Group #35316021 — subgroups

Subgroups — #35316021

Order 21248.

238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 95 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	#24909265	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic
3	C₈×#13050573	C₂	1	1	yes	maximal, characteristic
4	#24905532	C₂	1	1	yes	maximal, characteristic, complemented
5	#24905527	C₂	1	1	yes	maximal, characteristic, complemented
6	#24905526	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#1370	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₆×D₈₃	—	2	1	no	—
9	#19127752	C₄	1	1	yes	characteristic
10	C₄×#13050573	C₄	1	1	yes	characteristic
11	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
12	C₄⋊(C₈₃⋊C₁₆)	C₂²	1	1	yes	characteristic
13	C₄⋊(C₈₃⋊C₁₆)	C₂²	1	1	yes	characteristic
14	Dic₈₃⋊C₁₆	—	2	1	no	—
15	(C₂×D₈₃)⋊C₁₆	—	2	1	no	—
16	#19127476	—	2	1	no	—
17	#19127423	C₄	1	1	yes	characteristic
18	#19127422	C₄	1	1	yes	characteristic
19	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊C₁₆×C₈₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₁₆×C₈₃	C₂²	1	1	yes	characteristic
22	C₈²×C₈₃	C₂²	1	1	yes	characteristic
23	C₂×#13050573	—	2	1	no	—
24	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
25	C₂×C₈×D₈₃	Q₈	1	1	yes	characteristic
26	C₄²×D₈₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈₃⋊C₁₆	—	2	1	no	—
28	C₂×C₈₃⋊C₁₆	—	2	1	no	—
29	C₁₆×D₈₃	—	4	2	no	—
30	Dic₈₃⋊C₈	C₈	1	1	yes	characteristic
31	Dic₈₃⋊C₈	C₈	1	1	yes	characteristic
32	(C₂×D₈₃)⋊C₈	C₈	1	1	yes	characteristic
33	(C₂×D₈₃)⋊C₈	C₈	1	1	yes	characteristic
34	#14581702	—	2	1	no	—
35	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
38	C₈×Dic₈₃	D₄	1	1	yes	characteristic
39	C₈×Dic₈₃	Q₈	1	1	yes	characteristic
40	C₂×C₁₆×C₈₃	—	2	1	no	—
41	C₂×C₁₆×C₈₃	—	2	1	no	—
42	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
45	C₂×C₄×D₈₃	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×D₈₃	C₂×C₈	1	1	yes	characteristic
47	C₂×C₄×D₈₃	M₁₆	1	1	yes	characteristic
48	#13050573	—	2	4	no	—
49	C₂×C₈₃⋊C₈	—	2	1	no	—
50	C₂×C₈₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₈₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₈₃⋊C₈	C₂×C₈	1	1	yes	characteristic
53	C₂×C₈₃⋊C₈	C₂×C₈	1	1	yes	characteristic
54	C₈×D₈₃	—	2	1	no	—
55	C₈×D₈₃	—	2	1	no	—
56	C₈×D₈₃	—	4	1	no	—
57	C₄×Dic₈₃	C₄⋊C₄	1	1	yes	characteristic
58	C₄×Dic₈₃	C₂×C₈	1	1	yes	characteristic
59	C₄×Dic₈₃	M₁₆	1	1	yes	characteristic
60	C₈₃⋊C₁₆	—	4	1	no	—
61	C₈₃⋊C₁₆	—	4	1	no	—
62	C₂×C₈×C₈₃	—	2	1	no	—
63	C₂×C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
64	C₂×C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
65	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₈₃	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
68	C₁₆×C₈₃	—	4	1	no	—
69	C₁₆×C₈₃	—	4	1	no	—
70	C₂²×D₈₃	C₄⋊C₈	1	1	yes	characteristic
71	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₈₃	C₂²×C₈	1	1	yes	characteristic
73	C₂×C₄×C₈₃	C₂×M₁₆	1	1	yes	characteristic
74	C₂×Dic₈₃	C₄⋊C₈	1	1	yes	characteristic
75	C₂×Dic₈₃	C₄⋊C₈	1	1	yes	characteristic
76	C₂×Dic₈₃	C₄⋊C₈	1	1	yes	characteristic
77	C₄×D₈₃	—	2	2	no	—
78	C₄×D₈₃	—	2	1	no	—
79	C₄×D₈₃	—	2	1	no	—
80	C₄×D₈₃	—	2	1	no	—
81	C₄×D₈₃	—	2	1	no	—
82	C₈×C₈₃	—	2	2	no	—
83	C₈×C₈₃	—	2	1	no	—
84	C₈×C₈₃	—	2	1	no	—
85	C₈×C₈₃	—	2	1	no	—
86	C₈×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
87	C₈×C₈₃	#137	1	1	yes	characteristic
88	C₈₃⋊C₈	—	2	2	no	—
89	C₈₃⋊C₈	—	2	1	no	—
90	C₈₃⋊C₈	—	2	1	no	—
91	C₈₃⋊C₈	—	2	1	no	—
92	C₈₃⋊C₈	—	2	1	no	—
93	C₂²×C₈₃	C₂×C₄⋊C₈	1	1	yes	characteristic
94	C₂×D₈₃	—	2	1	no	—
