Group #35322777 — subgroups

Subgroups — #35322777

Order 21248.

438 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 135 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×Dic₆₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#19127504	C₂	1	2	yes	maximal
3	C₂×C₁₆×Dic₈₃	C₂	1	1	yes	maximal, characteristic
4	#24908322	C₂	1	2	yes	maximal
5	C₂×#366×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₃₂	C₂²	1	2	yes	—
7	C₂×Dic₆₆₄	—	2	2	no	—
8	C₂×Dic₆₆₄	—	2	2	no	—
9	C₂×Dic₆₆₄	C₄	1	4	yes	complemented
10	C₂²×C₈₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₂×#14581715	—	2	2	no	—
12	C₂×C₈×Dic₈₃	C₂²	1	1	yes	characteristic
13	#19127606	—	2	2	no	—
14	#19127504	—	2	4	no	—
15	C₁₆×Dic₈₃	—	2	2	no	—
16	C₂²×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
17	C₂×#107×C₈₃	C₂²	1	2	yes	—
18	#366×C₈₃	—	2	2	no	—
19	C₂²×Dic₁₆₆	—	2	2	no	—
20	C₂×Dic₃₃₂	—	2	2	no	—
21	C₂×Dic₃₃₂	—	2	2	no	—
22	C₂×Dic₃₃₂	—	2	2	no	—
23	C₂×Dic₃₃₂	—	2	2	no	—
24	C₂×Dic₃₃₂	—	2	2	no	—
25	C₂×Dic₃₃₂	C₂×C₄	1	4	yes	—
26	C₂²×C₈₃⋊C₈	D₄	1	1	yes	characteristic
27	C₂×C₄×Dic₈₃	D₄	1	1	yes	characteristic
28	Dic₆₆₄	—	2	8	no	—
29	C₂×C₈₃⋊C₁₆	—	2	1	no	—
30	C₂×C₈₃⋊C₁₆	—	2	1	no	—
31	C₂×C₈₃⋊C₁₆	D₄	1	2	yes	—
32	#14581715	—	4	4	no	—
33	C₈×Dic₈₃	—	2	1	no	—
34	C₈×Dic₈₃	—	2	1	no	—
35	C₈₃⋊#95	—	4	4	no	—
36	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
38	C₂×C₁₆×C₈₃	C₂×C₄	1	2	yes	—
39	C₂×C₁₆×C₈₃	D₄	1	2	yes	—
40	C₂×C₁₆×C₈₃	D₄	1	2	yes	—
41	#107×C₈₃	—	2	2	no	—
42	#107×C₈₃	—	2	2	no	—
43	C₂×Dic₁₆₆	—	2	4	no	—
44	C₂×Dic₁₆₆	—	4	2	no	—
45	C₂×Dic₁₆₆	—	4	2	no	—
46	C₂×Dic₁₆₆	—	4	2	no	—
47	C₂×Dic₁₆₆	—	4	2	no	—
48	C₂×Dic₁₆₆	—	4	2	no	—
49	C₂²×Dic₈₃	—	4	2	no	—
50	C₂²×Dic₈₃	D₈	1	2	yes	—
51	Dic₃₃₂	—	2	4	no	—
52	Dic₃₃₂	—	2	4	no	—
53	Dic₃₃₂	—	4	2	no	—
54	Dic₃₃₂	—	4	2	no	—
55	C₂×C₈₃⋊C₈	—	2	1	no	—
56	C₂×C₈₃⋊C₈	—	2	1	no	—
57	C₂×C₈₃⋊C₈	D₈	1	2	yes	—
58	C₄×Dic₈₃	—	2	1	no	—
59	C₄×Dic₈₃	—	2	1	no	—
60	C₈₃⋊C₁₆	—	2	2	no	—
61	C₂²×C₄×C₈₃	—	4	2	no	—
62	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₈₃	C₂×D₄	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	#41	1	1	yes	characteristic
68	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
69	C₄⋊C₄×C₈₃	—	4	2	no	—
70	C₄⋊C₄×C₈₃	—	4	2	no	—
71	C₁₆×C₈₃	C₂²⋊C₄	1	4	yes	—
72	C₂³×C₈₃	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄×C₈₃	—	8	2	no	—
