Group #35297397 — subgroups

Subgroups — #35297397

Order 21248.

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

normal subgroups only

This group has 320 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	#24916397	C₂	1	1	yes	maximal, characteristic
2	#24906226	C₂	1	1	yes	maximal, characteristic
3	#24906100	C₂	1	2	yes	maximal
4	#24905373	C₂	1	2	yes	maximal
5	C₈₃×#1568	C₂	1	1	yes	maximal, characteristic
6	#19128258	C₂²	1	1	yes	characteristic
7	#19127831	—	2	1	no	—
8	#19127831	—	2	1	no	—
9	C₈×Dic₁₆₆	—	2	1	no	—
10	C₈×Dic₁₆₆	—	2	1	no	—
11	#19127758	C₂²	1	2	yes	—
12	#19127727	C₄	1	2	yes	—
13	#19127725	C₂²	1	1	yes	characteristic
14	#19127656	C₄	1	2	yes	—
15	#19127454	—	2	1	no	—
16	#19127452	—	2	1	no	—
17	#19127442	—	2	4	no	—
18	#432×C₈₃	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
20	#335×C₈₃	—	2	1	no	—
21	#334×C₈₃	—	2	1	no	—
22	C₂×#13050574	C₂×C₄	1	2	yes	—
23	#14581792	Q₈	1	1	yes	characteristic
24	#14581792	Q₈	1	1	yes	characteristic
25	#14581784	D₄	1	2	yes	—
26	#14581771	—	2	1	no	—
27	#14581771	—	2	1	no	—
28	C₄×Dic₁₆₆	—	2	1	no	—
29	C₄×Dic₁₆₆	—	2	1	no	—
30	#14581751	C₂×C₄	1	2	yes	—
31	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
32	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
33	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
34	Dic₈₃⋊C₈	—	2	2	no	—
35	Dic₈₃⋊C₈	—	2	2	no	—
36	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
37	#14581703	—	2	2	no	—
38	#14581702	—	2	2	no	—
39	C₈×Dic₈₃	—	2	2	no	—
40	C₂²×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₈₃	—	2	2	no	—
44	C₂²⋊C₈×C₈₃	—	2	2	no	—
45	#97×C₈₃	—	2	2	no	—
46	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
47	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
48	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
49	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
50	C₂×Dic₁₆₆	—	2	1	no	—
51	C₂×Dic₁₆₆	—	2	1	no	—
52	#13050574	—	4	2	no	—
53	C₂×C₈₃⋊C₈	—	2	2	no	—
54	C₂×C₈₃⋊C₈	—	4	2	no	—
55	C₄⋊Dic₈₃	—	2	1	no	—
56	C₄⋊Dic₈₃	—	2	1	no	—
57	C₄⋊Dic₈₃	C₄⋊C₄	1	2	yes	—
58	C₄⋊Dic₈₃	C₄⋊C₄	1	2	yes	—
59	Dic₈₃⋊C₄	—	2	2	no	—
60	Dic₈₃⋊C₄	—	2	2	no	—
61	C₂²⋊Dic₈₃	—	2	2	no	—
62	C₄×Dic₈₃	—	2	2	no	—
63	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
65	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
66	C₂×C₈×C₈₃	—	2	2	no	—
67	C₂×C₈×C₈₃	—	4	1	no	—
68	C₂×C₈×C₈₃	—	4	2	no	—
69	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₈₃	C₂×Q₈	1	1	yes	characteristic
77	C₂³×C₈₃	#117	1	1	yes	characteristic
78	C₂×C₄×C₈₃	—	2	1	no	—
79	C₂×C₄×C₈₃	—	2	1	no	—
80	C₂×C₄×C₈₃	—	4	1	no	—
81	C₂×C₄×C₈₃	—	4	1	no	—
82	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
85	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
86	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×Dic₈₃	—	2	2	no	—
89	C₂×Dic₈₃	—	2	2	no	—
90	Dic₁₆₆	—	4	2	no	—
91	Dic₁₆₆	—	4	2	no	—
92	C₈×C₈₃	—	2	1	no	—
93	C₈×C₈₃	—	2	1	no	—
94	C₈×C₈₃	—	2	1	no	—
95	C₈×C₈₃	—	8	2	no	—
96	C₈×C₈₃	#101	1	2	yes	—
97	C₈₃⋊C₈	—	4	2	no	—
98	C₈₃⋊C₈	—	8	2	no	—
99	C₂²×C₈₃	—	2	1	no	—
100	C₂²×C₈₃	—	2	1	no	—
101	C₂²×C₈₃	—	2	1	no	—
102	C₂²×C₈₃	#380	1	1	yes	characteristic
103	C₄×C₈₃	—	2	1	no	—
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	C₂×#101	1	1	yes	characteristic
109	C₄×C₈₃	#413	1	1	yes	characteristic
110	Dic₈₃	—	4	2	no	—
111	Dic₈₃	—	4	2	no	—
112	#8631	—	83	1	no	maximal, Sylow
