Group #14656309 — subgroups

Subgroups — #14656309

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×#10622295	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622462	C₂	1	2	yes	maximal
3	#13069552	C₂	1	1	yes	maximal, characteristic
4	C₂×#10622120	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×#66882	—	2	2	no	—
12	C₂×#66880	—	2	2	no	—
13	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
14	#10622462	—	2	4	no	—
15	#10622462	—	2	4	no	—
16	#10622295	—	2	4	no	—
17	#10622188	—	2	2	no	—
18	#10622120	—	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	#66882	—	2	8	no	—
43	#66880	—	2	8	no	—
44	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
45	#10265	—	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	2	no	—
58	C₂×Dic₂₂	—	4	2	no	—
59	C₂×Dic₂₂	—	4	2	no	—
60	C₂×Dic₂₂	—	4	2	no	—
61	C₂×Dic₂₂	D₈	1	2	yes	—
62	C₂×C₈×C₁₁	—	2	2	no	—
63	C₂×C₈×C₁₁	—	2	4	no	—
64	C₂×C₈×C₁₁	—	2	2	no	—
65	C₂×C₈×C₁₁	—	4	2	no	—
66	C₂×C₈×C₁₁	—	4	2	no	—
67	C₂×C₈×C₁₁	Q₁₆	1	4	yes	complemented
68	C₄²×C₁₁	C₂×D₄	1	2	yes	—
69	C₄²×C₁₁	C₂×D₄	1	2	yes	—
70	C₄⋊Dic₁₁	—	2	2	no	—
71	C₄⋊Dic₁₁	—	2	4	no	—
72	C₄⋊Dic₁₁	—	2	4	no	—
73	C₄⋊Dic₁₁	—	4	2	no	—
74	C₄⋊Dic₁₁	—	4	2	no	—
75	Dic₁₁⋊C₄	—	4	2	no	—
76	C₄×Dic₁₁	—	4	1	no	—
77	C₄×Dic₁₁	—	4	1	no	—
78	C₂×C₁₁⋊C₈	—	4	1	no	—
79	C₂×C₁₁⋊C₈	—	4	2	no	—
80	Dic₄₄	—	4	16	no	—
81	C₂×#500	—	11	1	no	—
82	C₂×#462	—	11	2	no	—
83	#1984	—	11	1	no	—
84	C₂×#332	—	11	2	no	—
85	#1277	D₁₁	1	1	yes	characteristic
86	C₂³×C₁₁	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₁	—	2	2	no	—
88	C₂×C₄×C₁₁	#120	1	2	yes	—
89	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
90	C₂×C₄×C₁₁	#121	1	2	yes	—
91	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
94	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
95	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
96	C₂×C₄×C₁₁	#137	1	2	yes	—
97	C₂×Dic₁₁	—	2	2	no	—
98	C₂×Dic₁₁	—	4	1	no	—
99	C₂×Dic₁₁	—	4	1	no	—
100	C₂×Dic₁₁	—	4	1	no	—
101	C₂×Dic₁₁	—	4	4	no	—
102	C₂×Dic₁₁	—	4	2	no	—
103	C₂×Dic₁₁	—	8	2	no	—
104	C₂×Dic₁₁	—	8	2	no	—
105	Dic₂₂	—	2	4	no	—