74	C₂×C₄×C₈₃	—	8	4	no	—
75	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
76	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
77	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
78	C₂×C₄×C₈₃	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₈₃	#135	1	1	yes	characteristic
80	C₂×C₄×C₈₃	#135	1	1	yes	characteristic
81	C₂×Dic₈₃	—	2	2	no	—
82	C₂×Dic₈₃	—	2	2	no	—
83	C₂×Dic₈₃	—	4	4	no	—
84	C₂×Dic₈₃	—	8	2	no	—
85	C₂×Dic₈₃	—	8	2	no	—
86	C₂×Dic₈₃	Q₃₂	1	4	yes	complemented
87	Dic₁₆₆	—	4	4	no	—
88	Dic₁₆₆	—	4	4	no	—
89	Dic₁₆₆	—	8	2	no	—
90	Dic₁₆₆	—	8	2	no	—
91	C₈×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
93	C₈×C₈₃	#121	1	1	yes	characteristic
94	C₈×C₈₃	#124	1	1	yes	characteristic
95	C₈₃⋊C₈	—	2	2	no	—
96	C₂²×C₈₃	C₄×D₈	1	1	yes	characteristic
97	C₂²×C₈₃	#466	1	1	yes	characteristic
98	C₂²×C₈₃	#493	1	1	yes	characteristic
99	C₂²×C₈₃	C₂×Q₃₂	1	2	yes	—
100	C₂²×C₈₃	#508	1	2	yes	—
101	C₄×C₈₃	—	16	2	no	—
102	C₄×C₈₃	#390	1	1	yes	characteristic
103	C₄×C₈₃	C₄×D₈	1	1	yes	characteristic
104	C₄×C₈₃	#466	1	1	yes	characteristic
105	C₄×C₈₃	#495	1	1	yes	characteristic
106	Dic₈₃	—	2	4	no	—
107	Dic₈₃	—	8	4	no	—
108	#13236	—	83	1	no	maximal, Sylow
109	C₂×C₈₃	#1970	1	1	yes	characteristic
110	C₂×C₈₃	C₄×Q₃₂	1	2	yes	—
111	C₂×C₈₃	#2216	1	2	yes	—
112	C₂×C₈₃	#2247	1	1	yes	characteristic
113	C₂×C₈₃	#2249	1	1	yes	characteristic
114	C₂²×Q₃₂	—	83	1	no	—
115	C₂×#366	D₈₃	1	1	yes	characteristic
116	C₂×#358	—	83	2	no	—
117	C₂×C₄×C₁₆	—	83	1	no	—
118	#1969	—	83	2	no	—
119	C₈₃	#13236	1	1	yes	characteristic, complemented, Sylow
120	C₂²×Q₁₆	—	83	2	no	—
121	C₂×Q₃₂	—	83	4	no	—
122	C₂×Q₃₂	—	166	2	no	—
123	C₂×Q₃₂	—	166	2	no	—
124	C₂²×C₁₆	—	83	1	no	—
125	C₂²×C₁₆	C₂×D₈₃	1	1	yes	characteristic
126	C₂×#107	C₂×D₈₃	1	2	yes	—
127	C₂×#103	—	166	2	no	—
128	C₂×C₄×C₈	—	83	1	no	—
129	#391	—	166	2	no	—
130	#366	—	2	2	no	—
131	#358	—	166	4	no	—
132	C₄×C₁₆	—	166	2	no	—
133	C₂²×Q₈	—	166	2	no	—
134	C₂×Q₁₆	—	83	4	no	—
135	C₂×Q₁₆	—	166	2	no	—
136	C₂×Q₁₆	—	166	2	no	—
137	C₂×Q₁₆	—	166	2	no	—
138	C₂×Q₁₆	—	166	2	no	—
139	C₂×Q₁₆	—	166	2	no	—
140	C₂²×C₈	—	83	1	no	—
141	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄²	—	83	1	no	—
144	Q₃₂	—	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	#107	—	2	2	no	—
152	#107	—	2	2	no	—
153	#103	—	332	4	no	—
154	C₄×C₈	—	166	1	no	—
155	C₄×C₈	—	166	1	no	—
