Group #35304287 — subgroups

Subgroups — #35304287

Order 21248.

478 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 139 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	#24918049	C₂	1	1	yes	maximal, characteristic
2	#24908440	C₂	1	2	yes	maximal
3	#24906222	C₂	1	1	yes	maximal, characteristic
4	#24905919	C₂	1	2	yes	maximal
5	C₄²×C₈×C₈₃	C₂	1	1	yes	maximal, characteristic
6	#19128258	C₂²	1	2	yes	—
7	#19128106	C₄	1	1	yes	characteristic, complemented
8	#19128081	C₄	1	1	yes	characteristic, complemented
9	#19128052	C₄	1	2	yes	complemented
10	#19127942	—	2	2	no	—
11	C₄×Dic₃₃₂	—	2	2	no	—
12	#19127725	C₂²	1	2	yes	—
13	#19127461	—	2	4	no	—
14	#19127454	—	2	2	no	—
15	#19127433	—	2	4	no	—
16	C₂×C₄×C₈×C₈₃	—	2	2	no	—
17	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
19	C₄³×C₈₃	C₂²	1	1	yes	characteristic
20	C₂×Dic₃₃₂	—	2	2	no	—
21	C₂×#13050574	—	2	2	no	—
22	#14581792	C₂×C₄	1	2	yes	—
23	#14581792	C₂×C₄	1	2	yes	—
24	#14581784	—	2	2	no	—
25	#14581771	—	2	2	no	—
26	#14581771	—	2	2	no	—
27	C₄×Dic₁₆₆	—	2	2	no	—
28	C₄×Dic₁₆₆	—	2	2	no	—
29	#14581751	—	2	2	no	—
30	#14581726	—	2	2	no	—
31	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
32	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
33	#14581717	—	2	4	no	—
34	C₂²×C₈×C₈₃	—	2	1	no	—
35	C₂²×C₈×C₈₃	D₄	1	2	yes	—
36	C₂×C₄²×C₈₃	—	2	1	no	—
37	C₂×C₄²×C₈₃	—	2	1	no	—
38	C₂×C₄²×C₈₃	D₄	1	2	yes	—
39	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
40	C₄×C₈×C₈₃	—	2	8	no	—
41	C₄×C₈×C₈₃	—	2	1	no	—
42	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₈₃	D₄	1	2	yes	—
45	C₄×C₈×C₈₃	D₄	1	2	yes	—
46	C₂×Dic₁₆₆	—	2	2	no	—
47	C₂×Dic₁₆₆	—	2	2	no	—
48	Dic₃₃₂	—	4	4	no	—
49	#13050574	—	4	4	no	—
50	C₂×C₈₃⋊C₈	—	4	2	no	—
51	C₄⋊Dic₈₃	—	2	2	no	—
52	C₄⋊Dic₈₃	—	2	2	no	—
53	C₄⋊Dic₈₃	—	2	2	no	—
54	C₄⋊Dic₈₃	—	2	2	no	—
55	Dic₈₃⋊C₄	—	4	2	no	—
56	Dic₈₃⋊C₄	—	4	2	no	—
57	C₂²⋊Dic₈₃	—	4	2	no	—
58	C₄×Dic₈₃	—	4	2	no	—
59	C₂²×C₄×C₈₃	—	2	2	no	—
60	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
63	C₂×C₈×C₈₃	—	2	4	no	—
64	C₂×C₈×C₈₃	—	2	2	no	—
65	C₂×C₈×C₈₃	—	2	4	no	—
66	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
67	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₈₃	—	2	4	no	—
69	C₄²×C₈₃	—	2	4	no	—
70	C₄²×C₈₃	—	2	2	no	—
71	C₄²×C₈₃	Q₁₆	1	4	yes	complemented
72	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₈₃	#41	1	1	yes	characteristic
76	C₂³×C₈₃	#121	1	1	yes	characteristic
77	C₂×C₄×C₈₃	—	2	4	no	—
78	C₂×C₄×C₈₃	—	2	4	no	—
79	C₂×C₄×C₈₃	—	2	4	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	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₈₃	#135	1	2	yes	—
90	C₂×Dic₈₃	—	4	2	no	—
91	C₂×Dic₈₃	—	4	2	no	—
92	Dic₁₆₆	—	4	4	no	—
93	Dic₁₆₆	—	4	4	no	—
94	C₈×C₈₃	—	2	4	no	—
95	C₈×C₈₃	—	2	2	no	—
96	C₈×C₈₃	#104	1	4	yes	—
97	C₈₃⋊C₈	—	8	2	no	—
98	C₂²×C₈₃	—	2	1	no	—
99	C₂²×C₈₃	—	2	1	no	—
100	C₂²×C₈₃	#390	1	1	yes	characteristic
101	C₂²×C₈₃	#467	1	2	yes	—
102	C₄×C₈₃	—	2	8	no	—
103	C₄×C₈₃	—	2	1	no	—
104	C₄×C₈₃	—	2	1	no	—
105	C₄×C₈₃	C₂×#104	1	2	yes	—
106	C₄×C₈₃	C₄×Q₁₆	1	2	yes	—
107	C₄×C₈₃	#443	1	2	yes	—
108	C₄×C₈₃	#494	1	1	yes	characteristic
109	C₄×C₈₃	#495	1	1	yes	characteristic
110	Dic₈₃	—	8	2	no	—
111	Dic₈₃	—	8	2	no	—
112	#9845	—	83	1	no	maximal, Sylow
113	C₂×C₈₃	—	2	2	no	—
114	C₂×C₈₃	#1962	1	1	yes	characteristic
115	C₂×C₈₃	#1969	1	1	yes	characteristic
116	C₂×C₈₃	#1974	1	1	yes	characteristic
117	#3170	—	83	1	no	—
