Group #35309423 — subgroups

Subgroups — #35309423

Order 21248.

316 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 93 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	#24908443	C₂	1	1	yes	maximal, characteristic
2	#24907616	C₂	1	1	yes	maximal, characteristic
3	#24906239	C₂	1	1	yes	maximal, characteristic
4	#24905867	C₂	1	1	yes	maximal, characteristic
5	#24905865	C₂	1	1	yes	maximal, characteristic
6	#24905291	C₂	1	1	yes	maximal, characteristic
7	C₈₃×#1571	C₂	1	1	yes	maximal, characteristic
8	#19128258	C₂²	1	1	yes	characteristic
9	#19127754	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₈₃⋊C₈	—	2	2	no	—
12	#19127547	C₂²	1	1	yes	characteristic
13	#19127462	—	2	2	no	—
14	#19127453	—	2	2	no	—
15	#19127433	—	2	2	no	—
16	#19127431	—	2	2	no	—
17	#431×C₈₃	C₂²	1	1	yes	characteristic
18	#423×C₈₃	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
20	#335×C₈₃	—	2	2	no	—
21	C₂²×C₈₃⋊C₈	—	2	1	no	—
22	#14581792	Q₈	1	1	yes	characteristic
23	#14581792	Q₈	1	1	yes	characteristic
24	#14581784	—	2	1	no	—
25	#14581771	—	2	1	no	—
26	#14581771	—	2	1	no	—
27	C₄×Dic₁₆₆	—	2	1	no	—
28	C₄×Dic₁₆₆	—	2	1	no	—
29	#14581751	—	2	1	no	—
30	C₂×C₄×Dic₈₃	D₄	1	2	yes	—
31	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
32	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
33	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
34	Dic₈₃⋊C₈	—	4	4	no	—
35	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
36	C₄×C₈₃⋊C₈	D₄	1	2	yes	—
37	C₈₃⋊#95	—	2	1	no	—
38	C₈₃⋊#95	—	2	1	no	—
39	C₂×M₁₆×C₈₃	—	2	1	no	—
40	C₂²×C₈×C₈₃	—	2	1	no	—
41	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₈₃	—	2	1	no	—
43	C₄⋊C₈×C₈₃	—	2	1	no	—
44	C₄⋊C₈×C₈₃	—	2	1	no	—
45	C₄⋊C₈×C₈₃	—	2	1	no	—
46	C₄⋊C₈×C₈₃	—	2	1	no	—
47	C₂²⋊C₈×C₈₃	—	2	1	no	—
48	C₄×C₈×C₈₃	D₄	1	2	yes	—
49	C₂×Dic₁₆₆	—	2	1	no	—
50	C₂×Dic₁₆₆	—	2	1	no	—
51	C₂²×Dic₈₃	—	2	2	no	—
52	C₂×C₈₃⋊C₈	—	2	2	no	—
53	C₂×C₈₃⋊C₈	—	4	1	no	—
54	C₂×C₈₃⋊C₈	—	4	2	no	—
55	C₄⋊Dic₈₃	—	2	1	no	—
56	C₄⋊Dic₈₃	—	2	1	no	—
57	C₄⋊Dic₈₃	—	2	1	no	—
58	C₄⋊Dic₈₃	—	2	1	no	—
59	Dic₈₃⋊C₄	—	4	1	no	—
60	Dic₈₃⋊C₄	—	4	1	no	—
61	C₂²⋊Dic₈₃	—	4	1	no	—
62	C₄×Dic₈₃	—	2	2	no	—
63	C₄×Dic₈₃	—	4	1	no	—
64	C₄×Dic₈₃	Q₁₆	1	4	yes	—
65	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
67	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
68	M₁₆×C₈₃	—	4	2	no	—
69	C₂×C₈×C₈₃	—	2	2	no	—
70	C₂×C₈×C₈₃	—	4	1	no	—
71	C₂×C₈×C₈₃	—	4	1	no	—
72	C₂×C₈×C₈₃	—	4	2	no	—
73	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₈₃	C₂×Q₈	1	1	yes	characteristic
76	C₄²×C₈₃	#41	1	1	yes	characteristic
77	C₂³×C₈₃	#123	1	1	yes	characteristic
78	C₂×C₄×C₈₃	—	4	1	no	—
79	C₂×C₄×C₈₃	—	4	1	no	—
80	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₈₃	#123	1	1	yes	characteristic
84	C₂×C₄×C₈₃	#123	1	1	yes	characteristic
85	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
86	C₂×C₄×C₈₃	C₂×Q₁₆	1	2	yes	—
87	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
88	C₂×Dic₈₃	—	2	4	no	—
89	C₂×Dic₈₃	—	4	2	no	—
90	C₂×Dic₈₃	—	4	2	no	—
91	C₂×Dic₈₃	—	4	1	no	—
92	C₂×Dic₈₃	—	4	1	no	—
93	Dic₁₆₆	—	4	2	no	—
94	Dic₁₆₆	—	4	2	no	—
95	C₈×C₈₃	—	4	2	no	—
96	C₈×C₈₃	—	8	1	no	—
97	C₈×C₈₃	—	8	1	no	—
98	C₈₃⋊C₈	—	4	2	no	—
99	C₈₃⋊C₈	—	8	1	no	—
100	C₂²×C₈₃	—	2	1	no	—
101	C₂²×C₈₃	—	2	1	no	—
102	C₂²×C₈₃	#399	1	1	yes	characteristic
103	C₂²×C₈₃	#484	1	2	yes	—
104	C₄×C₈₃	—	2	1	no	—
105	C₄×C₈₃	—	2	1	no	—
106	C₄×C₈₃	—	2	1	no	—
107	C₄×C₈₃	—	2	1	no	—
108	C₄×C₈₃	#477	1	2	yes	—
109	C₄×C₈₃	#494	1	1	yes	characteristic
110	C₄×C₈₃	#496	1	1	yes	characteristic
