Group #35304315 — subgroups

Subgroups — #35304315

Order 21248.

454 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 135 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	#24908441	C₂	1	2	yes	maximal
2	C₄×#14581702	C₂	1	1	yes	maximal, characteristic
3	#24906219	C₂	1	1	yes	maximal, characteristic
4	#24905918	C₂	1	2	yes	maximal
5	C₈₃×#3170	C₂	1	1	yes	maximal, characteristic
6	#19127725	C₂²	1	2	yes	—
7	C₂×#14581702	—	2	2	no	—
8	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₄²×Dic₈₃	C₂²	1	1	yes	characteristic
10	#19127460	—	2	4	no	—
11	#19127452	—	2	2	no	—
12	Q₈⋊(C₈₃⋊C₈)	—	2	4	no	—
13	#533×C₈₃	C₂²	1	2	yes	—
14	#500×C₈₃	C₄	1	1	yes	characteristic, complemented
15	#494×C₈₃	C₄	1	1	yes	characteristic, complemented
16	#487×C₈₃	C₄	1	2	yes	complemented
17	#467×C₈₃	—	2	2	no	—
18	C₄×Q₁₆×C₈₃	—	2	2	no	—
19	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
20	C₂×#13050574	—	2	2	no	—
21	C₂²×C₈₃⋊C₈	—	2	1	no	—
22	C₂×C₄×Dic₈₃	—	2	1	no	—
23	C₂×C₄×Dic₈₃	—	2	1	no	—
24	C₂×C₄×Dic₈₃	D₄	1	2	yes	—
25	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
26	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
27	#14581702	—	2	8	no	—
28	C₄×C₈₃⋊C₈	—	2	1	no	—
29	C₄×C₈₃⋊C₈	D₄	1	2	yes	—
30	C₂×Q₁₆×C₈₃	—	2	2	no	—
31	C₂²×C₈×C₈₃	D₄	1	2	yes	—
32	C₄⋊Q₈×C₈₃	C₂×C₄	1	2	yes	—
33	C₄⋊Q₈×C₈₃	C₂×C₄	1	2	yes	—
34	#125×C₈₃	—	2	2	no	—
35	C₂²⋊Q₈×C₈₃	—	2	2	no	—
36	C₂²⋊Q₈×C₈₃	—	2	2	no	—
37	C₄×Q₈×C₈₃	—	2	2	no	—
38	C₄×Q₈×C₈₃	—	2	2	no	—
39	#117×C₈₃	—	2	2	no	—
40	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
41	#107×C₈₃	—	2	2	no	—
42	#103×C₈₃	—	2	4	no	—
43	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₈₃	D₄	1	2	yes	—
46	C₂²×Dic₈₃	—	2	2	no	—
47	#13050574	—	4	4	no	—
48	C₂×C₈₃⋊C₈	—	2	4	no	—
49	C₂×C₈₃⋊C₈	—	2	2	no	—
50	C₂×C₈₃⋊C₈	—	4	2	no	—
51	C₄×Dic₈₃	—	2	4	no	—
52	C₄×Dic₈₃	—	2	4	no	—
53	C₄×Dic₈₃	—	4	2	no	—
54	C₂×Q₈×C₈₃	—	2	2	no	—
55	C₂×Q₈×C₈₃	—	2	2	no	—
56	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
59	Q₁₆×C₈₃	—	4	4	no	—
60	C₂×C₈×C₈₃	—	2	4	no	—
61	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
63	C₄⋊C₄×C₈₃	—	2	2	no	—
64	C₄⋊C₄×C₈₃	—	2	2	no	—
65	C₄⋊C₄×C₈₃	—	2	2	no	—
66	C₄⋊C₄×C₈₃	—	2	2	no	—
67	C₄⋊C₄×C₈₃	—	4	2	no	—
68	C₄⋊C₄×C₈₃	—	4	2	no	—
69	C₂²⋊C₄×C₈₃	—	4	2	no	—
70	C₄²×C₈₃	—	4	2	no	—
71	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₈₃	#41	1	1	yes	characteristic
75	C₂³×C₈₃	#121	1	1	yes	characteristic
76	Q₈×C₈₃	—	4	4	no	—
77	Q₈×C₈₃	—	4	4	no	—
78	C₂×C₄×C₈₃	—	2	2	no	—
79	C₂×C₄×C₈₃	—	2	2	no	—
80	C₂×C₄×C₈₃	—	4	2	no	—
81	C₂×C₄×C₈₃	—	4	2	no	—
82	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
86	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
87	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
88	C₂×C₄×C₈₃	#137	1	4	yes	—
89	C₂×Dic₈₃	—	2	4	no	—
90	C₂×Dic₈₃	—	4	2	no	—
91	C₂×Dic₈₃	—	4	2	no	—
92	C₈×C₈₃	—	2	2	no	—
93	C₈×C₈₃	#104	1	4	yes	—
94	C₈₃⋊C₈	—	2	4	no	—
95	C₈₃⋊C₈	—	8	2	no	—
96	C₂²×C₈₃	—	2	1	no	—
97	C₂²×C₈₃	—	2	1	no	—
98	C₂²×C₈₃	#390	1	1	yes	characteristic
99	C₂²×C₈₃	#470	1	2	yes	—
100	C₄×C₈₃	—	2	1	no	—
101	C₄×C₈₃	—	2	1	no	—
102	C₄×C₈₃	—	8	2	no	—
103	C₄×C₈₃	—	8	2	no	—
104	C₄×C₈₃	C₂×#104	1	2	yes	—
105	C₄×C₈₃	#441	1	2	yes	—
106	C₄×C₈₃	#444	1	2	yes	—
107	C₄×C₈₃	#497	1	2	yes	—
108	Dic₈₃	—	4	4	no	—
109	#9850	—	83	1	no	maximal, Sylow
110	C₂×C₈₃	—	2	2	no	—
111	C₂×C₈₃	#1962	1	1	yes	characteristic
112	C₂×C₈₃	#1971	1	1	yes	characteristic
