Group #35321859 — subgroups

Subgroups — #35321859

Order 21248.

458 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 131 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	#24920566	C₂	1	1	yes	maximal, characteristic
2	#24909183	C₂	1	2	yes	maximal, complemented
3	#24907509	C₂	1	1	yes	maximal, characteristic
4	#24905564	C₂	1	2	yes	maximal, complemented
5	C₈₃×#3059	C₂	1	1	yes	maximal, characteristic
6	#19128118	—	2	4	no	—
7	C₂×#14581732	—	2	2	no	—
8	C₂×#14581732	C₂²	1	2	yes	—
9	#19127739	C₂²	1	2	yes	—
10	#19127675	—	2	1	no	—
11	#19127505	—	2	4	no	—
12	#19127458	—	2	1	no	—
13	C₂²×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
14	C₂×#131×C₈₃	C₂²	1	1	yes	characteristic
15	#536×C₈₃	—	2	1	no	—
16	#470×C₈₃	C₄	1	4	yes	complemented
17	#467×C₈₃	—	2	2	no	—
18	#427×C₈₃	C₂²	1	1	yes	characteristic
19	#419×C₈₃	—	2	1	no	—
20	#14581751	—	2	2	no	—
21	#14581732	—	2	4	no	—
22	#14581732	—	2	2	no	—
23	#14581732	—	2	2	no	—
24	C₂×C₈₃⋊C₁₆	—	2	4	no	—
25	C₂×C₈₃⋊C₁₆	D₄	1	4	yes	—
26	#14581726	—	2	2	no	—
27	#14581724	—	2	2	no	—
28	#14581707	—	4	2	no	—
29	C₂×#41×C₈₃	D₄	1	1	yes	characteristic
30	C₂²×Q₈×C₈₃	—	2	1	no	—
31	C₂×Q₁₆×C₈₃	—	2	2	no	—
32	C₂×Q₁₆×C₈₃	—	2	1	no	—
33	C₂×Q₁₆×C₈₃	—	2	2	no	—
34	C₂×Q₁₆×C₈₃	C₂×C₄	1	2	yes	—
35	#131×C₈₃	—	2	2	no	—
36	#131×C₈₃	—	2	2	no	—
37	C₂×M₁₆×C₈₃	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₈₃	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₈₃	D₄	1	2	yes	—
40	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
41	C₄⋊Q₈×C₈₃	—	4	1	no	—
42	#124×C₈₃	—	4	1	no	—
43	#123×C₈₃	—	4	2	no	—
44	C₂²⋊Q₈×C₈₃	—	2	4	no	—
45	#117×C₈₃	—	2	1	no	—
46	#107×C₈₃	—	2	1	no	—
47	#106×C₈₃	C₂×C₄	1	2	yes	—
48	#103×C₈₃	—	2	4	no	—
49	C₄⋊Dic₈₃	—	4	2	no	—
50	C₂²⋊Dic₈₃	—	4	2	no	—
51	C₄×Dic₈₃	—	4	2	no	—
52	C₈₃⋊C₁₆	—	2	4	no	—
53	#41×C₈₃	—	2	2	no	—
54	#41×C₈₃	—	2	2	no	—
55	C₂×Q₈×C₈₃	—	2	2	no	—
56	C₂×Q₈×C₈₃	—	4	1	no	—
57	C₂×Q₈×C₈₃	—	4	2	no	—
58	C₂×Q₈×C₈₃	—	4	2	no	—
59	C₂×Q₈×C₈₃	SD₁₆	1	1	yes	characteristic
60	C₂×D₄×C₈₃	D₈	1	2	yes	—
61	C₂×D₄×C₈₃	SD₁₆	1	1	yes	characteristic
62	C₂²×C₄×C₈₃	—	4	1	no	—
63	C₂²×C₄×C₈₃	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
65	Q₁₆×C₈₃	—	2	4	no	—
66	Q₁₆×C₈₃	—	4	1	no	—
67	Q₁₆×C₈₃	—	4	1	no	—
68	M₁₆×C₈₃	—	2	2	no	—
69	M₁₆×C₈₃	—	2	4	no	—
70	C₂×C₈×C₈₃	—	2	2	no	—
71	C₂×C₈×C₈₃	—	2	2	no	—
72	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₈×C₈₃	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₈₃	#41	1	2	yes	—