95	C₂×D₈₃	—	2	1	no	—
96	C₂×D₈₃	#364	1	2	yes	—
97	C₄×C₈₃	—	2	1	no	—
98	C₄×C₈₃	#428	1	1	yes	characteristic
99	C₄×C₈₃	#430	1	1	yes	characteristic
100	C₄×C₈₃	#504	1	1	yes	characteristic
101	C₄×C₈₃	#504	1	1	yes	characteristic
102	Dic₈₃	—	2	1	no	—
103	Dic₈₃	—	2	1	no	—
104	Dic₈₃	—	2	1	no	—
105	#12016	—	83	1	no	maximal, Sylow
106	C₂×C₈₃	#1565	1	1	yes	characteristic
107	C₂×C₈₃	#2151	1	1	yes	characteristic
108	C₂×C₈₃	C₂×#364	1	1	yes	characteristic
109	D₈₃	—	2	2	no	—
110	#2163	—	83	1	no	—
111	C₂×C₄⋊C₁₆	—	83	1	no	—
112	C₈×M₁₆	—	83	1	no	—
113	#1370	—	83	1	no	—
114	#1370	D₈₃	1	1	yes	characteristic, complemented
115	#1367	—	83	1	no	—
116	#1367	—	83	1	no	—
117	C₈₃	#12016	1	1	yes	characteristic, complemented, Sylow
118	C₂²×C₁₆	—	166	1	no	—
119	#431	—	83	1	no	—
120	C₄×M₁₆	—	83	1	no	—
121	C₂×C₄×C₈	—	83	1	no	—
122	C₄⋊C₁₆	—	83	1	no	—
123	C₄⋊C₁₆	—	83	1	no	—
124	C₄⋊C₁₆	—	166	1	no	—
125	C₄⋊C₁₆	C₂×D₈₃	1	1	yes	characteristic
126	C₄⋊C₁₆	C₂×D₈₃	1	1	yes	characteristic
127	C₂²⋊C₁₆	—	166	1	no	—
128	#346	—	166	1	no	—
129	#322	—	83	1	no	—
130	#322	—	83	1	no	—
131	C₈²	—	83	1	no	—
132	C₈²	C₂×D₈₃	1	1	yes	characteristic
133	C₂×M₁₆	—	166	1	no	—
134	C₂²×C₈	—	83	1	no	—
135	C₂²×C₈	—	83	1	no	—
136	C₂×C₄²	—	83	1	no	—
137	C₂×C₁₆	—	2	1	no	—
138	C₂×C₁₆	—	2	1	no	—
139	C₂×C₁₆	—	332	2	no	—
140	C₂×C₁₆	—	166	1	no	—
141	C₂×C₁₆	—	166	1	no	—
142	C₄⋊C₈	—	83	1	no	—
143	C₄⋊C₈	—	83	1	no	—
144	C₂²⋊C₈	—	83	1	no	—
145	C₂²⋊C₈	—	83	1	no	—
146	#97	—	166	1	no	—
147	C₄×C₈	—	83	1	no	—
148	C₄×C₈	—	83	1	no	—
149	C₄×C₈	—	83	1	no	—
150	C₄×C₈	—	83	1	no	—
151	C₄×C₈	—	83	1	no	—
152	C₄×C₈	C₄×D₈₃	1	1	yes	characteristic
153	C₄×C₈	C₄×D₈₃	1	1	yes	characteristic
154	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
155	C₂²×C₄	—	83	1	no	—
156	C₂²×C₄	—	83	1	no	—
157	C₂²×C₄	—	83	1	no	—
158	M₁₆	—	166	4	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	332	1	no	—
161	C₂×C₈	—	83	1	no	—
162	C₂×C₈	—	83	1	no	—
163	C₂×C₈	—	83	1	no	—
164	C₂×C₈	—	83	1	no	—
165	C₂×C₈	—	166	1	no	—
166	C₂×C₈	—	166	1	no	—
167	C₂×C₈	—	166	1	no	—
168	C₂×C₈	C₈×D₈₃	1	1	yes	characteristic
169	C₂×C₈	C₈×D₈₃	1	1	yes	characteristic
170	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
171	C₂×C₈	Q₈×D₈₃	1	1	yes	characteristic
172	C₄²	—	83	1	no	—
173	C₄²	—	83	1	no	—
174	C₄²	—	83	1	no	—
175	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
176	C₁₆	—	4	1	no	—
177	C₁₆	—	4	1	no	—
178	C₁₆	—	332	1	no	—
179	C₁₆	—	332	1	no	—
180	C₂³	—	83	1	no	—
181	C₂×C₄	—	83	1	no	—
182	C₂×C₄	—	83	1	no	—
183	C₂×C₄	—	83	1	no	—
184	C₂×C₄	—	166	2	no	—
185	C₂×C₄	—	166	1	no	—
186	C₂×C₄	—	166	1	no	—
187	C₂×C₄	—	166	1	no	—
188	C₂×C₄	—	166	1	no	—
189	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
190	C₂×C₄	C₂×C₈×D₈₃	1	1	yes	characteristic
191	C₂×C₄	M₁₆×D₈₃	1	1	yes	characteristic
192	C₈	—	2	2	no	—
193	C₈	—	2	1	no	—
194	C₈	—	2	1	no	—
195	C₈	—	2	1	no	—
196	C₈	—	166	2	no	—
197	C₈	—	166	1	no	—
198	C₈	—	166	1	no	—
199	C₈	—	166	1	no	—
200	C₈	—	166	1	no	—
201	C₈	#14581816	1	1	yes	characteristic
202	C₈	#14581824	1	1	yes	characteristic
203	C₂²	—	83	2	no	—
204	C₂²	—	166	1	no	—
205	C₂²	—	166	1	no	—
206	C₂²	C₄⋊C₈×D₈₃	1	1	yes	characteristic
207	C₄	—	2	1	no	—
208	C₄	—	166	1	no	—
209	C₄	—	166	1	no	—
210	C₄	—	166	1	no	—
211	C₄	#19127742	1	1	yes	characteristic
212	C₄	#19127748	1	1	yes	characteristic
213	C₄	#19128117	1	1	yes	characteristic
214	C₄	#19128119	1	1	yes	characteristic
215	C₂	—	166	2	no	—
216	C₂	#24906214	1	1	yes	characteristic
217	C₂	#24909220	1	1	yes	characteristic
218	C₂	#364×D₈₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24909265

