Group #31902448 — subgroups

Subgroups — #31902448

Order 18176.

304 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 91 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	#22589281	C₂	1	1	yes	maximal, characteristic
2	#22588480	C₂	1	1	yes	maximal, characteristic
3	#22587115	C₂	1	1	yes	maximal, characteristic
4	#22587112	C₂	1	1	yes	maximal, characteristic
5	#22586769	C₂	1	1	yes	maximal, characteristic
6	#22586170	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1487	C₂	1	1	yes	maximal, characteristic
8	#17986052	C₂²	1	1	yes	characteristic
9	#17986023	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#14556039	C₂²	1	1	yes	characteristic
12	#17985763	—	2	2	no	—
13	#17985754	—	2	2	no	—
14	#17985752	—	2	2	no	—
15	#17985749	—	2	2	no	—
16	Q₈⋊(C₇₁⋊C₈)	—	2	2	no	—
17	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
18	#431×C₇₁	C₂²	1	1	yes	characteristic
19	#423×C₇₁	C₂²	1	1	yes	characteristic
20	Q₈⋊C₈×C₇₁	—	2	2	no	—
21	C₂×#11765849	—	2	1	no	—
22	C₂²×C₇₁⋊C₈	—	2	1	no	—
23	C₂²×C₇₁⋊C₈	D₄	1	2	yes	—
24	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
25	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
26	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
27	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
28	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
29	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
30	#14556039	—	2	1	no	—
31	#14556039	—	2	1	no	—
32	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
33	C₂²×Q₈×C₇₁	Q₈	1	1	yes	characteristic
34	C₂×M₁₆×C₇₁	—	2	1	no	—
35	C₄×Q₈×C₇₁	—	2	1	no	—
36	C₄×Q₈×C₇₁	—	2	1	no	—
37	C₄×Q₈×C₇₁	—	2	1	no	—
38	C₄×Q₈×C₇₁	—	2	1	no	—
39	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
40	C₂×C₄⋊C₄×C₇₁	Q₈	1	1	yes	characteristic
41	C₂×C₄²×C₇₁	—	2	1	no	—
42	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₁	—	2	1	no	—
44	C₄⋊C₈×C₇₁	—	2	1	no	—
45	C₄⋊C₈×C₇₁	—	2	1	no	—
46	C₂²⋊C₈×C₇₁	—	2	1	no	—
47	C₄×C₈×C₇₁	D₄	1	2	yes	—
48	#11765849	—	4	2	no	—
49	C₂×C₇₁⋊C₈	—	2	2	no	—
50	C₂×C₇₁⋊C₈	—	2	2	no	—
51	C₂×C₇₁⋊C₈	—	2	2	no	—
52	C₂×C₇₁⋊C₈	—	2	2	no	—
53	C₂×C₇₁⋊C₈	—	4	1	no	—
54	C₂×C₇₁⋊C₈	—	4	1	no	—
55	C₂×C₇₁⋊C₈	—	4	2	no	—
56	C₂×Q₈×C₇₁	—	2	1	no	—
57	C₂×Q₈×C₇₁	—	2	1	no	—
58	C₂×Q₈×C₇₁	—	4	2	no	—
59	C₂²×C₄×C₇₁	—	2	1	no	—
60	C₂²×C₄×C₇₁	—	2	1	no	—
61	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
63	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
64	M₁₆×C₇₁	—	4	2	no	—
65	C₂×C₈×C₇₁	—	2	2	no	—
66	C₂×C₈×C₇₁	—	4	1	no	—
67	C₄⋊C₄×C₇₁	—	2	1	no	—
68	C₄⋊C₄×C₇₁	—	2	1	no	—
69	C₄⋊C₄×C₇₁	—	4	1	no	—
70	C₄⋊C₄×C₇₁	—	4	1	no	—
71	C₄²×C₇₁	—	4	1	no	—
72	C₄²×C₇₁	—	4	1	no	—
73	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₇₁	#41	1	1	yes	characteristic
76	C₄²×C₇₁	#41	1	1	yes	characteristic
77	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
78	Q₈×C₇₁	—	2	2	no	—
79	Q₈×C₇₁	—	2	2	no	—
80	Q₈×C₇₁	—	4	1	no	—
81	Q₈×C₇₁	—	4	1	no	—
82	C₂×C₄×C₇₁	—	2	2	no	—
83	C₂×C₄×C₇₁	—	4	1	no	—
84	C₂×C₄×C₇₁	—	4	1	no	—
85	C₂×C₄×C₇₁	—	4	1	no	—
86	C₂×C₄×C₇₁	—	4	1	no	—
87	C₂×C₄×C₇₁	—	4	2	no	—
88	C₂×C₄×C₇₁	—	4	1	no	—
89	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
92	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
93	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
94	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
95	C₂×C₄×C₇₁	#135	1	2	yes	—
96	C₂×C₄×C₇₁	#137	1	2	yes	—
97	C₈×C₇₁	—	4	2	no	—
98	C₈×C₇₁	—	8	1	no	—
99	C₇₁⋊C₈	—	4	2	no	—
100	C₇₁⋊C₈	—	4	2	no	—
101	C₇₁⋊C₈	—	8	1	no	—
102	C₇₁⋊C₈	—	8	1	no	—
103	C₂²×C₇₁	—	2	1	no	—
104	C₂²×C₇₁	—	2	1	no	—
105	C₂²×C₇₁	#399	1	1	yes	characteristic
