Group #35304297 — subgroups

Subgroups — #35304297

Order 21248.

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

normal subgroups only

This group has 498 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	#24918042	C₂	1	1	yes	maximal, characteristic
2	#24908290	C₂	1	2	yes	maximal, complemented
3	#24907208	C₂	1	1	yes	maximal, characteristic, complemented
4	#24905913	C₂	1	2	yes	maximal, complemented
5	C₈₃×#1567	C₂	1	1	yes	maximal, characteristic, complemented
6	#19128251	C₂²	1	2	yes	—
7	#19128106	C₄	1	1	yes	characteristic, complemented
8	#19128078	C₄	1	1	yes	characteristic, complemented
9	#19128048	C₄	1	2	yes	complemented
10	#19127937	—	2	2	no	—
11	C₄×D₆₆₄	—	2	2	no	—
12	C₂×#14581718	—	2	4	no	—
13	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₄²×Dic₈₃	C₂²	1	1	yes	characteristic
15	#19127455	—	2	2	no	—
16	#19127428	—	2	4	no	—
17	#423×C₈₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
19	#335×C₈₃	—	2	2	no	—
20	C₂×#13050590	—	2	2	no	—
21	C₂×D₆₆₄	—	2	2	no	—
22	C₂²×C₈₃⋊C₈	—	2	1	no	—
23	#14581792	C₂×C₄	1	2	yes	—
24	#14581789	C₂×C₄	1	2	yes	—
25	#14581780	—	2	2	no	—
26	#14581766	—	2	2	no	—
27	#14581766	—	2	2	no	—
28	C₄×D₃₃₂	—	2	2	no	—
29	C₄×D₃₃₂	—	2	2	no	—
30	C₂×C₄×Dic₈₃	—	2	1	no	—
31	C₂×C₄×Dic₈₃	—	2	1	no	—
32	C₂×C₄×Dic₈₃	D₄	1	2	yes	—
33	#14581726	—	2	2	no	—
34	#14581718	—	4	8	no	—
35	#14581714	—	2	4	no	—
36	C₄×C₈₃⋊C₈	—	2	1	no	—
37	C₄×C₈₃⋊C₈	D₄	1	2	yes	—
38	C₂×M₁₆×C₈₃	—	2	2	no	—
39	C₂²×C₈×C₈₃	D₄	1	2	yes	—
40	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₈₃	—	2	2	no	—
42	C₄⋊C₈×C₈₃	—	2	2	no	—
43	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₈₃	D₄	1	2	yes	—
46	#13050590	—	4	4	no	—
47	#13050590	—	4	4	no	—
48	C₂×Dic₁₆₆	—	2	2	no	—
49	C₂×D₃₃₂	—	2	2	no	—
50	C₂×D₃₃₂	—	2	2	no	—
51	C₂×D₃₃₂	—	2	2	no	—
52	C₂×C₂²⋊D₈₃	—	4	2	no	—
53	C₂²×Dic₈₃	—	2	2	no	—
54	C₂×C₄×D₈₃	—	4	2	no	—
55	D₆₆₄	—	4	4	no	—
56	C₂×C₈₃⋊C₈	—	2	2	no	—
57	C₂×C₈₃⋊C₈	—	4	2	no	—
58	C₄⋊Dic₈₃	—	2	2	no	—
59	C₄⋊Dic₈₃	—	2	2	no	—
60	(C₂×D₈₃)⋊C₄	—	4	2	no	—
61	(C₂×D₈₃)⋊C₄	—	4	2	no	—
62	C₄×Dic₈₃	—	2	2	no	—
63	C₄×Dic₈₃	—	4	2	no	—
64	C₄×Dic₈₃	—	4	2	no	—
65	C₄×Dic₈₃	D₈	1	4	yes	complemented
66	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
69	M₁₆×C₈₃	—	4	4	no	—
70	C₂×C₈×C₈₃	—	4	2	no	—
71	C₂×C₈×C₈₃	—	4	2	no	—
72	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
74	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₈₃	#41	1	1	yes	characteristic
78	C₂³×C₈₃	#121	1	1	yes	characteristic
