Group #35322821 — subgroups

Subgroups — #35322821

Order 21248.

402 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₂²×Dic₆₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#19127516	C₂	1	2	yes	maximal
3	#24909059	C₂	1	1	yes	maximal, characteristic
4	#24908376	C₂	1	2	yes	maximal
5	C₂×#368×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₃₂	C₂²	1	2	yes	—
7	C₂×Dic₆₆₄	—	2	1	no	—
8	C₂×Dic₆₆₄	—	2	1	no	—
9	C₂×Dic₆₆₄	—	2	2	no	—
10	C₂×Dic₆₆₄	C₄	1	4	yes	complemented
11	C₂×#14581732	C₂²	1	1	yes	characteristic
12	#19127711	—	2	2	no	—
13	C₂×#14581710	—	2	2	no	—
14	#19127656	C₂²	1	1	yes	characteristic
15	#19127516	—	2	4	no	—
16	#19127476	—	2	1	no	—
17	C₁₆×Dic₈₃	—	2	1	no	—
18	C₂²×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
19	C₂×#108×C₈₃	C₂²	1	2	yes	—
20	#368×C₈₃	—	2	2	no	—
21	C₂²×Dic₁₆₆	—	2	2	no	—
22	C₂×Dic₃₃₂	—	2	2	no	—
23	C₂×Dic₃₃₂	—	2	2	no	—
24	C₂×Dic₃₃₂	—	2	2	no	—
25	C₂×Dic₃₃₂	—	2	2	no	—
26	C₂×Dic₃₃₂	—	2	2	no	—
27	C₂×Dic₃₃₂	C₂×C₄	1	4	yes	—
28	C₂×#13050574	D₄	1	1	yes	characteristic
29	#14581751	D₄	1	1	yes	characteristic
30	Dic₆₆₄	—	2	4	no	—
31	Dic₆₆₄	—	2	4	no	—
32	#14581732	—	2	1	no	—
33	#14581732	D₄	1	2	yes	—
34	C₂×C₈₃⋊C₁₆	—	2	1	no	—
35	#14581717	—	4	4	no	—
36	#14581710	—	4	4	no	—
37	#14581702	—	2	1	no	—
38	C₈×Dic₈₃	—	2	1	no	—
39	C₂×M₁₆×C₈₃	—	2	2	no	—
40	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
41	C₂×C₁₆×C₈₃	C₂×C₄	1	2	yes	—
42	C₂×C₁₆×C₈₃	D₄	1	1	yes	characteristic
43	C₂×C₁₆×C₈₃	D₄	1	1	yes	characteristic
44	C₂×C₁₆×C₈₃	D₄	1	2	yes	—
45	#108×C₈₃	—	2	2	no	—
46	#108×C₈₃	—	2	2	no	—
47	C₂×Dic₁₆₆	—	2	4	no	—
48	C₂×Dic₁₆₆	—	4	2	no	—
49	C₂×Dic₁₆₆	—	4	2	no	—
50	C₂×Dic₁₆₆	—	4	2	no	—
51	C₂×Dic₁₆₆	—	4	2	no	—
52	C₂×Dic₁₆₆	—	4	2	no	—
53	C₂²×Dic₈₃	—	4	2	no	—
54	Dic₃₃₂	—	2	4	no	—
55	Dic₃₃₂	—	2	4	no	—
56	Dic₃₃₂	—	4	2	no	—
57	Dic₃₃₂	—	4	2	no	—
58	#13050574	—	2	1	no	—
59	#13050574	D₈	1	2	yes	—
60	C₂×C₈₃⋊C₈	—	2	1	no	—
61	C₄⋊Dic₈₃	D₈	1	2	yes	—
62	C₂²⋊Dic₈₃	—	2	1	no	—
63	C₄×Dic₈₃	—	2	1	no	—
64	C₈₃⋊C₁₆	—	2	2	no	—
65	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
66	M₁₆×C₈₃	—	4	2	no	—
67	M₁₆×C₈₃	—	4	2	no	—
68	C₂×C₈×C₈₃	—	4	2	no	—
69	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
74	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
75	C₁₆×C₈₃	C₂²⋊C₄	1	2	yes	—
76	C₁₆×C₈₃	C₂²⋊C₄	1	2	yes	—
