Group #31915874 — subgroups

Subgroups — #31915874

Order 18176.

442 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₂²×D₁₁₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985811	C₂	1	2	yes	maximal, complemented
3	#22589936	C₂	1	1	yes	maximal, characteristic, complemented
4	#22589248	C₂	1	2	yes	maximal, complemented
5	C₂×#368×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₅₆₈	C₂²	1	2	yes	—
7	C₂×D₁₁₃₆	—	2	1	no	—
8	C₂×D₁₁₃₆	—	2	1	no	—
9	C₂×D₁₁₃₆	—	2	2	no	—
10	C₂×D₁₁₃₆	C₄	1	4	yes	complemented
11	C₂×#14556068	C₂²	1	1	yes	characteristic
12	#17986005	—	2	2	no	—
13	C₂×#14556044	—	2	2	no	—
14	#17985954	C₂²	1	1	yes	characteristic
15	#17985811	—	2	4	no	—
16	#17985774	—	2	1	no	—
17	C₁₆×Dic₇₁	—	2	1	no	—
18	C₂²×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×#108×C₇₁	C₂²	1	2	yes	—
20	#368×C₇₁	—	2	2	no	—
21	C₂²×D₂₈₄	—	2	2	no	—
22	C₂×D₅₆₈	—	2	2	no	—
23	C₂×D₅₆₈	—	2	2	no	—
24	C₂×D₅₆₈	—	2	2	no	—
25	C₂×D₅₆₈	—	2	2	no	—
26	C₂×D₅₆₈	—	2	2	no	—
27	C₂×D₅₆₈	C₂×C₄	1	4	yes	—
28	C₂×#11765849	D₄	1	1	yes	characteristic
29	#14556087	D₄	1	1	yes	characteristic
30	D₁₁₃₆	—	2	4	no	—
31	D₁₁₃₆	—	2	4	no	—
32	#14556068	—	2	1	no	—
33	#14556068	D₄	1	2	yes	—
34	C₂×C₇₁⋊C₁₆	—	2	1	no	—
35	#14556050	—	4	4	no	—
36	#14556044	—	4	4	no	—
37	#14556038	—	2	1	no	—
38	C₈×Dic₇₁	—	2	1	no	—
39	C₂×M₁₆×C₇₁	—	2	2	no	—
40	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
41	C₂×C₁₆×C₇₁	C₂×C₄	1	2	yes	—
42	C₂×C₁₆×C₇₁	D₄	1	1	yes	characteristic
43	C₂×C₁₆×C₇₁	D₄	1	1	yes	characteristic
44	C₂×C₁₆×C₇₁	D₄	1	2	yes	—
45	#108×C₇₁	—	2	2	no	—
46	#108×C₇₁	—	2	2	no	—
47	C₂³×D₇₁	—	4	2	no	—
48	C₂×D₂₈₄	—	2	4	no	—
49	C₂×D₂₈₄	—	4	2	no	—
50	C₂×D₂₈₄	—	4	2	no	—
51	C₂×D₂₈₄	—	4	2	no	—
52	C₂×D₂₈₄	—	4	2	no	—
53	C₂×D₂₈₄	—	4	2	no	—
54	D₅₆₈	—	2	4	no	—
55	D₅₆₈	—	2	4	no	—
56	D₅₆₈	—	4	2	no	—
57	D₅₆₈	—	4	2	no	—
58	#11765849	—	2	1	no	—
59	#11765849	D₈	1	2	yes	—
60	C₂×C₇₁⋊C₈	—	2	1	no	—
61	C₄⋊Dic₇₁	D₈	1	2	yes	—
62	C₂²⋊Dic₇₁	—	2	1	no	—
63	C₄×Dic₇₁	—	2	1	no	—
64	C₇₁⋊C₁₆	—	2	2	no	—
65	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
66	M₁₆×C₇₁	—	4	2	no	—
67	M₁₆×C₇₁	—	4	2	no	—
68	C₂×C₈×C₇₁	—	4	2	no	—
69	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
74	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
75	C₁₆×C₇₁	C₂²⋊C₄	1	2	yes	—
76	C₁₆×C₇₁	C₂²⋊C₄	1	2	yes	—
77	C₂³×C₇₁	#135	1	1	yes	characteristic
78	C₂²×D₇₁	—	4	4	no	—