156	#95	—	332	4	no	—
157	C₂×Q₈	—	332	2	no	—
158	C₂×Q₈	—	332	2	no	—
159	C₂×Q₈	—	332	2	no	—
160	C₂×Q₈	—	332	2	no	—
161	C₂×Q₈	—	332	2	no	—
162	C₂×Q₈	—	166	4	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	—	332	2	no	—
165	C₂²×C₄	—	83	2	no	—
166	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
167	Q₁₆	—	332	2	no	—
168	Q₁₆	—	332	2	no	—
169	Q₁₆	—	166	4	no	—
170	Q₁₆	—	166	4	no	—
171	C₂×C₈	—	83	2	no	—
172	C₂×C₈	—	166	1	no	—
173	C₂×C₈	—	166	1	no	—
174	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
175	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
176	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
177	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
178	C₂×C₈	#13050591	1	1	yes	characteristic
179	C₂×C₈	#13050591	1	1	yes	characteristic
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄²	—	166	1	no	—
183	C₄²	—	166	1	no	—
184	C₁₆	—	166	2	no	—
185	C₁₆	(C₂×D₈₃)⋊C₄	1	4	yes	—
186	C₂³	D₈×D₈₃	1	1	yes	characteristic
187	Q₈	—	332	4	no	—
188	Q₈	—	332	4	no	—
189	Q₈	—	664	2	no	—
190	Q₈	—	664	2	no	—
191	C₂×C₄	—	8	2	no	—
192	C₂×C₄	—	8	4	no	—
193	C₂×C₄	—	332	4	no	—
194	C₂×C₄	—	83	4	no	—
195	C₂×C₄	—	664	2	no	—
196	C₂×C₄	—	664	2	no	—
197	C₂×C₄	—	166	2	no	—
198	C₂×C₄	—	166	2	no	—
199	C₂×C₄	#14581754	1	1	yes	characteristic
200	C₂×C₄	#14581767	1	1	yes	characteristic
201	C₂×C₄	#14581788	1	1	yes	characteristic
202	C₂×C₄	D₈×D₈₃	1	1	yes	characteristic
203	C₂×C₄	#14581815	1	1	yes	characteristic
204	C₂×C₄	#14581815	1	1	yes	characteristic
205	C₈	—	166	2	no	—
206	C₈	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
207	C₈	#14581754	1	1	yes	characteristic
208	C₈	#14581767	1	1	yes	characteristic
209	C₈	#14581781	1	1	yes	characteristic
210	C₂²	#19127783	1	1	yes	characteristic
211	C₂²	#19127938	1	1	yes	characteristic
212	C₂²	#19128076	1	1	yes	characteristic
213	C₂²	Q₃₂×D₈₃	1	2	yes	—
214	C₂²	#19128130	1	2	yes	—
215	C₄	—	16	2	no	—
216	C₄	—	664	4	no	—
217	C₄	—	166	4	no	—
218	C₄	#19127602	1	1	yes	characteristic
219	C₄	#19127783	1	1	yes	characteristic
220	C₄	#19127938	1	1	yes	characteristic
221	C₄	#19128086	1	1	yes	characteristic
222	C₂	#24908327	1	1	yes	characteristic
223	C₂	#24909321	1	2	yes	—
224	C₂	#24909555	1	2	yes	—
225	C₂	#24909714	1	1	yes	characteristic
226	C₂	#24909721	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₆₆₄