111	Dic₈₃	—	4	4	no	—
112	Dic₈₃	—	8	1	no	—
113	Dic₈₃	—	8	1	no	—
114	#10668	—	83	1	no	maximal, Sylow
115	C₂×C₈₃	—	2	2	no	—
116	C₂×C₈₃	#2095	1	1	yes	characteristic
117	C₂×C₈₃	#2098	1	1	yes	characteristic
118	C₂×C₈₃	#2098	1	1	yes	characteristic
119	#1995	—	83	1	no	—
120	#1843	—	83	1	no	—
121	#1571	—	83	1	no	—
122	#1571	D₈₃	1	1	yes	characteristic
123	#1481	—	83	1	no	—
124	#1481	—	83	1	no	—
125	#1274	—	83	1	no	—
126	C₈₃	#10668	1	1	yes	characteristic, complemented, Sylow
127	#533	—	83	1	no	—
128	#431	—	83	1	no	—
129	#431	C₂×D₈₃	1	1	yes	characteristic
130	#423	C₂×D₈₃	1	1	yes	characteristic
131	C₂×C₄⋊C₈	—	83	1	no	—
132	C₂×C₄⋊C₈	—	166	2	no	—
133	C₂×C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
134	#376	—	83	1	no	—
135	#339	—	166	2	no	—
136	#335	—	2	2	no	—
137	#335	—	166	2	no	—
138	Q₈⋊C₈	—	166	2	no	—
139	Q₈⋊C₈	—	166	2	no	—
140	C₂×M₁₆	—	2	1	no	—
141	C₂²×C₈	—	2	1	no	—
142	C₂²×C₈	—	166	1	no	—
143	C₄⋊Q₈	—	83	1	no	—
144	C₄⋊Q₈	—	83	1	no	—
145	#125	—	166	1	no	—
146	C₂²⋊Q₈	—	166	1	no	—
147	C₂²⋊Q₈	—	166	1	no	—
148	C₄×Q₈	—	166	1	no	—
149	C₄×Q₈	—	166	1	no	—
150	#117	—	166	1	no	—
151	C₂×C₄²	—	83	2	no	—
152	C₂×C₄²	C₂²×D₈₃	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	—	2	1	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	332	4	no	—
159	C₄⋊C₈	—	166	1	no	—
160	C₄⋊C₈	—	166	1	no	—
161	C₄⋊C₈	—	166	1	no	—
162	C₂²⋊C₈	—	2	1	no	—
163	C₂²⋊C₈	—	166	1	no	—
164	C₄×C₈	—	83	2	no	—
165	C₄×C₈	C₂²⋊D₈₃	1	2	yes	—
166	#95	—	166	1	no	—
167	#95	—	166	1	no	—
168	C₂×Q₈	—	166	1	no	—
169	C₂×Q₈	—	166	1	no	—
170	C₂²×C₄	—	166	2	no	—
171	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
172	C₂²×C₄	#13050590	1	1	yes	characteristic
173	C₂²×C₄	#13050591	1	1	yes	characteristic
174	M₁₆	—	4	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	—	4	1	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	332	1	no	—
180	C₂×C₈	—	332	2	no	—
181	C₂×C₈	—	166	2	no	—
182	C₄⋊C₄	—	332	1	no	—
183	C₄⋊C₄	—	332	1	no	—
184	C₄⋊C₄	—	166	1	no	—
185	C₄⋊C₄	—	166	1	no	—
186	C₄⋊C₄	—	166	1	no	—
187	C₄⋊C₄	—	166	1	no	—
188	C₂²⋊C₄	—	332	1	no	—
189	C₄²	—	332	1	no	—
190	C₄²	—	83	4	no	—
191	C₄²	—	166	2	no	—
192	C₄²	D₄×D₈₃	1	1	yes	characteristic
193	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
194	C₄²	Q₈×D₈₃	1	1	yes	characteristic
195	C₄²	#13050590	1	1	yes	characteristic
196	C₂³	#14581777	1	1	yes	characteristic
197	Q₈	—	332	2	no	—
198	Q₈	—	332	2	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	332	2	no	—
202	C₂×C₄	—	332	2	no	—
203	C₂×C₄	—	332	1	no	—
204	C₂×C₄	—	332	1	no	—
205	C₂×C₄	—	166	4	no	—
206	C₂×C₄	#14581768	1	1	yes	characteristic
207	C₂×C₄	#14581770	1	1	yes	characteristic
208	C₂×C₄	#14581770	1	1	yes	characteristic
209	C₂×C₄	#14581775	1	1	yes	characteristic
210	C₂×C₄	#14581777	1	1	yes	characteristic
211	C₂×C₄	#14581788	1	1	yes	characteristic
212	C₂×C₄	Q₁₆×D₈₃	1	2	yes	—
213	C₂×C₄	#14581816	1	2	yes	—
214	C₈	—	4	2	no	—
215	C₈	—	8	1	no	—
216	C₈	—	8	1	no	—
217	C₈	—	332	2	no	—
218	C₈	—	664	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#19127636	1	1	yes	characteristic
222	C₂²	#19128038	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	—	332	4	no	—
228	C₄	—	664	1	no	—
229	C₄	—	664	1	no	—
230	C₄	#19127995	1	2	yes	—
231	C₄	#19128079	1	1	yes	characteristic
232	C₄	#19128089	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	#24908998	1	1	yes	characteristic
235	C₂	#24909015	1	1	yes	characteristic
236	C₂	#24909019	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24908443