77	C₂³×C₈₃	#135	1	1	yes	characteristic
78	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
79	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
80	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
81	C₂×C₄×C₈₃	C₂×D₈	1	1	yes	characteristic
82	C₂×C₄×C₈₃	C₂×D₈	1	1	yes	characteristic
83	C₂×C₄×C₈₃	#135	1	1	yes	characteristic
84	C₂×Dic₈₃	—	2	2	no	—
85	C₂×Dic₈₃	—	4	4	no	—
86	C₂×Dic₈₃	—	8	2	no	—
87	C₂×Dic₈₃	—	8	2	no	—
88	Dic₁₆₆	—	4	4	no	—
89	Dic₁₆₆	—	4	4	no	—
90	Dic₁₆₆	—	8	2	no	—
91	Dic₁₆₆	—	8	2	no	—
92	C₈×C₈₃	—	8	2	no	—
93	C₈×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
95	C₈×C₈₃	#121	1	1	yes	characteristic
96	C₈×C₈₃	#124	1	1	yes	characteristic
97	C₈₃⋊C₈	—	2	2	no	—
98	C₂²×C₈₃	—	2	2	no	—
99	C₂²×C₈₃	C₄×D₈	1	1	yes	characteristic
100	C₂²×C₈₃	#466	1	1	yes	characteristic
101	C₂²×C₈₃	#495	1	1	yes	characteristic
102	C₄×C₈₃	#390	1	1	yes	characteristic
103	C₄×C₈₃	C₄×D₈	1	1	yes	characteristic
104	C₄×C₈₃	#466	1	1	yes	characteristic
105	C₄×C₈₃	#493	1	1	yes	characteristic
106	Dic₈₃	—	4	2	no	—
107	Dic₈₃	—	8	4	no	—
108	#13244	—	83	1	no	maximal, Sylow
109	C₂×C₈₃	—	2	1	no	—
110	C₂×C₈₃	—	2	1	no	—
111	C₂×C₈₃	#1970	1	1	yes	characteristic
112	C₂×C₈₃	#2222	1	2	yes	—
113	C₂²×Q₃₂	—	83	1	no	—
114	C₂×#368	D₈₃	1	1	yes	characteristic
115	C₂×#362	—	83	2	no	—
116	#2108	—	83	1	no	—
117	#1979	—	83	2	no	—
118	C₈₃	#13244	1	1	yes	characteristic, complemented, Sylow
119	C₂²×Q₁₆	—	83	2	no	—
120	C₂×Q₃₂	—	83	4	no	—
121	C₂×Q₃₂	—	166	1	no	—
122	C₂×Q₃₂	—	166	1	no	—
123	C₂×Q₃₂	—	166	2	no	—
124	C₂×M₃₂	—	83	1	no	—
125	C₂²×C₁₆	C₂×D₈₃	1	1	yes	characteristic
126	C₂×#108	C₂×D₈₃	1	2	yes	—
127	#419	—	166	2	no	—
128	C₂×#101	—	166	2	no	—
129	#405	—	83	1	no	—
130	#368	—	2	2	no	—
131	#362	—	166	4	no	—
132	#346	—	166	1	no	—
133	C₄×C₁₆	—	166	1	no	—
134	C₂²×Q₈	—	166	2	no	—
135	C₂×Q₁₆	—	83	4	no	—
136	C₂×Q₁₆	—	166	2	no	—
137	C₂×Q₁₆	—	166	2	no	—
138	C₂×Q₁₆	—	166	2	no	—
139	C₂×Q₁₆	—	166	2	no	—
140	C₂×Q₁₆	—	166	2	no	—
141	C₂×M₁₆	—	2	2	no	—
142	C₂×M₁₆	—	83	1	no	—
143	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
144	#117	—	83	1	no	—
145	Q₃₂	—	166	4	no	—
146	Q₃₂	—	166	4	no	—
147	M₃₂	—	83	2	no	—
148	M₃₂	—	166	1	no	—
149	C₂×C₁₆	—	166	1	no	—
150	C₂×C₁₆	C₄×D₈₃	1	2	yes	—
151	C₂×C₁₆	D₃₃₂	1	1	yes	characteristic
152	C₂×C₁₆	D₃₃₂	1	1	yes	characteristic
