Group #35304307 — subgroups

Subgroups — #35304307

Order 21248.

530 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 127 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	#24918042	C₂	1	1	yes	maximal, characteristic
2	#24908290	C₂	1	2	yes	maximal, complemented
3	C₄×#14581702	C₂	1	1	yes	maximal, characteristic, complemented
4	#24905913	C₂	1	2	yes	maximal, complemented
5	C₈₃×#1566	C₂	1	1	yes	maximal, characteristic, complemented
6	#19128251	C₂²	1	2	yes	—
7	#19128106	C₄	1	1	yes	characteristic, complemented
8	#19128078	C₄	1	1	yes	characteristic, complemented
9	#19128048	C₄	1	2	yes	complemented
10	#19127937	—	2	2	no	—
11	C₄×D₆₆₄	—	2	2	no	—
12	C₂×#14581718	—	2	4	no	—
13	C₂×#14581702	—	2	2	no	—
14	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₄²×Dic₈₃	C₂²	1	1	yes	characteristic
16	#19127428	—	2	4	no	—
17	#423×C₈₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
19	#334×C₈₃	—	2	2	no	—
20	C₂×#13050590	—	2	2	no	—
21	C₂×D₆₆₄	—	2	2	no	—
22	C₂²×C₈₃⋊C₈	—	2	1	no	—
23	#14581792	C₂×C₄	1	2	yes	—
24	#14581789	C₂×C₄	1	2	yes	—
25	#14581780	—	2	2	no	—
26	#14581766	—	2	2	no	—
27	#14581766	—	2	2	no	—
28	C₄×D₃₃₂	—	2	2	no	—
29	C₄×D₃₃₂	—	2	2	no	—
30	C₂×C₄×Dic₈₃	—	2	1	no	—
31	C₂×C₄×Dic₈₃	—	2	1	no	—
32	C₂×C₄×Dic₈₃	D₄	1	2	yes	—
33	#14581726	—	2	2	no	—
34	#14581718	—	4	8	no	—
35	#14581714	—	2	4	no	—
36	#14581702	—	2	8	no	—
37	C₄×C₈₃⋊C₈	—	2	1	no	—
38	C₄×C₈₃⋊C₈	D₄	1	2	yes	—
39	C₂×M₁₆×C₈₃	—	2	2	no	—
40	C₂²×C₈×C₈₃	D₄	1	2	yes	—
41	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₈₃	—	2	2	no	—
43	C₄⋊C₈×C₈₃	—	2	2	no	—
44	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₈₃	D₄	1	2	yes	—
47	#13050590	—	4	4	no	—
48	#13050590	—	4	4	no	—
49	C₂×Dic₁₆₆	—	2	2	no	—
50	C₂×D₃₃₂	—	2	2	no	—
51	C₂×D₃₃₂	—	2	2	no	—
52	C₂×D₃₃₂	—	2	2	no	—
53	C₂×C₂²⋊D₈₃	—	4	2	no	—
54	C₂²×Dic₈₃	—	2	2	no	—
55	C₂×C₄×D₈₃	—	4	2	no	—
56	D₆₆₄	—	4	4	no	—
57	C₂×C₈₃⋊C₈	—	2	4	no	—
58	C₂×C₈₃⋊C₈	—	2	2	no	—
59	C₄⋊Dic₈₃	—	2	2	no	—
60	C₄⋊Dic₈₃	—	2	2	no	—
61	(C₂×D₈₃)⋊C₄	—	4	2	no	—
62	(C₂×D₈₃)⋊C₄	—	4	2	no	—
63	C₄×Dic₈₃	—	2	4	no	—
64	C₄×Dic₈₃	—	2	4	no	—
65	C₄×Dic₈₃	—	4	2	no	—
66	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
69	M₁₆×C₈₃	—	4	4	no	—
70	C₂×C₈×C₈₃	—	2	4	no	—
71	C₂×C₈×C₈₃	—	4	2	no	—
72	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
74	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₈₃	#41	1	1	yes	characteristic
