11	2	no	—
133	#366	—	11	2	no	—
134	#358	—	11	8	no	—
135	C₂²×C₁₁	—	2	2	no	—
136	C₂²×C₁₁	#466	1	2	yes	—
137	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
138	C₂×D₁₁	—	2	4	no	—
139	C₂×D₁₁	—	2	2	no	—
140	C₄×C₁₁	—	8	4	no	—
141	C₄×C₁₁	#466	1	2	yes	—
142	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
143	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
144	Dic₁₁	—	2	2	no	—
145	Dic₁₁	—	8	4	no	—
146	C₂×#41	—	11	1	no	—
147	C₂²×Q₈	—	2	2	no	—
148	C₂×Q₁₆	—	2	2	no	—
149	C₂×Q₁₆	—	2	4	no	—
150	C₂×Q₁₆	—	2	4	no	—
151	C₂×Q₁₆	C₂²×D₁₁	1	4	yes	—
152	#131	—	22	2	no	—
153	#131	—	22	2	no	—
154	C₂×M₁₆	—	11	1	no	—
155	C₂×M₁₆	—	11	2	no	—
156	C₂²×C₈	—	11	2	no	—
157	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
158	C₄⋊Q₈	—	44	2	no	—
159	#124	—	44	2	no	—
160	#123	—	44	4	no	—
161	C₂²⋊Q₈	—	22	8	no	—
162	#117	—	22	2	no	—
163	Q₃₂	—	2	4	no	—
164	Q₃₂	—	2	4	no	—
165	M₃₂	—	22	2	no	—
166	M₃₂	—	22	4	no	—
167	C₂×C₁₆	—	11	2	no	—
168	C₂×C₁₆	—	22	4	no	—
169	C₂×C₁₆	C₂²⋊D₁₁	1	4	yes	—
170	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
171	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
172	#107	—	11	4	no	—
173	#106	—	22	2	no	—
174	#103	—	22	8	no	—
175	C₂×C₁₁	—	2	2	no	—
176	C₂×C₁₁	C₂×#466	1	1	yes	characteristic
177	C₂×C₁₁	#3417	1	2	yes	—
178	D₁₁	—	4	2	no	—
179	#41	—	22	2	no	—
180	#41	—	22	2	no	—
181	C₂×Q₈	—	2	4	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	4	no	—
184	C₂×Q₈	—	4	4	no	—
185	C₂×Q₈	—	11	1	no	—
186	C₂×D₄	—	11	2	no	—
187	C₂×D₄	—	11	1	no	—
188	C₂²×C₄	—	4	2	no	—
189	C₂²×C₄	—	11	2	no	—
190	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
191	Q₁₆	—	2	4	no	—
192	Q₁₆	—	2	4	no	—
193	Q₁₆	—	4	4	no	—
194	M₁₆	—	22	2	no	—
195	M₁₆	—	22	4	no	—
196	C₂×C₈	—	11	2	no	—
197	C₂×C₈	—	22	2	no	—
198	C₂×C₈	—	22	2	no	—
199	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
200	C₂×C₈	#4341	1	2	yes	—
201	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
202	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
203	C₄⋊C₄	—	22	4	no	—
204	C₄⋊C₄	—	44	8	no	—
205	C₂²⋊C₄	—	44	8	no	—
206	C₂²⋊C₄	—	44	2	no	—
207	C₄²	—	44	2	no	—
208	C₁₆	—	22	2	no	—
209	C₁₆	C₂×C₂²⋊D₁₁	1	2	yes	—
210	C₁₆	C₂×C₂²⋊D₁₁	1	2	yes	—
211	C₁₁	#33608	1	1	yes	characteristic, complemented, Sylow
212	C₂³	—	11	2	no	—
213	C₂³	D₈×D₁₁	1	1	yes	characteristic
214	Q₈	—	4	4	no	—
215	Q₈	—	4	4	no	—
216	Q₈	—	8	4	no	—
217	Q₈	—	22	2	no	—
218	D₄	—	22	4	no	—
219	D₄	—	22	2	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	8	4	no	—
222	C₂×C₄	—	11	2	no	—
223	C₂×C₄	—	22	2	no	—
224	C₂×C₄	—	22	2	no	—
225	C₂×C₄	—	44	4	no	—
226	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
227	C₂×C₄	#66965	1	2	yes	—
228	C₂×C₄	#66991	1	2	yes	—
229	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
230	C₈	—	22	2	no	—
231	C₈	#66991	1	2	yes	—
232	C₈	C₂×#4341	1	1	yes	characteristic
233	C₈	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	22	2	no	—
236	C₂²	—	22	4	no	—
237	C₂²	#10622770	1	2	yes	—
238	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
239	C₄	—	8	4	no	—
240	C₄	—	22	2	no	—
241	C₄	—	88	4	no	—
242	C₄	#10622770	1	2	yes	—
243	C₄	C₂×#66965	1	1	yes	characteristic
244	C₄	C₂×#66991	1	1	yes	characteristic
245	C₂	—	2	2	no	—
246	C₂	—	44	2	no	—
247	C₂	C₂×#10622770	1	1	yes	characteristic
248	C₂	#13081765	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622514