77	C₄⋊C₄×C₈₃	—	2	2	no	—
78	C₄⋊C₄×C₈₃	—	4	4	no	—
79	C₂²⋊C₄×C₈₃	—	4	4	no	—
80	C₂²⋊C₄×C₈₃	—	4	1	no	—
81	C₄²×C₈₃	—	4	1	no	—
82	C₂³×C₈₃	#102	1	2	yes	—
83	C₂³×C₈₃	C₂×D₈	1	1	yes	characteristic
84	Q₈×C₈₃	—	2	2	no	—
85	Q₈×C₈₃	—	4	2	no	—
86	Q₈×C₈₃	—	4	2	no	—
87	Q₈×C₈₃	—	8	2	no	—
88	D₄×C₈₃	—	2	4	no	—
89	D₄×C₈₃	—	2	2	no	—
90	C₂×C₄×C₈₃	—	2	2	no	—
91	C₂×C₄×C₈₃	—	2	2	no	—
92	C₂×C₄×C₈₃	—	4	2	no	—
93	C₂×C₄×C₈₃	—	4	2	no	—
94	C₂×C₄×C₈₃	—	8	2	no	—
95	C₂×C₄×C₈₃	#102	1	2	yes	—
96	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₈₃	#121	1	2	yes	—
98	C₂×C₄×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
99	C₂×C₄×C₈₃	#135	1	2	yes	—
100	C₂×Dic₈₃	—	8	2	no	—
101	C₈×C₈₃	—	2	2	no	—
102	C₈×C₈₃	C₄×D₄	1	2	yes	—
103	C₈×C₈₃	#120	1	1	yes	characteristic
104	C₈×C₈₃	#123	1	1	yes	characteristic
105	C₂²×C₈₃	—	2	2	no	—
106	C₂²×C₈₃	—	4	1	no	—
107	C₂²×C₈₃	—	4	2	no	—
108	C₂²×C₈₃	C₂×#102	1	1	yes	characteristic
109	C₂²×C₈₃	#466	1	2	yes	—
110	C₄×C₈₃	—	2	2	no	—
111	C₄×C₈₃	—	8	2	no	—
112	C₄×C₈₃	—	8	2	no	—
113	C₄×C₈₃	#386	1	1	yes	characteristic
114	C₄×C₈₃	#416	1	1	yes	characteristic
115	C₄×C₈₃	#465	1	2	yes	—
116	Dic₈₃	—	16	2	no	—
117	#13075	—	83	1	no	maximal, Sylow
118	C₂×C₈₃	—	2	2	no	—
119	C₂×C₈₃	—	2	1	no	—
120	C₂×C₈₃	—	4	2	no	—
121	C₂×C₈₃	#1893	1	1	yes	characteristic
122	#3407	—	83	1	no	—
123	#3059	D₈₃	1	1	yes	characteristic
124	#2141	—	83	2	no	—
125	#1812	—	83	1	no	—
126	#1384	—	83	2	no	—
127	C₈₃	#13075	1	1	yes	characteristic, complemented, Sylow
128	C₂²×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
129	C₂×#131	C₂×D₈₃	1	1	yes	characteristic
130	#536	—	2	1	no	—
131	#504	—	166	4	no	—
132	C₂×M₃₂	—	83	2	no	—
133	C₂×M₃₂	—	166	2	no	—
134	#470	Dic₈₃	1	4	yes	complemented
135	#467	—	2	2	no	—
136	#427	—	83	2	no	—
137	#427	C₂×D₈₃	1	1	yes	characteristic
138	#419	—	2	1	no	—
139	#410	—	166	1	no	—
140	#358	—	166	4	no	—
141	H(3,ℤ/4)	—	166	1	no	—
142	C₂×#41	C₂²⋊D₈₃	1	1	yes	characteristic
143	C₂²×Q₈	—	2	1	no	—
144	C₂×Q₁₆	—	2	2	no	—
145	C₂×Q₁₆	—	2	1	no	—
146	C₂×Q₁₆	—	2	2	no	—
147	C₂×Q₁₆	C₂×Dic₈₃	1	2	yes	—
148	#131	—	2	2	no	—
149	#131	—	2	2	no	—
150	C₂×M₁₆	C₂×Dic₈₃	1	2	yes	—
151	C₂×M₁₆	C₂²⋊D₈₃	1	1	yes	characteristic
152	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
153	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
154	C₄⋊Q₈	—	4	1	no	—