113	C₂×C₈₃	—	4	1	no	—
114	C₂×C₈₃	#1801	1	1	yes	characteristic
115	C₂×C₈₃	#1814	1	1	yes	characteristic
116	C₂×C₈₃	#1814	1	1	yes	characteristic
117	#2960	—	83	1	no	—
118	#1568	—	83	1	no	—
119	#1568	D₈₃	1	1	yes	characteristic
120	#1537	—	83	2	no	—
121	#1307	—	83	2	no	—
122	C₈₃	#8631	1	1	yes	characteristic, complemented, Sylow
123	#533	—	83	1	no	—
124	#446	—	166	1	no	—
125	#446	—	166	1	no	—
126	C₈×Q₈	—	166	1	no	—
127	C₈×Q₈	—	166	1	no	—
128	#432	—	83	2	no	—
129	#432	C₂×D₈₃	1	2	yes	—
130	#424	—	83	2	no	—
131	#423	—	83	1	no	—
132	#405	—	83	2	no	—
133	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
134	#335	—	2	1	no	—
135	#335	—	166	1	no	—
136	#334	—	2	1	no	—
137	#334	—	166	1	no	—
138	#330	—	166	4	no	—
139	C₂×M₁₆	—	83	2	no	—
140	C₂²×C₈	C₄×D₈₃	1	1	yes	characteristic
141	C₂²×C₈	C₄×D₈₃	1	1	yes	characteristic
142	C₄⋊Q₈	—	83	1	no	—
143	C₄⋊Q₈	—	83	1	no	—
144	#125	—	83	2	no	—
145	C₂²⋊Q₈	—	166	1	no	—
146	C₂²⋊Q₈	—	166	1	no	—
147	C₄×Q₈	—	166	1	no	—
148	C₄×Q₈	—	166	1	no	—
149	#117	—	83	2	no	—
150	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	166	2	no	—
153	C₄⋊C₈	—	166	2	no	—
154	C₄⋊C₈	—	166	1	no	—
155	C₄⋊C₈	—	166	2	no	—
156	C₄⋊C₈	—	166	1	no	—
157	C₂²⋊C₈	—	2	2	no	—
158	C₂²⋊C₈	—	166	2	no	—
159	#97	—	2	2	no	—
160	#97	—	166	2	no	—
161	#97	—	166	2	no	—
162	C₄×C₈	—	166	2	no	—
163	C₄×C₈	D₃₃₂	1	1	yes	characteristic
164	C₄×C₈	D₃₃₂	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
166	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
167	C₂×Q₈	—	166	1	no	—
168	C₂×Q₈	—	166	1	no	—
169	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
170	C₂²×C₄	#13050589	1	1	yes	characteristic
171	C₂²×C₄	#13050591	1	1	yes	characteristic
172	M₁₆	—	332	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	332	2	no	—
177	C₂×C₈	—	166	2	no	—
178	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
179	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
180	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
181	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
182	C₄⋊C₄	—	83	2	no	—
183	C₄⋊C₄	—	83	2	no	—
184	C₄⋊C₄	—	166	2	no	—
185	C₄⋊C₄	—	166	2	no	—
186	C₄⋊C₄	—	166	1	no	—
187	C₄⋊C₄	—	166	1	no	—
188	C₂²⋊C₄	—	166	2	no	—
189	C₄²	—	166	2	no	—
190	C₄²	D₄×D₈₃	1	1	yes	characteristic
191	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
192	C₄²	C₂×D₃₃₂	1	1	yes	characteristic
193	C₄²	Q₈×D₈₃	1	1	yes	characteristic
194	C₂³	#14581750	1	1	yes	characteristic
195	Q₈	—	332	2	no	—
196	Q₈	—	332	2	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	166	2	no	—
202	C₂×C₄	—	166	2	no	—
203	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
205	C₂×C₄	#14581763	1	1	yes	characteristic
206	C₂×C₄	#14581767	1	1	yes	characteristic
207	C₂×C₄	#14581768	1	1	yes	characteristic
208	C₂×C₄	#14581772	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	2	1	no	—
211	C₈	—	2	1	no	—
212	C₈	—	8	2	no	—
213	C₈	—	332	2	no	—
214	C₈	—	664	2	no	—
215	C₈	#14581710	1	2	yes	—
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	#19127558	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	332	2	no	—
226	C₄	—	332	2	no	—
227	C₄	C₂×#14581710	1	1	yes	characteristic
228	C₄	#19127683	1	1	yes	characteristic
229	C₂	—	4	1	no	—
230	C₂	#24907456	1	1	yes	characteristic
231	C₂	#24907514	1	1	yes	characteristic
232	C₂	#24907518	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24916397

