Finite Group Databasebeta

← C2×C5×C11×C3⋊(C7⋊D7) #44568947

Subgroups — C2×C5×C11×C3⋊(C7⋊D7) #44568947

Order 32340.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C11×C3⋊(C7⋊D7)C212yesmaximal, direct product factor
2C2×C3×C5×C72×C11C211yesmaximal, characteristic, complemented
3C2×C5×C11×C7⋊D7—31nomaximal, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C2×C11×C3⋊(C7⋊D7)C511yesmaximal, characteristic, direct product factor, Hall
6C5×C11×C7⋊D7—32no—
7C2×C5×C72×C11D311yescharacteristic, complemented
8C2×C5×C11×D21—78nomaximal
9C11×C3⋊(C7⋊D7)C2×C512yesdirect product factor
10C2×C3×C72×C11C2×C511yescharacteristic, complemented
11C2×C5×C3⋊(C7⋊D7)C1111yesmaximal, characteristic, direct product factor, Hall
12C5×C72×C11C2×D311yescharacteristic, complemented, Hall
13C5×C11×D21—716no—
14C2×C3×C5×C7×C11D718yescomplemented
15C2×C11×C7⋊D7—31noHall
16C3×C72×C11C22×C511yescharacteristic, complemented, Hall
17C2×C5×C11×D7—218no—
18C2×C3×C5×C72C2×C1111yescharacteristic, complemented
19C5×C3⋊(C7⋊D7)C2×C1112yesdirect product factor
20C3×C5×C7×C11C2×D718yescomplemented
21C2×C72×C11C5×D311yescharacteristic, complemented
22C11×C7⋊D7—32no—
23C2×C5×C7⋊D7—31noHall
24C2×C11×D21—78no—
25C2×C5×C7×C11D2118yescomplemented
26C5×C11×D7—2116no—
27C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
28C2×C5×D3×C11—491noHall
29C2×C3⋊(C7⋊D7)C5×C1111yescharacteristic, direct product factor, Hall
30C72×C11C2×C5×D311yescharacteristic, complemented, Hall
31C2×C5×C72D3×C1111yescharacteristic, complemented
32C5×C7⋊D7—32no—
33C2×C3×C7×C11C5×D718yescomplemented
34C11×D21—716no—
35C2×C5×D21—78no—
36C5×C7×C11C2×D2118yescomplemented
37C2×C3×C5×C11C7⋊D711yescharacteristic, complemented
38C5×D3×C11—492no—
39C2×C11×D7—218no—
40C2×C3×C72C2×C5×C1111yescharacteristic, complemented
41C3⋊(C7⋊D7)C2×C5×C1112yesdirect product factor
42C5×C72C2×D3×C1111yescharacteristic, complemented, Hall
43C3×C7×C11C2×C5×D718yescomplemented
44C22×C5×C11—1471noHall
45C2×C3×C5×C7C11×D718yescomplemented
46C5×D21—716no—
47C2×C7⋊D7—31noHall
48C3×C5×C11C2×C7⋊D711yescharacteristic, complemented, Hall
49C2×C7×C11C5×D2118yescomplemented
50C11×D7—2116no—
51C3×C72C22×C5×C1111yescharacteristic, complemented, Hall
52C2×C5×D7—218no—
53C2×D3×C11—491noHall
54C2×C5×C11—1472no—
55C2×C5×C11C3⋊(C7⋊D7)11yescharacteristic, direct product factor
56C3×C5×C7C2×C11×D718yescomplemented
57C2×C72C5×D3×C1111yescharacteristic, complemented
58C7⋊D7—32no—
59C2×D21—78no—
60C7×C11C2×C5×D2118yescomplemented
61C2×C5×C7C11×D2118yescomplemented
62C5×D7—2116no—
63C2×C3×C11C5×C7⋊D711yescharacteristic, complemented
64D3×C11—492no—
65C2×C5×D3—491noHall
66C5×C11C2×C3⋊(C7⋊D7)11yescharacteristic, direct product factor, Hall
67C72C2×C5×D3×C1111yescharacteristic, complemented, Sylow
68C22×C11—1471noHall
69C2×C3×C7C5×C11×D718yescomplemented
70D21—716no—
71C5×C7C2×C11×D2118yescomplemented
72C3×C11C2×C5×C7⋊D711yescharacteristic, complemented, Hall
73C2×C3×C5C11×C7⋊D711yescharacteristic, complemented
74C5×D3—492no—
75C2×D7—218no—
76C2×C11—1472no—
77C2×C11C5×C3⋊(C7⋊D7)11yescharacteristic, direct product factor
78C3×C7C2×C5×C11×D718yescomplemented
79C22×C5—1471noHall
80C3×C5C2×C11×C7⋊D711yescharacteristic, complemented, Hall
81C2×C7C5×C11×D2118yescomplemented
82D7—2116no—
83C2×D3—491noHall
84C11C2×C5×C3⋊(C7⋊D7)11yescharacteristic, direct product factor, Sylow
85C2×C5—1472no—
86C2×C5C11×C3⋊(C7⋊D7)11yescharacteristic, direct product factor
87C7C2×C5×C11×D2118yescomplemented
88C2×C3C5×C11×C7⋊D711yescharacteristic, complemented
89D3—492no—
90C5C2×C11×C3⋊(C7⋊D7)11yescharacteristic, direct product factor, Sylow
91C22—1471noSylow
92C3C2×C5×C11×C7⋊D711yescharacteristic, complemented, Sylow
93C2—1472no—
94C2C5×C11×C3⋊(C7⋊D7)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C11C3⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C72C22×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C3×C72
UCSC1 ◁ C2×C5×C11