118	#1994	—	83	2	no	—
119	C₄²×C₈	D₈₃	1	1	yes	characteristic
120	#1567	—	83	1	no	—
121	#1493	—	83	2	no	—
122	C₈₃	#9845	1	1	yes	characteristic, complemented, Sylow
123	#533	—	83	2	no	—
124	#500	—	83	1	no	—
125	#494	—	83	1	no	—
126	#487	—	83	2	no	—
127	#467	—	166	2	no	—
128	C₄×Q₁₆	—	166	2	no	—
129	#423	—	83	2	no	—
130	C₂×C₄×C₈	—	2	2	no	—
131	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
132	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
133	C₄³	C₂×D₈₃	1	1	yes	characteristic
134	#339	—	166	4	no	—
135	#335	—	166	2	no	—
136	Q₈⋊C₈	—	166	4	no	—
137	C₂×Q₁₆	—	166	2	no	—
138	C₂×M₁₆	—	166	2	no	—
139	C₂²×C₈	—	2	1	no	—
140	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
141	C₄⋊Q₈	—	83	2	no	—
142	C₄⋊Q₈	—	83	2	no	—
143	#125	—	166	2	no	—
144	C₂²⋊Q₈	—	166	2	no	—
145	C₂²⋊Q₈	—	166	2	no	—
146	C₄×Q₈	—	166	2	no	—
147	C₄×Q₈	—	166	2	no	—
148	#117	—	166	2	no	—
149	C₂×C₄²	—	2	1	no	—
150	C₂×C₄²	—	2	1	no	—
151	C₂×C₄²	D₃₃₂	1	2	yes	—
152	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
153	#107	—	166	2	no	—
154	C₄⋊C₈	—	166	2	no	—
155	C₄⋊C₈	—	166	2	no	—
156	#103	—	166	4	no	—
157	C₄×C₈	—	2	8	no	—
158	C₄×C₈	—	2	1	no	—
159	C₄×C₈	C₄×D₈₃	1	1	yes	characteristic
160	C₄×C₈	C₄×D₈₃	1	1	yes	characteristic
161	C₄×C₈	D₃₃₂	1	2	yes	—
162	C₄×C₈	D₃₃₂	1	2	yes	—
163	C₂×Q₈	—	166	2	no	—
164	C₂×Q₈	—	166	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
167	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
168	C₂²×C₄	#13050590	1	1	yes	characteristic
169	Q₁₆	—	332	4	no	—
170	M₁₆	—	332	4	no	—
171	C₂×C₈	—	2	4	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	332	2	no	—
175	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
176	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
177	C₄⋊C₄	—	332	2	no	—
178	C₄⋊C₄	—	332	2	no	—
179	C₄⋊C₄	—	166	2	no	—
180	C₄⋊C₄	—	166	2	no	—
181	C₄⋊C₄	—	166	2	no	—
182	C₄⋊C₄	—	166	2	no	—
183	C₂²⋊C₄	—	332	2	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	4	no	—
186	C₄²	—	2	2	no	—
187	C₄²	—	332	2	no	—
188	C₄²	Dic₃₃₂	1	4	yes	complemented
189	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
190	C₄²	C₂×D₃₃₂	1	1	yes	characteristic
191	C₄²	C₂×D₃₃₂	1	1	yes	characteristic
192	C₄²	#13050590	1	1	yes	characteristic
193	C₂³	#14581766	1	1	yes	characteristic
194	Q₈	—	332	4	no	—
195	Q₈	—	332	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	332	2	no	—
202	C₂×C₄	—	332	2	no	—
203	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₄×D₃₃₂	1	1	yes	characteristic
205	C₂×C₄	C₄×D₃₃₂	1	1	yes	characteristic
206	C₂×C₄	#14581766	1	1	yes	characteristic
207	C₂×C₄	#14581780	1	1	yes	characteristic
208	C₂×C₄	#14581789	1	1	yes	characteristic
209	C₂×C₄	C₂×Dic₃₃₂	1	2	yes	—
210	C₂×C₄	#14581814	1	2	yes	—
211	C₈	—	2	4	no	—
212	C₈	—	2	2	no	—
213	C₈	—	664	2	no	—
214	C₈	#14581720	1	4	yes	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	1	no	—
217	C₂²	#19127603	1	1	yes	characteristic
218	C₂²	#19127942	1	2	yes	—
219	C₄	—	2	8	no	—
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	664	2	no	—
223	C₄	—	664	2	no	—
224	C₄	C₂×#14581720	1	2	yes	—
225	C₄	C₄×Dic₃₃₂	1	2	yes	—
226	C₄	#19127819	1	2	yes	—
227	C₄	#19128081	1	1	yes	characteristic
228	C₄	#19128085	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	#24908291	1	1	yes	characteristic
231	C₂	#24908324	1	1	yes	characteristic
232	C₂	#24908351	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24918049

