Group #35307198 — subgroups

Subgroups — #35307198

Order 21248.

618 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 161 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	C₂×#19128104	C₂	1	2	yes	maximal
2	#24908425	C₂	1	2	yes	maximal
3	#24908265	C₂	1	1	yes	maximal, characteristic
4	C₈₃⋊#1273	C₂	1	1	yes	maximal, characteristic
5	C₂×#494×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#14581792	C₂²	1	1	yes	characteristic
7	#19128104	—	2	4	no	—
8	#19128104	—	2	4	no	—
9	C₂×#14581725	—	2	4	no	—
10	C₂×#14581717	—	2	2	no	—
11	C₂×C₄×C₈₃⋊C₈	C₂²	1	2	yes	—
12	#19127571	C₂²	1	1	yes	characteristic
13	#19127463	—	2	4	no	—
14	C₂²×Q₁₆×C₈₃	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₈₃	C₂²	1	2	yes	—
16	#494×C₈₃	—	2	4	no	—
17	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
18	C₂²×Dic₁₆₆	—	2	1	no	—
19	C₂²×C₈₃⋊C₈	D₄	1	4	yes	—
20	#14581792	—	2	2	no	—
21	#14581792	—	2	1	no	—
22	#14581792	D₄	1	2	yes	—
23	C₂×C₄⋊Dic₈₃	—	2	2	no	—
24	C₂×C₄⋊Dic₈₃	—	2	1	no	—
25	C₂×C₄⋊Dic₈₃	—	2	2	no	—
26	#14581725	—	2	16	no	—
27	#14581717	—	4	4	no	—
28	C₄×C₈₃⋊C₈	—	2	2	no	—
29	C₄×C₈₃⋊C₈	—	2	2	no	—
30	C₂²×Q₈×C₈₃	—	2	2	no	—
31	C₂×Q₁₆×C₈₃	—	2	8	no	—
32	C₂×Q₁₆×C₈₃	—	4	4	no	—
33	C₂×Q₁₆×C₈₃	—	4	4	no	—
34	C₂²×C₈×C₈₃	D₄	1	2	yes	—
35	C₄⋊Q₈×C₈₃	—	2	2	no	—
36	C₄⋊Q₈×C₈₃	—	2	2	no	—
37	C₄⋊Q₈×C₈₃	—	2	2	no	—
38	C₄⋊Q₈×C₈₃	D₄	1	4	yes	—
39	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
41	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
42	C₄×C₈×C₈₃	—	2	2	no	—
43	C₂×Dic₁₆₆	—	2	2	no	—
44	C₂×Dic₁₆₆	—	4	2	no	—
45	C₂×Dic₁₆₆	—	4	2	no	—
46	C₂×Dic₁₆₆	—	4	1	no	—
47	C₂²×Dic₈₃	—	4	1	no	—
48	C₂²×Dic₈₃	—	4	1	no	—
49	C₂×C₈₃⋊C₈	—	2	4	no	—
50	C₂×C₈₃⋊C₈	—	2	4	no	—
51	C₂×C₈₃⋊C₈	Q₁₆	1	8	yes	complemented
52	C₄⋊Dic₈₃	—	2	4	no	—
53	C₄⋊Dic₈₃	—	4	2	no	—
54	C₄⋊Dic₈₃	—	4	2	no	—
55	C₄⋊Dic₈₃	—	4	4	no	—
56	C₂×Q₈×C₈₃	—	2	4	no	—
57	C₂×Q₈×C₈₃	—	4	2	no	—
58	C₂×Q₈×C₈₃	—	4	4	no	—
59	C₂×Q₈×C₈₃	—	4	4	no	—
60	C₂²×C₄×C₈₃	—	4	2	no	—
61	C₂²×C₄×C₈₃	C₂×D₄	1	2	yes	—
62	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
63	Q₁₆×C₈₃	—	4	16	no	—
64	C₂×C₈×C₈₃	—	2	2	no	—
65	C₂×C₈×C₈₃	—	2	2	no	—
66	C₂×C₈×C₈₃	D₈	1	4	yes	—
67	C₄⋊C₄×C₈₃	—	2	4	no	—
68	C₄⋊C₄×C₈₃	—	2	4	no	—
69	C₄⋊C₄×C₈₃	—	4	2	no	—
70	C₄⋊C₄×C₈₃	—	4	2	no	—
