Finite Group Databasebeta

← C7×C11×C3⋊(C3⋊#261) #49114968

Subgroups — C7×C11×C3⋊(C3⋊#261) #49114968

Order 36036.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11×D13C211yesmaximal, characteristic
2C7×C11×C3⋊#261—34nomaximal
3C32×C7×C11×C13C411yescharacteristic, complemented, Hall
4C3×C7×C11×D13D314yes—
5C11×C3⋊(C3⋊#261)C711yesmaximal, characteristic, direct product factor, Hall
6C7×C11×#261—91noHall
7C7×C3⋊(C3⋊#261)C1111yesmaximal, characteristic, direct product factor, Hall
8C3×C7×C11×C13Dic314yescomplemented
9C7×C11×C3⋊Dic3—131nomaximal, Hall
10C32×C11×D13C2×C711yescharacteristic
11C7×C11×D13C3⋊D311yescharacteristic
12C11×C3⋊#261—34no—
13C32×C7×D13C2×C1111yescharacteristic
14C2×C32×C7×C11—131no—
15C32×C11×C13C4×C711yescharacteristic, complemented, Hall
16C7×C3⋊#261—34no—
17C7×C11×C13C3⋊Dic311yescharacteristic, complemented, Hall
18C7×C11×Dic3—394no—
19C3×C11×D13D3×C714yes—
20C32×C7×C13C4×C1111yescharacteristic, complemented, Hall
21C32×C7×C11#26111yescharacteristic, complemented, Hall
22C11×#261—91noHall
23C3×C7×D13D3×C1114yes—
24C3⋊(C3⋊#261)C7×C1111yescharacteristic, direct product factor, Hall
25C2×C3×C7×C11—134no—
26C3×C11×C13C7×Dic314yescomplemented
27C11×C3⋊Dic3—131noHall
28C7×#261—91noHall
29C4×C7×C11—1171noHall
30C11×D13C7×C3⋊D311yescharacteristic
31C3×C7×C13C11×Dic314yescomplemented
32C7×C3⋊Dic3—131noHall
33C32×D13C2×C7×C1111yescharacteristic
34C3×C7×C11C3⋊#26114yescomplemented
35C2×C32×C11—131no—
36C7×D13C11×C3⋊D311yescharacteristic
37C3⋊#261—34no—
38C2×C7×C11—131no—
39C11×C13C7×C3⋊Dic311yescharacteristic, complemented, Hall
40C11×Dic3—394no—
41C2×C32×C7—131no—
42C32×C13C4×C7×C1111yescharacteristic, complemented, Hall
43C32×C11C7×#26111yescharacteristic, complemented, Hall
44C7×C13C11×C3⋊Dic311yescharacteristic, complemented, Hall
45C7×Dic3—394no—
46C3×D13D3×C7×C1114yes—
47C7×C11C3⋊(C3⋊#261)11yescharacteristic, direct product factor, Hall
48C2×C3×C11—134no—
49C32×C7C11×#26111yescharacteristic, complemented, Hall
50#261—91noHall
51C4×C11—1171noHall
52C2×C3×C7—134no—
53C3×C13C7×C11×Dic314yescomplemented
54C3⋊Dic3—131noHall
55C3×C11C7×C3⋊#26114yescomplemented
56C4×C7—1171noHall
57D13C7×C11×C3⋊D311yescharacteristic
58C2×C11—131no—
59C3×C7C11×C3⋊#26114yescomplemented
60C2×C32—131no—
61C2×C7—131no—
62C13C7×C11×C3⋊Dic311yescharacteristic, complemented, Sylow
63Dic3—394no—
64C11C7×C3⋊(C3⋊#261)11yescharacteristic, direct product factor, Sylow
65C32C7×C11×#26111yescharacteristic, complemented, Sylow
66C7C11×C3⋊(C3⋊#261)11yescharacteristic, direct product factor, Sylow
67C2×C3—134no—
68C4—1171noSylow
69C3C7×C11×C3⋊#26114yescomplemented
70C2—131no—
subgroupG/H
center, hypercenterC7×C11C3⋊(C3⋊#261)
commutator, hypocenterC32×C13C4×C7×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC32×C7×C11×D13C2
cosocleC32×D13C2×C7×C11
LCSG ▷ C32×C13
UCSC1 ◁ C7×C11

Complements

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

NH ≅ G/Ntype
3. C32×C7×C11×C13C4semidirect
5. C11×C3⋊(C3⋊#261)C7direct (N × H)
7. C7×C3⋊(C3⋊#261)C11direct (N × H)
8. C3×C7×C11×C13Dic3semidirect
15. C32×C11×C13C4×C7semidirect
17. C7×C11×C13C3⋊Dic3semidirect
20. C32×C7×C13C4×C11semidirect
21. C32×C7×C11#261semidirect
24. C3⋊(C3⋊#261)C7×C11direct (N × H)
26. C3×C11×C13C7×Dic3semidirect
31. C3×C7×C13C11×Dic3semidirect
34. C3×C7×C11C3⋊#261semidirect
39. C11×C13C7×C3⋊Dic3semidirect
42. C32×C13C4×C7×C11semidirect
43. C32×C11C7×#261semidirect
44. C7×C13C11×C3⋊Dic3semidirect
47. C7×C11C3⋊(C3⋊#261)direct (N × H)
49. C32×C7C11×#261semidirect
53. C3×C13C7×C11×Dic3semidirect
55. C3×C11C7×C3⋊#261semidirect
59. C3×C7C11×C3⋊#261semidirect
62. C13C7×C11×C3⋊Dic3semidirect
64. C11C7×C3⋊(C3⋊#261)direct (N × H)
65. C32C7×C11×#261semidirect
66. C7C11×C3⋊(C3⋊#261)direct (N × H)
69. C3C7×C11×C3⋊#261semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11×D132
C7×C11×C3⋊#2613
C11×C3⋊(C3⋊#261)7
C7×C3⋊(C3⋊#261)11
C7×C11×C3⋊Dic313