78	C₂³×C₈₃	#121	1	1	yes	characteristic
79	C₂²×D₈₃	—	4	2	no	—
80	C₂×C₄×C₈₃	—	2	2	no	—
81	C₂×C₄×C₈₃	—	2	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	AGL(1,ℤ/8)	1	4	yes	—
89	C₂²⋊D₈₃	—	8	4	no	—
90	C₂×Dic₈₃	—	2	4	no	—
91	C₂×Dic₈₃	—	4	2	no	—
92	C₂×Dic₈₃	—	4	2	no	—
93	C₂×Dic₈₃	—	4	2	no	—
94	D₃₃₂	—	4	4	no	—
95	D₃₃₂	—	4	4	no	—
96	D₃₃₂	—	4	4	no	—
97	C₄×D₈₃	—	8	2	no	—
98	C₄×D₈₃	—	8	2	no	—
99	Dic₁₆₆	—	4	4	no	—
100	C₈×C₈₃	—	2	2	no	—
101	C₈×C₈₃	—	8	2	no	—
102	C₈×C₈₃	#104	1	4	yes	complemented
103	C₈₃⋊C₈	—	2	4	no	—
104	C₂²×C₈₃	—	2	1	no	—
105	C₂²×C₈₃	—	2	1	no	—
106	C₂²×C₈₃	#390	1	1	yes	characteristic
107	C₂²×C₈₃	#469	1	2	yes	—
108	C₂×D₈₃	—	8	2	no	—
109	C₂×D₈₃	—	8	2	no	—
110	C₂×D₈₃	—	8	2	no	—
111	C₄×C₈₃	—	2	1	no	—
112	C₄×C₈₃	—	2	1	no	—
113	C₄×C₈₃	C₂×#104	1	2	yes	—
114	C₄×C₈₃	#442	1	2	yes	—
115	C₄×C₈₃	#444	1	2	yes	—
116	C₄×C₈₃	#496	1	2	yes	—
117	Dic₈₃	—	4	4	no	—
118	Dic₈₃	—	8	2	no	—
119	#9849	—	83	1	no	maximal, Sylow
120	C₂×C₈₃	—	2	2	no	—
121	C₂×C₈₃	#1962	1	1	yes	characteristic
122	C₂×C₈₃	#1972	1	1	yes	characteristic
123	C₂×C₈₃	#1975	1	1	yes	characteristic
124	D₈₃	—	16	2	no	—
125	#3169	—	83	1	no	—
126	#1962	—	83	2	no	—
127	C₄×#97	—	83	1	no	—
128	#1566	D₈₃	1	1	yes	characteristic, complemented
129	#1492	—	83	2	no	—
130	C₈₃	#9849	1	1	yes	characteristic, complemented, Sylow
131	#532	—	83	2	no	—
132	#500	—	83	1	no	—
133	#493	—	83	1	no	—
134	#486	—	83	2	no	—
135	#466	—	166	2	no	—
136	C₄×D₈	—	166	2	no	—
137	#423	C₂×D₈₃	1	2	yes	—
138	C₂×#104	—	166	4	no	—
139	C₂×#97	—	166	2	no	—
140	C₂×C₄×C₈	—	83	1	no	—
141	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
142	C₄³	—	83	1	no	—
143	#334	—	2	2	no	—
144	D₄⋊C₈	—	166	4	no	—
145	C₂×#41	—	166	2	no	—
146	C₂×D₈	—	166	2	no	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂²×C₈	—	166	1	no	—
149	C₂²×C₈	D₃₃₂	1	2	yes	—
150	C₄⋊Q₈	—	83	2	no	—
151	#127	—	83	2	no	—
152	#124	—	166	2	no	—
153	#121	—	166	2	no	—
154	#121	—	166	2	no	—
155	C₄×D₄	—	166	2	no	—
156	C₄×D₄	—	166	2	no	—
157	C₂×C₄²	—	83	2	no	—
158	C₂×C₄²	—	166	1	no	—
159	C₂×C₄²	—	166	1	no	—
160	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
161	#107	—	166	2	no	—
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	#104	—	332	8	no	—
165	#102	—	166	4	no	—
166	#97	—	166	8	no	—
167	C₄×C₈	—	83	2	no	—
168	C₄×C₈	—	166	1	no	—
169	C₄×C₈	C₄×D₈₃	1	1	yes	characteristic
170	C₄×C₈	C₄×D₈₃	1	1	yes	characteristic