106	Dic₂₂	—	4	2	no	—
107	Dic₂₂	—	4	4	no	—
108	Dic₂₂	—	4	4	no	—
109	Dic₂₂	—	8	2	no	—
110	Dic₂₂	—	8	2	no	—
111	C₈×C₁₁	—	2	4	no	—
112	C₈×C₁₁	—	4	4	no	—
113	C₁₁⋊C₈	—	8	1	no	—
114	C₂²×Q₁₆	—	22	2	no	—
115	C₂×C₄⋊Q₈	—	11	2	no	—
116	C₂×C₄×Q₈	—	11	1	no	—
117	#500	—	22	4	no	—
118	#462	—	22	4	no	—
119	#462	—	22	4	no	—
120	C₂×#107	—	22	2	no	—
121	C₂×C₄⋊C₈	—	11	1	no	—
122	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
123	C₂×#103	—	22	2	no	—
124	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
125	#336	—	22	2	no	—
126	#332	—	22	4	no	—
127	C₂²×C₁₁	#392	1	1	yes	characteristic
128	C₂²×C₁₁	#462	1	2	yes	—
129	C₂²×C₁₁	#466	1	1	yes	characteristic
130	C₂²×C₁₁	#469	1	1	yes	characteristic
131	C₂²×C₁₁	#473	1	2	yes	—
132	C₄×C₁₁	—	2	2	no	—
133	C₄×C₁₁	#447	1	2	yes	—
134	C₄×C₁₁	#449	1	2	yes	—
135	C₄×C₁₁	#451	1	2	yes	—
136	C₄×C₁₁	#494	1	1	yes	characteristic
137	C₄×C₁₁	#497	1	1	yes	characteristic
138	Dic₁₁	—	4	2	no	—
139	Dic₁₁	—	8	4	no	—
140	Dic₁₁	—	8	1	no	—
141	C₂²×Q₈	—	11	1	no	—
142	C₂²×Q₈	—	22	2	no	—
143	C₂×Q₁₆	—	22	8	no	—
144	C₂×Q₁₆	—	44	4	no	—
145	C₂×Q₁₆	—	44	4	no	—
146	C₂²×C₈	—	2	2	no	—
147	C₂²×C₈	—	22	1	no	—
148	C₂²×C₈	D₄₄	1	2	yes	—
149	C₄⋊Q₈	—	11	4	no	—
150	C₄⋊Q₈	—	22	2	no	—
151	C₄⋊Q₈	—	22	2	no	—
152	C₄⋊Q₈	—	22	2	no	—
153	C₄×Q₈	—	22	2	no	—
154	C₄×Q₈	—	22	2	no	—
155	C₂×C₄⋊C₄	—	11	1	no	—
156	C₂×C₄⋊C₄	—	22	2	no	—
157	C₂×C₄⋊C₄	—	22	2	no	—
158	C₂×C₄⋊C₄	—	22	1	no	—
159	C₂×C₄²	—	22	1	no	—
160	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
161	#107	—	22	8	no	—
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	22	2	no	—
164	C₄⋊C₈	D₄₄	1	4	yes	—
165	#103	—	22	8	no	—
166	C₄×C₈	—	2	2	no	—
167	C₂×C₁₁	#1674	1	2	yes	—
168	C₂×C₁₁	#1694	1	2	yes	—
169	C₂×C₁₁	#1999	1	1	yes	characteristic
170	C₂×C₁₁	#2016	1	1	yes	characteristic
171	C₂×C₁₁	#2020	1	1	yes	characteristic
172	C₂×Q₈	—	11	2	no	—
173	C₂×Q₈	—	22	1	no	—
174	C₂×Q₈	—	22	2	no	—
175	C₂×Q₈	—	22	4	no	—
176	C₂×Q₈	—	22	2	no	—
177	C₂×Q₈	—	44	2	no	—
178	C₂×Q₈	—	44	2	no	—
179	C₂×Q₈	—	44	2	no	—
180	C₂×Q₈	—	44	2	no	—
181	C₂×Q₈	—	44	2	no	—
182	C₂²×C₄	—	22	1	no	—
183	C₂²×C₄	—	22	1	no	—
