Finite Group Databasebeta

← C2×C17×C3⋊D3×C11⋊C5 #46778035

Subgroups — C2×C17×C3⋊D3×C11⋊C5 #46778035

Order 33660.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C17×C11⋊C5C211yesmaximal, characteristic, complemented
2C17×C3⋊D3×C11⋊C5C212yesmaximal, direct product factor
3C2×D3×C17×C11⋊C5—34nomaximal
4C32×C17×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×C11×C17×C3⋊D3C511yesmaximal, characteristic, complemented, Hall
6D3×C17×C11⋊C5—38no—
7C2×C3×C17×C11⋊C5D314yescomplemented
8C22×C17×C11⋊C5—91noHall
9C11×C17×C3⋊D3C2×C512yescomplemented
10C2×C32×C11×C17C2×C511yescharacteristic, complemented
11C2×C5×C17×C3⋊D3—111nomaximal, Hall
12C3×C17×C11⋊C5C2×D314yescomplemented
13C2×D3×C11×C17—34no—
14C2×C3⋊D3×C11⋊C5C1711yesmaximal, characteristic, direct product factor, Hall
15C2×C17×C11⋊C5—92no—
16C2×C17×C11⋊C5C3⋊D311yescharacteristic, direct product factor
17C32×C11×C17C22×C511yescharacteristic, complemented, Hall
18C2×C32×C5×C17—111no—
19C5×C17×C3⋊D3—112no—
20C2×C3×C11×C17C5×D314yescomplemented
21D3×C11×C17—38no—
22C2×C5×D3×C17—334no—
23C2×C32×C11⋊C5C2×C1711yescharacteristic, complemented
24C3⋊D3×C11⋊C5C2×C1712yesdirect product factor
25C17×C11⋊C5C2×C3⋊D311yescharacteristic, direct product factor, Hall
26C32×C5×C17—111noHall
27C22×C11×C17—91noHall
28C2×D3×C11⋊C5—34no—
29C2×C17×C3⋊D3C11⋊C511yescharacteristic, direct product factor, Hall
30C3×C11×C17C2×C5×D314yescomplemented
31C2×C3×C5×C17—114no—
32C5×D3×C17—338no—
33C32×C11⋊C5C22×C1711yescharacteristic, complemented, Hall
34C2×C11×C3⋊D3C5×C1711yescharacteristic, complemented, Hall
35C2×C11×C17—92no—
36C2×C11×C17C5×C3⋊D311yescharacteristic, complemented
37C22×C5×C17—991noHall
38C2×C3×C11⋊C5D3×C1714yescomplemented
39D3×C11⋊C5—38no—
40C2×C32×C17C2×C11⋊C511yescharacteristic, complemented
41C17×C3⋊D3C2×C11⋊C512yesdirect product factor
42C3×C5×C17—114no—
43C22×C11⋊C5—91noHall
44C2×D3×C17—34no—
45C2×C32×C11C2×C5×C1711yescharacteristic, complemented
46C11×C3⋊D3C2×C5×C1712yescomplemented
47C11×C17C2×C5×C3⋊D311yescharacteristic, complemented, Hall
48C2×C5×C3⋊D3—111noHall
49C2×C5×C17—111no—
50C2×C5×C17—992no—
51C3×C11⋊C5C2×D3×C1714yescomplemented
52C32×C17C22×C11⋊C511yescharacteristic, complemented, Hall
53C2×D3×C11—34no—
54C2×C11⋊C5—92no—
55C2×C11⋊C5C17×C3⋊D311yescharacteristic, direct product factor
56C2×C3×C17D3×C11⋊C514yescomplemented
57D3×C17—38no—
58C32×C11C22×C5×C1711yescharacteristic, complemented, Hall
59C2×C32×C5—111no—
60C5×C3⋊D3—112no—
61C5×C17—111noHall
62C22×C17—91noHall
63C2×C3×C11C5×D3×C1714yescomplemented
64D3×C11—38no—
65C2×C5×D3—334no—
66C11⋊C5C2×C17×C3⋊D311yescharacteristic, direct product factor, Hall
67C3×C17C2×D3×C11⋊C514yescomplemented
68C32×C5—111noHall
69C22×C11—91noHall
70C2×C3⋊D3C17×C11⋊C511yescharacteristic, direct product factor, Hall
71C2×C17—92no—
72C2×C17C3⋊D3×C11⋊C511yescharacteristic, direct product factor
73C3×C11C2×C5×D3×C1714yescomplemented
74C2×C3×C5—114no—
75C5×D3—338no—
76C2×C11—92no—
77C2×C11C5×C17×C3⋊D311yescharacteristic, complemented
78C22×C5—991noHall
79C2×C32C2×C17×C11⋊C511yescharacteristic, complemented
80C3⋊D3C2×C17×C11⋊C512yesdirect product factor
81C17C2×C3⋊D3×C11⋊C511yescharacteristic, direct product factor, Sylow
82C3×C5—114no—
83C2×D3—34no—
84C11C2×C5×C17×C3⋊D311yescharacteristic, complemented, Sylow
85C2×C5—111no—
86C2×C5—992no—
87C32C22×C17×C11⋊C511yescharacteristic, complemented, Sylow
88C2×C3D3×C17×C11⋊C514yescomplemented
89D3—38no—
90C5—111noSylow
91C22—91noSylow
92C3C2×D3×C17×C11⋊C514yescomplemented
93C2—92no—
94C2C17×C3⋊D3×C11⋊C511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C17C3⋊D3×C11⋊C5
commutator, cosocle, hypocenterC32×C11C22×C5×C17
FrattiniC1G
Fitting, socleC2×C32×C11×C17C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C2×C17

