Group #31897353 — subgroups

Subgroups — #31897353

Order 18176.

422 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 131 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	#22589318	C₂	1	2	yes	maximal
2	#22588085	C₂	1	1	yes	maximal, characteristic
3	#22587099	C₂	1	1	yes	maximal, characteristic
4	#22586795	C₂	1	2	yes	maximal
5	C₇₁×#3170	C₂	1	1	yes	maximal, characteristic
6	#17986023	C₂²	1	2	yes	—
7	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
8	C₄²×Dic₇₁	C₂²	1	1	yes	characteristic
9	#17985758	—	2	4	no	—
10	#17985753	—	2	2	no	—
11	#17985752	—	2	2	no	—
12	Q₈⋊(C₇₁⋊C₈)	—	2	4	no	—
13	#533×C₇₁	C₂²	1	2	yes	—
14	#500×C₇₁	C₄	1	1	yes	characteristic, complemented
15	#494×C₇₁	C₄	1	1	yes	characteristic, complemented
16	#487×C₇₁	C₄	1	2	yes	complemented
17	#467×C₇₁	—	2	2	no	—
18	C₄×Q₁₆×C₇₁	—	2	2	no	—
19	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×#11765849	—	2	2	no	—
21	C₂²×C₇₁⋊C₈	—	2	1	no	—
22	C₂×C₄×Dic₇₁	—	2	1	no	—
23	C₂×C₄×Dic₇₁	—	2	1	no	—
24	C₂×C₄×Dic₇₁	D₄	1	2	yes	—
25	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
26	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
27	C₄×C₇₁⋊C₈	—	2	1	no	—
28	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
29	C₂×Q₁₆×C₇₁	—	2	2	no	—
30	C₂²×C₈×C₇₁	D₄	1	2	yes	—
31	C₄⋊Q₈×C₇₁	C₂×C₄	1	2	yes	—
32	C₄⋊Q₈×C₇₁	C₂×C₄	1	2	yes	—
33	#125×C₇₁	—	2	2	no	—
34	C₂²⋊Q₈×C₇₁	—	2	2	no	—
35	C₂²⋊Q₈×C₇₁	—	2	2	no	—
36	C₄×Q₈×C₇₁	—	2	2	no	—
37	C₄×Q₈×C₇₁	—	2	2	no	—
38	#117×C₇₁	—	2	2	no	—
39	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
40	#107×C₇₁	—	2	2	no	—
41	#103×C₇₁	—	2	4	no	—
42	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₇₁	D₄	1	2	yes	—
45	C₂²×Dic₇₁	—	2	2	no	—
46	#11765849	—	4	4	no	—
47	C₂×C₇₁⋊C₈	—	2	2	no	—
48	C₂×C₇₁⋊C₈	—	4	2	no	—
49	C₂×C₇₁⋊C₈	—	4	2	no	—
50	C₄×Dic₇₁	—	2	2	no	—
51	C₄×Dic₇₁	—	4	2	no	—
52	C₄×Dic₇₁	—	4	2	no	—
53	C₄×Dic₇₁	Q₁₆	1	4	yes	complemented
54	C₂×Q₈×C₇₁	—	2	2	no	—
55	C₂×Q₈×C₇₁	—	2	2	no	—
56	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
59	Q₁₆×C₇₁	—	4	4	no	—
60	C₂×C₈×C₇₁	—	4	2	no	—
61	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
63	C₄⋊C₄×C₇₁	—	2	2	no	—
64	C₄⋊C₄×C₇₁	—	2	2	no	—
65	C₄⋊C₄×C₇₁	—	2	2	no	—
66	C₄⋊C₄×C₇₁	—	2	2	no	—
67	C₄⋊C₄×C₇₁	—	4	2	no	—
68	C₄⋊C₄×C₇₁	—	4	2	no	—
69	C₂²⋊C₄×C₇₁	—	4	2	no	—
70	C₄²×C₇₁	—	4	2	no	—
71	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₇₁	#41	1	1	yes	characteristic
75	C₂³×C₇₁	#121	1	1	yes	characteristic
76	Q₈×C₇₁	—	4	4	no	—
77	Q₈×C₇₁	—	4	4	no	—
78	C₂×C₄×C₇₁	—	2	2	no	—
79	C₂×C₄×C₇₁	—	2	2	no	—
80	C₂×C₄×C₇₁	—	4	2	no	—
81	C₂×C₄×C₇₁	—	4	2	no	—
82	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
88	C₂×C₄×C₇₁	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₇₁	#135	1	2	yes	—
90	C₂×Dic₇₁	—	2	4	no	—
91	C₂×Dic₇₁	—	4	2	no	—
92	C₂×Dic₇₁	—	4	2	no	—
93	C₈×C₇₁	—	2	2	no	—
94	C₈×C₇₁	—	2	2	no	—
95	C₇₁⋊C₈	—	4	2	no	—
96	C₇₁⋊C₈	—	8	2	no	—
97	C₂²×C₇₁	—	2	1	no	—
98	C₂²×C₇₁	—	2	1	no	—
99	C₂²×C₇₁	#390	1	1	yes	characteristic
100	C₂²×C₇₁	#467	1	2	yes	—
101	C₄×C₇₁	—	2	1	no	—
102	C₄×C₇₁	—	2	1	no	—
103	C₄×C₇₁	—	8	2	no	—
104	C₄×C₇₁	—	8	2	no	—
105	C₄×C₇₁	#421	1	2	yes	—
106	C₄×C₇₁	C₄×Q₁₆	1	2	yes	—
107	C₄×C₇₁	#444	1	2	yes	—
108	C₄×C₇₁	#494	1	1	yes	characteristic
109	C₄×C₇₁	#495	1	1	yes	characteristic
110	Dic₇₁	—	4	4	no	—
111	#9848	—	71	1	no	maximal, Sylow
112	C₂×C₇₁	—	2	2	no	—
113	C₂×C₇₁	#1963	1	1	yes	characteristic
114	C₂×C₇₁	#1969	1	1	yes	characteristic
