Group #35320586 — subgroups

Subgroups — #35320586

Order 21248.

374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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	C₂²×#14581731	C₂	1	1	yes	maximal, characteristic
2	C₂×#19127531	C₂	1	1	yes	maximal, characteristic, complemented
3	#24907498	C₂	1	2	yes	maximal
4	#24905556	C₂	1	2	yes	maximal, complemented
5	C₂×#368×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₈₃	C₂²	1	1	yes	characteristic
7	C₂×#14581731	—	2	2	no	—
8	C₂×#14581731	—	2	2	no	—
9	C₂×#14581731	C₄	1	4	yes	—
10	C₂²×C₈₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₂×#14581728	C₂²	1	2	yes	—
12	#19127664	—	2	2	no	—
13	#19127531	—	2	2	no	—
14	#19127465	—	2	2	no	—
15	C₂²×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×#108×C₈₃	C₂²	1	2	yes	—
17	#368×C₈₃	—	2	2	no	—
18	C₂²×C₄×D₈₃	D₄	1	1	yes	characteristic
19	C₂×#13050574	—	2	2	no	—
20	C₂²×C₈₃⋊C₈	D₄	1	1	yes	characteristic
21	C₂×C₈×D₈₃	—	2	1	no	—
22	C₂×C₈×D₈₃	—	2	1	no	—
23	C₂×C₈×D₈₃	—	2	1	no	—
24	C₂×C₈×D₈₃	—	2	1	no	—
25	C₂×C₈×D₈₃	C₂×C₄	1	2	yes	—
26	C₂×C₈×D₈₃	Q₈	1	2	yes	—
27	#14581731	—	2	8	no	—
28	C₂×C₈₃⋊C₁₆	—	2	1	no	—
29	C₂×C₈₃⋊C₁₆	—	2	1	no	—
30	C₂×C₈₃⋊C₁₆	C₂×C₄	1	2	yes	—
31	#14581728	—	2	2	no	—
32	#14581728	—	2	2	no	—
33	(C₂×D₈₃)⋊C₈	—	4	4	no	—
34	C₂×M₁₆×C₈₃	—	2	2	no	—
35	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
36	C₂×C₁₆×C₈₃	C₂×C₄	1	2	yes	—
37	C₂×C₁₆×C₈₃	D₄	1	2	yes	—
38	C₂×C₁₆×C₈₃	D₄	1	2	yes	—
39	#108×C₈₃	—	2	2	no	—
40	#108×C₈₃	—	2	2	no	—
41	C₂³×D₈₃	Q₁₆	1	1	yes	characteristic
42	C₂²×Dic₈₃	Q₁₆	1	1	yes	characteristic
43	C₂×C₄×D₈₃	—	2	1	no	—
44	C₂×C₄×D₈₃	—	2	1	no	—
45	C₂×C₄×D₈₃	—	2	1	no	—
46	C₂×C₄×D₈₃	—	2	1	no	—
47	C₂×C₄×D₈₃	C₄⋊C₄	1	2	yes	—
48	C₂×C₄×D₈₃	D₈	1	2	yes	—
49	#13050574	—	4	2	no	—
50	#13050574	—	4	2	no	—
51	C₂×C₈₃⋊C₈	—	2	1	no	—
52	C₂×C₈₃⋊C₈	—	2	1	no	—
53	C₂×C₈₃⋊C₈	—	4	2	no	—
54	C₂×C₈₃⋊C₈	C₄⋊C₄	1	2	yes	—
55	C₈×D₈₃	—	2	2	no	—
56	C₈×D₈₃	—	2	2	no	—
57	C₈×D₈₃	—	2	2	no	—
58	C₈×D₈₃	—	2	2	no	—
59	C₈₃⋊C₁₆	—	2	2	no	—
60	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
61	M₁₆×C₈₃	—	4	2	no	—
62	M₁₆×C₈₃	—	4	2	no	—
63	C₂×C₈×C₈₃	—	4	2	no	—
64	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₈₃	C₂×Q₈	1	1	yes	characteristic
68	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
69	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
70	C₁₆×C₈₃	C₂²⋊C₄	1	4	yes	—
71	C₂³×C₈₃	C₂×Q₁₆	1	1	yes	characteristic
