Group #24920388 — subgroups

Subgroups — #24920388

Order 10624.

360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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	#19128426	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×Dic₁₆₆	C₂	1	1	yes	maximal, characteristic
3	#19128109	C₂	1	2	yes	maximal, complemented
4	#19128104	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128003	C₂	1	2	yes	maximal
6	#19127995	C₂	1	2	yes	maximal, complemented
7	#19127987	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127828	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127798	C₂	1	2	yes	maximal
10	C₄×#13050578	C₂	1	1	yes	maximal, characteristic
11	#474×C₈₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₁₆₆	—	2	1	no	—
13	C₂×#13050578	C₂²	1	1	yes	characteristic
14	#14581792	C₂²	1	1	yes	characteristic
15	#14581791	C₂²	1	2	yes	—
16	#14581790	—	2	1	no	—
17	#14581783	C₂²	1	2	yes	—
18	#14581782	—	2	2	no	—
19	#14581771	—	2	1	no	—
20	#14581769	—	2	2	no	—
21	Q₈×Dic₈₃	—	2	1	no	—
22	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
23	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
24	#14581757	C₂²	1	2	yes	—
25	D₄×Dic₈₃	C₂²	1	2	yes	—
26	#14581725	C₂²	1	2	yes	—
27	#14581725	C₂²	1	2	yes	—
28	#14581724	C₂²	1	2	yes	—
29	#14581723	C₂²	1	1	yes	characteristic
30	Dic₈₃⋊C₈	C₂²	1	2	yes	—
31	#14581717	C₂²	1	2	yes	—
32	#14581715	C₂²	1	1	yes	characteristic
33	#14581713	C₂²	1	1	yes	characteristic
34	#14581702	C₂²	1	2	yes	—
35	C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
38	#107×C₈₃	C₂²	1	2	yes	—
39	C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
40	#102×C₈₃	C₂²	1	2	yes	—
41	C₂×Dic₁₆₆	—	2	1	no	—
42	C₂×Dic₁₆₆	—	2	2	no	—
43	C₂×Dic₁₆₆	—	4	4	no	—
44	C₂×Dic₁₆₆	D₄	1	1	yes	characteristic
45	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
46	C₂²×Dic₈₃	—	2	2	no	—
47	#13050578	Q₈	1	4	yes	complemented
48	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
49	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
50	C₄⋊Dic₈₃	—	2	1	no	—
51	C₄⋊Dic₈₃	—	2	2	no	—
52	C₄⋊Dic₈₃	D₄	1	1	yes	characteristic
53	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
54	C₄⋊Dic₈₃	C₂³	1	2	yes	—
55	Dic₈₃⋊C₄	—	2	1	no	—
56	Dic₈₃⋊C₄	—	2	2	no	—
57	Dic₈₃⋊C₄	—	2	2	no	—
58	Dic₈₃⋊C₄	—	2	2	no	—
59	Dic₈₃⋊C₄	D₄	1	2	yes	—
60	C₂²⋊Dic₈₃	—	2	2	no	—
61	C₄×Dic₈₃	—	2	1	no	—
