Finite Group Databasebeta

← C11×C3⋊(C3⋊#63121) #38788268

Subgroups — C11×C3⋊(C3⋊#63121) #38788268

Order 25740.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C11×D65C211yesmaximal, characteristic
2C11×C3⋊#63121—34nomaximal
3C32×C5×C11×C13C411yescharacteristic, complemented, Hall
4C11×C3⋊(C3⋊#261)—51nomaximal, Hall
5C3×C11×D65D314yes—
6C11×#63121—91noHall
7C32×C11×D13—51no—
8C3⋊(C3⋊#63121)C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C11×C13Dic314yescomplemented
10C11×C3⋊ΓL(1,𝔽16)—131nomaximal, Hall
11C11×C3⋊#261—154no—
12C11×D65C3⋊D311yescharacteristic
13C32×C11×C13AGL(1,𝔽5)11yescharacteristic, complemented, Hall
14C32×D65C2×C1111yescharacteristic
15C32×D5×C11—131no—
16C3×C11×D13—54no—
17C3⋊#63121—34no—
18C5×C11×C13C3⋊Dic311yescharacteristic, complemented, Hall
19C11×ΓL(1,𝔽16)—394no—
20C32×C5×C13C4×C1111yescharacteristic, complemented, Hall
21C11×#261—451noHall
22C32×C5×C11#26111yescharacteristic, complemented, Hall
23C3⋊(C3⋊#261)—51noHall
24C3×C11×C13ΓL(1,𝔽16)14yescomplemented
25C11×C3⋊Dic3—651noHall
26C3×D65D3×C1114yes—
27C3×D5×C11—134no—
28C11×D13—51no—
29#63121—91noHall
30C32×D13—51no—
31C11×AGL(1,𝔽5)—1171noHall
32C2×C32×C11—651no—
33C3×C5×C13C11×Dic314yescomplemented
34C3⋊ΓL(1,𝔽16)—131noHall
35C3×C5×C11C3⋊#26114yescomplemented
36C3⋊#261—154no—
37C11×C13C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
38C11×Dic3—1954no—
39D65C11×C3⋊D311yescharacteristic
40C32×C13C11×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
41D5×C11—131no—
42C32×C11#6312111yescharacteristic, complemented, Hall
43C32×D5—131no—
44C3×D13—54no—
45C2×C3×C11—654no—
46C5×C13C11×C3⋊Dic311yescharacteristic, complemented, Hall
47ΓL(1,𝔽16)—394no—
48C5×C11C3⋊(C3⋊#261)11yescharacteristic, complemented, Hall
49#261—451noHall
50C32×C5C11×#26111yescharacteristic, complemented, Hall
51C4×C11—5851noHall
52C3×C13C11×ΓL(1,𝔽16)14yescomplemented
53C3⋊Dic3—651noHall
54C3×C11C3⋊#6312114yescomplemented
55C3×D5—134no—
56D13—51no—
57C2×C11—651no—
58AGL(1,𝔽5)—1171noHall
59C2×C32—651no—
60C3×C5C11×C3⋊#26114yescomplemented
61C13C11×C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
62Dic3—1954no—
63C11C3⋊(C3⋊#63121)11yescharacteristic, direct product factor, Sylow
64D5—131no—
65C32C11×#6312111yescharacteristic, complemented, Sylow
66C2×C3—654no—
67C5C11×C3⋊(C3⋊#261)11yescharacteristic, complemented, Sylow
68C4—5851noSylow
69C3C11×C3⋊#6312114yescomplemented
70C2—651no—
subgroupG/H
center, hypercenterC11C3⋊(C3⋊#63121)
commutator, hypocenterC32×C5×C13C4×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×C11×D65C2
cosocleC32×D65C2×C11
LCSG ▷ C32×C5×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
3. C32×C5×C11×C13C4semidirect
8. C3⋊(C3⋊#63121)C11direct (N × H)
9. C3×C5×C11×C13Dic3semidirect
13. C32×C11×C13AGL(1,𝔽5)semidirect
18. C5×C11×C13C3⋊Dic3semidirect
20. C32×C5×C13C4×C11semidirect
22. C32×C5×C11#261semidirect
24. C3×C11×C13ΓL(1,𝔽16)semidirect
33. C3×C5×C13C11×Dic3semidirect
35. C3×C5×C11C3⋊#261semidirect
37. C11×C13C3⋊ΓL(1,𝔽16)semidirect
40. C32×C13C11×AGL(1,𝔽5)semidirect
42. C32×C11#63121semidirect
46. C5×C13C11×C3⋊Dic3semidirect
48. C5×C11C3⋊(C3⋊#261)semidirect
50. C32×C5C11×#261semidirect
52. C3×C13C11×ΓL(1,𝔽16)semidirect
54. C3×C11C3⋊#63121semidirect
60. C3×C5C11×C3⋊#261semidirect
61. C13C11×C3⋊ΓL(1,𝔽16)semidirect
63. C11C3⋊(C3⋊#63121)direct (N × H)
65. C32C11×#63121semidirect
67. C5C11×C3⋊(C3⋊#261)semidirect
69. C3C11×C3⋊#63121semidirect

Maximal subgroups

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

subgroupindex
C32×C11×D652
C11×C3⋊#631213
C11×C3⋊(C3⋊#261)5
C3⋊(C3⋊#63121)11
C11×C3⋊ΓL(1,𝔽16)13