171	C₄×C₈	C₂²⋊D₈₃	1	2	yes	—
172	#41	—	332	4	no	—
173	#41	—	332	4	no	—
174	C₂×Q₈	—	166	2	no	—
175	C₂×D₄	—	332	2	no	—
176	C₂×D₄	—	166	2	no	—
177	C₂×D₄	—	166	2	no	—
178	C₂×D₄	—	166	2	no	—
179	C₂²×C₄	—	332	2	no	—
180	C₂²×C₄	—	166	2	no	—
181	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
182	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
183	C₂²×C₄	#13050591	1	1	yes	characteristic
184	D₈	—	332	4	no	—
185	M₁₆	—	4	4	no	—
186	C₂×C₈	—	2	4	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	166	4	no	—
189	C₂×C₈	—	166	2	no	—
190	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
191	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
192	C₄⋊C₄	—	166	2	no	—
193	C₄⋊C₄	—	166	2	no	—
194	C₂²⋊C₄	—	332	2	no	—
195	C₂²⋊C₄	—	332	2	no	—
196	C₄²	—	332	2	no	—
197	C₄²	—	166	4	no	—
198	C₄²	—	166	4	no	—
199	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
200	C₄²	D₄×D₈₃	1	1	yes	characteristic
201	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
202	C₄²	#13050591	1	1	yes	characteristic
203	C₂³	—	332	2	no	—
204	C₂³	#14581767	1	1	yes	characteristic
205	Q₈	—	332	4	no	—
206	D₄	—	332	4	no	—
207	D₄	—	332	4	no	—
208	D₄	—	332	4	no	—
209	D₄	—	664	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	332	2	no	—
213	C₂×C₄	—	332	2	no	—
214	C₂×C₄	—	332	2	no	—
215	C₂×C₄	—	664	2	no	—
216	C₂×C₄	—	664	2	no	—
217	C₂×C₄	—	166	4	no	—
218	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
219	C₂×C₄	#14581754	1	1	yes	characteristic
220	C₂×C₄	#14581754	1	1	yes	characteristic
221	C₂×C₄	#14581767	1	1	yes	characteristic
222	C₂×C₄	#14581781	1	1	yes	characteristic
223	C₂×C₄	#14581788	1	1	yes	characteristic
224	C₂×C₄	#14581819	1	4	yes	—
225	C₈	—	2	2	no	—
226	C₈	—	8	2	no	—
227	C₈	—	166	4	no	—
228	C₈	#14581718	1	4	yes	complemented
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	664	2	no	—
232	C₂²	—	664	2	no	—
233	C₂²	—	664	2	no	—
234	C₂²	#19127602	1	1	yes	characteristic
235	C₂²	#19127955	1	2	yes	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	332	4	no	—
239	C₄	—	664	2	no	—
240	C₄	C₂×#14581718	1	2	yes	—
241	C₄	#19127812	1	2	yes	—
242	C₄	#19127822	1	2	yes	—
243	C₄	#19128087	1	2	yes	—
244	C₂	—	2	2	no	—
245	C₂	—	1328	2	no	—
246	C₂	#24908290	1	1	yes	characteristic
247	C₂	#24908337	1	1	yes	characteristic
248	C₂	#24908354	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24918042