79	C₂²×D₈₃	—	4	2	no	—
80	C₂×C₄×C₈₃	—	2	2	no	—
81	C₂×C₄×C₈₃	—	2	2	no	—
82	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
86	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
87	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
88	C₂×C₄×C₈₃	C₂×D₈	1	2	yes	—
89	C₂×C₄×C₈₃	#135	1	2	yes	—
90	C₂²⋊D₈₃	—	8	4	no	—
91	C₂×Dic₈₃	—	2	4	no	—
92	C₂×Dic₈₃	—	4	2	no	—
93	C₂×Dic₈₃	—	4	2	no	—
94	C₂×Dic₈₃	—	4	2	no	—
95	D₃₃₂	—	4	4	no	—
96	D₃₃₂	—	4	4	no	—
97	D₃₃₂	—	4	4	no	—
98	C₄×D₈₃	—	8	2	no	—
99	C₄×D₈₃	—	8	2	no	—
100	Dic₁₆₆	—	4	4	no	—
101	C₈×C₈₃	—	2	2	no	—
102	C₈×C₈₃	—	2	2	no	—
103	C₈×C₈₃	—	8	2	no	—
104	C₈₃⋊C₈	—	4	2	no	—
105	C₂²×C₈₃	—	2	1	no	—
106	C₂²×C₈₃	—	2	1	no	—
107	C₂²×C₈₃	#390	1	1	yes	characteristic
108	C₂²×C₈₃	#466	1	2	yes	—
109	C₂×D₈₃	—	8	2	no	—
110	C₂×D₈₃	—	8	2	no	—
111	C₂×D₈₃	—	8	2	no	—
112	C₄×C₈₃	—	2	1	no	—
113	C₄×C₈₃	—	2	1	no	—
114	C₄×C₈₃	#421	1	2	yes	—
115	C₄×C₈₃	C₄×D₈	1	2	yes	—
116	C₄×C₈₃	#444	1	2	yes	—
117	C₄×C₈₃	#493	1	1	yes	characteristic
118	C₄×C₈₃	#495	1	1	yes	characteristic
119	Dic₈₃	—	4	4	no	—
120	Dic₈₃	—	8	2	no	—
121	#9847	—	83	1	no	maximal, Sylow
122	C₂×C₈₃	—	2	2	no	—
123	C₂×C₈₃	#1963	1	1	yes	characteristic
124	C₂×C₈₃	#1970	1	1	yes	characteristic
125	C₂×C₈₃	#1975	1	1	yes	characteristic
126	D₈₃	—	16	2	no	—
127	#3169	—	83	1	no	—
128	#1962	—	83	2	no	—
129	#1744	—	83	1	no	—
130	#1567	D₈₃	1	1	yes	characteristic, complemented
131	#1492	—	83	2	no	—
132	C₈₃	#9847	1	1	yes	characteristic, complemented, Sylow
133	#532	—	83	2	no	—
134	#500	—	83	1	no	—
135	#493	—	83	1	no	—
136	#486	—	83	2	no	—
137	#466	—	166	2	no	—
138	C₄×D₈	—	166	2	no	—
139	#423	C₂×D₈₃	1	2	yes	—
140	C₂×#104	—	166	4	no	—
141	C₂×C₄×C₈	—	83	1	no	—
142	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
143	C₄³	—	83	1	no	—
144	#336	—	166	2	no	—
145	#335	—	2	2	no	—
146	D₄⋊C₈	—	166	4	no	—
147	C₂×#41	—	166	2	no	—
148	C₂×D₈	—	166	2	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₂²×C₈	—	166	1	no	—
151	C₂²×C₈	D₃₃₂	1	2	yes	—
152	C₄⋊Q₈	—	83	2	no	—
153	#127	—	83	2	no	—
154	#124	—	166	2	no	—
155	#121	—	166	2	no	—
156	#121	—	166	2	no	—
157	C₄×D₄	—	166	2	no	—
158	C₄×D₄	—	166	2	no	—
159	C₂×C₄²	—	83	2	no	—
160	C₂×C₄²	—	166	1	no	—
161	C₂×C₄²	—	166	1	no	—
162	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
163	#107	—	166	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	#104	—	332	8	no	—
167	#102	—	166	4	no	—
168	C₄×C₈	—	83	2	no	—
169	C₄×C₈	—	166	1	no	—
170	C₄×C₈	C₄×D₈₃	1	1	yes	characteristic