C₂

yes

maximal, characteristic

C₄⋊C₁₆×D₈₃

C₂

yes

maximal, characteristic

C₈×#13050573

C₂

yes

maximal, characteristic

#24905532

C₂

yes

maximal, characteristic, complemented

#24905527

C₂

yes

maximal, characteristic, complemented

#24905526

C₂

yes

maximal, characteristic, complemented

C₈₃×#1370

C₂

yes

maximal, characteristic, complemented

C₂×C₁₆×D₈₃

—

#19127752

C₄

yes

characteristic

C₄×#13050573

C₄

yes

characteristic

C₄×C₈×D₈₃

C₂²

yes

characteristic

C₄⋊(C₈₃⋊C₁₆)

C₂²

yes

characteristic

C₄⋊(C₈₃⋊C₁₆)

C₂²

yes

characteristic

Dic₈₃⋊C₁₆

—

(C₂×D₈₃)⋊C₁₆

—

#19127476

—

#19127423

C₄

yes

characteristic

#19127422

C₄

yes

characteristic

C₈×C₈₃⋊C₈

C₂²

yes

characteristic

C₄⋊C₁₆×C₈₃

C₂²

yes

characteristic

C₄⋊C₁₆×C₈₃

C₂²

yes

characteristic

C₈²×C₈₃

C₂²

yes

characteristic

C₂×#13050573

—

C₂×C₈×D₈₃

D₄

yes

characteristic

C₂×C₈×D₈₃

Q₈

yes

characteristic

C₄²×D₈₃

C₂×C₄

yes

characteristic

C₂×C₈₃⋊C₁₆

—

C₂×C₈₃⋊C₁₆

—

C₁₆×D₈₃

—

Dic₈₃⋊C₈

C₈

yes

characteristic

Dic₈₃⋊C₈

C₈

yes

characteristic

(C₂×D₈₃)⋊C₈

C₈

yes

characteristic

(C₂×D₈₃)⋊C₈

C₈

yes

characteristic

#14581702

—

C₄×C₈₃⋊C₈

C₂×C₄

yes

characteristic

C₄×C₈₃⋊C₈

C₂×C₄

yes

characteristic

C₄×C₈₃⋊C₈

C₂×C₄

yes

characteristic

C₈×Dic₈₃

D₄

yes

characteristic

C₈×Dic₈₃

Q₈

yes

characteristic

C₂×C₁₆×C₈₃

—

C₂×C₁₆×C₈₃

—

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

C₂³

yes

characteristic

C₂×C₄×D₈₃

C₄⋊C₄

yes

characteristic

C₂×C₄×D₈₃

C₂×C₈

yes

characteristic

C₂×C₄×D₈₃

M₁₆

yes

characteristic

#13050573

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₈₃⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₈₃⋊C₈

