Group #24920384 — subgroups

Subgroups — #24920384

Order 10624.

360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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	#19128429	C₂	1	1	yes	maximal, characteristic, complemented
2	#19128107	C₂	1	2	yes	maximal, complemented
3	#19128104	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128001	C₂	1	2	yes	maximal
5	#19127993	C₂	1	2	yes	maximal, complemented
6	#19127983	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127981	C₂	1	1	yes	maximal, characteristic
8	#19127832	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127801	C₂	1	2	yes	maximal
10	C₄×#13050578	C₂	1	1	yes	maximal, characteristic
11	D₄×Q₈×C₈₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#13050578	C₂²	1	1	yes	characteristic
13	#14581792	C₂²	1	1	yes	characteristic
14	#14581790	—	2	1	no	—
15	#14581784	C₂²	1	2	yes	—
16	#14581782	—	2	2	no	—
17	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
18	C₄×Dic₁₆₆	C₂²	1	2	yes	—
19	#14581757	—	2	1	no	—
20	#14581725	C₂²	1	2	yes	—
21	#14581725	C₂²	1	2	yes	—
22	#14581725	C₂²	1	2	yes	—
23	#14581723	C₂²	1	1	yes	characteristic
24	#14581723	C₂²	1	2	yes	—
25	C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
26	C₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
27	#14581715	C₂²	1	2	yes	—
28	#14581715	C₂²	1	1	yes	characteristic
29	#14581713	C₂²	1	2	yes	—
30	#14581713	C₂²	1	1	yes	characteristic
31	#14581703	C₂²	1	2	yes	—
32	C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₂²×Q₈×C₈₃	—	2	1	no	—
34	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
35	C₄⋊Q₈×C₈₃	C₂²	1	2	yes	—
36	C₂²⋊Q₈×C₈₃	—	2	2	no	—
37	C₂²⋊Q₈×C₈₃	—	2	1	no	—
38	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
40	C₄×D₄×C₈₃	C₂²	1	2	yes	—
41	C₂×Dic₁₆₆	—	2	1	no	—
42	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
43	#13050578	Q₈	1	4	yes	complemented
44	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
45	C₂×C₈₃⋊C₈	C₂³	1	2	yes	—
46	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
47	C₄⋊Dic₈₃	—	2	1	no	—
48	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
49	C₄⋊Dic₈₃	C₂³	1	2	yes	—
50	Dic₈₃⋊C₄	—	2	1	no	—
51	Dic₈₃⋊C₄	—	2	2	no	—
52	Dic₈₃⋊C₄	—	2	2	no	—
53	Dic₈₃⋊C₄	—	2	2	no	—
54	C₄×Dic₈₃	—	2	2	no	—
55	C₄×Dic₈₃	—	2	1	no	—
56	C₂×Q₈×C₈₃	—	2	2	no	—
57	C₂×Q₈×C₈₃	—	2	1	no	—
58	C₂×Q₈×C₈₃	—	4	4	no	—
59	C₂×Q₈×C₈₃	D₄	1	1	yes	characteristic
