Group #31902437 — subgroups

Subgroups — #31902437

Order 18176.

320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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	#22589279	C₂	1	1	yes	maximal, characteristic
2	#22588514	C₂	1	1	yes	maximal, characteristic
3	#22587114	C₂	1	1	yes	maximal, characteristic
4	#22586770	C₂	1	1	yes	maximal, characteristic
5	#22586768	C₂	1	1	yes	maximal, characteristic
6	#22586170	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1571	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Dic₁₄₂	C₂²	1	1	yes	characteristic
9	#17986052	C₂²	1	1	yes	characteristic
10	C₂×#14556063	—	2	2	no	—
11	#17986023	C₂²	1	1	yes	characteristic
12	C₂×#14556039	C₂²	1	1	yes	characteristic
13	#17985753	—	2	2	no	—
14	#17985751	—	2	2	no	—
15	#17985731	—	2	2	no	—
16	#17985729	—	2	2	no	—
17	#431×C₇₁	C₂²	1	1	yes	characteristic
18	#423×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
20	#335×C₇₁	—	2	2	no	—
21	C₂²×Dic₁₄₂	Q₈	1	1	yes	characteristic
22	C₂×#11765849	—	2	1	no	—
23	C₂²×C₇₁⋊C₈	D₄	1	2	yes	—
24	C₄×Dic₁₄₂	—	2	1	no	—
25	C₄×Dic₁₄₂	—	2	1	no	—
26	C₄×Dic₁₄₂	—	2	1	no	—
27	C₄×Dic₁₄₂	—	2	1	no	—
28	C₂×C₄⋊Dic₇₁	Q₈	1	1	yes	characteristic
29	C₂×Dic₇₁⋊C₄	—	2	1	no	—
30	C₂×C₄×Dic₇₁	—	2	1	no	—
31	#14556063	—	4	4	no	—
32	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
33	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
34	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
35	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
36	#14556039	—	2	1	no	—
37	#14556039	—	2	1	no	—
38	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
39	C₂×M₁₆×C₇₁	—	2	1	no	—
40	C₂²×C₈×C₇₁	—	2	1	no	—
41	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₁	—	2	1	no	—
43	C₄⋊C₈×C₇₁	—	2	1	no	—
44	C₄⋊C₈×C₇₁	—	2	1	no	—
45	C₄⋊C₈×C₇₁	—	2	1	no	—
46	C₄⋊C₈×C₇₁	—	2	1	no	—
47	C₂²⋊C₈×C₇₁	—	2	1	no	—
48	C₄×C₈×C₇₁	D₄	1	2	yes	—
49	C₂×Dic₁₄₂	—	2	1	no	—
50	C₂×Dic₁₄₂	—	2	1	no	—
51	C₂×Dic₁₄₂	—	4	2	no	—
52	C₂²×Dic₇₁	—	2	1	no	—
53	C₂²×Dic₇₁	—	2	1	no	—
54	#11765849	—	4	2	no	—
55	C₂×C₇₁⋊C₈	—	2	2	no	—
56	C₂×C₇₁⋊C₈	—	2	2	no	—
57	C₂×C₇₁⋊C₈	—	2	2	no	—
58	C₂×C₇₁⋊C₈	—	4	1	no	—
59	C₂×C₇₁⋊C₈	Q₁₆	1	4	yes	—
60	C₄⋊Dic₇₁	—	2	1	no	—
61	C₄⋊Dic₇₁	—	2	1	no	—
62	Dic₇₁⋊C₄	—	4	1	no	—
63	Dic₇₁⋊C₄	—	4	1	no	—
64	C₄×Dic₇₁	—	4	1	no	—
65	C₄×Dic₇₁	—	4	1	no	—
66	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
69	M₁₆×C₇₁	—	4	2	no	—
