Group #35313758 — subgroups

Subgroups — #35313758

Order 21248.

292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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	#24909262	C₂	1	1	yes	maximal, characteristic
3	#24905404	C₂	1	4	yes	maximal
4	C₈₃×#2163	C₂	1	1	yes	maximal, characteristic
5	#19128258	C₄	1	1	yes	characteristic
6	#19127831	—	2	1	no	—
7	#19127831	—	2	1	no	—
8	C₈×Dic₁₆₆	—	2	1	no	—
9	C₈×Dic₁₆₆	—	2	1	no	—
10	#19127727	C₂²	1	2	yes	—
11	#19127725	C₄	1	1	yes	characteristic
12	#19127656	C₄	1	2	yes	—
13	C₄⋊(C₈₃⋊C₁₆)	—	2	1	no	—
14	C₂²⋊(C₈₃⋊C₁₆)	C₂²	1	2	yes	—
15	C₄×C₈₃⋊C₁₆	—	2	1	no	—
16	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
17	C₄⋊C₁₆×C₈₃	—	2	1	no	—
18	C₂²⋊C₁₆×C₈₃	C₂²	1	2	yes	—
19	#346×C₈₃	—	2	1	no	—
20	C₂×#13050574	C₂×C₄	1	2	yes	—
21	#14581792	C₈	1	1	yes	characteristic
22	#14581792	C₈	1	1	yes	characteristic
23	#14581784	C₈	1	2	yes	—
24	#14581771	—	2	1	no	—
25	#14581771	—	2	1	no	—
26	C₄×Dic₁₆₆	—	2	1	no	—
27	C₄×Dic₁₆₆	—	2	1	no	—
28	#14581751	C₂×C₄	1	2	yes	—
29	C₂×C₈₃⋊C₁₆	—	2	2	no	—
30	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
31	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
32	Dic₈₃⋊C₈	—	2	2	no	—
33	Dic₈₃⋊C₈	—	2	2	no	—
34	#14581702	—	2	2	no	—
35	C₈×Dic₈₃	—	2	2	no	—
36	C₂²×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
38	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₆×C₈₃	—	2	2	no	—
40	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
41	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
42	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
43	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
44	C₂×Dic₁₆₆	—	2	1	no	—
45	C₂×Dic₁₆₆	—	2	1	no	—
46	#13050574	—	4	2	no	—
47	C₂×C₈₃⋊C₈	—	2	2	no	—
48	C₄⋊Dic₈₃	—	2	1	no	—
49	C₄⋊Dic₈₃	—	2	1	no	—
50	C₄⋊Dic₈₃	C₂×C₈	1	2	yes	—
51	C₄⋊Dic₈₃	C₂×C₈	1	2	yes	—
52	Dic₈₃⋊C₄	—	2	2	no	—
53	Dic₈₃⋊C₄	—	2	2	no	—
54	C₂²⋊Dic₈₃	—	2	2	no	—
55	C₄×Dic₈₃	—	2	2	no	—
56	C₈₃⋊C₁₆	—	4	2	no	—
57	C₂²×C₄×C₈₃	M₁₆	1	1	yes	characteristic
58	C₂²×C₄×C₈₃	M₁₆	1	1	yes	characteristic
59	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₈×C₈₃	—	2	2	no	—
61	C₂×C₈×C₈₃	—	4	1	no	—
62	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₄²×C₈₃	C₂×C₈	1	1	yes	characteristic
69	C₄²×C₈₃	C₂×C₈	1	1	yes	characteristic
70	C₁₆×C₈₃	—	4	2	no	—
71	C₂³×C₈₃	C₂×M₁₆	1	1	yes	characteristic
72	C₂×C₄×C₈₃	—	2	2	no	—
73	C₂×C₄×C₈₃	—	2	1	no	—
74	C₂×C₄×C₈₃	—	2	1	no	—
75	C₂×C₄×C₈₃	—	4	1	no	—
76	C₂×C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
77	C₂×C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
78	C₂×C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
79	C₂×C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
80	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₈₃	C₂²×C₈	1	1	yes	characteristic
82	C₂×Dic₈₃	—	2	2	no	—
83	C₂×Dic₈₃	—	2	2	no	—
84	Dic₁₆₆	—	4	2	no	—
85	Dic₁₆₆	—	4	2	no	—
86	C₈×C₈₃	—	2	1	no	—
87	C₈×C₈₃	—	2	1	no	—
88	C₈×C₈₃	—	2	1	no	—
89	C₈×C₈₃	#101	1	2	yes	—
90	C₈₃⋊C₈	—	4	2	no	—
91	C₂²×C₈₃	—	2	1	no	—
92	C₂²×C₈₃	—	2	1	no	—
93	C₂²×C₈₃	—	2	1	no	—
94	C₂²×C₈₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
95	C₄×C₈₃	—	2	1	no	—
96	C₄×C₈₃	—	2	1	no	—
97	C₄×C₈₃	—	2	1	no	—
98	C₄×C₈₃	—	2	1	no	—
99	C₄×C₈₃	#350	1	2	yes	—
100	C₄×C₈₃	#410	1	1	yes	characteristic
101	C₄×C₈₃	C₂×#101	1	1	yes	characteristic
102	Dic₈₃	—	4	2	no	—
103	Dic₈₃	—	4	2	no	—
104	#11498	—	83	1	no	maximal, Sylow
105	C₂×C₈₃	—	4	1	no	—
106	C₂×C₈₃	#1461	1	1	yes	characteristic
107	C₂×C₈₃	C₂×#350	1	1	yes	characteristic
