Group #35309536 — subgroups

Subgroups — #35309536

Order 21248.

264 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 87 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	#24908184	C₂	1	1	yes	maximal, characteristic
2	#24907637	C₂	1	1	yes	maximal, characteristic
3	#24905365	C₂	1	1	yes	maximal, characteristic
4	#24905364	C₂	1	1	yes	maximal, characteristic
5	#24905360	C₂	1	1	yes	maximal, characteristic
6	#24905293	C₂	1	1	yes	maximal, characteristic
7	C₈₃×#1301	C₂	1	1	yes	maximal, characteristic
8	#19127754	C₂²	1	1	yes	characteristic
9	C₂×#14581727	—	2	1	no	—
10	C₂×#14581727	—	2	1	no	—
11	#19127725	C₂²	1	1	yes	characteristic
12	C₂×Dic₈₃⋊C₈	—	2	1	no	—
13	C₂×#14581703	C₂²	1	1	yes	characteristic
14	C₄×C₄⋊Dic₈₃	C₂²	1	1	yes	characteristic
15	#19127455	—	2	1	no	—
16	#431×C₈₃	C₂²	1	1	yes	characteristic
17	#423×C₈₃	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
19	C₂×#13050574	—	2	1	no	—
20	C₂²×C₈₃⋊C₈	D₄	1	1	yes	characteristic
21	C₂²×C₈₃⋊C₈	D₄	1	1	yes	characteristic
22	C₂×C₄⋊Dic₈₃	—	2	1	no	—
23	C₂×C₄×Dic₈₃	—	2	1	no	—
24	#14581727	—	4	2	no	—
25	#14581727	—	4	2	no	—
26	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
27	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
28	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
29	Dic₈₃⋊C₈	—	4	2	no	—
30	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
31	#14581703	—	2	1	no	—
32	#14581703	—	2	1	no	—
33	C₄×C₈₃⋊C₈	—	2	1	no	—
34	C₈₃⋊#95	Q₈	1	1	yes	characteristic
35	C₈₃⋊#95	Q₈	1	1	yes	characteristic
36	C₂×M₁₆×C₈₃	—	2	1	no	—
37	C₂²×C₈×C₈₃	—	2	1	no	—
38	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
39	C₄⋊C₈×C₈₃	—	2	1	no	—
40	C₄⋊C₈×C₈₃	—	2	1	no	—
41	C₄⋊C₈×C₈₃	—	2	1	no	—
42	C₄⋊C₈×C₈₃	—	2	1	no	—
43	C₄⋊C₈×C₈₃	—	2	1	no	—
44	C₂²⋊C₈×C₈₃	—	2	1	no	—
45	C₄×C₈×C₈₃	—	2	1	no	—
46	C₂²×Dic₈₃	—	2	1	no	—
47	C₂²×Dic₈₃	—	2	1	no	—
48	#13050574	—	4	1	no	—
49	#13050574	—	4	1	no	—
50	C₂×C₈₃⋊C₈	—	2	1	no	—
51	C₂×C₈₃⋊C₈	—	2	1	no	—
52	C₂×C₈₃⋊C₈	—	2	1	no	—
53	C₂×C₈₃⋊C₈	—	2	1	no	—
54	C₂×C₈₃⋊C₈	—	4	1	no	—
55	C₂×C₈₃⋊C₈	—	4	1	no	—
56	C₂×C₈₃⋊C₈	SD₁₆	1	2	yes	—
57	C₂×C₈₃⋊C₈	Q₁₆	1	2	yes	—
58	C₄⋊Dic₈₃	—	4	2	no	—
59	C₄×Dic₈₃	—	4	1	no	—
60	C₄×Dic₈₃	—	4	1	no	—
61	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
63	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
64	M₁₆×C₈₃	—	4	1	no	—
65	M₁₆×C₈₃	—	4	1	no	—
66	C₂×C₈×C₈₃	—	4	1	no	—
67	C₂×C₈×C₈₃	—	4	1	no	—
68	C₂×C₈×C₈₃	—	4	1	no	—
69	C₂×C₈×C₈₃	—	4	1	no	—
70	C₂×C₈×C₈₃	—	4	1	no	—
71	C₄²×C₈₃	#41	1	1	yes	characteristic
72	C₄²×C₈₃	#41	1	1	yes	characteristic
