Finite Group Databasebeta

← C7×C3⋊(C3⋊(C11⋊Dic11)) #44479037

Subgroups — C7×C3⋊(C3⋊(C11⋊Dic11)) #44479037

Order 30492.

504 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C7×C112C211yesmaximal, characteristic
2C7×C3⋊(C11⋊Dic11)—34nomaximal
3C32×C7×C112C411yescharacteristic, complemented, Hall
4C2×C3×C7×C112D314yes—
5C3⋊(C3⋊(C11⋊Dic11))C711yesmaximal, characteristic, direct product factor, Hall
6C7×C11⋊Dic11—91noHall
7C7×C3⋊Dic33—1112nomaximal
8C3×C7×C112Dic314yescomplemented
9C2×C32×C112C2×C711yescharacteristic
10C2×C7×C112C3⋊D311yescharacteristic
11C3⋊(C11⋊Dic11)—34no—
12C2×C32×C7×C11D11112yes—
13C32×C112C4×C711yescharacteristic, complemented, Hall
14C7×Dic33—3348no—
15C7×C112C3⋊Dic311yescharacteristic, complemented, Hall
16C2×C3×C112D3×C714yes—
17C32×C7×C11Dic11112yescomplemented
18C11⋊Dic11—91noHall
19C2×C3×C7×C11D33148yes—
20C3⋊Dic33—1112no—
21C3×C112C7×Dic314yescomplemented
22C7×Dic11—9912no—
23C7×C3⋊Dic3—1211noHall
24C2×C112C7×C3⋊D311yescharacteristic
25C3×C7×C11Dic33148yescomplemented
26C2×C32×C11C7×D11112yes—
27C2×C7×C11C3⋊D33112yes—
28Dic33—3348no—
29C2×C32×C7C11⋊D1111yescharacteristic
30C112C7×C3⋊Dic311yescharacteristic, complemented, Sylow
31C32×C11C7×Dic11112yescomplemented
32C7×Dic3—3634no—
33C7×C11C3⋊Dic33112yescomplemented
34C2×C3×C11C7×D33148yes—
35C32×C7C11⋊Dic1111yescharacteristic, complemented, Hall
36Dic11—9912no—
37C2×C3×C7C3⋊(C11⋊D11)14yes—
38C3⋊Dic3—1211noHall
39C3×C11C7×Dic33148yescomplemented
40C4×C7—10891noHall
41C2×C11C7×C3⋊D33112yes—
42C3×C7C3⋊(C11⋊Dic11)14yescomplemented
43C2×C32C7×C11⋊D1111yescharacteristic
44C2×C7C3⋊(C3⋊(C11⋊D11))11yescharacteristic
45Dic3—3634no—
46C11C7×C3⋊Dic33112yescomplemented
47C32C7×C11⋊Dic1111yescharacteristic, complemented, Sylow
48C7C3⋊(C3⋊(C11⋊Dic11))11yescharacteristic, direct product factor, Sylow
49C2×C3C7×C3⋊(C11⋊D11)14yes—
50C4—10891noSylow
51C3C7×C3⋊(C11⋊Dic11)14yescomplemented
52C2C7×C3⋊(C3⋊(C11⋊D11))11yescharacteristic
subgroupG/H
center, hypercenterC2×C7C3⋊(C3⋊(C11⋊D11))
commutator, hypocenterC32×C112C4×C7
FrattiniC2C7×C3⋊(C3⋊(C11⋊D11))
Fitting, socle, prime radicalC2×C32×C7×C112C2
cosocleC2×C32×C112C2×C7
LCSG ▷ C32×C112
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
3. C32×C7×C112C4semidirect
5. C3⋊(C3⋊(C11⋊Dic11))C7direct (N × H)
8. C3×C7×C112Dic3semidirect
13. C32×C112C4×C7semidirect
15. C7×C112C3⋊Dic3semidirect
17. C32×C7×C11Dic11semidirect
21. C3×C112C7×Dic3semidirect
25. C3×C7×C11Dic33semidirect
30. C112C7×C3⋊Dic3semidirect
31. C32×C11C7×Dic11semidirect
33. C7×C11C3⋊Dic33semidirect
35. C32×C7C11⋊Dic11semidirect
39. C3×C11C7×Dic33semidirect
42. C3×C7C3⋊(C11⋊Dic11)semidirect
46. C11C7×C3⋊Dic33semidirect
47. C32C7×C11⋊Dic11semidirect
48. C7C3⋊(C3⋊(C11⋊Dic11))direct (N × H)
51. C3C7×C3⋊(C11⋊Dic11)semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C7×C1122
C7×C3⋊(C11⋊Dic11)3
C3⋊(C3⋊(C11⋊Dic11))7
C7×C3⋊Dic3311