70	C₂×C₈×C₇₁	—	2	2	no	—
71	C₂×C₈×C₇₁	—	4	1	no	—
72	C₂×C₈×C₇₁	—	4	1	no	—
73	C₂×C₈×C₇₁	—	4	2	no	—
74	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₇₁	#41	1	1	yes	characteristic
77	C₄²×C₇₁	#41	1	1	yes	characteristic
78	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
79	C₂×C₄×C₇₁	—	4	1	no	—
80	C₂×C₄×C₇₁	—	4	1	no	—
81	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
84	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
87	C₂×C₄×C₇₁	C₂×Q₁₆	1	2	yes	—
88	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	2	yes	—
89	C₂×Dic₇₁	—	2	2	no	—
90	C₂×Dic₇₁	—	4	1	no	—
91	C₂×Dic₇₁	—	4	1	no	—
92	C₂×Dic₇₁	—	4	2	no	—
93	C₂×Dic₇₁	—	4	1	no	—
94	Dic₁₄₂	—	2	2	no	—
95	Dic₁₄₂	—	2	2	no	—
96	Dic₁₄₂	—	4	1	no	—
97	Dic₁₄₂	—	4	1	no	—
98	C₈×C₇₁	—	4	2	no	—
99	C₈×C₇₁	—	8	1	no	—
100	C₈×C₇₁	—	8	1	no	—
101	C₇₁⋊C₈	—	2	4	no	—
102	C₇₁⋊C₈	—	4	2	no	—
103	C₇₁⋊C₈	—	8	1	no	—
104	C₂²×C₇₁	—	2	1	no	—
105	C₂²×C₇₁	—	2	1	no	—
106	C₂²×C₇₁	#399	1	1	yes	characteristic
107	C₂²×C₇₁	#477	1	2	yes	—
108	C₄×C₇₁	—	2	1	no	—
109	C₄×C₇₁	—	2	1	no	—
110	C₄×C₇₁	—	2	1	no	—
111	C₄×C₇₁	—	2	1	no	—
112	C₄×C₇₁	#484	1	2	yes	—
113	C₄×C₇₁	#494	1	1	yes	characteristic
114	C₄×C₇₁	#496	1	1	yes	characteristic
115	Dic₇₁	—	4	2	no	—
116	Dic₇₁	—	8	1	no	—
117	#10662	—	71	1	no	maximal, Sylow
118	C₂×C₇₁	—	2	2	no	—
119	C₂×C₇₁	#2091	1	1	yes	characteristic
120	C₂×C₇₁	#2095	1	1	yes	characteristic
121	C₂×C₇₁	#2098	1	1	yes	characteristic
122	#1985	—	71	1	no	—
123	#1849	—	71	1	no	—
124	#1571	—	71	1	no	—
125	#1571	D₇₁	1	1	yes	characteristic
126	#1487	—	71	1	no	—
127	#1487	—	71	1	no	—
128	#1275	—	71	1	no	—
129	C₇₁	#10662	1	1	yes	characteristic, complemented, Sylow
130	C₂×C₄×Q₈	—	71	1	no	—
131	#431	—	71	1	no	—
132	#431	C₂×D₇₁	1	1	yes	characteristic
133	C₂×#108	—	142	2	no	—
134	#423	—	71	1	no	—
135	#423	C₂×D₇₁	1	1	yes	characteristic
136	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
137	C₂×#97	—	71	1	no	—
138	#336	—	142	2	no	—
139	#335	—	2	2	no	—
140	#335	—	142	2	no	—
141	Q₈⋊C₈	—	142	2	no	—
142	Q₈⋊C₈	—	142	2	no	—
143	C₂²×Q₈	—	71	1	no	—
144	C₂×M₁₆	—	2	1	no	—
145	C₂×M₁₆	—	142	1	no	—
146	C₂²×C₈	—	2	1	no	—
147	C₂²×C₈	—	71	2	no	—
148	C₄×Q₈	—	142	1	no	—
149	C₄×Q₈	—	142	1	no	—
150	C₄×Q₈	—	142	1	no	—
151	C₄×Q₈	—	142	1	no	—
152	C₂×C₄⋊C₄	—	71	1	no	—
153	C₂×C₄⋊C₄	—	142	1	no	—
154	C₂×C₄²	—	142	1	no	—
155	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
