Group #35322371 — subgroups

Subgroups — #35322371

Order 21248.

314 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 103 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	C₂×#19127517	C₂	1	1	yes	maximal, characteristic
2	C₂×#19127478	C₂	1	1	yes	maximal, characteristic
3	#24908335	C₂	1	1	yes	maximal, characteristic
4	#24908217	C₂	1	1	yes	maximal, characteristic
5	#24905568	C₂	1	1	yes	maximal, characteristic
6	#24905562	C₂	1	1	yes	maximal, characteristic
7	C₈₃×#2141	C₂	1	1	yes	maximal, characteristic
8	C₂×#14581732	C₂²	1	1	yes	characteristic
9	C₂×#14581728	C₂²	1	1	yes	characteristic
10	C₂×#14581724	C₂²	1	1	yes	characteristic
11	#19127728	—	2	1	no	—
12	C₂×#14581716	—	2	1	no	—
13	C₂×#14581702	C₂²	1	1	yes	characteristic
14	#19127608	—	2	1	no	—
15	#19127517	—	2	2	no	—
16	#19127478	—	2	2	no	—
17	#19127460	—	2	1	no	—
18	C₂²×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
19	C₂×M₃₂×C₈₃	C₂²	1	1	yes	characteristic
20	#427×C₈₃	C₂²	1	1	yes	characteristic
21	#358×C₈₃	C₄	1	4	yes	complemented
22	C₂×#13050574	—	2	1	no	—
23	C₂²×C₈₃⋊C₈	D₄	1	1	yes	characteristic
24	C₂×C₄⋊Dic₈₃	—	2	1	no	—
25	C₂×C₄×Dic₈₃	D₄	1	1	yes	characteristic
26	#14581732	—	2	1	no	—
27	#14581732	D₄	1	2	yes	—
28	C₂×C₈₃⋊C₁₆	—	2	1	no	—
29	#14581728	—	2	1	no	—
30	#14581728	—	2	1	no	—
31	#14581724	—	2	1	no	—
32	#14581724	—	2	1	no	—
33	C₄⋊(C₈₃⋊C₈)	—	4	2	no	—
34	#14581716	—	4	2	no	—
35	#14581702	—	2	1	no	—
36	#14581702	—	2	1	no	—
37	C₈₃⋊#95	—	4	2	no	—
38	C₂²×Q₈×C₈₃	—	2	1	no	—
39	C₂×Q₁₆×C₈₃	—	2	1	no	—
40	C₂×Q₁₆×C₈₃	—	2	1	no	—
41	C₂×Q₁₆×C₈₃	—	2	1	no	—
42	C₂×Q₁₆×C₈₃	—	2	1	no	—
43	C₂×Q₁₆×C₈₃	—	2	1	no	—
44	C₂×Q₁₆×C₈₃	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
46	#117×C₈₃	—	2	1	no	—
47	M₃₂×C₈₃	—	2	1	no	—
48	M₃₂×C₈₃	—	2	1	no	—
49	C₂×C₁₆×C₈₃	C₂×C₄	1	2	yes	—
50	#107×C₈₃	C₂×C₄	1	2	yes	—
51	#106×C₈₃	—	2	1	no	—
52	C₂²×Dic₈₃	—	2	1	no	—
53	C₂²×Dic₈₃	—	4	1	no	—
54	#13050574	—	4	1	no	—
55	#13050574	—	4	1	no	—
56	C₂×C₈₃⋊C₈	—	2	1	no	—
57	C₂×C₈₃⋊C₈	—	2	1	no	—
58	C₂×C₈₃⋊C₈	—	2	1	no	—
59	C₂×C₈₃⋊C₈	—	4	1	no	—
60	C₄⋊Dic₈₃	—	4	1	no	—
61	C₄⋊Dic₈₃	—	4	1	no	—
62	C₄×Dic₈₃	—	2	1	no	—
63	C₄×Dic₈₃	—	2	1	no	—
64	C₈₃⋊C₁₆	—	2	2	no	—
65	C₂×Q₈×C₈₃	—	2	2	no	—
66	C₂×Q₈×C₈₃	—	4	1	no	—
67	C₂×Q₈×C₈₃	—	4	1	no	—
68	C₂×Q₈×C₈₃	—	4	1	no	—
69	C₂×Q₈×C₈₃	—	4	1	no	—
70	C₂×Q₈×C₈₃	—	4	1	no	—
71	C₂²×C₄×C₈₃	—	4	1	no	—
72	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
73	Q₁₆×C₈₃	—	2	2	no	—
74	Q₁₆×C₈₃	—	2	2	no	—
75	Q₁₆×C₈₃	—	4	1	no	—
76	Q₁₆×C₈₃	—	4	1	no	—
77	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
80	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
