Group #31909312 — subgroups

Subgroups — #31909312

Order 18176.

242 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 83 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	#22590171	C₂	1	1	yes	maximal, characteristic, complemented
2	#22590159	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₅₆₈	C₂	1	1	yes	maximal, characteristic
4	#22586294	C₂	1	1	yes	maximal, characteristic, complemented
5	#22586294	C₂	1	1	yes	maximal, characteristic, complemented
6	#22586258	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#1367	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14556067	—	2	1	no	—
9	C₂×C₁₆×D₇₁	—	2	1	no	—
10	C₄×D₅₆₈	C₄	1	1	yes	characteristic
11	C₈×D₂₈₄	C₂²	1	1	yes	characteristic
12	C₈×D₂₈₄	C₂²	1	1	yes	characteristic
13	(C₂×D₇₁)⋊C₁₆	—	2	1	no	—
14	(C₂×D₇₁)⋊C₁₆	—	2	1	no	—
15	C₄×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₄×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
17	#17985752	C₄	1	1	yes	characteristic
18	#17985728	C₄	1	1	yes	characteristic
19	#17985728	C₄	1	1	yes	characteristic
20	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
21	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
22	C₈²×C₇₁	C₂²	1	1	yes	characteristic
23	C₂×D₅₆₈	C₈	1	1	yes	characteristic
24	C₂×C₈×D₇₁	—	2	1	no	—
25	C₂×C₈×D₇₁	—	2	1	no	—
26	C₄×D₂₈₄	C₂×C₄	1	1	yes	characteristic
27	C₄×D₂₈₄	C₂×C₄	1	1	yes	characteristic
28	#14556067	—	4	2	no	—
29	C₂×C₇₁⋊C₁₆	—	2	1	no	—
30	C₂×C₇₁⋊C₁₆	D₄	1	1	yes	characteristic
31	C₂×C₇₁⋊C₁₆	D₄	1	1	yes	characteristic
32	C₁₆×D₇₁	—	4	2	no	—
33	#14556062	C₈	1	1	yes	characteristic
34	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
35	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
36	#14556050	C₈	1	1	yes	characteristic
37	#14556050	C₈	1	1	yes	characteristic
38	(C₂×D₇₁)⋊C₈	—	2	1	no	—
39	(C₂×D₇₁)⋊C₈	—	2	1	no	—
40	C₂×C₁₆×C₇₁	—	2	1	no	—
41	C₂×C₁₆×C₇₁	—	2	1	no	—
42	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
45	C₂×D₂₈₄	C₂×C₈	1	1	yes	characteristic
46	C₂×D₂₈₄	C₂×C₈	1	1	yes	characteristic
47	C₂×C₄×D₇₁	—	2	1	no	—
48	C₂×C₄×D₇₁	—	2	1	no	—
49	D₅₆₈	—	2	2	no	—
50	C₂×C₇₁⋊C₈	—	2	1	no	—
51	C₂×C₇₁⋊C₈	—	2	1	no	—
52	C₈×D₇₁	—	4	1	no	—
53	C₈×D₇₁	—	4	1	no	—
54	C₈×D₇₁	—	4	1	no	—
55	C₈×D₇₁	—	4	1	no	—
56	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
57	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
58	(C₂×D₇₁)⋊C₄	—	2	1	no	—
59	(C₂×D₇₁)⋊C₄	—	2	1	no	—
60	C₇₁⋊C₁₆	—	2	1	no	—
61	C₇₁⋊C₁₆	—	2	1	no	—
62	C₇₁⋊C₁₆	—	4	1	no	—
63	C₂×C₈×C₇₁	—	2	1	no	—
64	C₂×C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
65	C₂×C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
66	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
68	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
69	C₁₆×C₇₁	—	4	1	no	—
70	C₁₆×C₇₁	—	4	1	no	—
71	C₂²×D₇₁	—	2	1	no	—
72	C₂²×D₇₁	—	2	1	no	—
73	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
74	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
75	C₂×C₄×C₇₁	#131	1	1	yes	characteristic
76	C₂×Dic₇₁	—	2	1	no	—
77	C₂×Dic₇₁	—	2	1	no	—
78	D₂₈₄	—	2	1	no	—
79	D₂₈₄	—	2	1	no	—
80	D₂₈₄	—	2	1	no	—
81	D₂₈₄	M₃₂	1	2	yes	complemented
82	C₄×D₇₁	—	4	1	no	—
83	C₄×D₇₁	—	4	1	no	—
84	C₄×D₇₁	—	4	1	no	—
85	C₄×D₇₁	—	4	1	no	—
86	C₈×C₇₁	—	2	2	no	—
87	C₈×C₇₁	—	2	1	no	—
88	C₈×C₇₁	—	2	1	no	—
89	C₈×C₇₁	—	2	1	no	—
90	C₈×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₈×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₇₁⋊C₈	—	4	1	no	—
93	C₇₁⋊C₈	—	4	1	no	—
94	C₂²×C₇₁	C₈×D₄	1	1	yes	characteristic
95	C₂×D₇₁	—	2	2	no	—
96	C₂×D₇₁	—	4	1	no	—
97	C₂×D₇₁	—	4	1	no	—
98	C₂×D₇₁	—	4	1	no	—
99	C₂×D₇₁	—	4	1	no	—
100	C₂×D₇₁	—	4	1	no	—
101	C₄×C₇₁	—	2	1	no	—