C₂

yes

maximal, characteristic

#24906226

C₂

yes

maximal, characteristic

#24906100

C₂

yes

maximal

#24905373

C₂

yes

maximal

C₈₃×#1568

C₂

yes

maximal, characteristic

#19128258

C₂²

yes

characteristic

#19127831

—

#19127831

—

C₈×Dic₁₆₆

—

C₈×Dic₁₆₆

—

#19127758

C₂²

yes

—

#19127727

C₄

yes

—

#19127725

C₂²

yes

characteristic

#19127656

C₄

yes

—

#19127454

—

#19127452

—

#19127442

—

#432×C₈₃

C₂²

yes

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

#335×C₈₃

—

#334×C₈₃

—

C₂×#13050574

C₂×C₄

yes

—

#14581792

Q₈

yes

characteristic

#14581792

Q₈

yes

characteristic

#14581784

D₄

yes

—

#14581771

—

#14581771

—

C₄×Dic₁₆₆

—

C₄×Dic₁₆₆

—

#14581751

C₂×C₄

yes

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

Dic₈₃⋊C₈

—

Dic₈₃⋊C₈

—

C₂²⋊(C₈₃⋊C₈)

—

#14581703

—

#14581702

—

C₈×Dic₈₃

—

C₂²×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄⋊C₈×C₈₃

—

C₂²⋊C₈×C₈₃

—

#97×C₈₃

—

C₄×C₈×C₈₃

D₄

yes

characteristic

C₄×C₈×C₈₃

D₄

yes

characteristic

C₄×C₈×C₈₃

D₄

yes

characteristic

C₄×C₈×C₈₃

D₄

yes

characteristic

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

C₄⋊C₄

yes

—

C₄⋊Dic₈₃

C₄⋊C₄

yes

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₂²×C₄×C₈₃

C₂²×C₄

yes

C₂²×C₄×C₈₃

yes

C₂²×C₄×C₈₃

yes

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×Q₈

yes

characteristic

C₂³×C₈₃

#117

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊Q₈

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

#101

yes

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

100

C₂²×C₈₃

—

101

C₂²×C₈₃

—

102

C₂²×C₈₃

#380

yes

characteristic

103

C₄×C₈₃

—

104

C₄×C₈₃

—

105

C₄×C₈₃

—

106

C₄×C₈₃

—

107

C₄×C₈₃

—

108

C₄×C₈₃

C₂×#101

yes

characteristic

109

C₄×C₈₃

#413

yes

characteristic

110

Dic₈₃

—

111

Dic₈₃

—

112

#8631

—

maximal, Sylow

113

C₂×C₈₃

—

114

C₂×C₈₃

#1801

yes

characteristic

115

C₂×C₈₃

#1814

yes

characteristic

116

C₂×C₈₃

#1814

yes

characteristic

117

#2960

—

118

#1568

—

119

#1568

D₈₃

yes

characteristic

120

#1537

—

121

#1307

—

122

C₈₃

#8631

yes

characteristic, complemented, Sylow

123

#533

—

124

#446

—

166

—

125

#446

—

166

—

126

C₈×Q₈

—

166

—

127

C₈×Q₈

—

166

—

128

#432

—

129

#432

C₂×D₈₃

yes

—

130

#424

—

131

#423

—

132

#405

—

133

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

134

#335

—

135

#335

—

166

—

136

#334

—

137

#334

—

166

—

138

#330

—

166

—

139

C₂×M₁₆

—

140

C₂²×C₈

C₄×D₈₃

yes

characteristic

141

C₂²×C₈

C₄×D₈₃

yes

characteristic

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

#125

—

145

C₂²⋊Q₈

—

166

—

146

C₂²⋊Q₈

—

166

—

147

C₄×Q₈

—

166

—

148

C₄×Q₈

—

166

—

149

#117

—

150

C₂×C₄²

C₂²×D₈₃

yes

characteristic

151

C₄⋊C₈

—

152

C₄⋊C₈

—

166

—

153

C₄⋊C₈

—

166

—

154

C₄⋊C₈

—

166

—

155

C₄⋊C₈

—

166

—

156

C₄⋊C₈

—

166

—

157