C₂

yes

maximal, characteristic

#24907616

C₂

yes

maximal, characteristic

#24906239

C₂

yes

maximal, characteristic

#24905867

C₂

yes

maximal, characteristic

#24905865

C₂

yes

maximal, characteristic

#24905291

C₂

yes

maximal, characteristic

C₈₃×#1571

C₂

yes

maximal, characteristic

#19128258

C₂²

yes

characteristic

#19127754

C₂²

yes

characteristic

C₂×C₄⋊(C₈₃⋊C₈)

C₂²

yes

characteristic

C₂×Dic₈₃⋊C₈

—

#19127547

C₂²

yes

—

—

—

—

#431×C₈₃

C₂²

yes

characteristic

#423×C₈₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₈₃

C₂²

yes

characteristic

#335×C₈₃

—

C₂²×C₈₃⋊C₈

—

#14581792

Q₈

yes

characteristic

#14581792

Q₈

yes

—

—

—

C₄×Dic₁₆₆

—

C₄×Dic₁₆₆

—

#14581751

—

C₂×C₄×Dic₈₃

D₄

yes

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

Dic₈₃⋊C₈

—

C₂²⋊(C₈₃⋊C₈)

—

C₄×C₈₃⋊C₈

D₄

yes

—

C₈₃⋊#95

—

C₈₃⋊#95

—

C₂×M₁₆×C₈₃

—

C₂²×C₈×C₈₃

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

C₂²⋊C₈×C₈₃

—

C₄×C₈×C₈₃

D₄

yes

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

Q₁₆

yes

—

C₂²×C₄×C₈₃

C₂×D₄

yes

C₂²×C₄×C₈₃

yes

C₂²×C₄×C₈₃

yes

M₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×Q₈

yes

C₄²×C₈₃

yes

C₂³×C₈₃

yes

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊Q₈

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

C₂×Q₁₆

yes

—

C₂×C₄×C₈₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

100

C₂²×C₈₃

—

101

C₂²×C₈₃

—

102

C₂²×C₈₃

#399

yes

characteristic

103

C₂²×C₈₃

#484

yes

—

104

C₄×C₈₃

—

105

C₄×C₈₃

—

106

C₄×C₈₃

—

107

C₄×C₈₃

—

108

C₄×C₈₃

#477

yes

—

109

C₄×C₈₃

#494

yes

characteristic

110

C₄×C₈₃

#496

yes

characteristic

111

Dic₈₃

—

112

Dic₈₃

—

113

Dic₈₃

—

114

#10668

—

maximal, Sylow

115

C₂×C₈₃

—

116

C₂×C₈₃

#2095

yes

characteristic

117

C₂×C₈₃

#2098

yes

characteristic

118

C₂×C₈₃

#2098

yes

characteristic

119

#1995

—

120

#1843

—

121

#1571

—

122

#1571

D₈₃

yes

characteristic

123

#1481

—

124

#1481

—

125

#1274

—

126

C₈₃

#10668

yes

characteristic, complemented, Sylow

127

#533

—

128

#431

—

129

#431

C₂×D₈₃

yes

characteristic

130

#423

C₂×D₈₃

yes

characteristic

131

C₂×C₄⋊C₈

—

132

C₂×C₄⋊C₈

—

166

—

133

C₂×C₄⋊C₈

C₂×D₈₃

yes

characteristic

134

#376

—

135

#339

—

166

—

136

#335

—

137

#335

—

166

—

138

Q₈⋊C₈

—

166

—

139

Q₈⋊C₈

—

166

—

140

C₂×M₁₆

—

141

C₂²×C₈

—

142

C₂²×C₈

—

166

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

#125

—

166

—

146

C₂²⋊Q₈

—

166

—

147

C₂²⋊Q₈

—

166

—

148

C₄×Q₈

—

166

—

149

C₄×Q₈

—

166

—

150

#117

—

166

—

151

C₂×C₄²

—

152

C₂×C₄²

C₂²×D₈₃

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

332

—

159

C₄⋊C₈

—

166

—

160

C₄⋊C₈

—

166

—

161