72	C₂²×D₈₃	—	2	1	no	—
73	C₂²×D₈₃	—	2	1	no	—
74	C₂²×D₈₃	—	4	2	no	—
75	C₂²×D₈₃	#107	1	2	yes	—
76	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
78	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
79	C₂×C₄×C₈₃	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₈₃	#135	1	1	yes	characteristic
81	C₂×C₄×C₈₃	#135	1	1	yes	characteristic
82	C₂×Dic₈₃	—	2	1	no	—
83	C₂×Dic₈₃	—	2	1	no	—
84	C₂×Dic₈₃	#107	1	2	yes	—
85	C₄×D₈₃	—	2	2	no	—
86	C₄×D₈₃	—	2	2	no	—
87	C₄×D₈₃	—	2	2	no	—
88	C₄×D₈₃	—	2	2	no	—
89	C₈×C₈₃	—	8	2	no	—
90	C₈×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₈×C₈₃	#117	1	1	yes	characteristic
92	C₈×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
93	C₈×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
94	C₈₃⋊C₈	—	2	2	no	—
95	C₈₃⋊C₈	—	8	2	no	—
96	C₂²×C₈₃	—	2	2	no	—
97	C₂²×C₈₃	C₂×#107	1	1	yes	characteristic
98	C₂²×C₈₃	#467	1	1	yes	characteristic
99	C₂²×C₈₃	#467	1	1	yes	characteristic
100	C₂×D₈₃	—	2	2	no	—
101	C₂×D₈₃	—	2	4	no	—
102	C₂×D₈₃	—	4	2	no	—
103	C₂×D₈₃	—	4	2	no	—
104	C₄×C₈₃	#380	1	1	yes	characteristic
105	C₄×C₈₃	#427	1	1	yes	characteristic
106	C₄×C₈₃	#466	1	1	yes	characteristic
107	C₄×C₈₃	#466	1	1	yes	characteristic
108	Dic₈₃	—	2	2	no	—
109	#12838	—	83	1	no	maximal, Sylow
110	C₂×C₈₃	—	2	1	no	—
111	C₂×C₈₃	—	2	1	no	—
112	C₂×C₈₃	#1808	1	1	yes	characteristic
113	C₂×C₈₃	#2161	1	2	yes	—
114	D₈₃	—	4	2	no	—
115	C₂²×M₃₂	—	83	1	no	—
116	C₂×#368	—	83	1	no	—
117	C₂×#368	D₈₃	1	1	yes	characteristic, complemented
118	#1810	—	83	2	no	—
119	#1381	—	83	2	no	—
120	C₈₃	#12838	1	1	yes	characteristic, complemented, Sylow
121	C₂³×C₈	—	83	1	no	—
122	C₂×M₃₂	—	83	4	no	—
123	C₂×M₃₂	—	166	2	no	—
124	C₂×M₃₂	—	166	2	no	—
125	C₂²×C₁₆	—	83	1	no	—
126	C₂²×C₁₆	C₂×D₈₃	1	1	yes	characteristic
127	C₂×#108	—	83	2	no	—
128	C₂×#108	C₂×D₈₃	1	2	yes	—
129	#407	—	166	2	no	—
130	#368	—	2	2	no	—
131	#368	—	166	2	no	—
132	#341	—	166	2	no	—
133	C₂³×C₄	—	83	1	no	—
134	C₂×M₁₆	—	2	2	no	—
135	C₂×M₁₆	—	166	2	no	—
136	C₂²×C₈	—	83	1	no	—
137	C₂²×C₈	—	83	2	no	—
138	C₂²×C₈	—	83	2	no	—
139	C₂²×C₈	—	166	1	no	—
140	C₂²×C₈	—	166	1	no	—
141	C₂²×C₈	—	166	1	no	—
142	C₂²×C₈	—	166	1	no	—
143	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
144	M₃₂	—	166	8	no	—
145	C₂×C₁₆	—	83	2	no	—
146	C₂×C₁₆	—	166	1	no	—
147	C₂×C₁₆	—	166	1	no	—
148	C₂×C₁₆	C₄×D₈₃	1	2	yes	—
149	C₂×C₁₆	D₃₃₂	1	2	yes	—
150	C₂×C₁₆	C₂²⋊D₈₃	1	2	yes	—
151	#108	—	2	2	no	—
152	#108	—	2	2	no	—
