Finite Group Databasebeta

← C13×C7⋊(C11⋊#157) #49114886

Subgroups — C13×C7⋊(C11⋊#157) #49114886

Order 36036.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C11×C13×C3⋊D3C211yesmaximal, characteristic
2C32×C7×C11×C13C411yescharacteristic, complemented, Hall
3D3×C7×C11×C13—62no—
4C13×C11⋊#157—71nomaximal, Hall
5C13×Dic77—91nomaximal, Hall
6C13×C7⋊#157—111nomaximal, Hall
7C3×C7×C11×C13—22no—
8C7⋊(C11⋊#157)C1311yesmaximal, characteristic, direct product factor, Hall
9C11×C13×C3⋊D3D711yescharacteristic
10C2×C7×C11×C13—91no—
11C7×C13×C3⋊D3D1111yescharacteristic
12C7×C11×C3⋊D3C2×C1311yescharacteristic
13C32×C11×C13Dic711yescharacteristic, complemented, Hall
14C7×C11×C13#15711yescharacteristic, complemented, Hall
15D3×C11×C13—62no—
16C32×C7×C13Dic1111yescharacteristic, complemented, Hall
17C32×C7×C11C4×C1311yescharacteristic, complemented, Hall
18C13×Dic11—631noHall
19D3×C7×C13—62no—
20C13×#157—771noHall
21D3×C7×C11—62no—
22C3×C11×C13—22no—
23C11⋊#157—71noHall
24C13×Dic7—991noHall
25Dic77—91noHall
26C2×C11×C13—91no—
27C3×C7×C13—22no—
28C7⋊#157—111noHall
29C13×C3⋊D3D7711yescharacteristic
30C3×C7×C11—22no—
31C11×C3⋊D3C13×D711yescharacteristic
32C2×C7×C13—91no—
33C2×C7×C11—91no—
34C11×C13C7⋊#15711yescharacteristic, complemented, Hall
35C7×C3⋊D3C13×D1111yescharacteristic
36C32×C13Dic7711yescharacteristic, complemented, Hall
37C32×C11C13×Dic711yescharacteristic, complemented, Hall
38C7×C13C11⋊#15711yescharacteristic, complemented, Hall
39D3×C13—62no—
40C7×C11C13×#15711yescharacteristic, complemented, Hall
41D3×C11—62no—
42C32×C7C13×Dic1111yescharacteristic, complemented, Hall
43C4×C13—6931noHall
44Dic11—631noHall
45D3×C7—62no—
46C3×C13—22no—
47#157—771noHall
48C3×C11—22no—
49Dic7—991noHall
50C2×C13—91no—
51C2×C11—91no—
52C3×C7—22no—
53C3⋊D3C13×D7711yescharacteristic
54C2×C7—91no—
55C13C7⋊(C11⋊#157)11yescharacteristic, direct product factor, Sylow
56C11C13×C7⋊#15711yescharacteristic, complemented, Sylow
57C32C13×Dic7711yescharacteristic, complemented, Sylow
58C7C13×C11⋊#15711yescharacteristic, complemented, Sylow
59D3—62no—
60C4—6931noSylow
61C3—22no—
62C2—91no—
subgroupG/H
center, hypercenterC13C7⋊(C11⋊#157)
commutator, hypocenterC32×C7×C11C4×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC7×C11×C13×C3⋊D3C2
cosocleC7×C11×C3⋊D3C2×C13
LCSG ▷ C32×C7×C11
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
2. C32×C7×C11×C13C4semidirect
8. C7⋊(C11⋊#157)C13direct (N × H)
13. C32×C11×C13Dic7semidirect
14. C7×C11×C13#157semidirect
16. C32×C7×C13Dic11semidirect
17. C32×C7×C11C4×C13semidirect
34. C11×C13C7⋊#157semidirect
36. C32×C13Dic77semidirect
37. C32×C11C13×Dic7semidirect
38. C7×C13C11⋊#157semidirect
40. C7×C11C13×#157semidirect
42. C32×C7C13×Dic11semidirect
55. C13C7⋊(C11⋊#157)direct (N × H)
56. C11C13×C7⋊#157semidirect
57. C32C13×Dic77semidirect
58. C7C13×C11⋊#157semidirect

Maximal subgroups

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

subgroupindex
C7×C11×C13×C3⋊D32
C13×C11⋊#1577
C13×Dic779
C13×C7⋊#15711
C7⋊(C11⋊#157)13