108	C₂×C₈₃	#2117	1	1	yes	characteristic
109	#2960	—	83	1	no	—
110	#2163	D₈₃	1	1	yes	characteristic
111	#2162	—	83	1	no	—
112	#1323	—	83	4	no	—
113	C₈₃	#11498	1	1	yes	characteristic, complemented, Sylow
114	#533	—	83	1	no	—
115	#446	—	166	1	no	—
116	#446	—	166	1	no	—
117	C₈×Q₈	—	166	1	no	—
118	C₈×Q₈	—	166	1	no	—
119	#424	—	83	2	no	—
120	#423	—	83	1	no	—
121	#405	—	83	2	no	—
122	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
123	C₄⋊C₁₆	—	2	1	no	—
124	C₄⋊C₁₆	—	166	1	no	—
125	C₂²⋊C₁₆	—	83	2	no	—
126	C₂²⋊C₁₆	C₂×D₈₃	1	2	yes	—
127	#346	—	2	1	no	—
128	C₄×C₁₆	—	166	1	no	—
129	C₂×M₁₆	—	83	2	no	—
130	C₂²×C₈	C₄×D₈₃	1	1	yes	characteristic
131	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
132	C₄⋊Q₈	—	83	1	no	—
133	C₄⋊Q₈	—	83	1	no	—
134	#125	—	83	2	no	—
135	C₂²⋊Q₈	—	166	1	no	—
136	C₂²⋊Q₈	—	166	1	no	—
137	C₄×Q₈	—	166	1	no	—
138	C₄×Q₈	—	166	1	no	—
139	#117	—	83	2	no	—
140	C₂×C₄²	C₄×D₈₃	1	1	yes	characteristic
141	C₂×C₁₆	—	2	2	no	—
142	C₂×C₁₆	—	166	2	no	—
143	C₄⋊C₈	—	166	2	no	—
144	C₄⋊C₈	—	166	2	no	—
145	C₄⋊C₈	—	166	1	no	—
146	C₄⋊C₈	—	166	1	no	—
147	#97	—	166	2	no	—
148	C₄×C₈	—	166	2	no	—
149	C₄×C₈	D₃₃₂	1	1	yes	characteristic
150	C₄×C₈	D₃₃₂	1	1	yes	characteristic
151	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
152	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
153	C₂×Q₈	—	166	1	no	—
154	C₂×Q₈	—	166	1	no	—
155	C₂²×C₄	#13050573	1	1	yes	characteristic
156	C₂²×C₄	#13050573	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
158	M₁₆	—	332	2	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	4	1	no	—
161	C₂×C₈	—	166	2	no	—
162	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
163	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
164	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
165	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
166	C₄⋊C₄	—	83	2	no	—
167	C₄⋊C₄	—	83	2	no	—
168	C₄⋊C₄	—	166	2	no	—
169	C₄⋊C₄	—	166	2	no	—
170	C₄⋊C₄	—	166	1	no	—
171	C₄⋊C₄	—	166	1	no	—
172	C₂²⋊C₄	—	166	2	no	—
173	C₄²	—	166	2	no	—
174	C₄²	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
175	C₄²	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
176	C₄²	C₈×D₈₃	1	1	yes	characteristic
177	C₄²	C₈×D₈₃	1	1	yes	characteristic
178	C₁₆	—	4	2	no	—
179	C₁₆	—	332	2	no	—
180	C₂³	C₂×#13050573	1	1	yes	characteristic
181	Q₈	—	332	2	no	—
182	Q₈	—	332	2	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	166	2	no	—
188	C₂×C₄	—	166	2	no	—
189	C₂×C₄	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
190	C₂×C₄	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
191	C₂×C₄	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
192	C₂×C₄	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
193	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
194	C₂×C₄	C₂×C₈×D₈₃	1	1	yes	characteristic
195	C₈	—	2	1	no	—
196	C₈	—	2	1	no	—
197	C₈	—	2	1	no	—
198	C₈	—	332	2	no	—
199	C₈	#14581710	1	2	yes	—
200	C₂²	—	2	1	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	2	1	no	—
203	C₂²	C₂×(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
204	C₄	—	2	1	no	—
205	C₄	—	2	1	no	—
206	C₄	—	2	1	no	—
207	C₄	—	2	1	no	—
208	C₄	—	332	2	no	—
209	C₄	—	332	2	no	—
210	C₄	#19127486	1	2	yes	—
211	C₄	#19127674	1	1	yes	characteristic
212	C₄	C₂×#14581710	1	1	yes	characteristic
213	C₂	—	4	1	no	—
214	C₂	#24905786	1	1	yes	characteristic
215	C₂	C₂×#19127486	1	1	yes	characteristic
216	C₂	#24909090	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24916397