156	#108	—	284	4	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	2	1	no	—
159	C₄⋊C₈	—	2	1	no	—
160	C₄⋊C₈	—	2	1	no	—
161	C₄⋊C₈	—	2	1	no	—
162	C₄⋊C₈	—	142	1	no	—
163	C₄⋊C₈	—	142	1	no	—
164	C₄⋊C₈	—	142	1	no	—
165	C₂²⋊C₈	—	2	1	no	—
166	C₂²⋊C₈	—	142	1	no	—
167	#97	—	142	1	no	—
168	#97	—	142	1	no	—
169	C₄×C₈	—	71	2	no	—
170	C₄×C₈	C₂²⋊D₇₁	1	2	yes	—
171	C₂×Q₈	—	284	2	no	—
172	C₂×Q₈	—	142	1	no	—
173	C₂×Q₈	—	142	1	no	—
174	C₂²×C₄	—	142	1	no	—
175	C₂²×C₄	—	142	1	no	—
176	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
177	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
178	C₂²×C₄	#11765865	1	1	yes	characteristic
179	M₁₆	—	4	2	no	—
180	M₁₆	—	284	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	4	1	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	284	1	no	—
186	C₂×C₈	—	71	4	no	—
187	C₂×C₈	—	142	2	no	—
188	C₂×C₈	—	142	2	no	—
189	C₂×C₈	—	142	2	no	—
190	C₄⋊C₄	—	284	1	no	—
191	C₄⋊C₄	—	284	1	no	—
192	C₄⋊C₄	—	142	1	no	—
193	C₄⋊C₄	—	142	1	no	—
194	C₄²	—	284	1	no	—
195	C₄²	—	284	1	no	—
196	C₄²	D₄×D₇₁	1	1	yes	characteristic
197	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
198	C₄²	#11765865	1	1	yes	characteristic
199	C₄²	#11765866	1	1	yes	characteristic
200	C₂³	#14556106	1	1	yes	characteristic
201	Q₈	—	284	1	no	—
202	Q₈	—	284	1	no	—
203	Q₈	—	142	2	no	—
204	Q₈	—	142	2	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	284	1	no	—
208	C₂×C₄	—	284	1	no	—
209	C₂×C₄	—	284	2	no	—
210	C₂×C₄	—	284	1	no	—
211	C₂×C₄	—	142	2	no	—
212	C₂×C₄	#14556104	1	1	yes	characteristic
213	C₂×C₄	#14556106	1	1	yes	characteristic
214	C₂×C₄	#14556111	1	1	yes	characteristic
215	C₂×C₄	#14556113	1	1	yes	characteristic
216	C₂×C₄	#14556113	1	1	yes	characteristic
217	C₂×C₄	#14556124	1	1	yes	characteristic
218	C₂×C₄	Q₁₆×D₇₁	1	2	yes	—
219	C₂×C₄	#14556152	1	2	yes	—
220	C₈	—	4	2	no	—
221	C₈	—	8	1	no	—
222	C₈	—	8	1	no	—
223	C₈	—	284	2	no	—
224	C₈	—	568	1	no	—
225	C₈	—	142	4	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#17985934	1	1	yes	characteristic
229	C₂²	#17986293	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	284	2	no	—
235	C₄	—	568	1	no	—
236	C₄	#17986336	1	2	yes	—
237	C₄	#17986377	1	1	yes	characteristic
238	C₄	#17986387	1	1	yes	characteristic
239	C₂	—	2	2	no	—
240	C₂	#22589855	1	1	yes	characteristic
241	C₂	#22589875	1	1	yes	characteristic
242	C₂	#22589896	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22589279

