Finite Group Databasebeta

← C2×C3×C11×C5⋊(C7⋊D7) #44568941

Subgroups — C2×C3×C11×C5⋊(C7⋊D7) #44568941

Order 32340.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×C5⋊(C7⋊D7)C212yesmaximal, direct product factor
2C2×C3×C5×C72×C11C211yesmaximal, characteristic, complemented
3C2×C11×C5⋊(C7⋊D7)C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C2×C3×C11×C7⋊D7—51nomaximal, Hall
6C11×C5⋊(C7⋊D7)C2×C312yesdirect product factor
7C2×C5×C72×C11C2×C311yescharacteristic, complemented
8C2×C3×C11×D35—78nomaximal
9C3×C11×C7⋊D7—52no—
10C2×C3×C72×C11D511yescharacteristic, complemented
11C2×C3×C5⋊(C7⋊D7)C1111yesmaximal, characteristic, direct product factor, Hall
12C5×C72×C11C22×C311yescharacteristic, complemented, Hall
13C3×C11×D35—716no—
14C2×C3×C5×C7×C11D718yescomplemented
15C2×C11×C7⋊D7—51noHall
16C3×C72×C11C2×D511yescharacteristic, complemented, Hall
17C2×C11×D35—78no—
18C2×C3×C5×C72C2×C1111yescharacteristic, complemented
19C3×C5⋊(C7⋊D7)C2×C1112yesdirect product factor
20C3×C5×C7×C11C2×D718yescomplemented
21C2×C72×C11C3×D511yescharacteristic, complemented
22C11×C7⋊D7—52no—
23C2×C5⋊(C7⋊D7)C3×C1111yescharacteristic, direct product factor, Hall
24C2×C3×C11×D7—358no—
25C2×C5×C7×C11C3×D718yescomplemented
26C11×D35—716no—
27C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
28C2×C3×D5×C11—491noHall
29C2×C3×C7⋊D7—51noHall
30C72×C11C2×C3×D511yescharacteristic, complemented, Hall
31C2×C5×C72C2×C3×C1111yescharacteristic, complemented
32C5⋊(C7⋊D7)C2×C3×C1112yesdirect product factor
33C2×C3×C7×C11D3518yescomplemented
34C3×C11×D7—3516no—
35C2×C3×D35—78no—
36C5×C7×C11C2×C3×D718yescomplemented
37C2×C3×C5×C11C7⋊D711yescharacteristic, complemented
38C3×D5×C11—492no—
39C2×C11×D7—358no—
40C2×C3×C72D5×C1111yescharacteristic, complemented
41C3×C7⋊D7—52no—
42C5×C72C22×C3×C1111yescharacteristic, complemented, Hall
43C3×C7×C11C2×D3518yescomplemented
44C2×D5×C11—491noHall
45C2×C3×C5×C7C11×D718yescomplemented
46C3×D35—716no—
47C2×C7⋊D7—51noHall
48C3×C5×C11C2×C7⋊D711yescharacteristic, complemented, Hall
49C2×C7×C11C3×D3518yescomplemented
50C11×D7—3516no—
51C3×C72C2×D5×C1111yescharacteristic, complemented, Hall
52C2×D35—78no—
53C22×C3×C11—2451noHall
54C2×C5×C11C3×C7⋊D711yescharacteristic, complemented
55D5×C11—492no—
56C3×C5×C7C2×C11×D718yescomplemented
57C2×C72C3×D5×C1111yescharacteristic, complemented
58C7⋊D7—52no—
59C2×C3×D7—358no—
60C7×C11C2×C3×D3518yescomplemented
61C2×C5×C7C3×C11×D718yescomplemented
62D35—716no—
63C2×C3×C11—2452no—
64C2×C3×C11C5⋊(C7⋊D7)11yescharacteristic, direct product factor
65C2×C3×D5—491noHall
66C5×C11C2×C3×C7⋊D711yescharacteristic, complemented, Hall
67C72C2×C3×D5×C1111yescharacteristic, complemented, Sylow
68C22×C11—2451noHall
69C2×C3×C7C11×D3518yescomplemented
70C3×D7—3516no—
71C5×C7C2×C3×C11×D718yescomplemented
72C3×C11C2×C5⋊(C7⋊D7)11yescharacteristic, direct product factor, Hall
73C2×C3×C5C11×C7⋊D711yescharacteristic, complemented