81	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
82	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
83	C₄⋊C₄×C₈₃	—	2	2	no	—
84	C₂²⋊C₄×C₈₃	—	4	1	no	—
85	C₄²×C₈₃	—	4	1	no	—
86	C₁₆×C₈₃	—	2	2	no	—
87	C₂³×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
88	Q₈×C₈₃	—	4	2	no	—
89	Q₈×C₈₃	—	4	2	no	—
90	Q₈×C₈₃	—	8	1	no	—
91	Q₈×C₈₃	—	8	1	no	—
92	C₂×C₄×C₈₃	—	4	2	no	—
93	C₂×C₄×C₈₃	—	4	2	no	—
94	C₂×C₄×C₈₃	—	8	1	no	—
95	C₂×C₄×C₈₃	—	8	1	no	—
96	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
98	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
99	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
100	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
101	C₂×C₄×C₈₃	#137	1	1	yes	characteristic
102	C₂×Dic₈₃	—	4	2	no	—
103	C₂×Dic₈₃	—	4	1	no	—
104	C₂×Dic₈₃	—	8	2	no	—
105	C₂×Dic₈₃	—	8	1	no	—
106	C₈×C₈₃	#117	1	1	yes	characteristic
107	C₈×C₈₃	C₄×D₄	1	1	yes	characteristic
108	C₈×C₈₃	#123	1	1	yes	characteristic
109	C₈×C₈₃	#126	1	1	yes	characteristic
110	C₈₃⋊C₈	—	4	1	no	—
111	C₈₃⋊C₈	—	8	1	no	—
112	C₂²×C₈₃	—	2	2	no	—
113	C₂²×C₈₃	#442	1	1	yes	characteristic
114	C₂²×C₈₃	#468	1	1	yes	characteristic
115	C₂²×C₈₃	#490	1	1	yes	characteristic
116	C₄×C₈₃	—	8	2	no	—
117	C₄×C₈₃	—	8	2	no	—
118	C₄×C₈₃	#388	1	1	yes	characteristic
119	C₄×C₈₃	#440	1	1	yes	characteristic
120	C₄×C₈₃	#469	1	1	yes	characteristic
121	C₄×C₈₃	#489	1	1	yes	characteristic
122	Dic₈₃	—	8	1	no	—
123	Dic₈₃	—	16	1	no	—
124	#13154	—	83	1	no	maximal, Sylow
125	C₂×C₈₃	—	2	1	no	—
126	C₂×C₈₃	—	2	1	no	—
127	C₂×C₈₃	#1936	1	1	yes	characteristic
128	C₂×C₈₃	#2180	1	2	yes	—
129	C₂×#362	—	83	1	no	—
130	#2141	D₈₃	1	1	yes	characteristic
131	C₂×#347	—	83	1	no	—
132	#1971	—	83	1	no	—
133	#1946	—	83	1	no	—
134	#1386	—	83	1	no	—
135	#1383	—	83	1	no	—
136	C₈₃	#13154	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
138	C₂×M₃₂	—	83	1	no	—
139	C₂×M₃₂	C₂×D₈₃	1	1	yes	characteristic
140	C₂×#108	—	83	1	no	—
141	#427	C₂×D₈₃	1	1	yes	characteristic
142	C₂×#106	—	83	1	no	—
143	#424	—	166	1	no	—
144	C₂×#103	—	166	1	no	—
145	C₂×#97	—	83	1	no	—
146	#391	—	166	1	no	—
147	#362	—	166	2	no	—
148	#358	Dic₈₃	1	4	yes	complemented
149	#347	—	166	2	no	—
150	#339	—	166	1	no	—
151	C₂²×Q₈	—	2	1	no	—
152	C₂×Q₁₆	—	2	1	no	—
153	C₂×Q₁₆	—	2	1	no	—
154	C₂×Q₁₆	—	2	1	no	—
155	C₂×Q₁₆	—	2	1	no	—
156	C₂×Q₁₆	—	2	1	no	—
157	C₂×Q₁₆	C₂×Dic₈₃	1	2	yes	—
158	C₂×M₁₆	—	166	1	no	—
159	C₂²×C₈	—	83	1	no	—
160	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
161	#117	—	2	1	no	—
162	C₂×C₄⋊C₄	—	166	1	no	—
163	C₂×C₄²	—	83	1	no	—
164	M₃₂	—	2	1	no	—
165	M₃₂	—	2	1	no	—
166	M₃₂	—	83	2	no	—
167	M₃₂	—	166	1	no	—
