Group #24920371 — subgroups

Subgroups — #24920371

Order 10624.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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	Q₈×Dic₁₆₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#19128408	C₂	1	1	yes	maximal, characteristic
3	#19128108	C₂	1	2	yes	maximal, complemented
4	#19128106	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128010	C₂	1	2	yes	maximal, complemented
6	#19127996	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127991	C₂	1	1	yes	maximal, characteristic
8	#19127979	C₂	1	2	yes	maximal
9	#19127831	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127802	C₂	1	2	yes	maximal
11	C₄×SD₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
12	#14581792	—	2	1	no	—
13	#14581792	C₂²	1	1	yes	characteristic
14	#14581792	C₂²	1	1	yes	characteristic
15	#14581791	—	2	2	no	—
16	#14581791	C₂²	1	2	yes	—
17	#14581783	C₂²	1	2	yes	—
18	#14581771	—	2	1	no	—
19	#14581769	—	2	2	no	—
20	Q₈×Dic₈₃	C₂²	1	2	yes	—
21	C₄×Dic₁₆₆	—	2	1	no	—
22	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
23	D₄×Dic₈₃	C₂²	1	2	yes	—
24	C₂×C₄⋊Dic₈₃	—	2	1	no	—
25	#14581726	C₂²	1	2	yes	—
26	#14581726	C₂²	1	2	yes	—
27	#14581725	C₂²	1	2	yes	—
28	#14581723	C₂²	1	2	yes	—
29	C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
30	Dic₈₃⋊C₈	C₂²	1	2	yes	—
31	#14581716	C₂²	1	2	yes	—
32	#14581713	C₂²	1	2	yes	—
33	#14581702	C₂²	1	2	yes	—
34	C₂×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
37	#106×C₈₃	C₂²	1	1	yes	characteristic
38	#103×C₈₃	C₂²	1	1	yes	characteristic
39	#102×C₈₃	C₂²	1	1	yes	characteristic
40	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₆₆	—	2	1	no	—
42	C₂×Dic₁₆₆	—	2	1	no	—
43	C₂×Dic₁₆₆	—	2	2	no	—
44	C₂×Dic₁₆₆	D₄	1	1	yes	characteristic
45	C₂²×Dic₈₃	—	2	2	no	—
46	C₂×C₈₃⋊C₈	C₂³	1	2	yes	—
47	C₄⋊Dic₈₃	—	2	1	no	—
48	C₄⋊Dic₈₃	—	2	1	no	—
49	C₄⋊Dic₈₃	—	2	2	no	—
50	C₄⋊Dic₈₃	—	2	2	no	—
51	C₄⋊Dic₈₃	D₄	1	1	yes	characteristic
52	C₄⋊Dic₈₃	C₂³	1	2	yes	—
53	C₄⋊Dic₈₃	C₂³	1	2	yes	—
54	Dic₈₃⋊C₄	—	2	2	no	—
55	Dic₈₃⋊C₄	—	2	2	no	—
56	Dic₈₃⋊C₄	D₄	1	2	yes	—
57	C₂²⋊Dic₈₃	—	2	2	no	—
58	C₄×Dic₈₃	—	2	2	no	—
59	C₄×Dic₈₃	C₂³	1	2	yes	—
60	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
61	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₈₃	—	2	1	no	—
63	SD₁₆×C₈₃	Q₈	1	4	yes	complemented
64	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
65	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×C₈₃	—	2	1	no	—
67	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
68	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
69	C₂²⋊C₄×C₈₃	—	2	1	no	—
70	C₄²×C₈₃	—	2	1	no	—
71	C₄²×C₈₃	C₂³	1	1	yes	characteristic
72	C₂³×C₈₃	—	2	1	no	—
73	Q₈×C₈₃	—	2	1	no	—
74	Q₈×C₈₃	C₂×Q₈	1	2	yes	—
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	1	no	—
79	C₂×C₄×C₈₃	—	2	1	no	—
80	C₂×C₄×C₈₃	—	4	2	no	—
81	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
84	C₂×Dic₈₃	—	2	2	no	—
85	C₂×Dic₈₃	—	2	2	no	—
86	C₂×Dic₈₃	—	8	2	no	—
87	C₂×Dic₈₃	C₂×D₄	1	2	yes	—
88	C₂×Dic₈₃	C₂×D₄	1	2	yes	—
89	Dic₁₆₆	—	2	2	no	—
90	Dic₁₆₆	—	8	2	no	—
91	Dic₁₆₆	—	8	1	no	—
92	Dic₁₆₆	—	8	1	no	—
93	C₈×C₈₃	—	2	1	no	—
94	C₈×C₈₃	C₂×Q₈	1	2	yes	—
95	C₈₃⋊C₈	—	2	2	no	—
96	C₂²×C₈₃	—	2	2	no	—
97	C₂²×C₈₃	—	4	1	no	—
98	C₂²×C₈₃	—	4	1	no	—
99	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
100	C₄×C₈₃	—	2	2	no	—
101	C₄×C₈₃	—	2	1	no	—
102	C₄×C₈₃	—	4	1	no	—
103	C₄×C₈₃	—	4	1	no	—
104	C₄×C₈₃	#137	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	—	4	2	no	—
