Finite Group Databasebeta

← C32×C7⋊(C11⋊#261) #49114894

Subgroups — C32×C7⋊(C11⋊#261) #49114894

Order 36036.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11×D13C211yesmaximal, characteristic
2C3×C7⋊(C11⋊#261)C314yesmaximal, direct product factor
3C32×C7×C11×C13C411yescharacteristic, complemented, Hall
4C3×C7×C11×D13C2×C314yes—
5C32×C11⋊#261—71nomaximal, Hall
6C7⋊(C11⋊#261)C3211yescharacteristic, direct product factor, Hall
7C32×C7⋊#261—111nomaximal, Hall
8C3×C7×C11×C13C3×C414yescomplemented
9C32×Dic77—131nomaximal, Hall
10C32×C11×D13D711yescharacteristic
11C7×C11×D13C2×C3211yescharacteristic
12C3×C11⋊#261—74no—
13C32×C7×D13D1111yescharacteristic
14C2×C32×C7×C11—131no—
15C32×C11×C13Dic711yescharacteristic, complemented, Hall
16C3×C7⋊#261—114no—
17C7×C11×C13C32×C411yescharacteristic, complemented, Hall
18C3×Dic77—134no—
19C3×C11×D13C3×D714yes—
20C32×C7×C13Dic1111yescharacteristic, complemented, Hall
21C32×C7×C11#26111yescharacteristic, complemented, Hall
22C11⋊#261—71noHall
23C3×C7×D13C3×D1114yes—
24C32×#261—771noHall
25C2×C3×C7×C11—134no—
26C3×C11×C13C3×Dic714yescomplemented
27C32×Dic11—911noHall
28C7⋊#261—111noHall
29Dic77—131noHall
30C11×D13C32×D711yescharacteristic
31C3×C7×C13C3×Dic1114yescomplemented
32C32×Dic7—1431noHall
33C32×D13D7711yescharacteristic
34C3×C7×C11C3×#26114yescomplemented
35C2×C32×C11—131no—
36C7×D13C32×D1111yescharacteristic
37C3×#261—774no—
38C2×C7×C11—131no—
39C11×C13C32×Dic711yescharacteristic, complemented, Hall
40C3×Dic11—914no—
41C2×C32×C7—131no—
42C32×C13Dic7711yescharacteristic, complemented, Hall
43C32×C11C7⋊#26111yescharacteristic, complemented, Hall
44C7×C13C32×Dic1111yescharacteristic, complemented, Hall
45C3×Dic7—1434no—
46C3×D13C3×D7714yes—
47C7×C11C32×#26111yescharacteristic, complemented, Hall
48C2×C3×C11—134no—
49C32×C7C11⋊#26111yescharacteristic, complemented, Hall
50#261—771noHall
51Dic11—911noHall
52C2×C3×C7—134no—
53C3×C13C3×Dic7714yescomplemented
54C32×C4—10011noHall
55C3×C11C3×C7⋊#26114yescomplemented
56Dic7—1431noHall
57D13C32×D7711yescharacteristic
58C2×C11—131no—
59C3×C7C3×C11⋊#26114yescomplemented
60C2×C32—131no—
61C2×C7—131no—
62C13C32×Dic7711yescharacteristic, complemented, Sylow
63C3×C4—10014no—
64C11C32×C7⋊#26111yescharacteristic, complemented, Sylow
65C32C7⋊(C11⋊#261)11yescharacteristic, direct product factor, Sylow
66C7C32×C11⋊#26111yescharacteristic, complemented, Sylow
67C2×C3—134no—
68C4—10011noSylow
69C3C3×C7⋊(C11⋊#261)14yesdirect product factor
70C2—131no—
subgroupG/H
center, hypercenterC32C7⋊(C11⋊#261)
commutator, hypocenterC7×C11×C13C32×C4
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC32×C7×C11×D13C2
cosocleC7×C11×D13C2×C32
LCSG ▷ C7×C11×C13
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
2. C3×C7⋊(C11⋊#261)C3direct (N × H)
3. C32×C7×C11×C13C4semidirect
6. C7⋊(C11⋊#261)C32direct (N × H)
8. C3×C7×C11×C13C3×C4semidirect
15. C32×C11×C13Dic7semidirect
17. C7×C11×C13C32×C4semidirect
20. C32×C7×C13Dic11semidirect
21. C32×C7×C11#261semidirect
26. C3×C11×C13C3×Dic7semidirect
31. C3×C7×C13C3×Dic11semidirect
34. C3×C7×C11C3×#261semidirect
39. C11×C13C32×Dic7semidirect
42. C32×C13Dic77semidirect
43. C32×C11C7⋊#261semidirect
44. C7×C13C32×Dic11semidirect
47. C7×C11C32×#261semidirect
49. C32×C7C11⋊#261semidirect
53. C3×C13C3×Dic77semidirect
55. C3×C11C3×C7⋊#261semidirect
59. C3×C7C3×C11⋊#261semidirect
62. C13C32×Dic77semidirect
64. C11C32×C7⋊#261semidirect
65. C32C7⋊(C11⋊#261)direct (N × H)
66. C7C32×C11⋊#261semidirect
69. C3C3×C7⋊(C11⋊#261)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C11×D132
C3×C7⋊(C11⋊#261)3
C32×C11⋊#2617
C32×C7⋊#26111
C32×Dic7713