168	C₂×C₁₆	—	166	1	no	—
169	C₂×C₁₆	C₂×Dic₈₃	1	2	yes	—
170	#108	—	166	1	no	—
171	#108	—	166	1	no	—
172	#107	C₂×Dic₈₃	1	2	yes	—
173	#106	—	2	1	no	—
174	#106	—	166	1	no	—
175	#106	—	166	1	no	—
176	C₄⋊C₈	—	332	2	no	—
177	#103	—	332	2	no	—
178	#97	—	166	1	no	—
179	#97	—	166	1	no	—
180	#95	—	332	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	1	no	—
183	C₂×Q₈	—	4	1	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂²×C₄	—	4	1	no	—
188	C₂²×C₄	—	332	1	no	—
189	C₂²×C₄	—	166	1	no	—
190	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
191	Q₁₆	—	2	2	no	—
192	Q₁₆	—	2	2	no	—
193	Q₁₆	—	4	1	no	—
194	Q₁₆	—	4	1	no	—
195	M₁₆	—	332	1	no	—
196	M₁₆	—	332	1	no	—
197	C₂×C₈	—	332	1	no	—
198	C₂×C₈	—	166	1	no	—
199	C₂×C₈	—	166	1	no	—
200	C₂×C₈	—	166	1	no	—
201	C₂×C₈	C₂²×Dic₈₃	1	1	yes	characteristic
202	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
203	C₂×C₈	#13050589	1	1	yes	characteristic
204	C₂×C₈	#13050589	1	1	yes	characteristic
205	C₂×C₈	#13050590	1	1	yes	characteristic
206	C₂×C₈	#13050590	1	1	yes	characteristic
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	332	1	no	—
209	C₄⋊C₄	—	332	1	no	—
210	C₂²⋊C₄	—	4	1	no	—
211	C₄²	—	4	1	no	—
212	C₄²	—	166	1	no	—
213	C₄²	—	166	1	no	—
214	C₁₆	—	2	2	no	—
215	C₁₆	—	166	2	no	—
216	C₂³	#14581816	1	1	yes	characteristic
217	Q₈	—	4	2	no	—
218	Q₈	—	4	2	no	—
219	Q₈	—	8	1	no	—
220	Q₈	—	8	1	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	8	1	no	—
224	C₂×C₄	—	8	1	no	—
225	C₂×C₄	—	332	2	no	—
226	C₂×C₄	—	332	1	no	—
227	C₂×C₄	—	664	2	no	—
228	C₂×C₄	—	664	1	no	—
229	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
230	C₂×C₄	#14581765	1	1	yes	characteristic
231	C₂×C₄	#14581778	1	1	yes	characteristic
232	C₂×C₄	#14581816	1	1	yes	characteristic
233	C₂×C₄	#14581819	1	1	yes	characteristic
234	C₂×C₄	#14581821	1	1	yes	characteristic
235	C₈	—	332	1	no	—
236	C₈	—	664	1	no	—
237	C₈	#14581751	1	1	yes	characteristic
238	C₈	D₄×Dic₈₃	1	1	yes	characteristic
239	C₈	#14581774	1	1	yes	characteristic
240	C₈	#14581785	1	1	yes	characteristic
241	C₂²	—	2	2	no	—
242	C₂²	#19127813	1	1	yes	characteristic
243	C₂²	#19127946	1	1	yes	characteristic
244	C₂²	#19128064	1	1	yes	characteristic
245	C₄	—	8	2	no	—
246	C₄	—	8	2	no	—
247	C₄	—	1328	1	no	—
248	C₄	—	664	1	no	—
249	C₄	#19127594	1	1	yes	characteristic
250	C₄	#19127802	1	1	yes	characteristic
251	C₄	#19127953	1	1	yes	characteristic
252	C₄	#19128059	1	1	yes	characteristic
253	C₂	—	2	1	no	—
254	C₂	—	2	1	no	—
255	C₂	#24908162	1	1	yes	characteristic
256	C₂	#24909355	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19127517