106	C₂²×C₇₁	#479	1	2	yes	—
107	C₄×C₇₁	—	2	1	no	—
108	C₄×C₇₁	—	2	1	no	—
109	C₄×C₇₁	—	2	1	no	—
110	C₄×C₇₁	—	2	1	no	—
111	C₄×C₇₁	—	4	2	no	—
112	C₄×C₇₁	—	8	1	no	—
113	C₄×C₇₁	#485	1	2	yes	—
114	C₄×C₇₁	#495	1	1	yes	characteristic
115	C₄×C₇₁	#497	1	1	yes	characteristic
116	#10664	—	71	1	no	maximal, Sylow
117	C₂×C₇₁	—	2	2	no	—
118	C₂×C₇₁	#2091	1	1	yes	characteristic
119	C₂×C₇₁	#2097	1	1	yes	characteristic
120	C₂×C₇₁	#2098	1	1	yes	characteristic
121	#1985	—	71	1	no	—
122	#1838	—	71	1	no	—
123	#1571	—	71	1	no	—
124	#1570	—	71	1	no	—
125	#1487	—	71	1	no	—
126	#1487	D₇₁	1	1	yes	characteristic
127	#1275	—	71	1	no	—
128	C₇₁	#10664	1	1	yes	characteristic, complemented, Sylow
129	C₂×C₄×Q₈	C₂×D₇₁	1	1	yes	characteristic
130	#431	—	71	1	no	—
131	#431	C₂×D₇₁	1	1	yes	characteristic
132	#423	—	71	1	no	—
133	#423	C₂×D₇₁	1	1	yes	characteristic
134	C₂×C₄⋊C₈	—	71	1	no	—
135	C₂×#97	—	71	1	no	—
136	#341	—	142	2	no	—
137	#336	—	142	2	no	—
138	#335	—	142	2	no	—
139	#334	—	142	2	no	—
140	Q₈⋊C₈	—	2	2	no	—
141	Q₈⋊C₈	—	142	2	no	—
142	C₂²×Q₈	Dic₁₄₂	1	1	yes	characteristic
143	C₂×M₁₆	—	2	1	no	—
144	C₂×M₁₆	—	142	1	no	—
145	C₂²×C₈	—	71	2	no	—
146	C₂²×C₈	—	142	1	no	—
147	C₄×Q₈	—	2	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	C₄×Q₈	—	2	1	no	—
151	C₂×C₄⋊C₄	—	2	1	no	—
152	C₂×C₄⋊C₄	Dic₁₄₂	1	1	yes	characteristic
153	C₂×C₄²	—	2	1	no	—
154	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	2	1	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	142	1	no	—
159	C₄⋊C₈	—	142	1	no	—
160	C₄⋊C₈	—	142	1	no	—
161	C₄⋊C₈	—	142	1	no	—
162	C₄⋊C₈	—	142	1	no	—
163	C₂²⋊C₈	—	2	1	no	—
164	C₂²⋊C₈	—	142	1	no	—
165	#97	—	142	1	no	—
166	#97	—	142	1	no	—
167	C₄×C₈	—	71	2	no	—
168	C₄×C₈	C₂²⋊D₇₁	1	2	yes	—
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	1	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
175	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
176	C₂²×C₄	#11765864	1	1	yes	characteristic
177	M₁₆	—	4	2	no	—
178	M₁₆	—	284	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	4	1	no	—
181	C₂×C₈	—	284	1	no	—
182	C₂×C₈	—	284	1	no	—
183	C₂×C₈	—	284	2	no	—
184	C₂×C₈	—	142	2	no	—
185	C₂×C₈	—	142	2	no	—
186	C₂×C₈	—	142	2	no	—
187	C₂×C₈	—	142	2	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	2	1	no	—
190	C₄⋊C₄	—	4	1	no	—
191	C₄⋊C₄	—	4	1	no	—
192	C₄²	—	4	1	no	—
193	C₄²	—	4	1	no	—
194	C₄²	D₄×D₇₁	1	1	yes	characteristic
195	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
196	C₄²	#11765864	1	1	yes	characteristic
197	C₄²	#11765865	1	1	yes	characteristic
198	C₂³	#14556105	1	1	yes	characteristic
199	Q₈	—	2	2	no	—
200	Q₈	—	2	2	no	—
201	Q₈	—	4	1	no	—
202	Q₈	—	4	1	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	#14556105	1	1	yes	characteristic
211	C₂×C₄	#14556107	1	1	yes	characteristic
212	C₂×C₄	#14556109	1	1	yes	characteristic
213	C₂×C₄	#14556110	1	1	yes	characteristic
214	C₂×C₄	#14556110	1	1	yes	characteristic
215	C₂×C₄	#14556124	1	1	yes	characteristic
216	C₂×C₄	#14556151	1	2	yes	—
217	C₂×C₄	#14556157	1	2	yes	—
218	C₈	—	4	2	no	—
219	C₈	—	8	1	no	—
220	C₈	—	284	2	no	—
221	C₈	—	284	2	no	—
222	C₈	—	568	1	no	—
223	C₈	—	568	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	#17985935	1	1	yes	characteristic
227	C₂²	#17986308	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	4	2	no	—
233	C₄	—	8	1	no	—
234	C₄	#17986339	1	2	yes	—
235	C₄	#17986384	1	1	yes	characteristic
236	C₄	#17986390	1	1	yes	characteristic
237	C₂	—	2	2	no	—
238	C₂	#22589856	1	1	yes	characteristic
239	C₂	#22589886	1	1	yes	characteristic
240	C₂	#22589895	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22589281

