Finite Group Databasebeta

← #34094890

Subgroups — #34094890

Order 20032.

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#23756493C211yesmaximal, characteristic, complemented
2#23756492C211yesmaximal, characteristic, complemented
3#23756490C211yesmaximal, characteristic, complemented
4#23756482C211yesmaximal, characteristic, complemented
5#23756481C211yesmaximal, characteristic, complemented
6#23756480C211yesmaximal, characteristic, complemented
7#23756471C211yesmaximal, characteristic, complemented
8#23756470C211yesmaximal, characteristic, complemented
9#23756469C211yesmaximal, characteristic, complemented
10#23756469C211yesmaximal, characteristic, complemented
11#23756468C211yesmaximal, characteristic, complemented
12#23756467C211yesmaximal, characteristic, complemented
13#23756465C211yesmaximal, characteristic, complemented
14#23756465C211yesmaximal, characteristic, complemented
15#121×C313C211yesmaximal, characteristic, complemented
16C23×D313C2211yescharacteristic
17C2×D1252C2211yescharacteristic
18C2×D1252C2211yescharacteristic
19C2×C22⋊D313C2211yescharacteristic
20C2×C22⋊D313C2211yescharacteristic
21C2×C22⋊D313C2211yescharacteristic
22C2×C22⋊D313C2211yescharacteristic
23C2×C22⋊D313C2211yescharacteristic
24C2×C22⋊D313C2211yescharacteristic, complemented
25C2×C22⋊D313C2211yescharacteristic, complemented
26C22×Dic313C2211yescharacteristic, complemented
27C2×C4×D313C2211yescharacteristic, complemented
28C4⋊Dic313C2211yescharacteristic, complemented
29C4⋊Dic313C2211yescharacteristic, complemented
30#19097540C2211yescharacteristic, complemented
31#19097540C2211yescharacteristic, complemented
32#19097540C2211yescharacteristic, complemented
33C22⋊Dic313C2211yescharacteristic
34C22⋊Dic313C2211yescharacteristic
35C22⋊Dic313C2211yescharacteristic, complemented
36#19097538C2211yescharacteristic
37#19097538C2211yescharacteristic
38#19097538C2211yescharacteristic
39#19097538C2211yescharacteristic
40#19097538C2211yescharacteristic
41#19097538C2211yescharacteristic
42#19097538C2211yescharacteristic, complemented
43C4×Dic313C2211yescharacteristic, complemented
44C2×D4×C313C2211yescharacteristic
45C2×D4×C313C2211yescharacteristic
46C2×D4×C313C2211yescharacteristic, complemented
47C22×C4×C313C2211yescharacteristic, complemented
48C4⋊C4×C313C2211yescharacteristic, complemented
49C22⋊C4×C313C2211yescharacteristic
50C22⋊C4×C313C2211yescharacteristic, complemented
51C22×D313—41no—
52C22×D313—41no—
53C22×D313—41no—
54C22×D313C2311yescharacteristic
55C22×D313C2311yescharacteristic
56C22×D313C2311yescharacteristic
57D1252—41no—
58D1252—41no—
59C22⋊D313—41no—
60C22⋊D313—41no—
61C22⋊D313—41no—
62C22⋊D313—41no—
63C22⋊D313—41no—
64C22⋊D313—41no—
65C22⋊D313—41no—
66C2×Dic313—41no—
67C2×Dic313C2311yescharacteristic
68C2×Dic313C2311yescharacteristic
69C2×Dic313C2311yescharacteristic
70C2×Dic313C2311yescharacteristic
71C2×Dic313C2311yescharacteristic
72C4×D313—41no—
73C23×C313C2311yescharacteristic
74C23×C313C2311yescharacteristic
75C23×C313C2311yescharacteristic
76D4×C313—41no—
77D4×C313—41no—
78D4×C313—41no—
79C2×C4×C313—41no—
80C2×C4×C313C2311yescharacteristic
81C2×C4×C313C2311yescharacteristic
82C2×C4×C313C2311yescharacteristic
83C2×C4×C313C2311yescharacteristic
84C22×C313—21no—
85C22×C313—21no—
86C22×C313—21no—
87C22×C313—21no—
88C22×C313—21no—
89C22×C313—21no—
90C22×C313—21no—
91C22×C313—21no—
92C22×C313—21no—
93C22×C313C2411yescharacteristic
94C2×D313—21no—
95C2×D313—21no—
96C2×D313—21no—
97C2×D313—21no—
98C2×D313—21no—
99C2×D313—21no—
100C2×D313—21no—
101C2×D313—21no—
102C2×D313—21no—
103C2×D313—44no—
104C4×C313—21no—
105C4×C313—21no—
106C4×C313—21no—
107C4×C313—21no—
108Dic313—21no—
109Dic313—21no—
110Dic313—21no—
111Dic313—21no—
112Dic313—21no—
113C2×C313—41no—
114C2×C313—41no—
115C2×C313—41no—
116C2×C313H(5,𝔽2)11yescharacteristic
117C2×C313H(5,𝔽2)11yescharacteristic
