Group #31902585 — subgroups

Subgroups — #31902585

Order 18176.

264 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 89 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	#22589064	C₂	1	1	yes	maximal, characteristic
2	#22588514	C₂	1	1	yes	maximal, characteristic
3	#22586243	C₂	1	1	yes	maximal, characteristic
4	#22586236	C₂	1	1	yes	maximal, characteristic
5	#22586235	C₂	1	1	yes	maximal, characteristic
6	#22586170	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1303	C₂	1	1	yes	maximal, characteristic
8	#17986052	C₂²	1	1	yes	characteristic
9	C₂×#14556063	—	2	1	no	—
10	C₂×#14556063	—	2	1	no	—
11	#17986023	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
13	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#14556039	C₂²	1	1	yes	characteristic
15	#17985754	—	2	1	no	—
16	#431×C₇₁	C₂²	1	1	yes	characteristic
17	#423×C₇₁	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×#11765849	—	2	1	no	—
20	C₂²×C₇₁⋊C₈	—	2	1	no	—
21	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
22	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
23	#14556063	—	4	2	no	—
24	#14556063	—	4	2	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	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
30	C₄⋊(C₇₁⋊C₈)	—	4	2	no	—
31	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
32	#14556039	—	2	1	no	—
33	#14556039	—	2	1	no	—
34	C₄×C₇₁⋊C₈	—	2	1	no	—
35	C₂×M₁₆×C₇₁	—	2	1	no	—
36	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
37	C₂×C₄²×C₇₁	—	2	1	no	—
38	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
39	C₄⋊C₈×C₇₁	—	2	1	no	—
40	C₄⋊C₈×C₇₁	—	2	1	no	—
41	C₄⋊C₈×C₇₁	—	2	1	no	—
42	C₂²⋊C₈×C₇₁	—	2	1	no	—
43	C₄×C₈×C₇₁	—	2	1	no	—
44	#95×C₇₁	Q₈	1	1	yes	characteristic
45	#95×C₇₁	Q₈	1	1	yes	characteristic
46	#11765849	—	4	1	no	—
47	#11765849	—	4	1	no	—
48	C₂×C₇₁⋊C₈	—	2	1	no	—
49	C₂×C₇₁⋊C₈	—	2	1	no	—
50	C₂×C₇₁⋊C₈	—	2	1	no	—
51	C₂×C₇₁⋊C₈	—	2	1	no	—
52	C₂×C₇₁⋊C₈	—	4	1	no	—
53	C₂×C₇₁⋊C₈	—	4	1	no	—
54	C₂×C₇₁⋊C₈	—	4	1	no	—
55	C₂×C₇₁⋊C₈	—	4	1	no	—
56	C₂×C₇₁⋊C₈	—	4	1	no	—
57	C₂×C₇₁⋊C₈	SD₁₆	1	2	yes	—
58	C₂×C₇₁⋊C₈	Q₁₆	1	2	yes	—
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	1	no	—
65	M₁₆×C₇₁	—	4	1	no	—
66	C₂×C₈×C₇₁	—	4	1	no	—
67	C₂×C₈×C₇₁	—	4	1	no	—
68	C₄⋊C₄×C₇₁	—	4	2	no	—
69	C₄²×C₇₁	—	4	1	no	—
70	C₄²×C₇₁	—	4	1	no	—
71	C₄²×C₇₁	#41	1	1	yes	characteristic
72	C₄²×C₇₁	#41	1	1	yes	characteristic
73	C₄²×C₇₁	#41	1	1	yes	characteristic
74	C₄²×C₇₁	#41	1	1	yes	characteristic
75	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
76	C₂×C₄×C₇₁	—	2	2	no	—
77	C₂×C₄×C₇₁	—	4	1	no	—
78	C₂×C₄×C₇₁	—	4	1	no	—
79	C₂×C₄×C₇₁	—	4	1	no	—
80	C₂×C₄×C₇₁	—	4	1	no	—
81	C₂×C₄×C₇₁	—	4	1	no	—
82	C₂×C₄×C₇₁	—	4	1	no	—
83	C₂×C₄×C₇₁	—	4	1	no	—
84	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
88	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
89	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
90	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×C₄×C₇₁	C₂×Q₁₆	1	1	yes	characteristic
92	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
93	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₈×C₇₁	—	8	1	no	—
95	C₈×C₇₁	—	8	1	no	—
96	C₇₁⋊C₈	—	2	2	no	—
97	C₇₁⋊C₈	—	2	2	no	—
98	C₇₁⋊C₈	—	8	1	no	—
99	C₇₁⋊C₈	—	8	1	no	—
100	C₇₁⋊C₈	—	8	1	no	—
101	C₂²×C₇₁	—	2	1	no	—
102	C₂²×C₇₁	—	2	1	no	—
103	C₂²×C₇₁	#400	1	1	yes	characteristic
104	C₂²×C₇₁	#476	1	1	yes	characteristic
105	C₂²×C₇₁	#477	1	1	yes	characteristic
106	C₄×C₇₁	—	2	1	no	—
107	C₄×C₇₁	—	2	1	no	—
108	C₄×C₇₁	—	2	1	no	—
109	C₄×C₇₁	—	2	1	no	—
110	C₄×C₇₁	—	4	2	no	—
111	C₄×C₇₁	—	8	1	no	—
112	C₄×C₇₁	#481	1	1	yes	characteristic
