Group #31915872 — subgroups

Subgroups — #31915872

Order 18176.

402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 123 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×#17985829	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985815	C₂	1	2	yes	maximal
3	#22589936	C₂	1	1	yes	maximal, characteristic
4	#22589256	C₂	1	2	yes	maximal
5	C₂²×Q₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556068	C₂²	1	1	yes	characteristic
7	C₂×#14556064	C₂²	1	2	yes	—
8	#17986008	—	2	2	no	—
9	C₂×#14556047	—	2	2	no	—
10	#17985954	C₂²	1	1	yes	characteristic
11	#17985829	—	2	2	no	—
12	#17985815	—	2	4	no	—
13	#17985774	—	2	1	no	—
14	C₁₆×Dic₇₁	—	2	1	no	—
15	C₂²×Q₁₆×C₇₁	C₂²	1	2	yes	—
16	C₂×Q₃₂×C₇₁	—	2	2	no	—
17	C₂×Q₃₂×C₇₁	—	2	1	no	—
18	C₂×Q₃₂×C₇₁	—	2	1	no	—
19	C₂×Q₃₂×C₇₁	C₄	1	4	yes	complemented
20	C₂²×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×#11765849	—	2	2	no	—
22	C₂×#11765849	D₄	1	1	yes	characteristic
23	#14556087	D₄	1	1	yes	characteristic
24	#14556068	—	2	1	no	—
25	#14556068	D₄	1	2	yes	—
26	C₂×C₇₁⋊C₁₆	—	2	1	no	—
27	#14556064	—	2	2	no	—
28	#14556064	—	2	2	no	—
29	#14556052	—	4	4	no	—
30	#14556047	—	4	4	no	—
31	#14556038	—	2	1	no	—
32	C₈×Dic₇₁	—	2	1	no	—
33	C₂²×Q₈×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	—	2	2	no	—
38	C₂×Q₁₆×C₇₁	—	2	2	no	—
39	C₂×Q₁₆×C₇₁	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
41	Q₃₂×C₇₁	—	2	4	no	—
42	Q₃₂×C₇₁	—	2	4	no	—
43	C₂×C₁₆×C₇₁	C₂×C₄	1	2	yes	—
44	C₂×C₁₆×C₇₁	D₄	1	2	yes	—
45	C₂×C₁₆×C₇₁	D₄	1	1	yes	characteristic
46	C₂×C₁₆×C₇₁	D₄	1	1	yes	characteristic
47	#11765849	—	2	1	no	—
48	#11765849	—	4	2	no	—
49	#11765849	—	4	2	no	—
50	#11765849	D₈	1	2	yes	—
51	C₂×C₇₁⋊C₈	—	2	1	no	—
52	C₂×C₇₁⋊C₈	—	4	2	no	—
53	C₄⋊Dic₇₁	D₈	1	2	yes	—
54	C₂²⋊Dic₇₁	—	2	1	no	—
55	C₄×Dic₇₁	—	2	1	no	—
56	C₇₁⋊C₁₆	—	2	2	no	—
57	C₂×Q₈×C₇₁	—	2	4	no	—
58	C₂×Q₈×C₇₁	—	4	2	no	—
59	C₂×Q₈×C₇₁	—	4	2	no	—
60	C₂×Q₈×C₇₁	—	4	2	no	—
61	C₂×Q₈×C₇₁	—	4	2	no	—
62	C₂×Q₈×C₇₁	—	4	2	no	—
63	C₂²×C₄×C₇₁	—	4	2	no	—
64	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
65	Q₁₆×C₇₁	—	2	4	no	—
66	Q₁₆×C₇₁	—	2	4	no	—
67	Q₁₆×C₇₁	—	4	2	no	—
68	Q₁₆×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	Q₈×C₇₁	—	4	4	no	—
79	Q₈×C₇₁	—	4	4	no	—
80	Q₈×C₇₁	—	8	2	no	—
81	Q₈×C₇₁	—	8	2	no	—
82	C₂×C₄×C₇₁	—	4	4	no	—
83	C₂×C₄×C₇₁	—	8	2	no	—
84	C₂×C₄×C₇₁	—	8	2	no	—
85	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
88	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₇₁	#135	1	1	yes	characteristic
91	C₂×Dic₇₁	—	2	2	no	—
92	C₈×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
94	C₈×C₇₁	#121	1	1	yes	characteristic
95	C₈×C₇₁	#124	1	1	yes	characteristic
96	C₇₁⋊C₈	—	2	2	no	—
97	C₇₁⋊C₈	—	8	2	no	—
98	C₂²×C₇₁	—	2	2	no	—
99	C₂²×C₇₁	C₄×D₈	1	1	yes	characteristic
100	C₂²×C₇₁	#466	1	1	yes	characteristic
101	C₂²×C₇₁	#495	1	1	yes	characteristic
102	C₄×C₇₁	—	8	4	no	—
103	C₄×C₇₁	#390	1	1	yes	characteristic
104	C₄×C₇₁	C₄×D₈	1	1	yes	characteristic
105	C₄×C₇₁	#466	1	1	yes	characteristic
106	C₄×C₇₁	#493	1	1	yes	characteristic
107	Dic₇₁	—	4	2	no	—
108	#13244	—	71	1	no	maximal, Sylow
109	C₂×C₇₁	—	2	1	no	—
110	C₂×C₇₁	—	2	1	no	—
111	C₂×C₇₁	#1970	1	1	yes	characteristic
112	C₂×C₇₁	#2222	1	2	yes	—
113	C₂²×Q₃₂	D₇₁	1	1	yes	characteristic
114	C₂×#368	—	71	1	no	—