153	C₂×C₁₆	C₂²⋊D₈₃	1	2	yes	—
154	#108	—	2	2	no	—
155	#108	—	2	2	no	—
156	#103	—	332	4	no	—
157	#101	—	332	4	no	—
158	#97	—	166	1	no	—
159	C₄×C₈	—	166	1	no	—
160	C₂×Q₈	—	332	2	no	—
161	C₂×Q₈	—	332	2	no	—
162	C₂×Q₈	—	332	2	no	—
163	C₂×Q₈	—	332	2	no	—
164	C₂×Q₈	—	332	2	no	—
165	C₂×Q₈	—	166	4	no	—
166	C₂²×C₄	—	332	2	no	—
167	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
168	Q₁₆	—	332	2	no	—
169	Q₁₆	—	332	2	no	—
170	Q₁₆	—	166	4	no	—
171	Q₁₆	—	166	4	no	—
172	M₁₆	—	4	2	no	—
173	M₁₆	—	4	2	no	—
174	M₁₆	—	83	2	no	—
175	M₁₆	—	166	1	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	166	1	no	—
178	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
179	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
180	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
181	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
182	C₂×C₈	#13050591	1	1	yes	characteristic
183	C₂×C₈	#13050591	1	1	yes	characteristic
184	C₄⋊C₄	—	83	2	no	—
185	C₂²⋊C₄	—	166	1	no	—
186	C₄²	—	166	1	no	—
187	C₁₆	—	166	2	no	—
188	C₁₆	(C₂×D₈₃)⋊C₄	1	2	yes	—
189	C₁₆	(C₂×D₈₃)⋊C₄	1	2	yes	—
190	C₂³	#14581815	1	1	yes	characteristic
191	Q₈	—	332	4	no	—
192	Q₈	—	332	4	no	—
193	Q₈	—	664	2	no	—
194	Q₈	—	664	2	no	—
195	C₂×C₄	—	332	4	no	—
196	C₂×C₄	—	664	2	no	—
197	C₂×C₄	—	664	2	no	—
198	C₂×C₄	—	166	2	no	—
199	C₂×C₄	#14581754	1	1	yes	characteristic
200	C₂×C₄	#14581767	1	1	yes	characteristic
201	C₂×C₄	#14581788	1	1	yes	characteristic
202	C₂×C₄	D₈×D₈₃	1	1	yes	characteristic
203	C₂×C₄	D₈×D₈₃	1	1	yes	characteristic
204	C₂×C₄	#14581815	1	1	yes	characteristic
205	C₈	—	8	2	no	—
206	C₈	—	166	2	no	—
207	C₈	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
208	C₈	#14581754	1	1	yes	characteristic
209	C₈	#14581767	1	1	yes	characteristic
210	C₈	#14581781	1	1	yes	characteristic
211	C₂²	—	2	2	no	—
212	C₂²	#19127783	1	1	yes	characteristic
213	C₂²	#19127938	1	1	yes	characteristic
214	C₂²	#19128086	1	1	yes	characteristic
215	C₄	—	332	2	no	—
216	C₄	—	664	4	no	—
217	C₄	#19127602	1	1	yes	characteristic
218	C₄	#19127783	1	1	yes	characteristic
219	C₄	#19127938	1	1	yes	characteristic
220	C₄	#19128076	1	1	yes	characteristic
221	C₂	—	2	1	no	—
222	C₂	—	2	1	no	—
223	C₂	#24908327	1	1	yes	characteristic
224	C₂	#24909589	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₆₆₄

