Group #31915852 — subgroups

Subgroups — #31915852

Order 18176.

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

normal subgroups only

This group has 430 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×#17985827	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985803	C₂	1	2	yes	maximal
3	C₂×#17985774	C₂	1	1	yes	maximal, characteristic
4	#22589202	C₂	1	2	yes	maximal
5	C₂²×Q₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₂×#14556062	C₂²	1	2	yes	—
8	C₂×#14556052	—	2	2	no	—
9	C₂×C₈×Dic₇₁	C₂²	1	1	yes	characteristic
10	#17985906	—	2	2	no	—
11	#17985827	—	2	2	no	—
12	#17985803	—	2	4	no	—
13	#17985774	—	2	2	no	—
14	C₂²×Q₁₆×C₇₁	C₂²	1	2	yes	—
15	C₂×Q₃₂×C₇₁	—	2	2	no	—
16	C₂×Q₃₂×C₇₁	—	2	2	no	—
17	C₂×Q₃₂×C₇₁	C₄	1	4	yes	complemented
18	C₂²×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
19	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
20	C₂×C₄⋊Dic₇₁	—	2	2	no	—
21	C₂×C₄×Dic₇₁	D₄	1	1	yes	characteristic
22	C₂×C₇₁⋊C₁₆	—	2	1	no	—
23	C₂×C₇₁⋊C₁₆	—	2	1	no	—
24	C₂×C₇₁⋊C₁₆	D₄	1	2	yes	—
25	#14556062	—	2	2	no	—
26	#14556062	—	2	2	no	—
27	#14556052	—	4	4	no	—
28	C₈×Dic₇₁	—	2	1	no	—
29	C₈×Dic₇₁	—	2	1	no	—
30	C₇₁⋊#95	—	4	4	no	—
31	C₂²×Q₈×C₇₁	—	2	2	no	—
32	C₂×Q₁₆×C₇₁	—	2	2	no	—
33	C₂×Q₁₆×C₇₁	—	2	2	no	—
34	C₂×Q₁₆×C₇₁	—	2	2	no	—
35	C₂×Q₁₆×C₇₁	—	2	2	no	—
36	C₂×Q₁₆×C₇₁	—	2	2	no	—
37	C₂×Q₁₆×C₇₁	C₂×C₄	1	4	yes	—
38	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
39	Q₃₂×C₇₁	—	2	8	no	—
40	C₂×C₁₆×C₇₁	C₂×C₄	1	2	yes	—
41	C₂×C₁₆×C₇₁	D₄	1	2	yes	—
42	C₂×C₁₆×C₇₁	D₄	1	2	yes	—
43	C₂²×Dic₇₁	—	4	2	no	—
44	C₂²×Dic₇₁	D₈	1	2	yes	—
45	C₂×C₇₁⋊C₈	—	2	1	no	—
46	C₂×C₇₁⋊C₈	—	2	1	no	—
47	C₂×C₇₁⋊C₈	D₈	1	2	yes	—
48	C₄⋊Dic₇₁	—	4	2	no	—
49	C₄⋊Dic₇₁	—	4	2	no	—
50	C₄×Dic₇₁	—	2	1	no	—
51	C₄×Dic₇₁	—	2	1	no	—
52	C₇₁⋊C₁₆	—	2	2	no	—
53	C₂×Q₈×C₇₁	—	2	4	no	—
54	C₂×Q₈×C₇₁	—	4	2	no	—
55	C₂×Q₈×C₇₁	—	4	2	no	—
56	C₂×Q₈×C₇₁	—	4	2	no	—
57	C₂×Q₈×C₇₁	—	4	2	no	—
58	C₂×Q₈×C₇₁	—	4	2	no	—
59	C₂²×C₄×C₇₁	—	4	2	no	—
60	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
61	Q₁₆×C₇₁	—	2	4	no	—
62	Q₁₆×C₇₁	—	2	4	no	—
63	Q₁₆×C₇₁	—	4	2	no	—
64	Q₁₆×C₇₁	—	4	2	no	—
65	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
70	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
71	C₁₆×C₇₁	C₂²⋊C₄	1	4	yes	—
72	C₂³×C₇₁	C₂×D₈	1	1	yes	characteristic
73	Q₈×C₇₁	—	4	4	no	—