C₂×C₈

yes

characteristic

C₂×C₈₃⋊C₈

C₂×C₈

yes

characteristic

C₈×D₈₃

—

C₈×D₈₃

—

C₈×D₈₃

—

C₄×Dic₈₃

C₄⋊C₄

yes

characteristic

C₄×Dic₈₃

C₂×C₈

yes

characteristic

C₄×Dic₈₃

M₁₆

yes

characteristic

C₈₃⋊C₁₆

—

C₈₃⋊C₁₆

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂×C₈

yes

characteristic

C₂×C₈×C₈₃

C₂×C₈

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂×Q₈

yes

characteristic

C₄²×C₈₃

C₂²×C₄

yes

characteristic

C₁₆×C₈₃

—

C₁₆×C₈₃

—

C₂²×D₈₃

C₄⋊C₈

yes

characteristic

C₂×C₄×C₈₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₈₃

C₂×M₁₆

yes

characteristic

C₂×Dic₈₃

C₄⋊C₈

yes

characteristic

C₂×Dic₈₃

C₄⋊C₈

yes

characteristic

C₂×Dic₈₃

C₄⋊C₈

yes

characteristic

C₄×D₈₃

—

C₄×D₈₃

—

C₄×D₈₃

—

C₄×D₈₃

—

C₄×D₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

yes

C₈×C₈₃

yes

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₂²×C₈₃

C₂×C₄⋊C₈

yes

characteristic

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

#364

yes

—

C₄×C₈₃

—

C₄×C₈₃

yes

C₄×C₈₃

yes

100

C₄×C₈₃

#504

yes

characteristic

101

C₄×C₈₃

#504

yes

characteristic

102

Dic₈₃

—

103

Dic₈₃

—

104

Dic₈₃

—

105

#12016

—

maximal, Sylow

106

C₂×C₈₃

#1565

yes

characteristic

107

C₂×C₈₃

#2151

yes

characteristic

108

C₂×C₈₃

C₂×#364

yes

characteristic

109

D₈₃

—

110

#2163

—

111

C₂×C₄⋊C₁₆

—

112

C₈×M₁₆

—

113

#1370

—

114

#1370

D₈₃

yes

characteristic, complemented

115

#1367

—

116

#1367

—

117

C₈₃

#12016

yes

characteristic, complemented, Sylow

118

C₂²×C₁₆

—

166

—

119

#431

—

120

C₄×M₁₆

—

121

C₂×C₄×C₈

—

122

C₄⋊C₁₆

—

123

C₄⋊C₁₆

—

124

C₄⋊C₁₆

—

166

—

125

C₄⋊C₁₆

C₂×D₈₃

yes

characteristic

126

C₄⋊C₁₆

C₂×D₈₃

yes

characteristic

127

C₂²⋊C₁₆

—

166

—

128

#346

—

166

—

129

#322

—

130

#322

—

131

C₈²

—

132

C₈²

C₂×D₈₃

yes

characteristic

133

C₂×M₁₆

—

166

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₂×C₄²

—

137

C₂×C₁₆

—

138

C₂×C₁₆

—

139

C₂×C₁₆

—

332

—

140

C₂×C₁₆

—

166

—

141

C₂×C₁₆

—

166

—

142

C₄⋊C₈

—

143

C₄⋊C₈

—

144

C₂²⋊C₈

—

145

C₂²⋊C₈

—

146

#97

—

166

—

147

C₄×C₈

—

148

C₄×C₈

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₄×C₈

—

152

C₄×C₈

C₄×D₈₃

yes

characteristic

153

C₄×C₈

C₄×D₈₃

yes

characteristic

154

C₄×C₈

C₂²×D₈₃

yes

characteristic

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

M₁₆

—

166

—

159

C₂×C₈

—

160

C₂×C₈

—

332

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