153	#108	—	166	2	no	—
154	#108	—	166	2	no	—
155	C₂²⋊C₈	—	332	4	no	—
156	C₂⁴	—	83	1	no	—
157	C₂²×C₄	—	83	1	no	—
158	C₂²×C₄	—	83	2	no	—
159	C₂²×C₄	—	83	2	no	—
160	C₂²×C₄	—	166	1	no	—
161	C₂²×C₄	—	166	1	no	—
162	C₂²×C₄	—	166	1	no	—
163	C₂²×C₄	—	166	1	no	—
164	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
165	M₁₆	—	4	2	no	—
166	M₁₆	—	4	2	no	—
167	M₁₆	—	332	2	no	—
168	M₁₆	—	332	2	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	332	2	no	—
171	C₂×C₈	—	83	2	no	—
172	C₂×C₈	—	166	1	no	—
173	C₂×C₈	—	166	1	no	—
174	C₂×C₈	—	166	2	no	—
175	C₂×C₈	—	166	2	no	—
176	C₂×C₈	—	166	2	no	—
177	C₂×C₈	—	166	2	no	—
178	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
179	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
180	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
181	C₂×C₈	Q₈×D₈₃	1	1	yes	characteristic
182	C₂×C₈	#13050589	1	1	yes	characteristic
183	C₂×C₈	#13050591	1	1	yes	characteristic
184	C₁₆	—	166	2	no	—
185	C₁₆	(C₂×D₈₃)⋊C₄	1	4	yes	—
186	C₂³	—	332	2	no	—
187	C₂³	—	83	2	no	—
188	C₂³	—	166	1	no	—
189	C₂³	—	166	1	no	—
190	C₂³	Q₁₆×D₈₃	1	1	yes	characteristic
191	C₂×C₄	—	83	2	no	—
192	C₂×C₄	—	166	1	no	—
193	C₂×C₄	—	166	1	no	—
194	C₂×C₄	—	166	2	no	—
195	C₂×C₄	—	166	2	no	—
196	C₂×C₄	—	166	2	no	—
197	C₂×C₄	—	166	2	no	—
198	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
199	C₂×C₄	#14581763	1	1	yes	characteristic
200	C₂×C₄	#14581767	1	1	yes	characteristic
201	C₂×C₄	D₈×D₈₃	1	1	yes	characteristic
202	C₂×C₄	#14581811	1	1	yes	characteristic
203	C₂×C₄	#14581815	1	1	yes	characteristic
204	C₈	—	8	2	no	—
205	C₈	—	664	2	no	—
206	C₈	—	166	2	no	—
207	C₈	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
208	C₈	#14581750	1	1	yes	characteristic
209	C₈	#14581768	1	1	yes	characteristic
210	C₈	#14581772	1	1	yes	characteristic
211	C₂²	—	2	2	no	—
212	C₂²	—	332	2	no	—
213	C₂²	—	332	2	no	—
214	C₂²	—	166	4	no	—
215	C₂²	—	166	2	no	—
216	C₂²	#107×D₈₃	1	1	yes	characteristic
217	C₂²	#19127939	1	1	yes	characteristic
218	C₂²	#19127943	1	1	yes	characteristic
219	C₄	—	166	2	no	—
220	C₄	#19127558	1	1	yes	characteristic
221	C₄	#19127738	1	1	yes	characteristic
222	C₄	#19127934	1	1	yes	characteristic
223	C₄	#19127938	1	1	yes	characteristic
224	C₂	—	2	1	no	—
225	C₂	—	2	1	no	—
226	C₂	—	332	2	no	—
227	C₂	#24907489	1	1	yes	characteristic
228	C₂	#24909256	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#14581731