113	C₄×C₇₁	#484	1	1	yes	characteristic
114	C₄×C₇₁	#487	1	1	yes	characteristic
115	C₄×C₇₁	#490	1	1	yes	characteristic
116	#10688	—	71	1	no	maximal, Sylow
117	C₂×C₇₁	—	2	1	no	—
118	C₂×C₇₁	—	2	1	no	—
119	C₂×C₇₁	#2100	1	1	yes	characteristic
120	C₂×C₇₁	#2102	1	1	yes	characteristic
121	C₂×C₇₁	#2103	1	1	yes	characteristic
122	#1940	—	71	1	no	—
123	#1849	—	71	1	no	—
124	#1303	—	71	1	no	—
125	#1303	D₇₁	1	1	yes	characteristic
126	#1301	—	71	1	no	—
127	#1301	—	71	1	no	—
128	#1275	—	71	1	no	—
129	C₇₁	#10688	1	1	yes	characteristic, complemented, Sylow
130	#431	—	71	1	no	—
131	#431	C₂×D₇₁	1	1	yes	characteristic
132	C₂×#108	—	142	1	no	—
133	C₂×#108	—	142	1	no	—
134	#423	—	71	1	no	—
135	#423	C₂×D₇₁	1	1	yes	characteristic
136	C₂×C₄⋊C₈	—	71	1	no	—
137	C₂×C₄⋊C₈	—	142	1	no	—
138	C₂×#97	—	71	1	no	—
139	C₄×C₄⋊C₄	C₂×D₇₁	1	1	yes	characteristic
140	#336	—	142	1	no	—
141	C₂×M₁₆	—	2	1	no	—
142	C₂×M₁₆	—	142	1	no	—
143	C₂²×C₈	—	71	1	no	—
144	C₂²×C₈	—	71	1	no	—
145	C₂²×C₈	—	142	1	no	—
146	C₂×C₄⋊C₄	—	2	1	no	—
147	C₂×C₄²	—	2	1	no	—
148	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
149	#108	—	284	2	no	—
150	#108	—	284	2	no	—
151	C₄⋊C₈	—	2	1	no	—
152	C₄⋊C₈	—	2	1	no	—
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	284	2	no	—
155	C₄⋊C₈	—	142	1	no	—
156	C₄⋊C₈	—	142	1	no	—
157	C₄⋊C₈	—	142	1	no	—
158	C₄⋊C₈	—	142	1	no	—
159	C₄⋊C₈	—	142	1	no	—
160	C₂²⋊C₈	—	2	1	no	—
161	C₂²⋊C₈	—	142	1	no	—
162	#97	—	142	1	no	—
163	#97	—	142	1	no	—
164	C₄×C₈	—	2	1	no	—
165	C₄×C₈	—	142	1	no	—
166	#95	Dic₁₄₂	1	1	yes	characteristic
167	#95	Dic₁₄₂	1	1	yes	characteristic
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
171	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
172	C₂²×C₄	#11765864	1	1	yes	characteristic
173	M₁₆	—	4	1	no	—
174	M₁₆	—	4	1	no	—
175	M₁₆	—	284	1	no	—
176	M₁₆	—	284	1	no	—
177	C₂×C₈	—	4	1	no	—
178	C₂×C₈	—	4	1	no	—
179	C₂×C₈	—	284	1	no	—
180	C₂×C₈	—	284	1	no	—
181	C₂×C₈	—	284	1	no	—
182	C₂×C₈	—	284	1	no	—
183	C₂×C₈	—	284	1	no	—
184	C₂×C₈	—	71	2	no	—
185	C₂×C₈	—	71	2	no	—
186	C₂×C₈	—	142	1	no	—
187	C₂×C₈	—	142	1	no	—
188	C₂×C₈	—	142	1	no	—
189	C₂×C₈	—	142	1	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄²	—	4	1	no	—
192	C₄²	—	4	1	no	—
193	C₄²	#11765864	1	1	yes	characteristic
194	C₄²	#11765865	1	1	yes	characteristic
195	C₄²	#11765865	1	1	yes	characteristic
196	C₄²	#11765866	1	1	yes	characteristic
197	C₂³	#14556105	1	1	yes	characteristic
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	#14556113	1	1	yes	characteristic
207	C₂×C₄	#14556114	1	1	yes	characteristic
208	C₂×C₄	#14556119	1	1	yes	characteristic
209	C₂×C₄	#14556120	1	1	yes	characteristic
210	C₂×C₄	#14556121	1	1	yes	characteristic
211	C₂×C₄	#14556123	1	1	yes	characteristic
212	C₂×C₄	SD₁₆×D₇₁	1	1	yes	characteristic
213	C₂×C₄	Q₁₆×D₇₁	1	1	yes	characteristic
214	C₂×C₄	#14556152	1	1	yes	characteristic
215	C₂×C₄	#14556155	1	1	yes	characteristic
216	C₈	—	8	1	no	—
217	C₈	—	8	1	no	—
218	C₈	—	568	1	no	—
219	C₈	—	568	1	no	—
220	C₈	—	568	1	no	—
221	C₈	—	142	2	no	—
222	C₈	—	142	2	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	#17985941	1	1	yes	characteristic
226	C₂²	#17986287	1	1	yes	characteristic
227	C₂²	#17986292	1	1	yes	characteristic
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	#17986319	1	1	yes	characteristic
235	C₄	#17986336	1	1	yes	characteristic
236	C₄	#17986348	1	1	yes	characteristic
237	C₄	#17986362	1	1	yes	characteristic
238	C₂	—	2	1	no	—
239	C₂	—	2	1	no	—
240	C₂	#22589906	1	1	yes	characteristic
241	C₂	#22589918	1	1	yes	characteristic
242	C₂	#22589923	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22589064