115	C₂×C₇₁	#1975	1	1	yes	characteristic
116	#3170	D₇₁	1	1	yes	characteristic
117	#1994	—	71	2	no	—
118	#1744	—	71	1	no	—
119	#1567	—	71	1	no	—
120	#1493	—	71	2	no	—
121	C₇₁	#9848	1	1	yes	characteristic, complemented, Sylow
122	#533	C₂×D₇₁	1	2	yes	—
123	#500	Dic₇₁	1	1	yes	characteristic, complemented
124	#494	Dic₇₁	1	1	yes	characteristic, complemented
125	#487	Dic₇₁	1	2	yes	complemented
126	#467	—	2	2	no	—
127	C₄×Q₁₆	—	2	2	no	—
128	#423	—	71	2	no	—
129	C₂×C₄×C₈	—	71	1	no	—
130	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
131	C₄³	—	71	1	no	—
132	#339	—	142	4	no	—
133	#336	—	142	2	no	—
134	#335	—	142	2	no	—
135	Q₈⋊C₈	—	142	4	no	—
136	C₂×Q₁₆	—	2	2	no	—
137	C₂×M₁₆	—	142	2	no	—
138	C₂²×C₈	—	142	1	no	—
139	C₂²×C₈	C₂²⋊D₇₁	1	2	yes	—
140	C₄⋊Q₈	C₂×Dic₇₁	1	2	yes	—
141	C₄⋊Q₈	C₂×Dic₇₁	1	2	yes	—
142	#125	—	2	2	no	—
143	C₂²⋊Q₈	—	2	2	no	—
144	C₂²⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	#117	—	2	2	no	—
148	C₂×C₄²	—	71	2	no	—
149	C₂×C₄²	—	142	1	no	—
150	C₂×C₄²	—	142	1	no	—
151	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
152	#107	—	2	2	no	—
153	C₄⋊C₈	—	142	2	no	—
154	C₄⋊C₈	—	142	2	no	—
155	#103	—	2	4	no	—
156	C₄×C₈	—	71	2	no	—
157	C₄×C₈	—	142	1	no	—
158	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
159	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
160	C₄×C₈	C₂²⋊D₇₁	1	2	yes	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	2	2	no	—
163	C₂²×C₄	—	142	2	no	—
164	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
165	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
166	C₂²×C₄	#11765864	1	1	yes	characteristic
167	Q₁₆	—	4	4	no	—
168	M₁₆	—	284	4	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	284	2	no	—
171	C₂×C₈	—	284	2	no	—
172	C₂×C₈	—	142	2	no	—
173	C₂×C₈	C₂²⋊Dic₇₁	1	2	yes	—
174	C₂×C₈	C₂²⋊Dic₇₁	1	2	yes	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	—	4	2	no	—
183	C₄²	—	284	2	no	—
184	C₄²	—	284	2	no	—
185	C₄²	—	71	4	no	—
186	C₄²	—	142	2	no	—
187	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
188	C₄²	D₄×D₇₁	1	1	yes	characteristic
189	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
190	C₄²	#11765864	1	1	yes	characteristic
191	C₂³	#14556099	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	4	4	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	284	2	no	—
199	C₂×C₄	—	284	2	no	—
200	C₂×C₄	—	142	4	no	—
201	C₂×C₄	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
202	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
203	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
204	C₂×C₄	#14556099	1	1	yes	characteristic
205	C₂×C₄	#14556115	1	1	yes	characteristic
206	C₂×C₄	#14556124	1	1	yes	characteristic
207	C₂×C₄	Q₁₆×D₇₁	1	2	yes	—
208	C₂×C₄	#14556151	1	2	yes	—
209	C₈	—	2	2	no	—
210	C₈	—	2	2	no	—
211	C₈	—	284	2	no	—
212	C₈	—	568	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#17985902	1	1	yes	characteristic
216	C₂²	#17986237	1	2	yes	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	8	2	no	—
220	C₄	—	8	2	no	—
221	C₄	—	284	4	no	—
222	C₄	#17986016	1	2	yes	—
223	C₄	Q₁₆×Dic₇₁	1	2	yes	—
224	C₄	#17986121	1	2	yes	—
225	C₄	#17986377	1	1	yes	characteristic
226	C₄	#17986384	1	1	yes	characteristic
227	C₂	—	2	2	no	—
228	C₂	#22589173	1	1	yes	characteristic
229	C₂	#22589202	1	1	yes	characteristic
230	C₂	#22589234	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22589318