60	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₈₃	—	2	2	no	—
62	C₂²×C₄×C₈₃	—	2	1	no	—
63	C₄⋊C₄×C₈₃	—	2	2	no	—
64	C₄⋊C₄×C₈₃	—	2	1	no	—
65	C₄⋊C₄×C₈₃	D₄	1	2	yes	—
66	C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
67	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
68	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
69	C₂²⋊C₄×C₈₃	—	2	2	no	—
70	C₂²⋊C₄×C₈₃	—	2	1	no	—
71	C₄²×C₈₃	C₂³	1	2	yes	—
72	C₄²×C₈₃	C₂³	1	1	yes	characteristic
73	C₂³×C₈₃	—	2	1	no	—
74	Q₈×C₈₃	—	2	2	no	—
75	Q₈×C₈₃	—	4	4	no	—
76	Q₈×C₈₃	—	4	2	no	—
77	D₄×C₈₃	—	2	1	no	—
78	D₄×C₈₃	C₂×Q₈	1	2	yes	—
79	C₂×C₄×C₈₃	—	2	2	no	—
80	C₂×C₄×C₈₃	—	2	1	no	—
81	C₂×C₄×C₈₃	—	4	4	no	—
82	C₂×C₄×C₈₃	—	4	2	no	—
83	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
86	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
88	C₂×Dic₈₃	—	2	1	no	—
89	C₂×Dic₈₃	—	2	1	no	—
90	C₂×Dic₈₃	—	2	2	no	—
91	Dic₁₆₆	—	2	1	no	—
92	Dic₁₆₆	—	4	2	no	—
93	Dic₁₆₆	C₂×Q₈	1	2	yes	complemented
94	C₈₃⋊C₈	—	2	1	no	—
95	C₈₃⋊C₈	—	2	2	no	—
96	C₈₃⋊C₈	C₂×Q₈	1	2	yes	complemented
97	C₂²×C₈₃	—	2	2	no	—
98	C₂²×C₈₃	—	4	1	no	—
99	C₂²×C₈₃	—	4	1	no	—
100	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
101	C₄×C₈₃	—	2	2	no	—
102	C₄×C₈₃	—	2	2	no	—
103	C₄×C₈₃	—	2	1	no	—
104	C₄×C₈₃	—	4	2	no	—
105	C₄×C₈₃	—	4	1	no	—
106	C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
107	C₄×C₈₃	C₂²×Q₈	1	1	yes	characteristic
108	C₄×C₈₃	2₋¹⁺⁴	1	1	yes	characteristic
109	Dic₈₃	—	2	2	no	—
110	Dic₈₃	—	4	2	no	—
111	Dic₈₃	—	4	1	no	—
112	C₂×C₈₃	—	4	2	no	—
113	C₂×C₈₃	D₄×Q₈	1	1	yes	characteristic
114	C₂×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
115	C₂×C₈₃	#578	1	1	yes	characteristic
116	#3386	—	83	1	no	maximal, Sylow
117	C₈₃	#3386	1	1	yes	characteristic, complemented, Sylow
118	#557	—	83	1	no	—
119	D₄×Q₈	D₈₃	1	1	yes	characteristic
120	#501	—	83	2	no	—
121	#500	—	83	1	no	—
122	#478	—	83	2	no	—
123	#477	—	83	2	no	—
124	#475	—	83	1	no	—
125	#474	—	83	1	no	—
126	#446	—	83	1	no	—
127	#440	—	83	2	no	—
128	C₄×SD₁₆	—	83	1	no	—
129	C₂²×Q₈	—	2	1	no	—
130	C₂×SD₁₆	—	83	1	no	—
131	C₄⋊Q₈	—	83	1	no	—
132	C₄⋊Q₈	—	166	1	no	—
133	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
134	C₄⋊Q₈	C₂×D₈₃	1	2	yes	—
135	#125	—	83	2	no	—
136	#125	—	166	2	no	—
137	C₂²⋊Q₈	—	2	1	no	—
138	C₂²⋊Q₈	—	2	2	no	—
139	C₄×Q₈	—	83	1	no	—
140	C₄×Q₈	—	83	2	no	—
141	C₄×Q₈	—	166	1	no	—
142	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
143	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
