Finite Group Databasebeta

← #20268529

Subgroups — #20268529

Order 6592.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15693017C211yesmaximal, characteristic, complemented
2#15693016C211yesmaximal, characteristic, complemented
3#15693014C211yesmaximal, characteristic, complemented
4#15693006C211yesmaximal, characteristic, complemented
5#15693005C211yesmaximal, characteristic, complemented
6#15693004C211yesmaximal, characteristic, complemented
7#15692995C211yesmaximal, characteristic, complemented
8#15692994C211yesmaximal, characteristic, complemented
9#15692993C211yesmaximal, characteristic, complemented
10#15692993C211yesmaximal, characteristic, complemented
11#15692992C211yesmaximal, characteristic, complemented
12#15692991C211yesmaximal, characteristic, complemented
13#15692989C211yesmaximal, characteristic, complemented
14#15692989C211yesmaximal, characteristic, complemented
15#121×C103C211yesmaximal, characteristic, complemented
16C23×D103C2211yescharacteristic
17C2×D412C2211yescharacteristic
18C2×D412C2211yescharacteristic
19C2×C22⋊D103C2211yescharacteristic
20C2×C22⋊D103C2211yescharacteristic
21C2×C22⋊D103C2211yescharacteristic
22C2×C22⋊D103C2211yescharacteristic
23C2×C22⋊D103C2211yescharacteristic
24C2×C22⋊D103C2211yescharacteristic, complemented
25C2×C22⋊D103C2211yescharacteristic, complemented
26C22×Dic103C2211yescharacteristic, complemented
27C2×C4×D103C2211yescharacteristic, complemented
28C4⋊Dic103C2211yescharacteristic, complemented
29C4⋊Dic103C2211yescharacteristic, complemented
30Dic103⋊C4C2211yescharacteristic, complemented
31Dic103⋊C4C2211yescharacteristic, complemented
32Dic103⋊C4C2211yescharacteristic, complemented
33C22⋊Dic103C2211yescharacteristic
34C22⋊Dic103C2211yescharacteristic
35C22⋊Dic103C2211yescharacteristic, complemented
36(C2×D103)⋊C4C2211yescharacteristic
37(C2×D103)⋊C4C2211yescharacteristic
38(C2×D103)⋊C4C2211yescharacteristic
39(C2×D103)⋊C4C2211yescharacteristic
40(C2×D103)⋊C4C2211yescharacteristic
41(C2×D103)⋊C4C2211yescharacteristic
42(C2×D103)⋊C4C2211yescharacteristic, complemented
43C4×Dic103C2211yescharacteristic, complemented
44C2×D4×C103C2211yescharacteristic
45C2×D4×C103C2211yescharacteristic
46C2×D4×C103C2211yescharacteristic, complemented
47C22×C4×C103C2211yescharacteristic, complemented
48C4⋊C4×C103C2211yescharacteristic, complemented
49C22⋊C4×C103C2211yescharacteristic
50C22⋊C4×C103C2211yescharacteristic, complemented
51C23×C103C2311yescharacteristic
52C23×C103C2311yescharacteristic
53C23×C103C2311yescharacteristic
54C22×D103—41no—
55C22×D103—41no—
56C22×D103—41no—
57C22×D103C2311yescharacteristic
58C22×D103C2311yescharacteristic
59C22×D103C2311yescharacteristic
60D4×C103—41no—
61D4×C103—41no—
62D4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103C2311yescharacteristic
65C2×C4×C103C2311yescharacteristic
66C2×C4×C103C2311yescharacteristic
67C2×C4×C103C2311yescharacteristic
68C22⋊D103—41no—
69C22⋊D103—41no—
70C22⋊D103—41no—
71C22⋊D103—41no—
72C22⋊D103—41no—
73C22⋊D103—41no—
74C22⋊D103—41no—
75C2×Dic103—41no—
76C2×Dic103C2311yescharacteristic
77C2×Dic103C2311yescharacteristic
78C2×Dic103C2311yescharacteristic
79C2×Dic103C2311yescharacteristic
80C2×Dic103C2311yescharacteristic
81D412—41no—
82D412—41no—
83C4×D103—41no—
84C22×C103—21no—
85C22×C103—21no—
86C22×C103—21no—
87C22×C103—21no—
88C22×C103—21no—
89C22×C103—21no—
90C22×C103—21no—
91C22×C103—21no—
92C22×C103—21no—
93C22×C103C2411yescharacteristic
94C2×D103—21no—
95C2×D103—21no—
96C2×D103—21no—
97C2×D103—21no—
98C2×D103—21no—
99C2×D103—21no—
100C2×D103—21no—
101C2×D103—21no—
102C2×D103—21no—
103C2×D103—44no—
104C4×C103—21no—
105C4×C103—21no—
106C4×C103—21no—
107C4×C103—21no—
108Dic103—21no—
109Dic103—21no—
110Dic103—21no—
111Dic103—21no—
112Dic103—21no—
113C2×C103—41no—
114C2×C103—41no—
115C2×C103—41no—
116C2×C103H(5,𝔽2)11yescharacteristic
117C2×C103H(5,𝔽2)11yescharacteristic
118C2×C103H(5,𝔽2)11yescharacteristic
119D103—41no—
120D103—41no—
121D103—41no—
122C103#56011yescharacteristic, complemented, Sylow
123#560—1031nomaximal, Sylow
124#127—1031no—
125#126—1031no—
126#126—1031no—
127#123—1031no—
128#123—1031no—
129#123—1031no—
130#121—1031no—
131#121—1031no—
132#121—1031no—
133#121—1031no—
134#121—1031no—
135#121D10311yescharacteristic, complemented
136#120—1031no—
137#120—1031no—
138#120—1031no—
139C24—1031no—
140C2×D4—1031no—
141C2×D4—1031no—
142C2×D4—1031no—
143C2×D4—1031no—
144C2×D4—1031no—
145C2×D4—1031no—
146C2×D4—1031no—
147C2×D4—1031no—
148C2×D4—1031no—
149C2×D4C2×D10311yescharacteristic
150C2×D4C2×D10311yescharacteristic
151C2×D4C2×D10311yescharacteristic, complemented
152C22×C4—1031no—
153C22×C4—1031no—
154C22×C4C2×D10311yescharacteristic, complemented
155C4⋊C4—1031no—
156C4⋊C4—1031no—
157C4⋊C4—1031no—
158C4⋊C4—1031no—
159C4⋊C4—1031no—
160C4⋊C4C2×D10311yescharacteristic, complemented
161C22⋊C4—1031no—
162C22⋊C4—1031no—
163C22⋊C4—1031no—
164C22⋊C4—1031no—
165C22⋊C4—1031no—
166C22⋊C4—1031no—
167C22⋊C4—1031no—
168C22⋊C4—1031no—
169C22⋊C4—1031no—
170C22⋊C4—1031no—
171C22⋊C4C2×D10311yescharacteristic
172C22⋊C4C2×D10311yescharacteristic, complemented
173C42—1031no—
174C23—1031no—
175C23—1031no—
176C23—1031no—
177C23—4121no—
178C23—4121no—
179C23—4121no—
180C23C22×D10311yescharacteristic
181C23C22×D10311yescharacteristic
182C23C22×D10311yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—4121no—
187D4—4121no—
188D4—4121no—
189D4—4121no—
190D4—4121no—
191D4—4121no—
192D4—4121no—
193D4—4121no—
194D4—4121no—
195C2×C4—41no—
196C2×C4—1031no—
197C2×C4—1031no—
198C2×C4—1031no—
199C2×C4—1031no—
200C2×C4—1031no—
201C2×C4—4121no—
202C2×C4—4121no—
203C2×C4C22×D10311yescharacteristic
204C2×C4C22×D10311yescharacteristic
205C2×C4C22×D10311yescharacteristic
206C2×C4C22×D10311yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—4124no—
217C22—2061no—
218C22—2061no—
219C22—2061no—
220C22—2061no—
221C22—2061no—
222C22—2061no—
223C22—2061no—
224C22—2061no—
225C22—2061no—
226C22C23×D10311yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—2061no—
232C4—2061no—
233C4—2061no—
234C4—2061no—
235C4—2061no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—4121no—
240C2—4121no—
241C2—4121no—
242C2#1569306611yescharacteristic
243C2#1569306611yescharacteristic
244C2#1569306711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D103
commutator, socleC22×C103C24
Fitting#121×C103C2
hypercenter#121D103
hypocenterC103#560
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #121

