Group #35309143 — subgroups

Subgroups — #35309143

Order 21248.

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

normal subgroups only

This group has 402 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	#24907591	C₂	1	1	yes	maximal, characteristic, complemented
2	#24907463	C₂	1	2	yes	maximal
3	#24905347	C₂	1	2	yes	maximal, complemented
4	#24905298	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
7	C₂×#14581713	—	2	2	no	—
8	#19127571	C₂²	1	2	yes	—
9	#19127464	—	2	2	no	—
10	#19127463	—	2	2	no	—
11	C₂×C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊C₈×C₈₃	—	2	2	no	—
14	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
15	C₂²×C₈₃⋊C₈	—	2	2	no	—
16	C₂×C₄⋊Dic₈₃	—	2	2	no	—
17	C₂×C₄⋊Dic₈₃	—	2	2	no	—
18	C₂×C₄⋊Dic₈₃	—	2	2	no	—
19	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
20	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
21	#14581713	—	4	4	no	—
22	C₂²×D₄×C₈₃	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₈₃	—	2	1	no	—
24	C₂²×C₈×C₈₃	—	2	1	no	—
25	C₂²×C₈×C₈₃	D₄	1	2	yes	—
26	C₄×D₄×C₈₃	—	2	2	no	—
27	C₄×D₄×C₈₃	—	2	2	no	—
28	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₈₃	—	2	1	no	—
30	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
31	C₄⋊C₈×C₈₃	—	2	2	no	—
32	C₂²⋊C₈×C₈₃	—	4	4	no	—
33	C₄×C₈×C₈₃	—	2	2	no	—
34	C₂²×Dic₈₃	—	4	2	no	—
35	C₂×C₈₃⋊C₈	—	4	2	no	—
36	C₂×C₈₃⋊C₈	—	4	2	no	—
37	C₂×C₈₃⋊C₈	—	4	2	no	—
38	C₄⋊Dic₈₃	—	4	2	no	—
39	C₄⋊Dic₈₃	—	4	2	no	—
40	C₄⋊Dic₈₃	—	4	2	no	—
41	C₄⋊Dic₈₃	—	4	2	no	—
42	C₄⋊Dic₈₃	—	8	2	no	—
43	C₂⁴×C₈₃	—	2	1	no	—
44	C₂×D₄×C₈₃	—	2	2	no	—
45	C₂×D₄×C₈₃	—	2	1	no	—
46	C₂×D₄×C₈₃	—	2	2	no	—
47	C₂×D₄×C₈₃	Q₁₆	1	2	yes	—
48	C₂²×C₄×C₈₃	—	2	1	no	—
49	C₂²×C₄×C₈₃	—	4	1	no	—
50	C₂²×C₄×C₈₃	—	4	1	no	—
51	C₂²×C₄×C₈₃	—	4	2	no	—
52	C₂²×C₄×C₈₃	—	4	2	no	—
53	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
56	C₂×C₈×C₈₃	—	2	2	no	—
57	C₂×C₈×C₈₃	—	2	2	no	—
58	C₂×C₈×C₈₃	—	2	2	no	—
59	C₂×C₈×C₈₃	—	4	1	no	—
60	C₂×C₈×C₈₃	—	4	2	no	—
61	C₄⋊C₄×C₈₃	—	2	2	no	—
62	C₂²⋊C₄×C₈₃	—	4	2	no	—
63	C₄²×C₈₃	#41	1	2	yes	—
64	C₄²×C₈₃	#41	1	2	yes	—
65	C₂³×C₈₃	—	2	2	no	—
66	C₂³×C₈₃	—	4	1	no	—
67	C₂³×C₈₃	—	4	2	no	—
68	C₂³×C₈₃	—	4	1	no	—
69	C₂³×C₈₃	—	4	2	no	—
70	C₂³×C₈₃	#121	1	1	yes	characteristic
71	D₄×C₈₃	—	2	4	no	—
72	D₄×C₈₃	—	4	2	no	—
73	C₂×C₄×C₈₃	—	2	2	no	—
74	C₂×C₄×C₈₃	—	4	1	no	—
75	C₂×C₄×C₈₃	—	4	2	no	—
76	C₂×C₄×C₈₃	—	8	2	no	—
77	C₂×C₄×C₈₃	—	8	1	no	—
78	C₂×C₄×C₈₃	—	8	1	no	—
79	C₂×C₄×C₈₃	#123	1	1	yes	characteristic
80	C₂×C₄×C₈₃	#123	1	2	yes	—
81	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
82	C₂×C₄×C₈₃	#126	1	2	yes	—
83	C₂×C₄×C₈₃	C₂×Q₁₆	1	1	yes	characteristic
84	C₂×C₄×C₈₃	#135	1	2	yes	—
85	C₂×C₄×C₈₃	#135	1	1	yes	characteristic
86	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
88	C₂×Dic₈₃	—	8	2	no	—
89	C₂×Dic₈₃	—	8	2	no	—
90	C₂×Dic₈₃	—	8	2	no	—
91	C₈×C₈₃	—	4	2	no	—
92	C₈×C₈₃	—	8	1	no	—
93	C₈₃⋊C₈	—	8	2	no	—
94	C₂²×C₈₃	—	4	2	no	—
95	C₂²×C₈₃	—	4	4	no	—
96	C₂²×C₈₃	—	8	1	no	—
97	C₂²×C₈₃	—	8	1	no	—
98	C₂²×C₈₃	—	8	2	no	—
99	C₂²×C₈₃	#397	1	1	yes	characteristic
100	C₂²×C₈₃	#463	1	2	yes	—
101	C₂²×C₈₃	#467	1	1	yes	characteristic
102	C₂²×C₈₃	#469	1	1	yes	characteristic
103	C₂²×C₈₃	#471	1	2	yes	—
104	C₄×C₈₃	—	2	2	no	—
105	C₄×C₈₃	—	8	1	no	—
106	C₄×C₈₃	#482	1	2	yes	—
107	C₄×C₈₃	#482	1	2	yes	—
108	C₄×C₈₃	#484	1	2	yes	—
109	C₄×C₈₃	#488	1	1	yes	characteristic
110	C₄×C₈₃	#490	1	1	yes	characteristic
111	Dic₈₃	—	16	2	no	—
112	#10622	—	83	1	no	maximal, Sylow
113	C₂×C₈₃	—	8	2	no	—
114	C₂×C₈₃	#1683	1	2	yes	—
115	C₂×C₈₃	#1701	1	2	yes	—
116	C₂×C₈₃	#2073	1	1	yes	characteristic