144	C₄×D₄	C₂×D₈₃	1	2	yes	—
145	#107	—	83	2	no	—
146	#107	—	83	2	no	—
147	#107	—	83	2	no	—
148	#106	—	83	1	no	—
149	#106	—	83	2	no	—
150	C₄⋊C₈	—	83	1	no	—
151	C₄⋊C₈	—	83	2	no	—
152	#103	—	83	1	no	—
153	#103	—	83	2	no	—
154	#102	—	83	1	no	—
155	#102	—	83	2	no	—
156	#97	—	83	2	no	—
157	C₄×C₈	—	83	1	no	—
158	C₂×Q₈	—	2	2	no	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×Q₈	—	4	4	no	—
161	C₂×Q₈	—	83	1	no	—
162	C₂×Q₈	—	166	1	no	—
163	C₂×Q₈	C₂²⋊D₈₃	1	1	yes	characteristic
164	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	2	1	no	—
167	SD₁₆	—	83	4	no	—
168	C₂×C₈	—	83	1	no	—
169	C₂×C₈	—	83	1	no	—
170	C₂×C₈	—	83	2	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	2	1	no	—
173	C₄⋊C₄	—	83	1	no	—
174	C₄⋊C₄	—	83	2	no	—
175	C₄⋊C₄	—	166	1	no	—
176	C₄⋊C₄	—	166	2	no	—
177	C₄⋊C₄	—	166	2	no	—
178	C₄⋊C₄	—	166	2	no	—
179	C₄⋊C₄	—	166	1	no	—
180	C₄⋊C₄	C₂²⋊D₈₃	1	1	yes	characteristic
181	C₄⋊C₄	C₂²⋊D₈₃	1	2	yes	—
182	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
183	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
184	C₂²⋊C₄	—	2	2	no	—
185	C₂²⋊C₄	—	2	1	no	—
186	C₄²	—	166	2	no	—
187	C₄²	—	166	1	no	—
188	C₄²	C₂²×D₈₃	1	1	yes	characteristic
189	C₄²	C₂²×D₈₃	1	2	yes	—
190	C₂³	—	2	1	no	—
191	Q₈	—	2	2	no	—
192	Q₈	—	4	4	no	—
193	Q₈	—	4	2	no	—
194	Q₈	—	332	2	no	—
195	Q₈	—	83	2	no	—
196	Q₈	—	166	1	no	—
197	D₄	—	2	1	no	—
198	D₄	Q₈×D₈₃	1	2	yes	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	166	1	no	—
204	C₂×C₄	—	166	2	no	—
205	C₂×C₄	—	166	1	no	—
206	C₂×C₄	C₂×C₂²⋊D₈₃	1	2	yes	—
207	C₂×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
208	C₂×C₄	C₂×C₂²⋊D₈₃	1	2	yes	—
209	C₂×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
210	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
211	C₈	—	83	2	no	—
212	C₈	—	166	1	no	—
213	C₈	—	166	2	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	4	1	no	—
216	C₂²	—	4	1	no	—
217	C₂²	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
218	C₄	—	2	2	no	—
219	C₄	—	2	2	no	—
220	C₄	—	2	1	no	—
221	C₄	—	4	2	no	—
222	C₄	—	4	1	no	—
223	C₄	—	332	2	no	—
224	C₄	—	332	1	no	—
225	C₄	—	166	2	no	—
226	C₄	#14581818	1	2	yes	—
227	C₄	C₂×Q₈×D₈₃	1	1	yes	characteristic
228	C₄	#14581840	1	1	yes	characteristic
229	C₂	—	4	2	no	—
230	C₂	Q₈×C₂²⋊D₈₃	1	1	yes	characteristic
231	C₂	C₂×#14581818	1	1	yes	characteristic
232	C₂	#19128516	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19128429

