Finite Group Databasebeta

← #38763260

Subgroups — #38763260

Order 25408.

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#27163092C211yesmaximal, characteristic, complemented
2#27163091C211yesmaximal, characteristic, complemented
3#27163089C211yesmaximal, characteristic, complemented
4#27163081C211yesmaximal, characteristic, complemented
5#27163080C211yesmaximal, characteristic, complemented
6#27163079C211yesmaximal, characteristic, complemented
7#27163070C211yesmaximal, characteristic, complemented
8#27163069C211yesmaximal, characteristic, complemented
9#27163068C211yesmaximal, characteristic, complemented
10#27163068C211yesmaximal, characteristic, complemented
11#27163067C211yesmaximal, characteristic, complemented
12#27163066C211yesmaximal, characteristic, complemented
13#27163064C211yesmaximal, characteristic, complemented
14#27163064C211yesmaximal, characteristic, complemented
15#121×C397C211yesmaximal, characteristic, complemented
16C23×D397C2211yescharacteristic
17C2×D1588C2211yescharacteristic
18C2×D1588C2211yescharacteristic
19C2×C22⋊D397C2211yescharacteristic
20C2×C22⋊D397C2211yescharacteristic
21C2×C22⋊D397C2211yescharacteristic
22C2×C22⋊D397C2211yescharacteristic
23C2×C22⋊D397C2211yescharacteristic
24C2×C22⋊D397C2211yescharacteristic, complemented
25C2×C22⋊D397C2211yescharacteristic, complemented
26C22×Dic397C2211yescharacteristic, complemented
27C2×C4×D397C2211yescharacteristic, complemented
28C4⋊Dic397C2211yescharacteristic, complemented
29C4⋊Dic397C2211yescharacteristic, complemented
30#20263710C2211yescharacteristic, complemented
31#20263710C2211yescharacteristic, complemented
32#20263710C2211yescharacteristic, complemented
33C22⋊Dic397C2211yescharacteristic
34C22⋊Dic397C2211yescharacteristic
35C22⋊Dic397C2211yescharacteristic, complemented
36#20263708C2211yescharacteristic
37#20263708C2211yescharacteristic
38#20263708C2211yescharacteristic
39#20263708C2211yescharacteristic
40#20263708C2211yescharacteristic
41#20263708C2211yescharacteristic
42#20263708C2211yescharacteristic, complemented
43C4×Dic397C2211yescharacteristic, complemented
44C2×D4×C397C2211yescharacteristic
45C2×D4×C397C2211yescharacteristic
46C2×D4×C397C2211yescharacteristic, complemented
47C22×C4×C397C2211yescharacteristic, complemented
48C4⋊C4×C397C2211yescharacteristic, complemented
49C22⋊C4×C397C2211yescharacteristic
50C22⋊C4×C397C2211yescharacteristic, complemented
51C22×D397—41no—
52C22×D397—41no—
53C22×D397—41no—
54C22×D397C2311yescharacteristic
55C22×D397C2311yescharacteristic
56C22×D397C2311yescharacteristic
57D1588—41no—
58D1588—41no—
59C22⋊D397—41no—
60C22⋊D397—41no—
61C22⋊D397—41no—
62C22⋊D397—41no—
63C22⋊D397—41no—
64C22⋊D397—41no—
65C22⋊D397—41no—
66C2×Dic397—41no—
67C2×Dic397C2311yescharacteristic
68C2×Dic397C2311yescharacteristic
69C2×Dic397C2311yescharacteristic
70C2×Dic397C2311yescharacteristic
71C2×Dic397C2311yescharacteristic
72C4×D397—41no—
73C23×C397C2311yescharacteristic
74C23×C397C2311yescharacteristic
75C23×C397C2311yescharacteristic
76D4×C397—41no—
77D4×C397—41no—
78D4×C397—41no—
79C2×C4×C397—41no—
80C2×C4×C397C2311yescharacteristic
81C2×C4×C397C2311yescharacteristic
82C2×C4×C397C2311yescharacteristic
83C2×C4×C397C2311yescharacteristic
84C22×C397—21no—
85C22×C397—21no—
86C22×C397—21no—
87C22×C397—21no—
88C22×C397—21no—
89C22×C397—21no—
90C22×C397—21no—
91C22×C397—21no—
92C22×C397—21no—
93C22×C397C2411yescharacteristic
94C2×D397—21no—
95C2×D397—21no—
96C2×D397—21no—
97C2×D397—21no—
98C2×D397—21no—
99C2×D397—21no—
100C2×D397—21no—
101C2×D397—21no—
102C2×D397—21no—
103C2×D397—44no—
104C4×C397—21no—
105C4×C397—21no—
106C4×C397—21no—
107C4×C397—21no—
108Dic397—21no—
109Dic397—21no—
110Dic397—21no—
111Dic397—21no—
112Dic397—21no—
113C2×C397—41no—
114C2×C397—41no—
115C2×C397—41no—
116C2×C397H(5,𝔽2)11yescharacteristic
117C2×C397H(5,𝔽2)11yescharacteristic