71	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₈₃	C₂×D₄	1	2	yes	—
73	C₄²×C₈₃	#41	1	1	yes	characteristic
74	C₂³×C₈₃	#127	1	1	yes	characteristic
75	Q₈×C₈₃	—	4	8	no	—
76	Q₈×C₈₃	—	8	4	no	—
77	C₂×C₄×C₈₃	—	4	4	no	—
78	C₂×C₄×C₈₃	—	8	2	no	—
79	C₂×C₄×C₈₃	—	8	2	no	—
80	C₂×C₄×C₈₃	#120	1	2	yes	—
81	C₂×C₄×C₈₃	#120	1	1	yes	characteristic
82	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
83	C₂×C₄×C₈₃	#121	1	2	yes	—
84	C₂×C₄×C₈₃	C₂×D₈	1	2	yes	—
85	C₂×C₄×C₈₃	C₂×Q₁₆	1	4	yes	—
86	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×C₄×C₈₃	#137	1	4	yes	—
88	C₂×Dic₈₃	—	4	2	no	—
89	C₂×Dic₈₃	—	8	1	no	—
90	C₂×Dic₈₃	—	8	1	no	—
91	C₂×Dic₈₃	—	8	1	no	—
92	C₂×Dic₈₃	—	8	2	no	—
93	Dic₁₆₆	—	4	4	no	—
94	Dic₁₆₆	—	8	2	no	—
95	C₈×C₈₃	—	2	4	no	—
96	C₈₃⋊C₈	—	2	8	no	—
97	C₂²×C₈₃	#392	1	1	yes	characteristic
98	C₂²×C₈₃	#493	1	1	yes	characteristic
99	C₂²×C₈₃	#494	1	2	yes	—
100	C₂²×C₈₃	#496	1	1	yes	characteristic
101	C₂²×C₈₃	#497	1	2	yes	—
102	C₄×C₈₃	—	8	4	no	—
103	C₄×C₈₃	#447	1	2	yes	—
104	C₄×C₈₃	#451	1	4	yes	—
105	C₄×C₈₃	#459	1	2	yes	—
106	C₄×C₈₃	#462	1	4	yes	—
107	Dic₈₃	—	8	2	no	—
108	Dic₈₃	—	16	1	no	—
109	#10309	—	83	1	no	maximal, Sylow
110	C₂×C₈₃	#1713	1	1	yes	characteristic
111	C₂×C₈₃	#1722	1	1	yes	characteristic
112	C₂×C₈₃	#1723	1	2	yes	—
113	C₂×C₈₃	#2011	1	1	yes	characteristic
114	C₂×C₈₃	#2016	1	2	yes	—
115	C₂×#500	—	83	2	no	—
116	C₂×#494	D₈₃	1	1	yes	characteristic
117	#1990	—	83	2	no	—
118	#1956	—	83	1	no	—
119	#1273	—	83	1	no	—
120	C₈₃	#10309	1	1	yes	characteristic, complemented, Sylow
121	C₂²×Q₁₆	—	2	2	no	—
122	C₂×C₄⋊Q₈	—	83	1	no	—
123	C₂×C₄⋊Q₈	C₂×D₈₃	1	2	yes	—
124	#500	—	166	4	no	—
125	#500	—	166	4	no	—
126	#494	—	2	4	no	—
127	C₂×#107	—	166	4	no	—
128	C₂×#103	—	166	2	no	—
129	C₂×C₄×C₈	—	83	2	no	—
130	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
131	#384	—	83	1	no	—
132	#340	—	166	4	no	—
133	C₂²×Q₈	—	2	2	no	—
134	C₂²×Q₈	—	166	1	no	—
135	C₂×Q₁₆	—	2	8	no	—
136	C₂×Q₁₆	—	4	4	no	—
137	C₂×Q₁₆	—	4	4	no	—
138	C₂²×C₈	—	83	4	no	—
139	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	—	2	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	83	2	no	—
144	C₄⋊Q₈	—	166	2	no	—
145	C₄⋊Q₈	—	166	1	no	—
146	C₄⋊Q₈	C₂²⋊D₈₃	1	4	yes	—
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	166	2	no	—
