Group #31908399 — subgroups

Subgroups — #31908399

Order 18176.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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	#22588468	C₂	1	1	yes	maximal, characteristic
3	#22586353	C₂	1	4	yes	maximal
4	C₇₁×#2162	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	#17985869	—	2	1	no	—
14	#17985762	—	2	1	no	—
15	#17985762	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₁₆×C₇₁	—	2	1	no	—
18	C₂²⋊C₁₆×C₇₁	C₂²	1	2	yes	—
19	C₄×C₁₆×C₇₁	—	2	1	no	—
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×C₄⋊Dic₇₁	—	2	2	no	—
31	C₂×C₄⋊Dic₇₁	—	4	1	no	—
32	C₂×C₄⋊Dic₇₁	—	4	1	no	—
33	#14556062	—	2	1	no	—
34	#14556062	C₂×C₄	1	2	yes	—
35	#14556053	—	2	2	no	—
36	#14556053	—	2	2	no	—
37	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
39	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
40	C₂×C₁₆×C₇₁	—	2	2	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	C₂×Dic₁₄₂	—	2	2	no	—
46	C₂×Dic₁₄₂	—	4	1	no	—
47	C₂²×Dic₇₁	—	4	2	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	C₄⋊Dic₇₁	—	4	2	no	—
55	C₄⋊Dic₇₁	—	4	2	no	—
56	C₄⋊Dic₇₁	—	8	2	no	—
57	C₄⋊Dic₇₁	—	8	2	no	—
58	Dic₇₁⋊C₄	—	4	2	no	—
59	Dic₇₁⋊C₄	—	4	2	no	—
60	C₂²⋊Dic₇₁	—	4	2	no	—
61	C₄×Dic₇₁	—	4	2	no	—
62	C₂²×C₄×C₇₁	D₈	1	1	yes	characteristic
63	C₂²×C₄×C₇₁	D₈	1	1	yes	characteristic
64	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₇₁	—	4	1	no	—
66	C₂×C₈×C₇₁	—	4	1	no	—
67	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₄²×C₇₁	SD₁₆	1	1	yes	characteristic
74	C₄²×C₇₁	SD₁₆	1	1	yes	characteristic
75	C₁₆×C₇₁	—	4	2	no	—
76	C₂³×C₇₁	C₂×D₈	1	1	yes	characteristic
77	C₂×C₄×C₇₁	—	2	2	no	—
78	C₂×C₄×C₇₁	—	2	1	no	—
79	C₂×C₄×C₇₁	—	2	1	no	—
80	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
81	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
82	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
83	C₂×C₄×C₇₁	#102	1	1	yes	characteristic
84	C₂×C₄×C₇₁	SD₃₂	1	2	yes	—
85	C₂×C₄×C₇₁	Q₃₂	1	2	yes	—
86	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
88	C₂×Dic₇₁	—	4	2	no	—
89	C₂×Dic₇₁	—	4	2	no	—
90	C₂×Dic₇₁	—	8	2	no	—
91	C₂×Dic₇₁	—	8	2	no	—
92	C₂×Dic₇₁	—	8	2	no	—
93	Dic₁₄₂	—	4	2	no	—
94	Dic₁₄₂	—	4	2	no	—
95	Dic₁₄₂	—	8	2	no	—
96	C₈×C₇₁	—	2	1	no	—
97	C₈×C₇₁	—	2	1	no	—
98	C₈×C₇₁	—	2	1	no	—
99	C₈×C₇₁	—	2	1	no	—
100	C₂²×C₇₁	—	2	1	no	—
101	C₂²×C₇₁	—	2	1	no	—
102	C₂²×C₇₁	C₂×#102	1	1	yes	characteristic
103	C₂²×C₇₁	C₂×SD₃₂	1	1	yes	characteristic
104	C₂²×C₇₁	C₂×Q₃₂	1	1	yes	characteristic
105	C₄×C₇₁	—	2	1	no	—
106	C₄×C₇₁	—	2	1	no	—
107	C₄×C₇₁	#358	1	2	yes	—
108	C₄×C₇₁	#358	1	2	yes	—
109	C₄×C₇₁	#360	1	2	yes	—
110	C₄×C₇₁	#410	1	1	yes	characteristic
111	C₄×C₇₁	#421	1	1	yes	characteristic
112	Dic₇₁	—	8	2	no	—
113	Dic₇₁	—	8	2	no	—
114	Dic₇₁	—	16	2	no	—
115	#11857	—	71	1	no	maximal, Sylow
116	C₂×C₇₁	—	2	1	no	—
117	C₂×C₇₁	—	2	1	no	—
118	C₂×C₇₁	#1517	1	1	yes	characteristic
119	C₂×C₇₁	C₂×#358	1	1	yes	characteristic
120	C₂×C₇₁	C₂×#360	1	1	yes	characteristic
121	#3170	—	71	1	no	—
122	#2162	D₇₁	1	1	yes	characteristic
123	#1834	—	71	1	no	—
124	#1348	—	71	4	no	—
125	C₇₁	#11857	1	1	yes	characteristic, complemented, Sylow
126	#533	—	142	1	no	—
127	#500	—	71	1	no	—
128	#494	—	71	1	no	—
129	#487	—	142	1	no	—
130	#467	—	71	2	no	—
131	#467	—	142	1	no	—
132	C₄×Q₁₆	—	71	2	no	—