62	C₄×Dic₈₃	—	2	2	no	—
63	C₄×Dic₈₃	C₂³	1	2	yes	—
64	C₂×Q₈×C₈₃	—	2	1	no	—
65	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₈₃	—	2	1	no	—
67	C₂×C₈×C₈₃	C₂³	1	2	yes	—
68	C₄⋊C₄×C₈₃	—	2	1	no	—
69	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
70	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
71	C₂²⋊C₄×C₈₃	—	2	1	no	—
72	C₄²×C₈₃	C₂³	1	1	yes	characteristic
73	C₂³×C₈₃	—	2	1	no	—
74	Q₈×C₈₃	—	4	2	no	—
75	D₄×C₈₃	—	2	1	no	—
76	D₄×C₈₃	C₂×Q₈	1	2	yes	—
77	C₂×C₄×C₈₃	—	2	1	no	—
78	C₂×C₄×C₈₃	—	2	2	no	—
79	C₂×C₄×C₈₃	—	4	2	no	—
80	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
83	C₂×Dic₈₃	—	2	1	no	—
84	C₂×Dic₈₃	—	2	1	no	—
85	C₂×Dic₈₃	—	2	2	no	—
86	C₂×Dic₈₃	—	4	4	no	—
87	C₂×Dic₈₃	C₂×D₄	1	2	yes	—
88	C₂×Dic₈₃	C₂×D₄	1	2	yes	—
89	Dic₁₆₆	—	2	2	no	—
90	Dic₁₆₆	—	2	1	no	—
91	Dic₁₆₆	—	4	4	no	—
92	Dic₁₆₆	—	4	2	no	—
93	Dic₁₆₆	C₂×Q₈	1	2	yes	complemented
94	C₈×C₈₃	—	2	2	no	—
95	C₈₃⋊C₈	—	2	1	no	—
96	C₈₃⋊C₈	C₂×Q₈	1	2	yes	complemented
97	C₂²×C₈₃	—	2	2	no	—
98	C₂²×C₈₃	—	4	1	no	—
99	C₂²×C₈₃	—	4	1	no	—
100	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
101	C₄×C₈₃	—	2	1	no	—
102	C₄×C₈₃	—	4	1	no	—
103	C₄×C₈₃	—	4	2	no	—
104	C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
105	C₄×C₈₃	C₂²×Q₈	1	1	yes	characteristic
106	C₄×C₈₃	2₋¹⁺⁴	1	1	yes	characteristic
107	Dic₈₃	—	2	2	no	—
108	Dic₈₃	—	2	2	no	—
109	Dic₈₃	—	2	2	no	—
110	Dic₈₃	—	4	2	no	—
111	Dic₈₃	—	4	1	no	—
112	C₂×C₈₃	—	4	2	no	—
113	C₂×C₈₃	D₄×Q₈	1	1	yes	characteristic
114	C₂×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
115	C₂×C₈₃	#578	1	1	yes	characteristic
116	#3386	—	83	1	no	maximal, Sylow
117	C₈₃	#3386	1	1	yes	characteristic, complemented, Sylow
118	#557	—	83	1	no	—
119	D₄×Q₈	—	83	1	no	—
120	#501	—	83	2	no	—
121	#500	—	83	1	no	—
122	#478	—	83	2	no	—
123	#477	—	83	2	no	—
124	#475	—	83	1	no	—
125	#474	D₈₃	1	1	yes	characteristic
126	#446	—	83	1	no	—
127	#440	—	83	2	no	—
128	C₄×SD₁₆	—	83	1	no	—
129	C₂²×Q₈	—	166	1	no	—
130	C₂×SD₁₆	—	83	1	no	—
131	C₄⋊Q₈	—	83	2	no	—
132	C₄⋊Q₈	—	83	1	no	—
133	C₄⋊Q₈	—	166	1	no	—
134	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
135	#125	—	83	2	no	—
136	#125	—	166	2	no	—
137	C₂²⋊Q₈	—	166	2	no	—
138	C₂²⋊Q₈	—	166	1	no	—
139	C₄×Q₈	—	83	1	no	—
140	C₄×Q₈	—	83	2	no	—
141	C₄×Q₈	—	83	1	no	—
142	C₄×Q₈	—	166	1	no	—
143	C₄×D₄	—	83	2	no	—
144	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