C₂

yes

maximal, characteristic, complemented

#19128107

C₂

yes

maximal, complemented

#19128104

C₂

yes

maximal, characteristic, complemented

#19128001

C₂

yes

maximal

#19127993

C₂

yes

maximal, complemented

#19127983

C₂

yes

maximal, characteristic, complemented

#19127981

C₂

yes

maximal, characteristic

#19127832

C₂

yes

maximal, characteristic, complemented

#19127801

C₂

yes

maximal

C₄×#13050578

C₂

yes

maximal, characteristic

D₄×Q₈×C₈₃

C₂

yes

maximal, characteristic

C₂×#13050578

C₂²

yes

characteristic

#14581792

C₂²

yes

characteristic

#14581790

—

#14581784

C₂²

yes

—

#14581782

—

C₄×Dic₁₆₆

C₂²

yes

characteristic

C₄×Dic₁₆₆

C₂²

yes

—

#14581757

—

#14581725

C₂²

yes

—

#14581725

C₂²

yes

—

#14581725

C₂²

yes

—

#14581723

C₂²

yes

characteristic

#14581723

C₂²

yes

—

C₄⋊(C₈₃⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₈₃⋊C₈)

C₂²

yes

—

#14581715

C₂²

yes

—

#14581715

C₂²

yes

characteristic

#14581713

C₂²

yes

—

#14581713

C₂²

yes

characteristic

#14581703

C₂²

yes

—

C₄×C₈₃⋊C₈

C₂²

yes

characteristic

C₂²×Q₈×C₈₃

—

C₄⋊Q₈×C₈₃

C₂²

yes

characteristic

C₄⋊Q₈×C₈₃

C₂²

yes

—

C₂²⋊Q₈×C₈₃

—

C₂²⋊Q₈×C₈₃

—

C₄×Q₈×C₈₃

C₂²

yes

characteristic

C₄×D₄×C₈₃

C₂²

yes

characteristic

C₄×D₄×C₈₃

C₂²

yes

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

C₂³

yes

characteristic

#13050578

Q₈

yes

complemented

C₂×C₈₃⋊C₈

C₂³

yes

characteristic

C₂×C₈₃⋊C₈

C₂³

yes

—

C₂×C₈₃⋊C₈

C₂³

yes

characteristic

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

C₂³

yes

characteristic

C₄⋊Dic₈₃

C₂³

yes

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

D₄

yes

characteristic

C₂×D₄×C₈₃

C₂³

yes

characteristic

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

D₄

yes

—

C₄⋊C₄×C₈₃

D₄

yes

characteristic

C₄⋊C₄×C₈₃

C₂³

yes

characteristic

C₄⋊C₄×C₈₃

C₂³

yes

—

C₂²⋊C₄×C₈₃

—

C₂²⋊C₄×C₈₃

—

C₄²×C₈₃

C₂³

yes

—

C₄²×C₈₃

C₂³

yes

characteristic

C₂³×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

—

D₄×C₈₃

—

D₄×C₈₃

C₂×Q₈

yes

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂×D₄

yes

—

C₂×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂×C₄×C₈₃

C₂×D₄

yes

—

C₂×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂×C₄×C₈₃

C₂⁴

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

C₂×Q₈

yes

complemented

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₈₃⋊C₈

C₂×Q₈

yes

complemented

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

100

C₂²×C₈₃

C₂²×D₄

yes

characteristic

101

C₄×C₈₃

—

102

C₄×C₈₃

—

103

C₄×C₈₃

—

104

C₄×C₈₃

—

105

C₄×C₈₃

—

106

C₄×C₈₃

AGL(1,ℤ/8)

yes

—

107

C₄×C₈₃

C₂²×Q₈

yes

characteristic

108

C₄×C₈₃

2₋¹⁺⁴

yes

characteristic

109

Dic₈₃

—

110

Dic₈₃

—

111

Dic₈₃

—

112

C₂×C₈₃

—

113

C₂×C₈₃

D₄×Q₈

yes

characteristic

114

C₂×C₈₃

C₂×AGL(1,ℤ/8)