Complements

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

NH ≅ G/Ntype
1. C2×C32×C17×C11⋊C5C2semidirect
2. C17×C3⋊D3×C11⋊C5C2direct (N × H)
4. C32×C17×C11⋊C5C22semidirect
5. C2×C11×C17×C3⋊D3C5semidirect
7. C2×C3×C17×C11⋊C5D3semidirect
9. C11×C17×C3⋊D3C2×C5semidirect
10. C2×C32×C11×C17C2×C5semidirect
12. C3×C17×C11⋊C5C2×D3semidirect
14. C2×C3⋊D3×C11⋊C5C17direct (N × H)
16. C2×C17×C11⋊C5C3⋊D3direct (N × H)
17. C32×C11×C17C22×C5semidirect
20. C2×C3×C11×C17C5×D3semidirect
23. C2×C32×C11⋊C5C2×C17semidirect
24. C3⋊D3×C11⋊C5C2×C17direct (N × H)
25. C17×C11⋊C5C2×C3⋊D3direct (N × H)
29. C2×C17×C3⋊D3C11⋊C5direct (N × H)
30. C3×C11×C17C2×C5×D3semidirect
33. C32×C11⋊C5C22×C17semidirect
34. C2×C11×C3⋊D3C5×C17semidirect
36. C2×C11×C17C5×C3⋊D3semidirect
38. C2×C3×C11⋊C5D3×C17semidirect
40. C2×C32×C17C2×C11⋊C5semidirect
41. C17×C3⋊D3C2×C11⋊C5direct (N × H)
45. C2×C32×C11C2×C5×C17semidirect
46. C11×C3⋊D3C2×C5×C17semidirect
47. C11×C17C2×C5×C3⋊D3semidirect
51. C3×C11⋊C5C2×D3×C17semidirect
52. C32×C17C22×C11⋊C5semidirect
55. C2×C11⋊C5C17×C3⋊D3direct (N × H)
56. C2×C3×C17D3×C11⋊C5semidirect
58. C32×C11C22×C5×C17semidirect
63. C2×C3×C11C5×D3×C17semidirect
66. C11⋊C5C2×C17×C3⋊D3direct (N × H)
67. C3×C17C2×D3×C11⋊C5semidirect
70. C2×C3⋊D3C17×C11⋊C5direct (N × H)
72. C2×C17C3⋊D3×C11⋊C5direct (N × H)
73. C3×C11C2×C5×D3×C17semidirect
77. C2×C11C5×C17×C3⋊D3semidirect
79. C2×C32C2×C17×C11⋊C5semidirect
80. C3⋊D3C2×C17×C11⋊C5direct (N × H)
81. C17C2×C3⋊D3×C11⋊C5direct (N × H)
84. C11C2×C5×C17×C3⋊D3semidirect
87. C32C22×C17×C11⋊C5semidirect
88. C2×C3D3×C17×C11⋊C5semidirect
92. C3C2×D3×C17×C11⋊C5semidirect
94. C2C17×C3⋊D3×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C17×C11⋊C52
C17×C3⋊D3×C11⋊C52
C2×D3×C17×C11⋊C53
C2×C11×C17×C3⋊D35
C2×C5×C17×C3⋊D311
C2×C3⋊D3×C11⋊C517