C₂

yes

maximal

#22588085

C₂

yes

maximal, characteristic

#22587099

C₂

yes

maximal, characteristic

#22586795

C₂

yes

maximal

C₇₁×#3170

C₂

yes

maximal, characteristic

#17986023

C₂²

yes

—

C₂×C₄×C₇₁⋊C₈

C₂²

yes

characteristic

C₄²×Dic₇₁

C₂²

yes

—

—

—

Q₈⋊(C₇₁⋊C₈)

—

#533×C₇₁

C₂²

yes

—

#500×C₇₁

C₄

yes

characteristic, complemented

#494×C₇₁

C₄

yes

characteristic, complemented

#487×C₇₁

C₄

yes

complemented

#467×C₇₁

—

C₄×Q₁₆×C₇₁

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×#11765849

—

C₂²×C₇₁⋊C₈

—

C₂×C₄×Dic₇₁

—

C₂×C₄×Dic₇₁

—

C₂×C₄×Dic₇₁

D₄

yes

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄×C₇₁⋊C₈

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₂×Q₁₆×C₇₁

—

C₂²×C₈×C₇₁

D₄

yes

—

C₄⋊Q₈×C₇₁

C₂×C₄

yes

—

C₄⋊Q₈×C₇₁

C₂×C₄

yes

—

#125×C₇₁

—

C₂²⋊Q₈×C₇₁

—

C₂²⋊Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

#117×C₇₁

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

#107×C₇₁

—

#103×C₇₁

—

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

—

C₂²×Dic₇₁

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

Q₁₆

yes

complemented

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

#41

yes

characteristic

Q₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₂²⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