C₂

yes

maximal, characteristic

#24909262

C₂

yes

maximal, characteristic

#24905404

C₂

yes

maximal

C₈₃×#2163

C₂

yes

maximal, characteristic

#19128258

C₄

yes

characteristic

#19127831

—

#19127831

—

C₈×Dic₁₆₆

—

C₈×Dic₁₆₆

—

#19127727

C₂²

yes

—

#19127725

C₄

yes

characteristic

#19127656

C₄

yes

—

C₄⋊(C₈₃⋊C₁₆)

—

C₂²⋊(C₈₃⋊C₁₆)

C₂²

yes

—

C₄×C₈₃⋊C₁₆

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₄⋊C₁₆×C₈₃

—

C₂²⋊C₁₆×C₈₃

C₂²

yes

—

#346×C₈₃

—

C₂×#13050574

C₂×C₄

yes

—

#14581792

C₈

yes

characteristic

#14581792

C₈

yes

characteristic

#14581784

C₈

yes

—

#14581771

—

#14581771

—

C₄×Dic₁₆₆

—

C₄×Dic₁₆₆

—

#14581751

C₂×C₄

yes

—

C₂×C₈₃⋊C₁₆

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

Dic₈₃⋊C₈

—

Dic₈₃⋊C₈

—

#14581702

—

C₈×Dic₈₃

—

C₂²×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₈₃

C₂³

yes

characteristic

C₂×C₄²×C₈₃

C₂×C₄

yes

characteristic

C₂×C₁₆×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

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

C₂×C₈

yes

—

C₄⋊Dic₈₃

C₂×C₈

yes

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₈₃⋊C₁₆

—

C₂²×C₄×C₈₃

M₁₆

yes

characteristic

C₂²×C₄×C₈₃

M₁₆

yes

characteristic

C₂²×C₄×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂²⋊C₄

yes

characteristic

C₄²×C₈₃

C₂²⋊C₄

yes

characteristic

C₄²×C₈₃

C₂×C₈

yes

characteristic

C₄²×C₈₃

C₂×C₈

yes

characteristic

C₁₆×C₈₃

—

C₂³×C₈₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₈₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₂²×C₈