118C2×C313H(5,𝔽2)11yescharacteristic
119D313—41no—
120D313—41no—
121D313—41no—
122C313#56011yescharacteristic, complemented, Sylow
123#560—3131nomaximal, Sylow
124#127—3131no—
125#126—3131no—
126#126—3131no—
127#123—3131no—
128#123—3131no—
129#123—3131no—
130#121—3131no—
131#121—3131no—
132#121—3131no—
133#121—3131no—
134#121—3131no—
135#121D31311yescharacteristic, complemented
136#120—3131no—
137#120—3131no—
138#120—3131no—
139C24—3131no—
140C2×D4—3131no—
141C2×D4—3131no—
142C2×D4—3131no—
143C2×D4—3131no—
144C2×D4—3131no—
145C2×D4—3131no—
146C2×D4—3131no—
147C2×D4—3131no—
148C2×D4—3131no—
149C2×D4C2×D31311yescharacteristic
150C2×D4C2×D31311yescharacteristic
151C2×D4C2×D31311yescharacteristic, complemented
152C22×C4—3131no—
153C22×C4—3131no—
154C22×C4C2×D31311yescharacteristic, complemented
155C4⋊C4—3131no—
156C4⋊C4—3131no—
157C4⋊C4—3131no—
158C4⋊C4—3131no—
159C4⋊C4—3131no—
160C4⋊C4C2×D31311yescharacteristic, complemented
161C22⋊C4—3131no—
162C22⋊C4—3131no—
163C22⋊C4—3131no—
164C22⋊C4—3131no—
165C22⋊C4—3131no—
166C22⋊C4—3131no—
167C22⋊C4—3131no—
168C22⋊C4—3131no—
169C22⋊C4—3131no—
170C22⋊C4—3131no—
171C22⋊C4C2×D31311yescharacteristic
172C22⋊C4C2×D31311yescharacteristic, complemented
173C42—3131no—
174C23—3131no—
175C23—3131no—
176C23—3131no—
177C23—12521no—
178C23—12521no—
179C23—12521no—
180C23C22×D31311yescharacteristic
181C23C22×D31311yescharacteristic
182C23C22×D31311yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—12521no—
187D4—12521no—
188D4—12521no—
189D4—12521no—
190D4—12521no—
191D4—12521no—
192D4—12521no—
193D4—12521no—
194D4—12521no—
195C2×C4—41no—
196C2×C4—3131no—
197C2×C4—3131no—
198C2×C4—3131no—
199C2×C4—3131no—
200C2×C4—3131no—
201C2×C4—12521no—
202C2×C4—12521no—
203C2×C4C22×D31311yescharacteristic
204C2×C4C22×D31311yescharacteristic
205C2×C4C22×D31311yescharacteristic
206C2×C4C22×D31311yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—6261no—
217C22—6261no—
218C22—6261no—
219C22—6261no—
220C22—6261no—
221C22—6261no—
222C22—6261no—
223C22—6261no—
224C22—6261no—
225C22—12524no—
226C22C23×D31311yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—6261no—
232C4—6261no—
233C4—6261no—
234C4—6261no—
235C4—6261no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—12521no—
240C2—12521no—
241C2—12521no—
242C2#2375654211yescharacteristic
243C2#2375654211yescharacteristic
244C2#2375654311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D313
commutator, socle, cosocleC22×C313C24
Fitting#121×C313C2
hypercenter#121D313
hypocenterC313#560
LCSG ▷ C22×C313 ▷ C313
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #23756493C2semidirect
2. #23756492C2semidirect
3. #23756490C2semidirect
4. #23756482C2semidirect
5. #23756481C2semidirect
6. #23756480C2semidirect
7. #23756471C2semidirect
8. #23756470C2semidirect
9. #23756469C2semidirect
10. #23756469C2semidirect
11. #23756468C2semidirect
12. #23756467C2semidirect
13. #23756465C2semidirect
14. #23756465C2semidirect
15. #121×C313C2semidirect
24. C2×C22⋊D313C22semidirect
25. C2×C22⋊D313C22semidirect
26. C22×Dic313C22semidirect
27. C2×C4×D313C22semidirect
28. C4⋊Dic313C22semidirect
29. C4⋊Dic313C22semidirect
30. #19097540C22semidirect
31. #19097540C22semidirect
32. #19097540C22semidirect
35. C22⋊Dic313C22semidirect
42. #19097538C22semidirect
43. C4×Dic313C22semidirect
46. C2×D4×C313C22semidirect
47. C22×C4×C313C22semidirect
48. C4⋊C4×C313C22semidirect
50. C22⋊C4×C313C22semidirect
122. C313#560semidirect
135. #121D313semidirect
151. C2×D4C2×D313semidirect
154. C22×C4C2×D313semidirect
160. C4⋊C4C2×D313semidirect
172. C22⋊C4C2×D313semidirect

Maximal subgroups

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

subgroupindex
#237564932
#237564922
#237564902
#237564822
#237564812
#237564802
#237564712
#237564702
#237564692
#237564682
#237564672
#237564652
#121×C3132
#560313