113	C₂×C₈₃	#1975	1	1	yes	characteristic
114	#3170	D₈₃	1	1	yes	characteristic
115	#1994	—	83	2	no	—
116	C₄×#97	—	83	1	no	—
117	#1566	—	83	1	no	—
118	#1493	—	83	2	no	—
119	C₈₃	#9850	1	1	yes	characteristic, complemented, Sylow
120	#533	C₂×D₈₃	1	2	yes	—
121	#500	Dic₈₃	1	1	yes	characteristic, complemented
122	#494	Dic₈₃	1	1	yes	characteristic, complemented
123	#487	Dic₈₃	1	2	yes	complemented
124	#467	—	2	2	no	—
125	C₄×Q₁₆	—	2	2	no	—
126	#423	—	83	2	no	—
127	C₂×#97	—	166	2	no	—
128	C₂×C₄×C₈	—	83	1	no	—
129	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
130	C₄³	—	83	1	no	—
131	#339	—	166	4	no	—
132	#334	—	166	2	no	—
133	Q₈⋊C₈	—	166	4	no	—
134	C₂×Q₁₆	—	2	2	no	—
135	C₂×M₁₆	—	166	2	no	—
136	C₂²×C₈	—	166	1	no	—
137	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
138	C₄⋊Q₈	C₂×Dic₈₃	1	2	yes	—
139	C₄⋊Q₈	C₂×Dic₈₃	1	2	yes	—
140	#125	—	2	2	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₂²⋊Q₈	—	2	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	#117	—	2	2	no	—
146	C₂×C₄²	—	83	2	no	—
147	C₂×C₄²	—	166	1	no	—
148	C₂×C₄²	—	166	1	no	—
149	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
150	#107	—	2	2	no	—
151	C₄⋊C₈	—	166	2	no	—
152	C₄⋊C₈	—	166	2	no	—
153	#103	—	2	4	no	—
154	#97	—	166	8	no	—
155	C₄×C₈	—	83	2	no	—
156	C₄×C₈	—	166	1	no	—
157	C₄×C₈	C₂×Dic₈₃	1	1	yes	characteristic
158	C₄×C₈	C₂×Dic₈₃	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₈₃	1	2	yes	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂²×C₄	—	166	2	no	—
163	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
164	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
165	C₂²×C₄	#13050589	1	1	yes	characteristic
166	Q₁₆	—	4	4	no	—
167	M₁₆	—	332	4	no	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	332	2	no	—
170	C₂×C₈	—	166	4	no	—
171	C₂×C₈	—	166	2	no	—
172	C₂×C₈	C₂²⋊Dic₈₃	1	2	yes	—
173	C₂×C₈	C₂²⋊Dic₈₃	1	2	yes	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₂²⋊C₄	—	4	2	no	—
181	C₄²	—	4	2	no	—
182	C₄²	—	332	2	no	—
183	C₄²	—	166	4	no	—
184	C₄²	—	166	4	no	—
185	C₄²	C₂²×Dic₈₃	1	1	yes	characteristic
186	C₄²	D₄×D₈₃	1	1	yes	characteristic
187	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
188	C₄²	#13050589	1	1	yes	characteristic
189	C₂³	#14581763	1	1	yes	characteristic
190	Q₈	—	4	4	no	—
191	Q₈	—	4	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	332	2	no	—
197	C₂×C₄	—	332	2	no	—
198	C₂×C₄	—	166	4	no	—
199	C₂×C₄	C₂×C₂²⋊Dic₈₃	1	1	yes	characteristic
200	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
201	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
202	C₂×C₄	#14581763	1	1	yes	characteristic
203	C₂×C₄	#14581779	1	1	yes	characteristic
204	C₂×C₄	#14581788	1	1	yes	characteristic
205	C₂×C₄	#14581824	1	4	yes	—
206	C₈	—	2	2	no	—
207	C₈	—	664	2	no	—
208	C₈	—	166	4	no	—
209	C₈	#14581719	1	4	yes	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	#19127604	1	1	yes	characteristic
213	C₂²	#19127956	1	2	yes	—
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	8	2	no	—
217	C₄	—	8	2	no	—
218	C₄	—	332	4	no	—
219	C₄	C₂×#14581719	1	2	yes	—
220	C₄	#19127808	1	2	yes	—
221	C₄	#19127823	1	2	yes	—
222	C₄	#19128094	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	#24908292	1	1	yes	characteristic
225	C₂	#24908335	1	1	yes	characteristic
226	C₂	#24908357	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24908441