115	C₂×#362	—	71	2	no	—
116	#2108	—	71	1	no	—
117	#1979	—	71	2	no	—
118	C₇₁	#13244	1	1	yes	characteristic, complemented, Sylow
119	C₂²×Q₁₆	C₂×D₇₁	1	2	yes	—
120	C₂×Q₃₂	—	2	1	no	—
121	C₂×Q₃₂	—	2	1	no	—
122	C₂×Q₃₂	—	2	2	no	—
123	C₂×Q₃₂	Dic₇₁	1	4	yes	complemented
124	C₂×M₃₂	—	71	1	no	—
125	C₂²×C₁₆	C₂×D₇₁	1	1	yes	characteristic
126	C₂×#108	—	71	2	no	—
127	#419	—	142	2	no	—
128	C₂×#101	—	142	2	no	—
129	#405	—	71	1	no	—
130	#368	—	142	2	no	—
131	#362	—	142	4	no	—
132	#346	—	142	1	no	—
133	C₄×C₁₆	—	142	1	no	—
134	C₂²×Q₈	—	2	2	no	—
135	C₂×Q₁₆	—	2	2	no	—
136	C₂×Q₁₆	—	2	2	no	—
137	C₂×Q₁₆	—	2	2	no	—
138	C₂×Q₁₆	—	2	2	no	—
139	C₂×Q₁₆	—	2	2	no	—
140	C₂×Q₁₆	C₂×Dic₇₁	1	4	yes	—
141	C₂×M₁₆	—	71	1	no	—
142	C₂×M₁₆	—	142	2	no	—
143	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
144	#117	—	71	1	no	—
145	Q₃₂	—	2	4	no	—
146	Q₃₂	—	2	4	no	—
147	M₃₂	—	71	2	no	—
148	M₃₂	—	142	1	no	—
149	C₂×C₁₆	—	142	1	no	—
150	C₂×C₁₆	C₂×Dic₇₁	1	2	yes	—
151	C₂×C₁₆	C₂²⋊D₇₁	1	1	yes	characteristic
152	C₂×C₁₆	C₂²⋊D₇₁	1	1	yes	characteristic
153	C₂×C₁₆	C₂²⋊D₇₁	1	2	yes	—
154	#108	—	142	2	no	—
155	#108	—	142	2	no	—
156	#103	—	284	4	no	—
157	#101	—	284	4	no	—
158	#97	—	142	1	no	—
159	C₄×C₈	—	142	1	no	—
160	C₂×Q₈	—	2	4	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	4	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
168	Q₁₆	—	2	4	no	—
169	Q₁₆	—	2	4	no	—
170	Q₁₆	—	4	2	no	—
171	Q₁₆	—	4	2	no	—
172	M₁₆	—	284	2	no	—
173	M₁₆	—	284	2	no	—
174	M₁₆	—	71	2	no	—
175	M₁₆	—	142	1	no	—
176	C₂×C₈	—	284	2	no	—
177	C₂×C₈	—	142	1	no	—
178	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
179	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
180	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
181	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
182	C₂×C₈	#11765864	1	1	yes	characteristic
183	C₂×C₈	#11765864	1	1	yes	characteristic
184	C₄⋊C₄	—	71	2	no	—
185	C₂²⋊C₄	—	142	1	no	—
186	C₄²	—	142	1	no	—
187	C₁₆	—	142	2	no	—
188	C₁₆	C₂²⋊Dic₇₁	1	2	yes	—
189	C₁₆	C₂²⋊Dic₇₁	1	2	yes	—
190	C₂³	#14556147	1	1	yes	characteristic
191	Q₈	—	4	4	no	—
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	Q₈	—	8	2	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	8	2	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	—	142	2	no	—
199	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
200	C₂×C₄	#14556099	1	1	yes	characteristic
201	C₂×C₄	#14556124	1	1	yes	characteristic
202	C₂×C₄	D₈×D₇₁	1	1	yes	characteristic
203	C₂×C₄	D₈×D₇₁	1	1	yes	characteristic
204	C₂×C₄	#14556147	1	1	yes	characteristic
205	C₈	—	568	2	no	—
206	C₈	—	142	2	no	—
207	C₈	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
208	C₈	D₄×Dic₇₁	1	1	yes	characteristic
209	C₈	#14556099	1	1	yes	characteristic
210	C₈	#14556115	1	1	yes	characteristic
211	C₂²	—	2	2	no	—
212	C₂²	D₈×Dic₇₁	1	1	yes	characteristic
213	C₂²	#17986232	1	1	yes	characteristic
214	C₂²	#17986382	1	1	yes	characteristic
215	C₄	—	8	4	no	—
216	C₄	—	284	2	no	—
217	C₄	#17985902	1	1	yes	characteristic
218	C₄	D₈×Dic₇₁	1	1	yes	characteristic
219	C₄	#17986232	1	1	yes	characteristic
220	C₄	#17986374	1	1	yes	characteristic
221	C₂	—	2	1	no	—
222	C₂	—	2	1	no	—
223	C₂	#22589207	1	1	yes	characteristic
224	C₂	#22590462	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17985829

