Finite Group Databasebeta

← C3⋊(C11⋊(C11⋊#1044)) #49137808

Subgroups — C3⋊(C11⋊(C11⋊#1044)) #49137808

Order 36300.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C112×C5⋊D5C211yesmaximal, characteristic
2C11⋊(C11⋊#1044)—31nomaximal, Hall
3C3×C52×C112C411yescharacteristic, complemented, Hall
4C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))—52nomaximal
5C112×C5⋊D5D311yescharacteristic
6C3×D5×C112—52no—
7C3×D5×C112—102no—
8C3⋊(C11⋊#1044)—1112nomaximal
9C52×C112Dic311yescharacteristic, complemented, Hall
10C11⋊(C11⋊AGL(1,𝔽5))—152no—
11C3×C5×C112—22no—
12C3×C5×C112AGL(1,𝔽5)12yescomplemented
13C3×C11×C5⋊D5D11112yes—
14C3⋊(C11⋊Dic11)—251noHall
15D5×C112—52no—
16D5×C112—102no—
17C11⋊#1044—3312no—
18C3×C52×C11Dic11112yescomplemented
19C2×C3×C112—251no—
20C3⋊(C11⋊AGL(1,𝔽5))—5524no—
21C5×C112—22no—
22C5×C112ΓL(1,𝔽16)12yescomplemented
23C11×C5⋊D5D33112yes—
24C11⋊Dic11—751noHall
25C3×C112#104411yescharacteristic, complemented, Hall
26C3×D5×C11—524no—
27C3×D5×C11—1024no—
28C3⋊#1044—1211noHall
29C52×C11Dic33112yescomplemented
30C2×C112—251no—
31C11⋊AGL(1,𝔽5)—16524no—
32C3×C5×C11—224no—
33C3×C5×C11C11⋊AGL(1,𝔽5)124yescomplemented
34C3×C5⋊D5C11⋊D1111yescharacteristic
35Dic33—27512no—
36C112C3⋊#104411yescharacteristic, complemented, Sylow
37D5×C11—524no—
38D5×C11—1024no—
39#1044—3631noHall
40C3×C52C11⋊Dic1111yescharacteristic, complemented, Hall
41C2×C3×C11—2512no—
42ΓL(1,𝔽16)—6052no—
43C5×C11—224no—
44C5×C11C3⋊(C11⋊AGL(1,𝔽5))124yescomplemented
45C5⋊D5C3⋊(C11⋊D11)11yescharacteristic
46Dic11—82512no—
47C3×C11C11⋊#1044112yescomplemented
48C3×D5—52no—
49C3×D5—102no—
50C52C3⋊(C11⋊Dic11)11yescharacteristic, complemented, Sylow
51C2×C11—2512no—
52AGL(1,𝔽5)—18152no—
53C3×C5—22no—
54C3×C5C11⋊(C11⋊AGL(1,𝔽5))12yescomplemented
55Dic3—30251noHall
56C11C3⋊(C11⋊#1044)112yescomplemented
57D5—52no—
58D5—102no—
59C2×C3—251no—
60C5—22no—
61C5C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))12yescomplemented
62C4—90751noSylow
63C3C11⋊(C11⋊#1044)11yescharacteristic, complemented, Sylow
64C2—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
9. C52×C112Dic3semidirect
12. C3×C5×C112AGL(1,𝔽5)semidirect
18. C3×C52×C11Dic11semidirect
22. C5×C112ΓL(1,𝔽16)semidirect
25. C3×C112#1044semidirect
29. C52×C11Dic33semidirect
33. C3×C5×C11C11⋊AGL(1,𝔽5)semidirect
36. C112C3⋊#1044semidirect
40. C3×C52C11⋊Dic11semidirect
44. C5×C11C3⋊(C11⋊AGL(1,𝔽5))semidirect
47. C3×C11C11⋊#1044semidirect
50. C52C3⋊(C11⋊Dic11)semidirect
54. C3×C5C11⋊(C11⋊AGL(1,𝔽5))semidirect
56. C11C3⋊(C11⋊#1044)semidirect
61. C5C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))semidirect
63. C3C11⋊(C11⋊#1044)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⋊#1044)3
C3⋊(C11⋊(C11⋊AGL(1,𝔽5)))5
C3⋊(C11⋊#1044)11