C₂

yes

maximal

C₄×#14581702

C₂

yes

maximal, characteristic

#24906219

C₂

yes

maximal, characteristic

#24905918

C₂

yes

maximal

C₈₃×#3170

C₂

yes

maximal, characteristic

#19127725

C₂²

yes

—

C₂×#14581702

—

C₂×C₄×C₈₃⋊C₈

C₂²

yes

characteristic

C₄²×Dic₈₃

C₂²

yes

characteristic

#19127460

—

#19127452

—

Q₈⋊(C₈₃⋊C₈)

—

#533×C₈₃

C₂²

yes

—

#500×C₈₃

C₄

yes

characteristic, complemented

#494×C₈₃

C₄

yes

characteristic, complemented

#487×C₈₃

C₄

yes

complemented

#467×C₈₃

—

C₄×Q₁₆×C₈₃

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₂×#13050574

—

C₂²×C₈₃⋊C₈

—

C₂×C₄×Dic₈₃

—

C₂×C₄×Dic₈₃

—

C₂×C₄×Dic₈₃

D₄

yes

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

#14581702

—

C₄×C₈₃⋊C₈

—

C₄×C₈₃⋊C₈

D₄

yes

—

C₂×Q₁₆×C₈₃

—

C₂²×C₈×C₈₃

D₄

yes

—

C₄⋊Q₈×C₈₃

C₂×C₄

yes

—

C₄⋊Q₈×C₈₃

C₂×C₄

yes

—

#125×C₈₃

—

C₂²⋊Q₈×C₈₃

—

C₂²⋊Q₈×C₈₃

—

C₄×Q₈×C₈₃

—

C₄×Q₈×C₈₃

—

#117×C₈₃

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

#107×C₈₃

—

#103×C₈₃

—

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

D₄

yes

—

C₂²×Dic₈₃

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

#41

yes

characteristic

Q₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₂²⋊C₄×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