117	C₂×C₈₃	#2076	1	1	yes	characteristic
118	C₂×C₈₃	#2079	1	1	yes	characteristic
119	#1954	D₈₃	1	1	yes	characteristic
120	#1834	—	83	1	no	—
121	#1802	—	83	2	no	—
122	#1296	—	83	2	no	—
123	#1277	—	83	1	no	—
124	C₈₃	#10622	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
126	C₂×C₄⋊C₈	—	83	2	no	—
127	C₂×C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
128	C₂×#102	—	166	2	no	—
129	C₂×C₂²⋊C₈	—	2	2	no	—
130	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
131	#384	—	83	2	no	—
132	#340	—	166	2	no	—
133	#340	—	166	2	no	—
134	C₂²×D₄	D₃₃₂	1	1	yes	characteristic
135	C₂³×C₄	—	2	1	no	—
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	—	166	2	no	—
138	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
139	C₄×D₄	—	2	2	no	—
140	C₄×D₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	166	2	no	—
142	C₂×C₄⋊C₄	—	166	2	no	—
143	C₂×C₄⋊C₄	—	166	2	no	—
144	C₂×C₄⋊C₄	D₃₃₂	1	1	yes	characteristic
145	C₂×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	166	2	no	—
149	C₄⋊C₈	—	166	2	no	—
150	#102	—	332	4	no	—
151	C₂²⋊C₈	—	4	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂⁴	—	2	1	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	1	no	—
156	C₂×D₄	—	2	2	no	—
157	C₂×D₄	Dic₃₃₂	1	2	yes	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	4	1	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	—	4	2	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	332	2	no	—
164	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
165	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
166	C₂²×C₄	#13050590	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	1	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	332	2	no	—
173	C₂×C₈	—	332	2	no	—
174	C₂×C₈	—	332	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	332	2	no	—
177	C₄⋊C₄	—	332	2	no	—
178	C₄⋊C₄	—	332	2	no	—
179	C₄⋊C₄	—	332	2	no	—
180	C₄⋊C₄	—	664	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	#13050589	1	2	yes	—
183	C₄²	#13050589	1	2	yes	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	1	no	—
186	C₂³	—	4	2	no	—
187	C₂³	—	4	1	no	—
188	C₂³	—	4	2	no	—
189	C₂³	#14581766	1	1	yes	characteristic
190	D₄	—	2	4	no	—
191	D₄	—	4	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	8	1	no	—
196	C₂×C₄	—	8	2	no	—
197	C₂×C₄	—	8	1	no	—
198	C₂×C₄	—	664	2	no	—
199	C₂×C₄	—	664	2	no	—
200	C₂×C₄	—	664	2	no	—
201	C₂×C₄	#14581773	1	1	yes	characteristic
202	C₂×C₄	#14581776	1	2	yes	—
203	C₂×C₄	#14581779	1	1	yes	characteristic
204	C₂×C₄	#14581785	1	2	yes	—
205	C₂×C₄	C₂×Dic₃₃₂	1	1	yes	characteristic
206	C₂×C₄	#14581812	1	2	yes	—
207	C₂×C₄	#14581814	1	1	yes	characteristic
208	C₂×C₄	#14581818	1	2	yes	—
209	C₂×C₄	#14581820	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	8	1	no	—
212	C₈	—	664	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	4	no	—
215	C₂²	—	8	2	no	—
216	C₂²	—	8	1	no	—
217	C₂²	—	8	1	no	—
218	C₂²	#19127626	1	1	yes	characteristic
219	C₂²	#19127916	1	2	yes	—
220	C₂²	#19127942	1	1	yes	characteristic
221	C₂²	#19127954	1	1	yes	characteristic
222	C₂²	#19127964	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	1	no	—
225	C₄	—	1328	2	no	—
226	C₄	#19128022	1	2	yes	—
227	C₄	#19128026	1	2	yes	—
228	C₄	#19128037	1	2	yes	—
229	C₄	#19128055	1	1	yes	characteristic
230	C₄	#19128065	1	1	yes	characteristic
231	C₂	—	8	2	no	—
232	C₂	#24906914	1	2	yes	—
233	C₂	#24907024	1	2	yes	—
234	C₂	#24908876	1	1	yes	characteristic
235	C₂	#24908891	1	1	yes	characteristic
236	C₂	#24908908	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24907591