110	Dic₈₃	—	4	2	no	—
111	C₂×C₈₃	—	4	2	no	—
112	C₂×C₈₃	D₄×Q₈	1	1	yes	characteristic
113	C₂×C₈₃	C₂×#137	1	1	yes	characteristic
114	C₂×C₈₃	#576	1	1	yes	characteristic
115	#3385	—	83	1	no	maximal, Sylow
116	C₈₃	#3385	1	1	yes	characteristic, complemented, Sylow
117	Q₈²	—	83	1	no	—
118	#554	—	83	1	no	—
119	#501	—	83	2	no	—
120	#500	—	83	1	no	—
121	#479	—	83	2	no	—
122	#477	—	83	1	no	—
123	#476	—	83	1	no	—
124	#474	—	83	2	no	—
125	#446	—	83	1	no	—
126	#440	—	83	2	no	—
127	C₄×SD₁₆	D₈₃	1	1	yes	characteristic
128	C₂×SD₁₆	C₂×D₈₃	1	1	yes	characteristic
129	C₄⋊Q₈	—	83	2	no	—
130	C₄⋊Q₈	—	83	1	no	—
131	C₄⋊Q₈	—	83	1	no	—
132	C₄⋊Q₈	—	166	1	no	—
133	C₄⋊Q₈	—	166	2	no	—
134	#125	—	83	2	no	—
135	C₂²⋊Q₈	—	166	2	no	—
136	C₂²⋊Q₈	—	166	1	no	—
137	C₄×Q₈	—	83	1	no	—
138	C₄×Q₈	—	83	2	no	—
139	C₄×Q₈	—	166	1	no	—
140	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
141	C₄×D₄	—	83	2	no	—
142	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
143	C₂×C₄⋊C₄	—	166	1	no	—
144	#107	—	83	2	no	—
145	#107	—	83	2	no	—
146	#107	—	83	2	no	—
147	#106	—	83	2	no	—
148	#106	C₂×D₈₃	1	1	yes	characteristic
149	C₄⋊C₈	—	83	2	no	—
150	C₄⋊C₈	—	83	1	no	—
151	#103	—	83	2	no	—
152	#103	C₂×D₈₃	1	1	yes	characteristic
153	#102	—	83	2	no	—
154	#102	C₂×D₈₃	1	1	yes	characteristic
155	#97	—	83	2	no	—
156	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
157	C₂×Q₈	—	83	1	no	—
158	C₂×Q₈	—	166	2	no	—
159	C₂×Q₈	—	166	1	no	—
160	C₂×Q₈	—	166	1	no	—
161	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
162	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	166	2	no	—
165	SD₁₆	Dic₁₆₆	1	4	yes	complemented
166	C₂×C₈	—	83	2	no	—
167	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
168	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
169	C₄⋊C₄	—	2	1	no	—
170	C₄⋊C₄	—	83	1	no	—
171	C₄⋊C₄	—	83	2	no	—
172	C₄⋊C₄	—	83	2	no	—
173	C₄⋊C₄	—	83	2	no	—
174	C₄⋊C₄	—	166	2	no	—
175	C₄⋊C₄	—	166	2	no	—
176	C₄⋊C₄	—	166	2	no	—
177	C₄⋊C₄	—	166	2	no	—
178	C₄⋊C₄	—	166	1	no	—
179	C₄⋊C₄	—	166	1	no	—
180	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
181	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
182	C₂²⋊C₄	—	2	1	no	—
183	C₂²⋊C₄	—	166	2	no	—
184	C₄²	—	2	1	no	—
185	C₄²	—	83	2	no	—
186	C₄²	—	166	2	no	—
187	C₄²	C₂²×D₈₃	1	1	yes	characteristic
188	C₂³	—	2	1	no	—
189	Q₈	—	2	1	no	—
190	Q₈	—	664	1	no	—
191	Q₈	—	664	1	no	—
192	Q₈	—	664	2	no	—
193	Q₈	—	166	2	no	—
194	Q₈	C₂×Dic₁₆₆	1	2	yes	—
195	D₄	—	2	1	no	—
196	D₄	C₂×Dic₁₆₆	1	2	yes	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	83	2	no	—
202	C₂×C₄	—	83	2	no	—
203	C₂×C₄	—	664	2	no	—
204	C₂×C₄	—	166	2	no	—
205	C₂×C₄	—	166	2	no	—
206	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
207	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
208	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	166	2	no	—
211	C₈	C₂×Dic₁₆₆	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	4	1	no	—
214	C₂²	—	4	1	no	—
215	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	2	1	no	—
218	C₄	—	4	1	no	—
219	C₄	—	4	1	no	—
220	C₄	—	332	2	no	—
221	C₄	—	332	2	no	—
222	C₄	—	166	2	no	—
223	C₄	—	166	2	no	—
224	C₄	#14581821	1	2	yes	—
225	C₄	C₂²×Dic₁₆₆	1	1	yes	characteristic
226	C₄	#14581839	1	1	yes	characteristic
227	C₂	—	4	2	no	—
228	C₂	D₄×Dic₁₆₆	1	1	yes	characteristic
229	C₂	C₂×#14581821	1	1	yes	characteristic
230	C₂	#19128503	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×Dic₁₆₆

