Group #31907871 — subgroups

Subgroups — #31907871

Order 18176.

346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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	#22598926	C₂	1	1	yes	maximal, characteristic
2	#22590143	C₂	1	1	yes	maximal, characteristic
3	#22586351	C₂	1	4	yes	maximal
4	C₄×#106×C₇₁	C₂	1	1	yes	maximal, characteristic
5	#17986556	—	2	1	no	—
6	#17986404	C₄	1	1	yes	characteristic, complemented
7	#17986379	C₄	1	1	yes	characteristic, complemented
8	#17986350	—	2	1	no	—
9	#17986240	—	2	1	no	—
10	#17986240	C₂²	1	2	yes	—
11	C₄×Dic₂₈₄	—	2	1	no	—
12	C₄×Dic₂₈₄	C₄	1	2	yes	complemented
13	C₄⋊(C₇₁⋊C₁₆)	—	2	1	no	—
14	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	—
15	#17985775	—	2	1	no	—
16	C₂×#106×C₇₁	—	2	1	no	—
17	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₇₁	—	2	1	no	—
19	#340×C₇₁	C₂²	1	2	yes	—
20	C₂×Dic₂₈₄	—	2	1	no	—
21	C₂×Dic₂₈₄	C₂×C₄	1	2	yes	—
22	#14556128	—	2	1	no	—
23	#14556128	—	2	1	no	—
24	#14556120	—	4	1	no	—
25	#14556107	—	2	2	no	—
26	#14556107	—	4	1	no	—
27	C₄×Dic₁₄₂	—	2	2	no	—
28	C₄×Dic₁₄₂	—	4	1	no	—
29	#14556087	—	4	1	no	—
30	C₂×C₇₁⋊C₁₆	—	2	2	no	—
31	#14556062	—	2	1	no	—
32	#14556062	C₂×C₄	1	2	yes	—
33	#14556053	—	2	2	no	—
34	#14556053	—	2	2	no	—
35	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
38	C₂×C₄²×C₇₁	—	4	1	no	—
39	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
40	#106×C₇₁	—	2	4	no	—
41	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
44	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
45	#95×C₇₁	—	4	1	no	—
46	C₂×Dic₁₄₂	—	2	2	no	—
47	C₂×Dic₁₄₂	—	4	1	no	—
48	Dic₂₈₄	—	4	2	no	—
49	Dic₂₈₄	—	4	2	no	—
50	C₄⋊Dic₇₁	—	2	2	no	—
51	C₄⋊Dic₇₁	—	4	1	no	—
52	C₄⋊Dic₇₁	—	4	1	no	—
53	C₄⋊Dic₇₁	—	4	1	no	—
54	Dic₇₁⋊C₄	—	4	2	no	—
55	Dic₇₁⋊C₄	—	4	2	no	—
56	C₂²⋊Dic₇₁	—	4	2	no	—
57	C₄×Dic₇₁	—	4	2	no	—
58	C₇₁⋊C₁₆	—	4	2	no	—
59	C₂²×C₄×C₇₁	—	4	2	no	—
60	C₂²×C₄×C₇₁	D₈	1	1	yes	characteristic
61	C₂²×C₄×C₇₁	D₈	1	1	yes	characteristic
62	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₇₁	—	2	2	no	—
64	C₂×C₈×C₇₁	—	4	1	no	—
65	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
69	C₄⋊C₄×C₇₁	—	2	4	no	—
70	C₄⋊C₄×C₇₁	—	4	2	no	—
71	C₄²×C₇₁	—	8	2	no	—
72	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₄²×C₇₁	SD₁₆	1	1	yes	characteristic
75	C₄²×C₇₁	SD₁₆	1	1	yes	characteristic
76	C₂³×C₇₁	C₂×D₈	1	1	yes	characteristic
77	C₂×C₄×C₇₁	—	2	2	no	—
78	C₂×C₄×C₇₁	—	2	2	no	—
79	C₂×C₄×C₇₁	—	2	1	no	—
80	C₂×C₄×C₇₁	—	2	1	no	—
81	C₂×C₄×C₇₁	—	4	4	no	—
82	C₂×C₄×C₇₁	—	8	2	no	—
83	C₂×C₄×C₇₁	—	8	2	no	—
84	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
88	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×Dic₇₁	—	4	2	no	—
91	C₂×Dic₇₁	—	4	2	no	—
92	Dic₁₄₂	—	4	2	no	—
93	Dic₁₄₂	—	4	2	no	—
94	Dic₁₄₂	—	8	2	no	—
95	C₈×C₇₁	—	2	1	no	—
96	C₈×C₇₁	—	2	1	no	—
97	C₈×C₇₁	—	2	1	no	—
98	C₈×C₇₁	#104	1	2	yes	—
99	C₂²×C₇₁	—	2	1	no	—
100	C₂²×C₇₁	—	2	1	no	—
101	C₂²×C₇₁	C₂×#102	1	1	yes	characteristic
102	C₂²×C₇₁	#510	1	2	yes	—
103	C₄×C₇₁	—	2	1	no	—
104	C₄×C₇₁	—	2	1	no	—
105	C₄×C₇₁	—	2	1	no	—
106	C₄×C₇₁	—	2	1	no	—
107	C₄×C₇₁	—	8	4	no	—
108	C₄×C₇₁	#360	1	2	yes	—
109	C₄×C₇₁	#410	1	1	yes	characteristic
110	C₄×C₇₁	C₂×#104	1	1	yes	characteristic
111	Dic₇₁	—	8	2	no	—
112	Dic₇₁	—	8	2	no	—
113	#11745	—	71	1	no	maximal, Sylow
114	C₂×C₇₁	—	2	2	no	—
115	C₂×C₇₁	#1502	1	1	yes	characteristic
116	C₂×C₇₁	#2141	1	1	yes	characteristic
117	C₂×C₇₁	C₂×#360	1	1	yes	characteristic
118	#3170	—	71	1	no	—
119	#2163	—	71	1	no	—
120	C₄×#106	D₇₁	1	1	yes	characteristic