C₂

yes

maximal, characteristic

#24908290

C₂

yes

maximal, complemented

C₄×#14581702

C₂

yes

maximal, characteristic, complemented

#24905913

C₂

yes

maximal, complemented

C₈₃×#1566

C₂

yes

maximal, characteristic, complemented

#19128251

C₂²

yes

—

#19128106

C₄

yes

characteristic, complemented

#19128078

C₄

yes

characteristic, complemented

#19128048

C₄

yes

complemented

#19127937

—

C₄×D₆₆₄

—

C₂×#14581718

—

C₂×#14581702

—

C₂×C₄×C₈₃⋊C₈

C₂²

yes

characteristic

C₄²×Dic₈₃

C₂²

yes

characteristic

#19127428

—

#423×C₈₃

C₂²

yes

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

#334×C₈₃

—

C₂×#13050590

—

C₂×D₆₆₄

—

C₂²×C₈₃⋊C₈

—

#14581792

C₂×C₄

yes

—

#14581789

C₂×C₄

yes

—

#14581780

—

#14581766

—

#14581766

—

C₄×D₃₃₂

—

C₄×D₃₃₂

—

C₂×C₄×Dic₈₃

—

C₂×C₄×Dic₈₃

—

C₂×C₄×Dic₈₃

D₄

yes

—

—

—

—

—

C₄×C₈₃⋊C₈

—

C₄×C₈₃⋊C₈

D₄

yes

—

C₂×M₁₆×C₈₃

—

C₂²×C₈×C₈₃

D₄

yes

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

D₄

yes

—

#13050590

—

#13050590

—

C₂×Dic₁₆₆

—

C₂×D₃₃₂

—

C₂×D₃₃₂

—

C₂×D₃₃₂

—

C₂×C₂²⋊D₈₃

—

C₂²×Dic₈₃

—

C₂×C₄×D₈₃

—

D₆₆₄

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

(C₂×D₈₃)⋊C₄

—

(C₂×D₈₃)⋊C₄

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

#41

yes

characteristic

M₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

—

C₄²×C₈₃

C₂²×C₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

C₄²×C₈₃

yes

C₂³×C₈₃

yes

C₂²×D₈₃

—

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

—

C₂²⋊D₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

D₃₃₂

—

D₃₃₂

—

D₃₃₂

—

C₄×D₈₃

—

C₄×D₈₃

—

Dic₁₆₆

—

100

C₈×C₈₃

—

101

C₈×C₈₃

—

102

C₈×C₈₃

#104

yes

complemented

103

C₈₃⋊C₈

—

104

C₂²×C₈₃

—

105

C₂²×C₈₃

—

106

C₂²×C₈₃

#390

yes

characteristic

107

C₂²×C₈₃

#469

yes

—

108

C₂×D₈₃

—

109

C₂×D₈₃

—

110

C₂×D₈₃

—

111

C₄×C₈₃

—

112

C₄×C₈₃

—

113

C₄×C₈₃

C₂×#104

yes

—

114

C₄×C₈₃

#442

yes

—

115

C₄×C₈₃

#444

yes

—

116

C₄×C₈₃

#496

yes

—

117

Dic₈₃

—

118

Dic₈₃

—

119

#9849

—

maximal, Sylow

120

C₂×C₈₃

—

121

C₂×C₈₃

#1962

yes

characteristic

122

C₂×C₈₃

#1972

yes

characteristic

123

C₂×C₈₃

#1975

yes

characteristic

124

D₈₃

—

125

#3169

—

126

#1962

—

127

C₄×#97

—

128

#1566

D₈₃

yes

characteristic, complemented

129

#1492

—

130

C₈₃

#9849

yes

characteristic, complemented, Sylow

131

#532

—

132

#500

—

133

#493

—

134

#486

—

135

#466

—

166

—

136

C₄×D₈

—

166

—

137

#423

C₂×D₈₃

yes

—

138

C₂×#104

—

166

—

139

C₂×#97

—

166

—

140

C₂×C₄×C₈

—

141

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

142

C₄³

—

143

#334

—

144

D₄⋊C₈

—

166

—

145

C₂×#41

—

166

—

146

C₂×D₈

—

166

—

147

C₂×M₁₆

—

148

C₂²×C₈

—

166

—

149

C₂²×C₈

D₃₃₂

yes

—

150

C₄⋊Q₈

—

151

#127

—

152

#124

—

166

—

153

#121

—

166

—

154

#121

—

166

—

155

C₄×D₄

—

166

—

156

C₄×D₄

—

166

—

157

C₂×C₄²

—

158

C₂×C₄²

—

166

—

159

C₂×C₄²

—

166

—

160

C₂×C₄²

C₂²×D₈₃

yes

characteristic

161

#107

—

166

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

#104

—

332

—

165

#102

—

166

—

166

#97

—

166

—

167

C₄×C₈

—

168

C₄×C₈

—

166

—

169

C₄×C₈

C₄×D₈₃

yes

characteristic

170

C₄×C₈

C₄×D₈₃

yes

characteristic

171

C₄×C₈

C₂²⋊D₈₃

yes

—

172

#41

—

332

—

173

#41

—

332

—

174

C₂×Q₈

—

166

