Group #31902472 — subgroups

Subgroups — #31902472

Order 18176.

316 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 95 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	#22589322	C₂	1	1	yes	maximal, characteristic
2	#22588493	C₂	1	1	yes	maximal, characteristic
3	#22587115	C₂	1	1	yes	maximal, characteristic
4	#22587114	C₂	1	1	yes	maximal, characteristic
5	#22586743	C₂	1	1	yes	maximal, characteristic
6	#22586168	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1481	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×Dic₇₁⋊C₈	—	2	2	no	—
12	#17985845	C₂²	1	1	yes	characteristic
13	#17985758	—	2	2	no	—
14	#17985752	—	2	2	no	—
15	#17985751	—	2	2	no	—
16	Q₈⋊(C₇₁⋊C₈)	—	2	2	no	—
17	#533×C₇₁	C₂²	1	1	yes	characteristic
18	#431×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×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	C₂×C₄×Dic₇₁	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	Dic₇₁⋊C₈	—	4	4	no	—
30	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
31	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
32	C₇₁⋊#95	—	2	1	no	—
33	C₇₁⋊#95	—	2	1	no	—
34	C₂²×C₈×C₇₁	—	2	1	no	—
35	C₄⋊Q₈×C₇₁	Q₈	1	1	yes	characteristic
36	C₄⋊Q₈×C₇₁	Q₈	1	1	yes	characteristic
37	#125×C₇₁	—	2	1	no	—
38	C₂²⋊Q₈×C₇₁	—	2	1	no	—
39	C₂²⋊Q₈×C₇₁	—	2	1	no	—
40	C₄×Q₈×C₇₁	—	2	1	no	—
41	C₄×Q₈×C₇₁	—	2	1	no	—
42	#117×C₇₁	—	2	1	no	—
43	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
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	C₂²×Dic₇₁	—	2	2	no	—
50	#11765849	—	4	2	no	—
51	C₂×C₇₁⋊C₈	—	2	2	no	—
52	C₂×C₇₁⋊C₈	—	4	1	no	—
53	C₂×C₇₁⋊C₈	—	4	1	no	—
54	C₂×C₇₁⋊C₈	—	4	2	no	—
55	C₄×Dic₇₁	—	2	2	no	—
56	C₄×Dic₇₁	Q₁₆	1	4	yes	—
57	C₂×Q₈×C₇₁	—	2	1	no	—
58	C₂×Q₈×C₇₁	—	2	1	no	—
59	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
61	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
62	C₂×C₈×C₇₁	—	2	2	no	—
63	C₂×C₈×C₇₁	—	4	1	no	—
64	C₂×C₈×C₇₁	—	4	2	no	—
65	C₄⋊C₄×C₇₁	—	2	1	no	—
66	C₄⋊C₄×C₇₁	—	2	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	C₂²⋊C₄×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	C₂×Q₈	1	1	yes	characteristic
76	C₄²×C₇₁	#41	1	1	yes	characteristic
77	C₂³×C₇₁	#123	1	1	yes	characteristic
78	Q₈×C₇₁	—	4	2	no	—
79	Q₈×C₇₁	—	4	2	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	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
88	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
89	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
90	C₂×C₄×C₇₁	C₂×Q₁₆	1	2	yes	—
91	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	2	yes	—
92	C₂×Dic₇₁	—	2	4	no	—
93	C₂×Dic₇₁	—	4	2	no	—
94	C₂×Dic₇₁	—	4	2	no	—
95	C₈×C₇₁	—	4	2	no	—
96	C₈×C₇₁	—	8	1	no	—
97	C₇₁⋊C₈	—	4	2	no	—
98	C₇₁⋊C₈	—	8	1	no	—
99	C₇₁⋊C₈	—	8	1	no	—
100	C₂²×C₇₁	—	2	1	no	—
101	C₂²×C₇₁	—	2	1	no	—
102	C₂²×C₇₁	#399	1	1	yes	characteristic
103	C₂²×C₇₁	#484	1	2	yes	—
104	C₄×C₇₁	—	2	1	no	—
105	C₄×C₇₁	—	2	1	no	—
106	C₄×C₇₁	—	2	1	no	—
107	C₄×C₇₁	—	2	1	no	—
108	C₄×C₇₁	—	8	1	no	—
109	C₄×C₇₁	—	8	1	no	—
110	C₄×C₇₁	#477	1	2	yes	—
111	C₄×C₇₁	#494	1	1	yes	characteristic
112	C₄×C₇₁	#496	1	1	yes	characteristic
113	Dic₇₁	—	4	4	no	—
114	#10668	—	71	1	no	maximal, Sylow
115	C₂×C₇₁	—	2	2	no	—
116	C₂×C₇₁	#2095	1	1	yes	characteristic