C₂

yes

maximal, characteristic, complemented

#19128408

C₂

yes

maximal, characteristic

#19128108

C₂

yes

maximal, complemented

#19128106

C₂

yes

maximal, characteristic, complemented

#19128010

C₂

yes

maximal, complemented

#19127996

C₂

yes

maximal, characteristic, complemented

#19127991

C₂

yes

maximal, characteristic

#19127979

C₂

yes

maximal

#19127831

C₂

yes

maximal, characteristic, complemented

#19127802

C₂

yes

maximal

C₄×SD₁₆×C₈₃

C₂

yes

maximal, characteristic

#14581792

—

#14581792

C₂²

yes

characteristic

#14581792

C₂²

yes

characteristic

#14581791

—

#14581791

C₂²

yes

—

#14581783

C₂²

yes

—

#14581771

—

#14581769

—

Q₈×Dic₈₃

C₂²

yes

—

C₄×Dic₁₆₆

—

C₄×Dic₁₆₆

C₂²

yes

characteristic

D₄×Dic₈₃

C₂²

yes

—

C₂×C₄⋊Dic₈₃

—

#14581726

C₂²

yes

—

#14581726

C₂²

yes

—

#14581725

C₂²

yes

—

#14581723

C₂²

yes

—

C₄⋊(C₈₃⋊C₈)