184	C₂²×C₄	—	44	2	no	—
185	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
186	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
187	C₂²×C₄	#4343	1	1	yes	characteristic
188	Q₁₆	—	44	16	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	4	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	44	1	no	—
195	C₂×C₈	—	44	2	no	—
196	C₂×C₈	Dic₄₄	1	4	yes	complemented
197	C₄⋊C₄	—	22	2	no	—
198	C₄⋊C₄	—	22	4	no	—
199	C₄⋊C₄	—	22	4	no	—
200	C₄⋊C₄	—	44	2	no	—
201	C₄⋊C₄	—	44	2	no	—
202	C₄⋊C₄	—	44	2	no	—
203	C₄²	—	44	1	no	—
204	C₄²	—	44	1	no	—
205	C₄²	C₂×D₄₄	1	2	yes	—
206	C₄²	D₄×D₁₁	1	2	yes	—
207	C₁₁	#10265	1	1	yes	characteristic, complemented, Sylow
208	C₂³	#66948	1	1	yes	characteristic
209	Q₈	—	22	4	no	—
210	Q₈	—	44	2	no	—
211	Q₈	—	44	4	no	—
212	Q₈	—	44	4	no	—
213	Q₈	—	88	2	no	—
214	Q₈	—	88	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	22	2	no	—
217	C₂×C₄	—	44	1	no	—
218	C₂×C₄	—	44	1	no	—
219	C₂×C₄	—	44	2	no	—
220	C₂×C₄	—	44	1	no	—
221	C₂×C₄	—	44	4	no	—
222	C₂×C₄	—	88	2	no	—
223	C₂×C₄	—	88	2	no	—
224	C₂×C₄	#66927	1	1	yes	characteristic
225	C₂×C₄	#66935	1	1	yes	characteristic
226	C₂×C₄	#66935	1	2	yes	—
227	C₂×C₄	#66948	1	2	yes	—
228	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
229	C₂×C₄	#66962	1	2	yes	—
230	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
231	C₂×C₄	#66967	1	2	yes	—
232	C₂×C₄	#66972	1	1	yes	characteristic
233	C₈	—	2	4	no	—
234	C₈	—	4	4	no	—
235	C₈	—	88	1	no	—
236	C₂²	#10622284	1	1	yes	characteristic
237	C₂²	#10622462	1	2	yes	—
238	C₂²	#10622478	1	1	yes	characteristic
239	C₂²	#10622496	1	1	yes	characteristic
240	C₂²	#10622509	1	2	yes	—
241	C₄	—	2	2	no	—
242	C₄	—	44	2	no	—
243	C₄	—	88	4	no	—
244	C₄	—	88	1	no	—
245	C₄	#10622312	1	1	yes	characteristic
246	C₄	#10622328	1	1	yes	characteristic
247	C₄	#10622352	1	2	yes	—
248	C₄	#10622386	1	2	yes	—
249	C₄	#10622424	1	2	yes	—
250	C₂	#13068011	1	2	yes	—
251	C₂	#13068135	1	2	yes	—
252	C₂	#13069615	1	1	yes	characteristic
253	C₂	#13069718	1	1	yes	characteristic
254	C₂	#13069738	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622295

