Finite Group Databasebeta

← C11×C3⋊Dic255 #46777968

Subgroups — C11×C3⋊Dic255 #46777968

Order 33660.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C5×C11×C17C211yesmaximal, characteristic
2C11×Dic255—34nomaximal
3C32×C5×C11×C17C411yescharacteristic, complemented, Hall
4C11×C3⋊Dic51—51nomaximal, Hall
5C2×C3×C5×C11×C17D314yes—
6C11×Dic85—91noHall
7C2×C32×C11×C17D511yescharacteristic
8C3⋊Dic255C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C11×C17Dic314yescomplemented
10C11×Dic51—154no—
11C11×C3⋊Dic15—171nomaximal, Hall
12C2×C5×C11×C17C3⋊D311yescharacteristic
13C32×C11×C17Dic511yescharacteristic, complemented, Hall
14C2×C32×C5×C17C2×C1111yescharacteristic
15C2×C3×C11×C17D1514yes—
16Dic255—34no—
17C2×C32×C5×C11D1711yescharacteristic
18C5×C11×C17C3⋊Dic311yescharacteristic, complemented, Hall
19C32×C5×C17C4×C1111yescharacteristic, complemented, Hall
20C11×Dic17—451noHall
21C11×Dic15—514no—
22C3⋊Dic51—51noHall
23C3×C11×C17Dic1514yescomplemented
24C2×C3×C5×C17D3×C1114yes—
25C32×C5×C11Dic1711yescharacteristic, complemented, Hall
26C11×C3⋊Dic3—851noHall
27C2×C11×C17C3⋊D1511yescharacteristic
28Dic85—91noHall
29C2×C3×C5×C11D5114yes—
30C2×C32×C17D5×C1111yescharacteristic
31C3×C5×C17C11×Dic314yescomplemented
32C11×Dic5—1531noHall
33Dic51—154no—
34C2×C32×C11D8511yescharacteristic
35C11×C17C3⋊Dic1511yescharacteristic, complemented, Hall
36C3⋊Dic15—171noHall
37C2×C5×C17C11×C3⋊D311yescharacteristic
38C3×C5×C11Dic5114yescomplemented
39C32×C17C11×Dic511yescharacteristic, complemented, Hall
40C11×Dic3—2554no—
41C2×C5×C11C3⋊D5111yescharacteristic
42C2×C3×C17C11×D1514yes—
43C32×C11Dic8511yescharacteristic, complemented, Hall
44C2×C32×C5C11×D1711yescharacteristic
45C5×C17C11×C3⋊Dic311yescharacteristic, complemented, Hall
46Dic17—451noHall
47C2×C3×C11D25514yes—
48Dic15—514no—
49C5×C11C3⋊Dic5111yescharacteristic, complemented, Hall
50C3×C17C11×Dic1514yescomplemented
51C32×C5C11×Dic1711yescharacteristic, complemented, Hall
52C4×C11—7651noHall
53C3⋊Dic3—851noHall
54C2×C17C11×C3⋊D1511yescharacteristic
55C3×C11Dic25514yescomplemented
56C2×C3×C5C11×D5114yes—
57C2×C11C3⋊D25511yescharacteristic
58Dic5—1531noHall
59C2×C32C11×D8511yescharacteristic
60C17C11×C3⋊Dic1511yescharacteristic, complemented, Sylow
61C3×C5C11×Dic5114yescomplemented
62Dic3—2554no—
63C11C3⋊Dic25511yescharacteristic, direct product factor, Sylow
64C2×C5C11×C3⋊D5111yescharacteristic
65C32C11×Dic8511yescharacteristic, complemented, Sylow
66C2×C3C11×D25514yes—
67C5C11×C3⋊Dic5111yescharacteristic, complemented, Sylow
68C4—7651noSylow
69C3C11×Dic25514yescomplemented
70C2C11×C3⋊D25511yescharacteristic
subgroupG/H
center, hypercenterC2×C11C3⋊D255
commutator, hypocenterC32×C5×C17C4×C11
FrattiniC2C11×C3⋊D255
Fitting, socle, prime radicalC2×C32×C5×C11×C17C2
cosocleC2×C32×C5×C17C2×C11
LCSG ▷ C32×C5×C17
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
3. C32×C5×C11×C17C4semidirect
8. C3⋊Dic255C11direct (N × H)
9. C3×C5×C11×C17Dic3semidirect
13. C32×C11×C17Dic5semidirect
18. C5×C11×C17C3⋊Dic3semidirect
19. C32×C5×C17C4×C11semidirect
23. C3×C11×C17Dic15semidirect
25. C32×C5×C11Dic17semidirect
31. C3×C5×C17C11×Dic3semidirect
35. C11×C17C3⋊Dic15semidirect
38. C3×C5×C11Dic51semidirect
39. C32×C17C11×Dic5semidirect
43. C32×C11Dic85semidirect
45. C5×C17C11×C3⋊Dic3semidirect
49. C5×C11C3⋊Dic51semidirect
50. C3×C17C11×Dic15semidirect
51. C32×C5C11×Dic17semidirect
55. C3×C11Dic255semidirect
60. C17C11×C3⋊Dic15semidirect
61. C3×C5C11×Dic51semidirect
63. C11C3⋊Dic255direct (N × H)
65. C32C11×Dic85semidirect
67. C5C11×C3⋊Dic51semidirect
69. C3C11×Dic255semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C5×C11×C172
C11×Dic2553
C11×C3⋊Dic515
C3⋊Dic25511
C11×C3⋊Dic1517