Finite Group Databasebeta

← C3⋊(C3⋊((C11⋊C5)⋊Dic11)) #36345005

Subgroups — C3⋊(C3⋊((C11⋊C5)⋊Dic11)) #36345005

Order 21780.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C11×C11⋊C5C211yesmaximal, characteristic
2C3⋊((C11⋊C5)⋊Dic11)—34nomaximal
3C32×C11×C11⋊C5C411yescharacteristic, complemented, Hall
4C3⋊(C3⋊(C11⋊Dic11))C511yesmaximal, characteristic, complemented, Hall
5C2×C3×C11×C11⋊C5D314yes—
6(C11⋊C5)⋊Dic11—91noHall
7C2×C32×C112C2×C511yescharacteristic
8C5×C3⋊Dic33—111nomaximal
9C3⋊(C3⋊(Dic11⋊C5))—111nomaximal
10C3×C11×C11⋊C5Dic314yescomplemented
11C3⋊(C11⋊Dic11)—34no—
12C2×C11×C11⋊C5C3⋊D311yescharacteristic
13C32×C112C4×C511yescharacteristic, complemented, Hall
14C2×C32×C5×C11—111no—
15C2×C32×C11⋊C5D1111yescharacteristic
16C2×C3×C112C5×D314yes—
17C5×Dic33—334no—
18C3⋊(Dic11⋊C5)—334no—
19C11×C11⋊C5C3⋊Dic311yescharacteristic, complemented, Hall
20C32×C5×C11—111no—
21C32×C11⋊C5Dic1111yescharacteristic, complemented
22C11⋊Dic11—91noHall
23C3⋊Dic33—111no—
24C3⋊Dic33—111no—
25C3⋊Dic33—552no—
26C3×C112C5×Dic314yescomplemented
27C2×C3×C5×C11—114no—
28C2×C3×C11⋊C5D3314yes—
29C2×C112C5×C3⋊D311yescharacteristic
30C5×Dic11—991no—
31Dic11⋊C5—991no—
32C2×C32×C11—52no—
33C2×C32×C11AGL(1,𝔽11)11yescharacteristic
34C2×C32×C11C5×D1111yescharacteristic
35C5×C3⋊Dic3—1211noHall
36C3×C5×C11—114no—
37C3×C11⋊C5Dic3314yescomplemented
38Dic33—334no—
39Dic33—334no—
40Dic33—1658no—
41C112C5×C3⋊Dic311yescharacteristic, complemented, Sylow
42C2×C5×C11—111no—
43C2×C11⋊C5C3⋊D3311yescharacteristic
44C32×C11—52no—
45C32×C11Dic11⋊C511yescharacteristic, complemented
46C32×C11C5×Dic1111yescharacteristic, complemented
47C2×C32×C5—111no—
48C2×C3×C11—58no—
49C2×C3×C11C3⋊AGL(1,𝔽11)14yes—
50C2×C3×C11C5×D3314yes—
51C5×Dic3—3634no—
52C5×C11—111no—
53C11⋊C5C3⋊Dic3311yescharacteristic, complemented
54C32×C5—111noHall
55Dic11—991no—
56Dic11—991no—
57Dic11—4952no—
58C3⋊Dic3—1211noHall
59C3×C11—58no—
60C3×C11C3⋊(Dic11⋊C5)14yescomplemented
61C3×C11C5×Dic3314yescomplemented
62C2×C3×C5—114no—
63C2×C11—52no—
64C2×C11C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic
65C2×C11C5×C3⋊D3311yescharacteristic
66C4×C5—10891noHall
67C2×C32(C11⋊C5)⋊D1111yescharacteristic
68C3×C5—114no—
69Dic3—3634no—
70C11—52no—
71C11C3⋊(C3⋊(Dic11⋊C5))11yescharacteristic, complemented
72C11C5×C3⋊Dic3311yescharacteristic, complemented
73C2×C5—111no—
74C32(C11⋊C5)⋊Dic1111yescharacteristic, complemented, Sylow
75C2×C3C3⋊((C11⋊C5)⋊D11)14yes—
76C5—111noSylow
77C4—10891noSylow
78C3C3⋊((C11⋊C5)⋊Dic11)14yescomplemented
79C2C3⋊(C3⋊((C11⋊C5)⋊D11))11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊(C3⋊((C11⋊C5)⋊D11))
commutator, hypocenterC32×C112C4×C5
Fitting, socle, cosocleC2×C32×C112C2×C5
prime radicalC2×C32×C11×C11⋊C5C2
LCSG ▷ C32×C112
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. C32×C11×C11⋊C5C4semidirect
4. C3⋊(C3⋊(C11⋊Dic11))C5semidirect
10. C3×C11×C11⋊C5Dic3semidirect
13. C32×C112C4×C5semidirect
19. C11×C11⋊C5C3⋊Dic3semidirect
21. C32×C11⋊C5Dic11semidirect
26. C3×C112C5×Dic3semidirect
37. C3×C11⋊C5Dic33semidirect
41. C112C5×C3⋊Dic3semidirect
45. C32×C11Dic11⋊C5semidirect
46. C32×C11C5×Dic11semidirect
53. C11⋊C5C3⋊Dic33semidirect
60. C3×C11C3⋊(Dic11⋊C5)semidirect
61. C3×C11C5×Dic33semidirect
71. C11C3⋊(C3⋊(Dic11⋊C5))semidirect
72. C11C5×C3⋊Dic33semidirect
74. C32(C11⋊C5)⋊Dic11semidirect
78. C3C3⋊((C11⋊C5)⋊Dic11)semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C11×C11⋊C52
C3⋊((C11⋊C5)⋊Dic11)3
C3⋊(C3⋊(C11⋊Dic11))5
C5×C3⋊Dic3311
C3⋊(C3⋊(Dic11⋊C5))11