74	Q₈×C₇₁	—	4	4	no	—
75	Q₈×C₇₁	—	8	2	no	—
76	Q₈×C₇₁	—	8	2	no	—
77	C₂×C₄×C₇₁	—	4	4	no	—
78	C₂×C₄×C₇₁	—	8	2	no	—
79	C₂×C₄×C₇₁	—	8	2	no	—
80	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
81	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
82	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
83	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₇₁	#135	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#135	1	1	yes	characteristic
86	C₂×Dic₇₁	—	2	2	no	—
87	C₂×Dic₇₁	—	2	4	no	—
88	C₂×Dic₇₁	—	8	2	no	—
89	C₂×Dic₇₁	—	8	4	no	—
90	C₈×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
92	C₈×C₇₁	#121	1	1	yes	characteristic
93	C₈×C₇₁	#124	1	1	yes	characteristic
94	C₇₁⋊C₈	—	2	2	no	—
95	C₂²×C₇₁	C₄×D₈	1	1	yes	characteristic
96	C₂²×C₇₁	#466	1	1	yes	characteristic
97	C₂²×C₇₁	#493	1	1	yes	characteristic
98	C₂²×C₇₁	#510	1	4	yes	—
99	C₄×C₇₁	—	8	4	no	—
100	C₄×C₇₁	#390	1	1	yes	characteristic
101	C₄×C₇₁	C₄×D₈	1	1	yes	characteristic
102	C₄×C₇₁	#466	1	1	yes	characteristic
103	C₄×C₇₁	#495	1	1	yes	characteristic
104	Dic₇₁	—	4	2	no	—
105	Dic₇₁	—	16	2	no	—
106	#13240	—	71	1	no	maximal, Sylow
107	C₂×C₇₁	#1970	1	1	yes	characteristic
108	C₂×C₇₁	#2176	1	2	yes	—
109	C₂×C₇₁	#2219	1	2	yes	—
110	C₂×C₇₁	#2251	1	2	yes	—
111	C₂²×Q₃₂	D₇₁	1	1	yes	characteristic
112	C₂×#367	—	71	1	no	—
113	C₂×#358	—	71	2	no	—
114	C₂×#346	—	71	1	no	—
115	#1969	—	71	2	no	—
116	C₇₁	#13240	1	1	yes	characteristic, complemented, Sylow
117	C₂²×Q₁₆	C₂×D₇₁	1	2	yes	—
118	C₂×Q₃₂	—	2	2	no	—
119	C₂×Q₃₂	—	2	2	no	—
120	C₂×Q₃₂	Dic₇₁	1	4	yes	complemented
121	C₂²×C₁₆	—	71	1	no	—
122	C₂²×C₁₆	C₂×D₇₁	1	1	yes	characteristic
123	C₂×#107	—	71	2	no	—
124	C₂×#103	—	142	2	no	—
125	C₂×C₄×C₈	—	71	1	no	—
126	#391	—	142	2	no	—
127	#367	—	142	2	no	—
128	#358	—	142	4	no	—
129	#346	—	142	2	no	—
130	C₂²×Q₈	—	2	2	no	—
131	C₂×Q₁₆	—	2	2	no	—
132	C₂×Q₁₆	—	2	2	no	—
133	C₂×Q₁₆	—	2	2	no	—
134	C₂×Q₁₆	—	2	2	no	—
135	C₂×Q₁₆	—	2	2	no	—
136	C₂×Q₁₆	C₂×Dic₇₁	1	4	yes	—
137	C₂²×C₈	—	71	1	no	—
138	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
139	C₂×C₄⋊C₄	—	142	2	no	—
140	C₂×C₄²	—	71	1	no	—
141	Q₃₂	—	2	8	no	—
142	C₂×C₁₆	—	71	2	no	—
143	C₂×C₁₆	—	142	1	no	—
144	C₂×C₁₆	—	142	1	no	—
145	C₂×C₁₆	C₂×Dic₇₁	1	2	yes	—
146	C₂×C₁₆	C₂²⋊D₇₁	1	2	yes	—
147	C₂×C₁₆	C₂²⋊D₇₁	1	2	yes	—
148	#107	—	142	2	no	—
149	#107	—	142	2	no	—