117	C₂×C₇₁	#2098	1	1	yes	characteristic
118	C₂×C₇₁	#2098	1	1	yes	characteristic
119	#1995	—	71	1	no	—
120	#1843	—	71	1	no	—
121	#1571	—	71	1	no	—
122	#1571	—	71	1	no	—
123	#1481	—	71	1	no	—
124	#1481	D₇₁	1	1	yes	characteristic
125	#1274	—	71	1	no	—
126	C₇₁	#10668	1	1	yes	characteristic, complemented, Sylow
127	#533	C₂×D₇₁	1	1	yes	characteristic
128	#431	—	71	1	no	—
129	#431	C₂×D₇₁	1	1	yes	characteristic
130	#423	—	71	1	no	—
131	C₂×C₄⋊C₈	—	71	1	no	—
132	C₂×C₄⋊C₈	—	142	2	no	—
133	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
134	#376	—	71	1	no	—
135	#339	—	142	2	no	—
136	#335	—	142	2	no	—
137	#335	—	142	2	no	—
138	Q₈⋊C₈	—	2	2	no	—
139	Q₈⋊C₈	—	142	2	no	—
140	C₂×M₁₆	—	142	1	no	—
141	C₂²×C₈	—	2	1	no	—
142	C₂²×C₈	—	142	1	no	—
143	C₄⋊Q₈	Dic₁₄₂	1	1	yes	characteristic
144	C₄⋊Q₈	Dic₁₄₂	1	1	yes	characteristic
145	#125	—	2	1	no	—
146	C₂²⋊Q₈	—	2	1	no	—
147	C₂²⋊Q₈	—	2	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	#117	—	2	1	no	—
151	C₂×C₄²	—	71	2	no	—
152	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	284	4	no	—
157	C₄⋊C₈	—	142	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	C₂²⋊C₈	—	2	1	no	—
163	C₂²⋊C₈	—	142	1	no	—
164	C₄×C₈	—	71	2	no	—
165	C₄×C₈	C₂²⋊D₇₁	1	2	yes	—
166	#95	—	142	1	no	—
167	#95	—	142	1	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂²×C₄	—	142	2	no	—
171	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
172	C₂²×C₄	#11765864	1	1	yes	characteristic
173	C₂²×C₄	#11765865	1	1	yes	characteristic
174	M₁₆	—	284	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	284	1	no	—
179	C₂×C₈	—	284	1	no	—
180	C₂×C₈	—	284	2	no	—
181	C₂×C₈	—	142	2	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	2	1	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	4	1	no	—
187	C₄⋊C₄	—	4	1	no	—
188	C₂²⋊C₄	—	4	1	no	—
189	C₄²	—	4	1	no	—
190	C₄²	—	71	4	no	—
191	C₄²	—	142	2	no	—
192	C₄²	D₄×D₇₁	1	1	yes	characteristic
193	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
194	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
195	C₄²	#11765864	1	1	yes	characteristic
196	C₂³	#14556110	1	1	yes	characteristic
197	Q₈	—	4	2	no	—
198	Q₈	—	4	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	—	284	2	no	—
204	C₂×C₄	—	284	2	no	—
205	C₂×C₄	—	142	4	no	—
206	C₂×C₄	#14556105	1	1	yes	characteristic
207	C₂×C₄	#14556105	1	1	yes	characteristic
208	C₂×C₄	#14556107	1	1	yes	characteristic
209	C₂×C₄	#14556109	1	1	yes	characteristic
210	C₂×C₄	#14556110	1	1	yes	characteristic
211	C₂×C₄	#14556124	1	1	yes	characteristic
212	C₂×C₄	Q₁₆×D₇₁	1	2	yes	—
213	C₂×C₄	#14556155	1	2	yes	—
214	C₈	—	4	2	no	—
215	C₈	—	8	1	no	—
216	C₈	—	284	2	no	—
217	C₈	—	568	1	no	—
218	C₈	—	568	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#17985935	1	1	yes	characteristic
222	C₂²	#17986333	1	2	yes	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	8	1	no	—
228	C₄	—	8	1	no	—
229	C₄	—	284	4	no	—
230	C₄	#17986292	1	2	yes	—
231	C₄	#17986377	1	1	yes	characteristic
232	C₄	#17986385	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	#22589876	1	1	yes	characteristic
235	C₂	#22589893	1	1	yes	characteristic
236	C₂	#22589895	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22589322