C₂

yes

maximal, characteristic

#24908440

C₂

yes

maximal

#24906222

C₂

yes

maximal, characteristic

#24905919

C₂

yes

maximal

C₄²×C₈×C₈₃

C₂

yes

maximal, characteristic

#19128258

C₂²

yes

—

#19128106

C₄

yes

characteristic, complemented

#19128081

C₄

yes

characteristic, complemented

#19128052

C₄

yes

complemented

#19127942

—

C₄×Dic₃₃₂

—

#19127725

C₂²

yes

—

#19127461

—

#19127454

—

#19127433

—

C₂×C₄×C₈×C₈₃

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₄³×C₈₃

C₂²

yes

characteristic

C₂×Dic₃₃₂

—

C₂×#13050574

—

#14581792

C₂×C₄

yes

—

#14581792

C₂×C₄

yes

—

#14581784

—

#14581771

—

#14581771

—

C₄×Dic₁₆₆

—

C₄×Dic₁₆₆

—

#14581751

—

#14581726

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

#14581717

—

C₂²×C₈×C₈₃

—

C₂²×C₈×C₈₃

D₄

yes

—

C₂×C₄²×C₈₃

—

C₂×C₄²×C₈₃

—

C₂×C₄²×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

—

C₄×C₈×C₈₃

D₄

yes

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

Dic₃₃₂

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

#41

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

—

C₄²×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

Q₁₆

yes

complemented

C₄²×C₈₃

C₂²×C₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

C₄²×C₈₃

yes

C₂³×C₈₃

yes

C₂×C₄×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

C₂×Q₁₆

yes

—

C₂×C₄×C₈₃

#135

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

#104

yes

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

100

C₂²×C₈₃

#390

yes

characteristic

101

C₂²×C₈₃

#467

yes

—

102

C₄×C₈₃

—

103

C₄×C₈₃

—

104

C₄×C₈₃

—

105

C₄×C₈₃

C₂×#104

yes

—

106

C₄×C₈₃

C₄×Q₁₆

yes

—

107

C₄×C₈₃

#443

yes

—

108

C₄×C₈₃

#494

yes

characteristic

109

C₄×C₈₃

#495

yes

characteristic

110

Dic₈₃

—

111

Dic₈₃

—

112

#9845

—

maximal, Sylow

113

C₂×C₈₃

—

114

C₂×C₈₃

#1962

yes

characteristic

115

C₂×C₈₃

#1969

yes

characteristic

116

C₂×C₈₃

#1974

yes

characteristic

117

#3170

—

118

#1994

—

119

C₄²×C₈

D₈₃

yes

characteristic

120

#1567

—

121

#1493

—

122

C₈₃

#9845

yes

characteristic, complemented, Sylow

123

#533

—

124

#500

—

125

#494

—

126

#487

—

127

#467

—

166

—

128

C₄×Q₁₆

—

166

—

129

#423

—

130

C₂×C₄×C₈

—

131

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

132

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

133

C₄³

C₂×D₈₃

yes

characteristic

134

#339

—

166

—

135

#335

—

166

—

136

Q₈⋊C₈

—

166

—

137

C₂×Q₁₆

—

166

—

138

C₂×M₁₆

—

166

—

139

C₂²×C₈

—

140

C₂²×C₈

C₂²⋊D₈₃

yes

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

#125

—

166

—

144

C₂²⋊Q₈

—

166

—

145

C₂²⋊Q₈

—

166

—

146

C₄×Q₈

—

166

—

147

C₄×Q₈

—

166

—

148

#117

—

166

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

D₃₃₂

yes

—

152

C₂×C₄²

C₂²×D₈₃

yes

characteristic

153

#107

—

166

—

154

C₄⋊C₈

—

166

—

155

C₄⋊C₈

—

166

—

156

#103

—

166

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

C₄×D₈₃

yes

characteristic

160

C₄×C₈

C₄×D₈₃

yes

characteristic

161

C₄×C₈

D₃₃₂

yes

