Finite Group Databasebeta

← C2×C7×C3⋊(C3⋊(C11⋊D11)) #44479270

Subgroups — C2×C7×C3⋊(C3⋊(C11⋊D11)) #44479270

Order 30492.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C3⋊(C3⋊(C11⋊D11))C212yesmaximal, direct product factor
2C2×C32×C7×C112C211yesmaximal, characteristic, complemented
3C2×C7×C3⋊(C11⋊D11)—34nomaximal
4C32×C7×C112C2211yescharacteristic, complemented, Hall
5C7×C3⋊(C11⋊D11)—38no—
6C2×C3×C7×C112D314yescomplemented
7C2×C3⋊(C3⋊(C11⋊D11))C711yesmaximal, characteristic, direct product factor, Hall
8C2×C7×C11⋊D11—91noHall
9C2×C7×C3⋊D33—1112nomaximal
10C3×C7×C112C2×D314yescomplemented
11C3⋊(C3⋊(C11⋊D11))C2×C712yesdirect product factor
12C2×C32×C112C2×C711yescharacteristic, complemented
13C2×C7×C112C3⋊D311yescharacteristic, complemented
14C7×C11⋊D11—92no—
15C2×C3⋊(C11⋊D11)—34no—
16C2×C32×C7×C11D11112yescomplemented
17C7×C3⋊D33—1124no—
18C32×C112C22×C711yescharacteristic, complemented, Hall
19C2×C7×D33—3348no—
20C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
21C2×C3×C112D3×C714yescomplemented
22C3⋊(C11⋊D11)—38no—
23C32×C7×C11C2×D11112yescomplemented
24C2×C11⋊D11—91noHall
25C2×C3×C7×C11D33148yescomplemented
26C7×D33—3396no—
27C2×C3⋊D33—1112no—
28C3×C112C2×D3×C714yescomplemented
29C2×C7×D11—9912no—
30C2×C7×C3⋊D3—1211noHall
31C2×C112C7×C3⋊D311yescharacteristic, complemented
32C11⋊D11—92no—
33C3×C7×C11C2×D33148yescomplemented
34C2×C32×C11C7×D11112yescomplemented
35C3⋊D33—1124no—
36C2×C7×C11C3⋊D33112yescomplemented
37C7×D11—9924no—
38C2×D33—3348no—
39C2×C32×C7C11⋊D1111yescharacteristic, complemented
40C7×C3⋊D3—1212no—
41C112C2×C7×C3⋊D311yescharacteristic, complemented, Sylow
42C32×C11C2×C7×D11112yescomplemented
43C2×D3×C7—3634no—
44C7×C11C2×C3⋊D33112yescomplemented
45C2×C3×C11C7×D33148yescomplemented
46D33—3396no—
47C32×C7C2×C11⋊D1111yescharacteristic, complemented, Hall
48C2×D11—9912no—
49C2×C3×C7C3⋊(C11⋊D11)14yescomplemented
50D3×C7—3638no—
51C2×C3⋊D3—1211noHall
52C3×C11C2×C7×D33148yescomplemented
53C22×C7—10891noHall
54C2×C11C7×C3⋊D33112yescomplemented
55D11—9924no—
56C3×C7C2×C3⋊(C11⋊D11)14yescomplemented
57C2×C32C7×C11⋊D1111yescharacteristic, complemented
58C3⋊D3—1212no—
59C2×C7—10892no—
60C2×C7C3⋊(C3⋊(C11⋊D11))11yescharacteristic, direct product factor
61C2×D3—3634no—
62C11C2×C7×C3⋊D33112yescomplemented
63C32C2×C7×C11⋊D1111yescharacteristic, complemented, Sylow
64C7C2×C3⋊(C3⋊(C11⋊D11))11yescharacteristic, direct product factor, Sylow
65C2×C3C7×C3⋊(C11⋊D11)14yescomplemented
66D3—3638no—
67C22—10891noSylow
68C3C2×C7×C3⋊(C11⋊D11)14yescomplemented
69C2—10892no—
70C2C7×C3⋊(C3⋊(C11⋊D11))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7C3⋊(C3⋊(C11⋊D11))
commutator, cosocle, hypocenterC32×C112C22×C7
FrattiniC1G
Fitting, socleC2×C32×C7×C112C2
LCSG ▷ C32×C112
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
1. C7×C3⋊(C3⋊(C11⋊D11))C2direct (N × H)
2. C2×C32×C7×C112C2semidirect
4. C32×C7×C112C22semidirect
6. C2×C3×C7×C112D3semidirect
7. C2×C3⋊(C3⋊(C11⋊D11))C7direct (N × H)
10. C3×C7×C112C2×D3semidirect
11. C3⋊(C3⋊(C11⋊D11))C2×C7direct (N × H)
12. C2×C32×C112C2×C7semidirect
13. C2×C7×C112C3⋊D3semidirect
16. C2×C32×C7×C11D11semidirect
18. C32×C112C22×C7semidirect
20. C7×C112C2×C3⋊D3semidirect
21. C2×C3×C112D3×C7semidirect
23. C32×C7×C11C2×D11semidirect
25. C2×C3×C7×C11D33semidirect
28. C3×C112C2×D3×C7semidirect
31. C2×C112C7×C3⋊D3semidirect
33. C3×C7×C11C2×D33semidirect
34. C2×C32×C11C7×D11semidirect
36. C2×C7×C11C3⋊D33semidirect
39. C2×C32×C7C11⋊D11semidirect
41. C112C2×C7×C3⋊D3semidirect
42. C32×C11C2×C7×D11semidirect
44. C7×C11C2×C3⋊D33semidirect
45. C2×C3×C11C7×D33semidirect
47. C32×C7C2×C11⋊D11semidirect
49. C2×C3×C7C3⋊(C11⋊D11)semidirect
52. C3×C11C2×C7×D33semidirect
54. C2×C11C7×C3⋊D33semidirect
56. C3×C7C2×C3⋊(C11⋊D11)semidirect
57. C2×C32C7×C11⋊D11semidirect
60. C2×C7C3⋊(C3⋊(C11⋊D11))direct (N × H)
62. C11C2×C7×C3⋊D33semidirect
63. C32C2×C7×C11⋊D11semidirect
64. C7C2×C3⋊(C3⋊(C11⋊D11))direct (N × H)
65. C2×C3C7×C3⋊(C11⋊D11)semidirect
68. C3C2×C7×C3⋊(C11⋊D11)semidirect
70. C2C7×C3⋊(C3⋊(C11⋊D11))direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C3⋊(C3⋊(C11⋊D11))2
C2×C32×C7×C1122
C2×C7×C3⋊(C11⋊D11)3
C2×C3⋊(C3⋊(C11⋊D11))7
C2×C7×C3⋊D3311