C₂

yes

maximal, characteristic

C₂×#19127531

C₂

yes

maximal, characteristic, complemented

#24907498

C₂

yes

maximal

#24905556

C₂

yes

maximal, complemented

C₂×#368×C₈₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₈₃

C₂²

yes

—

—

C₄

yes

—

C₂²×C₈₃⋊C₁₆

C₂²

yes

characteristic

C₂×#14581728

C₂²

yes

—

#19127664

—

#19127531

—

#19127465

—

C₂²×C₁₆×C₈₃

C₂²

yes

characteristic

C₂×#108×C₈₃

C₂²

yes

—

#368×C₈₃

—

C₂²×C₄×D₈₃

D₄

yes

characteristic

C₂×#13050574

—

C₂²×C₈₃⋊C₈

D₄

yes

characteristic

C₂×C₈×D₈₃

—

C₂×C₈×D₈₃

—

C₂×C₈×D₈₃

—

C₂×C₈×D₈₃

—

C₂×C₈×D₈₃

C₂×C₄

yes

—

C₂×C₈×D₈₃

Q₈

yes

—

#14581731

—

C₂×C₈₃⋊C₁₆

—

C₂×C₈₃⋊C₁₆

—

C₂×C₈₃⋊C₁₆

C₂×C₄

yes

—

#14581728

—

#14581728

—

(C₂×D₈₃)⋊C₈

—

C₂×M₁₆×C₈₃

—

C₂²×C₈×C₈₃

C₂³

yes

characteristic

C₂×C₁₆×C₈₃

C₂×C₄

yes

—

C₂×C₁₆×C₈₃

D₄

yes

—

C₂×C₁₆×C₈₃

D₄

yes

—

#108×C₈₃

—

#108×C₈₃

—

C₂³×D₈₃

Q₁₆

yes

characteristic

C₂²×Dic₈₃

Q₁₆

yes

characteristic

C₂×C₄×D₈₃

—

C₂×C₄×D₈₃

—

C₂×C₄×D₈₃

—

C₂×C₄×D₈₃

—

C₂×C₄×D₈₃

C₄⋊C₄

yes

—

C₂×C₄×D₈₃

D₈

yes

—

#13050574

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

C₄⋊C₄

yes

—

C₈×D₈₃

—

C₈×D₈₃

—

C₈×D₈₃

—

C₈×D₈₃

—

C₈₃⋊C₁₆

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

M₁₆×C₈₃

—

M₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₂×Q₈

yes

C₂×C₈×C₈₃

yes

C₂×C₈×C₈₃

yes

C₁₆×C₈₃

C₂²⋊C₄

yes

—

C₂³×C₈₃

C₂×Q₁₆

yes

characteristic

C₂²×D₈₃

—

C₂²×D₈₃

—

C₂²×D₈₃

—

C₂²×D₈₃

#107

yes

—

C₂×C₄×C₈₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

C₂×D₈

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

#107

yes

—

C₄×D₈₃

—

C₄×D₈₃

—

C₄×D₈₃

—

C₄×D₈₃

—

C₈×C₈₃

—

C₈×C₈₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₈₃

#117

yes

characteristic

C₈×C₈₃

C₂²⋊Q₈

yes

characteristic

C₈×C₈₃

C₂²⋊Q₈

yes

characteristic

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

yes

C₂²×C₈₃

yes

C₂²×C₈₃

yes

100

C₂×D₈₃

—

101

C₂×D₈₃

—

102

C₂×D₈₃

—

103

C₂×D₈₃

—

104

C₄×C₈₃

#380

yes

characteristic

105

C₄×C₈₃

#427

yes

characteristic

106

C₄×C₈₃

#466

yes

characteristic

107

C₄×C₈₃

#466

yes

characteristic

108

Dic₈₃

—

109

#12838

—

maximal, Sylow

110

C₂×C₈₃

—

111

C₂×C₈₃

—

112

C₂×C₈₃

#1808

yes

characteristic

113

C₂×C₈₃

#2161

yes

—

114

D₈₃

—

115

C₂²×M₃₂

—

116

C₂×#368

—

117

C₂×#368

D₈₃

yes

characteristic, complemented

118

#1810

—

119

#1381

—

120

C₈₃

#12838

yes

characteristic, complemented, Sylow

121

C₂³×C₈

—

122

C₂×M₃₂

—

123

C₂×M₃₂

—

166

—

124

C₂×M₃₂

—

166

—

125

C₂²×C₁₆

—

126

C₂²×C₁₆

C₂×D₈₃

yes

characteristic

127

C₂×#108

—

128

C₂×#108

C₂×D₈₃

yes

—

129

#407

—

166

—

130

#368

—

131

#368

—

166

—

132

#341

—

166

—

133

C₂³×C₄

—

134

C₂×M₁₆

—

135

C₂×M₁₆

—

166

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

—

166

—

140

C₂²×C₈

—

166

—

141

C₂²×C₈

—

166

—

142

C₂²×C₈

—

166

—

143

C₂²×C₈

C₂²×D₈₃

yes

characteristic

144

M₃₂

—

166

—

145

C₂×C₁₆

—

146

C₂×C₁₆

—

166

—

147

C₂×C₁₆

—

166

—

148

C₂×C₁₆

C₄×D₈₃

yes

—

149

C₂×C₁₆

D₃₃₂

yes

—

150

C₂×C₁₆

C₂²⋊D₈₃

yes

—

151

#108

—

152

#108

—

153

#108

—