102	C₄×C₇₁	#442	1	1	yes	characteristic
103	C₄×C₇₁	#444	1	1	yes	characteristic
104	C₄×C₇₁	C₂×M₃₂	1	1	yes	characteristic
105	C₄×C₇₁	#504	1	1	yes	characteristic
106	Dic₇₁	—	4	1	no	—
107	Dic₇₁	—	4	1	no	—
108	#12063	—	71	1	no	maximal, Sylow
109	C₂×C₇₁	#1580	1	1	yes	characteristic
110	C₂×C₇₁	#2168	1	1	yes	characteristic
111	C₂×C₇₁	#2170	1	1	yes	characteristic
112	D₇₁	—	4	2	no	—
113	D₇₁	—	8	1	no	—
114	#2169	—	71	1	no	—
115	D₄×C₁₆	—	71	1	no	—
116	C₈×D₈	—	71	1	no	—
117	#1367	D₇₁	1	1	yes	characteristic, complemented
118	D₄⋊C₁₆	—	71	1	no	—
119	D₄⋊C₁₆	—	71	1	no	—
120	#1312	—	71	1	no	—
121	C₇₁	#12063	1	1	yes	characteristic, complemented, Sylow
122	C₂×M₃₂	—	142	1	no	—
123	C₂²×C₁₆	—	142	1	no	—
124	C₄×D₈	—	71	1	no	—
125	C₈×D₄	—	71	1	no	—
126	C₈×D₄	—	71	1	no	—
127	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
128	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
129	C₂²⋊C₁₆	—	142	1	no	—
130	C₂²⋊C₁₆	—	142	1	no	—
131	C₄×C₁₆	—	71	1	no	—
132	C₄×C₁₆	—	71	1	no	—
133	#335	—	71	1	no	—
134	D₄⋊C₈	—	71	1	no	—
135	D₄⋊C₈	—	71	1	no	—
136	C₈²	C₂×D₇₁	1	1	yes	characteristic
137	C₂×D₈	—	71	1	no	—
138	C₂²×C₈	—	142	1	no	—
139	C₂²×C₈	—	142	1	no	—
140	C₄×D₄	—	71	1	no	—
141	C₄×D₄	—	71	1	no	—
142	M₃₂	—	284	2	no	—
143	C₂×C₁₆	—	2	1	no	—
144	C₂×C₁₆	—	2	1	no	—
145	C₂×C₁₆	—	284	2	no	—
146	C₂×C₁₆	—	71	1	no	—
147	C₂×C₁₆	—	71	1	no	—
148	C₂×C₁₆	—	142	1	no	—
149	#107	—	71	1	no	—
150	C₄⋊C₈	—	71	1	no	—
151	C₄⋊C₈	—	71	1	no	—
152	#102	—	71	1	no	—
153	#102	—	71	1	no	—
154	C₂²⋊C₈	—	142	1	no	—
155	C₂²⋊C₈	—	142	1	no	—
156	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
157	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
158	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
159	C₂×D₄	—	71	1	no	—
160	C₂×D₄	—	71	1	no	—
161	C₂²×C₄	—	142	1	no	—
162	C₂²×C₄	—	142	1	no	—
163	D₈	—	142	2	no	—
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	284	1	no	—
166	C₂×C₈	—	284	1	no	—
167	C₂×C₈	—	284	1	no	—
168	C₂×C₈	—	284	1	no	—
169	C₂×C₈	—	142	1	no	—
170	C₂×C₈	—	142	1	no	—
171	C₂×C₈	C₈×D₇₁	1	1	yes	characteristic
172	C₂×C₈	C₈×D₇₁	1	1	yes	characteristic
173	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
174	C₂×C₈	#11765866	1	1	yes	characteristic
175	C₄⋊C₄	—	71	1	no	—
176	C₄⋊C₄	—	71	1	no	—
177	C₂²⋊C₄	—	142	1	no	—
178	C₂²⋊C₄	—	142	1	no	—
179	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
180	C₁₆	—	4	1	no	—
181	C₁₆	—	4	1	no	—
182	C₁₆	—	284	1	no	—
183	C₁₆	—	142	1	no	—
184	C₁₆	—	142	1	no	—
185	C₂³	—	142	1	no	—
186	C₂³	—	142	1	no	—
187	D₄	—	71	2	no	—
188	D₄	—	142	1	no	—
189	D₄	—	142	1	no	—
190	D₄	—	142	1	no	—
191	C₂×C₄	—	284	1	no	—
192	C₂×C₄	—	284	1	no	—
193	C₂×C₄	—	284	1	no	—
194	C₂×C₄	—	284	1	no	—
195	C₂×C₄	—	142	1	no	—
196	C₂×C₄	—	142	1	no	—
197	C₂×C₄	#14556090	1	1	yes	characteristic
198	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
199	C₂×C₄	#14556136	1	1	yes	characteristic
200	C₈	—	2	2	no	—
201	C₈	—	2	1	no	—
202	C₈	—	2	1	no	—
203	C₈	—	2	1	no	—
204	C₈	—	284	1	no	—
205	C₈	—	284	1	no	—
206	C₈	#14556155	1	1	yes	characteristic
207	C₈	#14556155	1	1	yes	characteristic
208	C₂²	—	284	1	no	—
209	C₂²	—	284	1	no	—
210	C₂²	—	284	1	no	—
211	C₂²	—	284	1	no	—
212	C₂²	—	284	1	no	—
213	C₂²	—	142	2	no	—
214	C₂²	#17986064	1	1	yes	characteristic
215	C₄	—	2	1	no	—
216	C₄	—	284	1	no	—
217	C₄	—	284	1	no	—
218	C₄	#17986110	1	1	yes	characteristic
219	C₄	#17986120	1	1	yes	characteristic
220	C₄	M₃₂×D₇₁	1	1	yes	characteristic
221	C₄	#17986415	1	1	yes	characteristic
222	C₂	—	284	2	no	—
223	C₂	—	568	1	no	—
224	C₂	#22587163	1	1	yes	characteristic
225	C₂	#22590164	1	1	yes	characteristic
226	C₂	#22590176	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22590171