C₂

yes

maximal, characteristic, complemented

#24907463

C₂

yes

maximal

#24905347

C₂

yes

maximal, complemented

#24905298

C₂

yes

maximal, characteristic, complemented

C₈₃×#1954

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₈₃⋊C₈)

C₂²

yes

—

C₂×#14581713

—

#19127571

C₂²

yes

—

#19127464

—

#19127463

—

C₂×C₄×D₄×C₈₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₈₃

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₈₃

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₂²×C₈₃⋊C₈

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

#14581713

—

C₂²×D₄×C₈₃

D₄

yes

characteristic

C₂³×C₄×C₈₃

—

C₂²×C₈×C₈₃

—

C₂²×C₈×C₈₃

D₄

yes

—

C₄×D₄×C₈₃

—

C₄×D₄×C₈₃

—

C₂×C₄⋊C₄×C₈₃

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₈₃

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄⋊C₈×C₈₃

—

C₂²⋊C₈×C₈₃

—

C₄×C₈×C₈₃

—

C₂²×Dic₈₃

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₂⁴×C₈₃

—

C₂×D₄×C₈₃

—

C₂×D₄×C₈₃

—

C₂×D₄×C₈₃

—

C₂×D₄×C₈₃

Q₁₆

yes

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

—

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

—

C₂×C₈×C₈₃

—

C₄⋊C₄×C₈₃

—

C₂²⋊C₄×C₈₃

—

C₄²×C₈₃

#41

yes

—

C₄²×C₈₃

#41

yes

—

C₂³×C₈₃

—

C₂³×C₈₃

—

C₂³×C₈₃

—

C₂³×C₈₃

—

C₂³×C₈₃

—

C₂³×C₈₃

#121

yes

characteristic

D₄×C₈₃

—

D₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#123

yes

characteristic

C₂×C₄×C₈₃

#123

yes

—

C₂×C₄×C₈₃

#124

yes

characteristic

C₂×C₄×C₈₃

#126

yes

—

C₂×C₄×C₈₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₈₃

#135

yes

—

C₂×C₄×C₈₃

#135

yes

characteristic

C₂×C₄×C₈₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₈₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