C₂

yes

maximal, characteristic

#22588514

C₂

yes

maximal, characteristic

#22586243

C₂

yes

maximal, characteristic

#22586236

C₂

yes

maximal, characteristic

#22586235

C₂

yes

maximal, characteristic

#22586170

C₂

yes

maximal, characteristic

C₇₁×#1303

C₂

yes

maximal, characteristic

#17986052

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×C₄⋊(C₇₁⋊C₈)

—

C₂×C₄⋊(C₇₁⋊C₈)

C₂²

yes

characteristic

C₂×#14556039

C₂²

yes

characteristic

#17985754

—

#431×C₇₁

C₂²

yes

characteristic

#423×C₇₁

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₇₁

C₂²

yes

characteristic

C₂×#11765849

—

C₂²×C₇₁⋊C₈

—

C₂²×C₇₁⋊C₈

D₄

yes

characteristic

C₂²×C₇₁⋊C₈

D₄

yes

characteristic

#14556063

—

#14556063

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₂²⋊(C₇₁⋊C₈)

—

#14556039

—

#14556039

—

C₄×C₇₁⋊C₈

—

C₂×M₁₆×C₇₁

—

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄²×C₇₁

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₂²⋊C₈×C₇₁

—

C₄×C₈×C₇₁

—

#95×C₇₁

Q₈

yes

characteristic

#95×C₇₁

Q₈

yes

characteristic

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

SD₁₆

yes

—

C₂×C₇₁⋊C₈

Q₁₆

yes

—

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

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

yes

C₄²×C₇₁

yes

C₄²×C₇₁

yes

C₄²×C₇₁

yes

C₂³×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×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