121	#1348	—	71	4	no	—
122	C₇₁	#11745	1	1	yes	characteristic, complemented, Sylow
123	#533	—	142	1	no	—
124	#500	—	71	1	no	—
125	#494	—	71	1	no	—
126	#487	—	142	1	no	—
127	#467	—	71	2	no	—
128	#467	—	142	1	no	—
129	C₄×Q₁₆	—	71	2	no	—
130	C₄×Q₁₆	—	142	1	no	—
131	C₂×#106	—	2	1	no	—
132	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
133	C₄×C₄⋊C₄	—	2	1	no	—
134	C₄⋊C₁₆	—	142	1	no	—
135	C₂²⋊C₁₆	—	71	2	no	—
136	#346	—	142	1	no	—
137	#340	C₂×D₇₁	1	2	yes	—
138	C₂×Q₁₆	—	71	2	no	—
139	C₂×Q₁₆	—	142	1	no	—
140	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
141	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
142	C₄⋊Q₈	—	142	1	no	—
143	C₄⋊Q₈	—	142	1	no	—
144	#125	—	284	1	no	—
145	C₂²⋊Q₈	—	284	1	no	—
146	C₂²⋊Q₈	—	142	2	no	—
147	C₄×Q₈	—	284	1	no	—
148	C₄×Q₈	—	142	2	no	—
149	#117	—	284	1	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄²	—	4	1	no	—
152	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
153	C₂×C₁₆	—	142	2	no	—
154	#107	—	71	2	no	—
155	#107	—	142	1	no	—
156	#106	—	2	4	no	—
157	#103	—	142	2	no	—
158	#103	—	142	2	no	—
159	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
160	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
161	C₄×C₈	D₂₈₄	1	1	yes	characteristic
162	C₄×C₈	D₂₈₄	1	1	yes	characteristic
163	#95	—	4	1	no	—
164	C₂×Q₈	—	284	1	no	—
165	C₂×Q₈	—	142	2	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	#11765850	1	1	yes	characteristic
168	C₂²×C₄	#11765850	1	1	yes	characteristic
169	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
170	Q₁₆	—	284	2	no	—
171	Q₁₆	—	284	2	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	4	1	no	—
174	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
175	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
176	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
177	C₂×C₈	C₂×D₂₈₄	1	1	yes	characteristic
178	C₄⋊C₄	—	2	4	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	284	2	no	—
181	C₄⋊C₄	—	284	1	no	—
182	C₄⋊C₄	—	284	1	no	—
183	C₄⋊C₄	—	284	1	no	—
184	C₄⋊C₄	—	284	2	no	—
185	C₄⋊C₄	—	142	2	no	—
186	C₂²⋊C₄	—	284	2	no	—
187	C₄²	—	8	2	no	—
188	C₄²	—	284	2	no	—
189	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
190	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
191	C₄²	#11765852	1	1	yes	characteristic
192	C₄²	#11765852	1	1	yes	characteristic
193	C₁₆	—	284	2	no	—
194	C₂³	C₂×#11765850	1	1	yes	characteristic
195	Q₈	—	284	2	no	—
196	Q₈	—	284	2	no	—
197	Q₈	—	568	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	4	4	no	—
203	C₂×C₄	—	8	2	no	—
204	C₂×C₄	—	8	2	no	—
205	C₂×C₄	—	284	2	no	—
206	C₂×C₄	—	284	2	no	—
207	C₂×C₄	#14556048	1	1	yes	characteristic
208	C₂×C₄	#14556048	1	1	yes	characteristic
209	C₂×C₄	#14556048	1	1	yes	characteristic
210	C₂×C₄	#14556048	1	1	yes	characteristic
211	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
212	C₂×C₄	C₂×#11765852	1	1	yes	characteristic
213	C₈	—	2	1	no	—
214	C₈	—	2	1	no	—
215	C₈	—	2	1	no	—
216	C₈	#14556056	1	2	yes	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	C₂×#14556048	1	1	yes	characteristic
220	C₂²	#17986439	1	2	yes	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	8	4	no	—
226	C₄	—	568	2	no	—
227	C₄	—	568	2	no	—
228	C₄	#17985808	1	2	yes	—
229	C₄	#17985972	1	1	yes	characteristic
230	C₄	C₂×#14556056	1	1	yes	characteristic
231	C₂	—	2	2	no	—
232	C₂	#22586834	1	1	yes	characteristic
233	C₂	#22590059	1	1	yes	characteristic
234	C₂	C₂×#17985808	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22598926