C₂

yes

maximal, characteristic

#22588480

C₂

yes

maximal, characteristic

#22587115

C₂

yes

maximal, characteristic

#22587112

C₂

yes

maximal, characteristic

#22586769

C₂

yes

maximal, characteristic

#22586170

C₂

yes

maximal, characteristic

C₇₁×#1487

C₂

yes

maximal, characteristic

#17986052

C₂²

yes

characteristic

#17986023

C₂²

yes

characteristic

C₂×C₄⋊(C₇₁⋊C₈)

C₂²

yes

characteristic

C₂×#14556039

C₂²

yes

—

—

—

—

Q₈⋊(C₇₁⋊C₈)

—

C₂×C₄×Q₈×C₇₁

C₂²

yes

characteristic

#431×C₇₁

C₂²

yes

characteristic

#423×C₇₁

C₂²

yes

characteristic

Q₈⋊C₈×C₇₁

—

C₂×#11765849

—

C₂²×C₇₁⋊C₈

—

C₂²×C₇₁⋊C₈

D₄

yes

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₂²⋊(C₇₁⋊C₈)

—

#14556039

—

#14556039

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₂²×Q₈×C₇₁

Q₈

yes

characteristic

C₂×M₁₆×C₇₁

—

C₄×Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄⋊C₄×C₇₁

Q₈

yes

characteristic

C₂×C₄²×C₇₁

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₂²⋊C₈×C₇₁

—

C₄×C₈×C₇₁

D₄

yes

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

—

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

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

C₄²×C₇₁

yes

C₄²×C₇₁

yes

C₂³×C₇₁

C₂²⋊Q₈

yes

characteristic

Q₈×C₇₁

—

Q₈×C₇₁

—

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

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

yes

—

C₂×C₄×C₇₁

#137

yes

—

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

100

C₇₁⋊C₈

—

101

C₇₁⋊C₈

—

102

C₇₁⋊C₈

—

103

C₂²×C₇₁

—

104

C₂²×C₇₁

—

105

C₂²×C₇₁

#399

yes

characteristic

106

C₂²×C₇₁

#479

yes

—

107

C₄×C₇₁

—

108

C₄×C₇₁

—

109

C₄×C₇₁

—

110

C₄×C₇₁

—

111

C₄×C₇₁

—

112

C₄×C₇₁

—

113

C₄×C₇₁

#485

yes

—

114

C₄×C₇₁

#495

yes

characteristic

115

C₄×C₇₁

yes

116

—

117

C₂×C₇₁

—

118

C₂×C₇₁

#2091

yes

characteristic

119

C₂×C₇₁

#2097

yes

characteristic

120

C₂×C₇₁

#2098

yes

characteristic

121

#1985

—

122

#1838

—

123

#1571

—

124

#1570

—

125

#1487

—

126

#1487

D₇₁

yes

characteristic

127

#1275

—

128

C₇₁

#10664

yes

characteristic, complemented, Sylow

129

C₂×C₄×Q₈

C₂×D₇₁

yes

characteristic

130

#431

—

131

#431

C₂×D₇₁

yes

characteristic

132

#423

—

133

#423

C₂×D₇₁

yes

characteristic

134

C₂×C₄⋊C₈

—

135

C₂×#97

—

136

#341

—

142

—

137

#336

—

142

—

138

#335

—

142

—

139

#334

—

142

—

140

Q₈⋊C₈

—

141

Q₈⋊C₈

—

142

—

142

C₂²×Q₈

Dic₁₄₂

yes

characteristic

143

C₂×M₁₆

—

144

C₂×M₁₆

—

142

—

145

C₂²×C₈

—

146

C₂²×C₈

—

142

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

Dic₁₄₂

yes

characteristic

153

C₂×C₄²

—