171	C₄×C₈	C₄×D₈₃	1	1	yes	characteristic
172	C₄×C₈	C₂²⋊D₈₃	1	2	yes	—
173	#41	—	332	4	no	—
174	#41	—	332	4	no	—
175	C₂×Q₈	—	166	2	no	—
176	C₂×D₄	—	332	2	no	—
177	C₂×D₄	—	166	2	no	—
178	C₂×D₄	—	166	2	no	—
179	C₂×D₄	—	166	2	no	—
180	C₂²×C₄	—	332	2	no	—
181	C₂²×C₄	—	166	2	no	—
182	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
183	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
184	C₂²×C₄	#13050591	1	1	yes	characteristic
185	D₈	—	332	4	no	—
186	M₁₆	—	4	4	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	332	2	no	—
190	C₂×C₈	—	166	2	no	—
191	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
192	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
193	C₄⋊C₄	—	166	2	no	—
194	C₄⋊C₄	—	166	2	no	—
195	C₂²⋊C₄	—	332	2	no	—
196	C₂²⋊C₄	—	332	2	no	—
197	C₄²	—	332	2	no	—
198	C₄²	—	332	2	no	—
199	C₄²	—	83	4	no	—
200	C₄²	—	166	2	no	—
201	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
202	C₄²	D₄×D₈₃	1	1	yes	characteristic
203	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
204	C₄²	#13050591	1	1	yes	characteristic
205	C₂³	—	332	2	no	—
206	C₂³	#14581767	1	1	yes	characteristic
207	Q₈	—	332	4	no	—
208	D₄	—	332	4	no	—
209	D₄	—	332	4	no	—
210	D₄	—	332	4	no	—
211	D₄	—	664	4	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	332	2	no	—
215	C₂×C₄	—	332	2	no	—
216	C₂×C₄	—	332	2	no	—
217	C₂×C₄	—	664	2	no	—
218	C₂×C₄	—	664	2	no	—
219	C₂×C₄	—	166	4	no	—
220	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
221	C₂×C₄	#14581754	1	1	yes	characteristic
222	C₂×C₄	#14581754	1	1	yes	characteristic
223	C₂×C₄	#14581767	1	1	yes	characteristic
224	C₂×C₄	#14581781	1	1	yes	characteristic
225	C₂×C₄	#14581788	1	1	yes	characteristic
226	C₂×C₄	D₈×D₈₃	1	2	yes	—
227	C₂×C₄	#14581815	1	2	yes	—
228	C₈	—	2	2	no	—
229	C₈	—	2	2	no	—
230	C₈	—	8	2	no	—
231	C₈	—	332	2	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	664	2	no	—
235	C₂²	—	664	2	no	—
236	C₂²	—	664	2	no	—
237	C₂²	#19127602	1	1	yes	characteristic
238	C₂²	#19127938	1	2	yes	—
239	C₄	—	2	1	no	—
240	C₄	—	2	1	no	—
241	C₄	—	332	4	no	—
242	C₄	—	664	2	no	—
243	C₄	#19127717	1	2	yes	—
244	C₄	#19127783	1	2	yes	—
245	C₄	#19127822	1	2	yes	—
246	C₄	#19128076	1	1	yes	characteristic
247	C₄	#19128086	1	1	yes	characteristic
248	C₂	—	2	2	no	—
249	C₂	—	1328	2	no	—
250	C₂	#24908294	1	1	yes	characteristic
251	C₂	#24908327	1	1	yes	characteristic
252	C₂	#24908354	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#24918042

