Finite Group Databasebeta

← C2×C11×C13×C3⋊D21 #49115028

Subgroups — C2×C11×C13×C3⋊D21 #49115028

Order 36036.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C13×C3⋊D21C212yesmaximal, direct product factor
2C2×C32×C7×C11×C13C211yesmaximal, characteristic, complemented
3C2×C11×C13×D21—34nomaximal
4C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
5C11×C13×D21—38no—
6C2×C3×C7×C11×C13D314yescomplemented
7C2×C11×C13×C3⋊D3—71nomaximal, Hall
8C2×C11×C13×D7—91noHall
9C2×C13×C3⋊D21C1111yesmaximal, characteristic, direct product factor, Hall
10C3×C7×C11×C13C2×D314yescomplemented
11C2×C11×C3⋊D21C1311yesmaximal, characteristic, direct product factor, Hall
12C11×C13×C3⋊D3—72no—
13C2×C32×C11×C13D711yescharacteristic, complemented
14C11×C13×D7—92no—
15C2×C7×C11×C13C3⋊D311yescharacteristic, complemented
16C2×D3×C11×C13—214no—
17C2×C32×C7×C13C2×C1111yescharacteristic, complemented
18C13×C3⋊D21C2×C1112yesdirect product factor
19C2×C32×C7×C11C2×C1311yescharacteristic, complemented
20C11×C3⋊D21C2×C1312yesdirect product factor
21C32×C11×C13C2×D711yescharacteristic, complemented, Hall
22C2×C13×D21—34no—
23C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
24C2×C11×D21—34no—
25C2×C3×C11×C13D2114yescomplemented
26D3×C11×C13—218no—
27C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
28C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
29C22×C11×C13—631noHall
30C2×C3×C7×C13D3×C1114yescomplemented
31C13×D21—38no—
32C2×C13×C3⋊D3—71noHall
33C2×C3×C7×C11D3×C1314yescomplemented
34C11×D21—38no—
35C3×C11×C13C2×D2114yescomplemented
36C2×C11×C3⋊D3—71noHall
37C2×C13×D7—91noHall
38C2×C11×D7—91noHall
39C2×C11×C13—632no—
40C2×C11×C13C3⋊D2111yescharacteristic, direct product factor
41C3×C7×C13C2×D3×C1114yescomplemented
42C2×C3⋊D21C11×C1311yescharacteristic, direct product factor, Hall
43C2×C32×C13C11×D711yescharacteristic, complemented
44C13×C3⋊D3—72no—
45C3×C7×C11C2×D3×C1314yescomplemented
46C2×C32×C11C13×D711yescharacteristic, complemented
47C11×C3⋊D3—72no—
48C2×C7×C13C11×C3⋊D311yescharacteristic, complemented
49C13×D7—92no—
50C2×D3×C13—214no—
51C2×C7×C11C13×C3⋊D311yescharacteristic, complemented
52C11×D7—92no—
53C11×C13C2×C3⋊D2111yescharacteristic, direct product factor, Hall
54C2×D3×C11—214no—
55C2×C32×C7C2×C11×C1311yescharacteristic, complemented
56C3⋊D21C2×C11×C1312yesdirect product factor
57C32×C13C2×C11×D711yescharacteristic, complemented, Hall
58C32×C11C2×C13×D711yescharacteristic, complemented, Hall
59C7×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
60C2×D21—34no—
61C2×C3×C13C11×D2114yescomplemented
62D3×C13—218no—
63C7×C11C2×C13×C3⋊D311yescharacteristic, complemented, Hall
64C2×C3×C11C13×D2114yescomplemented
65D3×C11—218no—
66C32×C7C22×C11×C1311yescharacteristic, complemented, Hall
67C22×C13—631noHall
68C22×C11—631noHall
69C2×C3×C7D3×C11×C1314yescomplemented
70D21—38no—
71C3×C13C2×C11×D2114yescomplemented
72C2×C3⋊D3—71noHall
73C3×C11C2×C13×D2114yescomplemented
74C2×D7—91noHall
75C2×C13—632no—
76C2×C13C11×C3⋊D2111yescharacteristic, direct product factor
77C2×C11—632no—
78C2×C11C13×C3⋊D2111yescharacteristic, direct product factor
79C3×C7C2×D3×C11×C1314yescomplemented
80C2×C32C11×C13×D711yescharacteristic, complemented
81C3⋊D3—72no—
82C2×C7C11×C13×C3⋊D311yescharacteristic, complemented
83D7—92no—
84C13C2×C11×C3⋊D2111yescharacteristic, direct product factor, Sylow
85C2×D3—214no—
86C11C2×C13×C3⋊D2111yescharacteristic, direct product factor, Sylow
87C32C2×C11×C13×D711yescharacteristic, complemented, Sylow
88C7C2×C11×C13×C3⋊D311yescharacteristic, complemented, Sylow
89C2×C3C11×C13×D2114yescomplemented
90D3—218no—
91C22—631noSylow
92C3C2×C11×C13×D2114yescomplemented
93C2—632no—
94C2C11×C13×C3⋊D2111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C11×C13C3⋊D21
commutator, cosocle, hypocenterC32×C7C22×C11×C13
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C32×C7
UCSC1 ◁ C2×C11×C13