C₂

yes

maximal, characteristic

C₂×#19127516

C₂

yes

maximal

#24909059

C₂

yes

maximal, characteristic

#24908376

C₂

yes

maximal

C₂×#368×C₈₃

C₂

yes

maximal, characteristic

C₂²×Dic₃₃₂

C₂²

yes

—

C₂×Dic₆₆₄

—

C₂×Dic₆₆₄

—

C₂×Dic₆₆₄

—

C₂×Dic₆₆₄

C₄

yes

complemented

C₂×#14581732

C₂²

yes

—

—

C₂²

yes

characteristic

#19127516

—

#19127476

—

C₁₆×Dic₈₃

—

C₂²×C₁₆×C₈₃

C₂²

yes

characteristic

C₂×#108×C₈₃

C₂²

yes

—

#368×C₈₃

—

C₂²×Dic₁₆₆

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

C₂×C₄

yes

—

C₂×#13050574

D₄

yes

characteristic

#14581751

D₄

yes

characteristic

Dic₆₆₄

—

Dic₆₆₄

—

#14581732

—

#14581732

D₄

yes

—

C₂×C₈₃⋊C₁₆

—

#14581717

—

#14581710

—

#14581702

—

C₈×Dic₈₃

—

C₂×M₁₆×C₈₃

—

C₂²×C₈×C₈₃

C₂³

yes

characteristic

C₂×C₁₆×C₈₃

C₂×C₄

yes

—

C₂×C₁₆×C₈₃

D₄

yes

characteristic

C₂×C₁₆×C₈₃

D₄

yes

characteristic

C₂×C₁₆×C₈₃

D₄

yes

—

#108×C₈₃

—

#108×C₈₃

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

#13050574

—

#13050574

D₈

yes

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

D₈

yes

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₈₃⋊C₁₆

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

M₁₆×C₈₃

—

M₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

C₂×C₈×C₈₃

yes

C₂×C₈×C₈₃

yes

C₁₆×C₈₃

C₂²⋊C₄

yes

—

C₁₆×C₈₃

C₂²⋊C₄

yes

—

C₂³×C₈₃

#135

yes

characteristic

C₂×C₄×C₈₃

C₄×D₄

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

C₂×D₈

yes

characteristic

C₂×C₄×C₈₃

C₂×D₈

yes

characteristic

C₂×C₄×C₈₃

#135

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

—

C₈×C₈₃

—

C₈×C₈₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₈₃

C₄×D₄

yes

C₈×C₈₃

yes

C₈×C₈₃

yes

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

C₄×D₈

yes

characteristic

100

C₂²×C₈₃

#466

yes

characteristic

101

C₂²×C₈₃

#495

yes

characteristic

102

C₄×C₈₃

#390

yes

characteristic

103

C₄×C₈₃

C₄×D₈

yes

characteristic

104

C₄×C₈₃

#466

yes

characteristic

105

C₄×C₈₃

#493

yes

characteristic

106

Dic₈₃

—

107

Dic₈₃

—

108

#13244

—

maximal, Sylow

109

C₂×C₈₃

—

110

C₂×C₈₃

—

111

C₂×C₈₃

#1970

yes

characteristic

112

C₂×C₈₃

#2222

yes

—

113

C₂²×Q₃₂

—

114

C₂×#368

D₈₃

yes

characteristic

115

C₂×#362

—

116

#2108

—

117

#1979

—

118

C₈₃

#13244

yes

characteristic, complemented, Sylow

119

C₂²×Q₁₆

—

120

C₂×Q₃₂

—

121

C₂×Q₃₂

—

166

—

122

C₂×Q₃₂

—

166

—

123

C₂×Q₃₂

—

166

—

124

C₂×M₃₂

—

125

C₂²×C₁₆

C₂×D₈₃

yes

characteristic

126

C₂×#108

C₂×D₈₃

yes

—

127

#419

—

166

—

128

C₂×#101

—

166

—

129

#405

—

130

#368

—

131

#362

—

166

—

132

#346

—

166

—

133

C₄×C₁₆

—

166

—

134

C₂²×Q₈

—

166

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

—

166

—

137

C₂×Q₁₆

—

166

—

138

C₂×Q₁₆

—

166

—

139

C₂×Q₁₆

—

166

—

140

C₂×Q₁₆

—

166

—

141

C₂×M₁₆

—

142

C₂×M₁₆

—

143

C₂²×C₈

C₂²×D₈₃

yes

characteristic

144

#117

—

145

Q₃₂

—

166

—

146

Q₃₂

—

166

—

147

M₃₂

—

148

M₃₂

—

166

—

149

C₂×C₁₆

—

166

—

150

C₂×C₁₆