C₂

yes

maximal, characteristic

#22590143

C₂

yes

maximal, characteristic

#22586351

C₂

yes

maximal

C₄×#106×C₇₁

C₂

yes

maximal, characteristic

#17986556

—

#17986404

C₄

yes

characteristic, complemented

#17986379

C₄

yes

characteristic, complemented

#17986350

—

#17986240

—

#17986240

C₂²

yes

—

C₄×Dic₂₈₄

—

C₄×Dic₂₈₄

C₄

yes

complemented

C₄⋊(C₇₁⋊C₁₆)

—

C₂²⋊(C₇₁⋊C₁₆)

C₂²

yes

—

#17985775

—

C₂×#106×C₇₁

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₇₁

—

#340×C₇₁

C₂²

yes

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

C₂×C₄

yes

—

—

—

—

—

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

#14556087

—

C₂×C₇₁⋊C₁₆

—

#14556062

—

#14556062

C₂×C₄

yes

—

#14556053

—

#14556053

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄²×C₇₁

—

C₂×C₄²×C₇₁

D₄

yes

characteristic

#106×C₇₁

—

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

#95×C₇₁

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

Dic₂₈₄

—

Dic₂₈₄

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

D₈

yes

characteristic

C₂²×C₄×C₇₁

D₈

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

C₂²⋊C₄

yes

characteristic

C₄²×C₇₁

C₂²⋊C₄

yes

characteristic

C₄²×C₇₁

SD₁₆

yes

characteristic

C₄²×C₇₁

SD₁₆

yes

characteristic

C₂³×C₇₁

C₂×D₈

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

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₂×SD₁₆

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

#104

yes

—

C₂²×C₇₁

—

100

C₂²×C₇₁

—

101

C₂²×C₇₁

C₂×#102

yes

characteristic

102

C₂²×C₇₁

#510

yes

—

103

C₄×C₇₁

—

104

C₄×C₇₁

—

105

C₄×C₇₁

—

106

C₄×C₇₁

—

107

C₄×C₇₁

—

108

C₄×C₇₁

#360

yes

—

109

C₄×C₇₁

#410

yes

characteristic

110

C₄×C₇₁

C₂×#104

yes

characteristic

111

Dic₇₁

—

112

Dic₇₁

—

113

#11745

—

maximal, Sylow

114

C₂×C₇₁

—

115

C₂×C₇₁

#1502

yes

characteristic

116

C₂×C₇₁

#2141

yes

characteristic

117

C₂×C₇₁

C₂×#360

yes

characteristic

118

#3170

—

119

#2163

—

120

C₄×#106

D₇₁

yes

characteristic

121

#1348

—

122

C₇₁

#11745

yes

characteristic, complemented, Sylow

123

#533

—

142

—

124

#500

—

125

#494

—

126

#487

—

142

—

127

#467

—

128

#467

—

142

—

129

C₄×Q₁₆

—

130

C₄×Q₁₆

—

142

—

131

C₂×#106

—

132

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

133

C₄×C₄⋊C₄

—

134

C₄⋊C₁₆

—

142

—

135

C₂²⋊C₁₆

—

136

#346

—

142

—

137

#340

C₂×D₇₁

yes

—

138

C₂×Q₁₆

—

139

C₂×Q₁₆

—

142

—

140

C₂²×C₈

C₂²⋊D₇₁

yes

characteristic

141

C₂²×C₈

C₂²×D₇₁

yes

characteristic

142

C₄⋊Q₈

—

142

—

143

C₄⋊Q₈

—

142

—

144

#125

—

284

—

145

C₂²⋊Q₈

—

284

—

146

C₂²⋊Q₈

—

142

—

147

C₄×Q₈

—

284

—

148

C₄×Q₈

—

142

—

149

#117

—

284

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄²

—

152

C₂×C₄²

C₂²⋊D₇₁

yes

characteristic

153

C₂×C₁₆

—

142

—

154

#107

—

155

#107

—

142

—

156

#106

—

157

#103

—

142

—

158

#103

—

142

—

159

C₄×C₈

C₄×D₇₁

yes

characteristic

160

C₄×C₈