C₂²×C₄

yes

characteristic

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

—

C₂×C₄×C₈₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₄×D₄

yes

characteristic

C₂×C₄×C₈₃

C₄×D₄

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₈×C₈₃

—

C₈×C₈₃

#104

yes

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

#390

yes

characteristic

C₂²×C₈₃

#470

yes

—

100

C₄×C₈₃

—

101

C₄×C₈₃

—

102

C₄×C₈₃

—

103

C₄×C₈₃

—

104

C₄×C₈₃

C₂×#104

yes

—

105

C₄×C₈₃

#441

yes

—

106

C₄×C₈₃

#444

yes

—

107

C₄×C₈₃

#497

yes

—

108

Dic₈₃

—

109

#9850

—

maximal, Sylow

110

C₂×C₈₃

—

111

C₂×C₈₃

#1962

yes

characteristic

112

C₂×C₈₃

#1971

yes

characteristic

113

C₂×C₈₃

#1975

yes

characteristic

114

#3170

D₈₃

yes

characteristic

115

#1994

—

116

C₄×#97

—

117

#1566

—

118

#1493

—

119

C₈₃

#9850

yes

characteristic, complemented, Sylow

120

#533

C₂×D₈₃

yes

—

121

#500

Dic₈₃

yes

characteristic, complemented

122

#494

Dic₈₃

yes

characteristic, complemented

123

#487

Dic₈₃

yes

complemented

124

#467

—

125

C₄×Q₁₆

—

126

#423

—

127

C₂×#97

—

166

—

128

C₂×C₄×C₈

—

129

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

130

C₄³

—

131

#339

—

166

—

132

#334

—

166

—

133

Q₈⋊C₈

—

166

—

134

C₂×Q₁₆

—

135

C₂×M₁₆

—

166

—

136

C₂²×C₈

—

166

—

137

C₂²×C₈

C₂²⋊D₈₃

yes

—

138

C₄⋊Q₈

C₂×Dic₈₃

yes

—

139

C₄⋊Q₈

C₂×Dic₈₃

yes

—

140

#125

—

141

C₂²⋊Q₈

—

142

C₂²⋊Q₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

#117

—

146

C₂×C₄²

—

147

C₂×C₄²

—

166

—

148

C₂×C₄²

—

166

—

149

C₂×C₄²

C₂²×D₈₃

yes

characteristic

150

#107

—

151

C₄⋊C₈

—

166

—

152

C₄⋊C₈

—

166

—

153

#103

—

154

#97

—

166

—

155

C₄×C₈

—

156

C₄×C₈

—

166

—

157

C₄×C₈

C₂×Dic₈₃

yes

characteristic

158

C₄×C₈

C₂×Dic₈₃

yes

characteristic

159

C₄×C₈

C₂²⋊D₈₃

yes

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂²×C₄

—

166

—

163

C₂²×C₄

D₄×D₈₃

yes

characteristic

164

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

165

C₂²×C₄

#13050589

yes

characteristic

166

Q₁₆

—

167

M₁₆

—

332

—

168

C₂×C₈

—

169

C₂×C₈

—

332

—

170

C₂×C₈

—

166

—

171

C₂×C₈

—

166

—

172

C₂×C₈

C₂²⋊Dic₈₃

yes

—

173

C₂×C₈

C₂²⋊Dic₈₃

yes

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₂²⋊C₄

—

181

C₄²

—

182

C₄²

—

332

—

183

C₄²

—

166

—

184

C₄²

—

166

—

185

C₄²

C₂²×Dic₈₃

yes

characteristic

186

C₄²

D₄×D₈₃

yes

characteristic

187

C₄²

C₂×C₂²⋊D₈₃

yes

characteristic

188

C₄²

#13050589

yes

characteristic

189

C₂³

#14581763

yes

characteristic

190

Q₈

—

191

Q₈

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

332

—

197

C₂×C₄

—

332

—

198

C₂×C₄

—

166

—

199

C₂×C₄

C₂×C₂²⋊Dic₈₃

yes

characteristic

200

C₂×C₄

D₄×Dic₈₃

yes

characteristic

201

C₂×C₄

D₄×Dic₈₃

yes

characteristic

202

C₂×C₄

#14581763

yes

characteristic

203

C₂×C₄

#14581779

yes

characteristic

204

C₂×C₄

#14581788

yes

characteristic

205

C₂×C₄

#14581824

yes

—

206

C₈

—

207

C₈

—

664

—

208

C₈

—

166

—

209

C₈

#14581719

yes

—

210

C₂²

—

211

C₂²

—

212

C₂²

#19127604

yes

characteristic

213

C₂²

#19127956

yes

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

—

332

—

219

C₄

C₂×#14581719

yes

—

220

C₄

#19127808

yes

—

221

C₄

#19127823

yes

—

222

C₄

#19128094

yes

—

223

C₂

—

224

C₂

#24908292

yes

characteristic

225

C₂

#24908335

yes

characteristic

226

C₂

#24908357

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14581788
commutator	C₄²×C₈₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#3170	C₂
socle	C₂²×C₈₃	#390
prime radical	C₂³×C₈₃	#121
cosocle	C₂×C₄²×C₈₃	C₂³
hypercenter	#3170	D₈₃
hypocenter	C₈₃	#9850
LCS	G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#14581788

commutator

C₄²×C₈₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#3170

C₂

C₂²×C₈₃

C₂³×C₈₃

C₂×C₄²×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
14. #500×C₈₃	C₄	semidirect
15. #494×C₈₃	C₄	semidirect
16. #487×C₈₃	C₄	semidirect
119. C₈₃	#9850	semidirect
121. #500	Dic₈₃	semidirect
122. #494	Dic₈₃	semidirect
123. #487	Dic₈₃	semidirect

H ≅ G/N

type

14. #500×C₈₃

C₄

semidirect

15. #494×C₈₃

C₄

semidirect

16. #487×C₈₃

C₄

semidirect

119. C₈₃

#9850

semidirect

121. #500

Dic₈₃

semidirect

122. #494

Dic₈₃

semidirect

123. #487

Dic₈₃

semidirect

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

subgroup	index
#24908441	2
C₄×#14581702	2
#24906219	2
#24905918	2
C₈₃×#3170	2
#9850	83

subgroup

index

C₈₃×#3170

Subgroups — #35304315

Conjugacy classes of subgroups

Complements

Maximal subgroups