C₂

yes

maximal, characteristic, complemented

#22590159

C₂

yes

maximal, characteristic, complemented

C₈×D₅₆₈

C₂

yes

maximal, characteristic

#22586294

C₂

yes

maximal, characteristic, complemented

#22586294

C₂

yes

maximal, characteristic, complemented

#22586258

C₂

yes

maximal, characteristic, complemented

C₇₁×#1367

C₂

yes

maximal, characteristic, complemented

C₂×#14556067

—

C₂×C₁₆×D₇₁

—

C₄×D₅₆₈

C₄

yes

characteristic

C₈×D₂₈₄

C₂²

yes

characteristic

C₈×D₂₈₄

C₂²

yes

characteristic

(C₂×D₇₁)⋊C₁₆

—

(C₂×D₇₁)⋊C₁₆

—

C₄×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₄×C₇₁⋊C₁₆

C₂²

yes

characteristic

#17985752

C₄

yes

characteristic

#17985728

C₄

yes

characteristic

#17985728

C₄

yes

characteristic

C₄⋊C₁₆×C₇₁

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₁

C₂²

yes

characteristic

C₈²×C₇₁

C₂²

yes

characteristic

C₂×D₅₆₈

C₈

yes

characteristic

C₂×C₈×D₇₁

—

C₂×C₈×D₇₁

—

C₄×D₂₈₄

C₂×C₄

yes

characteristic

C₄×D₂₈₄

C₂×C₄

yes

characteristic

#14556067

—

C₂×C₇₁⋊C₁₆

—

C₂×C₇₁⋊C₁₆

D₄

yes

characteristic

C₂×C₇₁⋊C₁₆

D₄

yes

characteristic

C₁₆×D₇₁

—

#14556062

C₈

yes

characteristic

C₄⋊(C₇₁⋊C₈)

