Finite Group Databasebeta

← C2×C11×C3⋊D273 #49115029

Subgroups — C2×C11×C3⋊D273 #49115029

Order 36036.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C3⋊D273C212yesmaximal, direct product factor
2C2×C32×C7×C11×C13C211yesmaximal, characteristic, complemented
3C2×C11×D273—34nomaximal
4C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
5C11×D273—38no—
6C2×C3×C7×C11×C13D314yescomplemented
7C2×C11×C3⋊D39—71nomaximal, Hall
8C2×C11×D91—91noHall
9C2×C3⋊D273C1111yesmaximal, characteristic, direct product factor, Hall
10C3×C7×C11×C13C2×D314yescomplemented
11C2×C11×C3⋊D21—131nomaximal, Hall
12C11×C3⋊D39—72no—
13C2×C32×C11×C13D711yescharacteristic, complemented
14C11×D91—92no—
15C2×C7×C11×C13C3⋊D311yescharacteristic, complemented
16C2×C11×D39—214no—
17C2×C32×C7×C13C2×C1111yescharacteristic, complemented
18C3⋊D273C2×C1112yesdirect product factor
19C2×C32×C7×C11D1311yescharacteristic, complemented
20C11×C3⋊D21—132no—
21C32×C11×C13C2×D711yescharacteristic, complemented, Hall
22C2×D273—34no—
23C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
24C2×C11×D21—394no—
25C2×C3×C11×C13D2114yescomplemented
26C11×D39—218no—
27C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
28C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
29C2×C11×D13—631noHall
30C2×C3×C7×C13D3×C1114yescomplemented
31D273—38no—
32C2×C3⋊D39—71noHall
33C2×C3×C7×C11D3914yescomplemented
34C11×D21—398no—
35C3×C11×C13C2×D2114yescomplemented
36C2×C11×C3⋊D3—911noHall
37C2×D91—91noHall
38C2×C11×D7—1171noHall
39C2×C11×C13C3⋊D2111yescharacteristic, complemented
40C11×D13—632no—
41C3×C7×C13C2×D3×C1114yescomplemented
42C2×C3⋊D21—131noHall
43C2×C32×C13C11×D711yescharacteristic, complemented
44C3⋊D39—72no—
45C3×C7×C11C2×D3914yescomplemented
46C2×C32×C11D9111yescharacteristic, complemented
47C11×C3⋊D3—912no—
48C2×C7×C13C11×C3⋊D311yescharacteristic, complemented
49D91—92no—
50C2×D39—214no—
51C2×C7×C11C3⋊D3911yescharacteristic, complemented
52C11×D7—1172no—
53C11×C13C2×C3⋊D2111yescharacteristic, complemented, Hall
54C2×D3×C11—2734no—
55C2×C32×C7C11×D1311yescharacteristic, complemented
56C3⋊D21—132no—
57C32×C13C2×C11×D711yescharacteristic, complemented, Hall
58C32×C11C2×D9111yescharacteristic, complemented, Hall
59C7×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
60C2×D21—394no—
61C2×C3×C13C11×D2114yescomplemented
62D39—218no—
63C7×C11C2×C3⋊D3911yescharacteristic, complemented, Hall
64C2×C3×C11D27314yescomplemented
65D3×C11—2738no—
66C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
67C2×D13—631noHall
68C22×C11—8191noHall
69C2×C3×C7C11×D3914yescomplemented
70D21—398no—
71C3×C13C2×C11×D2114yescomplemented
72C2×C3⋊D3—911noHall
73C3×C11C2×D27314yescomplemented
74C2×D7—1171noHall
75C2×C13C11×C3⋊D2111yescharacteristic, complemented
76D13—632no—
77C2×C11—8192no—
78C2×C11C3⋊D27311yescharacteristic, direct product factor
79C3×C7C2×C11×D3914yescomplemented
80C2×C32C11×D9111yescharacteristic, complemented
81C3⋊D3—912no—
82C2×C7C11×C3⋊D3911yescharacteristic, complemented
83D7—1172no—
84C13C2×C11×C3⋊D2111yescharacteristic, complemented, Sylow
85C2×D3—2734no—
86C11C2×C3⋊D27311yescharacteristic, direct product factor, Sylow
87C32C2×C11×D9111yescharacteristic, complemented, Sylow
88C7C2×C11×C3⋊D3911yescharacteristic, complemented, Sylow
89C2×C3C11×D27314yescomplemented
90D3—2738no—
91C22—8191noSylow
92C3C2×C11×D27314yescomplemented
93C2—8192no—
94C2C11×C3⋊D27311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C11C3⋊D273
commutator, cosocle, hypocenterC32×C7×C13C22×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C32×C7×C13
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
1. C11×C3⋊D273C2direct (N × H)
2. C2×C32×C7×C11×C13C2semidirect
4. C32×C7×C11×C13C22semidirect
6. C2×C3×C7×C11×C13D3semidirect
9. C2×C3⋊D273C11direct (N × H)
10. C3×C7×C11×C13C2×D3semidirect
13. C2×C32×C11×C13D7semidirect
15. C2×C7×C11×C13C3⋊D3semidirect
17. C2×C32×C7×C13C2×C11semidirect
18. C3⋊D273C2×C11direct (N × H)
19. C2×C32×C7×C11D13semidirect
21. C32×C11×C13C2×D7semidirect
23. C7×C11×C13C2×C3⋊D3semidirect
25. C2×C3×C11×C13D21semidirect
27. C32×C7×C13C22×C11semidirect
28. C32×C7×C11C2×D13semidirect
30. C2×C3×C7×C13D3×C11semidirect
33. C2×C3×C7×C11D39semidirect
35. C3×C11×C13C2×D21semidirect
39. C2×C11×C13C3⋊D21semidirect
41. C3×C7×C13C2×D3×C11semidirect
43. C2×C32×C13C11×D7semidirect
45. C3×C7×C11C2×D39semidirect
46. C2×C32×C11D91semidirect
48. C2×C7×C13C11×C3⋊D3semidirect
51. C2×C7×C11C3⋊D39semidirect
53. C11×C13C2×C3⋊D21semidirect
55. C2×C32×C7C11×D13semidirect
57. C32×C13C2×C11×D7semidirect
58. C32×C11C2×D91semidirect
59. C7×C13C2×C11×C3⋊D3semidirect
61. C2×C3×C13C11×D21semidirect
63. C7×C11C2×C3⋊D39semidirect
64. C2×C3×C11D273semidirect
66. C32×C7C2×C11×D13semidirect
69. C2×C3×C7C11×D39semidirect
71. C3×C13C2×C11×D21semidirect
73. C3×C11C2×D273semidirect
75. C2×C13C11×C3⋊D21semidirect
78. C2×C11C3⋊D273direct (N × H)
79. C3×C7C2×C11×D39semidirect
80. C2×C32C11×D91semidirect
82. C2×C7C11×C3⋊D39semidirect
84. C13C2×C11×C3⋊D21semidirect
86. C11C2×C3⋊D273direct (N × H)
87. C32C2×C11×D91semidirect
88. C7C2×C11×C3⋊D39semidirect
89. C2×C3C11×D273semidirect
92. C3C2×C11×D273semidirect
94. C2C11×C3⋊D273direct (N × H)

Maximal subgroups

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

subgroupindex
C11×C3⋊D2732
C2×C32×C7×C11×C132
C2×C11×D2733
C2×C11×C3⋊D397
C2×C3⋊D27311
C2×C11×C3⋊D2113