Complements

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

NH ≅ G/Ntype
1. C11×C13×C3⋊D21C2direct (N × H)
2. C2×C32×C7×C11×C13C2semidirect
4. C32×C7×C11×C13C22semidirect
6. C2×C3×C7×C11×C13D3semidirect
9. C2×C13×C3⋊D21C11direct (N × H)
10. C3×C7×C11×C13C2×D3semidirect
11. C2×C11×C3⋊D21C13direct (N × H)
13. C2×C32×C11×C13D7semidirect
15. C2×C7×C11×C13C3⋊D3semidirect
17. C2×C32×C7×C13C2×C11semidirect
18. C13×C3⋊D21C2×C11direct (N × H)
19. C2×C32×C7×C11C2×C13semidirect
20. C11×C3⋊D21C2×C13direct (N × H)
21. C32×C11×C13C2×D7semidirect
23. C7×C11×C13C2×C3⋊D3semidirect
25. C2×C3×C11×C13D21semidirect
27. C32×C7×C13C22×C11semidirect
28. C32×C7×C11C22×C13semidirect
30. C2×C3×C7×C13D3×C11semidirect
33. C2×C3×C7×C11D3×C13semidirect
35. C3×C11×C13C2×D21semidirect
40. C2×C11×C13C3⋊D21direct (N × H)
41. C3×C7×C13C2×D3×C11semidirect
42. C2×C3⋊D21C11×C13direct (N × H)
43. C2×C32×C13C11×D7semidirect
45. C3×C7×C11C2×D3×C13semidirect
46. C2×C32×C11C13×D7semidirect
48. C2×C7×C13C11×C3⋊D3semidirect
51. C2×C7×C11C13×C3⋊D3semidirect
53. C11×C13C2×C3⋊D21direct (N × H)
55. C2×C32×C7C2×C11×C13semidirect
56. C3⋊D21C2×C11×C13direct (N × H)
57. C32×C13C2×C11×D7semidirect
58. C32×C11C2×C13×D7semidirect
59. C7×C13C2×C11×C3⋊D3semidirect
61. C2×C3×C13C11×D21semidirect
63. C7×C11C2×C13×C3⋊D3semidirect
64. C2×C3×C11C13×D21semidirect
66. C32×C7C22×C11×C13semidirect
69. C2×C3×C7D3×C11×C13semidirect
71. C3×C13C2×C11×D21semidirect
73. C3×C11C2×C13×D21semidirect
76. C2×C13C11×C3⋊D21direct (N × H)
78. C2×C11C13×C3⋊D21direct (N × H)
79. C3×C7C2×D3×C11×C13semidirect
80. C2×C32C11×C13×D7semidirect
82. C2×C7C11×C13×C3⋊D3semidirect
84. C13C2×C11×C3⋊D21direct (N × H)
86. C11C2×C13×C3⋊D21direct (N × H)
87. C32C2×C11×C13×D7semidirect
88. C7C2×C11×C13×C3⋊D3semidirect
89. C2×C3C11×C13×D21semidirect
92. C3C2×C11×C13×D21semidirect
94. C2C11×C13×C3⋊D21direct (N × H)

Maximal subgroups

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

subgroupindex
C11×C13×C3⋊D212
C2×C32×C7×C11×C132
C2×C11×C13×D213
C2×C11×C13×C3⋊D37
C2×C13×C3⋊D2111
C2×C11×C3⋊D2113