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

#101

yes

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

#350

yes

—

100

C₄×C₈₃

#410

yes

characteristic

101

C₄×C₈₃

C₂×#101

yes

characteristic

102

Dic₈₃

—

103

Dic₈₃

—

104

#11498

—

maximal, Sylow

105

C₂×C₈₃

—

106

C₂×C₈₃

#1461

yes

characteristic

107

C₂×C₈₃

C₂×#350

yes

characteristic

108

C₂×C₈₃

#2117

yes

characteristic

109

#2960

—

110

#2163

D₈₃

yes

characteristic

111

#2162

—

112

#1323

—

113

C₈₃

#11498

yes

characteristic, complemented, Sylow

114

#533

—

115

#446

—

166

—

116

#446

—

166

—

117

C₈×Q₈

—

166

—

118

C₈×Q₈

—

166

—

119

#424

—

120

#423

—

121

#405

—

122

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

123

C₄⋊C₁₆

—

124

C₄⋊C₁₆

—

166

—

125

C₂²⋊C₁₆

—

126

C₂²⋊C₁₆

C₂×D₈₃

yes

—

127

#346

—

128

C₄×C₁₆

—

166

—

129

C₂×M₁₆

—

130

C₂²×C₈

C₄×D₈₃

yes

characteristic

131

C₂²×C₈

C₂²×D₈₃

yes

characteristic

132

C₄⋊Q₈

—

133

C₄⋊Q₈

—

134

#125

—

135

C₂²⋊Q₈

—

166

—

136

C₂²⋊Q₈

—

166

—

137

C₄×Q₈

—

166

—

138

C₄×Q₈

—

166

—

139

#117

—

140

C₂×C₄²

C₄×D₈₃

yes

characteristic

141

C₂×C₁₆

—

142

C₂×C₁₆

—

166

—

143

C₄⋊C₈

—

166

—

144

C₄⋊C₈

—

166

—

145

C₄⋊C₈

—

166

—

146

C₄⋊C₈

—

166

—

147

#97

—

166

—

148

C₄×C₈

—

166

—

149

C₄×C₈

D₃₃₂

yes

characteristic

150

C₄×C₈

D₃₃₂

yes

characteristic

151

C₄×C₈

C₂²⋊D₈₃

yes

characteristic

152

C₄×C₈

C₂²⋊D₈₃

yes

characteristic

153

C₂×Q₈

—

166

—

154

C₂×Q₈

—

166

—

155

C₂²×C₄

#13050573

yes

characteristic

156

C₂²×C₄

#13050573

yes

characteristic

157

C₂²×C₄

C₂×C₄×D₈₃

yes

characteristic

158

M₁₆

—

332

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

166

—

162

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

characteristic

163

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

characteristic

164

C₂×C₈

C₂×C₂²⋊D₈₃

yes

characteristic

165

C₂×C₈

C₂×D₃₃₂

yes

characteristic

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

166

—

169

C₄⋊C₄

—

166

—

170

C₄⋊C₄

—

166

—

171

C₄⋊C₄

—

166

—

172

C₂²⋊C₄

—

166

—

173

C₄²

—

166

—

174

C₄²

(C₂×D₈₃)⋊C₄

yes

characteristic

175

C₄²

(C₂×D₈₃)⋊C₄

yes

characteristic

176

C₄²

C₈×D₈₃

yes

characteristic

177

C₄²

C₈×D₈₃

yes

characteristic

178

C₁₆

—

179

C₁₆

—

332

—

180

C₂³

C₂×#13050573

yes

characteristic

181

Q₈

—

332

—

182

Q₈

—

332

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

166

—

188

C₂×C₄

—

166

—

189

C₂×C₄

(C₂×D₈₃)⋊C₈

yes

characteristic

190

C₂×C₄

(C₂×D₈₃)⋊C₈

yes

characteristic

191

C₂×C₄

(C₂×D₈₃)⋊C₈

yes

characteristic

192

C₂×C₄

(C₂×D₈₃)⋊C₈

yes

characteristic

193

C₂×C₄

C₂×(C₂×D₈₃)⋊C₄

yes

characteristic

194

C₂×C₄

C₂×C₈×D₈₃

yes

characteristic

195

C₈

—

196

C₈

—

197

C₈

—

198

C₈

—

332

—

199

C₈

#14581710

yes

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

C₂×(C₂×D₈₃)⋊C₈

yes

characteristic

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

—

332

—

209

C₄

—

332

—

210

C₄

#19127486

yes

—

211

C₄

#19127674

yes

characteristic

212

C₄

C₂×#14581710

yes

characteristic

213

C₂

—

214

C₂

#24905786

yes

characteristic

215

C₂

C₂×#19127486

yes

characteristic

216

C₂

#24909090

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄
commutator	C₂×C₄×C₈₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₈₃×#2163	C₂
socle	C₂²×C₈₃	C₂×C₂²⋊C₈
prime radical	C₂³×C₈₃	C₂×M₁₆
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	#2163	D₈₃
hypocenter	C₈₃	#11498
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

subgroup

G/H

center

C₂×C₄

C₂×(C₂×D₈₃)⋊C₄

commutator

C₂×C₄×C₈₃

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₈₃×#2163

C₂

socle

C₂²×C₈₃

C₂×C₂²⋊C₈

prime radical

C₂³×C₈₃

C₂×M₁₆

cosocle

C₂²×C₈×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

N	H ≅ G/N	type
113. C₈₃	#11498	semidirect

H ≅ G/N

type

113. C₈₃

#11498

semidirect

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

subgroup	index
#24916397	2
#24909262	2
#24905404	2
C₈₃×#2163	2
#11498	83

subgroup

index

C₈₃×#2163

Subgroups — #35313758

Conjugacy classes of subgroups

Complements

Maximal subgroups