C₄×D₇₁

yes

characteristic

161

C₄×C₈

D₂₈₄

yes

characteristic

162

C₄×C₈

D₂₈₄

yes

characteristic

163

#95

—

164

C₂×Q₈

—

284

—

165

C₂×Q₈

—

142

—

166

C₂²×C₄

—

167

C₂²×C₄

#11765850

yes

characteristic

168

C₂²×C₄

#11765850

yes

characteristic

169

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

170

Q₁₆

—

284

—

171

Q₁₆

—

284

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

175

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

176

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

177

C₂×C₈

C₂×D₂₈₄

yes

characteristic

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

284

—

181

C₄⋊C₄

—

284

—

182

C₄⋊C₄

—

284

—

183

C₄⋊C₄

—

284

—

184

C₄⋊C₄

—

284

—

185

C₄⋊C₄

—

142

—

186

C₂²⋊C₄

—

284

—

187

C₄²

—

188

C₄²

—

284

—

189

C₄²

(C₂×D₇₁)⋊C₄

yes

characteristic

190

C₄²

(C₂×D₇₁)⋊C₄

yes

characteristic

191

C₄²

#11765852

yes

characteristic

192

C₄²

#11765852

yes

characteristic

193

C₁₆

—

284

—

194

C₂³

C₂×#11765850

yes

characteristic

195

Q₈

—

284

—

196

Q₈

—

284

—

197

Q₈

—

568

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

284

—

206

C₂×C₄

—

284

—

207

C₂×C₄

#14556048

yes

characteristic

208

C₂×C₄

#14556048

yes

characteristic

209

C₂×C₄

#14556048

yes

characteristic

210

C₂×C₄

#14556048

yes

characteristic

211

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

212

C₂×C₄

C₂×#11765852

yes

characteristic

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

#14556056

yes

—

217

C₂²

—

218

C₂²

—

219

C₂²

C₂×#14556048

yes

characteristic

220

C₂²

#17986439

yes

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

568

—

227

C₄

—

568

—

228

C₄

#17985808

yes

—

229

C₄

#17985972

yes

characteristic

230

C₄

C₂×#14556056

yes

characteristic

231

C₂

—

232

C₂

#22586834

yes

characteristic

233

C₂

#22590059

yes

characteristic

234

C₂

C₂×#17985808

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#14556048
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₄×#106×C₇₁	C₂
socle	C₂²×C₇₁	C₂×#102
prime radical	C₂³×C₇₁	C₂×D₈
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	C₄×#106	D₇₁
hypocenter	C₇₁	#11745
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#106

subgroup

G/H

center

C₂²

C₂×#14556048

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₄×#106×C₇₁

C₂

socle

C₂²×C₇₁

C₂×#102

prime radical

C₂³×C₇₁

C₂×D₈

cosocle

C₂²×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#106

N	H ≅ G/N	type
6. #17986404	C₄	semidirect
7. #17986379	C₄	semidirect
12. C₄×Dic₂₈₄	C₄	semidirect
122. C₇₁	#11745	semidirect

H ≅ G/N

type

6. #17986404

C₄

semidirect

7. #17986379

C₄

semidirect

12. C₄×Dic₂₈₄

C₄

semidirect

122. C₇₁

#11745

semidirect

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

subgroup	index
#22598926	2
#22590143	2
#22586351	2
C₄×#106×C₇₁	2
#11745	71

subgroup

index

C₄×#106×C₇₁

Subgroups — #31907871

Conjugacy classes of subgroups

Complements

Maximal subgroups