C₂

yes

maximal, characteristic

#13078267

C₂

yes

maximal

#13070721

C₂

yes

maximal, complemented

#13070704

C₂

yes

maximal, complemented

#13070400

C₂

yes

maximal, characteristic, complemented

#13070336

C₂

yes

maximal, complemented

C₂²×C₁₁×Q₃₂

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₁×Q₁₆

C₂²

yes

—

#10623347

—

C₂×#66954

C₂²

yes

characteristic

C₂×C₁₁×Q₃₂

—

C₂×C₁₁×Q₃₂

C₂²

yes

—

C₂×C₁₁×Q₃₂

C₂²

yes

—

C₂²×C₁₁×C₁₆

C₂²

yes

—

—

C₂²

yes

—

#10622719

C₂²

yes

—

C₂×#66876

C₂²

yes

characteristic

#10622514

—

C₂×#66862

C₂²

yes

—

C₂×C₁₆×D₁₁

C₂²

yes

—

#10622202

C₂²

yes

—

#10622143

C₂²

yes

—

#10622142

C₂²

yes

—

C₂²×Q₈×C₁₁

—

C₂×#4339

D₄

yes

characteristic

C₂×C₁₁×Q₁₆

—

C₂×C₁₁×Q₁₆

—

C₂×C₁₁×Q₁₆

—

C₂×C₁₁×Q₁₆

C₂³

yes

—

C₂²×C₈×C₁₁

C₂³

yes

—

—

—

—

—

D₄

yes

—

—

D₄

yes

—

C₂×C₈×D₁₁

C₂³

yes

—

C₁₁×Q₃₂

—

C₁₁×Q₃₂

—

C₂×C₁₁×C₁₆

D₄

yes

—

C₂×C₁₁×C₁₆

C₂³

yes

characteristic

C₂×C₁₁×C₁₆

C₂³

yes

characteristic

#66899

—

#66882

C₂³

yes

—

#66881

—

#66876

—

C₂×C₁₁⋊C₁₆

C₂³

yes

—

#66862

—

C₁₆×D₁₁

—

#33608

—

maximal, Sylow

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₁

D₈

yes

—

#4339

—

#4339

—

C₂×D₄₄

D₈

yes

characteristic

C₂×C₄×D₁₁

C₂×D₄

yes

—

C₂×Dic₂₂

D₈

yes

characteristic

C₁₁×Q₁₆

—

C₁₁×Q₁₆

—

C₁₁×Q₁₆

—

C₂×C₈×C₁₁

C₂×D₄

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

#41

yes

—

C₂×C₈×C₁₁

C₂⁴

yes

characteristic

C₂²⋊Dic₁₁

—

(C₂×D₁₁)⋊C₄

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

#4318

—

C₂×C₁₁⋊C₈

C₂×D₄

yes

—

#4313

—

C₈×D₁₁

—

C₈×D₁₁

—

C₁₁×C₁₆

C₂×D₄

yes

—

C₁₁×C₁₆

C₂×D₄

yes

—

C₁₁⋊C₁₆

—

C₂²×Q₃₂

D₁₁

yes

characteristic, complemented

—

—

—

—

—

—

C₂³×C₁₁

C₂×D₈

yes

characteristic

C₂²×D₁₁

C₂×D₈

yes

—

Q₈×C₁₁

—

Q₈×C₁₁

—

Q₈×C₁₁

—

100

C₂×C₄×C₁₁

—

101

C₂×C₄×C₁₁

—

102

C₂×C₄×C₁₁

#121

yes

—

103

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

104

C₂×C₄×C₁₁

#135

yes

—

105

C₂×C₄×C₁₁

C₂²×D₄

yes

characteristic

106

C₂²⋊D₁₁

—

107

C₂×Dic₁₁

—

108

C₂×Dic₁₁

C₂×D₈

yes

—

109

D₄₄

—

110

C₄×D₁₁

—

111

C₄×D₁₁

—

112

Dic₂₂

—

113

C₈×C₁₁

#121

yes

—

114

C₈×C₁₁

C₂²×D₄

yes

characteristic

115

C₈×C₁₁

C₂×#41

yes

characteristic

116

C₁₁⋊C₈

—

117

C₂²×Q₁₆

C₂×D₁₁

yes

—

118

C₂×#131

—

119

#536

—

120

C₂×Q₃₂

—

121

C₂×Q₃₂

C₂×D₁₁

yes

—

122

C₂×Q₃₂

C₂×D₁₁

yes

—

123

#504

—

124

C₂×M₃₂

—

125

C₂×M₃₂

—

126

C₂²×C₁₆

—

127

C₂²×C₁₆

C₂×D₁₁

yes

characteristic

128

#470

—

129

#467

—

130

#427

—

131

#419

—

132

#367

—

133

#366

—

134

#358

—

135

C₂²×C₁₁

—

136

C₂²×C₁₁

#466

yes

—

137

C₂²×C₁₁

C₂²×D₈

yes

characteristic

138

C₂×D₁₁

—

139

C₂×D₁₁

—

140

C₄×C₁₁

—

141

C₄×C₁₁

#466

yes

—

142

C₄×C₁₁

C₂×#121

yes

characteristic

143

C₄×C₁₁

C₂×#135

yes

characteristic

144

Dic₁₁

—

145

Dic₁₁

—

146

C₂×#41

—

147

C₂²×Q₈

—

148

C₂×Q₁₆

—

149

C₂×Q₁₆

—

150

C₂×Q₁₆

—

151

C₂×Q₁₆

C₂²×D₁₁

yes

—

152

#131

—

153

