Finite Group Databasebeta

← C2×C11×C3⋊D195 #38788321

Subgroups — C2×C11×C3⋊D195 #38788321

Order 25740.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C3⋊D195C212yesmaximal, direct product factor
2C2×C32×C5×C11×C13C211yesmaximal, characteristic, complemented
3C2×C11×D195—34nomaximal
4C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
5C2×C11×C3⋊D39—51nomaximal, Hall
6C11×D195—38no—
7C2×C3×C5×C11×C13D314yescomplemented
8C2×C11×D65—91noHall
9C11×C3⋊D39—52no—
10C2×C32×C11×C13D511yescharacteristic, complemented
11C2×C3⋊D195C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C5×C11×C13C2×D314yescomplemented
13C2×C11×C3⋊D15—131nomaximal, Hall
14C2×C11×D39—154no—
15C2×C5×C11×C13C3⋊D311yescharacteristic, complemented
16C11×D65—92no—
17C32×C11×C13C2×D511yescharacteristic, complemented, Hall
18C2×C32×C5×C13C2×C1111yescharacteristic, complemented
19C3⋊D195C2×C1112yesdirect product factor
20C2×C32×C5×C11D1311yescharacteristic, complemented
21C11×C3⋊D15—132no—
22C2×C3×C11×C13D1514yescomplemented
23C11×D39—158no—
24C2×D195—34no—
25C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
26C2×C11×D15—394no—
27C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
28C2×C11×D13—451noHall
29C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
30C2×C3⋊D39—51noHall
31C3×C11×C13C2×D1514yescomplemented
32C2×C11×C3⋊D3—651noHall
33C2×C3×C5×C13D3×C1114yescomplemented
34D195—38no—
35C2×C3×C5×C11D3914yescomplemented
36C11×D15—398no—
37C2×C11×C13C3⋊D1511yescharacteristic, complemented
38C11×D13—452no—
39C2×D65—91noHall
40C2×C32×C13D5×C1111yescharacteristic, complemented
41C3⋊D39—52no—
42C2×D5×C11—1171noHall
43C2×C32×C11D6511yescharacteristic, complemented
44C11×C3⋊D3—652no—
45C3×C5×C13C2×D3×C1114yescomplemented
46C2×C3⋊D15—131noHall
47C3×C5×C11C2×D3914yescomplemented
48C2×D39—154no—
49C11×C13C2×C3⋊D1511yescharacteristic, complemented, Hall
50C2×D3×C11—1954no—
51C2×C5×C13C11×C3⋊D311yescharacteristic, complemented
52D65—92no—
53C32×C13C2×D5×C1111yescharacteristic, complemented, Hall
54C2×C5×C11C3⋊D3911yescharacteristic, complemented
55D5×C11—1172no—
56C32×C11C2×D6511yescharacteristic, complemented, Hall
57C2×C32×C5C11×D1311yescharacteristic, complemented
58C3⋊D15—132no—
59C2×C3×C13C11×D1514yescomplemented
60D39—158no—
61C2×C3×C11D19514yescomplemented
62D3×C11—1958no—
63C5×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
64C2×D15—394no—
65C5×C11C2×C3⋊D3911yescharacteristic, complemented, Hall
66C2×D13—451noHall
67C32×C5C2×C11×D1311yescharacteristic, complemented, Hall
68C22×C11—5851noHall
69C3×C13C2×C11×D1514yescomplemented
70C2×C3⋊D3—651noHall
71C3×C11C2×D19514yescomplemented
72C2×C3×C5C11×D3914yescomplemented
73D15—398no—
74C2×C13C11×C3⋊D1511yescharacteristic, complemented
75D13—452no—
76C2×C11—5852no—
77C2×C11C3⋊D19511yescharacteristic, direct product factor
78C2×D5—1171noHall
79C2×C32C11×D6511yescharacteristic, complemented
80C3⋊D3—652no—
81C3×C5C2×C11×D3914yescomplemented
82C13C2×C11×C3⋊D1511yescharacteristic, complemented, Sylow
83C2×D3—1954no—
84C11C2×C3⋊D19511yescharacteristic, direct product factor, Sylow
85C2×C5C11×C3⋊D3911yescharacteristic, complemented
86D5—1172no—
87C32C2×C11×D6511yescharacteristic, complemented, Sylow
88C2×C3C11×D19514yescomplemented
89D3—1958no—
90C5C2×C11×C3⋊D3911yescharacteristic, complemented, Sylow
91C22—5851noSylow
92C3C2×C11×D19514yescomplemented
93C2—5852no—
94C2C11×C3⋊D19511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C11C3⋊D195
commutator, cosocle, hypocenterC32×C5×C13C22×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C32×C5×C13
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
1. C11×C3⋊D195C2direct (N × H)
2. C2×C32×C5×C11×C13C2semidirect
4. C32×C5×C11×C13C22semidirect
7. C2×C3×C5×C11×C13D3semidirect
10. C2×C32×C11×C13D5semidirect
11. C2×C3⋊D195C11direct (N × H)
12. C3×C5×C11×C13C2×D3semidirect
15. C2×C5×C11×C13C3⋊D3semidirect
17. C32×C11×C13C2×D5semidirect
18. C2×C32×C5×C13C2×C11semidirect
19. C3⋊D195C2×C11direct (N × H)
20. C2×C32×C5×C11D13semidirect
22. C2×C3×C11×C13D15semidirect
25. C5×C11×C13C2×C3⋊D3semidirect
27. C32×C5×C13C22×C11semidirect
29. C32×C5×C11C2×D13semidirect
31. C3×C11×C13C2×D15semidirect
33. C2×C3×C5×C13D3×C11semidirect
35. C2×C3×C5×C11D39semidirect
37. C2×C11×C13C3⋊D15semidirect
40. C2×C32×C13D5×C11semidirect
43. C2×C32×C11D65semidirect
45. C3×C5×C13C2×D3×C11semidirect
47. C3×C5×C11C2×D39semidirect
49. C11×C13C2×C3⋊D15semidirect
51. C2×C5×C13C11×C3⋊D3semidirect
53. C32×C13C2×D5×C11semidirect
54. C2×C5×C11C3⋊D39semidirect
56. C32×C11C2×D65semidirect
57. C2×C32×C5C11×D13semidirect
59. C2×C3×C13C11×D15semidirect
61. C2×C3×C11D195semidirect
63. C5×C13C2×C11×C3⋊D3semidirect
65. C5×C11C2×C3⋊D39semidirect
67. C32×C5C2×C11×D13semidirect
69. C3×C13C2×C11×D15semidirect
71. C3×C11C2×D195semidirect
72. C2×C3×C5C11×D39semidirect
74. C2×C13C11×C3⋊D15semidirect
77. C2×C11C3⋊D195direct (N × H)
79. C2×C32C11×D65semidirect
81. C3×C5C2×C11×D39semidirect
82. C13C2×C11×C3⋊D15semidirect
84. C11C2×C3⋊D195direct (N × H)
85. C2×C5C11×C3⋊D39semidirect
87. C32C2×C11×D65semidirect
88. C2×C3C11×D195semidirect
90. C5C2×C11×C3⋊D39semidirect
92. C3C2×C11×D195semidirect
94. C2C11×C3⋊D195direct (N × H)

Maximal subgroups

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

subgroupindex
C11×C3⋊D1952
C2×C32×C5×C11×C132
C2×C11×D1953
C2×C11×C3⋊D395
C2×C3⋊D19511
C2×C11×C3⋊D1513