C₂²×C₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

C₄²×C₇₁

yes

C₂³×C₇₁

yes

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂×Q₁₆

yes

—

C₂×C₄×C₇₁

#135

yes

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

#390

yes

characteristic

100

C₂²×C₇₁

#467

yes

—

101

C₄×C₇₁

—

102

C₄×C₇₁

—

103

C₄×C₇₁

—

104

C₄×C₇₁

—

105

C₄×C₇₁

#421

yes

—

106

C₄×C₇₁

C₄×Q₁₆

yes

—

107

C₄×C₇₁

#444

yes

—

108

C₄×C₇₁

#494

yes

characteristic

109

C₄×C₇₁

#495

yes

characteristic

110

Dic₇₁

—

111

#9848

—

maximal, Sylow

112

C₂×C₇₁

—

113

C₂×C₇₁

#1963

yes

characteristic

114

C₂×C₇₁

#1969

yes

characteristic

115

C₂×C₇₁

#1975

yes

characteristic

116

#3170

D₇₁

yes

characteristic

117

#1994

—

118

#1744

—

119

#1567

—

120

#1493

—

121

C₇₁

#9848

yes

characteristic, complemented, Sylow

122

#533

C₂×D₇₁

yes

—

123

#500

Dic₇₁

yes

characteristic, complemented

124

#494

Dic₇₁

yes

characteristic, complemented

125

#487

Dic₇₁

yes

complemented

126

#467

—

127

C₄×Q₁₆

—

128

#423

—

129

C₂×C₄×C₈

—

130

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

131

C₄³

—

132

#339

—

142

—

133

#336

—

142

—

134

#335

—

142

—

135

Q₈⋊C₈

—

142

—

136

C₂×Q₁₆

—

137

C₂×M₁₆

—

142

—

138

C₂²×C₈

—

142

—

139

C₂²×C₈

C₂²⋊D₇₁

yes

—

140

C₄⋊Q₈

C₂×Dic₇₁

yes

—

141

C₄⋊Q₈

C₂×Dic₇₁

yes

—

142

#125

—

143

C₂²⋊Q₈

—

144

C₂²⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

#117

—

148

C₂×C₄²

—

149

C₂×C₄²

—

142

—

150

C₂×C₄²

—

142

—

151

C₂×C₄²

C₂²×D₇₁

yes

characteristic

152

#107

—

153

C₄⋊C₈

—

142

—

154

C₄⋊C₈

—

142

—

155

#103

—

156

C₄×C₈

—

157

C₄×C₈

—

142

—

158

C₄×C₈

C₂×Dic₇₁

yes

characteristic

159

C₄×C₈

C₂×Dic₇₁

yes

characteristic

160

C₄×C₈

C₂²⋊D₇₁

yes

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂²×C₄

—

142

—

164

C₂²×C₄

D₄×D₇₁

yes

characteristic

165

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

166

C₂²×C₄

#11765864

yes

characteristic

167

Q₁₆

—

168

M₁₆

—

284

—

169

C₂×C₈

—

170

C₂×C₈

—

284

—

171

C₂×C₈

—

284

—

172

C₂×C₈

—

142

—

173

C₂×C₈

C₂²⋊Dic₇₁

yes

—

174

C₂×C₈

C₂²⋊Dic₇₁

yes

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

—

183

C₄²

—

284

—

184

C₄²

—

284

—

185

C₄²

—

186

C₄²

—

142

—

187

C₄²

C₂²×Dic₇₁

yes

characteristic

188

C₄²

D₄×D₇₁

yes

characteristic

189

C₄²

C₂×C₂²⋊D₇₁

yes

characteristic

190

C₄²

#11765864

yes

characteristic

191

C₂³

#14556099

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

284

—

199

C₂×C₄

—

284

—

200

C₂×C₄

—

142

—

201

C₂×C₄

C₂×C₂²⋊Dic₇₁

yes

characteristic

202

C₂×C₄

D₄×Dic₇₁

yes

characteristic

203

C₂×C₄

D₄×Dic₇₁

yes

characteristic

204

C₂×C₄

#14556099

yes

characteristic

205

C₂×C₄

#14556115

yes

characteristic

206

C₂×C₄

#14556124

yes

characteristic

207

C₂×C₄

Q₁₆×D₇₁

yes

—

208

C₂×C₄

#14556151

yes

—

209

C₈

—

210

C₈

—

211

C₈

—

284

—

212

C₈

—

568

—

213

C₂²

—

214

C₂²

—

215

C₂²

#17985902

yes

characteristic

216

C₂²

#17986237

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

284

—

222

C₄

#17986016

yes

—

223

C₄

Q₁₆×Dic₇₁

yes

—

224

C₄

#17986121

yes

—

225

C₄

#17986377

yes

characteristic

226

C₄

#17986384

yes

characteristic

227

C₂

—

228

C₂

#22589173

yes

characteristic

229

C₂

#22589202

yes

characteristic

230

C₂

#22589234

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556124
commutator	C₄²×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#3170	C₂
socle	C₂²×C₇₁	#390
prime radical	C₂³×C₇₁	#121
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#3170	D₇₁
hypocenter	C₇₁	#9848
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#14556124

commutator

C₄²×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#3170

C₂

C₂²×C₇₁

C₂³×C₇₁

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
14. #500×C₇₁	C₄	semidirect
15. #494×C₇₁	C₄	semidirect
16. #487×C₇₁	C₄	semidirect
53. C₄×Dic₇₁	Q₁₆	semidirect
121. C₇₁	#9848	semidirect
123. #500	Dic₇₁	semidirect
124. #494	Dic₇₁	semidirect
125. #487	Dic₇₁	semidirect

H ≅ G/N

type

14. #500×C₇₁

C₄

semidirect

15. #494×C₇₁

C₄

semidirect

16. #487×C₇₁

C₄

semidirect

53. C₄×Dic₇₁

Q₁₆

semidirect

121. C₇₁

#9848

semidirect

123. #500

Dic₇₁

semidirect

124. #494

Dic₇₁

semidirect

125. #487

Dic₇₁

semidirect

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

subgroup	index
#22589318	2
#22588085	2
#22587099	2
#22586795	2
C₇₁×#3170	2
#9848	71

subgroup

index

C₇₁×#3170

Subgroups — #31897353

Conjugacy classes of subgroups

Complements

Maximal subgroups