C₂

yes

maximal, characteristic

C₂×#19127504

C₂

yes

maximal

C₂×C₁₆×Dic₈₃

C₂

yes

maximal, characteristic

#24908322

C₂

yes

maximal

C₂×#366×C₈₃

C₂

yes

maximal, characteristic

C₂²×Dic₃₃₂

C₂²

yes

—

C₂×Dic₆₆₄

—

C₂×Dic₆₆₄

—

C₂×Dic₆₆₄

C₄

yes

complemented

C₂²×C₈₃⋊C₁₆

C₂²

yes

characteristic

C₂×#14581715

—

C₂×C₈×Dic₈₃

C₂²

yes

characteristic

#19127606

—

#19127504

—

C₁₆×Dic₈₃

—

C₂²×C₁₆×C₈₃

C₂²

yes

characteristic

C₂×#107×C₈₃

C₂²

yes

—

#366×C₈₃

—

C₂²×Dic₁₆₆

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

—

C₂×Dic₃₃₂

C₂×C₄

yes

—

C₂²×C₈₃⋊C₈

D₄

yes

characteristic

C₂×C₄×Dic₈₃

D₄

yes

characteristic

Dic₆₆₄

—

C₂×C₈₃⋊C₁₆

—

C₂×C₈₃⋊C₁₆

—

C₂×C₈₃⋊C₁₆

D₄

yes

—

#14581715

—

C₈×Dic₈₃

—

C₈×Dic₈₃

—

C₈₃⋊#95

—

C₂²×C₈×C₈₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₈₃

—

C₂×C₁₆×C₈₃

C₂×C₄

yes

—

C₂×C₁₆×C₈₃

D₄

yes

—

C₂×C₁₆×C₈₃

D₄

yes

—

#107×C₈₃

—

#107×C₈₃

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

D₈

yes

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

Dic₃₃₂

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

D₈

yes

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₈₃⋊C₁₆

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

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×D₄

yes

C₂×C₈×C₈₃

yes

C₂×C₈×C₈₃

yes

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₁₆×C₈₃

C₂²⋊C₄

yes

—

C₂³×C₈₃

C₂×D₈

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₄×D₄

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

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

Q₃₂

yes

complemented

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

—

C₈×C₈₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₈₃

C₄×D₄

yes

C₈×C₈₃

yes

C₈×C₈₃

yes

C₈₃⋊C₈

—

C₂²×C₈₃

C₄×D₈

yes

C₂²×C₈₃

yes

C₂²×C₈₃

yes

C₂²×C₈₃

C₂×Q₃₂

yes

—

100

C₂²×C₈₃

#508

yes

—

101

C₄×C₈₃

—

102

C₄×C₈₃

#390

yes

characteristic

103

C₄×C₈₃

C₄×D₈

yes

characteristic

104

C₄×C₈₃

#466

yes

characteristic

105

C₄×C₈₃

#495

yes

characteristic

106

Dic₈₃

—

107

Dic₈₃

—

108

#13236

—

maximal, Sylow

109

C₂×C₈₃

#1970

yes

characteristic

110

C₂×C₈₃

C₄×Q₃₂

yes

—

111

C₂×C₈₃

#2216

yes

—

112

C₂×C₈₃

#2247

yes

characteristic

113

C₂×C₈₃

#2249

yes

characteristic

114

C₂²×Q₃₂

—

115

C₂×#366

D₈₃

yes

characteristic

116

C₂×#358

—

117

C₂×C₄×C₁₆

—

118

#1969

—

119

C₈₃

#13236

yes

characteristic, complemented, Sylow

120

C₂²×Q₁₆

—

121

C₂×Q₃₂

—

122

C₂×Q₃₂

—

166

—

123

C₂×Q₃₂

—

166

—

124

C₂²×C₁₆

—

125

C₂²×C₁₆

C₂×D₈₃

yes

characteristic

126

C₂×#107

C₂×D₈₃

yes

—

127

C₂×#103

—

166

—

128

C₂×C₄×C₈

—

129

#391

—

166

—

130

#366

—

131

#358

—

166

—

132

C₄×C₁₆

—

166

—

133

C₂²×Q₈

—

166

—

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

166

—

136

C₂×Q₁₆

—

166

—

137

C₂×Q₁₆

—

166

—

138

C₂×Q₁₆

—

166

—

139

C₂×Q₁₆

—

166

—

140

C₂²×C₈

—

141

C₂²×C₈

C₂²×D₈₃

yes

characteristic

142

C₂×C₄⋊C₄

—

143

C₂×C₄²

—

144

Q₃₂

—

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

#107

—

152

#107

—

153

#103

—

332

—

154

C₄×C₈

—

166

—

