Finite Group Databasebeta

← #14581074

Subgroups — #14581074

Order 2624.

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#13050160C211yesmaximal, characteristic, complemented
2#13050159C211yesmaximal, characteristic, complemented
3#13050157C211yesmaximal, characteristic, complemented
4#13050149C211yesmaximal, characteristic, complemented
5#13050148C211yesmaximal, characteristic, complemented
6#13050147C211yesmaximal, characteristic, complemented
7#13050138C211yesmaximal, characteristic, complemented
8#13050137C211yesmaximal, characteristic, complemented
9#13050136C211yesmaximal, characteristic, complemented
10#13050136C211yesmaximal, characteristic, complemented
11#13050135C211yesmaximal, characteristic, complemented
12#13050134C211yesmaximal, characteristic, complemented
13#13050132C211yesmaximal, characteristic, complemented
14#13050132C211yesmaximal, characteristic, complemented
15#121×C41C211yesmaximal, characteristic, complemented
16C23×D41C2211yescharacteristic
17C2×D4×C41C2211yescharacteristic
18C2×D4×C41C2211yescharacteristic
19C2×D4×C41C2211yescharacteristic, complemented
20C22×C4×C41C2211yescharacteristic, complemented
21C2×C22⋊D41C2211yescharacteristic
22C2×C22⋊D41C2211yescharacteristic
23C2×C22⋊D41C2211yescharacteristic
24C2×C22⋊D41C2211yescharacteristic
25C2×C22⋊D41C2211yescharacteristic
26C2×C22⋊D41C2211yescharacteristic, complemented
27C2×C22⋊D41C2211yescharacteristic, complemented
28C22×Dic41C2211yescharacteristic, complemented
29C2×D164C2211yescharacteristic
30C2×D164C2211yescharacteristic
31C2×C4×D41C2211yescharacteristic, complemented
32C4⋊C4×C41C2211yescharacteristic, complemented
33C22⋊C4×C41C2211yescharacteristic
34C22⋊C4×C41C2211yescharacteristic, complemented
35C22⋊Dic41C2211yescharacteristic
36C22⋊Dic41C2211yescharacteristic
37C22⋊Dic41C2211yescharacteristic, complemented
38#10620281C2211yescharacteristic
39#10620281C2211yescharacteristic
40#10620281C2211yescharacteristic
41#10620281C2211yescharacteristic
42#10620281C2211yescharacteristic
43#10620281C2211yescharacteristic
44#10620281C2211yescharacteristic, complemented
45C4⋊Dic41C2211yescharacteristic, complemented
46C4⋊Dic41C2211yescharacteristic, complemented
47#10620279C2211yescharacteristic, complemented
48#10620279C2211yescharacteristic, complemented
49#10620279C2211yescharacteristic, complemented
50C4×Dic41C2211yescharacteristic, complemented
51C23×C41C2311yescharacteristic
52C23×C41C2311yescharacteristic
53C23×C41C2311yescharacteristic
54C22×D41—41no—
55C22×D41—41no—
56C22×D41—41no—
57C22×D41C2311yescharacteristic
58C22×D41C2311yescharacteristic
59C22×D41C2311yescharacteristic
60D4×C41—41no—
61D4×C41—41no—
62D4×C41—41no—
63C2×C4×C41—41no—
64C2×C4×C41C2311yescharacteristic
65C2×C4×C41C2311yescharacteristic
66C2×C4×C41C2311yescharacteristic
67C2×C4×C41C2311yescharacteristic
68C22⋊D41—41no—
69C22⋊D41—41no—
70C22⋊D41—41no—
71C22⋊D41—41no—
72C22⋊D41—41no—
73C22⋊D41—41no—
74C22⋊D41—41no—
75C2×Dic41—41no—
76C2×Dic41C2311yescharacteristic
77C2×Dic41C2311yescharacteristic
78C2×Dic41C2311yescharacteristic
79C2×Dic41C2311yescharacteristic
80C2×Dic41C2311yescharacteristic
81D164—41no—
82D164—41no—
83C4×D41—41no—
84C22×C41—21no—
85C22×C41—21no—
86C22×C41—21no—
87C22×C41—21no—
88C22×C41—21no—
89C22×C41—21no—
90C22×C41—21no—
91C22×C41—21no—
92C22×C41—21no—
93C22×C41C2411yescharacteristic
94C2×D41—21no—
95C2×D41—21no—
96C2×D41—21no—
97C2×D41—21no—
98C2×D41—21no—
99C2×D41—21no—
100C2×D41—21no—
101C2×D41—21no—
102C2×D41—21no—
103C2×D41—44no—
104C4×C41—21no—
105C4×C41—21no—
106C4×C41—21no—
107C4×C41—21no—
108Dic41—21no—
109Dic41—21no—
110Dic41—21no—
111Dic41—21no—
112Dic41—21no—
113C2×C41—41no—
114C2×C41—41no—
115C2×C41—41no—
