Finite Group Databasebeta

← C3⋊(C11⋊#11759815) #45689604

Subgroups — C3⋊(C11⋊#11759815) #45689604

Order 33462.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×#92788C211yesmaximal, characteristic, complemented, Hall
2C3⋊(C11⋊(C13⋊D13))C311yesmaximal, characteristic, complemented
3C11⋊#11759815—31nomaximal
4C11×#92788—21no—
5C11×#92788D311yescharacteristic, complemented
6C3×C11×C132C2×C311yescharacteristic, complemented
7C11⋊(C13⋊D13)—31noHall
8C3⋊#11759815—111nomaximal, Hall
9C3⋊(C11⋊(D13⋊C3))—1314nomaximal
10C11×C132C3×D311yescharacteristic, complemented, Hall
11C3×#92788D1111yescharacteristic, complemented, Hall
12C3×C11×C13⋊C3—1314no—
13C3⋊(C13⋊D13)—111no—
14#11759815—331no—
15D429—1314no—
16C11⋊(D13⋊C3)—3914no—
17C3×C132C3×D1111yescharacteristic, complemented
18#92788—21no—
19#92788D3311yescharacteristic, complemented
20C3×C11×C13D13⋊C3114yescomplemented
21C11×C13⋊C3—1314no—
22C11×C13⋊C3—2614no—
23C13⋊D13—331noHall
24D143—3914no—
25C3⋊(D13⋊C3)—14314no—
26C3×D33—1691noHall
27C132C3×D3311yescharacteristic, complemented, Sylow
28C11×C13C3⋊(D13⋊C3)114yescomplemented
29C3×C13⋊C3—1314no—
30C32×C11—1691noHall
31D39—14314no—
32D13⋊C3—42914no—
33D33—1691no—
34C3×D11—5071no—
35C3×C13C11⋊(D13⋊C3)114yescomplemented
36C13⋊C3—1314no—
37C13⋊C3—2614no—
38C3×C11—3381no—
39C3×C11—1691no—
40C3×C11#1175981511yescharacteristic, complemented
41D13—42914no—
42D11—5071noHall
43C3×D3—18591noHall
44C13C3⋊(C11⋊(D13⋊C3))114yescomplemented
45C11C3⋊#1175981511yescharacteristic, complemented, Sylow
46C32—1691noSylow
47C2×C3—55771no—
48D3—18591no—
49C3—3381no—
50C3—1691no—
51C3C11⋊#1175981511yescharacteristic, complemented
52C2—55771noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C132C2×C3
LCSG ▷ C3×C11×C132
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C11×#92788C2semidirect
2. C3⋊(C11⋊(C13⋊D13))C3semidirect
5. C11×#92788D3semidirect
6. C3×C11×C132C2×C3semidirect
10. C11×C132C3×D3semidirect
11. C3×#92788D11semidirect
17. C3×C132C3×D11semidirect
19. #92788D33semidirect
20. C3×C11×C13D13⋊C3semidirect
27. C132C3×D33semidirect
28. C11×C13C3⋊(D13⋊C3)semidirect
35. C3×C13C11⋊(D13⋊C3)semidirect
40. C3×C11#11759815semidirect
44. C13C3⋊(C11⋊(D13⋊C3))semidirect
45. C11C3⋊#11759815semidirect
51. C3C11⋊#11759815semidirect

Maximal subgroups

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

subgroupindex
C3×C11×#927882
C3⋊(C11⋊(C13⋊D13))3
C11⋊#117598153
C3⋊#1175981511
C3⋊(C11⋊(D13⋊C3))13