C₂

yes

maximal, characteristic

C₂×#17985815

C₂

yes

maximal

#22589936

C₂

yes

maximal, characteristic

#22589256

C₂

yes

maximal

C₂²×Q₃₂×C₇₁

C₂

yes

maximal, characteristic

C₂×#14556068

C₂²

yes

characteristic

C₂×#14556064

C₂²

yes

—

#17986008

—

C₂×#14556047

—

#17985954

C₂²

yes

—

—

—

C₁₆×Dic₇₁

—

C₂²×Q₁₆×C₇₁

C₂²

yes

—

C₂×Q₃₂×C₇₁

—

C₂×Q₃₂×C₇₁

—

C₂×Q₃₂×C₇₁

—

C₂×Q₃₂×C₇₁

C₄

yes

complemented

C₂²×C₁₆×C₇₁

C₂²

yes

characteristic

C₂×#11765849

—

C₂×#11765849

D₄

yes

characteristic

#14556087

D₄

yes

characteristic

#14556068

—

#14556068

D₄

yes

—

C₂×C₇₁⋊C₁₆

—

—

—

—

—

—

C₈×Dic₇₁

—

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

—

Q₃₂×C₇₁

—

C₂×C₁₆×C₇₁

C₂×C₄

yes

—

C₂×C₁₆×C₇₁

D₄

yes

—

C₂×C₁₆×C₇₁

D₄

yes

characteristic

C₂×C₁₆×C₇₁

D₄

yes

—

—

—

D₈

yes

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

D₈

yes

—

C₂²⋊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

—

C₁₆×C₇₁

C₂²⋊C₄

yes

—

C₂³×C₇₁

#135

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

characteristic

C₂×C₄×C₇₁

C₂×D₈

yes

characteristic

C₂×C₄×C₇₁

#135

yes

characteristic

C₂×Dic₇₁

—

C₈×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₇₁

C₄×D₄

yes

C₈×C₇₁

yes

C₈×C₇₁

yes

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

C₄×D₈

yes

characteristic

100

C₂²×C₇₁

#466

yes

characteristic

101

C₂²×C₇₁

#495

yes

characteristic

102

C₄×C₇₁

—

103

C₄×C₇₁

#390

yes

characteristic

104

C₄×C₇₁

C₄×D₈

yes

characteristic

105

C₄×C₇₁

#466

yes

characteristic

106

C₄×C₇₁

#493

yes

characteristic

107

Dic₇₁

—

108

#13244

—

maximal, Sylow

109

C₂×C₇₁

—

110

C₂×C₇₁

—

111

C₂×C₇₁

#1970

yes

characteristic

112

C₂×C₇₁

#2222

yes

—

113

C₂²×Q₃₂

D₇₁

yes

characteristic

114

C₂×#368

—

115

C₂×#362

—

116

#2108

—

117

#1979

—

118

C₇₁

#13244

yes

characteristic, complemented, Sylow

119

C₂²×Q₁₆

C₂×D₇₁

yes

—

120

C₂×Q₃₂

—

121

C₂×Q₃₂

—

122

C₂×Q₃₂

—

123

C₂×Q₃₂

Dic₇₁

yes

complemented

124

C₂×M₃₂

—

125

C₂²×C₁₆

C₂×D₇₁

yes

characteristic

126

C₂×#108

—

127

#419

—

142

—

128

C₂×#101

—

142

—

129

#405

—

130

#368

—

142

—

131

#362

—

142

—

132

#346

—

142

—

133

C₄×C₁₆

—

142

—

134

C₂²×Q₈

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂×Q₁₆

—

139

C₂×Q₁₆

—

140

C₂×Q₁₆

C₂×Dic₇₁

yes

—

141

C₂×M₁₆

—

142

C₂×M₁₆

—

142

—

143

C₂²×C₈

C₂²×D₇₁

yes

characteristic

144

#117

—

145

Q₃₂

—

146

Q₃₂

—

147

M₃₂

—

148

M₃₂

—

142

—

149

C₂×C₁₆

—

142

—

150

C₂×C₁₆

C₂×Dic₇₁

yes

—

151

C₂×C₁₆

C₂²⋊D₇₁

yes

characteristic

152

C₂×C₁₆

C₂²⋊D₇₁

yes

characteristic

153

C₂×C₁₆

C₂²⋊D₇₁

yes

—

154

#108

—

142

—

155

#108

—

142

—

156

#103

—

284

—

157

#101

—