74C3×D5—492no—
75C2×D7—358no—
76C2×C11—2452no—
77C2×C11C3×C5⋊(C7⋊D7)11yescharacteristic, direct product factor
78C3×C7C2×C11×D3518yescomplemented
79C2×D5—491noHall
80C3×C5C2×C11×C7⋊D711yescharacteristic, complemented, Hall
81C2×C7C3×C11×D3518yescomplemented
82D7—3516no—
83C22×C3—2451noHall
84C11C2×C3×C5⋊(C7⋊D7)11yescharacteristic, direct product factor, Sylow
85C2×C5C3×C11×C7⋊D711yescharacteristic, complemented
86D5—492no—
87C7C2×C3×C11×D3518yescomplemented
88C2×C3—2452no—
89C2×C3C11×C5⋊(C7⋊D7)11yescharacteristic, direct product factor
90C5C2×C3×C11×C7⋊D711yescharacteristic, complemented, Sylow
91C22—2451noSylow
92C3C2×C11×C5⋊(C7⋊D7)11yescharacteristic, direct product factor, Sylow
93C2—2452no—
94C2C3×C11×C5⋊(C7⋊D7)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11C5⋊(C7⋊D7)
commutator, cosocle, hypocenterC5×C72C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C5×C72
UCSC1 ◁ C2×C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×C5⋊(C7⋊D7)C2direct (N × H)
2. C2×C3×C5×C72×C11C2semidirect
3. C2×C11×C5⋊(C7⋊D7)C3direct (N × H)
4. C3×C5×C72×C11C22semidirect
6. C11×C5⋊(C7⋊D7)C2×C3direct (N × H)
7. C2×C5×C72×C11C2×C3semidirect
10. C2×C3×C72×C11D5semidirect
11. C2×C3×C5⋊(C7⋊D7)C11direct (N × H)
12. C5×C72×C11C22×C3semidirect
14. C2×C3×C5×C7×C11D7semidirect
16. C3×C72×C11C2×D5semidirect
18. C2×C3×C5×C72C2×C11semidirect
19. C3×C5⋊(C7⋊D7)C2×C11direct (N × H)
20. C3×C5×C7×C11C2×D7semidirect
21. C2×C72×C11C3×D5semidirect
23. C2×C5⋊(C7⋊D7)C3×C11direct (N × H)
25. C2×C5×C7×C11C3×D7semidirect
27. C3×C5×C72C22×C11semidirect
30. C72×C11C2×C3×D5semidirect
31. C2×C5×C72C2×C3×C11semidirect
32. C5⋊(C7⋊D7)C2×C3×C11direct (N × H)
33. C2×C3×C7×C11D35semidirect
36. C5×C7×C11C2×C3×D7semidirect
37. C2×C3×C5×C11C7⋊D7semidirect
40. C2×C3×C72D5×C11semidirect
42. C5×C72C22×C3×C11semidirect
43. C3×C7×C11C2×D35semidirect
45. C2×C3×C5×C7C11×D7semidirect
48. C3×C5×C11C2×C7⋊D7semidirect
49. C2×C7×C11C3×D35semidirect
51. C3×C72C2×D5×C11semidirect
54. C2×C5×C11C3×C7⋊D7semidirect
56. C3×C5×C7C2×C11×D7semidirect
57. C2×C72C3×D5×C11semidirect
60. C7×C11C2×C3×D35semidirect
61. C2×C5×C7C3×C11×D7semidirect
64. C2×C3×C11C5⋊(C7⋊D7)direct (N × H)
66. C5×C11C2×C3×C7⋊D7semidirect
67. C72C2×C3×D5×C11semidirect
69. C2×C3×C7C11×D35semidirect
71. C5×C7C2×C3×C11×D7semidirect
72. C3×C11C2×C5⋊(C7⋊D7)direct (N × H)
73. C2×C3×C5C11×C7⋊D7semidirect
77. C2×C11C3×C5⋊(C7⋊D7)direct (N × H)
78. C3×C7C2×C11×D35semidirect
80. C3×C5C2×C11×C7⋊D7semidirect
81. C2×C7C3×C11×D35semidirect
84. C11C2×C3×C5⋊(C7⋊D7)direct (N × H)
85. C2×C5C3×C11×C7⋊D7semidirect
87. C7C2×C3×C11×D35semidirect
89. C2×C3C11×C5⋊(C7⋊D7)direct (N × H)
90. C5C2×C3×C11×C7⋊D7semidirect
92. C3C2×C11×C5⋊(C7⋊D7)direct (N × H)
94. C2C3×C11×C5⋊(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
C3×C11×C5⋊(C7⋊D7)2
C2×C3×C5×C72×C112
C2×C11×C5⋊(C7⋊D7)3
C2×C3×C11×C7⋊D75
C2×C3×C11×D357
C2×C3×C5⋊(C7⋊D7)11