79	C₂²×D₇₁	—	8	2	no	—
80	C₂²×D₇₁	—	8	2	no	—
81	C₂²×D₇₁	—	16	4	no	—
82	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
84	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
85	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
86	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#135	1	1	yes	characteristic
88	C₂×Dic₇₁	—	2	2	no	—
89	D₂₈₄	—	4	4	no	—
90	D₂₈₄	—	4	4	no	—
91	D₂₈₄	—	8	2	no	—
92	D₂₈₄	—	8	2	no	—
93	C₈×C₇₁	—	8	2	no	—
94	C₈×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
96	C₈×C₇₁	#121	1	1	yes	characteristic
97	C₈×C₇₁	#124	1	1	yes	characteristic
98	C₇₁⋊C₈	—	2	2	no	—
99	C₂²×C₇₁	—	2	2	no	—
100	C₂²×C₇₁	C₄×D₈	1	1	yes	characteristic
101	C₂²×C₇₁	#466	1	1	yes	characteristic
102	C₂²×C₇₁	#495	1	1	yes	characteristic
103	C₂×D₇₁	—	8	4	no	—
104	C₂×D₇₁	—	16	4	no	—
105	C₂×D₇₁	—	16	4	no	—
106	C₂×D₇₁	—	16	4	no	—
107	C₄×C₇₁	#390	1	1	yes	characteristic
108	C₄×C₇₁	C₄×D₈	1	1	yes	characteristic
109	C₄×C₇₁	#466	1	1	yes	characteristic
110	C₄×C₇₁	#493	1	1	yes	characteristic
111	Dic₇₁	—	4	2	no	—
112	#13245	—	71	1	no	maximal, Sylow
113	C₂×C₇₁	—	2	1	no	—
114	C₂×C₇₁	—	2	1	no	—
115	C₂×C₇₁	#1970	1	1	yes	characteristic
116	C₂×C₇₁	#2221	1	2	yes	—
117	D₇₁	—	16	4	no	—
118	C₂²×D₁₆	—	71	1	no	—
119	C₂×#368	D₇₁	1	1	yes	characteristic, complemented
120	C₂×#361	—	71	2	no	—
121	#2108	—	71	1	no	—
122	#1978	—	71	2	no	—
123	C₇₁	#13245	1	1	yes	characteristic, complemented, Sylow
124	C₂²×D₈	—	71	2	no	—
125	C₂×D₁₆	—	71	4	no	—
126	C₂×D₁₆	—	142	1	no	—
127	C₂×D₁₆	—	142	1	no	—
128	C₂×D₁₆	—	142	2	no	—
129	C₂×M₃₂	—	71	1	no	—
130	C₂²×C₁₆	C₂×D₇₁	1	1	yes	characteristic
131	C₂×#108	C₂×D₇₁	1	2	yes	—
132	#418	—	142	2	no	—
133	C₂×#100	—	142	2	no	—
134	#405	—	71	1	no	—
135	#368	—	2	2	no	—
136	#361	—	142	4	no	—
137	#346	—	142	1	no	—
138	C₄×C₁₆	—	142	1	no	—
139	C₂²×D₄	—	142	2	no	—
140	C₂×D₈	—	71	4	no	—
141	C₂×D₈	—	142	2	no	—
142	C₂×D₈	—	142	2	no	—
143	C₂×D₈	—	142	2	no	—
144	C₂×D₈	—	142	2	no	—
145	C₂×D₈	—	142	2	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	71	1	no	—
148	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
149	#117	—	71	1	no	—
150	D₁₆	—	142	4	no	—
151	D₁₆	—	142	4	no	—
152	M₃₂	—	71	2	no	—
153	M₃₂	—	142	1	no	—
154	C₂×C₁₆	—	142	1	no	—
155	C₂×C₁₆	C₄×D₇₁	1	2	yes	—
156	C₂×C₁₆	D₂₈₄	1	1	yes	characteristic
157	C₂×C₁₆	D₂₈₄	1	1	yes	characteristic
158	C₂×C₁₆	C₂²⋊D₇₁	1	2	yes	—