155	#124	—	4	1	no	—
156	#123	—	4	2	no	—
157	C₂²⋊Q₈	—	2	4	no	—
158	#117	—	2	1	no	—
159	#117	—	166	2	no	—
160	M₃₂	—	166	4	no	—
161	M₃₂	—	166	2	no	—
162	M₃₂	—	166	2	no	—
163	C₂×C₁₆	—	83	4	no	—
164	C₂×C₁₆	—	166	4	no	—
165	#107	—	2	1	no	—
166	#107	—	166	2	no	—
167	#106	—	166	2	no	—
168	#106	C₂×Dic₈₃	1	2	yes	—
169	#103	—	2	4	no	—
170	#99	—	332	2	no	—
171	#41	—	2	2	no	—
172	#41	—	2	2	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	—	4	1	no	—
175	C₂×Q₈	—	4	2	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	#13050578	1	1	yes	characteristic
178	C₂×D₄	#13050575	1	2	yes	—
179	C₂×D₄	#13050578	1	1	yes	characteristic
180	C₂²×C₄	—	4	1	no	—
181	C₂²×C₄	C₂²⋊Dic₈₃	1	2	yes	—
182	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
183	Q₁₆	—	2	4	no	—
184	Q₁₆	—	4	1	no	—
185	Q₁₆	—	4	1	no	—
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	4	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	C₂²⋊Dic₈₃	1	2	yes	—
191	C₂×C₈	C₂²×Dic₈₃	1	1	yes	characteristic
192	C₂×C₈	D₄×D₈₃	1	2	yes	—
193	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
194	C₂×C₈	#13050589	1	2	yes	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	4	4	no	—
197	C₄⋊C₄	—	332	2	no	—
198	C₂²⋊C₄	—	4	1	no	—
199	C₂²⋊C₄	—	4	4	no	—
200	C₂²⋊C₄	—	332	2	no	—
201	C₄²	—	4	1	no	—
202	C₄²	—	332	2	no	—
203	C₁₆	—	166	4	no	—
204	C₂³	#14581713	1	2	yes	—
205	C₂³	C₂×#13050575	1	1	yes	characteristic
206	Q₈	—	2	2	no	—
207	Q₈	—	4	2	no	—
208	Q₈	—	4	2	no	—
209	Q₈	—	8	2	no	—
210	D₄	—	2	4	no	—
211	D₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	8	2	no	—
217	C₂×C₄	—	664	2	no	—
218	C₂×C₄	#14581713	1	2	yes	—
219	C₂×C₄	C₂×C₂²⋊Dic₈₃	1	1	yes	characteristic
220	C₂×C₄	#14581764	1	2	yes	—
221	C₂×C₄	C₂×#13050578	1	1	yes	characteristic
222	C₂×C₄	#14581812	1	2	yes	—
223	C₈	—	2	2	no	—
224	C₈	D₄×Dic₈₃	1	2	yes	—
225	C₈	#14581760	1	1	yes	characteristic
226	C₈	#14581773	1	1	yes	characteristic
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	2	no	—
230	C₂²	C₂×#14581713	1	1	yes	characteristic
231	C₂²	#19127935	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	8	2	no	—
234	C₄	—	8	2	no	—
235	C₄	—	1328	2	no	—
236	C₄	#19127581	1	1	yes	characteristic
237	C₄	#19127697	1	1	yes	characteristic
238	C₄	#19127928	1	2	yes	—
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	4	2	no	—
242	C₂	#24907892	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24920566