73	C₄²×C₈₃	#41	1	1	yes	characteristic
74	C₄²×C₈₃	#41	1	1	yes	characteristic
75	C₂³×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
76	C₂×C₄×C₈₃	—	4	1	no	—
77	C₂×C₄×C₈₃	—	4	1	no	—
78	C₂×C₄×C₈₃	#123	1	1	yes	characteristic
79	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
80	C₂×C₄×C₈₃	#125	1	1	yes	characteristic
81	C₂×C₄×C₈₃	#125	1	1	yes	characteristic
82	C₂×C₄×C₈₃	#126	1	1	yes	characteristic
83	C₂×C₄×C₈₃	#126	1	1	yes	characteristic
84	C₂×C₄×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
85	C₂×C₄×C₈₃	C₂×Q₁₆	1	1	yes	characteristic
86	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
87	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×Dic₈₃	—	2	2	no	—
89	C₂×Dic₈₃	—	4	1	no	—
90	C₂×Dic₈₃	—	4	1	no	—
91	C₂×Dic₈₃	—	4	1	no	—
92	C₂×Dic₈₃	—	4	1	no	—
93	C₂×Dic₈₃	—	4	1	no	—
94	C₈×C₈₃	—	8	1	no	—
95	C₈×C₈₃	—	8	1	no	—
96	C₈×C₈₃	—	8	1	no	—
97	C₈₃⋊C₈	—	2	2	no	—
98	C₈₃⋊C₈	—	2	2	no	—
99	C₈₃⋊C₈	—	8	1	no	—
100	C₈₃⋊C₈	—	8	1	no	—
101	C₂²×C₈₃	—	2	1	no	—
102	C₂²×C₈₃	—	2	1	no	—
103	C₂²×C₈₃	#400	1	1	yes	characteristic
104	C₂²×C₈₃	#476	1	1	yes	characteristic
105	C₂²×C₈₃	#477	1	1	yes	characteristic
106	C₄×C₈₃	—	2	1	no	—
107	C₄×C₈₃	—	2	1	no	—
108	C₄×C₈₃	—	2	1	no	—
109	C₄×C₈₃	—	2	1	no	—
110	C₄×C₈₃	#481	1	1	yes	characteristic
111	C₄×C₈₃	#484	1	1	yes	characteristic
112	C₄×C₈₃	#487	1	1	yes	characteristic
113	C₄×C₈₃	#490	1	1	yes	characteristic
114	Dic₈₃	—	4	2	no	—
115	Dic₈₃	—	8	1	no	—
116	#10688	—	83	1	no	maximal, Sylow
117	C₂×C₈₃	—	2	1	no	—
118	C₂×C₈₃	—	2	1	no	—
119	C₂×C₈₃	#2100	1	1	yes	characteristic
120	C₂×C₈₃	#2102	1	1	yes	characteristic
121	C₂×C₈₃	#2103	1	1	yes	characteristic
122	#1940	—	83	1	no	—
123	#1849	—	83	1	no	—
124	#1303	—	83	1	no	—
125	#1303	—	83	1	no	—
126	#1301	—	83	1	no	—
127	#1301	D₈₃	1	1	yes	characteristic
128	#1275	—	83	1	no	—
129	C₈₃	#10688	1	1	yes	characteristic, complemented, Sylow
130	#431	—	83	1	no	—
131	#431	C₂×D₈₃	1	1	yes	characteristic
132	C₂×#108	—	166	1	no	—
133	C₂×#108	—	166	1	no	—
134	#423	—	83	1	no	—
135	#423	C₂×D₈₃	1	1	yes	characteristic
136	C₂×C₄⋊C₈	—	166	1	no	—
137	C₂×C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
138	C₂×#97	—	83	1	no	—
139	C₄×C₄⋊C₄	—	83	1	no	—
140	#336	—	166	1	no	—
141	C₂×M₁₆	—	2	1	no	—
142	C₂×M₁₆	—	166	1	no	—
143	C₂²×C₈	—	2	1	no	—
144	C₂²×C₈	—	83	1	no	—
145	C₂²×C₈	—	83	1	no	—
146	C₂×C₄⋊C₄	—	166	1	no	—
147	C₂×C₄²	—	166	1	no	—
148	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
149	#108	—	332	2	no	—
150	#108	—	332	2	no	—
151	C₄⋊C₈	—	2	1	no	—
152	C₄⋊C₈	—	2	1	no	—