284

—

158

#97

—

142

—

159

C₄×C₈

—

142

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂²×C₄

—

167

C₂²×C₄

D₄×D₇₁

yes

characteristic

168

Q₁₆

—

169

Q₁₆

—

170

Q₁₆

—

171

Q₁₆

—

172

M₁₆

—

284

—

173

M₁₆

—

284

—

174

M₁₆

—

175

M₁₆

—

142

—

176

C₂×C₈

—

284

—

177

C₂×C₈

—

142

—

178

C₂×C₈

C₂²×Dic₇₁

yes

characteristic

179

C₂×C₈

D₄×D₇₁

yes

characteristic

180

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

181

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

182

C₂×C₈

#11765864

yes

characteristic

183

C₂×C₈

#11765864

yes

characteristic

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

142

—

186

C₄²

—

142

—

187

C₁₆

—

142

—

188

C₁₆

C₂²⋊Dic₇₁

yes

—

189

C₁₆

C₂²⋊Dic₇₁

yes

—

190

C₂³

#14556147

yes

characteristic

191

Q₈

—

192

Q₈

—

193

Q₈

—

194

Q₈

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

142

—

199

C₂×C₄

D₄×Dic₇₁

yes

characteristic

200

C₂×C₄

#14556099

yes

characteristic

201

C₂×C₄

#14556124

yes

characteristic

202

C₂×C₄

D₈×D₇₁

yes

characteristic

203

C₂×C₄

D₈×D₇₁

yes

characteristic

204

C₂×C₄

#14556147

yes

characteristic

205

C₈

—

568

—

206

C₈

—

142

—

207

C₈

C₂×C₂²⋊Dic₇₁

yes

characteristic

208

C₈

D₄×Dic₇₁

yes

characteristic

209

C₈

#14556099

yes

characteristic

210

C₈

#14556115

yes

characteristic

211

C₂²

—

212

C₂²

D₈×Dic₇₁

yes

characteristic

213

C₂²

#17986232

yes

characteristic

214

C₂²

#17986382

yes

characteristic

215

C₄

—

216

C₄

—

284

—

217

C₄

#17985902

yes

characteristic

218

C₄

D₈×Dic₇₁

yes

characteristic

219

C₄

#17986232

yes

characteristic

220

C₄

#17986374

yes

characteristic

221

C₂

—

222

C₂

—

223

C₂

#22589207

yes

characteristic

224

C₂

#22590462

yes

—

	subgroup	G/H
center	C₂²	#17986232
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₂²×Q₃₂×C₇₁	C₂
socle	C₂²×C₇₁	#466
prime radical	C₂³×C₇₁	#135
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	C₂²×Q₃₂	D₇₁
hypocenter	C₇₁	#13244
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂²

#17986232

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₂²×Q₃₂×C₇₁

C₂

C₂²×C₇₁

C₂³×C₇₁

C₂²×C₈×C₇₁

C₂³

hypercenter

C₂²×Q₃₂

D₇₁

hypocenter

C₇₁

#13244

LCS

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
19. C₂×Q₃₂×C₇₁	C₄	semidirect
118. C₇₁	#13244	semidirect
123. C₂×Q₃₂	Dic₇₁	semidirect

H ≅ G/N

type

19. C₂×Q₃₂×C₇₁

C₄

semidirect

118. C₇₁

#13244

semidirect

123. C₂×Q₃₂

Dic₇₁

semidirect

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

subgroup	index
C₂×#17985829	2
C₂×#17985815	2
#22589936	2
#22589256	2
C₂²×Q₃₂×C₇₁	2
#13244	71

subgroup

index

C₂²×Q₃₂×C₇₁

Subgroups — #31915872

Conjugacy classes of subgroups

Complements

Maximal subgroups