C₄⋊C₈

—

166

—

162

C₂²⋊C₈

—

163

C₂²⋊C₈

—

166

—

164

C₄×C₈

—

165

C₄×C₈

C₂²⋊D₈₃

yes

—

166

#95

—

166

—

167

#95

—

166

—

168

C₂×Q₈

—

166

—

169

C₂×Q₈

—

166

—

170

C₂²×C₄

—

166

—

171

C₂²×C₄

D₄×D₈₃

yes

characteristic

172

C₂²×C₄

#13050590

yes

characteristic

173

C₂²×C₄

#13050591

yes

characteristic

174

M₁₆

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

332

—

180

C₂×C₈

—

332

—

181

C₂×C₈

—

166

—

182

C₄⋊C₄

—

332

—

183

C₄⋊C₄

—

332

—

184

C₄⋊C₄

—

166

—

185

C₄⋊C₄

—

166

—

186

C₄⋊C₄

—

166

—

187

C₄⋊C₄

—

166

—

188

C₂²⋊C₄

—

332

—

189

C₄²

—

332

—

190

C₄²

—

191

C₄²

—

166

—

192

C₄²

D₄×D₈₃

yes

characteristic

193

C₄²

C₂×C₂²⋊D₈₃

yes

characteristic

194

C₄²

Q₈×D₈₃

yes

characteristic

195

C₄²

#13050590

yes

characteristic

196

C₂³

#14581777

yes

characteristic

197

Q₈

—

332

—

198

Q₈

—

332

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

332

—

202

C₂×C₄

—

332

—

203

C₂×C₄

—

332

—

204

C₂×C₄

—

332

—

205

C₂×C₄

—

166

—

206

C₂×C₄

#14581768

yes

characteristic

207

C₂×C₄

#14581770

yes

characteristic

208

C₂×C₄

#14581770

yes

characteristic

209

C₂×C₄

#14581775

yes

characteristic

210

C₂×C₄

#14581777

yes

characteristic

211

C₂×C₄

#14581788

yes

characteristic

212

C₂×C₄

Q₁₆×D₈₃

yes

—

213

C₂×C₄

#14581816

yes

—

214

C₈

—

215

C₈

—

216

C₈

—

217

C₈

—

332

—

218

C₈

—

664

—

219

C₂²

—

220

C₂²

—

221

C₂²

#19127636

yes

characteristic

222

C₂²

#19128038

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

332

—

228

C₄

—

664

—

229

C₄

—

664

—

230

C₄

#19127995

yes

—

231

C₄

#19128079

yes

characteristic

232

C₄

#19128089

yes

characteristic

233

C₂

—

234

C₂

#24908998

yes

characteristic

235

C₂

#24909015

yes

characteristic

236

C₂

#24909019

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14581788
commutator, cosocle	C₂×C₄²×C₈₃	C₂³
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1571	C₂
socle	C₂²×C₈₃	#399
prime radical	C₂³×C₈₃	#123
hypercenter	#1571	D₈₃
hypocenter	C₈₃	#10668
LCS	G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

subgroup

G/H

center

C₂×C₄

#14581788

commutator, cosocle

C₂×C₄²×C₈₃

C₂³

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1571

C₂

C₂²×C₈₃

C₂³×C₈₃

D₈₃

C₈₃

G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

N	H ≅ G/N	type
126. C₈₃	#10668	semidirect

H ≅ G/N

type

126. C₈₃

#10668

semidirect

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

subgroup	index
#24908443	2
#24907616	2
#24906239	2
#24905867	2
#24905865	2
#24905291	2
C₈₃×#1571	2
#10668	83

subgroup

index

C₈₃×#1571

Subgroups — #35309423

Conjugacy classes of subgroups

Complements

Maximal subgroups