—

175

C₂×D₄

—

332

—

176

C₂×D₄

—

166

—

177

C₂×D₄

—

166

—

178

C₂×D₄

—

166

—

179

C₂²×C₄

—

332

—

180

C₂²×C₄

—

166

—

181

C₂²×C₄

D₄×D₈₃

yes

characteristic

182

C₂²×C₄

C₂×D₃₃₂

yes

characteristic

183

C₂²×C₄

#13050591

yes

characteristic

184

D₈

—

332

—

185

M₁₆

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

166

—

189

C₂×C₈

—

166

—

190

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

—

191

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

—

192

C₄⋊C₄

—

166

—

193

C₄⋊C₄

—

166

—

194

C₂²⋊C₄

—

332

—

195

C₂²⋊C₄

—

332

—

196

C₄²

—

332

—

197

C₄²

—

166

—

198

C₄²

—

166

—

199

C₄²

C₂×C₄×D₈₃

yes

characteristic

200

C₄²

D₄×D₈₃

yes

characteristic

201

C₄²

C₂×C₂²⋊D₈₃

yes

characteristic

202

C₄²

#13050591

yes

characteristic

203

C₂³

—

332

—

204

C₂³

#14581767

yes

characteristic

205

Q₈

—

332

—

206

D₄

—

332

—

207

D₄

—

332

—

208

D₄

—

332

—

209

D₄

—

664

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

332

—

213

C₂×C₄

—

332

—

214

C₂×C₄

—

332

—

215

C₂×C₄

—

664

—

216

C₂×C₄

—

664

—

217

C₂×C₄

—

166

—

218

C₂×C₄

C₂×(C₂×D₈₃)⋊C₄

yes

characteristic

219

C₂×C₄

#14581754

yes

characteristic

220

C₂×C₄

#14581754

yes

characteristic

221

C₂×C₄

#14581767

yes

characteristic

222

C₂×C₄

#14581781

yes

characteristic

223

C₂×C₄

#14581788

yes

characteristic

224

C₂×C₄

#14581819

yes

—

225

C₈

—

226

C₈

—

227

C₈

—

166

—

228

C₈

#14581718

yes

complemented

229

C₂²

—

230

C₂²

—

231

C₂²

—

664

—

232

C₂²

—

664

—

233

C₂²

—

664

—

234

C₂²

#19127602

yes

characteristic

235

C₂²

#19127955

yes

—

236

C₄

—

237

C₄

—

238

C₄

—

332

—

239

C₄

—

664

—

240

C₄

C₂×#14581718

yes

—

241

C₄

#19127812

yes

—

242

C₄

#19127822

yes

—

243

C₄

#19128087

yes

—

244

C₂

—

245

C₂

—

1328

—

246

C₂

#24908290

yes

characteristic

247

C₂

#24908337

yes

characteristic

248

C₂

#24908354

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14581788
commutator	C₄²×C₈₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1566	C₂
socle	C₂²×C₈₃	#390
prime radical	#24918042	C₂
cosocle	C₂×C₄²×C₈₃	C₂³
hypercenter	#1566	D₈₃
hypocenter	C₈₃	#9849
LCS	G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂×C₄

#14581788

commutator

C₄²×C₈₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1566

C₂

C₂²×C₈₃

C₂

C₂×C₄²×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
2. #24908290	C₂	semidirect
3. C₄×#14581702	C₂	semidirect
4. #24905913	C₂	semidirect
5. C₈₃×#1566	C₂	semidirect
7. #19128106	C₄	semidirect
8. #19128078	C₄	semidirect
9. #19128048	C₄	semidirect
102. C₈×C₈₃	#104	semidirect
128. #1566	D₈₃	semidirect
130. C₈₃	#9849	semidirect
228. C₈	#14581718	semidirect

H ≅ G/N

type

2. #24908290

C₂

semidirect

3. C₄×#14581702

C₂

semidirect

4. #24905913

C₂

semidirect

5. C₈₃×#1566

C₂

semidirect

7. #19128106

C₄

semidirect

8. #19128078

C₄

semidirect

9. #19128048

C₄

semidirect

102. C₈×C₈₃

#104

semidirect

128. #1566

D₈₃

semidirect

130. C₈₃

#9849

semidirect

228. C₈

#14581718

semidirect

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

subgroup	index
#24918042	2
#24908290	2
C₄×#14581702	2
#24905913	2
C₈₃×#1566	2
#9849	83

subgroup

index

C₈₃×#1566

Subgroups — #35304307

Conjugacy classes of subgroups

Complements

Maximal subgroups