150	C₂×C₄⋊C₄	—	166	1	no	—
151	C₂×C₄⋊C₄	—	166	2	no	—
152	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
153	#107	—	166	16	no	—
154	#103	—	332	4	no	—
155	C₄×C₈	—	2	2	no	—
156	C₄×C₈	—	166	2	no	—
157	C₄×C₈	—	166	2	no	—
158	C₂×Q₈	—	2	4	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂×Q₈	—	4	4	no	—
161	C₂×Q₈	—	4	4	no	—
162	C₂×Q₈	—	332	1	no	—
163	C₂×Q₈	—	332	2	no	—
164	C₂×Q₈	—	332	2	no	—
165	C₂×Q₈	—	166	2	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	—	332	1	no	—
168	C₂²×C₄	—	332	1	no	—
169	C₂²×C₄	D₄×D₈₃	1	2	yes	—
170	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
171	Q₁₆	—	4	16	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	83	8	no	—
175	C₂×C₈	—	166	4	no	—
176	C₂×C₈	—	166	4	no	—
177	C₂×C₈	#13050575	1	4	yes	—
178	C₄⋊C₄	—	2	4	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	332	2	no	—
183	C₄⋊C₄	—	332	2	no	—
184	C₄⋊C₄	—	332	4	no	—
185	C₄⋊C₄	—	166	4	no	—
186	C₄²	D₄×D₈₃	1	1	yes	characteristic
187	C₄²	C₂×C₂²⋊D₈₃	1	2	yes	—
188	C₄²	#13050589	1	1	yes	characteristic
189	C₂³	#14581788	1	1	yes	characteristic
190	Q₈	—	4	8	no	—
191	Q₈	—	8	4	no	—
192	Q₈	—	332	4	no	—
193	Q₈	—	664	2	no	—
194	C₂×C₄	—	4	4	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	—	8	2	no	—
197	C₂×C₄	—	332	2	no	—
198	C₂×C₄	—	664	1	no	—
199	C₂×C₄	—	664	2	no	—
200	C₂×C₄	—	664	1	no	—
201	C₂×C₄	—	664	1	no	—
202	C₂×C₄	#14581760	1	2	yes	—
203	C₂×C₄	#14581761	1	1	yes	characteristic
204	C₂×C₄	#14581763	1	1	yes	characteristic
205	C₂×C₄	#14581764	1	2	yes	—
206	C₂×C₄	C₂×#13050575	1	2	yes	—
207	C₂×C₄	Q₁₆×D₈₃	1	4	yes	—
208	C₂×C₄	#14581818	1	2	yes	—
209	C₂×C₄	#14581824	1	4	yes	—
210	C₈	—	2	4	no	—
211	C₈	—	166	8	no	—
212	C₂²	#19127609	1	1	yes	characteristic
213	C₂²	#19128077	1	1	yes	characteristic
214	C₂²	#19128079	1	2	yes	—
215	C₂²	#19128088	1	1	yes	characteristic
216	C₂²	#19128094	1	2	yes	—
217	C₄	—	8	4	no	—
218	C₄	—	1328	1	no	—
219	C₄	—	664	2	no	—
220	C₄	#19127835	1	2	yes	—
221	C₄	#19127855	1	4	yes	—
222	C₄	#19127893	1	2	yes	—
223	C₄	#19127909	1	4	yes	—
224	C₂	#24907079	1	1	yes	characteristic
225	C₂	#24907135	1	1	yes	characteristic
226	C₂	#24907138	1	2	yes	—
227	C₂	#24908534	1	1	yes	characteristic
228	C₂	#24908561	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19128104

