Finite Group Databasebeta

← C11×C17×#4380 #46778044

Subgroups — C11×C17×#4380 #46778044

Order 33660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C17×C3⋊D15C211yesmaximal, characteristic
2C32×C5×C11×C17C411yescharacteristic, complemented, Hall
3C11×C17×#157—51nomaximal, Hall
4C11×C17×D15—62no—
5C11×C17×AGL(1,𝔽5)—91nomaximal, Hall
6C11×C17×C3⋊D3—51no—
7C17×#4380C1111yesmaximal, characteristic, direct product factor, Hall
8C3×C5×C11×C17—22no—
9C11×#4380C1711yesmaximal, characteristic, direct product factor, Hall
10D5×C11×C17—91no—
11C32×C11×C17AGL(1,𝔽5)11yescharacteristic, complemented, Hall
12C17×C3⋊D15C2×C1111yescharacteristic
13D3×C11×C17—302no—
14C11×C3⋊D15C2×C1711yescharacteristic
15C5×C11×C17#15711yescharacteristic, complemented, Hall
16C32×C5×C17C4×C1111yescharacteristic, complemented, Hall
17C4×C11×C17—451noHall
18C17×#157—51noHall
19C3×C11×C17—22no—
20C17×D15—62no—
21C32×C5×C11C4×C1711yescharacteristic, complemented, Hall
22C11×#157—51noHall
23C2×C11×C17—451no—
24C17×AGL(1,𝔽5)—91noHall
25C11×D15—62no—
26C17×C3⋊D3—51no—
27C3×C5×C17—22no—
28C11×AGL(1,𝔽5)—91noHall
29C11×C3⋊D3—51no—
30C11×C17#438011yescharacteristic, direct product factor, Hall
31#4380C11×C1711yescharacteristic, direct product factor, Hall
32D5×C17—91no—
33C3×C5×C11—22no—
34C32×C17C11×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
35D5×C11—91no—
36D3×C17—302no—
37C32×C11C17×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
38C3⋊D15C2×C11×C1711yescharacteristic
39C5×C17C11×#15711yescharacteristic, complemented, Hall
40C4×C17—451noHall
41D3×C11—302no—
42C5×C11C17×#15711yescharacteristic, complemented, Hall
43C3×C17—22no—
44C32×C5C4×C11×C1711yescharacteristic, complemented, Hall
45C4×C11—451noHall
46#157—51noHall
47C2×C17—451no—
48C3×C11—22no—
49D15—62no—
50C2×C11—451no—
51AGL(1,𝔽5)—91noHall
52C3⋊D3—51no—
53C17C11×#438011yescharacteristic, direct product factor, Sylow
54C3×C5—22no—
55C11C17×#438011yescharacteristic, direct product factor, Sylow
56D5—91no—
57C32C11×C17×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
58D3—302no—
59C5C11×C17×#15711yescharacteristic, complemented, Sylow
60C4—451noSylow
61C3—22no—
62C2—451no—
subgroupG/H
center, hypercenterC11×C17#4380
commutator, hypocenterC32×C5C4×C11×C17
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC11×C17×C3⋊D15C2
cosocleC3⋊D15C2×C11×C17
LCSG ▷ C32×C5
UCSC1 ◁ C11×C17

Complements

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

NH ≅ G/Ntype
2. C32×C5×C11×C17C4semidirect
7. C17×#4380C11direct (N × H)
9. C11×#4380C17direct (N × H)
11. C32×C11×C17AGL(1,𝔽5)semidirect
15. C5×C11×C17#157semidirect
16. C32×C5×C17C4×C11semidirect
21. C32×C5×C11C4×C17semidirect
30. C11×C17#4380direct (N × H)
31. #4380C11×C17direct (N × H)
34. C32×C17C11×AGL(1,𝔽5)semidirect
37. C32×C11C17×AGL(1,𝔽5)semidirect
39. C5×C17C11×#157semidirect
42. C5×C11C17×#157semidirect
44. C32×C5C4×C11×C17semidirect
53. C17C11×#4380direct (N × H)
55. C11C17×#4380direct (N × H)
57. C32C11×C17×AGL(1,𝔽5)semidirect
59. C5C11×C17×#157semidirect

Maximal subgroups

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

subgroupindex
C11×C17×C3⋊D152
C11×C17×#1575
C11×C17×AGL(1,𝔽5)9
C17×#438011
C11×#438017