#397

yes

characteristic

100

C₂²×C₈₃

#463

yes

—

101

C₂²×C₈₃

#467

yes

characteristic

102

C₂²×C₈₃

#469

yes

characteristic

103

C₂²×C₈₃

#471

yes

—

104

C₄×C₈₃

—

105

C₄×C₈₃

—

106

C₄×C₈₃

#482

yes

—

107

C₄×C₈₃

#482

yes

—

108

C₄×C₈₃

#484

yes

—

109

C₄×C₈₃

#488

yes

characteristic

110

C₄×C₈₃

#490

yes

characteristic

111

Dic₈₃

—

112

#10622

—

maximal, Sylow

113

C₂×C₈₃

—

114

C₂×C₈₃

#1683

yes

—

115

C₂×C₈₃

#1701

yes

—

116

C₂×C₈₃

#2073

yes

characteristic

117

C₂×C₈₃

#2076

yes

characteristic

118

C₂×C₈₃

#2079

yes

characteristic

119

#1954

D₈₃

yes

characteristic

120

#1834

—

121

#1802

—

122

#1296

—

123

#1277

—

124

C₈₃

#10622

yes

characteristic, complemented, Sylow

125

C₂×C₄×D₄

C₂×D₈₃

yes

characteristic

126

C₂×C₄⋊C₈

—

127

C₂×C₄⋊C₈

C₂×D₈₃

yes

characteristic

128

C₂×#102

—

166

—

129

C₂×C₂²⋊C₈

—

130

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

131

#384

—

132

#340

—

166

—

133

#340

—

166

—

134

C₂²×D₄

D₃₃₂

yes

characteristic

135

C₂³×C₄

—

136

C₂²×C₈

—

137

C₂²×C₈

—

166

—

138

C₂²×C₈

C₂²⋊D₈₃

yes

—

139

C₄×D₄

—

140

C₄×D₄

—

141

C₂×C₄⋊C₄

—

166

—

142

C₂×C₄⋊C₄

—

166

—

143

C₂×C₄⋊C₄

—

166

—

144

C₂×C₄⋊C₄

D₃₃₂

yes

characteristic

145

C₂×C₂²⋊C₄

—

146

C₂×C₄²

C₂²×D₈₃

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

166

—

149

C₄⋊C₈

—

166

—

150

#102

—

332

—

151

C₂²⋊C₈

—

152

C₄×C₈

—

153

C₂⁴

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

Dic₃₃₂

yes

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

332

—

164

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

165

C₂²×C₄

C₂×D₃₃₂

yes

characteristic

166

C₂²×C₄

#13050590

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

332

—

173

C₂×C₈

—

332

—

174

C₂×C₈

—

332

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

332

—

177

C₄⋊C₄

—

332

—

178

C₄⋊C₄

—

332

—

179

C₄⋊C₄

—

332

—

180

C₄⋊C₄

—

664

—

181

C₂²⋊C₄

—

182

C₄²

#13050589

yes

—

183

C₄²

#13050589

yes

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

#14581766

yes

characteristic

190

D₄

—

191

D₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

664

—

199

C₂×C₄

—

664

—

200

C₂×C₄

—

664

—

201

C₂×C₄

#14581773

yes

characteristic

202

C₂×C₄

#14581776

yes

—

203

C₂×C₄

#14581779

yes

characteristic

204

C₂×C₄

#14581785

yes

—

205

C₂×C₄

C₂×Dic₃₃₂

yes

characteristic

206

C₂×C₄

#14581812

yes

—

207

C₂×C₄

#14581814

yes

characteristic

208

C₂×C₄

#14581818

yes

—

209

C₂×C₄

#14581820

yes

—

210

C₈

—

211

C₈

—

212

C₈

—

664

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

#19127626

yes

characteristic

219

C₂²

#19127916

yes

—

220

C₂²

#19127942

yes

characteristic

221

C₂²

#19127954

yes

characteristic

222

C₂²

#19127964

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

1328

—

226

C₄

#19128022

yes

—

227

C₄

#19128026

yes

—

228

C₄

#19128037

yes

—

229

C₄

#19128055

yes

characteristic

230

C₄

#19128065

yes

characteristic

231

C₂

—

232

C₂

#24906914

yes

—

233

C₂

#24907024

yes

—

234

C₂

#24908876

yes

characteristic

235

C₂

#24908891

yes

characteristic

236

C₂

#24908908

yes

characteristic

	subgroup	G/H
center	C₂³	#14581766
commutator, cosocle	C₂×C₄²×C₈₃	C₂³
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1954	C₂
socle	C₂³×C₈₃	#121
prime radical	C₂²×D₄×C₈₃	D₄
hypercenter	#1954	D₈₃
hypocenter	C₈₃	#10622
LCS	G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂³

#14581766

commutator, cosocle

C₂×C₄²×C₈₃

C₂³

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1954

C₂

socle

C₂³×C₈₃

#121

prime radical

C₂²×D₄×C₈₃

D₄

D₈₃

C₈₃

G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
1. #24907591	C₂	semidirect
3. #24905347	C₂	semidirect
4. #24905298	C₂	semidirect
124. C₈₃	#10622	semidirect

H ≅ G/N

type

1. #24907591

C₂

semidirect

3. #24905347

C₂

semidirect

4. #24905298

C₂

semidirect

124. C₈₃

#10622

semidirect

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

subgroup	index
#24907591	2
#24907463	2
#24905347	2
#24905298	2
C₈₃×#1954	2
#10622	83

subgroup

index

C₈₃×#1954

Subgroups — #35309143

Conjugacy classes of subgroups

Complements

Maximal subgroups