—

166

C₂×C₈

—

166

—

167

C₂×C₈

—

166

—

168

C₂×C₈

C₈×D₈₃

yes

characteristic

169

C₂×C₈

C₈×D₈₃

yes

characteristic

170

C₂×C₈

D₄×D₈₃

yes

characteristic

171

C₂×C₈

Q₈×D₈₃

yes

characteristic

172

C₄²

—

173

C₄²

—

174

C₄²

—

175

C₄²

C₂×C₄×D₈₃

yes

characteristic

176

C₁₆

—

177

C₁₆

—

178

C₁₆

—

332

—

179

C₁₆

—

332

—

180

C₂³

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

166

—

185

C₂×C₄

—

166

—

186

C₂×C₄

—

166

—

187

C₂×C₄

—

166

—

188

C₂×C₄

—

166

—

189

C₂×C₄

C₄⋊C₄×D₈₃

yes

characteristic

190

C₂×C₄

C₂×C₈×D₈₃

yes

characteristic

191

C₂×C₄

M₁₆×D₈₃

yes

characteristic

192

C₈

—

193

C₈

—

194

C₈

—

195

C₈

—

196

C₈

—

166

—

197

C₈

—

166

—

198

C₈

—

166

—

199

C₈

—

166

—

200

C₈

—

166

—

201

C₈

#14581816

yes

characteristic

202

C₈

#14581824

yes

characteristic

203

C₂²

—

204

C₂²

—

166

—

205

C₂²

—

166

—

206

C₂²

C₄⋊C₈×D₈₃

yes

characteristic

207

C₄

—

208

C₄

—

166

—

209

C₄

—

166

—

210

C₄

—

166

—

211

C₄

#19127742

yes

characteristic

212

C₄

#19127748

yes

characteristic

213

C₄

#19128117

yes

characteristic

214

C₄

#19128119

yes

characteristic

215

C₂

—

166

—

216

C₂

#24906214

yes

characteristic

217

C₂

#24909220

yes

characteristic

218

C₂

#364×D₈₃

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₈₃
Fitting	C₈₃×#1370	C₂
socle	C₂²×C₈₃	C₂×C₄⋊C₈
prime radical	C₂²×D₈₃	C₄⋊C₈
cosocle	C₄×C₈×C₈₃	C₂³
hypercenter	#1370	D₈₃
hypocenter	C₈₃	#12016
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

subgroup

G/H

center

C₂×C₈

D₄×D₈₃

commutator

C₂×C₄×C₈₃

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₈₃

Fitting

C₈₃×#1370

C₂

socle

C₂²×C₈₃

C₂×C₄⋊C₈

prime radical

C₂²×D₈₃

C₄⋊C₈

cosocle

C₄×C₈×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

N	H ≅ G/N	type
4. #24905532	C₂	semidirect
5. #24905527	C₂	semidirect
6. #24905526	C₂	semidirect
7. C₈₃×#1370	C₂	semidirect
114. #1370	D₈₃	semidirect
117. C₈₃	#12016	semidirect

H ≅ G/N

type

4. #24905532

C₂

semidirect

5. #24905527

C₂

semidirect

6. #24905526

C₂

semidirect

7. C₈₃×#1370

C₂

semidirect

114. #1370

D₈₃

semidirect

117. C₈₃

#12016

semidirect

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

subgroup	index
#24909265	2
C₄⋊C₁₆×D₈₃	2
C₈×#13050573	2
#24905532	2
#24905527	2
#24905526	2
C₈₃×#1370	2
#12016	83

subgroup

index

C₄⋊C₁₆×D₈₃

C₈₃×#1370

Subgroups — #35316021

Conjugacy classes of subgroups

Complements

Maximal subgroups