C₂

yes

maximal, characteristic

#24909183

C₂

yes

maximal, complemented

#24907509

C₂

yes

maximal, characteristic

#24905564

C₂

yes

maximal, complemented

C₈₃×#3059

C₂

yes

maximal, characteristic

#19128118

—

C₂×#14581732

—

C₂×#14581732

C₂²

yes

—

#19127739

C₂²

yes

—

#19127675

—

#19127505

—

#19127458

—

C₂²×Q₁₆×C₈₃

C₂²

yes

characteristic

C₂×#131×C₈₃

C₂²

yes

characteristic

#536×C₈₃

—

#470×C₈₃

C₄

yes

complemented

#467×C₈₃

—

#427×C₈₃

C₂²

yes

characteristic

#419×C₈₃

—

—

—

—

—

C₂×C₈₃⋊C₁₆

—

C₂×C₈₃⋊C₁₆

D₄

yes

—

#14581726

—

#14581724

—

#14581707

—

C₂×#41×C₈₃

D₄

yes

characteristic

C₂²×Q₈×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

C₂×C₄

yes

—

#131×C₈₃

—

#131×C₈₃

—

C₂×M₁₆×C₈₃

C₂×C₄

yes

—

C₂×M₁₆×C₈₃

D₄

yes

characteristic

C₂²×C₈×C₈₃

D₄

yes

—

C₂²×C₈×C₈₃

C₂³

yes

characteristic

C₄⋊Q₈×C₈₃

—

#124×C₈₃

—

#123×C₈₃

—

C₂²⋊Q₈×C₈₃

—

#117×C₈₃

—

#107×C₈₃

—

#106×C₈₃

C₂×C₄

yes

—

#103×C₈₃

—

C₄⋊Dic₈₃

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₈₃⋊C₁₆

—

#41×C₈₃

—

#41×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

SD₁₆

yes

characteristic

C₂×D₄×C₈₃

D₈

yes

—

C₂×D₄×C₈₃

SD₁₆

yes

characteristic

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

Q₁₆×C₈₃

—

Q₁₆×C₈₃

—

Q₁₆×C₈₃

—

M₁₆×C₈₃

—

M₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

—

C₂×C₈×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

—

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

#41

yes

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₂²⋊C₄×C₈₃

—

C₂²⋊C₄×C₈₃

—

C₄²×C₈₃

—

C₂³×C₈₃

#102

yes

—

C₂³×C₈₃

C₂×D₈

yes

characteristic

Q₈×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

—

D₄×C₈₃

—

D₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#102

yes

—

C₂×C₄×C₈₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

#121

yes

—

C₂×C₄×C₈₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₈₃

#135

yes

—

100

C₂×Dic₈₃

—

101

C₈×C₈₃

—

102

C₈×C₈₃

C₄×D₄

yes

—

103

C₈×C₈₃

#120

yes

characteristic

104

C₈×C₈₃

#123

yes

characteristic

105

C₂²×C₈₃

—

106

C₂²×C₈₃

—

107

C₂²×C₈₃

—

108

C₂²×C₈₃

C₂×#102

yes

characteristic

109

C₂²×C₈₃

#466

yes

—

110

C₄×C₈₃

—

111

C₄×C₈₃

—

112

C₄×C₈₃

—

113

C₄×C₈₃

#386

yes

characteristic

114

C₄×C₈₃

#416

yes

characteristic

115

C₄×C₈₃

#465

yes

—

116

Dic₈₃

—

117

#13075

—

maximal, Sylow

118

C₂×C₈₃

—

119

C₂×C₈₃

—

120

C₂×C₈₃

—

121

C₂×C₈₃

#1893

yes

characteristic

122

#3407

—

123

#3059

D₈₃

yes

characteristic

124

#2141

—

125

#1812

—

126

#1384

—

127

C₈₃

#13075

yes

characteristic, complemented, Sylow

128

C₂²×Q₁₆

C₂×D₈₃

yes

characteristic

129

C₂×#131

C₂×D₈₃

yes

characteristic

130

#536

—

131

#504

—

166

—

132

C₂×M₃₂

—

133

C₂×M₃₂

—

166

—

134

#470

Dic₈₃

yes

complemented

135

#467

—

136

#427

—

137

#427

C₂×D₈₃

yes

characteristic

138

#419

—

139

#410

—

166

—

140

#358

—

166

—

141

H(3,ℤ/4)