yes

characteristic

115

C₂×C₈₃

yes

116

—

117

C₈₃

#3386

yes

characteristic, complemented, Sylow

118

#557

—

119

D₄×Q₈

D₈₃

yes

characteristic

120

#501

—

121

#500

—

122

#478

—

123

#477

—

124

#475

—

125

#474

—

126

#446

—

127

#440

—

128

C₄×SD₁₆

—

129

C₂²×Q₈

—

130

C₂×SD₁₆

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

166

—

133

C₄⋊Q₈

C₂×D₈₃

yes

characteristic

134

C₄⋊Q₈

C₂×D₈₃

yes

—

135

#125

—

136

#125

—

166

—

137

C₂²⋊Q₈

—

138

C₂²⋊Q₈

—

139

C₄×Q₈

—

140

C₄×Q₈

—

141

C₄×Q₈

—

166

—

142

C₄×Q₈

C₂×D₈₃

yes

characteristic

143

C₄×D₄

C₂×D₈₃

yes

characteristic

144

C₄×D₄

C₂×D₈₃

yes

—

145

#107

—

146

#107

—

147

#107

—

148

#106

—

149

#106

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

#103

—

153

#103

—

154

#102

—

155

#102

—

156

#97

—

157

C₄×C₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

166

—

163

C₂×Q₈

C₂²⋊D₈₃

yes

characteristic

164

C₂×D₄

C₂²×D₈₃

yes

characteristic

165

C₂²×C₄

—

166

C₂²×C₄

—

167

SD₁₆

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

166

—

176

C₄⋊C₄

—

166

—

177

C₄⋊C₄

—

166

—

178

C₄⋊C₄

—

166

—

179

C₄⋊C₄

—

166

—

180

C₄⋊C₄

C₂²⋊D₈₃

yes

characteristic

181

C₄⋊C₄

C₂²⋊D₈₃

yes

—

182

C₄⋊C₄

C₂²×D₈₃

yes

characteristic

183

C₄⋊C₄

C₂²×D₈₃

yes

—

184

C₂²⋊C₄

—

185

C₂²⋊C₄

—

186

C₄²

—

166

—

187

C₄²

—

166

—

188

C₄²

C₂²×D₈₃

yes

characteristic

189

C₄²

C₂²×D₈₃

yes

—

190

C₂³

—

191

Q₈

—

192

Q₈

—

193

Q₈

—

194

Q₈

—

332

—

195

Q₈

—

196

Q₈

—

166

—

197

D₄

—

198

D₄

Q₈×D₈₃

yes

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

166

—

204

C₂×C₄

—

166

—

205

C₂×C₄

—

166

—

206

C₂×C₄

C₂×C₂²⋊D₈₃

yes

—

207

C₂×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

208

C₂×C₄

C₂×C₂²⋊D₈₃

yes

—

209

C₂×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

210

C₂×C₄

C₂³×D₈₃

yes

characteristic

211

C₈

—

212

C₈

—

166

—

213

C₈

—

166

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₂²×C₂²⋊D₈₃

yes

characteristic

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

332

—

224

C₄

—

332

—

225

C₄

—

166

—

226

C₄

#14581818

yes

—

227

C₄

C₂×Q₈×D₈₃

yes

characteristic

228

C₄

#14581840

yes

characteristic

229

C₂

—

230

C₂

Q₈×C₂²⋊D₈₃

yes

characteristic

231

C₂

C₂×#14581818

yes

characteristic

232

C₂

#19128516

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	D₄×Q₈×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
prime radical	C₂×D₄×C₈₃	C₂³
hypercenter	D₄×Q₈	D₈₃
hypocenter	C₈₃	#3386
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ D₄×Q₈

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₈₃

commutator, cosocle

C₂×C₄×C₈₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₃

Fitting

D₄×Q₈×C₈₃

C₂

socle

C₂²×C₈₃

C₂²×D₄

prime radical

C₂×D₄×C₈₃

C₂³

hypercenter

D₄×Q₈

D₈₃

hypocenter

C₈₃

#3386

LCS

G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ D₄×Q₈

N	H ≅ G/N	type
1. #19128429	C₂	semidirect
2. #19128107	C₂	semidirect
3. #19128104	C₂	semidirect
5. #19127993	C₂	semidirect
6. #19127983	C₂	semidirect
8. #19127832	C₂	semidirect
43. #13050578	Q₈	semidirect
93. Dic₁₆₆	C₂×Q₈	semidirect
96. C₈₃⋊C₈	C₂×Q₈	semidirect
117. C₈₃	#3386	semidirect

H ≅ G/N

type

1. #19128429

C₂

semidirect

2. #19128107

C₂

semidirect

3. #19128104

C₂

semidirect

5. #19127993

C₂

semidirect

6. #19127983

C₂

semidirect

8. #19127832

C₂

semidirect

43. #13050578

Q₈

semidirect

93. Dic₁₆₆

C₂×Q₈

semidirect

96. C₈₃⋊C₈

C₂×Q₈

semidirect

117. C₈₃

#3386

semidirect

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

subgroup	index
#19128429	2
#19128107	2
#19128104	2
#19128001	2
#19127993	2
#19127983	2
#19127981	2
#19127832	2
#19127801	2
C₄×#13050578	2
D₄×Q₈×C₈₃	2
#3386	83

subgroup

index

D₄×Q₈×C₈₃

Subgroups — #24920384

Conjugacy classes of subgroups

Complements

Maximal subgroups