Finite Group Databasebeta

← C3⋊(C11⋊((C67⋊C3)⋊C4)) #40997635

Subgroups — C3⋊(C11⋊((C67⋊C3)⋊C4)) #40997635

Order 26532.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C11×C67⋊C3C211yesmaximal, characteristic
2C11⋊((C67⋊C3)⋊C4)—31nomaximal
3Dic2211C311yesmaximal, characteristic, complemented
4C3×C11×C67⋊C3C411yescharacteristic, complemented, Hall
5C2×C11×C67⋊C3—21no—
6C2×C11×C67⋊C3D311yescharacteristic
7C2×C3×C11×C67C2×C311yescharacteristic
8Dic737—31noHall
9C3⋊((C67⋊C3)⋊C4)—111nomaximal, Hall
10C3×C11×C67C3×C411yescharacteristic, complemented
11C11×C67⋊C3—21no—
12C11×C67⋊C3Dic311yescharacteristic, complemented
13C2×C11×C67C3×D311yescharacteristic
14C2×C3×C67⋊C3D1111yescharacteristic
15Dic201—111no—
16(C67⋊C3)⋊C4—331no—
17C11×C67C3×Dic311yescharacteristic, complemented, Hall
18C3×C67⋊C3Dic1111yescharacteristic, complemented, Hall
19C2×C3×C67C3×D1111yescharacteristic
20C2×C67⋊C3—21no—
21C2×C67⋊C3D3311yescharacteristic
22C3×Dic33—671nomaximal, Hall
23Dic67—331noHall
24C3×C67C3×Dic1111yescharacteristic, complemented
25C67⋊C3—21no—
26C67⋊C3Dic3311yescharacteristic, complemented
27C2×C32×C11—1341no—
28C2×C67C3×D3311yescharacteristic
29Dic33—671no—
30C3×Dic11—2011no—
31C32×C11—1341noHall
32C67C3×Dic3311yescharacteristic, complemented, Sylow
33C2×C3×C11—1341no—
34C2×C3×C11—1341no—
35C2×C3×C11D67⋊C311yescharacteristic
36Dic11—2011noHall
37C3×Dic3—7371noHall
38C3×C11—1341no—
39C3×C11—1341no—
40C3×C11(C67⋊C3)⋊C411yescharacteristic, complemented
41C2×C11C3⋊(D67⋊C3)11yescharacteristic
42C2×C32—1341no—
43C3×C4—22111no—
44Dic3—7371no—
45C11C3⋊((C67⋊C3)⋊C4)11yescharacteristic, complemented, Sylow
46C32—1341noSylow
47C2×C3—1341no—
48C2×C3—1341no—
49C2×C3C11⋊(D67⋊C3)11yescharacteristic
50C4—22111noSylow
51C3—1341no—
52C3—1341no—
53C3C11⋊((C67⋊C3)⋊C4)11yescharacteristic, complemented
54C2C3⋊(C11⋊(D67⋊C3))11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊(C11⋊(D67⋊C3))
commutator, hypocenterC3×C11×C67C3×C4
Fitting, socle, cosocleC2×C3×C11×C67C2×C3
prime radicalC2×C3×C11×C67⋊C3C2
LCSG ▷ C3×C11×C67
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. Dic2211C3semidirect
4. C3×C11×C67⋊C3C4semidirect
10. C3×C11×C67C3×C4semidirect
12. C11×C67⋊C3Dic3semidirect
17. C11×C67C3×Dic3semidirect
18. C3×C67⋊C3Dic11semidirect
24. C3×C67C3×Dic11semidirect
26. C67⋊C3Dic33semidirect
32. C67C3×Dic33semidirect
40. C3×C11(C67⋊C3)⋊C4semidirect
45. C11C3⋊((C67⋊C3)⋊C4)semidirect
53. C3C11⋊((C67⋊C3)⋊C4)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C11×C67⋊C32
C11⋊((C67⋊C3)⋊C4)3
Dic22113
C3⋊((C67⋊C3)⋊C4)11
C3×Dic3367