Complements

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

NH ≅ G/Ntype
1. C5×C11×C3⋊(C7⋊D7)C2direct (N × H)
2. C2×C3×C5×C72×C11C2semidirect
4. C3×C5×C72×C11C22semidirect
5. C2×C11×C3⋊(C7⋊D7)C5direct (N × H)
7. C2×C5×C72×C11D3semidirect
9. C11×C3⋊(C7⋊D7)C2×C5direct (N × H)
10. C2×C3×C72×C11C2×C5semidirect
11. C2×C5×C3⋊(C7⋊D7)C11direct (N × H)
12. C5×C72×C11C2×D3semidirect
14. C2×C3×C5×C7×C11D7semidirect
16. C3×C72×C11C22×C5semidirect
18. C2×C3×C5×C72C2×C11semidirect
19. C5×C3⋊(C7⋊D7)C2×C11direct (N × H)
20. C3×C5×C7×C11C2×D7semidirect
21. C2×C72×C11C5×D3semidirect
25. C2×C5×C7×C11D21semidirect
27. C3×C5×C72C22×C11semidirect
29. C2×C3⋊(C7⋊D7)C5×C11direct (N × H)
30. C72×C11C2×C5×D3semidirect
31. C2×C5×C72D3×C11semidirect
33. C2×C3×C7×C11C5×D7semidirect
36. C5×C7×C11C2×D21semidirect
37. C2×C3×C5×C11C7⋊D7semidirect
40. C2×C3×C72C2×C5×C11semidirect
41. C3⋊(C7⋊D7)C2×C5×C11direct (N × H)
42. C5×C72C2×D3×C11semidirect
43. C3×C7×C11C2×C5×D7semidirect
45. C2×C3×C5×C7C11×D7semidirect
48. C3×C5×C11C2×C7⋊D7semidirect
49. C2×C7×C11C5×D21semidirect
51. C3×C72C22×C5×C11semidirect
55. C2×C5×C11C3⋊(C7⋊D7)direct (N × H)
56. C3×C5×C7C2×C11×D7semidirect
57. C2×C72C5×D3×C11semidirect
60. C7×C11C2×C5×D21semidirect
61. C2×C5×C7C11×D21semidirect
63. C2×C3×C11C5×C7⋊D7semidirect
66. C5×C11C2×C3⋊(C7⋊D7)direct (N × H)
67. C72C2×C5×D3×C11semidirect
69. C2×C3×C7C5×C11×D7semidirect
71. C5×C7C2×C11×D21semidirect
72. C3×C11C2×C5×C7⋊D7semidirect
73. C2×C3×C5C11×C7⋊D7semidirect
77. C2×C11C5×C3⋊(C7⋊D7)direct (N × H)
78. C3×C7C2×C5×C11×D7semidirect
80. C3×C5C2×C11×C7⋊D7semidirect
81. C2×C7C5×C11×D21semidirect
84. C11C2×C5×C3⋊(C7⋊D7)direct (N × H)
86. C2×C5C11×C3⋊(C7⋊D7)direct (N × H)
87. C7C2×C5×C11×D21semidirect
88. C2×C3C5×C11×C7⋊D7semidirect
90. C5C2×C11×C3⋊(C7⋊D7)direct (N × H)
92. C3C2×C5×C11×C7⋊D7semidirect
94. C2C5×C11×C3⋊(C7⋊D7)direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C11×C3⋊(C7⋊D7)2
C2×C3×C5×C72×C112
C2×C5×C11×C7⋊D73
C2×C11×C3⋊(C7⋊D7)5
C2×C5×C11×D217
C2×C5×C3⋊(C7⋊D7)11