150	#103	—	284	4	no	—
151	C₄×C₈	—	142	1	no	—
152	C₄×C₈	—	142	1	no	—
153	#95	—	284	4	no	—
154	C₂×Q₈	—	2	4	no	—
155	C₂×Q₈	—	4	2	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂×Q₈	—	4	2	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂²×C₄	—	4	2	no	—
161	C₂²×C₄	—	284	2	no	—
162	C₂²×C₄	—	71	2	no	—
163	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
164	Q₁₆	—	2	4	no	—
165	Q₁₆	—	2	4	no	—
166	Q₁₆	—	4	2	no	—
167	Q₁₆	—	4	2	no	—
168	C₂×C₈	—	71	2	no	—
169	C₂×C₈	—	142	1	no	—
170	C₂×C₈	—	142	1	no	—
171	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
172	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
173	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
174	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
175	C₂×C₈	#11765864	1	1	yes	characteristic
176	C₂×C₈	#11765864	1	1	yes	characteristic
177	C₄⋊C₄	—	284	2	no	—
178	C₄⋊C₄	—	284	2	no	—
179	C₄²	—	142	1	no	—
180	C₄²	—	142	1	no	—
181	C₁₆	—	142	2	no	—
182	C₁₆	C₂²⋊Dic₇₁	1	4	yes	—
183	C₂³	D₈×D₇₁	1	1	yes	characteristic
184	Q₈	—	4	4	no	—
185	Q₈	—	4	4	no	—
186	Q₈	—	8	2	no	—
187	Q₈	—	8	2	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	—	8	2	no	—
190	C₂×C₄	—	8	2	no	—
191	C₂×C₄	—	568	2	no	—
192	C₂×C₄	—	568	4	no	—
193	C₂×C₄	—	142	4	no	—
194	C₂×C₄	—	142	2	no	—
195	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
196	C₂×C₄	#14556099	1	1	yes	characteristic
197	C₂×C₄	#14556124	1	1	yes	characteristic
198	C₂×C₄	D₈×D₇₁	1	1	yes	characteristic
199	C₂×C₄	#14556147	1	1	yes	characteristic
200	C₂×C₄	#14556147	1	1	yes	characteristic
201	C₈	—	142	2	no	—
202	C₈	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
203	C₈	D₄×Dic₇₁	1	1	yes	characteristic
204	C₈	#14556099	1	1	yes	characteristic
205	C₈	#14556115	1	1	yes	characteristic
206	C₂²	D₈×Dic₇₁	1	1	yes	characteristic
207	C₂²	#17986232	1	1	yes	characteristic
208	C₂²	#17986374	1	1	yes	characteristic
209	C₂²	#17986441	1	4	yes	—
210	C₄	—	8	4	no	—
211	C₄	—	284	2	no	—
212	C₄	—	1136	2	no	—
213	C₄	#17985902	1	1	yes	characteristic
214	C₄	D₈×Dic₇₁	1	1	yes	characteristic
215	C₄	#17986232	1	1	yes	characteristic
216	C₄	#17986382	1	1	yes	characteristic
217	C₂	#22589207	1	1	yes	characteristic
218	C₂	#22590211	1	2	yes	—
219	C₂	#22590445	1	2	yes	—
220	C₂	#22590608	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17985827