C₂

yes

maximal, characteristic

C₂×#19127478

C₂

yes

maximal, characteristic

#24908335

C₂

yes

maximal, characteristic

#24908217

C₂

yes

maximal, characteristic

#24905568

C₂

yes

maximal, characteristic

#24905562

C₂

yes

maximal, characteristic

C₈₃×#2141

C₂

yes

maximal, characteristic

C₂×#14581732

C₂²

yes

characteristic

C₂×#14581728

C₂²

yes

characteristic

C₂×#14581724

C₂²

yes

—

—

C₂²

yes

—

—

—

—

C₂²×Q₁₆×C₈₃

C₂²

yes

characteristic

C₂×M₃₂×C₈₃

C₂²

yes

characteristic

#427×C₈₃

C₂²

yes

characteristic

#358×C₈₃

C₄

yes

complemented

C₂×#13050574

—

C₂²×C₈₃⋊C₈

D₄

yes

characteristic

C₂×C₄⋊Dic₈₃

—

C₂×C₄×Dic₈₃

D₄

yes

characteristic

#14581732

—

#14581732

D₄

yes

—

C₂×C₈₃⋊C₁₆

—

—

—

—

—

C₄⋊(C₈₃⋊C₈)

—

#14581716

—

#14581702

—

#14581702

—

C₈₃⋊#95

—

C₂²×Q₈×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

C₂×C₄

yes

—

C₂²×C₈×C₈₃

C₂³

yes

characteristic

#117×C₈₃

—

M₃₂×C₈₃

—

M₃₂×C₈₃

—

C₂×C₁₆×C₈₃

C₂×C₄

yes

—

#107×C₈₃

C₂×C₄

yes

—

#106×C₈₃

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

—

#13050574

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₈₃⋊C₁₆

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

Q₁₆×C₈₃

—

Q₁₆×C₈₃

—

Q₁₆×C₈₃

—

Q₁₆×C₈₃

—

C₂×C₈×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×D₄

yes

C₂×C₈×C₈₃

yes

C₂×C₈×C₈₃

yes

C₂×C₈×C₈₃

yes

C₂×C₈×C₈₃

yes

C₄⋊C₄×C₈₃

—

C₂²⋊C₄×C₈₃

—

C₄²×C₈₃

—

C₁₆×C₈₃

—

C₂³×C₈₃

AGL(1,ℤ/8)

yes

characteristic

Q₈×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₄×D₄

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

100

C₂×C₄×C₈₃

AGL(1,ℤ/8)