116C2×C41H(5,𝔽2)11yescharacteristic
117C2×C41H(5,𝔽2)11yescharacteristic
118C2×C41H(5,𝔽2)11yescharacteristic
119D41—41no—
120D41—41no—
121D41—41no—
122#560—411nomaximal, Sylow
123C41#56011yescharacteristic, complemented, Sylow
124#127—411no—
125#126—411no—
126#126—411no—
127#123—411no—
128#123—411no—
129#123—411no—
130#121—411no—
131#121—411no—
132#121—411no—
133#121—411no—
134#121—411no—
135#121D4111yescharacteristic, complemented
136#120—411no—
137#120—411no—
138#120—411no—
139C24—411no—
140C2×D4—411no—
141C2×D4—411no—
142C2×D4—411no—
143C2×D4—411no—
144C2×D4—411no—
145C2×D4—411no—
146C2×D4—411no—
147C2×D4—411no—
148C2×D4—411no—
149C2×D4C2×D4111yescharacteristic
150C2×D4C2×D4111yescharacteristic
151C2×D4C2×D4111yescharacteristic, complemented
152C22×C4—411no—
153C22×C4—411no—
154C22×C4C2×D4111yescharacteristic, complemented
155C4⋊C4—411no—
156C4⋊C4—411no—
157C4⋊C4—411no—
158C4⋊C4—411no—
159C4⋊C4—411no—
160C4⋊C4C2×D4111yescharacteristic, complemented
161C22⋊C4—411no—
162C22⋊C4—411no—
163C22⋊C4—411no—
164C22⋊C4—411no—
165C22⋊C4—411no—
166C22⋊C4—411no—
167C22⋊C4—411no—
168C22⋊C4—411no—
169C22⋊C4—411no—
170C22⋊C4—411no—
171C22⋊C4C2×D4111yescharacteristic
172C22⋊C4C2×D4111yescharacteristic, complemented
173C42—411no—
174C23—411no—
175C23—411no—
176C23—411no—
177C23—1641no—
178C23—1641no—
179C23—1641no—
180C23C22×D4111yescharacteristic
181C23C22×D4111yescharacteristic
182C23C22×D4111yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—1641no—
187D4—1641no—
188D4—1641no—
189D4—1641no—
190D4—1641no—
191D4—1641no—
192D4—1641no—
193D4—1641no—
194D4—1641no—
195C2×C4—41no—
196C2×C4—411no—
197C2×C4—411no—
198C2×C4—411no—
199C2×C4—411no—
200C2×C4—411no—
201C2×C4—1641no—
202C2×C4—1641no—
203C2×C4C22×D4111yescharacteristic
204C2×C4C22×D4111yescharacteristic
205C2×C4C22×D4111yescharacteristic
206C2×C4C22×D4111yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—821no—
217C22—821no—
218C22—821no—
219C22—821no—
220C22—821no—
221C22—821no—
222C22—821no—
223C22—821no—
224C22—821no—
225C22—1644no—
226C22C23×D4111yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—821no—
232C4—821no—
233C4—821no—
234C4—821no—
235C4—821no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—1641no—
240C2—1641no—
241C2—1641no—
242C2#1305020911yescharacteristic
243C2#1305020911yescharacteristic
244C2#1305021011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
Fitting#121×C41C2
hypercenter#121D41
hypocenterC41#560
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #13050160C2semidirect
2. #13050159C2semidirect
3. #13050157C2semidirect
4. #13050149C2semidirect
5. #13050148C2semidirect
6. #13050147C2semidirect
7. #13050138C2semidirect
8. #13050137C2semidirect
9. #13050136C2semidirect
10. #13050136C2semidirect
11. #13050135C2semidirect
12. #13050134C2semidirect
13. #13050132C2semidirect
14. #13050132C2semidirect
15. #121×C41C2semidirect
19. C2×D4×C41C22semidirect
20. C22×C4×C41C22semidirect
26. C2×C22⋊D41C22semidirect
27. C2×C22⋊D41C22semidirect
28. C22×Dic41C22semidirect
31. C2×C4×D41C22semidirect
32. C4⋊C4×C41C22semidirect
34. C22⋊C4×C41C22semidirect
37. C22⋊Dic41C22semidirect
44. #10620281C22semidirect
45. C4⋊Dic41C22semidirect
46. C4⋊Dic41C22semidirect
47. #10620279C22semidirect
48. #10620279C22semidirect
49. #10620279C22semidirect
50. C4×Dic41C22semidirect
123. C41#560semidirect
135. #121D41semidirect
151. C2×D4C2×D41semidirect
154. C22×C4C2×D41semidirect
160. C4⋊C4C2×D41semidirect
172. C22⋊C4C2×D41semidirect

Maximal subgroups

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

subgroupindex
#130501602
#130501592
#130501572
#130501492
#130501482
#130501472
#130501382
#130501372
#130501362
#130501352
#130501342
#130501322
#121×C412
#56041