155

C₄×C₈

—

166

—

156

#95

—

332

—

157

C₂×Q₈

—

332

—

158

C₂×Q₈

—

332

—

159

C₂×Q₈

—

332

—

160

C₂×Q₈

—

332

—

161

C₂×Q₈

—

332

—

162

C₂×Q₈

—

166

—

163

C₂²×C₄

—

164

C₂²×C₄

—

332

—

165

C₂²×C₄

—

166

C₂²×C₄

D₄×D₈₃

yes

characteristic

167

Q₁₆

—

332

—

168

Q₁₆

—

332

—

169

Q₁₆

—

166

—

170

Q₁₆

—

166

—

171

C₂×C₈

—

172

C₂×C₈

—

166

—

173

C₂×C₈

—

166

—

174

C₂×C₈

C₂×C₄×D₈₃

yes

characteristic

175

C₂×C₈

D₄×D₈₃

yes

characteristic

176

C₂×C₈

C₂×C₂²⋊D₈₃

yes

characteristic

177

C₂×C₈

C₂×D₃₃₂

yes

characteristic

178

C₂×C₈

#13050591

yes

characteristic

179

C₂×C₈

#13050591

yes

characteristic

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄²

—

166

—

183

C₄²

—

166

—

184

C₁₆

—

166

—

185

C₁₆

(C₂×D₈₃)⋊C₄

yes

—

186

C₂³

D₈×D₈₃

yes

characteristic

187

Q₈

—

332

—

188

Q₈

—

332

—

189

Q₈

—

664

—

190

Q₈

—

664

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

332

—

194

C₂×C₄

—

195

C₂×C₄

—

664

—

196

C₂×C₄

—

664

—

197

C₂×C₄

—

166

—

198

C₂×C₄

—

166

—

199

C₂×C₄

#14581754

yes

characteristic

200

C₂×C₄

#14581767

yes

characteristic

201

C₂×C₄

#14581788

yes

characteristic

202

C₂×C₄

D₈×D₈₃

yes

characteristic

203

C₂×C₄

#14581815

yes

characteristic

204

C₂×C₄

#14581815

yes

characteristic

205

C₈

—

166

—

206

C₈

C₂×(C₂×D₈₃)⋊C₄

yes

characteristic

207

C₈

#14581754

yes

characteristic

208

C₈

#14581767

yes

characteristic

209

C₈

#14581781

yes

characteristic

210

C₂²

#19127783

yes

characteristic

211

C₂²

#19127938

yes

characteristic

212

C₂²

#19128076

yes

characteristic

213

C₂²

Q₃₂×D₈₃

yes

—

214

C₂²

#19128130

yes

—

215

C₄

—

216

C₄

—

664

—

217

C₄

—

166

—

218

C₄

#19127602

yes

characteristic

219

C₄

#19127783

yes

characteristic

220

C₄

#19127938

yes

characteristic

221

C₄

#19128086

yes

characteristic

222

C₂

#24908327

yes

characteristic

223

C₂

#24909321

yes

—

224

C₂

#24909555

yes

—

225

C₂

#24909714

yes

characteristic

226

C₂

#24909721

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₈₃
commutator	C₂×C₈×C₈₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₂×#366×C₈₃	C₂
socle, prime radical	C₂³×C₈₃	C₂×D₈
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	C₂×#366	D₈₃
hypocenter	C₈₃	#13236
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

subgroup

G/H

center

C₂³

D₈×D₈₃

commutator

C₂×C₈×C₈₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₂×#366×C₈₃

C₂

socle, prime radical

C₂³×C₈₃

C₂×D₈

cosocle

C₂²×C₈×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

N	H ≅ G/N	type
9. C₂×Dic₆₆₄	C₄	semidirect
86. C₂×Dic₈₃	Q₃₂	semidirect
119. C₈₃	#13236	semidirect

H ≅ G/N

type

9. C₂×Dic₆₆₄

C₄

semidirect

86. C₂×Dic₈₃

Q₃₂

semidirect

119. C₈₃

#13236

semidirect

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

subgroup	index
C₂²×Dic₆₆₄	2
C₂×#19127504	2
C₂×C₁₆×Dic₈₃	2
#24908322	2
C₂×#366×C₈₃	2
#13236	83

subgroup

index

C₂²×Dic₆₆₄

C₂×#19127504

C₂×C₁₆×Dic₈₃

#24908322

C₂×#366×C₈₃

#13236

Subgroups — #35322777

Conjugacy classes of subgroups

Complements

Maximal subgroups