133	C₄×Q₁₆	—	142	1	no	—
134	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
135	#384	—	142	1	no	—
136	C₄⋊C₁₆	—	2	1	no	—
137	C₂²⋊C₁₆	C₂×D₇₁	1	2	yes	—
138	C₄×C₁₆	—	2	1	no	—
139	#340	—	71	2	no	—
140	#340	—	142	1	no	—
141	C₂×Q₁₆	—	71	2	no	—
142	C₂×Q₁₆	—	142	1	no	—
143	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
144	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
145	C₄⋊Q₈	—	142	1	no	—
146	C₄⋊Q₈	—	142	1	no	—
147	#125	—	284	1	no	—
148	C₂²⋊Q₈	—	284	1	no	—
149	C₂²⋊Q₈	—	142	2	no	—
150	C₄×Q₈	—	284	1	no	—
151	C₄×Q₈	—	142	2	no	—
152	#117	—	284	1	no	—
153	C₂×C₄⋊C₄	—	284	1	no	—
154	C₂×C₄⋊C₄	—	284	1	no	—
155	C₂×C₄⋊C₄	—	142	2	no	—
156	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
157	C₂×C₁₆	—	2	2	no	—
158	#107	—	71	2	no	—
159	#107	—	142	1	no	—
160	#103	—	142	2	no	—
161	#103	—	142	2	no	—
162	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
163	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
164	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
166	C₂×Q₈	—	284	1	no	—
167	C₂×Q₈	—	142	2	no	—
168	C₂²×C₄	—	284	2	no	—
169	C₂²×C₄	D₅₆₈	1	1	yes	characteristic
170	C₂²×C₄	D₅₆₈	1	1	yes	characteristic
171	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
172	Q₁₆	—	284	2	no	—
173	Q₁₆	—	284	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
177	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
178	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
179	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
180	C₄⋊C₄	—	284	2	no	—
181	C₄⋊C₄	—	284	2	no	—
182	C₄⋊C₄	—	284	2	no	—
183	C₄⋊C₄	—	284	1	no	—
184	C₄⋊C₄	—	284	1	no	—
185	C₄⋊C₄	—	284	1	no	—
186	C₄⋊C₄	—	284	2	no	—
187	C₄⋊C₄	—	568	2	no	—
188	C₄⋊C₄	—	568	2	no	—
189	C₄⋊C₄	—	142	2	no	—
190	C₂²⋊C₄	—	284	2	no	—
191	C₄²	—	284	2	no	—
192	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
193	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
194	C₄²	#11765854	1	1	yes	characteristic
195	C₄²	#11765854	1	1	yes	characteristic
196	C₁₆	—	4	2	no	—
197	C₂³	C₂×D₅₆₈	1	1	yes	characteristic
198	Q₈	—	284	2	no	—
199	Q₈	—	284	2	no	—
200	Q₈	—	568	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	284	2	no	—
205	C₂×C₄	—	284	2	no	—
206	C₂×C₄	—	568	2	no	—
207	C₂×C₄	—	568	2	no	—
208	C₂×C₄	—	568	2	no	—
209	C₂×C₄	#14556050	1	1	yes	characteristic
210	C₂×C₄	#14556050	1	1	yes	characteristic
211	C₂×C₄	#14556050	1	1	yes	characteristic
212	C₂×C₄	#14556050	1	1	yes	characteristic
213	C₂×C₄	#14556073	1	2	yes	—
214	C₂×C₄	Dic₅₆₈	1	2	yes	—
215	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
216	C₂×C₄	C₂×#11765854	1	1	yes	characteristic
217	C₈	—	2	1	no	—
218	C₈	—	2	1	no	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	—	2	1	no	—
223	C₂²	C₂×#14556050	1	1	yes	characteristic
224	C₂²	C₂×#14556073	1	1	yes	characteristic
225	C₂²	C₂×Dic₅₆₈	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	568	2	no	—
229	C₄	—	568	2	no	—
230	C₄	—	1136	2	no	—
231	C₄	#17985804	1	2	yes	—
232	C₄	#17985804	1	2	yes	—
233	C₄	#17985810	1	2	yes	—
234	C₄	#17985972	1	1	yes	characteristic
235	C₄	#17986015	1	1	yes	characteristic
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	#22586901	1	1	yes	characteristic
239	C₂	C₂×#17985804	1	1	yes	characteristic
240	C₂	C₂×#17985810	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22598926