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₁

C₂×Q₁₆

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

100

C₇₁⋊C₈

—

101

C₂²×C₇₁

—

102

C₂²×C₇₁

—

103

C₂²×C₇₁

#400

yes

characteristic

104

C₂²×C₇₁

#476

yes

characteristic

105

C₂²×C₇₁

#477

yes

characteristic

106

C₄×C₇₁

—

107

C₄×C₇₁

—

108

C₄×C₇₁

—

109

C₄×C₇₁

—

110

C₄×C₇₁

—

111

C₄×C₇₁

—

112

C₄×C₇₁

#481

yes

characteristic

113

C₄×C₇₁

#484

yes

characteristic

114

C₄×C₇₁

#487

yes

characteristic

115

C₄×C₇₁

yes

116

—

117

C₂×C₇₁

—

118

C₂×C₇₁

—

119

C₂×C₇₁

#2100

yes

characteristic

120

C₂×C₇₁

#2102

yes

characteristic

121

C₂×C₇₁

#2103

yes

characteristic

122

#1940

—

123

#1849

—

124

#1303

—

125

#1303

D₇₁

yes

characteristic

126

#1301

—

127

#1301

—

128

#1275

—

129

C₇₁

#10688

yes

characteristic, complemented, Sylow

130

#431

—

131

#431

C₂×D₇₁

yes

characteristic

132

C₂×#108

—

142

—

133

C₂×#108

—

142

—

134

#423

—

135

#423

C₂×D₇₁

yes

characteristic

136

C₂×C₄⋊C₈

—

137

C₂×C₄⋊C₈

—

142

—

138

C₂×#97

—

139

C₄×C₄⋊C₄

C₂×D₇₁

yes

characteristic

140

#336

—

142

—

141

C₂×M₁₆

—

142

C₂×M₁₆

—

142

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₂²×C₈

—

142

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄²

—

148

C₂×C₄²

C₂²×D₇₁

yes

characteristic

149

#108

—

284

—

150

#108

—

284

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

284

—

155

C₄⋊C₈

—

142

—

156

C₄⋊C₈

—

142

—

157

C₄⋊C₈

—

142

—

158

C₄⋊C₈

—

142

—

159

C₄⋊C₈

—

142

—

160

C₂²⋊C₈

—

161

C₂²⋊C₈

—

142

—

162

#97

—

142

—

163

#97

—

142

—

164

C₄×C₈

—

165

C₄×C₈

—

142

—

166

#95

Dic₁₄₂

yes

characteristic

167

#95

Dic₁₄₂

yes

characteristic

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

D₄×D₇₁

yes

characteristic

171

C₂²×C₄

C₂×Dic₁₄₂

yes

characteristic

172

C₂²×C₄

#11765864

yes

characteristic

173

M₁₆

—

174

M₁₆

—

175

M₁₆

—

284

—

176

M₁₆

—

284

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

284

—

180

C₂×C₈

—

284

—

181

C₂×C₈

—

284

—

182

C₂×C₈

—

284

—

183

C₂×C₈

—

284

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

142

—

187

C₂×C₈

—

142

—

188

C₂×C₈

—

142

—

189

C₂×C₈

—

142

—

190

C₄⋊C₄

—

191

C₄²

—

192

C₄²

—

193

C₄²

#11765864

yes

characteristic

194

C₄²

#11765865

yes

characteristic

195

C₄²

#11765865

yes

characteristic

196

C₄²

#11765866

yes

characteristic

197

C₂³

#14556105

yes

characteristic

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

#14556113

yes

characteristic

207

C₂×C₄

#14556114

yes

characteristic

208

C₂×C₄

#14556119

yes

characteristic

209

C₂×C₄

#14556120

yes

characteristic

210

C₂×C₄

#14556121

yes

characteristic

211

C₂×C₄

#14556123

yes

characteristic

212

C₂×C₄

SD₁₆×D₇₁

yes

characteristic

213

C₂×C₄

Q₁₆×D₇₁

yes

characteristic

214

C₂×C₄

#14556152

yes

characteristic

215

C₂×C₄

#14556155

yes

characteristic

216

C₈

—

217

C₈

—

218

C₈

—

568

—

219

C₈

—

568

—

220

C₈

—

568

—

221

C₈

—

142

—

222

C₈

—

142

—

223

C₂²

—

224

C₂²

—

225

C₂²

#17985941

yes

characteristic

226

C₂²

#17986287

yes

characteristic

227

C₂²

#17986292

yes

characteristic

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

#17986319

yes

characteristic

235

C₄

#17986336

yes

characteristic

236

C₄

#17986348

yes

characteristic

237

C₄

#17986362

yes

characteristic

238

C₂

—

239

C₂

—

240

C₂

#22589906

yes

characteristic

241

C₂

#22589918

yes

characteristic

242

C₂

#22589923

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556114
commutator, cosocle	C₂×C₄²×C₇₁	C₂³
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1303	C₂
socle	C₂²×C₇₁	#400
prime radical	C₂³×C₇₁	C₂²⋊Q₈
hypercenter	#1303	D₇₁
hypocenter	C₇₁	#10688
LCS	G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

subgroup

G/H

center

C₂×C₄

#14556114

commutator, cosocle

C₂×C₄²×C₇₁

C₂³

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1303

C₂

socle

C₂²×C₇₁

#400

prime radical

C₂³×C₇₁

C₂²⋊Q₈

D₇₁

C₇₁

G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

N	H ≅ G/N	type
129. C₇₁	#10688	semidirect

H ≅ G/N

type

129. C₇₁

#10688

semidirect

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

subgroup	index
#22589064	2
#22588514	2
#22586243	2
#22586236	2
#22586235	2
#22586170	2
C₇₁×#1303	2
#10688	71

subgroup

index

C₇₁×#1303

Subgroups — #31902585

Conjugacy classes of subgroups

Complements

Maximal subgroups