C₂

yes

maximal, characteristic

#22588514

C₂

yes

maximal, characteristic

#22587114

C₂

yes

maximal, characteristic

#22586770

C₂

yes

maximal, characteristic

#22586768

C₂

yes

maximal, characteristic

#22586170

C₂

yes

maximal, characteristic

C₇₁×#1571

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₄₂

C₂²

yes

characteristic

#17986052

C₂²

yes

characteristic

C₂×#14556063

—

#17986023

C₂²

yes

characteristic

C₂×#14556039

C₂²

yes

—

—

—

—

#431×C₇₁

C₂²

yes

characteristic

#423×C₇₁

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₁

C₂²

yes

characteristic

#335×C₇₁

—

C₂²×Dic₁₄₂

Q₈

yes

characteristic

C₂×#11765849

—

C₂²×C₇₁⋊C₈

D₄

yes

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₂×C₄⋊Dic₇₁

Q₈

yes

characteristic

C₂×Dic₇₁⋊C₄

—

C₂×C₄×Dic₇₁

—

#14556063

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₂²⋊(C₇₁⋊C₈)

—

#14556039

—

#14556039

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₂×M₁₆×C₇₁

—

C₂²×C₈×C₇₁

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₂²⋊C₈×C₇₁

—

C₄×C₈×C₇₁

D₄

yes

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

C₂²×Dic₇₁

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

Q₁₆

yes

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×Q₈

yes

characteristic

C₂²×C₄×C₇₁

#41

yes

characteristic

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

C₄²×C₇₁

yes

C₄²×C₇₁

yes

C₂³×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂×Q₁₆

yes

—

C₂×C₄×C₇₁

AGL(1,ℤ/8)