145	#107	—	83	2	no	—
146	#107	—	83	2	no	—
147	#107	C₂×D₈₃	1	2	yes	—
148	#106	—	83	2	no	—
149	#106	—	83	1	no	—
150	C₄⋊C₈	—	83	2	no	—
151	C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
152	#103	—	83	2	no	—
153	#103	—	83	1	no	—
154	#102	—	83	1	no	—
155	#102	C₂×D₈₃	1	2	yes	—
156	#97	—	83	2	no	—
157	C₄×C₈	—	83	1	no	—
158	C₂×Q₈	—	2	1	no	—
159	C₂×Q₈	—	332	4	no	—
160	C₂×Q₈	—	83	1	no	—
161	C₂×Q₈	—	83	1	no	—
162	C₂×Q₈	—	166	2	no	—
163	C₂×Q₈	—	166	1	no	—
164	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	—	166	2	no	—
167	SD₁₆	—	83	4	no	—
168	C₂×C₈	—	83	1	no	—
169	C₂×C₈	—	83	1	no	—
170	C₂×C₈	C₂²×D₈₃	1	2	yes	—
171	C₄⋊C₄	—	2	1	no	—
172	C₄⋊C₄	—	83	1	no	—
173	C₄⋊C₄	—	83	2	no	—
174	C₄⋊C₄	—	83	1	no	—
175	C₄⋊C₄	—	83	2	no	—
176	C₄⋊C₄	—	166	2	no	—
177	C₄⋊C₄	—	166	2	no	—
178	C₄⋊C₄	—	166	2	no	—
179	C₄⋊C₄	—	166	2	no	—
180	C₄⋊C₄	—	166	1	no	—
181	C₄⋊C₄	—	166	1	no	—
182	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
183	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
184	C₂²⋊C₄	—	2	1	no	—
185	C₂²⋊C₄	—	166	2	no	—
186	C₄²	—	83	2	no	—
187	C₄²	—	166	2	no	—
188	C₄²	—	166	1	no	—
189	C₄²	C₂²×D₈₃	1	1	yes	characteristic
190	C₂³	—	2	1	no	—
191	Q₈	—	4	2	no	—
192	Q₈	—	332	4	no	—
193	Q₈	—	332	2	no	—
194	Q₈	—	83	2	no	—
195	Q₈	—	166	2	no	—
196	Q₈	—	166	1	no	—
197	D₄	—	2	1	no	—
198	D₄	Q₈×D₈₃	1	2	yes	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	332	4	no	—
203	C₂×C₄	—	83	2	no	—
204	C₂×C₄	—	83	2	no	—
205	C₂×C₄	—	166	1	no	—
206	C₂×C₄	—	166	2	no	—
207	C₂×C₄	—	166	1	no	—
208	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
209	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
210	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
211	C₈	—	2	2	no	—
212	C₈	—	83	2	no	—
213	C₈	—	166	1	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	4	1	no	—
216	C₂²	—	4	1	no	—
217	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
218	C₄	—	2	1	no	—
219	C₄	—	4	1	no	—
220	C₄	—	4	2	no	—
221	C₄	—	332	2	no	—
222	C₄	—	332	1	no	—
223	C₄	—	166	2	no	—
224	C₄	—	166	2	no	—
225	C₄	—	166	2	no	—
226	C₄	#14581816	1	2	yes	—
227	C₄	C₂×Q₈×D₈₃	1	1	yes	characteristic
228	C₄	#14581839	1	1	yes	characteristic
229	C₂	—	4	2	no	—
230	C₂	#19128364	1	1	yes	characteristic
231	C₂	C₂×#14581816	1	1	yes	characteristic
232	C₂	#19128517	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19128426