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	332	2	no	—
157	C₄⋊C₈	—	166	1	no	—
158	C₄⋊C₈	—	166	1	no	—
159	C₄⋊C₈	—	166	1	no	—
160	C₂²⋊C₈	—	2	1	no	—
161	C₂²⋊C₈	—	166	1	no	—
162	#97	—	166	1	no	—
163	#97	—	166	1	no	—
164	C₄×C₈	—	2	1	no	—
165	C₄×C₈	—	166	1	no	—
166	#95	—	83	1	no	—
167	#95	—	83	1	no	—
168	C₂²×C₄	—	166	1	no	—
169	C₂²×C₄	—	166	1	no	—
170	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
171	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
172	C₂²×C₄	#13050590	1	1	yes	characteristic
173	M₁₆	—	4	1	no	—
174	M₁₆	—	4	1	no	—
175	M₁₆	—	332	1	no	—
176	M₁₆	—	332	1	no	—
177	C₂×C₈	—	4	1	no	—
178	C₂×C₈	—	4	1	no	—
179	C₂×C₈	—	4	1	no	—
180	C₂×C₈	—	4	1	no	—
181	C₂×C₈	—	4	1	no	—
182	C₂×C₈	—	332	1	no	—
183	C₂×C₈	—	332	1	no	—
184	C₂×C₈	—	83	2	no	—
185	C₂×C₈	—	83	2	no	—
186	C₂×C₈	—	166	1	no	—
187	C₂×C₈	—	166	1	no	—
188	C₂×C₈	—	166	1	no	—
189	C₂×C₈	—	166	1	no	—
190	C₄⋊C₄	—	332	2	no	—
191	C₄²	—	332	1	no	—
192	C₄²	—	332	1	no	—
193	C₄²	#13050589	1	1	yes	characteristic
194	C₄²	#13050589	1	1	yes	characteristic
195	C₄²	#13050590	1	1	yes	characteristic
196	C₄²	#13050590	1	1	yes	characteristic
197	C₂³	#14581770	1	1	yes	characteristic
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	332	1	no	—
201	C₂×C₄	—	332	1	no	—
202	C₂×C₄	—	332	1	no	—
203	C₂×C₄	—	332	1	no	—
204	C₂×C₄	—	332	1	no	—
205	C₂×C₄	—	166	2	no	—
206	C₂×C₄	#14581774	1	1	yes	characteristic
207	C₂×C₄	#14581778	1	1	yes	characteristic
208	C₂×C₄	#14581782	1	1	yes	characteristic
209	C₂×C₄	#14581782	1	1	yes	characteristic
210	C₂×C₄	#14581785	1	1	yes	characteristic
211	C₂×C₄	#14581786	1	1	yes	characteristic
212	C₂×C₄	SD₁₆×D₈₃	1	1	yes	characteristic
213	C₂×C₄	Q₁₆×D₈₃	1	1	yes	characteristic
214	C₂×C₄	#14581816	1	1	yes	characteristic
215	C₂×C₄	#14581819	1	1	yes	characteristic
216	C₈	—	8	1	no	—
217	C₈	—	8	1	no	—
218	C₈	—	8	1	no	—
219	C₈	—	664	1	no	—
220	C₈	—	664	1	no	—
221	C₈	—	166	2	no	—
222	C₈	—	166	2	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	#19127642	1	1	yes	characteristic
226	C₂²	#19127990	1	1	yes	characteristic
227	C₂²	#19127995	1	1	yes	characteristic
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	332	2	no	—
233	C₄	—	664	1	no	—
234	C₄	#19128018	1	1	yes	characteristic
235	C₄	#19128035	1	1	yes	characteristic
236	C₄	#19128050	1	1	yes	characteristic
237	C₄	#19128064	1	1	yes	characteristic
238	C₂	—	2	1	no	—
239	C₂	—	2	1	no	—
240	C₂	#24909028	1	1	yes	characteristic
241	C₂	#24909040	1	1	yes	characteristic
242	C₂	#24909045	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24908184

