Finite Group Databasebeta

← C11×C7⋊(C11⋊#157) #44479177

Subgroups — C11×C7⋊(C11⋊#157) #44479177

Order 30492.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C112×C3⋊D3C211yesmaximal, characteristic
2C32×C7×C112C411yescharacteristic, complemented, Hall
3D3×C7×C112—62no—
4C11×C11⋊#157—71nomaximal, Hall
5C11×Dic77—91nomaximal, Hall
6C7⋊(C11⋊#157)C1111yesmaximal, characteristic, direct product factor
7C11×C7⋊#157—111nomaximal
8C3×C7×C112—22no—
9C112×C3⋊D3D711yescharacteristic
10C2×C7×C112—91no—
11C7×C11×C3⋊D3—25no—
12C7×C11×C3⋊D3D1111yescharacteristic
13C7×C11×C3⋊D3C2×C1111yescharacteristic
14C32×C112Dic711yescharacteristic, complemented, Hall
15C7×C112#15711yescharacteristic, complemented, Hall
16D3×C112—62no—
17C32×C7×C11—25no—
18C32×C7×C11Dic1111yescharacteristic, complemented
19C32×C7×C11C4×C1111yescharacteristic, complemented
20C11×Dic11—631noHall
21D3×C7×C11—62no—
22D3×C7×C11—62no—
23D3×C7×C11—620no—
24C11⋊#157—71no—
25C11×#157—771no—
26C3×C112—22no—
27Dic77—91no—
28C11×Dic7—991no—
29C7⋊#157—111noHall
30C2×C112—91no—
31C3×C7×C11—220no—
32C3×C7×C11—22no—
33C3×C7×C11—22no—
34C11×C3⋊D3—25no—
35C11×C3⋊D3C11×D711yescharacteristic
36C11×C3⋊D3D7711yescharacteristic
37C2×C7×C11—91no—
38C2×C7×C11—91no—
39C2×C7×C11—185no—
40C7×C3⋊D3C11×D1111yescharacteristic
41C112C7⋊#15711yescharacteristic, complemented, Sylow
42C32×C11—25no—
43C32×C11C11×Dic711yescharacteristic, complemented
44C32×C11Dic7711yescharacteristic, complemented
45C7×C11—25no—
46C7×C11C11×#15711yescharacteristic, complemented
47C7×C11C11⋊#15711yescharacteristic, complemented
48D3×C11—62no—
49D3×C11—62no—
50D3×C11—620no—
51C32×C7C11×Dic1111yescharacteristic, complemented, Hall
52C4×C11—6931no—
53Dic11—631no—
54D3×C7—62no—
55#157—771noHall
56C3×C11—220no—
57C3×C11—22no—
58C3×C11—22no—
59Dic7—991noHall
60C2×C11—91no—
61C2×C11—91no—
62C2×C11—185no—
63C3×C7—22no—
64C3⋊D3C11×D7711yescharacteristic
65C2×C7—91no—
66C11—25no—
67C11C11×C7⋊#15711yescharacteristic, complemented
68C11C7⋊(C11⋊#157)11yescharacteristic, direct product factor
69C32C11×Dic7711yescharacteristic, complemented, Sylow
70C7C11×C11⋊#15711yescharacteristic, complemented, Sylow
71D3—62no—
72C4—6931noSylow
73C3—22no—
74C2—91no—
subgroupG/H
center, hypercenterC11C7⋊(C11⋊#157)
commutator, hypocenterC32×C7×C11C4×C11
FrattiniC1G
Fitting, socleC32×C7×C112C4
prime radicalC7×C112×C3⋊D3C2
cosocleC7×C11×C3⋊D3C2×C11
LCSG ▷ C32×C7×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
2. C32×C7×C112C4semidirect
6. C7⋊(C11⋊#157)C11direct (N × H)
14. C32×C112Dic7semidirect
15. C7×C112#157semidirect
18. C32×C7×C11Dic11semidirect
19. C32×C7×C11C4×C11semidirect
41. C112C7⋊#157semidirect
43. C32×C11C11×Dic7semidirect
44. C32×C11Dic77semidirect
46. C7×C11C11×#157semidirect
47. C7×C11C11⋊#157semidirect
51. C32×C7C11×Dic11semidirect
67. C11C11×C7⋊#157semidirect
68. C11C7⋊(C11⋊#157)direct (N × H)
69. C32C11×Dic77semidirect
70. C7C11×C11⋊#157semidirect

Maximal subgroups

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

subgroupindex
C7×C112×C3⋊D32
C11×C11⋊#1577
C11×Dic779
C7⋊(C11⋊#157)11
C11×C7⋊#15711