166

—

154

#108

—

166

—

155

C₂²⋊C₈

—

332

—

156

C₂⁴

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

166

—

161

C₂²×C₄

—

166

—

162

C₂²×C₄

—

166

—

163

C₂²×C₄

—

166

—

164

C₂²×C₄

D₄×D₈₃

yes

characteristic

165

M₁₆

—

166

M₁₆

—

167

M₁₆

—

332

—

168

M₁₆

—

332

—

169

C₂×C₈

—

170

C₂×C₈

—

332

—

171

C₂×C₈

—

172

C₂×C₈

—

166

—

173

C₂×C₈

—

166

—

174

C₂×C₈

—

166

—

175

C₂×C₈

—

166

—

176

C₂×C₈

—

166

—

177

C₂×C₈

—

166

—

178

C₂×C₈

C₂×C₄×D₈₃

yes

characteristic

179

C₂×C₈

C₂×C₂²⋊D₈₃

yes

characteristic

180

C₂×C₈

C₂×D₃₃₂

yes

characteristic

181

C₂×C₈

Q₈×D₈₃

yes

characteristic

182

C₂×C₈

#13050589

yes

characteristic

183

C₂×C₈

#13050591

yes

characteristic

184

C₁₆

—

166

—

185

C₁₆

(C₂×D₈₃)⋊C₄

yes

—

186

C₂³

—

332

—

187

C₂³

—

188

C₂³

—

166

—

189

C₂³

—

166

—

190

C₂³

Q₁₆×D₈₃

yes

characteristic

191

C₂×C₄

—

192

C₂×C₄

—

166

—

193

C₂×C₄

—

166

—

194

C₂×C₄

—

166

—

195

C₂×C₄

—

166

—

196

C₂×C₄

—

166

—

197

C₂×C₄

—

166

—

198

C₂×C₄

C₄⋊C₄×D₈₃

yes

characteristic

199

C₂×C₄

#14581763

yes

characteristic

200

C₂×C₄

#14581767

yes

characteristic

201

C₂×C₄

D₈×D₈₃

yes

characteristic

202

C₂×C₄

#14581811

yes

characteristic

203

C₂×C₄

#14581815

yes

characteristic

204

C₈

—

205

C₈

—

664

—

206

C₈

—

166

—

207

C₈

C₂×(C₂×D₈₃)⋊C₄

yes

characteristic

208

C₈

#14581750

yes

characteristic

209

C₈

#14581768

yes

characteristic

210

C₈

#14581772

yes

characteristic

211

C₂²

—

212

C₂²

—

332

—

213

C₂²

—

332

—

214

C₂²

—

166

—

215

C₂²

—

166

—

216

C₂²

#107×D₈₃

yes

characteristic

217

C₂²

#19127939

yes

characteristic

218

C₂²

#19127943

yes

characteristic

219

C₄

—

166

—

220

C₄

#19127558

yes

characteristic

221

C₄

#19127738

yes

characteristic

222

C₄

#19127934

yes

characteristic

223

C₄

#19127938

yes

characteristic

224

C₂

—

225

C₂

—

226

C₂

—

332

—

227

C₂

#24907489

yes

characteristic

228

C₂

#24909256

yes

—

	subgroup	G/H
center	C₂×C₄	D₈×D₈₃
commutator	C₂×C₈×C₈₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₂×#368×C₈₃	C₂
socle	C₂²×C₈₃	C₂×#107
prime radical	C₂³×D₈₃	Q₁₆
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	C₂×#368	D₈₃
hypocenter	C₈₃	#12838
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

subgroup

G/H

center

C₂×C₄

D₈×D₈₃

commutator

C₂×C₈×C₈₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₂×#368×C₈₃

C₂

socle

C₂²×C₈₃

C₂×#107

prime radical

C₂³×D₈₃

Q₁₆

cosocle

C₂²×C₈×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

N	H ≅ G/N	type
2. C₂×#19127531	C₂	semidirect
4. #24905556	C₂	semidirect
5. C₂×#368×C₈₃	C₂	semidirect
117. C₂×#368	D₈₃	semidirect
120. C₈₃	#12838	semidirect

H ≅ G/N

type

2. C₂×#19127531

C₂

semidirect

4. #24905556

C₂

semidirect

5. C₂×#368×C₈₃

C₂

semidirect

117. C₂×#368

D₈₃

semidirect

120. C₈₃

#12838

semidirect

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

subgroup	index
C₂²×#14581731	2
C₂×#19127531	2
#24907498	2
#24905556	2
C₂×#368×C₈₃	2
#12838	83

subgroup

index

C₂×#368×C₈₃

Subgroups — #35320586

Conjugacy classes of subgroups

Complements

Maximal subgroups