154

C₂×C₄²

C₂²×D₇₁

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

142

—

159

C₄⋊C₈

—

142

—

160

C₄⋊C₈

—

142

—

161

C₄⋊C₈

—

142

—

162

C₄⋊C₈

—

142

—

163

C₂²⋊C₈

—

164

C₂²⋊C₈

—

142

—

165

#97

—

142

—

166

#97

—

142

—

167

C₄×C₈

—

168

C₄×C₈

C₂²⋊D₇₁

yes

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

D₄×D₇₁

yes

characteristic

175

C₂²×C₄

C₂×Dic₁₄₂

yes

characteristic

176

C₂²×C₄

#11765864

yes

characteristic

177

M₁₆

—

178

M₁₆

—

284

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

284

—

182

C₂×C₈

—

284

—

183

C₂×C₈

—

284

—

184

C₂×C₈

—

142

—

185

C₂×C₈

—

142

—

186

C₂×C₈

—

142

—

187

C₂×C₈

—

142

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄²

—

193

C₄²

—

194

C₄²

D₄×D₇₁

yes

characteristic

195

C₄²

C₂×C₂²⋊D₇₁

yes

characteristic

196

C₄²

#11765864

yes

characteristic

197

C₄²

#11765865

yes

characteristic

198

C₂³

#14556105

yes

characteristic

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#14556105

yes

characteristic

211

C₂×C₄

#14556107

yes

characteristic

212

C₂×C₄

#14556109

yes

characteristic

213

C₂×C₄

#14556110

yes

characteristic

214

C₂×C₄

#14556110

yes

characteristic

215

C₂×C₄

#14556124

yes

characteristic

216

C₂×C₄

#14556151

yes

—

217

C₂×C₄

#14556157

yes

—

218

C₈

—

219

C₈

—

220

C₈

—

284

—

221

C₈

—

284

—

222

C₈

—

568

—

223

C₈

—

568

—

224

C₂²

—

225

C₂²

—

226

C₂²

#17985935

yes

characteristic

227

C₂²

#17986308

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

#17986339

yes

—

235

C₄

#17986384

yes

characteristic

236

C₄

#17986390

yes

characteristic

237

C₂

—

238

C₂

#22589856

yes

characteristic

239

C₂

#22589886

yes

characteristic

240

C₂

#22589895

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556124
commutator, cosocle	C₂×C₄²×C₇₁	C₂³
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1487	C₂
socle	C₂²×C₇₁	#399
prime radical	C₂³×C₇₁	C₂²⋊Q₈
hypercenter	#1487	D₇₁
hypocenter	C₇₁	#10664
LCS	G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

subgroup

G/H

center

C₂×C₄

#14556124

commutator, cosocle

C₂×C₄²×C₇₁

C₂³

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1487

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 ◁ #1487

N	H ≅ G/N	type
128. C₇₁	#10664	semidirect

H ≅ G/N

type

128. C₇₁

#10664

semidirect

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

subgroup	index
#22589281	2
#22588480	2
#22587115	2
#22587112	2
#22586769	2
#22586170	2
C₇₁×#1487	2
#10664	71

subgroup

index

C₇₁×#1487

Subgroups — #31902448

Conjugacy classes of subgroups

Complements

Maximal subgroups