C₂

yes

maximal, characteristic

#24908290

C₂

yes

maximal, complemented

#24907208

C₂

yes

maximal, characteristic, complemented

#24905913

C₂

yes

maximal, complemented

C₈₃×#1567

C₂

yes

maximal, characteristic, complemented

#19128251

C₂²

yes

—

#19128106

C₄

yes

characteristic, complemented

#19128078

C₄

yes

characteristic, complemented

#19128048

C₄

yes

complemented

#19127937

—

C₄×D₆₆₄

—

C₂×#14581718

—

C₂×C₄×C₈₃⋊C₈

C₂²

yes

characteristic

C₄²×Dic₈₃

C₂²

yes

characteristic

#19127455

—

#19127428

—

#423×C₈₃

C₂²

yes

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

#335×C₈₃

—

C₂×#13050590

—

C₂×D₆₆₄

—

C₂²×C₈₃⋊C₈

—

#14581792

C₂×C₄

yes

—

#14581789

C₂×C₄

yes

—

#14581780

—

#14581766

—

#14581766

—

C₄×D₃₃₂

—

C₄×D₃₃₂

—

C₂×C₄×Dic₈₃

—

C₂×C₄×Dic₈₃

—

C₂×C₄×Dic₈₃

D₄

yes

—

#14581726

—

#14581718

—

#14581714

—

C₄×C₈₃⋊C₈

—

C₄×C₈₃⋊C₈

D₄

yes

—

C₂×M₁₆×C₈₃

—

C₂²×C₈×C₈₃

D₄

yes

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

D₄

yes

—

#13050590

—

#13050590

—

C₂×Dic₁₆₆

—

C₂×D₃₃₂

—

C₂×D₃₃₂

—

C₂×D₃₃₂

—

C₂×C₂²⋊D₈₃

—

C₂²×Dic₈₃

—

C₂×C₄×D₈₃

—

D₆₆₄

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

(C₂×D₈₃)⋊C₄

—

(C₂×D₈₃)⋊C₄

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

D₈

yes

complemented

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

#41

yes

characteristic

M₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

—

C₄²×C₈₃

C₂²×C₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

C₄²×C₈₃

yes

C₂³×C₈₃

yes

C₂²×D₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₄×D₄

yes

characteristic

C₂×C₄×C₈₃

C₄×D₄

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

yes

C₂×C₄×C₈₃

C₂×D₈

yes

—

C₂×C₄×C₈₃

#135

yes

—

C₂²⋊D₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

D₃₃₂

—

D₃₃₂

—

D₃₃₂

—

C₄×D₈₃

—

C₄×D₈₃

—

100

Dic₁₆₆

—

101

C₈×C₈₃

—

102

C₈×C₈₃

—

103

C₈×C₈₃

—

104

C₈₃⋊C₈

—

105

C₂²×C₈₃

—

106

C₂²×C₈₃

—

107

C₂²×C₈₃

#390

yes

characteristic

108

C₂²×C₈₃

#466

yes

—

109

C₂×D₈₃

—

110

C₂×D₈₃

—

111

C₂×D₈₃

—

112

C₄×C₈₃

—

113

C₄×C₈₃

—

114

C₄×C₈₃

#421

yes

—

115

C₄×C₈₃

C₄×D₈

yes

—

116

C₄×C₈₃

#444

yes

—

117

C₄×C₈₃

#493

yes

characteristic

118

C₄×C₈₃

#495

yes

characteristic

119

Dic₈₃

—

120

Dic₈₃

—

121

#9847

—

maximal, Sylow

122

C₂×C₈₃

—

123

C₂×C₈₃

#1963

yes

characteristic

124

C₂×C₈₃

#1970

yes

characteristic

125

C₂×C₈₃

#1975

yes

characteristic

126

D₈₃

—

127

#3169

—

128

#1962

—

129

#1744

—

130

#1567

D₈₃

yes

characteristic, complemented

131

#1492

—

132

C₈₃

#9847

yes

characteristic, complemented, Sylow

133

#532

—

134

#500

—

135

#493

—

136

#486

—

137

#466

—

166

—

138

C₄×D₈

—

166

—

139

#423

C₂×D₈₃

yes

—

140

C₂×#104

—

166

—

141

C₂×C₄×C₈

—

142

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

143

C₄³

—

144

#336

—

166

—

145

#335

—

146

D₄⋊C₈

—

166

—

147

C₂×#41

—

166

—

148

C₂×D₈

—

166

—

149

C₂×M₁₆

—

150

C₂²×C₈

—

166

—

151

C₂²×C₈

D₃₃₂

yes

—

152

C₄⋊Q₈

—

153

#127

—

154

#124

—

166

—

155

#121

—

166

—

156

#121

—

166

—

157

C₄×D₄

—

166

—

158

C₄×D₄

—

166

—

159

C₂×C₄²

—

160

C₂×C₄²

—

166

—

161

C₂×C₄²

—

166

—

162

C₂×C₄²

C₂²×D₈₃

yes

characteristic

163

#107

—

166

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#104

—

332

—

167

#102

—

166

—

168

C₄×C₈

—

169

C₄×C₈

—

166

—

170

C₄×C₈

C₄×D₈₃

yes

characteristic

171

C₄×C₈