yes

characteristic

101

C₂×C₄×C₈₃

#137

yes

characteristic

102

C₂×Dic₈₃

—

103

C₂×Dic₈₃

—

104

C₂×Dic₈₃

—

105

C₂×Dic₈₃

—

106

C₈×C₈₃

#117

yes

characteristic

107

C₈×C₈₃

C₄×D₄

yes

characteristic

108

C₈×C₈₃

#123

yes

characteristic

109

C₈×C₈₃

#126

yes

characteristic

110

C₈₃⋊C₈

—

111

C₈₃⋊C₈

—

112

C₂²×C₈₃

—

113

C₂²×C₈₃

#442

yes

characteristic

114

C₂²×C₈₃

#468

yes

characteristic

115

C₂²×C₈₃

#490

yes

characteristic

116

C₄×C₈₃

—

117

C₄×C₈₃

—

118

C₄×C₈₃

#388

yes

characteristic

119

C₄×C₈₃

#440

yes

characteristic

120

C₄×C₈₃

#469

yes

characteristic

121

C₄×C₈₃

#489

yes

characteristic

122

Dic₈₃

—

123

Dic₈₃

—

124

#13154

—

maximal, Sylow

125

C₂×C₈₃

—

126

C₂×C₈₃

—

127

C₂×C₈₃

#1936

yes

characteristic

128

C₂×C₈₃

#2180

yes

—

129

C₂×#362

—

130

#2141

D₈₃

yes

characteristic

131

C₂×#347

—

132

#1971

—

133

#1946

—

134

#1386

—

135

#1383

—

136

C₈₃

#13154

yes

characteristic, complemented, Sylow

137

C₂²×Q₁₆

C₂×D₈₃

yes

characteristic

138

C₂×M₃₂

—

139

C₂×M₃₂

C₂×D₈₃

yes

characteristic

140

C₂×#108

—

141

#427

C₂×D₈₃

yes

characteristic

142

C₂×#106

—

143

#424

—

166

—

144

C₂×#103

—

166

—

145

C₂×#97

—

146

#391

—

166

—

147

#362

—

166

—

148

#358

Dic₈₃

yes

complemented

149

#347

—

166

—

150

#339

—

166

—

151

C₂²×Q₈

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

C₂×Dic₈₃

yes

—

158

C₂×M₁₆

—

166

—

159

C₂²×C₈

—

160

C₂²×C₈

C₂²×D₈₃

yes

characteristic

161

#117

—

162

C₂×C₄⋊C₄

—

166

—

163

C₂×C₄²

—

164

M₃₂

—

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

166

—

168

C₂×C₁₆

—

166

—

169

C₂×C₁₆

C₂×Dic₈₃

yes

—

170

#108

—

166

—

171

#108

—

166

—

172

#107

C₂×Dic₈₃

yes

—

173

#106

—

174

#106

—

166

—

175

#106

—

166

—

176

C₄⋊C₈

—

332

—

177

#103

—

332

—

178

#97

—

166

—

179

#97

—

166

—

180

#95

—

332

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂²×C₄

—

188

C₂²×C₄

—

332

—

189

C₂²×C₄

—

166

—

190

C₂²×C₄

D₄×D₈₃

yes

characteristic

191

Q₁₆

—

192

Q₁₆

—

193

Q₁₆

—

194

Q₁₆

—

195

M₁₆

—

332

—

196

M₁₆

—

332

—

197

C₂×C₈

—

332

—

198

C₂×C₈

—

166

—

199

C₂×C₈

—

166

—

200

C₂×C₈

—

166

—

201

C₂×C₈

C₂²×Dic₈₃

yes

characteristic

202

C₂×C₈

D₄×D₈₃

yes

characteristic

203

C₂×C₈

#13050589

yes

characteristic

204

C₂×C₈

#13050589

yes

characteristic

205

C₂×C₈

#13050590

yes

characteristic

206

C₂×C₈

#13050590

yes

characteristic

207

C₄⋊C₄

—

208

C₄⋊C₄

—

332

—

209

C₄⋊C₄

—

332

—

210

C₂²⋊C₄

—

211

C₄²

—

212

C₄²

—

166

—

213

C₄²

—

166

—

214

C₁₆

—

215

C₁₆

—

166

—

216

C₂³

#14581816

yes

characteristic

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

332

—

226

C₂×C₄

—

332

—

227

C₂×C₄

—

664

—

228

C₂×C₄

—

664

—

229

C₂×C₄

D₄×Dic₈₃

yes

characteristic

230

C₂×C₄

#14581765

yes

characteristic

231

C₂×C₄

#14581778

yes

characteristic

232

C₂×C₄

#14581816

yes

characteristic

233

C₂×C₄

#14581819

yes

characteristic

234

C₂×C₄

#14581821

yes

characteristic

235

C₈

—

332

—

236

C₈

—

664

—

237

C₈

#14581751

yes

characteristic

238

C₈

D₄×Dic₈₃

yes

characteristic

239

C₈

#14581774

yes

characteristic

240

C₈

#14581785

yes

characteristic

241

C₂²

—

242

C₂²

#19127813

yes

characteristic

243

C₂²

#19127946

yes

characteristic

244

C₂²

#19128064

yes

characteristic

245

C₄

—

246

C₄

—

247

C₄

—

1328

—

248

C₄

—

664

—

249

C₄

#19127594

yes

characteristic

250

C₄

#19127802

yes

characteristic

251

C₄

#19127953

yes

characteristic

252

C₄

#19128059

yes

characteristic

253

C₂

—

254

C₂

—

255

C₂

#24908162

yes

characteristic

256

C₂

#24909355

yes

—

	subgroup	G/H
center	C₂²	#19127813
commutator	C₂×C₈×C₈₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₈₃×#2141	C₂
socle	C₂²×C₈₃	#442
prime radical	C₂³×C₈₃	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	#2141	D₈₃
hypocenter	C₈₃	#13154
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2141

subgroup

G/H

center

C₂²

#19127813

commutator

C₂×C₈×C₈₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₈₃×#2141

C₂

C₂²×C₈₃

C₂³×C₈₃

C₂²×C₈×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2141

N	H ≅ G/N	type
21. #358×C₈₃	C₄	semidirect
136. C₈₃	#13154	semidirect
148. #358	Dic₈₃	semidirect

H ≅ G/N

type

21. #358×C₈₃

C₄

semidirect

136. C₈₃

#13154

semidirect

148. #358

Dic₈₃

semidirect

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

subgroup	index
C₂×#19127517	2
C₂×#19127478	2
#24908335	2
#24908217	2
#24905568	2
#24905562	2
C₈₃×#2141	2
#13154	83

subgroup

index

C₈₃×#2141

Subgroups — #35322371

Conjugacy classes of subgroups

Complements

Maximal subgroups