C₂

yes

maximal, characteristic

#24907637

C₂

yes

maximal, characteristic

#24905365

C₂

yes

maximal, characteristic

#24905364

C₂

yes

maximal, characteristic

#24905360

C₂

yes

maximal, characteristic

#24905293

C₂

yes

maximal, characteristic

C₈₃×#1301

C₂

yes

maximal, characteristic

#19127754

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×Dic₈₃⋊C₈

—

C₂×#14581703

C₂²

yes

characteristic

C₄×C₄⋊Dic₈₃

C₂²

yes

characteristic

#19127455

—

#431×C₈₃

C₂²

yes

characteristic

#423×C₈₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₈₃

C₂²

yes

characteristic

C₂×#13050574

—

C₂²×C₈₃⋊C₈

D₄

yes

characteristic

C₂²×C₈₃⋊C₈

D₄

yes

characteristic

C₂×C₄⋊Dic₈₃

—

C₂×C₄×Dic₈₃

—

#14581727

—

#14581727

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

Dic₈₃⋊C₈

—

C₂²⋊(C₈₃⋊C₈)

—

#14581703

—

#14581703

—

C₄×C₈₃⋊C₈

—

C₈₃⋊#95

Q₈

yes

characteristic

C₈₃⋊#95

Q₈

yes

characteristic

C₂×M₁₆×C₈₃

—

C₂²×C₈×C₈₃

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

C₂²⋊C₈×C₈₃

—

C₄×C₈×C₈₃

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

—

#13050574

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

SD₁₆

yes

—

C₂×C₈₃⋊C₈

Q₁₆

yes

—

C₄⋊Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

C₂×Q₈

yes

characteristic

C₂²×C₄×C₈₃

#41

yes

characteristic

M₁₆×C₈₃

—

M₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₄²×C₈₃

yes

C₄²×C₈₃

yes

C₄²×C₈₃

yes

C₄²×C₈₃

yes

C₂³×C₈₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₈₃

C₂×Q₁₆

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

100

C₈₃⋊C₈

—

101

C₂²×C₈₃

—

102

C₂²×C₈₃

—

103

C₂²×C₈₃

#400

yes

characteristic

104

C₂²×C₈₃

#476

yes

characteristic

105

C₂²×C₈₃

#477

yes

characteristic

106

C₄×C₈₃

—

107

C₄×C₈₃

—

108

C₄×C₈₃

—

109

C₄×C₈₃

—

110

C₄×C₈₃

#481

yes

characteristic

111

C₄×C₈₃

#484

yes

characteristic

112

C₄×C₈₃

#487

yes

characteristic

113

C₄×C₈₃

#490

yes

characteristic

114

Dic₈₃

—

115

Dic₈₃

—

116

#10688

—

maximal, Sylow

117

C₂×C₈₃

—

118

C₂×C₈₃

—

119

C₂×C₈₃

#2100

yes

characteristic

120

C₂×C₈₃

#2102

yes

characteristic

121

C₂×C₈₃

#2103

yes

characteristic

122

#1940

—

123

#1849

—

124

#1303

—

125

#1303

—

126

#1301

—

127

#1301

D₈₃

yes

characteristic

128

#1275

—

129

C₈₃

#10688

yes

characteristic, complemented, Sylow

130

#431

—

131

#431

C₂×D₈₃

yes

characteristic

132

C₂×#108

—

166

—

133

C₂×#108

—

166

—

134

#423

—

135

#423

C₂×D₈₃

yes

characteristic

136

C₂×C₄⋊C₈

—

166

—

137

C₂×C₄⋊C₈

C₂×D₈₃

yes

characteristic

138

C₂×#97

—

139

C₄×C₄⋊C₄

—

140

#336

—

166

—

141

C₂×M₁₆

—

142

C₂×M₁₆

—

166

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂×C₄⋊C₄

—

166

—

147

C₂×C₄²

—

166

—

148

C₂×C₄²

C₂²×D₈₃

yes

characteristic

149

#108

—

332

—

150

#108

—

332

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

332

—

157

C₄⋊C₈

—

166

—

158

C₄⋊C₈

—

166

—

159

C₄⋊C₈

—

166

—

160

C₂²⋊C₈

—

161