C₄×D₈₃

yes

characteristic

172

C₄×C₈

C₂²⋊D₈₃

yes

—

173

#41

—

332

—

174

#41

—

332

—

175

C₂×Q₈

—

166

—

176

C₂×D₄

—

332

—

177

C₂×D₄

—

166

—

178

C₂×D₄

—

166

—

179

C₂×D₄

—

166

—

180

C₂²×C₄

—

332

—

181

C₂²×C₄

—

166

—

182

C₂²×C₄

D₄×D₈₃

yes

characteristic

183

C₂²×C₄

C₂×D₃₃₂

yes

characteristic

184

C₂²×C₄

#13050591

yes

characteristic

185

D₈

—

332

—

186

M₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

332

—

190

C₂×C₈

—

166

—

191

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

—

192

C₂×C₈

(C₂×D₈₃)⋊C₄

yes

—

193

C₄⋊C₄

—

166

—

194

C₄⋊C₄

—

166

—

195

C₂²⋊C₄

—

332

—

196

C₂²⋊C₄

—

332

—

197

C₄²

—

332

—

198

C₄²

—

332

—

199

C₄²

—

200

C₄²

—

166

—

201

C₄²

C₂×C₄×D₈₃

yes

characteristic

202

C₄²

D₄×D₈₃

yes

characteristic

203

C₄²

C₂×C₂²⋊D₈₃

yes

characteristic

204

C₄²

#13050591

yes

characteristic

205

C₂³

—

332

—

206

C₂³

#14581767

yes

characteristic

207

Q₈

—

332

—

208

D₄

—

332

—

209

D₄

—

332

—

210

D₄

—

332

—

211

D₄

—

664

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

332

—

215

C₂×C₄

—

332

—

216

C₂×C₄

—

332

—

217

C₂×C₄

—

664

—

218

C₂×C₄

—

664

—

219

C₂×C₄

—

166

—

220

C₂×C₄

C₂×(C₂×D₈₃)⋊C₄

yes

characteristic

221

C₂×C₄

#14581754

yes

characteristic

222

C₂×C₄

#14581754

yes

characteristic

223

C₂×C₄

#14581767

yes

characteristic

224

C₂×C₄

#14581781

yes

characteristic

225

C₂×C₄

#14581788

yes

characteristic

226

C₂×C₄

D₈×D₈₃

yes

—

227

C₂×C₄

#14581815

yes

—

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

332

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

664

—

235

C₂²

—

664

—

236

C₂²

—

664

—

237

C₂²

#19127602

yes

characteristic

238

C₂²

#19127938

yes

—

239

C₄

—

240

C₄

—

241

C₄

—

332

—

242

C₄

—

664

—

243

C₄

#19127717

yes

—

244

C₄

#19127783

yes

—

245

C₄

#19127822

yes

—

246

C₄

#19128076

yes

characteristic

247

C₄

#19128086

yes

characteristic

248

C₂

—

249

C₂

—

1328

—

250

C₂

#24908294

yes

characteristic

251

C₂

#24908327

yes

characteristic

252

C₂

#24908354

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14581788
commutator	C₄²×C₈₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1567	C₂
socle	C₂²×C₈₃	#390
prime radical	#24918042	C₂
cosocle	C₂×C₄²×C₈₃	C₂³
hypercenter	#1567	D₈₃
hypocenter	C₈₃	#9847
LCS	G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

subgroup

G/H

center

C₂×C₄

#14581788

commutator

C₄²×C₈₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1567

C₂

C₂²×C₈₃

C₂

C₂×C₄²×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

N	H ≅ G/N	type
2. #24908290	C₂	semidirect
3. #24907208	C₂	semidirect
4. #24905913	C₂	semidirect
5. C₈₃×#1567	C₂	semidirect
7. #19128106	C₄	semidirect
8. #19128078	C₄	semidirect
9. #19128048	C₄	semidirect
65. C₄×Dic₈₃	D₈	semidirect
130. #1567	D₈₃	semidirect
132. C₈₃	#9847	semidirect

H ≅ G/N

type

2. #24908290

C₂

semidirect

3. #24907208

C₂

semidirect

4. #24905913

C₂

semidirect

5. C₈₃×#1567

C₂

semidirect

7. #19128106

C₄

semidirect

8. #19128078

C₄

semidirect

9. #19128048

C₄

semidirect

65. C₄×Dic₈₃

D₈

semidirect

130. #1567

D₈₃

semidirect

132. C₈₃

#9847

semidirect

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

subgroup	index
#24918042	2
#24908290	2
#24907208	2
#24905913	2
C₈₃×#1567	2
#9847	83

subgroup

index

C₈₃×#1567

Subgroups — #35304297

Conjugacy classes of subgroups

Complements

Maximal subgroups