C₂

yes

maximal, characteristic

C₂×#10622462

C₂

yes

maximal

#13069552

C₂

yes

maximal, characteristic

C₂×#10622120

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×#66882

—

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

—

#66882

—

#66880

—

C₄⋊(C₁₁⋊C₈)

—

#10265

—

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

—

C₂×Dic₂₂

—

C₂×Dic₂₂

D₈

yes

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

Q₁₆

yes

complemented

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

—

C₂×C₄×C₁₁

#120

yes

characteristic

C₂×C₄×C₁₁

#121

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₂×C₄×C₁₁

#135

yes

characteristic

C₂×C₄×C₁₁

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₁

#137

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

100

C₂×Dic₁₁

—

101

C₂×Dic₁₁

—

102

C₂×Dic₁₁

—

103

C₂×Dic₁₁

—

104

C₂×Dic₁₁

—

105

Dic₂₂

—

106

Dic₂₂

—

107

Dic₂₂

—

108

Dic₂₂

—

109

Dic₂₂

—

110

Dic₂₂

—

111

C₈×C₁₁

—

112

C₈×C₁₁

—

113

C₁₁⋊C₈

—

114

C₂²×Q₁₆

—

115

C₂×C₄⋊Q₈

—

116

C₂×C₄×Q₈

—

117

#500

—

118

#462

—

119

#462

—

120

C₂×#107

—

121

C₂×C₄⋊C₈

—

122

C₂×C₄⋊C₈

C₂×D₁₁

yes

—

123

C₂×#103

—

124

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

125

#336

—

126

#332

—

127

C₂²×C₁₁

#392

yes

characteristic

128

C₂²×C₁₁

#462

yes

—

129

C₂²×C₁₁

#466

yes

characteristic

130

C₂²×C₁₁

#469

yes

characteristic

131

C₂²×C₁₁

#473

yes

—

132

C₄×C₁₁

—

133

C₄×C₁₁

#447

yes

—

134

C₄×C₁₁

#449

yes

—

135

C₄×C₁₁

#451

yes

—

136

C₄×C₁₁

#494

yes

characteristic

137

C₄×C₁₁

#497

yes

characteristic

138

Dic₁₁

—

139

Dic₁₁

—

140

Dic₁₁

—

141

C₂²×Q₈

—

142

C₂²×Q₈

—

143

C₂×Q₁₆

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂²×C₈

—

147

C₂²×C₈

—

148

C₂²×C₈

D₄₄

yes

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

C₄×Q₈

—

154

C₄×Q₈

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄²

—

160

C₂×C₄²

C₂²×D₁₁

yes

characteristic

161

#107

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

D₄₄

yes

—

165

#103

—

166

C₄×C₈

—

167

C₂×C₁₁

#1674

yes

—

168

C₂×C₁₁

#1694

yes

—

169

C₂×C₁₁

#1999

yes

characteristic

170

C₂×C₁₁

#2016

yes

characteristic

171

C₂×C₁₁

#2020

yes

characteristic

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

C₂×D₄₄

yes

characteristic

186

C₂²×C₄

D₄×D₁₁

yes

characteristic

187

C₂²×C₄

#4343

yes

characteristic

188

Q₁₆

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

Dic₄₄

yes

complemented

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄²

—

204

C₄²

—

205

C₄²

C₂×D₄₄

yes

—

206

C₄²

D₄×D₁₁

yes

—

207

C₁₁

#10265

yes

characteristic, complemented, Sylow

208

C₂³

#66948

yes

characteristic

209

Q₈

—

210

Q₈

—

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

Q₈

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

#66927

yes

characteristic

225

C₂×C₄

#66935

yes

characteristic

226

C₂×C₄

#66935

yes

—

227

C₂×C₄

#66948

yes

—

228

C₂×C₄

C₂×Dic₄₄

yes

—

229

C₂×C₄

#66962

yes

—

230

C₂×C₄

D₈×D₁₁

yes

characteristic

231

C₂×C₄

#66967

yes

—

232

C₂×C₄

#66972

yes

characteristic

233

C₈

—

234

C₈

—

235

C₈

—

236

C₂²

#10622284

yes

characteristic

237

C₂²

#10622462

yes

—

238

C₂²

#10622478

yes

characteristic

239

C₂²

#10622496

yes

characteristic

240

C₂²

#10622509

yes

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

#10622312

yes

characteristic

246

C₄

#10622328

yes

characteristic

247

C₄

#10622352

yes

—

248

C₄

#10622386

yes

—

249

C₄

#10622424

yes

—

250

C₂

#13068011

yes

—

251

C₂

#13068135

yes

—

252

C₂

#13069615

yes

characteristic

253

C₂

#13069718

yes

characteristic

254

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	#10265
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
67. C₂×C₈×C₁₁	Q₁₆	semidirect
196. C₂×C₈	Dic₄₄	semidirect
207. C₁₁	#10265	semidirect

H ≅ G/N

type

67. C₂×C₈×C₁₁

Q₁₆

semidirect

196. C₂×C₈

Dic₄₄

semidirect

207. C₁₁

#10265

semidirect

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

subgroup	index
C₂×#10622295	2
C₂×#10622462	2
#13069552	2
C₂×#10622120	2
C₁₁×#1277	2
#10265	11

subgroup

index

C₁₁×#1277

Subgroups — #14656309

Conjugacy classes of subgroups

Complements

Maximal subgroups