C₂²⋊C₈

—

166

—

162

#97

—

166

—

163

#97

—

166

—

164

C₄×C₈

—

165

C₄×C₈

—

166

—

166

#95

—

167

#95

—

168

C₂²×C₄

—

166

—

169

C₂²×C₄

—

166

—

170

C₂²×C₄

D₄×D₈₃

yes

characteristic

171

C₂²×C₄

Q₈×D₈₃

yes

characteristic

172

C₂²×C₄

#13050590

yes

characteristic

173

M₁₆

—

174

M₁₆

—

175

M₁₆

—

332

—

176

M₁₆

—

332

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

332

—

183

C₂×C₈

—

332

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

166

—

187

C₂×C₈

—

166

—

188

C₂×C₈

—

166

—

189

C₂×C₈

—

166

—

190

C₄⋊C₄

—

332

—

191

C₄²

—

332

—

192

C₄²

—

332

—

193

C₄²

#13050589

yes

characteristic

194

C₄²

#13050589

yes

characteristic

195

C₄²

#13050590

yes

characteristic

196

C₄²

#13050590

yes

characteristic

197

C₂³

#14581770

yes

characteristic

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

332

—

201

C₂×C₄

—

332

—

202

C₂×C₄

—

332

—

203

C₂×C₄

—

332

—

204

C₂×C₄

—

332

—

205

C₂×C₄

—

166

—

206

C₂×C₄

#14581774

yes

characteristic

207

C₂×C₄

#14581778

yes

characteristic

208

C₂×C₄

#14581782

yes

characteristic

209

C₂×C₄

#14581782

yes

characteristic

210

C₂×C₄

#14581785

yes

characteristic

211

C₂×C₄

#14581786

yes

characteristic

212

C₂×C₄

SD₁₆×D₈₃

yes

characteristic

213

C₂×C₄

Q₁₆×D₈₃

yes

characteristic

214

C₂×C₄

#14581816

yes

characteristic

215

C₂×C₄

#14581819

yes

characteristic

216

C₈

—

217

C₈

—

218

C₈

—

219

C₈

—

664

—

220

C₈

—

664

—

221

C₈

—

166

—

222

C₈

—

166

—

223

C₂²

—

224

C₂²

—

225

C₂²

#19127642

yes

characteristic

226

C₂²

#19127990

yes

characteristic

227

C₂²

#19127995

yes

characteristic

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

332

—

233

C₄

—

664

—

234

C₄

#19128018

yes

characteristic

235

C₄

#19128035

yes

characteristic

236

C₄

#19128050

yes

characteristic

237

C₄

#19128064

yes

characteristic

238

C₂

—

239

C₂

—

240

C₂

#24909028

yes

characteristic

241

C₂

#24909040

yes

characteristic

242

C₂

#24909045

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14581778
commutator, cosocle	C₂×C₄²×C₈₃	C₂³
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1301	C₂
socle	C₂²×C₈₃	#400
prime radical	C₂³×C₈₃	C₂²⋊Q₈
hypercenter	#1301	D₈₃
hypocenter	C₈₃	#10688
LCS	G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

subgroup

G/H

center

C₂×C₄

#14581778

commutator, cosocle

C₂×C₄²×C₈₃

C₂³

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1301

C₂

socle

C₂²×C₈₃

#400

prime radical

C₂³×C₈₃

C₂²⋊Q₈

D₈₃

C₈₃

G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

N	H ≅ G/N	type
129. C₈₃	#10688	semidirect

H ≅ G/N

type

129. C₈₃

#10688

semidirect

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

subgroup	index
#24908184	2
#24907637	2
#24905365	2
#24905364	2
#24905360	2
#24905293	2
C₈₃×#1301	2
#10688	83

subgroup

index

C₈₃×#1301

Subgroups — #35309536

Conjugacy classes of subgroups

Complements

Maximal subgroups