159	#108	—	2	2	no	—
160	#108	—	2	2	no	—
161	#102	—	284	4	no	—
162	#100	—	284	4	no	—
163	#97	—	142	1	no	—
164	C₄×C₈	—	142	1	no	—
165	C₂⁴	—	284	2	no	—
166	C₂×D₄	—	284	2	no	—
167	C₂×D₄	—	284	2	no	—
168	C₂×D₄	—	284	2	no	—
169	C₂×D₄	—	284	2	no	—
170	C₂×D₄	—	284	2	no	—
171	C₂×D₄	—	142	4	no	—
172	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
173	D₈	—	284	2	no	—
174	D₈	—	284	2	no	—
175	D₈	—	142	4	no	—
176	D₈	—	142	4	no	—
177	M₁₆	—	4	2	no	—
178	M₁₆	—	4	2	no	—
179	M₁₆	—	71	2	no	—
180	M₁₆	—	142	1	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	142	1	no	—
183	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
184	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
185	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
186	C₂×C₈	C₂×D₂₈₄	1	1	yes	characteristic
187	C₂×C₈	#11765866	1	1	yes	characteristic
188	C₂×C₈	#11765866	1	1	yes	characteristic
189	C₄⋊C₄	—	71	2	no	—
190	C₂²⋊C₄	—	142	1	no	—
191	C₄²	—	142	1	no	—
192	C₁₆	—	142	2	no	—
193	C₁₆	(C₂×D₇₁)⋊C₄	1	2	yes	—
194	C₁₆	(C₂×D₇₁)⋊C₄	1	2	yes	—
195	C₂³	—	284	4	no	—
196	C₂³	—	568	2	no	—
197	C₂³	—	568	2	no	—
198	C₂³	—	1136	4	no	—
199	C₂³	#14556151	1	1	yes	characteristic
200	D₄	—	284	4	no	—
201	D₄	—	284	4	no	—
202	D₄	—	568	2	no	—
203	D₄	—	568	2	no	—
204	C₂×C₄	—	142	2	no	—
205	C₂×C₄	#14556090	1	1	yes	characteristic
206	C₂×C₄	#14556103	1	1	yes	characteristic
207	C₂×C₄	#14556124	1	1	yes	characteristic
208	C₂×C₄	D₈×D₇₁	1	1	yes	characteristic
209	C₂×C₄	D₈×D₇₁	1	1	yes	characteristic
210	C₂×C₄	#14556151	1	1	yes	characteristic
211	C₈	—	8	2	no	—
212	C₈	—	142	2	no	—
213	C₈	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
214	C₈	#14556090	1	1	yes	characteristic
215	C₈	#14556103	1	1	yes	characteristic
216	C₈	#14556117	1	1	yes	characteristic
217	C₂²	—	2	2	no	—
218	C₂²	—	568	4	no	—
219	C₂²	—	1136	4	no	—
220	C₂²	—	1136	4	no	—
221	C₂²	—	1136	4	no	—
222	C₂²	#17986081	1	1	yes	characteristic
223	C₂²	#17986236	1	1	yes	characteristic
224	C₂²	#17986384	1	1	yes	characteristic
225	C₄	—	284	2	no	—
226	C₄	#17985900	1	1	yes	characteristic
227	C₄	#17986081	1	1	yes	characteristic
228	C₄	#17986236	1	1	yes	characteristic
229	C₄	#17986374	1	1	yes	characteristic
230	C₂	—	2	1	no	—
231	C₂	—	2	1	no	—
232	C₂	—	1136	4	no	—
233	C₂	#22589204	1	1	yes	characteristic
234	C₂	#22590461	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₁₁₃₆