C₂×C₄

yes

characteristic

C₄⋊(C₇₁⋊C₈)

C₂×C₄

yes

characteristic

#14556050

C₈

yes

characteristic

#14556050

C₈

yes

characteristic

(C₂×D₇₁)⋊C₈

—

(C₂×D₇₁)⋊C₈

—

C₂×C₁₆×C₇₁

—

C₂×C₁₆×C₇₁

—

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

C₂³

yes

characteristic

C₂×D₂₈₄

C₂×C₈

yes

characteristic

C₂×D₂₈₄

C₂×C₈

yes

characteristic

C₂×C₄×D₇₁

—

C₂×C₄×D₇₁

—

D₅₆₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₈×D₇₁

—

C₈×D₇₁

—

C₈×D₇₁

—

C₈×D₇₁

—

C₄⋊Dic₇₁

C₂×C₈

yes

characteristic

C₄⋊Dic₇₁

C₂×C₈

yes

characteristic

(C₂×D₇₁)⋊C₄

—

(C₂×D₇₁)⋊C₄

—

C₇₁⋊C₁₆

—

C₇₁⋊C₁₆

—

C₇₁⋊C₁₆

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂×C₈

yes

characteristic

C₂×C₈×C₇₁

C₂×C₈

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

#41

yes

characteristic

C₄²×C₇₁

C₂²×C₄

yes

characteristic

C₁₆×C₇₁

—

C₁₆×C₇₁

—

C₂²×D₇₁

—

C₂²×D₇₁

—

C₂×C₄×C₇₁

C₄×D₄

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₁

#131

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

D₂₈₄

—

D₂₈₄

—

D₂₈₄

—

D₂₈₄

M₃₂

yes

complemented

C₄×D₇₁

—

C₄×D₇₁

—

C₄×D₇₁

—

C₄×D₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

yes

C₈×C₇₁

yes

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

C₈×D₄

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

100

C₂×D₇₁

—

101

C₄×C₇₁

—

102

C₄×C₇₁

#442

yes

characteristic

103

C₄×C₇₁

#444

yes

characteristic

104

C₄×C₇₁

C₂×M₃₂

yes

characteristic

105

C₄×C₇₁

#504

yes

characteristic

106

Dic₇₁

—

107

Dic₇₁

—

108

#12063

—

maximal, Sylow

109

C₂×C₇₁

#1580

yes

characteristic

110

C₂×C₇₁

#2168

yes

characteristic

111

C₂×C₇₁

#2170

yes

characteristic

112

D₇₁

—

113

D₇₁

—

114

#2169

—

115

D₄×C₁₆

—

116

C₈×D₈

—

117

#1367

D₇₁

yes

characteristic, complemented

118

D₄⋊C₁₆

—

119

D₄⋊C₁₆

—

120

#1312

—

121

C₇₁

#12063

yes

characteristic, complemented, Sylow

122

C₂×M₃₂

—

142

—

123

C₂²×C₁₆

—

142

—

124

C₄×D₈

—

125

C₈×D₄

—

126

C₈×D₄

—

127

C₄⋊C₁₆

C₂×D₇₁

yes

characteristic

128

C₄⋊C₁₆

C₂×D₇₁

yes

characteristic

129

C₂²⋊C₁₆

—

142

—

130

C₂²⋊C₁₆

—

142

—

131

C₄×C₁₆

—

132

C₄×C₁₆

—

133

#335

—

134

D₄⋊C₈

—

135

D₄⋊C₈

—

136

C₈²

C₂×D₇₁

yes

characteristic

137

C₂×D₈

—

138

C₂²×C₈

—

142

—

139

C₂²×C₈

—

142

—

140

C₄×D₄

—

141

C₄×D₄

—

142

M₃₂

—

284

—

143

C₂×C₁₆

—

144

C₂×C₁₆

—

145

C₂×C₁₆

—

284

—

146

C₂×C₁₆

—

147

C₂×C₁₆

—

148

C₂×C₁₆

—

142

—

149

#107

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

#102

—

153

#102

—

154

C₂²⋊C₈

—

142

—

155

C₂²⋊C₈

—

142

—

156

C₄×C₈

C₄×D₇₁

yes

characteristic

157

C₄×C₈

C₄×D₇₁

yes

characteristic

158

C₄×C₈

C₂²×D₇₁

yes

characteristic

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂²×C₄

—

142

—

162

C₂²×C₄

—

142

—

163

D₈

—

142

—

164

C₂×C₈

—

165

C₂×C₈

—

284

—

166

C₂×C₈

—

284

—

167

C₂×C₈

—