#131

—

154

C₂×M₁₆

—

155

C₂×M₁₆

—

156

C₂²×C₈

—

157

C₂²×C₈

C₂²×D₁₁

yes

characteristic

158

C₄⋊Q₈

—

159

#124

—

160

#123

—

161

C₂²⋊Q₈

—

162

#117

—

163

Q₃₂

—

164

Q₃₂

—

165

M₃₂

—

166

M₃₂

—

167

C₂×C₁₆

—

168

C₂×C₁₆

—

169

C₂×C₁₆

C₂²⋊D₁₁

yes

—

170

C₂×C₁₆

C₂²×D₁₁

yes

characteristic

171

C₂×C₁₆

C₂²×D₁₁

yes

characteristic

172

#107

—

173

#106

—

174

#103

—

175

C₂×C₁₁

—

176

C₂×C₁₁

C₂×#466

yes

characteristic

177

C₂×C₁₁

#3417

yes

—

178

D₁₁

—

179

#41

—

180

#41

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

D₄×D₁₁

yes

characteristic

191

Q₁₆

—

192

Q₁₆

—

193

Q₁₆

—

194

M₁₆

—

195

M₁₆

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

D₄×D₁₁

yes

characteristic

200

C₂×C₈

#4341

yes

—

201

C₂×C₈

C₂×C₂²⋊D₁₁

yes

—

202

C₂×C₈

C₂³×D₁₁

yes

characteristic

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

—

208

C₁₆

—

209

C₁₆

C₂×C₂²⋊D₁₁

yes

—

210

C₁₆

C₂×C₂²⋊D₁₁

yes

—

211

C₁₁

#33608

yes

characteristic, complemented, Sylow

212

C₂³

—

213

C₂³

D₈×D₁₁

yes

characteristic

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

Q₈

—

218

D₄

—

219

D₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

D₈×D₁₁

yes

characteristic

227

C₂×C₄

#66965

yes

—

228

C₂×C₄

#66991

yes

—

229

C₂×C₄

C₂×D₄×D₁₁

yes

characteristic

230

C₈

—

231

C₈

#66991

yes

—

232

C₈

C₂×#4341

yes

characteristic

233

C₈

C₂²×C₂²⋊D₁₁

yes

characteristic

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

#10622770

yes

—

238

C₂²

C₂×D₈×D₁₁

yes

characteristic

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

#10622770

yes

—

243

C₄

C₂×#66965

yes

characteristic

244

C₄

C₂×#66991

yes

characteristic

245

C₂

—

246

C₂

—

247

C₂

C₂×#10622770

yes

characteristic

248

C₂

#13081765

yes

—

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂²×C₁₁×Q₃₂	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂×#4339	D₄
hypercenter	C₂²×Q₃₂	D₁₁
hypocenter	C₁₁	#33608
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂²

C₂×D₈×D₁₁

commutator, cosocle

C₂×C₈×C₁₁

C₂⁴

Frattini

C₂×C₈

C₂³×D₁₁

Fitting

C₂²×C₁₁×Q₃₂

C₂

socle

C₂²×C₁₁

C₂²×D₈

prime radical

C₂×#4339

D₄

hypercenter

C₂²×Q₃₂

D₁₁

hypocenter

C₁₁

#33608

LCS

G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
3. #13070721	C₂	semidirect
4. #13070704	C₂	semidirect
5. #13070400	C₂	semidirect
6. #13070336	C₂	semidirect
7. C₂²×C₁₁×Q₃₂	C₂	semidirect
88. C₂²×Q₃₂	D₁₁	semidirect
211. C₁₁	#33608	semidirect

H ≅ G/N

type

3. #13070721

C₂

semidirect

4. #13070704

C₂

semidirect

5. #13070400

C₂

semidirect

6. #13070336

C₂

semidirect

7. C₂²×C₁₁×Q₃₂

C₂

semidirect

88. C₂²×Q₃₂

D₁₁

semidirect

211. C₁₁

#33608

semidirect

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

subgroup	index
C₂×#10622514	2
#13078267	2
#13070721	2
#13070704	2
#13070400	2
#13070336	2
C₂²×C₁₁×Q₃₂	2
#33608	11

subgroup

index

C₂²×C₁₁×Q₃₂

Subgroups — #14908273

Conjugacy classes of subgroups

Complements

Maximal subgroups