Finite Group Databasebeta

← C7×C3⋊D3×C11⋊D11 #44479234

Subgroups — C7×C3⋊D3×C11⋊D11 #44479234

Order 30492.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11⋊D11C211yesmaximal, characteristic, complemented
2C7×C112×C3⋊D3C211yesmaximal, characteristic, complemented
3C7×C3⋊(C3⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
4D3×C7×C11⋊D11—34nomaximal
5C32×C7×C112C2211yescharacteristic, complemented, Hall
6C7×C3⋊(C11⋊D11)—34no—
7D3×C7×C112—34no—
8C3×C7×C11⋊D11D314yescomplemented
9C3⋊D3×C11⋊D11C711yesmaximal, characteristic, direct product factor, Hall
10C2×C7×C11⋊D11—91noHall
11C7×C3⋊D3×D11—1112nomaximal
12C3×C7×C112C2×D314yescomplemented
13C3⋊(C3⋊(C11⋊D11))C2×C711yescharacteristic, complemented
14C112×C3⋊D3C2×C711yescharacteristic, complemented
15C32×C11⋊D11C2×C711yescharacteristic, complemented
16C2×C7×C112—91no—
17C7×C11⋊D11—91no—
18C7×C11⋊D11C3⋊D311yescharacteristic, direct product factor
19D3×C11⋊D11—34no—
20C7×C3⋊D33—1112no—
21C7×C11×C3⋊D3D11112yescomplemented
22C32×C7×D11—1112no—
23C32×C112C22×C711yescharacteristic, complemented, Hall
24D3×C7×D11—3348no—
25C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
26C3⋊(C11⋊D11)—34no—
27D3×C112—34no—
28C3×C11⋊D11D3×C714yescomplemented
29C32×C7×C11C2×D11112yescomplemented
30C2×C11⋊D11—91noHall
31C7×D33—3348no—
32D3×C7×C11—348no—
33C3×C7×D11—1148no—
34C3⋊D3×D11—1112no—
35C3×C112C2×D3×C714yescomplemented
36C2×C7×D11—9912no—
37C2×C7×C3⋊D3—1211noHall
38C2×C112—91no—
39C11⋊D11—91no—
40C11⋊D11C7×C3⋊D311yescharacteristic, direct product factor
41C3×C7×C11D3×D11148yescomplemented
42C3⋊D33—1112no—
43C11×C3⋊D3C7×D11112yescomplemented
44C32×D11—1112no—
45C2×C7×C11—912no—
46C7×D11—1112no—
47C7×D11—9912no—
48D3×D11—3348no—
49C2×C32×C7—1211no—
50C7×C3⋊D3—1211no—
51C7×C3⋊D3C11⋊D1111yescharacteristic, direct product factor
52C112C2×C7×C3⋊D311yescharacteristic, complemented, Sylow
53C32×C11C2×C7×D11112yescomplemented
54C2×D3×C7—3634no—
55C7×C11C3⋊D3×D11112yescomplemented
56D33—3348no—
57C3×D11—1148no—
58D3×C11—348no—
59C32×C7C2×C11⋊D1111yescharacteristic, complemented, Hall
60C2×D11—9912no—
61C2×C3×C7—1214no—
62D3×C7—34no—
63D3×C7—3634no—
64C2×C3⋊D3—1211noHall
65C3×C11D3×C7×D11148yescomplemented
66C22×C7—10891noHall
67C2×C11—912no—
68D11—1112no—
69D11—9912no—
70C3×C7D3×C11⋊D1114yescomplemented
71C2×C32—1211no—
72C3⋊D3—1211no—
73C3⋊D3C7×C11⋊D1111yescharacteristic, direct product factor
74C2×C7—91no—
75C2×C7—10891no—
76C2×C7—1211no—
77C2×D3—3634no—
78C11C7×C3⋊D3×D11112yescomplemented
79C32C2×C7×C11⋊D1111yescharacteristic, complemented, Sylow
80C7C3⋊D3×C11⋊D1111yescharacteristic, direct product factor, Sylow
81C2×C3—1214no—
82D3—34no—
83D3—3634no—
84C22—10891noSylow
85C3D3×C7×C11⋊D1114yescomplemented
86C2—91no—
87C2—10891no—
88C2—1211no—
subgroupG/H
center, hypercenterC7C3⋊D3×C11⋊D11
commutator, cosocle, hypocenterC32×C112C22×C7
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C32×C112
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11⋊D11C2semidirect
2. C7×C112×C3⋊D3C2semidirect
3. C7×C3⋊(C3⋊(C11⋊D11))C2semidirect
5. C32×C7×C112C22semidirect
8. C3×C7×C11⋊D11D3semidirect
9. C3⋊D3×C11⋊D11C7direct (N × H)
12. C3×C7×C112C2×D3semidirect
13. C3⋊(C3⋊(C11⋊D11))C2×C7semidirect
14. C112×C3⋊D3C2×C7semidirect
15. C32×C11⋊D11C2×C7semidirect
18. C7×C11⋊D11C3⋊D3direct (N × H)
21. C7×C11×C3⋊D3D11semidirect
23. C32×C112C22×C7semidirect
25. C7×C112C2×C3⋊D3semidirect
28. C3×C11⋊D11D3×C7semidirect
29. C32×C7×C11C2×D11semidirect
35. C3×C112C2×D3×C7semidirect
40. C11⋊D11C7×C3⋊D3direct (N × H)
41. C3×C7×C11D3×D11semidirect
43. C11×C3⋊D3C7×D11semidirect
51. C7×C3⋊D3C11⋊D11direct (N × H)
52. C112C2×C7×C3⋊D3semidirect
53. C32×C11C2×C7×D11semidirect
55. C7×C11C3⋊D3×D11semidirect
59. C32×C7C2×C11⋊D11semidirect
65. C3×C11D3×C7×D11semidirect
70. C3×C7D3×C11⋊D11semidirect
73. C3⋊D3C7×C11⋊D11direct (N × H)
78. C11C7×C3⋊D3×D11semidirect
79. C32C2×C7×C11⋊D11semidirect
80. C7C3⋊D3×C11⋊D11direct (N × H)
85. C3D3×C7×C11⋊D11semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11⋊D112
C7×C112×C3⋊D32
C7×C3⋊(C3⋊(C11⋊D11))2
D3×C7×C11⋊D113
C3⋊D3×C11⋊D117
C7×C3⋊D3×D1111