C₂²

yes

characteristic

Dic₈₃⋊C₈

C₂²

yes

—

#14581716

C₂²

yes

—

#14581713

C₂²

yes

—

#14581702

C₂²

yes

—

C₂×SD₁₆×C₈₃

C₂²

yes

characteristic

C₄×Q₈×C₈₃

C₂²

yes

characteristic

C₄×D₄×C₈₃

C₂²

yes

characteristic

#106×C₈₃

C₂²

yes

characteristic

#103×C₈₃

C₂²

yes

characteristic

#102×C₈₃

C₂²

yes

characteristic

C₄×C₈×C₈₃

C₂²

yes

characteristic

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

D₄

yes

characteristic

C₂²×Dic₈₃

—

C₂×C₈₃⋊C₈

C₂³

yes

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

D₄

yes

characteristic

C₄⋊Dic₈₃

C₂³

yes

—

C₄⋊Dic₈₃

C₂³

yes

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

D₄

yes

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

C₂³

yes

—

C₂×Q₈×C₈₃

C₂³

yes

characteristic

C₂×D₄×C₈₃

C₂³

yes

characteristic

C₂²×C₄×C₈₃

—

SD₁₆×C₈₃

Q₈

yes

complemented

C₂×C₈×C₈₃

C₂³

yes

characteristic

C₂×C₈×C₈₃

C₂³

yes

characteristic

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

C₂³

yes

characteristic

C₄⋊C₄×C₈₃

C₂³

yes

characteristic

C₂²⋊C₄×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

C₂³

yes

characteristic

C₂³×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

C₂×Q₈

yes

—

D₄×C₈₃

—

D₄×C₈₃

C₂×Q₈

yes

—

C₂×C₄×C₈₃

—

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×D₄

yes

—

C₂×Dic₈₃

C₂×D₄

yes

—

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

—

C₈×C₈₃

—

C₈×C₈₃

C₂×Q₈

yes

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

C₂²×D₄

yes

characteristic

100

C₄×C₈₃

—

101

C₄×C₈₃

—

102

C₄×C₈₃

—

103

C₄×C₈₃

—

104

C₄×C₈₃

#137

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

C₂×C₈₃

—

112

C₂×C₈₃

D₄×Q₈

yes

characteristic

113

C₂×C₈₃

C₂×#137

yes

characteristic

114

C₂×C₈₃

yes

115

—

116

C₈₃

#3385

yes

characteristic, complemented, Sylow

117

Q₈²

—

118

#554

—

119

#501

—

120

#500

—

121

#479

—

122

#477

—

123

#476

—

124

#474

—

125

#446

—

126

#440

—

127

C₄×SD₁₆

D₈₃

yes

characteristic

128

C₂×SD₁₆

C₂×D₈₃

yes

characteristic

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

166

—

133

C₄⋊Q₈

—

166

—

134

#125

—

135

C₂²⋊Q₈

—

166

—

136

C₂²⋊Q₈

—

166

—

137

C₄×Q₈

—

138

C₄×Q₈

—

139

C₄×Q₈

—

166

—

140

C₄×Q₈

C₂×D₈₃

yes

characteristic

141

C₄×D₄

—

142

C₄×D₄

C₂×D₈₃

yes

characteristic

143

C₂×C₄⋊C₄

—

166

—

144

#107

—

145

#107

—

146

#107

—

147

#106

—

148

#106

C₂×D₈₃

yes

characteristic

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

#103

—

152

#103

C₂×D₈₃

yes

characteristic

153

#102

—

154

#102

C₂×D₈₃

yes

characteristic

155

#97

—

156

C₄×C₈

C₂×D₈₃

yes

characteristic

157

C₂×Q₈

—

158

C₂×Q₈

—

166

—

159

C₂×Q₈

—

166

—

160

C₂×Q₈

—

166

—

161

C₂×Q₈

C₂²×D₈₃

yes

characteristic

162

C₂×D₄

C₂²×D₈₃

yes

characteristic

163

C₂²×C₄

—

164