C₂²⋊C₈

—

158

C₂²⋊C₈

—

166

—

159

#97

—

160

#97

—

166

—

161

#97

—

166

—

162

C₄×C₈

—

166

—

163

C₄×C₈

D₃₃₂

yes

characteristic

164

C₄×C₈

D₃₃₂

yes

characteristic

165

C₄×C₈

C₂²⋊D₈₃

yes

characteristic

166

C₄×C₈

C₂²⋊D₈₃

yes

characteristic

167

C₂×Q₈

—

166

—

168

C₂×Q₈

—

166

—

169

C₂²×C₄

C₂×C₄×D₈₃

yes

characteristic

170

C₂²×C₄

#13050589

yes

characteristic

171

C₂²×C₄

#13050591

yes

characteristic

172

M₁₆

—

332

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

332

—

177

C₂×C₈

—

166

—

178

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

characteristic

179

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

characteristic

180

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

characteristic

181

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

characteristic

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

166

—

185

C₄⋊C₄

—

166

—

186

C₄⋊C₄

—

166

—

187

C₄⋊C₄

—

166

—

188

C₂²⋊C₄

—

166

—

189

C₄²

—

166

—

190

C₄²

D₄×D₈₃

yes

characteristic

191

C₄²

C₂×C₂²⋊D₈₃

yes

characteristic

192

C₄²

C₂×D₃₃₂

yes

characteristic

193

C₄²

Q₈×D₈₃

yes

characteristic

194

C₂³

#14581750

yes

characteristic

195

Q₈

—

332

—

196

Q₈

—

332

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

166

—

202

C₂×C₄

—

166

—

203

C₂×C₄

C₂×(C₂×D₈₃)⋊C₄

yes

characteristic

204

C₂×C₄

C₄⋊C₄×D₈₃

yes

characteristic

205

C₂×C₄

#14581763

yes

characteristic

206

C₂×C₄

#14581767

yes

characteristic

207

C₂×C₄

#14581768

yes

characteristic

208

C₂×C₄

#14581772

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

213

C₈

—

332

—

214

C₈

—

664

—

215

C₈

#14581710

yes

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

#19127558

yes

characteristic

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

332

—

226

C₄

—

332

—

227

C₄

C₂×#14581710

yes

characteristic

228

C₄

#19127683

yes

characteristic

229

C₂

—

230

C₂

#24907456

yes

characteristic

231

C₂

#24907514

yes

characteristic

232

C₂

#24907518

yes

characteristic

	subgroup	G/H
center	C₂²	#19127558
commutator	C₂²×C₄×C₈₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1568	C₂
socle	C₂²×C₈₃	#380
prime radical	C₂³×C₈₃	#117
cosocle	C₂×C₄²×C₈₃	C₂³
hypercenter	#1568	D₈₃
hypocenter	C₈₃	#8631
LCS	G ▷ C₂²×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#19127558

commutator

C₂²×C₄×C₈₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1568

C₂

C₂²×C₈₃

C₂³×C₈₃

C₂×C₄²×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂²×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
122. C₈₃	#8631	semidirect

H ≅ G/N

type

122. C₈₃

#8631

semidirect

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

subgroup	index
#24916397	2
#24906226	2
#24906100	2
#24905373	2
C₈₃×#1568	2
#8631	83

subgroup

index

C₈₃×#1568

Subgroups — #35297397

Conjugacy classes of subgroups

Complements

Maximal subgroups