Finite Group Databasebeta

← C3⋊(C11⋊(C11⋊#1043)) #49137804

Subgroups — C3⋊(C11⋊(C11⋊#1043)) #49137804

Order 36300.

672 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C112×C5⋊D5C211yesmaximal, characteristic
2C11⋊(C11⋊#1043)—31nomaximal, Hall
3C3×C52×C112C411yescharacteristic, complemented, Hall
4C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))—56nomaximal
5C112×C5⋊D5D311yescharacteristic
6C3×D5×C112—56no—
7C3⋊(C11⋊#1043)—1112nomaximal
8C52×C112Dic311yescharacteristic, complemented, Hall
9C11⋊(C11⋊AGL(1,𝔽5))—156no—
10C3×C5×C112AGL(1,𝔽5)16yescomplemented
11C3×C11×C5⋊D5D11112yes—
12C3⋊(C11⋊Dic11)—251noHall
13D5×C112—56no—
14C11⋊#1043—3312no—
15C3×C52×C11Dic11112yescomplemented
16C2×C3×C112—251no—
17C3⋊(C11⋊AGL(1,𝔽5))—5572no—
18C5×C112ΓL(1,𝔽16)16yescomplemented
19C11×C5⋊D5D33112yes—
20C11⋊Dic11—751noHall
21C3×C112#104311yescharacteristic, complemented, Hall
22C3×D5×C11—572no—
23C3⋊#1043—1211noHall
24C52×C11Dic33112yescomplemented
25C2×C112—251no—
26C11⋊AGL(1,𝔽5)—16572no—
27C3×C5×C11C11⋊AGL(1,𝔽5)172yescomplemented
28C3×C5⋊D5C11⋊D1111yescharacteristic
29Dic33—27512no—
30C112C3⋊#104311yescharacteristic, complemented, Sylow
31D5×C11—572no—
32#1043—3631noHall
33C3×C52C11⋊Dic1111yescharacteristic, complemented, Hall
34C2×C3×C11—2512no—
35ΓL(1,𝔽16)—6056no—
36C5×C11C3⋊(C11⋊AGL(1,𝔽5))172yescomplemented
37C5⋊D5C3⋊(C11⋊D11)11yescharacteristic
38Dic11—82512no—
39C3×C11C11⋊#1043112yescomplemented
40C3×D5—56no—
41C52C3⋊(C11⋊Dic11)11yescharacteristic, complemented, Sylow
42C2×C11—2512no—
43AGL(1,𝔽5)—18156no—
44C3×C5C11⋊(C11⋊AGL(1,𝔽5))16yescomplemented
45Dic3—30251noHall
46C11C3⋊(C11⋊#1043)112yescomplemented
47D5—56no—
48C2×C3—251no—
49C5C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))16yescomplemented
50C4—90751noSylow
51C3C11⋊(C11⋊#1043)11yescharacteristic, complemented, Sylow
52C2—251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C52×C112C4
prime radical, cosocleC3×C112×C5⋊D5C2
LCSG ▷ C3×C52×C112
UCSC1

Complements

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

NH ≅ G/Ntype
3. C3×C52×C112C4semidirect
8. C52×C112Dic3semidirect
10. C3×C5×C112AGL(1,𝔽5)semidirect
15. C3×C52×C11Dic11semidirect
18. C5×C112ΓL(1,𝔽16)semidirect
21. C3×C112#1043semidirect
24. C52×C11Dic33semidirect
27. C3×C5×C11C11⋊AGL(1,𝔽5)semidirect
30. C112C3⋊#1043semidirect
33. C3×C52C11⋊Dic11semidirect
36. C5×C11C3⋊(C11⋊AGL(1,𝔽5))semidirect
39. C3×C11C11⋊#1043semidirect
41. C52C3⋊(C11⋊Dic11)semidirect
44. C3×C5C11⋊(C11⋊AGL(1,𝔽5))semidirect
46. C11C3⋊(C11⋊#1043)semidirect
49. C5C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))semidirect
51. C3C11⋊(C11⋊#1043)semidirect

Maximal subgroups

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

subgroupindex
C3×C112×C5⋊D52
C11⋊(C11⋊#1043)3
C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))5
C3⋊(C11⋊#1043)11