yes

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

100

C₈×C₇₁

—

101

C₇₁⋊C₈

—

102

C₇₁⋊C₈

—

103

C₇₁⋊C₈

—

104

C₂²×C₇₁

—

105

C₂²×C₇₁

—

106

C₂²×C₇₁

#399

yes

characteristic

107

C₂²×C₇₁

#477

yes

—

108

C₄×C₇₁

—

109

C₄×C₇₁

—

110

C₄×C₇₁

—

111

C₄×C₇₁

—

112

C₄×C₇₁

#484

yes

—

113

C₄×C₇₁

#494

yes

characteristic

114

C₄×C₇₁

#496

yes

characteristic

115

Dic₇₁

—

116

Dic₇₁

—

117

#10662

—

maximal, Sylow

118

C₂×C₇₁

—

119

C₂×C₇₁

#2091

yes

characteristic

120

C₂×C₇₁

#2095

yes

characteristic

121

C₂×C₇₁

#2098

yes

characteristic

122

#1985

—

123

#1849

—

124

#1571

—

125

#1571

D₇₁

yes

characteristic

126

#1487

—

127

#1487

—

128

#1275

—

129

C₇₁

#10662

yes

characteristic, complemented, Sylow

130

C₂×C₄×Q₈

—

131

#431

—

132

#431

C₂×D₇₁

yes

characteristic

133

C₂×#108

—

142

—

134

#423

—

135

#423

C₂×D₇₁

yes

characteristic

136

C₂×C₄⋊C₈

C₂×D₇₁

yes

characteristic

137

C₂×#97

—

138

#336

—

142

—

139

#335

—

140

#335

—

142

—

141

Q₈⋊C₈

—

142

—

142

Q₈⋊C₈

—

142

—

143

C₂²×Q₈

—

144

C₂×M₁₆

—

145

C₂×M₁₆

—

142

—

146

C₂²×C₈

—

147

C₂²×C₈

—

148

C₄×Q₈

—

142

—

149

C₄×Q₈

—

142

—

150

C₄×Q₈

—

142

—

151

C₄×Q₈

—

142

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

142

—

154

C₂×C₄²

—

142

—

155

C₂×C₄²

C₂²×D₇₁

yes

characteristic

156

#108

—

284

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

142

—

163

C₄⋊C₈

—

142

—

164

C₄⋊C₈

—

142

—

165

C₂²⋊C₈

—

166

C₂²⋊C₈

—

142

—

167

#97

—

142

—

168

#97

—

142

—

169

C₄×C₈

—

170

C₄×C₈

C₂²⋊D₇₁

yes

—

171

C₂×Q₈

—

284

—

172

C₂×Q₈

—

142

—

173

C₂×Q₈

—

142

—

174

C₂²×C₄

—

142

—

175

C₂²×C₄

—

142

—

176

C₂²×C₄

D₄×D₇₁

yes

characteristic

177

C₂²×C₄

Q₈×D₇₁

yes

characteristic

178

C₂²×C₄

#11765865

yes

characteristic

179

M₁₆

—

180

M₁₆

—

284

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

284

—

186

C₂×C₈

—

187

C₂×C₈

—

142

—

188

C₂×C₈

—

142

—

189

C₂×C₈

—

142

—

190

C₄⋊C₄

—

284

—

191

C₄⋊C₄

—

284

—

192

C₄⋊C₄

—

142

—

193

C₄⋊C₄

—

142

—

194

C₄²

—

284

—

195

C₄²

—

284

—

196

C₄²

D₄×D₇₁

yes

characteristic

197

C₄²

C₂×C₂²⋊D₇₁

yes

characteristic

198

C₄²

#11765865

yes

characteristic

199

C₄²

#11765866

yes

characteristic

200

C₂³

#14556106

yes

characteristic

201

Q₈

—

284

—

202

Q₈

—

284

—

203

Q₈

—

142

—

204

Q₈

—

142

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

284

—

208

C₂×C₄

—

284

—

209

C₂×C₄

—

284

—

210

C₂×C₄

—

284

—

211

C₂×C₄

—

142

—

212

C₂×C₄

#14556104

yes

characteristic

213

C₂×C₄

#14556106

yes

characteristic

214

C₂×C₄

#14556111

yes

characteristic

215

C₂×C₄

#14556113

yes

characteristic

216

C₂×C₄

#14556113

yes

characteristic

217

C₂×C₄

#14556124

yes

characteristic

218

C₂×C₄

Q₁₆×D₇₁

yes

—

219

C₂×C₄

#14556152

yes

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

284

—

224

C₈

—

568

—

225

C₈

—

142

—

226

C₂²

—

227

C₂²

—

228

C₂²

#17985934

yes

characteristic

229

C₂²

#17986293

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

284

—

235

C₄

—

568

—

236

C₄

#17986336

yes

—

237

C₄

#17986377

yes

characteristic

238

C₄

#17986387

yes

characteristic

239

C₂

—

240

C₂

#22589855

yes

characteristic

241

C₂

#22589875

yes

characteristic

242

C₂

#22589896

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556124
commutator, cosocle	C₂×C₄²×C₇₁	C₂³
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1571	C₂
socle	C₂²×C₇₁	#399
prime radical	C₂³×C₇₁	C₂²⋊Q₈
hypercenter	#1571	D₇₁
hypocenter	C₇₁	#10662
LCS	G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

subgroup

G/H

center

C₂×C₄

#14556124

commutator, cosocle

C₂×C₄²×C₇₁

C₂³

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1571

C₂

socle

C₂²×C₇₁

#399

prime radical

C₂³×C₇₁

C₂²⋊Q₈

D₇₁

C₇₁

G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

N	H ≅ G/N	type
129. C₇₁	#10662	semidirect

H ≅ G/N

type

129. C₇₁

#10662

semidirect

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

subgroup	index
#22589279	2
#22588514	2
#22587114	2
#22586770	2
#22586768	2
#22586170	2
C₇₁×#1571	2
#10662	71

subgroup

index

C₇₁×#1571

Subgroups — #31902437

Conjugacy classes of subgroups

Complements

Maximal subgroups