118C2×C397H(5,𝔽2)11yescharacteristic
119D397—41no—
120D397—41no—
121D397—41no—
122C397#56011yescharacteristic, complemented, Sylow
123#560—3971nomaximal, Sylow
124#127—3971no—
125#126—3971no—
126#126—3971no—
127#123—3971no—
128#123—3971no—
129#123—3971no—
130#121—3971no—
131#121—3971no—
132#121—3971no—
133#121—3971no—
134#121—3971no—
135#121D39711yescharacteristic, complemented
136#120—3971no—
137#120—3971no—
138#120—3971no—
139C24—3971no—
140C2×D4—3971no—
141C2×D4—3971no—
142C2×D4—3971no—
143C2×D4—3971no—
144C2×D4—3971no—
145C2×D4—3971no—
146C2×D4—3971no—
147C2×D4—3971no—
148C2×D4—3971no—
149C2×D4C2×D39711yescharacteristic
150C2×D4C2×D39711yescharacteristic
151C2×D4C2×D39711yescharacteristic, complemented
152C22×C4—3971no—
153C22×C4—3971no—
154C22×C4C2×D39711yescharacteristic, complemented
155C4⋊C4—3971no—
156C4⋊C4—3971no—
157C4⋊C4—3971no—
158C4⋊C4—3971no—
159C4⋊C4—3971no—
160C4⋊C4C2×D39711yescharacteristic, complemented
161C22⋊C4—3971no—
162C22⋊C4—3971no—
163C22⋊C4—3971no—
164C22⋊C4—3971no—
165C22⋊C4—3971no—
166C22⋊C4—3971no—
167C22⋊C4—3971no—
168C22⋊C4—3971no—
169C22⋊C4—3971no—
170C22⋊C4—3971no—
171C22⋊C4C2×D39711yescharacteristic
172C22⋊C4C2×D39711yescharacteristic, complemented
173C42—3971no—
174C23—15881no—
175C23—15881no—
176C23—15881no—
177C23—3971no—
178C23—3971no—
179C23—3971no—
180C23C22×D39711yescharacteristic
181C23C22×D39711yescharacteristic
182C23C22×D39711yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—15881no—
187D4—15881no—
188D4—15881no—
189D4—15881no—
190D4—15881no—
191D4—15881no—
192D4—15881no—
193D4—15881no—
194D4—15881no—
195C2×C4—41no—
196C2×C4—15881no—
197C2×C4—15881no—
198C2×C4—3971no—
199C2×C4—3971no—
200C2×C4—3971no—
201C2×C4—3971no—
202C2×C4—3971no—
203C2×C4C22×D39711yescharacteristic
204C2×C4C22×D39711yescharacteristic
205C2×C4C22×D39711yescharacteristic
206C2×C4C22×D39711yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—7941no—
217C22—7941no—
218C22—7941no—
219C22—7941no—
220C22—7941no—
221C22—7941no—
222C22—7941no—
223C22—7941no—
224C22—7941no—
225C22—15884no—
226C22C23×D39711yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—7941no—
232C4—7941no—
233C4—7941no—
234C4—7941no—
235C4—7941no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—15881no—
240C2—15881no—
241C2—15881no—
242C2#2716314111yescharacteristic
243C2#2716314111yescharacteristic
244C2#2716314211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D397
commutator, socle, cosocleC22×C397C24
Fitting#121×C397C2
hypercenter#121D397
hypocenterC397#560
LCSG ▷ C22×C397 ▷ C397
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #27163092C2semidirect
2. #27163091C2semidirect
3. #27163089C2semidirect
4. #27163081C2semidirect
5. #27163080C2semidirect
6. #27163079C2semidirect
7. #27163070C2semidirect
8. #27163069C2semidirect
9. #27163068C2semidirect
10. #27163068C2semidirect
11. #27163067C2semidirect
12. #27163066C2semidirect
13. #27163064C2semidirect
14. #27163064C2semidirect
15. #121×C397C2semidirect
24. C2×C22⋊D397C22semidirect
25. C2×C22⋊D397C22semidirect
26. C22×Dic397C22semidirect
27. C2×C4×D397C22semidirect
28. C4⋊Dic397C22semidirect
29. C4⋊Dic397C22semidirect
30. #20263710C22semidirect
31. #20263710C22semidirect
32. #20263710C22semidirect
35. C22⋊Dic397C22semidirect
42. #20263708C22semidirect
43. C4×Dic397C22semidirect
46. C2×D4×C397C22semidirect
47. C22×C4×C397C22semidirect
48. C4⋊C4×C397C22semidirect
50. C22⋊C4×C397C22semidirect
122. C397#560semidirect
135. #121D397semidirect
151. C2×D4C2×D397semidirect
154. C22×C4C2×D397semidirect
160. C4⋊C4C2×D397semidirect
172. C22⋊C4C2×D397semidirect

Maximal subgroups

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

subgroupindex
#271630922
#271630912
#271630892
#271630812
#271630802
#271630792
#271630702
#271630692
#271630682
#271630672
#271630662
#271630642
#121×C3972
#560397