C₂

yes

maximal, characteristic

#22588468

C₂

yes

maximal, characteristic

#22586353

C₂

yes

maximal

C₇₁×#2162

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

—

—

C₂²

yes

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₁

—

C₂²⋊C₁₆×C₇₁

C₂²

yes

—

C₄×C₁₆×C₇₁

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

C₂×C₄

yes

—

—

—

—

—

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

#14556087

—

C₂×C₄⋊Dic₇₁

—

C₂×C₄⋊Dic₇₁

—

C₂×C₄⋊Dic₇₁

—

#14556062

—

#14556062

C₂×C₄

yes

—

#14556053

—

#14556053

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

C₂³

yes

characteristic

C₂×C₄²×C₇₁

D₄

yes

characteristic

C₂×C₁₆×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

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

Dic₂₈₄

—

Dic₂₈₄

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

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

C₄²×C₇₁

C₂²⋊C₄

yes

characteristic

C₄²×C₇₁

C₂²⋊C₄

yes

characteristic

C₄²×C₇₁

SD₁₆

yes

characteristic

C₄²×C₇₁

SD₁₆

yes

characteristic

C₁₆×C₇₁

—

C₂³×C₇₁

C₂×D₈

yes

characteristic

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

SD₃₂

yes

—

C₂×C₄×C₇₁

Q₃₂

yes

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₂×SD₁₆

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

100

C₂²×C₇₁

—

101

C₂²×C₇₁

—

102

C₂²×C₇₁

C₂×#102

yes

characteristic

103

C₂²×C₇₁

C₂×SD₃₂

yes

characteristic

104

C₂²×C₇₁

C₂×Q₃₂

yes

characteristic

105

C₄×C₇₁

—

106

C₄×C₇₁

—

107

C₄×C₇₁

#358

yes

—

108

C₄×C₇₁

#358

yes

—

109

C₄×C₇₁

#360

yes

—

110

C₄×C₇₁

#410

yes

characteristic

111

C₄×C₇₁

#421

yes

characteristic

112

Dic₇₁

—

113

Dic₇₁

—

114

Dic₇₁

—

115

#11857

—

maximal, Sylow

116

C₂×C₇₁

—

117

C₂×C₇₁

—

118

C₂×C₇₁

#1517

yes

characteristic

119

C₂×C₇₁

C₂×#358

yes

characteristic

120

C₂×C₇₁

C₂×#360

yes

characteristic

121

#3170

—

122

#2162

D₇₁

yes

characteristic

123

#1834

—

124

#1348

—

125

C₇₁

#11857

yes

characteristic, complemented, Sylow

126

#533

—

142

—

127

#500

—

128

#494

—

129

#487

—

142

—

130

#467

—

131

#467

—

142

—

132

C₄×Q₁₆

—

133

C₄×Q₁₆

—

142

—

134

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

135

#384

—

142

—

136

C₄⋊C₁₆

—

137

C₂²⋊C₁₆

C₂×D₇₁

yes

—

138

C₄×C₁₆

—

139

#340

—

140

#340

—

142

—

141

C₂×Q₁₆

—

142

C₂×Q₁₆

—

142

—

143

C₂²×C₈

D₂₈₄

yes

characteristic

144

C₂²×C₈

C₂²×D₇₁

yes

characteristic

145

C₄⋊Q₈

—

142

—

146

C₄⋊Q₈

—

142

—

147

#125

—

284

—

148

C₂²⋊Q₈

—

284

—

149

C₂²⋊Q₈

—

142

—

150

C₄×Q₈

—

284

—

151

C₄×Q₈

—

142

—

152

#117

—

284

—

153

C₂×C₄⋊C₄

—

284

—

154

C₂×C₄⋊C₄

—

284

—

155

C₂×C₄⋊C₄

—

142

—

156

C₂×C₄²

D₂₈₄

yes

characteristic

157

C₂×C₁₆

—

158

#107

—

159

#107

—

142

—

160

#103

—

142

—

161

#103

—

142

—

162

C₄×C₈

C₄×D₇₁

yes

characteristic

163

C₄×C₈

C₄×D₇₁

yes

characteristic

164

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

165

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