C₂

yes

maximal, characteristic

C₂×#17985803

C₂

yes

maximal

C₂×#17985774

C₂

yes

maximal, characteristic

#22589202

C₂

yes

maximal

C₂²×Q₃₂×C₇₁

C₂

yes

maximal, characteristic

C₂²×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₂×#14556062

C₂²

yes

—

C₂×#14556052

—

C₂×C₈×Dic₇₁

C₂²

yes

—

—

—

—

C₂²×Q₁₆×C₇₁

C₂²

yes

—

C₂×Q₃₂×C₇₁

—

C₂×Q₃₂×C₇₁

—

C₂×Q₃₂×C₇₁

C₄

yes

complemented

C₂²×C₁₆×C₇₁

C₂²

yes

characteristic

C₂²×C₇₁⋊C₈

D₄

yes

characteristic

C₂×C₄⋊Dic₇₁

—

C₂×C₄×Dic₇₁

D₄

yes

characteristic

C₂×C₇₁⋊C₁₆

—

C₂×C₇₁⋊C₁₆

—

C₂×C₇₁⋊C₁₆

D₄

yes

—

#14556062

—

#14556062

—

#14556052

—

C₈×Dic₇₁

—

C₈×Dic₇₁

—

C₇₁⋊#95

—

C₂²×Q₈×C₇₁

—

C₂×Q₁₆×C₇₁

—

C₂×Q₁₆×C₇₁

—

C₂×Q₁₆×C₇₁

—

C₂×Q₁₆×C₇₁

—

C₂×Q₁₆×C₇₁

—

C₂×Q₁₆×C₇₁

C₂×C₄

yes

—

C₂²×C₈×C₇₁

C₂³

yes

characteristic

Q₃₂×C₇₁

—

C₂×C₁₆×C₇₁

C₂×C₄

yes

—

C₂×C₁₆×C₇₁

D₄

yes

—

C₂×C₁₆×C₇₁

D₄

yes

—

C₂²×Dic₇₁

—

C₂²×Dic₇₁

D₈

yes

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

D₈

yes

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

Q₁₆×C₇₁

—

Q₁₆×C₇₁

—

Q₁₆×C₇₁

—

Q₁₆×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

—

C₂³×C₇₁

C₂×D₈

yes

characteristic

Q₈×C₇₁

—

Q₈×C₇₁

—

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₄×D₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂×D₈

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₈×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₇₁