C₂

yes

maximal, characteristic, complemented

D₄×Dic₁₆₆

C₂

yes

maximal, characteristic

#19128109

C₂

yes

maximal, complemented

#19128104

C₂

yes

maximal, characteristic, complemented

#19128003

C₂

yes

maximal

#19127995

C₂

yes

maximal, complemented

#19127987

C₂

yes

maximal, characteristic, complemented

#19127828

C₂

yes

maximal, characteristic, complemented

#19127798

C₂

yes

maximal

C₄×#13050578

C₂

yes

maximal, characteristic

#474×C₈₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₆₆

—

C₂×#13050578

C₂²

yes

characteristic

#14581792

C₂²

yes

characteristic

#14581791

C₂²

yes

—

#14581790

—

#14581783

C₂²

yes

—

#14581782

—

#14581771

—

#14581769

—

Q₈×Dic₈₃

—

C₄×Dic₁₆₆

C₂²

yes

characteristic

C₄×Dic₁₆₆

C₂²

yes

characteristic

#14581757

C₂²

yes

—

D₄×Dic₈₃

C₂²

yes

—

#14581725

C₂²

yes

—

#14581725

C₂²

yes

—

#14581724

C₂²

yes

—

#14581723

C₂²

yes

characteristic

Dic₈₃⋊C₈

C₂²

yes

—

#14581717

C₂²

yes

—

#14581715

C₂²

yes

characteristic

#14581713

C₂²

yes

characteristic

#14581702

C₂²

yes

—

C₄×C₈₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₈₃

C₂²

yes

characteristic

C₄×D₄×C₈₃

C₂²

yes

characteristic

#107×C₈₃

C₂²

yes

—

C₄⋊C₈×C₈₃

C₂²

yes

characteristic

#102×C₈₃

C₂²

yes

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

D₄

yes

characteristic

C₂×Dic₁₆₆

C₂³

yes

characteristic

C₂²×Dic₈₃

—

#13050578

Q₈

yes

complemented

C₂×C₈₃⋊C₈

C₂³

yes

characteristic

C₂×C₈₃⋊C₈

C₂³

yes

characteristic

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

D₄

yes

characteristic

C₄⋊Dic₈₃

C₂³

yes

characteristic

C₄⋊Dic₈₃

C₂³

yes

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

D₄

yes

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

C₂³

yes

—

C₂×Q₈×C₈₃

—

C₂×D₄×C₈₃

C₂³

yes

characteristic

C₂²×C₄×C₈₃

—

C₂×C₈×C₈₃

C₂³

yes

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

C₂³

yes

—

C₄⋊C₄×C₈₃

C₂³

yes

characteristic

C₂²⋊C₄×C₈₃

—

C₄²×C₈₃

C₂³

yes

characteristic

C₂³×C₈₃

—

Q₈×C₈₃

—

D₄×C₈₃

—

D₄×C₈₃

C₂×Q₈

yes

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂×C₄×C₈₃

C₂⁴

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

C₂×D₄

yes

—

C₂×Dic₈₃

C₂×D₄

yes

—

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

C₂×Q₈

yes

complemented

C₈×C₈₃

—

C₈₃⋊C₈

—

C₈₃⋊C₈

C₂×Q₈

yes

complemented

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

100

C₂²×C₈₃

C₂²×D₄

yes

characteristic

101

C₄×C₈₃

—

102

C₄×C₈₃

—

103

C₄×C₈₃

—

104

C₄×C₈₃

AGL(1,ℤ/8)

yes

—

105

C₄×C₈₃

C₂²×Q₈

yes

characteristic

106

C₄×C₈₃

2₋¹⁺⁴

yes

characteristic

107

Dic₈₃

—

108

Dic₈₃

—

109

Dic₈₃

—

110

Dic₈₃

—

111

Dic₈₃

—

112

C₂×C₈₃

—

113

C₂×C₈₃

D₄×Q₈

yes

characteristic

114

C₂×C₈₃

C₂×AGL(1,ℤ/8)