C₂

yes

maximal

#24908425

C₂

yes

maximal

#24908265

C₂

yes

maximal, characteristic

C₈₃⋊#1273

C₂

yes

maximal, characteristic

C₂×#494×C₈₃

C₂

yes

maximal, characteristic

C₂×#14581792

C₂²

yes

—

—

—

—

C₂×C₄×C₈₃⋊C₈

C₂²

yes

—

#19127571

C₂²

yes

characteristic

#19127463

—

C₂²×Q₁₆×C₈₃

—

C₂×C₄⋊Q₈×C₈₃

C₂²

yes

—

#494×C₈₃

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₂²×Dic₁₆₆

—

C₂²×C₈₃⋊C₈

D₄

yes

—

#14581792

—

#14581792

—

#14581792

D₄

yes

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

#14581725

—

#14581717

—

C₄×C₈₃⋊C₈

—

C₄×C₈₃⋊C₈

—

C₂²×Q₈×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂²×C₈×C₈₃

D₄

yes

—

C₄⋊Q₈×C₈₃

—

C₄⋊Q₈×C₈₃

—

C₄⋊Q₈×C₈₃

—

C₄⋊Q₈×C₈₃

D₄

yes

—

C₂×C₄⋊C₄×C₈₃

—

C₂×C₄⋊C₄×C₈₃

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄×C₈×C₈₃

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

Q₁₆

yes

complemented

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

Q₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

D₈

yes

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

—

C₄²×C₈₃

yes

C₂³×C₈₃

yes

Q₈×C₈₃

—

Q₈×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#120

yes

—

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

—

C₂×C₄×C₈₃

C₂×D₈

yes

—

C₂×C₄×C₈₃

C₂×Q₁₆

yes

—

C₂×C₄×C₈₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₈₃

#137

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₂²×C₈₃

yes

C₂²×C₈₃

yes

C₂²×C₈₃

yes

—

100

C₂²×C₈₃

#496

yes

characteristic

101

C₂²×C₈₃

#497

yes

—

102

C₄×C₈₃

—

103

C₄×C₈₃

#447

yes

—

104

C₄×C₈₃

#451

yes

—

105

C₄×C₈₃

#459

yes

—

106

C₄×C₈₃

#462

yes

—

107

Dic₈₃

—

108

Dic₈₃

—

109

#10309

—

maximal, Sylow

110

C₂×C₈₃

#1713

yes

characteristic

111

C₂×C₈₃

#1722

yes

characteristic

112

C₂×C₈₃

#1723

yes

—

113

C₂×C₈₃

#2011

yes

characteristic

114

C₂×C₈₃

#2016

yes

—

115

C₂×#500

—

116

C₂×#494

D₈₃

yes

characteristic

117

#1990

—

118

#1956

—

119

#1273

—

120

C₈₃

#10309

yes

characteristic, complemented, Sylow

121

C₂²×Q₁₆

—

122

C₂×C₄⋊Q₈

—

123

C₂×C₄⋊Q₈

C₂×D₈₃

yes

—

124

#500

—

166

—

125

#500

—

166

—

126

#494

—

127

C₂×#107

—

166

—

128

C₂×#103

—

166

—

129

C₂×C₄×C₈

—

130

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

131

#384

—

132

#340

—

166

—

133

C₂²×Q₈

—

134

C₂²×Q₈

—

166

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂²×C₈

—

139

C₂²×C₈

C₂²⋊D₈₃

yes

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

166

—

145

C₄⋊Q₈

—

166

—

146

C₄⋊Q₈

C₂²⋊D₈₃

yes

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

166

—

150

C₂×C₄⋊C₄

—

166

—

151

C₂×C₄⋊C₄

—

166

—

152

C₂×C₄²

C₂²×D₈₃

yes

characteristic