—

166

—

142

C₂×#41

C₂²⋊D₈₃

yes

characteristic

143

C₂²×Q₈

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

C₂×Dic₈₃

yes

—

148

#131

—

149

#131

—

150

C₂×M₁₆

C₂×Dic₈₃

yes

—

151

C₂×M₁₆

C₂²⋊D₈₃

yes

characteristic

152

C₂²×C₈

C₂²⋊D₈₃

yes

—

153

C₂²×C₈

C₂²×D₈₃

yes

characteristic

154

C₄⋊Q₈

—

155

#124

—

156

#123

—

157

C₂²⋊Q₈

—

158

#117

—

159

#117

—

166

—

160

M₃₂

—

166

—

161

M₃₂

—

166

—

162

M₃₂

—

166

—

163

C₂×C₁₆

—

164

C₂×C₁₆

—

166

—

165

#107

—

166

#107

—

166

—

167

#106

—

166

—

168

#106

C₂×Dic₈₃

yes

—

169

#103

—

170

#99

—

332

—

171

#41

—

172

#41

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

#13050578

yes

characteristic

178

C₂×D₄

#13050575

yes

—

179

C₂×D₄

#13050578

yes

characteristic

180

C₂²×C₄

—

181

C₂²×C₄

C₂²⋊Dic₈₃

yes

—

182

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

183

Q₁₆

—

184

Q₁₆

—

185

Q₁₆

—

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

C₂²⋊Dic₈₃

yes

—

191

C₂×C₈

C₂²×Dic₈₃

yes

characteristic

192

C₂×C₈

D₄×D₈₃

yes

—

193

C₂×C₈

C₂×C₂²⋊D₈₃

yes

characteristic

194

C₂×C₈

#13050589

yes

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

332

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

332

—

201

C₄²

—

202

C₄²

—

332

—

203

C₁₆

—

166

—

204

C₂³

#14581713

yes

—

205

C₂³

C₂×#13050575

yes

characteristic

206

Q₈

—

207

Q₈

—

208

Q₈

—

209

Q₈

—

210

D₄

—

211

D₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

664

—

218

C₂×C₄

#14581713

yes

—

219

C₂×C₄

C₂×C₂²⋊Dic₈₃

yes

characteristic

220

C₂×C₄

#14581764

yes

—

221

C₂×C₄

C₂×#13050578

yes

characteristic

222

C₂×C₄

#14581812

yes

—

223

C₈

—

224

C₈

D₄×Dic₈₃

yes

—

225

C₈

#14581760

yes

characteristic

226

C₈

#14581773

yes

characteristic

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₂×#14581713

yes

characteristic

231

C₂²

#19127935

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

1328

—

236

C₄

#19127581

yes

characteristic

237

C₄

#19127697

yes

characteristic

238

C₄

#19127928

yes

—

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

#24907892

yes

characteristic

	subgroup	G/H
center	C₂	#24907892
commutator	C₂×C₈×C₈₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₈₃×#3059	C₂
socle	C₂×C₈₃	#1893
prime radical	C₂×#41×C₈₃	D₄
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	#3059	D₈₃
hypocenter	C₈₃	#13075
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3059

subgroup

G/H

center

C₂

#24907892

commutator

C₂×C₈×C₈₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₈₃×#3059

C₂

socle

C₂×C₈₃

#1893

prime radical

C₂×#41×C₈₃

D₄

cosocle

C₂²×C₈×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3059

N	H ≅ G/N	type
2. #24909183	C₂	semidirect
4. #24905564	C₂	semidirect
16. #470×C₈₃	C₄	semidirect
127. C₈₃	#13075	semidirect
134. #470	Dic₈₃	semidirect

H ≅ G/N

type

2. #24909183

C₂

semidirect

4. #24905564

C₂

semidirect

16. #470×C₈₃

C₄

semidirect

127. C₈₃

#13075

semidirect

134. #470

Dic₈₃

semidirect

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

subgroup	index
#24920566	2
#24909183	2
#24907509	2
#24905564	2
C₈₃×#3059	2
#13075	83

subgroup

index

C₈₃×#3059

Subgroups — #35321859

Conjugacy classes of subgroups

Complements

Maximal subgroups