C₂

yes

maximal, characteristic

#22588493

C₂

yes

maximal, characteristic

#22587115

C₂

yes

maximal, characteristic

#22587114

C₂

yes

maximal, characteristic

#22586743

C₂

yes

maximal, characteristic

#22586168

C₂

yes

maximal, characteristic

C₇₁×#1481

C₂

yes

maximal, characteristic

#17986052

C₂²

yes

characteristic

#17986023

C₂²

yes

characteristic

C₂×C₄⋊(C₇₁⋊C₈)

C₂²

yes

characteristic

C₂×Dic₇₁⋊C₈

—

#17985845

C₂²

yes

—

—

—

Q₈⋊(C₇₁⋊C₈)

—

#533×C₇₁

C₂²

yes

characteristic

#431×C₇₁

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₁

C₂²

yes

characteristic

Q₈⋊C₈×C₇₁

—

C₂×#11765849

—

C₂²×C₇₁⋊C₈

—

C₂×C₄×Dic₇₁

D₄

yes

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

Dic₇₁⋊C₈

—

C₂²⋊(C₇₁⋊C₈)

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₇₁⋊#95

—

C₇₁⋊#95

—

C₂²×C₈×C₇₁

—

C₄⋊Q₈×C₇₁

Q₈

yes

characteristic

C₄⋊Q₈×C₇₁

Q₈

yes

characteristic

#125×C₇₁

—

C₂²⋊Q₈×C₇₁

—

C₂²⋊Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

#117×C₇₁

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₂²⋊C₈×C₇₁

—

C₄×C₈×C₇₁

D₄

yes

—

C₂²×Dic₇₁

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄×Dic₇₁

—

C₄×Dic₇₁

Q₁₆

yes

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

C₂²×C₄×C₇₁

yes

C₂²×C₄×C₇₁

yes

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

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

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×Q₈

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

C₂²⋊Q₈

yes

characteristic

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

C₂×Q₁₆

yes

—

C₂×C₄×C₇₁

AGL(1,ℤ/8)

