Finite Group Databasebeta

← #44442814

Subgroups — #44442814

Order 29504.

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#28414114C211yesmaximal, characteristic, complemented
2#28414113C211yesmaximal, characteristic, complemented
3#28414111C211yesmaximal, characteristic, complemented
4#28414103C211yesmaximal, characteristic, complemented
5#28414102C211yesmaximal, characteristic, complemented
6#28414101C211yesmaximal, characteristic, complemented
7#28414092C211yesmaximal, characteristic, complemented
8#28414091C211yesmaximal, characteristic, complemented
9#28414090C211yesmaximal, characteristic, complemented
10#28414090C211yesmaximal, characteristic, complemented
11#28414089C211yesmaximal, characteristic, complemented
12#28414088C211yesmaximal, characteristic, complemented
13#28414086C211yesmaximal, characteristic, complemented
14#28414086C211yesmaximal, characteristic, complemented
15#121×C461C211yesmaximal, characteristic, complemented
16C23×D461C2211yescharacteristic
17C2×D1844C2211yescharacteristic
18C2×D1844C2211yescharacteristic
19C2×C22⋊D461C2211yescharacteristic
20C2×C22⋊D461C2211yescharacteristic
21C2×C22⋊D461C2211yescharacteristic
22C2×C22⋊D461C2211yescharacteristic
23C2×C22⋊D461C2211yescharacteristic
24C2×C22⋊D461C2211yescharacteristic, complemented
25C2×C22⋊D461C2211yescharacteristic, complemented
26C22×Dic461C2211yescharacteristic, complemented
27C2×C4×D461C2211yescharacteristic, complemented
28C4⋊Dic461C2211yescharacteristic, complemented
29C4⋊Dic461C2211yescharacteristic, complemented
30#20301480C2211yescharacteristic, complemented
31#20301480C2211yescharacteristic, complemented
32#20301480C2211yescharacteristic, complemented
33C22⋊Dic461C2211yescharacteristic
34C22⋊Dic461C2211yescharacteristic
35C22⋊Dic461C2211yescharacteristic, complemented
36#20301478C2211yescharacteristic
37#20301478C2211yescharacteristic
38#20301478C2211yescharacteristic
39#20301478C2211yescharacteristic
40#20301478C2211yescharacteristic
41#20301478C2211yescharacteristic
42#20301478C2211yescharacteristic, complemented
43C4×Dic461C2211yescharacteristic, complemented
44C2×D4×C461C2211yescharacteristic
45C2×D4×C461C2211yescharacteristic
46C2×D4×C461C2211yescharacteristic, complemented
47C22×C4×C461C2211yescharacteristic, complemented
48C4⋊C4×C461C2211yescharacteristic, complemented
49C22⋊C4×C461C2211yescharacteristic
50C22⋊C4×C461C2211yescharacteristic, complemented
51C22×D461—41no—
52C22×D461—41no—
53C22×D461—41no—
54C22×D461C2311yescharacteristic
55C22×D461C2311yescharacteristic
56C22×D461C2311yescharacteristic
57D1844—41no—
58D1844—41no—
59C22⋊D461—41no—
60C22⋊D461—41no—
61C22⋊D461—41no—
62C22⋊D461—41no—
63C22⋊D461—41no—
64C22⋊D461—41no—
65C22⋊D461—41no—
66C2×Dic461—41no—
67C2×Dic461C2311yescharacteristic
68C2×Dic461C2311yescharacteristic
69C2×Dic461C2311yescharacteristic
70C2×Dic461C2311yescharacteristic
71C2×Dic461C2311yescharacteristic
72C4×D461—41no—
73C23×C461C2311yescharacteristic
74C23×C461C2311yescharacteristic
75C23×C461C2311yescharacteristic
76D4×C461—41no—
77D4×C461—41no—
78D4×C461—41no—
79C2×C4×C461—41no—
80C2×C4×C461C2311yescharacteristic
81C2×C4×C461C2311yescharacteristic
82C2×C4×C461C2311yescharacteristic
83C2×C4×C461C2311yescharacteristic
84C22×C461—21no—
85C22×C461—21no—
86C22×C461—21no—
87C22×C461—21no—
88C22×C461—21no—
89C22×C461—21no—
90C22×C461—21no—
91C22×C461—21no—
92C22×C461—21no—
93C22×C461C2411yescharacteristic
94C2×D461—21no—
95C2×D461—21no—
96C2×D461—21no—
97C2×D461—21no—
98C2×D461—21no—
99C2×D461—21no—
100C2×D461—21no—
101C2×D461—21no—
102C2×D461—21no—
103C2×D461—44no—
104C4×C461—21no—
105C4×C461—21no—
106C4×C461—21no—
107C4×C461—21no—
108Dic461—21no—
109Dic461—21no—
110Dic461—21no—
111Dic461—21no—
112Dic461—21no—
113C2×C461—41no—
114C2×C461—41no—
115C2×C461—41no—
116C2×C461H(5,𝔽2)11yescharacteristic
117C2×C461H(5,𝔽2)11yescharacteristic
