Finite Group Databasebeta

← C3⋊(C3⋊(C7⋊(C7⋊#261))) #37525644

Subgroups — C3⋊(C3⋊(C7⋊(C7⋊#261))) #37525644

Order 22932.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C72×D13C211yesmaximal, characteristic
2C3⋊(C7⋊(C7⋊#261))—34nomaximal
3C32×C72×C13C411yescharacteristic, complemented, Hall
4C3×C72×D13D314yes—
5C3⋊(C3⋊(C7⋊#261))—78nomaximal
6C7⋊(C7⋊#261)—91noHall
7C3×C72×C13Dic314yescomplemented
8C3⋊(C3⋊(C7⋊Dic7))—131nomaximal, Hall
9C32×C7×D13D718yes—
10C72×D13C3⋊D311yescharacteristic
11C3⋊(C7⋊#261)—2132no—
12C2×C32×C72—131no—
13C32×C7×C13Dic718yescomplemented
14C72×C13C3⋊Dic311yescharacteristic, complemented, Hall
15C3⋊(C7⋊Dic7)—394no—
16C3×C7×D13D21132yes—
17C3⋊(C3⋊#261)—491noHall
18C32×C72#26111yescharacteristic, complemented, Hall
19C7⋊#261—638no—
20C2×C3×C72—134no—
21C3×C7×C13Dic21132yescomplemented
22C3⋊Dic21—918no—
23C32×D13C7⋊D711yescharacteristic
24C7⋊Dic7—1171noHall
25C7×D13C3⋊D2118yes—
26C3⋊#261—1474no—
27C3×C72C3⋊#26114yescomplemented
28C2×C32×C7—138no—
29C32×C13C7⋊Dic711yescharacteristic, complemented, Hall
30C2×C72—131no—
31C7×C13C3⋊Dic2118yescomplemented
32Dic21—27332no—
33C3×D13C3⋊(C7⋊D7)14yes—
34C32×C7C7⋊#26118yescomplemented
35#261—4411noHall
36C72C3⋊(C3⋊#261)11yescharacteristic, complemented, Sylow
37C2×C3×C7—1332no—
38C3×C13C3⋊(C7⋊Dic7)14yescomplemented
39C3⋊Dic3—6371noHall
40Dic7—8198no—
41D13C3⋊(C3⋊(C7⋊D7))11yescharacteristic
42C3×C7C3⋊(C7⋊#261)132yescomplemented
43C2×C32—131no—
44C2×C7—138no—
45C13C3⋊(C3⋊(C7⋊Dic7))11yescharacteristic, complemented, Sylow
46Dic3—19114no—
47C32C7⋊(C7⋊#261)11yescharacteristic, complemented, Sylow
48C7C3⋊(C3⋊(C7⋊#261))18yescomplemented
49C2×C3—134no—
50C4—57331noSylow
51C3C3⋊(C7⋊(C7⋊#261))14yescomplemented
52C2—131no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C72×C13C4
prime radical, cosocleC32×C72×D13C2
LCSG ▷ C32×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
3. C32×C72×C13C4semidirect
7. C3×C72×C13Dic3semidirect
13. C32×C7×C13Dic7semidirect
14. C72×C13C3⋊Dic3semidirect
18. C32×C72#261semidirect
21. C3×C7×C13Dic21semidirect
27. C3×C72C3⋊#261semidirect
29. C32×C13C7⋊Dic7semidirect
31. C7×C13C3⋊Dic21semidirect
34. C32×C7C7⋊#261semidirect
36. C72C3⋊(C3⋊#261)semidirect
38. C3×C13C3⋊(C7⋊Dic7)semidirect
42. C3×C7C3⋊(C7⋊#261)semidirect
45. C13C3⋊(C3⋊(C7⋊Dic7))semidirect
47. C32C7⋊(C7⋊#261)semidirect
48. C7C3⋊(C3⋊(C7⋊#261))semidirect
51. C3C3⋊(C7⋊(C7⋊#261))semidirect

Maximal subgroups

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

subgroupindex
C32×C72×D132
C3⋊(C7⋊(C7⋊#261))3
C3⋊(C3⋊(C7⋊#261))7
C3⋊(C3⋊(C7⋊Dic7))13