Finite Group Databasebeta

← C11×C3⋊(C3⋊(C7⋊#261)) #49114976

Subgroups — C11×C3⋊(C3⋊(C7⋊#261)) #49114976

Order 36036.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11×D13C211yesmaximal, characteristic
2C11×C3⋊(C7⋊#261)—34nomaximal
3C32×C7×C11×C13C411yescharacteristic, complemented, Hall
4C3×C7×C11×D13D314yes—
5C11×C3⋊(C3⋊#261)—71nomaximal, Hall
6C11×C7⋊#261—91noHall
7C3⋊(C3⋊(C7⋊#261))C1111yesmaximal, characteristic, direct product factor, Hall
8C3×C7×C11×C13Dic314yescomplemented
9C11×C3⋊Dic21—131nomaximal, Hall
10C32×C11×D13D711yescharacteristic
11C7×C11×D13C3⋊D311yescharacteristic
12C11×C3⋊#261—214no—
13C32×C7×D13C2×C1111yescharacteristic
14C2×C32×C7×C11—131no—
15C32×C11×C13Dic711yescharacteristic, complemented, Hall
16C3⋊(C7⋊#261)—34no—
17C7×C11×C13C3⋊Dic311yescharacteristic, complemented, Hall
18C11×Dic21—394no—
19C3×C11×D13D2114yes—
20C32×C7×C13C4×C1111yescharacteristic, complemented, Hall
21C32×C7×C11#26111yescharacteristic, complemented, Hall
22C11×#261—631noHall
23C3×C7×D13D3×C1114yes—
24C3⋊(C3⋊#261)—71noHall
25C2×C3×C7×C11—134no—
26C3×C11×C13Dic2114yescomplemented
27C11×C3⋊Dic3—911noHall
28C7⋊#261—91noHall
29C11×Dic7—1171noHall
30C11×D13C3⋊D2111yescharacteristic
31C3×C7×C13C11×Dic314yescomplemented
32C3⋊Dic21—131noHall
33C32×D13C11×D711yescharacteristic
34C3×C7×C11C3⋊#26114yescomplemented
35C2×C32×C11—131no—
36C7×D13C11×C3⋊D311yescharacteristic
37C3⋊#261—214no—
38C2×C7×C11—131no—
39C11×C13C3⋊Dic2111yescharacteristic, complemented, Hall
40C11×Dic3—2734no—
41C2×C32×C7—131no—
42C32×C13C11×Dic711yescharacteristic, complemented, Hall
43C32×C11C7⋊#26111yescharacteristic, complemented, Hall
44C7×C13C11×C3⋊Dic311yescharacteristic, complemented, Hall
45Dic21—394no—
46C3×D13C11×D2114yes—
47C7×C11C3⋊(C3⋊#261)11yescharacteristic, complemented, Hall
48C2×C3×C11—134no—
49C32×C7C11×#26111yescharacteristic, complemented, Hall
50#261—631noHall
51C4×C11—8191noHall
52C2×C3×C7—134no—
53C3×C13C11×Dic2114yescomplemented
54C3⋊Dic3—911noHall
55C3×C11C3⋊(C7⋊#261)14yescomplemented
56Dic7—1171noHall
57D13C11×C3⋊D2111yescharacteristic
58C2×C11—131no—
59C3×C7C11×C3⋊#26114yescomplemented
60C2×C32—131no—
61C2×C7—131no—
62C13C11×C3⋊Dic2111yescharacteristic, complemented, Sylow
63Dic3—2734no—
64C11C3⋊(C3⋊(C7⋊#261))11yescharacteristic, direct product factor, Sylow
65C32C11×C7⋊#26111yescharacteristic, complemented, Sylow
66C7C11×C3⋊(C3⋊#261)11yescharacteristic, complemented, Sylow
67C2×C3—134no—
68C4—8191noSylow
69C3C11×C3⋊(C7⋊#261)14yescomplemented
70C2—131no—
subgroupG/H
center, hypercenterC11C3⋊(C3⋊(C7⋊#261))
commutator, hypocenterC32×C7×C13C4×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC32×C7×C11×D13C2
cosocleC32×C7×D13C2×C11
LCSG ▷ C32×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
3. C32×C7×C11×C13C4semidirect
7. C3⋊(C3⋊(C7⋊#261))C11direct (N × H)
8. C3×C7×C11×C13Dic3semidirect
15. C32×C11×C13Dic7semidirect
17. C7×C11×C13C3⋊Dic3semidirect
20. C32×C7×C13C4×C11semidirect
21. C32×C7×C11#261semidirect
26. C3×C11×C13Dic21semidirect
31. C3×C7×C13C11×Dic3semidirect
34. C3×C7×C11C3⋊#261semidirect
39. C11×C13C3⋊Dic21semidirect
42. C32×C13C11×Dic7semidirect
43. C32×C11C7⋊#261semidirect
44. C7×C13C11×C3⋊Dic3semidirect
47. C7×C11C3⋊(C3⋊#261)semidirect
49. C32×C7C11×#261semidirect
53. C3×C13C11×Dic21semidirect
55. C3×C11C3⋊(C7⋊#261)semidirect
59. C3×C7C11×C3⋊#261semidirect
62. C13C11×C3⋊Dic21semidirect
64. C11C3⋊(C3⋊(C7⋊#261))direct (N × H)
65. C32C11×C7⋊#261semidirect
66. C7C11×C3⋊(C3⋊#261)semidirect
69. C3C11×C3⋊(C7⋊#261)semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11×D132
C11×C3⋊(C7⋊#261)3
C11×C3⋊(C3⋊#261)7
C3⋊(C3⋊(C7⋊#261))11
C11×C3⋊Dic2113