118C2×C461H(5,𝔽2)11yescharacteristic
119D461—41no—
120D461—41no—
121D461—41no—
122C461#56011yescharacteristic, complemented, Sylow
123#560—4611nomaximal, Sylow
124#127—4611no—
125#126—4611no—
126#126—4611no—
127#123—4611no—
128#123—4611no—
129#123—4611no—
130#121—4611no—
131#121—4611no—
132#121—4611no—
133#121—4611no—
134#121—4611no—
135#121D46111yescharacteristic, complemented
136#120—4611no—
137#120—4611no—
138#120—4611no—
139C24—4611no—
140C2×D4—4611no—
141C2×D4—4611no—
142C2×D4—4611no—
143C2×D4—4611no—
144C2×D4—4611no—
145C2×D4—4611no—
146C2×D4—4611no—
147C2×D4—4611no—
148C2×D4—4611no—
149C2×D4C2×D46111yescharacteristic
150C2×D4C2×D46111yescharacteristic
151C2×D4C2×D46111yescharacteristic, complemented
152C22×C4—4611no—
153C22×C4—4611no—
154C22×C4C2×D46111yescharacteristic, complemented
155C4⋊C4—4611no—
156C4⋊C4—4611no—
157C4⋊C4—4611no—
158C4⋊C4—4611no—
159C4⋊C4—4611no—
160C4⋊C4C2×D46111yescharacteristic, complemented
161C22⋊C4—4611no—
162C22⋊C4—4611no—
163C22⋊C4—4611no—
164C22⋊C4—4611no—
165C22⋊C4—4611no—
166C22⋊C4—4611no—
167C22⋊C4—4611no—
168C22⋊C4—4611no—
169C22⋊C4—4611no—
170C22⋊C4—4611no—
171C22⋊C4C2×D46111yescharacteristic
172C22⋊C4C2×D46111yescharacteristic, complemented
173C42—4611no—
174C23—18441no—
175C23—18441no—
176C23—18441no—
177C23—4611no—
178C23—4611no—
179C23—4611no—
180C23C22×D46111yescharacteristic
181C23C22×D46111yescharacteristic
182C23C22×D46111yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—18441no—
187D4—18441no—
188D4—18441no—
189D4—18441no—
190D4—18441no—
191D4—18441no—
192D4—18441no—
193D4—18441no—
194D4—18441no—
195C2×C4—41no—
196C2×C4—18441no—
197C2×C4—18441no—
198C2×C4—4611no—
199C2×C4—4611no—
200C2×C4—4611no—
201C2×C4—4611no—
202C2×C4—4611no—
203C2×C4C22×D46111yescharacteristic
204C2×C4C22×D46111yescharacteristic
205C2×C4C22×D46111yescharacteristic
206C2×C4C22×D46111yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—18444no—
217C22—9221no—
218C22—9221no—
219C22—9221no—
220C22—9221no—
221C22—9221no—
222C22—9221no—
223C22—9221no—
224C22—9221no—
225C22—9221no—
226C22C23×D46111yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—9221no—
232C4—9221no—
233C4—9221no—
234C4—9221no—
235C4—9221no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—18441no—
240C2—18441no—
241C2—18441no—
242C2#2841416311yescharacteristic
243C2#2841416311yescharacteristic
244C2#2841416411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D461
commutator, socle, cosocleC22×C461C24
Fitting#121×C461C2
hypercenter#121D461
hypocenterC461#560
LCSG ▷ C22×C461 ▷ C461
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #28414114C2semidirect
2. #28414113C2semidirect
3. #28414111C2semidirect
4. #28414103C2semidirect
5. #28414102C2semidirect
6. #28414101C2semidirect
7. #28414092C2semidirect
8. #28414091C2semidirect
9. #28414090C2semidirect
10. #28414090C2semidirect
11. #28414089C2semidirect
12. #28414088C2semidirect
13. #28414086C2semidirect
14. #28414086C2semidirect
15. #121×C461C2semidirect
24. C2×C22⋊D461C22semidirect
25. C2×C22⋊D461C22semidirect
26. C22×Dic461C22semidirect
27. C2×C4×D461C22semidirect
28. C4⋊Dic461C22semidirect
29. C4⋊Dic461C22semidirect
30. #20301480C22semidirect
31. #20301480C22semidirect
32. #20301480C22semidirect
35. C22⋊Dic461C22semidirect
42. #20301478C22semidirect
43. C4×Dic461C22semidirect
46. C2×D4×C461C22semidirect
47. C22×C4×C461C22semidirect
48. C4⋊C4×C461C22semidirect
50. C22⋊C4×C461C22semidirect
122. C461#560semidirect
135. #121D461semidirect
151. C2×D4C2×D461semidirect
154. C22×C4C2×D461semidirect
160. C4⋊C4C2×D461semidirect
172. C22⋊C4C2×D461semidirect

Maximal subgroups

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

subgroupindex
#284141142
#284141132
#284141112
#284141032
#284141022
#284141012
#284140922
#284140912
#284140902
#284140892
#284140882
#284140862
#121×C4612
#560461