yes

characteristic

115

C₂×C₈₃

yes

116

—

117

C₈₃

#3386

yes

characteristic, complemented, Sylow

118

#557

—

119

D₄×Q₈

—

120

#501

—

121

#500

—

122

#478

—

123

#477

—

124

#475

—

125

#474

D₈₃

yes

characteristic

126

#446

—

127

#440

—

128

C₄×SD₁₆

—

129

C₂²×Q₈

—

166

—

130

C₂×SD₁₆

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

133

C₄⋊Q₈

—

166

—

134

C₄⋊Q₈

C₂×D₈₃

yes

characteristic

135

#125

—

136

#125

—

166

—

137

C₂²⋊Q₈

—

166

—

138

C₂²⋊Q₈

—

166

—

139

C₄×Q₈

—

140

C₄×Q₈

—

141

C₄×Q₈

—

142

C₄×Q₈

—

166

—

143

C₄×D₄

—

144

C₄×D₄

C₂×D₈₃

yes

characteristic

145

#107

—

146

#107

—

147

#107

C₂×D₈₃

yes

—

148

#106

—

149

#106

—

150

C₄⋊C₈

—

151

C₄⋊C₈

C₂×D₈₃

yes

characteristic

152

#103

—

153

#103

—

154

#102

—

155

#102

C₂×D₈₃

yes

—

156

#97

—

157

C₄×C₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

332

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

166

—

163

C₂×Q₈

—

166

—

164

C₂×D₄

C₂²×D₈₃

yes

characteristic

165

C₂²×C₄

—

166

C₂²×C₄

—

166

—

167

SD₁₆

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

C₂²×D₈₃

yes

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

166

—

177

C₄⋊C₄

—

166

—

178

C₄⋊C₄

—

166

—

179

C₄⋊C₄

—

166

—

180

C₄⋊C₄

—

166

—

181

C₄⋊C₄

—

166

—

182

C₄⋊C₄

C₂²×D₈₃

yes

—

183

C₄⋊C₄

C₂²×D₈₃

yes

characteristic

184

C₂²⋊C₄

—

185

C₂²⋊C₄

—

166

—

186

C₄²

—

187

C₄²

—

166

—

188

C₄²

—

166

—

189

C₄²

C₂²×D₈₃

yes

characteristic

190

C₂³

—

191

Q₈

—

192

Q₈

—

332

—

193

Q₈

—

332

—

194

Q₈

—

195

Q₈

—

166

—

196

Q₈

—

166

—

197

D₄

—

198

D₄

Q₈×D₈₃

yes

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

332

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

166

—

206

C₂×C₄

—

166

—

207

C₂×C₄

—

166

—

208

C₂×C₄

D₄×D₈₃

yes

characteristic

209

C₂×C₄

D₄×D₈₃

yes

characteristic

210

C₂×C₄

C₂³×D₈₃

yes

characteristic

211

C₈

—

212

C₈

—

213

C₈

—

166

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₂×D₄×D₈₃

yes

characteristic

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

332

—

222

C₄

—

332

—

223

C₄

—

166

—

224

C₄

—

166

—

225

C₄

—

166

—

226

C₄

#14581816

yes

—

227

C₄

C₂×Q₈×D₈₃

yes

characteristic

228

C₄

#14581839

yes

characteristic

229

C₂

—

230

C₂

#19128364

yes

characteristic

231

C₂

C₂×#14581816

yes

characteristic

232

C₂

#19128517

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	#474×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
prime radical	C₂×D₄×C₈₃	C₂³
hypercenter	#474	D₈₃
hypocenter	C₈₃	#3386
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #474

subgroup

G/H

center

C₂²

C₂×D₄×D₈₃

commutator, cosocle

C₂×C₄×C₈₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₃

Fitting

#474×C₈₃

C₂

socle

C₂²×C₈₃

C₂²×D₄

prime radical

C₂×D₄×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #474

N	H ≅ G/N	type
1. #19128426	C₂	semidirect
3. #19128109	C₂	semidirect
4. #19128104	C₂	semidirect
6. #19127995	C₂	semidirect
7. #19127987	C₂	semidirect
8. #19127828	C₂	semidirect
47. #13050578	Q₈	semidirect
93. Dic₁₆₆	C₂×Q₈	semidirect
96. C₈₃⋊C₈	C₂×Q₈	semidirect
117. C₈₃	#3386	semidirect

H ≅ G/N

type

1. #19128426

C₂

semidirect

3. #19128109

C₂

semidirect

4. #19128104

C₂

semidirect

6. #19127995

C₂

semidirect

7. #19127987

C₂

semidirect

8. #19127828

C₂

semidirect

47. #13050578

Q₈

semidirect

93. Dic₁₆₆

C₂×Q₈

semidirect

96. C₈₃⋊C₈

C₂×Q₈

semidirect

117. C₈₃

#3386

semidirect

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

subgroup	index
#19128426	2
D₄×Dic₁₆₆	2
#19128109	2
#19128104	2
#19128003	2
#19127995	2
#19127987	2
#19127828	2
#19127798	2
C₄×#13050578	2
#474×C₈₃	2
#3386	83

subgroup

index

D₄×Dic₁₆₆

#474×C₈₃

Subgroups — #24920388

Conjugacy classes of subgroups

Complements

Maximal subgroups