Finite Group Databasebeta

← C7×C11⋊#90865 #49114882

Subgroups — C7×C11⋊#90865 #49114882

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—
4C11⋊#90865C711yesmaximal, characteristic, direct product factor, Hall
5C7×Dic143—91nomaximal, Hall
6C7×#90865—111nomaximal, Hall
7C3×C7×C11×C13—22no—
8C7×C11⋊#157—131nomaximal, Hall
9C11×C13×C3⋊D3C2×C711yescharacteristic
10C2×C7×C11×C13—91no—
11C7×C13×C3⋊D3D1111yescharacteristic
12C7×C11×C3⋊D3D1311yescharacteristic
13C32×C11×C13C4×C711yescharacteristic, complemented, Hall
14C7×C11×C13#15711yescharacteristic, complemented, Hall
15D3×C11×C13—62no—
16C32×C7×C13Dic1111yescharacteristic, complemented, Hall
17C32×C7×C11Dic1311yescharacteristic, complemented, Hall
18Dic143—91noHall
19D3×C7×C13—62no—
20#90865—111noHall
21D3×C7×C11—62no—
22C3×C11×C13—22no—
23C11⋊#157—131noHall
24C7×Dic13—991noHall
25C7×Dic11—1171noHall
26C2×C11×C13—91no—
27C3×C7×C13—22no—
28C7×#157—1431noHall
29C13×C3⋊D3C7×D1111yescharacteristic
30C3×C7×C11—22no—
31C11×C3⋊D3C7×D1311yescharacteristic
32C2×C7×C13—91no—
33C2×C7×C11—91no—
34C11×C13C7×#15711yescharacteristic, complemented, Hall
35C7×C3⋊D3D14311yescharacteristic
36C32×C13C7×Dic1111yescharacteristic, complemented, Hall
37C32×C11C7×Dic1311yescharacteristic, complemented, Hall
38C7×C13C11⋊#15711yescharacteristic, complemented, Hall
39D3×C13—62no—
40C7×C11#9086511yescharacteristic, complemented, Hall
41D3×C11—62no—
42C32×C7Dic14311yescharacteristic, complemented, Hall
43Dic13—991noHall
44Dic11—1171noHall
45D3×C7—62no—
46C3×C13—22no—
47#157—1431noHall
48C3×C11—22no—
49C4×C7—12871noHall
50C2×C13—91no—
51C2×C11—91no—
52C3×C7—22no—
53C3⋊D3C7×D14311yescharacteristic
54C2×C7—91no—
55C13C7×C11⋊#15711yescharacteristic, complemented, Sylow
56C11C7×#9086511yescharacteristic, complemented, Sylow
57C32C7×Dic14311yescharacteristic, complemented, Sylow
58C7C11⋊#9086511yescharacteristic, direct product factor, Sylow
59D3—62no—
60C4—12871noSylow
61C3—22no—
62C2—91no—
subgroupG/H
center, hypercenterC7C11⋊#90865
commutator, hypocenterC32×C11×C13C4×C7
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC7×C11×C13×C3⋊D3C2
cosocleC11×C13×C3⋊D3C2×C7
LCSG ▷ C32×C11×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
2. C32×C7×C11×C13C4semidirect
4. C11⋊#90865C7direct (N × H)
13. C32×C11×C13C4×C7semidirect
14. C7×C11×C13#157semidirect
16. C32×C7×C13Dic11semidirect
17. C32×C7×C11Dic13semidirect
34. C11×C13C7×#157semidirect
36. C32×C13C7×Dic11semidirect
37. C32×C11C7×Dic13semidirect
38. C7×C13C11⋊#157semidirect
40. C7×C11#90865semidirect
42. C32×C7Dic143semidirect
55. C13C7×C11⋊#157semidirect
56. C11C7×#90865semidirect
57. C32C7×Dic143semidirect
58. C7C11⋊#90865direct (N × H)

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
C11⋊#908657
C7×Dic1439
C7×#9086511
C7×C11⋊#15713