—

162

C₄×C₈

D₃₃₂

yes

—

163

C₂×Q₈

—

166

—

164

C₂×Q₈

—

166

—

165

C₂²×C₄

—

166

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

167

C₂²×C₄

C₂×D₃₃₂

yes

characteristic

168

C₂²×C₄

#13050590

yes

characteristic

169

Q₁₆

—

332

—

170

M₁₆

—

332

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

332

—

175

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

—

176

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

—

177

C₄⋊C₄

—

332

—

178

C₄⋊C₄

—

332

—

179

C₄⋊C₄

—

166

—

180

C₄⋊C₄

—

166

—

181

C₄⋊C₄

—

166

—

182

C₄⋊C₄

—

166

—

183

C₂²⋊C₄

—

332

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

332

—

188

C₄²

Dic₃₃₂

yes

complemented

189

C₄²

C₂×C₄×D₈₃

yes

characteristic

190

C₄²

C₂×D₃₃₂

yes

characteristic

191

C₄²

C₂×D₃₃₂

yes

characteristic

192

C₄²

#13050590

yes

characteristic

193

C₂³

#14581766

yes

characteristic

194

Q₈

—

332

—

195

Q₈

—

332

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

332

—

202

C₂×C₄

—

332

—

203

C₂×C₄

C₂×(C₂×D₈₃)⋊C₄

yes

characteristic

204

C₂×C₄

C₄×D₃₃₂

yes

characteristic

205

C₂×C₄

C₄×D₃₃₂

yes

characteristic

206

C₂×C₄

#14581766

yes

characteristic

207

C₂×C₄

#14581780

yes

characteristic

208

C₂×C₄

#14581789

yes

characteristic

209

C₂×C₄

C₂×Dic₃₃₂

yes

—

210

C₂×C₄

#14581814

yes

—

211

C₈

—

212

C₈

—

213

C₈

—

664

—

214

C₈

#14581720

yes

—

215

C₂²

—

216

C₂²

—

217

C₂²

#19127603

yes

characteristic

218

C₂²

#19127942

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

664

—

223

C₄

—

664

—

224

C₄

C₂×#14581720

yes

—

225

C₄

C₄×Dic₃₃₂

yes

—

226

C₄

#19127819

yes

—

227

C₄

#19128081

yes

characteristic

228

C₄

#19128085

yes

characteristic

229

C₂

—

230

C₂

#24908291

yes

characteristic

231

C₂

#24908324

yes

characteristic

232

C₂

#24908351

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14581789
commutator	C₄²×C₈₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₄²×C₈×C₈₃	C₂
socle	C₂²×C₈₃	#390
prime radical	C₂³×C₈₃	#121
cosocle	C₂×C₄²×C₈₃	C₂³
hypercenter	C₄²×C₈	D₈₃
hypocenter	C₈₃	#9845
LCS	G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄²×C₈

subgroup

G/H

center

C₂×C₄

#14581789

commutator

C₄²×C₈₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₄²×C₈×C₈₃

C₂

C₂²×C₈₃

C₂³×C₈₃

C₂×C₄²×C₈₃

C₂³

hypercenter

C₄²×C₈

D₈₃

hypocenter

C₈₃

#9845

LCS

G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄²×C₈

N	H ≅ G/N	type
7. #19128106	C₄	semidirect
8. #19128081	C₄	semidirect
9. #19128052	C₄	semidirect
71. C₄²×C₈₃	Q₁₆	semidirect
122. C₈₃	#9845	semidirect
188. C₄²	Dic₃₃₂	semidirect

H ≅ G/N

type

7. #19128106

C₄

semidirect

8. #19128081

C₄

semidirect

9. #19128052

C₄

semidirect

71. C₄²×C₈₃

Q₁₆

semidirect

122. C₈₃

#9845

semidirect

188. C₄²

Dic₃₃₂

semidirect

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

subgroup	index
#24918049	2
#24908440	2
#24906222	2
#24905919	2
C₄²×C₈×C₈₃	2
#9845	83

subgroup

index

C₄²×C₈×C₈₃

Subgroups — #35304287

Conjugacy classes of subgroups

Complements

Maximal subgroups