C₄×D₄

yes

C₈×C₇₁

yes

C₈×C₇₁

yes

C₇₁⋊C₈

—

C₂²×C₇₁

C₄×D₈

yes

C₂²×C₇₁

yes

C₂²×C₇₁

yes

C₂²×C₇₁

yes

—

C₄×C₇₁

—

100

C₄×C₇₁

#390

yes

characteristic

101

C₄×C₇₁

C₄×D₈

yes

characteristic

102

C₄×C₇₁

#466

yes

characteristic

103

C₄×C₇₁

#495

yes

characteristic

104

Dic₇₁

—

105

Dic₇₁

—

106

#13240

—

maximal, Sylow

107

C₂×C₇₁

#1970

yes

characteristic

108

C₂×C₇₁

#2176

yes

—

109

C₂×C₇₁

#2219

yes

—

110

C₂×C₇₁

#2251

yes

—

111

C₂²×Q₃₂

D₇₁

yes

characteristic

112

C₂×#367

—

113

C₂×#358

—

114

C₂×#346

—

115

#1969

—

116

C₇₁

#13240

yes

characteristic, complemented, Sylow

117

C₂²×Q₁₆

C₂×D₇₁

yes

—

118

C₂×Q₃₂

—

119

C₂×Q₃₂

—

120

C₂×Q₃₂

Dic₇₁

yes

complemented

121

C₂²×C₁₆

—

122

C₂²×C₁₆

C₂×D₇₁

yes

characteristic

123

C₂×#107

—

124

C₂×#103

—

142

—

125

C₂×C₄×C₈

—

126

#391

—

142

—

127

#367

—

142

—

128

#358

—

142

—

129

#346

—

142

—

130

C₂²×Q₈

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

133

C₂×Q₁₆

—

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

C₂×Dic₇₁

yes

—

137

C₂²×C₈

—

138

C₂²×C₈

C₂²×D₇₁

yes

characteristic

139

C₂×C₄⋊C₄

—

142

—

140

C₂×C₄²

—

141

Q₃₂

—

142

C₂×C₁₆

—

143

C₂×C₁₆

—

142

—

144

C₂×C₁₆

—

142

—

145

C₂×C₁₆

C₂×Dic₇₁

yes

—

146

C₂×C₁₆

C₂²⋊D₇₁

yes

—

147

C₂×C₁₆

C₂²⋊D₇₁

yes

—

148

#107

—

142

—

149

#107

—

142

—

150

#103

—

284

—

151

C₄×C₈

—

142

—

152

C₄×C₈

—

142

—

153

#95

—

284

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂²×C₄

—

161

C₂²×C₄

—

284

—

162

C₂²×C₄

—

163

C₂²×C₄

D₄×D₇₁

yes

characteristic

164

Q₁₆

—

165

Q₁₆

—

166

Q₁₆

—

167

Q₁₆

—

168

C₂×C₈

—

169

C₂×C₈

—

142

—

170

C₂×C₈

—

142

—

171

C₂×C₈

C₂²×Dic₇₁

yes

characteristic

172

C₂×C₈

D₄×D₇₁

yes

characteristic

173

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

174

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

175

C₂×C₈

#11765864

yes

characteristic

176

C₂×C₈

#11765864

yes

characteristic

177

C₄⋊C₄

—

284

—

178

C₄⋊C₄

—

284

—

179

C₄²

—

142

—

180

C₄²

—

142

—

181

C₁₆

—

142

—

182

C₁₆

C₂²⋊Dic₇₁

yes

—

183

C₂³

D₈×D₇₁

yes

characteristic

184

Q₈

—

185

Q₈

—

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

568

—

192

C₂×C₄

—

568

—

193

C₂×C₄

—

142

—

194

C₂×C₄

—

142

—

195

C₂×C₄

D₄×Dic₇₁

yes

characteristic

196

C₂×C₄

#14556099

yes

characteristic

197

C₂×C₄

#14556124

yes

characteristic

198

C₂×C₄

D₈×D₇₁

yes

characteristic

199

C₂×C₄

#14556147

yes

characteristic

200

C₂×C₄

#14556147

yes

characteristic

201

C₈

—

142

—

202

C₈

C₂×C₂²⋊Dic₇₁

yes

characteristic

203

C₈

D₄×Dic₇₁

yes

characteristic

204

C₈

#14556099

yes

characteristic

205

C₈

#14556115

yes

characteristic

206

C₂²

D₈×Dic₇₁

yes

characteristic

207

C₂²

#17986232

yes

characteristic

208

C₂²

#17986374

yes

characteristic

209

C₂²

#17986441

yes

—

210

C₄

—

211

C₄

—

284

—

212

C₄

—

1136

—

213

C₄

#17985902

yes

characteristic

214

C₄

D₈×Dic₇₁

yes

characteristic

215

C₄

#17986232

yes

characteristic

216

C₄

#17986382

yes

characteristic

217

C₂

#22589207

yes

characteristic

218

C₂

#22590211

yes

—

219

C₂

#22590445

yes

—

220

C₂

#22590608

yes

—

	subgroup	G/H
center	C₂³	D₈×D₇₁
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₂²×Q₃₂×C₇₁	C₂
socle, prime radical	C₂³×C₇₁	C₂×D₈
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	C₂²×Q₃₂	D₇₁
hypocenter	C₇₁	#13240
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂³

D₈×D₇₁

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₂²×Q₃₂×C₇₁

C₂

socle, prime radical

C₂³×C₇₁

C₂×D₈

cosocle

C₂²×C₈×C₇₁

C₂³

hypercenter

C₂²×Q₃₂

D₇₁

hypocenter

C₇₁

#13240

LCS

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
17. C₂×Q₃₂×C₇₁	C₄	semidirect
116. C₇₁	#13240	semidirect
120. C₂×Q₃₂	Dic₇₁	semidirect

H ≅ G/N

type

17. C₂×Q₃₂×C₇₁

C₄

semidirect

116. C₇₁

#13240

semidirect

120. C₂×Q₃₂

Dic₇₁

semidirect

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

subgroup	index
C₂×#17985827	2
C₂×#17985803	2
C₂×#17985774	2
#22589202	2
C₂²×Q₃₂×C₇₁	2
#13240	71

subgroup

index

C₂²×Q₃₂×C₇₁

Subgroups — #31915852

Conjugacy classes of subgroups

Complements

Maximal subgroups