C₂²×C₄

—

166

—

165

SD₁₆

Dic₁₆₆

yes

complemented

166

C₂×C₈

—

167

C₂×C₈

C₂²×D₈₃

yes

characteristic

168

C₂×C₈

C₂²×D₈₃

yes

characteristic

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

166

—

175

C₄⋊C₄

—

166

—

176

C₄⋊C₄

—

166

—

177

C₄⋊C₄

—

166

—

178

C₄⋊C₄

—

166

—

179

C₄⋊C₄

—

166

—

180

C₄⋊C₄

C₂²×D₈₃

yes

characteristic

181

C₄⋊C₄

C₂²×D₈₃

yes

characteristic

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

166

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

166

—

187

C₄²

C₂²×D₈₃

yes

characteristic

188

C₂³

—

189

Q₈

—

190

Q₈

—

664

—

191

Q₈

—

664

—

192

Q₈

—

664

—

193

Q₈

—

166

—

194

Q₈

C₂×Dic₁₆₆

yes

—

195

D₄

—

196

D₄

C₂×Dic₁₆₆

yes

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

664

—

204

C₂×C₄

—

166

—

205

C₂×C₄

—

166

—

206

C₂×C₄

D₄×D₈₃

yes

characteristic

207

C₂×C₄

D₄×D₈₃

yes

characteristic

208

C₂×C₄

C₂³×D₈₃

yes

characteristic

209

C₈

—

210

C₈

—

166

—

211

C₈

C₂×Dic₁₆₆

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

C₂×D₄×D₈₃

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

332

—

221

C₄

—

332

—

222

C₄

—

166

—

223

C₄

—

166

—

224

C₄

#14581821

yes

—

225

C₄

C₂²×Dic₁₆₆

yes

characteristic

226

C₄

#14581839

yes

characteristic

227

C₂

—

228

C₂

D₄×Dic₁₆₆

yes

characteristic

229

C₂

C₂×#14581821

yes

characteristic

230

C₂

#19128503

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	C₄×SD₁₆×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
prime radical	C₂×D₄×C₈₃	C₂³
hypercenter	C₄×SD₁₆	D₈₃
hypocenter	C₈₃	#3385
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

subgroup

G/H

center

C₂²

C₂×D₄×D₈₃

commutator, cosocle

C₂×C₄×C₈₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₃

Fitting

C₄×SD₁₆×C₈₃

C₂

socle

C₂²×C₈₃

C₂²×D₄

prime radical

C₂×D₄×C₈₃

C₂³

hypercenter

C₄×SD₁₆

D₈₃

hypocenter

C₈₃

#3385

LCS

G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

N	H ≅ G/N	type
1. Q₈×Dic₁₆₆	C₂	semidirect
3. #19128108	C₂	semidirect
4. #19128106	C₂	semidirect
5. #19128010	C₂	semidirect
6. #19127996	C₂	semidirect
9. #19127831	C₂	semidirect
63. SD₁₆×C₈₃	Q₈	semidirect
116. C₈₃	#3385	semidirect
165. SD₁₆	Dic₁₆₆	semidirect

H ≅ G/N

type

1. Q₈×Dic₁₆₆

C₂

semidirect

3. #19128108

C₂

semidirect

4. #19128106

C₂

semidirect

5. #19128010

C₂

semidirect

6. #19127996

C₂

semidirect

9. #19127831

C₂

semidirect

63. SD₁₆×C₈₃

Q₈

semidirect

116. C₈₃

#3385

semidirect

165. SD₁₆

Dic₁₆₆

semidirect

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

subgroup	index
Q₈×Dic₁₆₆	2
#19128408	2
#19128108	2
#19128106	2
#19128010	2
#19127996	2
#19127991	2
#19127979	2
#19127831	2
#19127802	2
C₄×SD₁₆×C₈₃	2
#3385	83

subgroup

index

Q₈×Dic₁₆₆

C₄×SD₁₆×C₈₃

Subgroups — #24920371

Conjugacy classes of subgroups

Complements

Maximal subgroups