C₄×D₈₃

yes

—

151

C₂×C₁₆

D₃₃₂

yes

characteristic

152

C₂×C₁₆

D₃₃₂

yes

characteristic

153

C₂×C₁₆

C₂²⋊D₈₃

yes

—

154

#108

—

155

#108

—

156

#103

—

332

—

157

#101

—

332

—

158

#97

—

166

—

159

C₄×C₈

—

166

—

160

C₂×Q₈

—

332

—

161

C₂×Q₈

—

332

—

162

C₂×Q₈

—

332

—

163

C₂×Q₈

—

332

—

164

C₂×Q₈

—

332

—

165

C₂×Q₈

—

166

—

166

C₂²×C₄

—

332

—

167

C₂²×C₄

D₄×D₈₃

yes

characteristic

168

Q₁₆

—

332

—

169

Q₁₆

—

332

—

170

Q₁₆

—

166

—

171

Q₁₆

—

166

—

172

M₁₆

—

173

M₁₆

—

174

M₁₆

—

175

M₁₆

—

166

—

176

C₂×C₈

—

177

C₂×C₈

—

166

—

178

C₂×C₈

C₂×C₄×D₈₃

yes

characteristic

179

C₂×C₈

D₄×D₈₃

yes

characteristic

180

C₂×C₈

C₂×C₂²⋊D₈₃

yes

characteristic

181

C₂×C₈

C₂×D₃₃₂

yes

characteristic

182

C₂×C₈

#13050591

yes

characteristic

183

C₂×C₈

#13050591

yes

characteristic

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

166

—

186

C₄²

—

166

—

187

C₁₆

—

166

—

188

C₁₆

(C₂×D₈₃)⋊C₄

yes

—

189

C₁₆

(C₂×D₈₃)⋊C₄

yes

—

190

C₂³

#14581815

yes

characteristic

191

Q₈

—

332

—

192

Q₈

—

332

—

193

Q₈

—

664

—

194

Q₈

—

664

—

195

C₂×C₄

—

332

—

196

C₂×C₄

—

664

—

197

C₂×C₄

—

664

—

198

C₂×C₄

—

166

—

199

C₂×C₄

#14581754

yes

characteristic

200

C₂×C₄

#14581767

yes

characteristic

201

C₂×C₄

#14581788

yes

characteristic

202

C₂×C₄

D₈×D₈₃

yes

characteristic

203

C₂×C₄

D₈×D₈₃

yes

characteristic

204

C₂×C₄

#14581815

yes

characteristic

205

C₈

—

206

C₈

—

166

—

207

C₈

C₂×(C₂×D₈₃)⋊C₄

yes

characteristic

208

C₈

#14581754

yes

characteristic

209

C₈

#14581767

yes

characteristic

210

C₈

#14581781

yes

characteristic

211

C₂²

—

212

C₂²

#19127783

yes

characteristic

213

C₂²

#19127938

yes

characteristic

214

C₂²

#19128086

yes

characteristic

215

C₄

—

332

—

216

C₄

—

664

—

217

C₄

#19127602

yes

characteristic

218

C₄

#19127783

yes

characteristic

219

C₄

#19127938

yes

characteristic

220

C₄

#19128076

yes

characteristic

221

C₂

—

222

C₂

—

223

C₂

#24908327

yes

characteristic

224

C₂

#24909589

yes

—

	subgroup	G/H
center	C₂²	#19127938
commutator	C₂×C₈×C₈₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₂×#368×C₈₃	C₂
socle	C₂²×C₈₃	#466
prime radical	C₂³×C₈₃	#135
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	C₂×#368	D₈₃
hypocenter	C₈₃	#13244
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

subgroup

G/H

center

C₂²

#19127938

commutator

C₂×C₈×C₈₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₂×#368×C₈₃

C₂

C₂²×C₈₃

C₂³×C₈₃

C₂²×C₈×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

N	H ≅ G/N	type
10. C₂×Dic₆₆₄	C₄	semidirect
118. C₈₃	#13244	semidirect

H ≅ G/N

type

10. C₂×Dic₆₆₄

C₄

semidirect

118. C₈₃

#13244

semidirect

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

subgroup	index
C₂²×Dic₆₆₄	2
C₂×#19127516	2
#24909059	2
#24908376	2
C₂×#368×C₈₃	2
#13244	83

subgroup

index

C₂²×Dic₆₆₄

C₂×#368×C₈₃

Subgroups — #35322821

Conjugacy classes of subgroups

Complements

Maximal subgroups