C₂

yes

maximal, characteristic

C₂×#17985811

C₂

yes

maximal, complemented

#22589936

C₂

yes

maximal, characteristic, complemented

#22589248

C₂

yes

maximal, complemented

C₂×#368×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂²×D₅₆₈

C₂²

yes

—

C₂×D₁₁₃₆

—

C₂×D₁₁₃₆

—

C₂×D₁₁₃₆

—

C₂×D₁₁₃₆

C₄

yes

complemented

C₂×#14556068

C₂²

yes

—

—

C₂²

yes

characteristic

#17985811

—

#17985774

—

C₁₆×Dic₇₁

—

C₂²×C₁₆×C₇₁

C₂²

yes

characteristic

C₂×#108×C₇₁

C₂²

yes

—

#368×C₇₁

—

C₂²×D₂₈₄

—

C₂×D₅₆₈

—

C₂×D₅₆₈

—

C₂×D₅₆₈

—

C₂×D₅₆₈

—

C₂×D₅₆₈

—

C₂×D₅₆₈

C₂×C₄

yes

—

C₂×#11765849

D₄

yes

characteristic

#14556087

D₄

yes

characteristic

D₁₁₃₆

—

D₁₁₃₆

—

#14556068

—

#14556068

D₄

yes

—

C₂×C₇₁⋊C₁₆

—

#14556050

—

#14556044

—

#14556038

—

C₈×Dic₇₁

—

C₂×M₁₆×C₇₁

—

C₂²×C₈×C₇₁

C₂³

yes

characteristic

C₂×C₁₆×C₇₁

C₂×C₄

yes

—

C₂×C₁₆×C₇₁

D₄

yes

characteristic

C₂×C₁₆×C₇₁

D₄

yes

characteristic

C₂×C₁₆×C₇₁

D₄

yes

—

#108×C₇₁

—

#108×C₇₁

—

C₂³×D₇₁

—

C₂×D₂₈₄

—

C₂×D₂₈₄

—

C₂×D₂₈₄

—

C₂×D₂₈₄

—

C₂×D₂₈₄

—

C₂×D₂₈₄

—

D₅₆₈

—

D₅₆₈

—

D₅₆₈

—

D₅₆₈

—

#11765849

—

#11765849

D₈

yes

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

D₈

yes

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

C₂×C₈×C₇₁

yes

C₂×C₈×C₇₁

yes

C₁₆×C₇₁

C₂²⋊C₄

yes

—

C₁₆×C₇₁

C₂²⋊C₄

yes

—

C₂³×C₇₁

#135

yes

characteristic

C₂²×D₇₁

—

C₂²×D₇₁

—

C₂²×D₇₁

—

C₂²×D₇₁

—

C₂×C₄×C₇₁

C₄×D₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂×D₈

yes

characteristic

C₂×C₄×C₇₁

C₂×D₈

yes

characteristic

C₂×C₄×C₇₁

#135

yes

characteristic

C₂×Dic₇₁

—

D₂₈₄

—

D₂₈₄

—

D₂₈₄

—

D₂₈₄

—

C₈×C₇₁

—

C₈×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₇₁

C₄×D₄

yes

C₈×C₇₁

yes

C₈×C₇₁

yes

C₇₁⋊C₈

—

C₂²×C₇₁

—

100

C₂²×C₇₁

C₄×D₈

yes

characteristic

101

C₂²×C₇₁

#466

yes

characteristic

102

C₂²×C₇₁

#495

yes

characteristic

103

C₂×D₇₁

—

104

C₂×D₇₁

—

105

C₂×D₇₁

—

106

C₂×D₇₁

—

107

C₄×C₇₁

#390

yes

characteristic

108

C₄×C₇₁

C₄×D₈

yes

characteristic

109

C₄×C₇₁

#466

yes

characteristic

110

C₄×C₇₁

#493

yes

characteristic

111

Dic₇₁

—

112

#13245

—

maximal, Sylow

113

C₂×C₇₁

—

114

C₂×C₇₁

—

115

C₂×C₇₁

#1970

yes

characteristic

116

C₂×C₇₁

#2221

yes

—

117

D₇₁

—

118

C₂²×D₁₆

—

119

C₂×#368

D₇₁

yes

characteristic, complemented

120

C₂×#361

—

121

#2108

—

122

#1978

—

123

C₇₁

#13245

yes

characteristic, complemented, Sylow

124

C₂²×D₈

—

125

C₂×D₁₆

—

126

C₂×D₁₆

—

142

—

127

C₂×D₁₆

—

142

—

128

C₂×D₁₆

—

142

—

129

C₂×M₃₂

—

130

C₂²×C₁₆

C₂×D₇₁

yes

characteristic

131

C₂×#108

C₂×D₇₁

yes

—

132

#418

—

142

—

133

C₂×#100

—

142

—

134

#405

—

135

#368

—

136

#361

—

142

—

137

#346

—

142

—

138

C₄×C₁₆

—

142

—

139

C₂²×D₄

—

142

—

140

C₂×D₈

—

141

C₂×D₈

—

142

—

142

C₂×D₈

—

142

—

143

C₂×D₈

—

142

—

144

C₂×D₈

—

142

—

145

C₂×D₈

—

142

—

146

C₂×M₁₆

—

147

C₂×M₁₆

—

148

C₂²×C₈

C₂²×D₇₁

yes

characteristic

149

#117

—

150

D₁₆

—

142

—

151

D₁₆

—

142

—

152

M₃₂

—

153

M₃₂

—

142

—

154

C₂×C₁₆

—

142

—

155

C₂×C₁₆

C₄×D₇₁

yes

—

156

C₂×C₁₆

D₂₈₄

yes

characteristic

157

C₂×C₁₆

D₂₈₄

yes

characteristic

158

C₂×C₁₆

C₂²⋊D₇₁

yes

—

159

#108

—

160

#108

—

161

#102

