Finite Group Databasebeta

← C32×C11⋊#66776 #46778067

Subgroups — C32×C11⋊#66776 #46778067

Order 33660.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C11×D85C211yesmaximal, characteristic
2C3×C11⋊#66776C314yesmaximal, direct product factor
3C32×C5×C11×C17C411yescharacteristic, complemented, Hall
4C32×C11⋊#595—51nomaximal, Hall
5C3×C11×D85C2×C314yes—
6C11⋊#66776C3211yescharacteristic, direct product factor, Hall
7C32×C11×D17—51no—
8C32×#66776—111nomaximal, Hall
9C3×C5×C11×C17C3×C414yescomplemented
10C3×C11⋊#595—54no—
11C32×C11⋊AGL(1,𝔽5)—171nomaximal, Hall
12C11×D85C2×C3211yescharacteristic
13C32×C11×C17AGL(1,𝔽5)11yescharacteristic, complemented, Hall
14C32×D85D1111yescharacteristic
15C3×C11×D17—54no—
16C3×#66776—114no—
17C32×D5×C11—171no—
18C5×C11×C17C32×C411yescharacteristic, complemented, Hall
19C32×C5×C17Dic1111yescharacteristic, complemented, Hall
20C11⋊#595—51noHall
21C3×C11⋊AGL(1,𝔽5)—174no—
22C32×#595—551noHall
23C3×C11×C17C3×AGL(1,𝔽5)14yescomplemented
24C3×D85C3×D1114yes—
25C32×C5×C11#59511yescharacteristic, complemented, Hall
26C32×Dic11—851noHall
27C11×D17—51no—
28#66776—111noHall
29C3×D5×C11—174no—
30C32×D17—51no—
31C3×C5×C17C3×Dic1114yescomplemented
32C11⋊AGL(1,𝔽5)—171noHall
33C3×#595—554no—
34C2×C32×C11—851no—
35C11×C17C32×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
36C32×AGL(1,𝔽5)—1871noHall
37D85C32×D1111yescharacteristic
38C3×C5×C11C3×#59514yescomplemented
39C32×C17C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
40C3×Dic11—854no—
41D5×C11—171no—
42C3×D17—54no—
43C32×C11#6677611yescharacteristic, complemented, Hall
44C32×D5—171no—
45C5×C17C32×Dic1111yescharacteristic, complemented, Hall
46#595—551noHall
47C2×C3×C11—854no—
48C3×AGL(1,𝔽5)—1874no—
49C5×C11C32×#59511yescharacteristic, complemented, Hall
50C3×C17C3×C11⋊AGL(1,𝔽5)14yescomplemented
51C32×C5C11⋊#59511yescharacteristic, complemented, Hall
52Dic11—851noHall
53C32×C4—9351noHall
54D17—51no—
55C3×C11C3×#6677614yescomplemented
56C3×D5—174no—
57C2×C11—851no—
58AGL(1,𝔽5)—1871noHall
59C2×C32—851no—
60C17C32×C11⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
61C3×C5C3×C11⋊#59514yescomplemented
62C3×C4—9354no—
63C11C32×#6677611yescharacteristic, complemented, Sylow
64D5—171no—
65C32C11⋊#6677611yescharacteristic, direct product factor, Sylow
66C2×C3—854no—
67C5C32×C11⋊#59511yescharacteristic, complemented, Sylow
68C4—9351noSylow
69C3C3×C11⋊#6677614yesdirect product factor
70C2—851no—
subgroupG/H
center, hypercenterC32C11⋊#66776
commutator, hypocenterC5×C11×C17C32×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×C11×D85C2
cosocleC11×D85C2×C32
LCSG ▷ C5×C11×C17
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
2. C3×C11⋊#66776C3direct (N × H)
3. C32×C5×C11×C17C4semidirect
6. C11⋊#66776C32direct (N × H)
9. C3×C5×C11×C17C3×C4semidirect
13. C32×C11×C17AGL(1,𝔽5)semidirect
18. C5×C11×C17C32×C4semidirect
19. C32×C5×C17Dic11semidirect
23. C3×C11×C17C3×AGL(1,𝔽5)semidirect
25. C32×C5×C11#595semidirect
31. C3×C5×C17C3×Dic11semidirect
35. C11×C17C32×AGL(1,𝔽5)semidirect
38. C3×C5×C11C3×#595semidirect
39. C32×C17C11⋊AGL(1,𝔽5)semidirect
43. C32×C11#66776semidirect
45. C5×C17C32×Dic11semidirect
49. C5×C11C32×#595semidirect
50. C3×C17C3×C11⋊AGL(1,𝔽5)semidirect
51. C32×C5C11⋊#595semidirect
55. C3×C11C3×#66776semidirect
60. C17C32×C11⋊AGL(1,𝔽5)semidirect
61. C3×C5C3×C11⋊#595semidirect
63. C11C32×#66776semidirect
65. C32C11⋊#66776direct (N × H)
67. C5C32×C11⋊#595semidirect
69. C3C3×C11⋊#66776direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×D852
C3×C11⋊#667763
C32×C11⋊#5955
C32×#6677611
C32×C11⋊AGL(1,𝔽5)17