153

#107

—

166

—

154

#103

—

332

—

155

C₄×C₈

—

156

C₄×C₈

—

166

—

157

C₄×C₈

—

166

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

332

—

163

C₂×Q₈

—

332

—

164

C₂×Q₈

—

332

—

165

C₂×Q₈

—

166

—

166

C₂²×C₄

—

167

C₂²×C₄

—

332

—

168

C₂²×C₄

—

332

—

169

C₂²×C₄

D₄×D₈₃

yes

—

170

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

171

Q₁₆

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

166

—

176

C₂×C₈

—

166

—

177

C₂×C₈

#13050575

yes

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

332

—

183

C₄⋊C₄

—

332

—

184

C₄⋊C₄

—

332

—

185

C₄⋊C₄

—

166

—

186

C₄²

D₄×D₈₃

yes

characteristic

187

C₄²

C₂×C₂²⋊D₈₃

yes

—

188

C₄²

#13050589

yes

characteristic

189

C₂³

#14581788

yes

characteristic

190

Q₈

—

191

Q₈

—

192

Q₈

—

332

—

193

Q₈

—

664

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

332

—

198

C₂×C₄

—

664

—

199

C₂×C₄

—

664

—

200

C₂×C₄

—

664

—

201

C₂×C₄

—

664

—

202

C₂×C₄

#14581760

yes

—

203

C₂×C₄

#14581761

yes

characteristic

204

C₂×C₄

#14581763

yes

characteristic

205

C₂×C₄

#14581764

yes

—

206

C₂×C₄

C₂×#13050575

yes

—

207

C₂×C₄

Q₁₆×D₈₃

yes

—

208

C₂×C₄

#14581818

yes

—

209

C₂×C₄

#14581824

yes

—

210

C₈

—

211

C₈

—

166

—

212

C₂²

#19127609

yes

characteristic

213

C₂²

#19128077

yes

characteristic

214

C₂²

#19128079

yes

—

215

C₂²

#19128088

yes

characteristic

216

C₂²

#19128094

yes

—

217

C₄

—

218

C₄

—

1328

—

219

C₄

—

664

—

220

C₄

#19127835

yes

—

221

C₄

#19127855

yes

—

222

C₄

#19127893

yes

—

223

C₄

#19127909

yes

—

224

C₂

#24907079

yes

characteristic

225

C₂

#24907135

yes

characteristic

226

C₂

#24907138

yes

—

227

C₂

#24908534

yes

characteristic

228

C₂

#24908561

yes

—

	subgroup	G/H
center	C₂³	#14581788
commutator, cosocle	C₂×C₄²×C₈₃	C₂³
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₂×#494×C₈₃	C₂
socle, prime radical	C₂³×C₈₃	#127
hypercenter	C₂×#494	D₈₃
hypocenter	C₈₃	#10309
LCS	G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂³

#14581788

commutator, cosocle

C₂×C₄²×C₈₃

C₂³

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₂×#494×C₈₃

C₂

C₂³×C₈₃

D₈₃

C₈₃

G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
51. C₂×C₈₃⋊C₈	Q₁₆	semidirect
120. C₈₃	#10309	semidirect

H ≅ G/N

type

51. C₂×C₈₃⋊C₈

Q₁₆

semidirect

120. C₈₃

#10309

semidirect

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

subgroup	index
C₂×#19128104	2
#24908425	2
#24908265	2
C₈₃⋊#1273	2
C₂×#494×C₈₃	2
#10309	83

subgroup

index

C₂×#19128104

#24908425

#24908265

C₈₃⋊#1273

C₂×#494×C₈₃

#10309

Subgroups — #35307198

Conjugacy classes of subgroups

Complements

Maximal subgroups