—

284

—

162

#100

—

284

—

163

#97

—

142

—

164

C₄×C₈

—

142

—

165

C₂⁴

—

284

—

166

C₂×D₄

—

284

—

167

C₂×D₄

—

284

—

168

C₂×D₄

—

284

—

169

C₂×D₄

—

284

—

170

C₂×D₄

—

284

—

171

C₂×D₄

—

142

—

172

C₂²×C₄

D₄×D₇₁

yes

characteristic

173

D₈

—

284

—

174

D₈

—

284

—

175

D₈

—

142

—

176

D₈

—

142

—

177

M₁₆

—

178

M₁₆

—

179

M₁₆

—

180

M₁₆

—

142

—

181

C₂×C₈

—

182

C₂×C₈

—

142

—

183

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

184

C₂×C₈

D₄×D₇₁

yes

characteristic

185

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

186

C₂×C₈

C₂×D₂₈₄

yes

characteristic

187

C₂×C₈

#11765866

yes

characteristic

188

C₂×C₈

#11765866

yes

characteristic

189

C₄⋊C₄

—

190

C₂²⋊C₄

—

142

—

191

C₄²

—

142

—

192

C₁₆

—

142

—

193

C₁₆

(C₂×D₇₁)⋊C₄

yes

—

194

C₁₆

(C₂×D₇₁)⋊C₄

yes

—

195

C₂³

—

284

—

196

C₂³

—

568

—

197

C₂³

—

568

—

198

C₂³

—

1136

—

199

C₂³

#14556151

yes

characteristic

200

D₄

—

284

—

201

D₄

—

284

—

202

D₄

—

568

—

203

D₄

—

568

—

204

C₂×C₄

—

142

—

205

C₂×C₄

#14556090

yes

characteristic

206

C₂×C₄

#14556103

yes

characteristic

207

C₂×C₄

#14556124

yes

characteristic

208

C₂×C₄

D₈×D₇₁

yes

characteristic

209

C₂×C₄

D₈×D₇₁

yes

characteristic

210

C₂×C₄

#14556151

yes

characteristic

211

C₈

—

212

C₈

—

142

—

213

C₈

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

214

C₈

#14556090

yes

characteristic

215

C₈

#14556103

yes

characteristic

216

C₈

#14556117

yes

characteristic

217

C₂²

—

218

C₂²

—

568

—

219

C₂²

—

1136

—

220

C₂²

—

1136

—

221

C₂²

—

1136

—

222

C₂²

#17986081

yes

characteristic

223

C₂²

#17986236

yes

characteristic

224

C₂²

#17986384

yes

characteristic

225

C₄

—

284

—

226

C₄

#17985900

yes

characteristic

227

C₄

#17986081

yes

characteristic

228

C₄

#17986236

yes

characteristic

229

C₄

#17986374

yes

characteristic

230

C₂

—

231

C₂

—

232

C₂

—

1136

—

233

C₂

#22589204

yes

characteristic

234

C₂

#22590461

yes

—

	subgroup	G/H
center	C₂²	#17986236
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₂×#368×C₇₁	C₂
socle	C₂²×C₇₁	#466
prime radical	C₂²×D₁₁₃₆	C₂
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	C₂×#368	D₇₁
hypocenter	C₇₁	#13245
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

subgroup

G/H

center

C₂²

#17986236

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₂×#368×C₇₁

C₂

socle

C₂²×C₇₁

#466

prime radical

C₂²×D₁₁₃₆

C₂

cosocle

C₂²×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

N	H ≅ G/N	type
2. C₂×#17985811	C₂	semidirect
3. #22589936	C₂	semidirect
4. #22589248	C₂	semidirect
5. C₂×#368×C₇₁	C₂	semidirect
10. C₂×D₁₁₃₆	C₄	semidirect
119. C₂×#368	D₇₁	semidirect
123. C₇₁	#13245	semidirect

H ≅ G/N

type

2. C₂×#17985811

C₂

semidirect

3. #22589936

C₂

semidirect

4. #22589248

C₂

semidirect

5. C₂×#368×C₇₁

C₂

semidirect

10. C₂×D₁₁₃₆

C₄

semidirect

119. C₂×#368

D₇₁

semidirect

123. C₇₁

#13245

semidirect

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

subgroup	index
C₂²×D₁₁₃₆	2
C₂×#17985811	2
#22589936	2
#22589248	2
C₂×#368×C₇₁	2
#13245	71

subgroup

index

C₂²×D₁₁₃₆

C₂×#368×C₇₁

Subgroups — #31915874

Conjugacy classes of subgroups

Complements

Maximal subgroups