166

C₂×Q₈

—

284

—

167

C₂×Q₈

—

142

—

168

C₂²×C₄

—

284

—

169

C₂²×C₄

D₅₆₈

yes

characteristic

170

C₂²×C₄

D₅₆₈

yes

characteristic

171

C₂²×C₄

C₂×D₂₈₄

yes

characteristic

172

Q₁₆

—

284

—

173

Q₁₆

—

284

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

177

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

178

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

179

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

180

C₄⋊C₄

—

284

—

181

C₄⋊C₄

—

284

—

182

C₄⋊C₄

—

284

—

183

C₄⋊C₄

—

284

—

184

C₄⋊C₄

—

284

—

185

C₄⋊C₄

—

284

—

186

C₄⋊C₄

—

284

—

187

C₄⋊C₄

—

568

—

188

C₄⋊C₄

—

568

—

189

C₄⋊C₄

—

142

—

190

C₂²⋊C₄

—

284

—

191

C₄²

—

284

—

192

C₄²

(C₂×D₇₁)⋊C₄

yes

characteristic

193

C₄²

(C₂×D₇₁)⋊C₄

yes

characteristic

194

C₄²

#11765854

yes

characteristic

195

C₄²

#11765854

yes

characteristic

196

C₁₆

—

197

C₂³

C₂×D₅₆₈

yes

characteristic

198

Q₈

—

284

—

199

Q₈

—

284

—

200

Q₈

—

568

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

284

—

205

C₂×C₄

—

284

—

206

C₂×C₄

—

568

—

207

C₂×C₄

—

568

—

208

C₂×C₄

—

568

—

209

C₂×C₄

#14556050

yes

characteristic

210

C₂×C₄

#14556050

yes

characteristic

211

C₂×C₄

#14556050

yes

characteristic

212

C₂×C₄

#14556050

yes

characteristic

213

C₂×C₄

#14556073

yes

—

214

C₂×C₄

Dic₅₆₈

yes

—

215

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

216

C₂×C₄

C₂×#11765854

yes

characteristic

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

221

C₂²

—

222

C₂²

—

223

C₂²

C₂×#14556050

yes

characteristic

224

C₂²

C₂×#14556073

yes

characteristic

225

C₂²

C₂×Dic₅₆₈

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

568

—

229

C₄

—

568

—

230

C₄

—

1136

—

231

C₄

#17985804

yes

—

232

C₄

#17985804

yes

—

233

C₄

#17985810

yes

—

234

C₄

#17985972

yes

characteristic

235

C₄

#17986015

yes

characteristic

236

C₂

—

237

C₂

—

238

C₂

#22586901

yes

characteristic

239

C₂

C₂×#17985804

yes

characteristic

240

C₂

C₂×#17985810

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#14556050
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₇₁×#2162	C₂
socle	C₂²×C₇₁	C₂×#102
prime radical	C₂³×C₇₁	C₂×D₈
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	#2162	D₇₁
hypocenter	C₇₁	#11857
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

subgroup

G/H

center

C₂²

C₂×#14556050

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₇₁×#2162

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 ◁ #2162

N	H ≅ G/N	type
6. #17986404	C₄	semidirect
7. #17986379	C₄	semidirect
12. C₄×Dic₂₈₄	C₄	semidirect
125. C₇₁	#11857	semidirect

H ≅ G/N

type

6. #17986404

C₄

semidirect

7. #17986379

C₄

semidirect

12. C₄×Dic₂₈₄

C₄

semidirect

125. C₇₁

#11857

semidirect

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

subgroup	index
#22598926	2
#22588468	2
#22586353	2
C₇₁×#2162	2
#11857	71

subgroup

index

C₇₁×#2162

Subgroups — #31908399

Conjugacy classes of subgroups

Complements

Maximal subgroups