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15693017C2semidirect
2. #15693016C2semidirect
3. #15693014C2semidirect
4. #15693006C2semidirect
5. #15693005C2semidirect
6. #15693004C2semidirect
7. #15692995C2semidirect
8. #15692994C2semidirect
9. #15692993C2semidirect
10. #15692993C2semidirect
11. #15692992C2semidirect
12. #15692991C2semidirect
13. #15692989C2semidirect
14. #15692989C2semidirect
15. #121×C103C2semidirect
24. C2×C22⋊D103C22semidirect
25. C2×C22⋊D103C22semidirect
26. C22×Dic103C22semidirect
27. C2×C4×D103C22semidirect
28. C4⋊Dic103C22semidirect
29. C4⋊Dic103C22semidirect
30. Dic103⋊C4C22semidirect
31. Dic103⋊C4C22semidirect
32. Dic103⋊C4C22semidirect
35. C22⋊Dic103C22semidirect
42. (C2×D103)⋊C4C22semidirect
43. C4×Dic103C22semidirect
46. C2×D4×C103C22semidirect
47. C22×C4×C103C22semidirect
48. C4⋊C4×C103C22semidirect
50. C22⋊C4×C103C22semidirect
122. C103#560semidirect
135. #121D103semidirect
151. C2×D4C2×D103semidirect
154. C22×C4C2×D103semidirect
160. C4⋊C4C2×D103semidirect
172. C22⋊C4C2×D103semidirect