yes

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

100

C₂²×C₇₁

—

101

C₂²×C₇₁

—

102

C₂²×C₇₁

#399

yes

characteristic

103

C₂²×C₇₁

#484

yes

—

104

C₄×C₇₁

—

105

C₄×C₇₁

—

106

C₄×C₇₁

—

107

C₄×C₇₁

—

108

C₄×C₇₁

—

109

C₄×C₇₁

—

110

C₄×C₇₁

#477

yes

—

111

C₄×C₇₁

#494

yes

characteristic

112

C₄×C₇₁

#496

yes

characteristic

113

Dic₇₁

—

114

#10668

—

maximal, Sylow

115

C₂×C₇₁

—

116

C₂×C₇₁

#2095

yes

characteristic

117

C₂×C₇₁

#2098

yes

characteristic

118

C₂×C₇₁

#2098

yes

characteristic

119

#1995

—

120

#1843

—

121

#1571

—

122

#1571

—

123

#1481

—

124

#1481

D₇₁

yes

characteristic

125

#1274

—

126

C₇₁

#10668

yes

characteristic, complemented, Sylow

127

#533

C₂×D₇₁

yes

characteristic

128

#431

—

129

#431

C₂×D₇₁

yes

characteristic

130

#423

—

131

C₂×C₄⋊C₈

—

132

C₂×C₄⋊C₈

—

142

—

133

C₂×C₄⋊C₈

C₂×D₇₁

yes

characteristic

134

#376

—

135

#339

—

142

—

136

#335

—

142

—

137

#335

—

142

—

138

Q₈⋊C₈

—

139

Q₈⋊C₈

—

142

—

140

C₂×M₁₆

—

142

—

141

C₂²×C₈

—

142

C₂²×C₈

—

142

—

143

C₄⋊Q₈

Dic₁₄₂

yes

characteristic

144

C₄⋊Q₈

Dic₁₄₂

yes

characteristic

145

#125

—

146

C₂²⋊Q₈

—

147

C₂²⋊Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

#117

—

151

C₂×C₄²

—

152

C₂×C₄²

C₂²×D₇₁

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

284

—

157

C₄⋊C₈

—

142

—

158

C₄⋊C₈

—

142

—

159

C₄⋊C₈

—

142

—

160

C₄⋊C₈

—

142

—

161

C₄⋊C₈

—

142

—

162

C₂²⋊C₈

—

163

C₂²⋊C₈

—

142

—

164

C₄×C₈

—

165

C₄×C₈

C₂²⋊D₇₁

yes

—

166

#95

—

142

—

167

#95

—

142

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂²×C₄

—

142

—

171

C₂²×C₄

D₄×D₇₁

yes

characteristic

172

C₂²×C₄

#11765864

yes

characteristic

173

C₂²×C₄

#11765865

yes

characteristic

174

M₁₆

—

284

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

284

—

179

C₂×C₈

—

284

—

180

C₂×C₈

—

284

—

181

C₂×C₈

—

142

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₂²⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

142

—

192

C₄²

D₄×D₇₁

yes

characteristic

193

C₄²

C₂×C₂²⋊D₇₁

yes

characteristic

194

C₄²

C₂×Dic₁₄₂

yes

characteristic

195

C₄²

#11765864

yes

characteristic

196

C₂³

#14556110

yes

characteristic

197

Q₈

—

198

Q₈

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

284

—

204

C₂×C₄

—

284

—

205

C₂×C₄

—

142

—

206

C₂×C₄

#14556105

yes

characteristic

207

C₂×C₄

#14556105

yes

characteristic

208

C₂×C₄

#14556107

yes

characteristic

209

C₂×C₄

#14556109

yes

characteristic

210

C₂×C₄

#14556110

yes

characteristic

211

C₂×C₄

#14556124

yes

characteristic

212

C₂×C₄

Q₁₆×D₇₁

yes

—

213

C₂×C₄

#14556155

yes

—

214

C₈

—

215

C₈

—

216

C₈

—

284

—

217

C₈

—

568

—

218

C₈

—

568

—

219

C₂²

—

220

C₂²

—

221

C₂²

#17985935

yes

characteristic

222

C₂²

#17986333

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

284

—

230

C₄

#17986292

yes

—

231

C₄

#17986377

yes

characteristic

232

C₄

#17986385

yes

characteristic

233

C₂

—

234

C₂

#22589876

yes

characteristic

235

C₂

#22589893

yes

characteristic

236

C₂

#22589895

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556124
commutator, cosocle	C₂×C₄²×C₇₁	C₂³
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1481	C₂
socle	C₂²×C₇₁	#399
prime radical	C₂³×C₇₁	#123
hypercenter	#1481	D₇₁
hypocenter	C₇₁	#10668
LCS	G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1481

subgroup

G/H

center

C₂×C₄

#14556124

commutator, cosocle

C₂×C₄²×C₇₁

C₂³

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1481

C₂

C₂²×C₇₁

C₂³×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1481

N	H ≅ G/N	type
126. C₇₁	#10668	semidirect

H ≅ G/N

type

126. C₇₁

#10668

semidirect

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

subgroup	index
#22589322	2
#22588493	2
#22587115	2
#22587114	2
#22586743	2
#22586168	2
C₇₁×#1481	2
#10668	71

subgroup

index

C₇₁×#1481

Subgroups — #31902472

Conjugacy classes of subgroups

Complements

Maximal subgroups