284

—

168

C₂×C₈

—

284

—

169

C₂×C₈

—

142

—

170

C₂×C₈

—

142

—

171

C₂×C₈

C₈×D₇₁

yes

characteristic

172

C₂×C₈

C₈×D₇₁

yes

characteristic

173

C₂×C₈

D₄×D₇₁

yes

characteristic

174

C₂×C₈

#11765866

yes

characteristic

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₂²⋊C₄

—

142

—

178

C₂²⋊C₄

—

142

—

179

C₄²

C₂×C₄×D₇₁

yes

characteristic

180

C₁₆

—

181

C₁₆

—

182

C₁₆

—

284

—

183

C₁₆

—

142

—

184

C₁₆

—

142

—

185

C₂³

—

142

—

186

C₂³

—

142

—

187

D₄

—

188

D₄

—

142

—

189

D₄

—

142

—

190

D₄

—

142

—

191

C₂×C₄

—

284

—

192

C₂×C₄

—

284

—

193

C₂×C₄

—

284

—

194

C₂×C₄

—

284

—

195

C₂×C₄

—

142

—

196

C₂×C₄

—

142

—

197

C₂×C₄

#14556090

yes

characteristic

198

C₂×C₄

C₂×C₈×D₇₁

yes

characteristic

199

C₂×C₄

#14556136

yes

characteristic

200

C₈

—

201

C₈

—

202

C₈

—

203

C₈

—

204

C₈

—

284

—

205

C₈

—

284

—

206

C₈

#14556155

yes

characteristic

207

C₈

#14556155

yes

characteristic

208

C₂²

—

284

—

209

C₂²

—

284

—

210

C₂²

—

284

—

211

C₂²

—

284

—

212

C₂²

—

284

—

213

C₂²

—

142

—

214

C₂²

#17986064

yes

characteristic

215

C₄

—

216

C₄

—

284

—

217

C₄

—

284

—

218

C₄

#17986110

yes

characteristic

219

C₄

#17986120

yes

characteristic

220

C₄

M₃₂×D₇₁

yes

characteristic

221

C₄

#17986415

yes

characteristic

222

C₂

—

284

—

223

C₂

—

568

—

224

C₂

#22587163

yes

characteristic

225

C₂

#22590164

yes

characteristic

226

C₂

#22590176

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₇₁
commutator	C₂×C₄×C₇₁	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₇₁
Fitting	C₇₁×#1367	C₂
socle	C₂²×C₇₁	C₈×D₄
prime radical	C₂×D₅₆₈	C₈
cosocle	C₄×C₈×C₇₁	C₂³
hypercenter	#1367	D₇₁
hypocenter	C₇₁	#12063
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1367

subgroup

G/H

center

C₂×C₈

D₄×D₇₁

commutator

C₂×C₄×C₇₁

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₇₁

Fitting

C₇₁×#1367

C₂

socle

C₂²×C₇₁

C₈×D₄

prime radical

C₂×D₅₆₈

C₈

cosocle

C₄×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1367

N	H ≅ G/N	type
1. #22590171	C₂	semidirect
2. #22590159	C₂	semidirect
4. #22586294	C₂	semidirect
5. #22586294	C₂	semidirect
6. #22586258	C₂	semidirect
7. C₇₁×#1367	C₂	semidirect
81. D₂₈₄	M₃₂	semidirect
117. #1367	D₇₁	semidirect
121. C₇₁	#12063	semidirect

H ≅ G/N

type

1. #22590171

C₂

semidirect

2. #22590159

C₂

semidirect

4. #22586294

C₂

semidirect

5. #22586294

C₂

semidirect

6. #22586258

C₂

semidirect

7. C₇₁×#1367

C₂

semidirect

81. D₂₈₄

M₃₂

semidirect

117. #1367

D₇₁

semidirect

121. C₇₁

#12063

semidirect

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

subgroup	index
#22590171	2
#22590159	2
C₈×D₅₆₈	2
#22586294	2
#22586258	2
C₇₁×#1367	2
#12063	71

subgroup

index

C₈×D₅₆₈

C₇₁×#1367

Subgroups — #31909312

Conjugacy classes of subgroups

Complements

Maximal subgroups