Finite Group Databasebeta

← C2×C7×C11×C3⋊D33 #44479269

Subgroups — C2×C7×C11×C3⋊D33 #44479269

Order 30492.

360 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C11×C3⋊D33C212yesmaximal, direct product factor
2C2×C32×C7×C112C211yesmaximal, characteristic, complemented
3C2×C7×C11×D33—34nomaximal
4C32×C7×C112C2211yescharacteristic, complemented, Hall
5C7×C11×D33—38no—
6C2×C3×C7×C112D314yescomplemented
7C2×C11×C3⋊D33C711yesmaximal, characteristic, direct product factor, Hall
8C2×C7×C11×D11—91noHall
9C2×C7×C11×C3⋊D3—111nomaximal
10C2×C7×C3⋊D33C1111yesmaximal, characteristic, direct product factor
11C3×C7×C112C2×D314yescomplemented
12C11×C3⋊D33C2×C712yesdirect product factor
13C2×C32×C112C2×C711yescharacteristic, complemented
14C2×C7×C112C3⋊D311yescharacteristic, complemented
15C7×C11×D11—92no—
16C2×C11×D33—34no—
17C2×C32×C7×C11—25no—
18C2×C32×C7×C11D1111yescharacteristic, complemented
19C2×C32×C7×C11C2×C1111yescharacteristic, complemented
20C7×C3⋊D33C2×C1112yesdirect product factor
21C7×C11×C3⋊D3—112no—
22C32×C112C22×C711yescharacteristic, complemented, Hall
23C2×C7×D33—34no—
24C2×D3×C7×C11—334no—
25C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
26C2×C3×C112D3×C714yescomplemented
27C11×D33—38no—
28C32×C7×C11—25no—
29C32×C7×C11C2×D1111yescharacteristic, complemented
30C32×C7×C11C22×C1111yescharacteristic, complemented
31C2×C11×D11—91noHall
32C2×C3×C7×C11—220no—
33C2×C3×C7×C11D3×C1114yescomplemented
34C2×C3×C7×C11D3314yescomplemented
35C7×D33—38no—
36D3×C7×C11—338no—
37C2×C3⋊D33C7×C1111yescharacteristic, direct product factor
38C2×C11×C3⋊D3—111no—
39C3×C112C2×D3×C714yescomplemented
40C22×C7×C11—991no—
41C2×C7×D11—91no—
42C2×C7×C3⋊D3—111noHall
43C2×C112C7×C3⋊D311yescharacteristic, complemented
44C11×D11—92no—
45C3×C7×C11—220no—
46C3×C7×C11C2×D3×C1114yescomplemented
47C3×C7×C11C2×D3314yescomplemented
48C2×C32×C11—25no—
49C2×C32×C11C7×D1111yescharacteristic, complemented
50C2×C32×C11C2×C7×C1111yescharacteristic, complemented
51C3⋊D33C2×C7×C1112yesdirect product factor
52C11×C3⋊D3—112no—
53C2×C7×C11—25no—
54C2×C7×C11—992no—
55C2×C7×C11C11×C3⋊D311yescharacteristic, complemented
56C2×C7×C11C3⋊D3311yescharacteristic, direct product factor
57C7×D11—92no—
58C2×D33—34no—
59C2×D3×C11—334no—
60C2×C32×C7C11×D1111yescharacteristic, complemented
61C7×C3⋊D3—112no—
62C112C2×C7×C3⋊D311yescharacteristic, complemented, Sylow
63C32×C11—25no—
64C32×C11C2×C7×D1111yescharacteristic, complemented
65C32×C11C22×C7×C1111yescharacteristic, complemented
66C2×D3×C7—334no—
67C7×C11—25no—
68C7×C11C2×C11×C3⋊D311yescharacteristic, complemented
69C7×C11C2×C3⋊D3311yescharacteristic, direct product factor
70C2×C3×C11—220no—
71C2×C3×C11D3×C7×C1114yescomplemented
72C2×C3×C11C7×D3314yescomplemented
73D33—38no—
74D3×C11—338no—
75C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
76C22×C11—991no—
77C2×D11—91no—
78C2×C3×C7C11×D3314yescomplemented
79D3×C7—338no—
80C2×C3⋊D3—111noHall
81C3×C11—220no—
82C3×C11C2×D3×C7×C1114yescomplemented
83C3×C11C2×C7×D3314yescomplemented
84C22×C7—991noHall
85C2×C11—25no—
86C2×C11—992no—
87C2×C11C7×C11×C3⋊D311yescharacteristic, complemented
88C2×C11C7×C3⋊D3311yescharacteristic, direct product factor
89D11—92no—
90C3×C7C2×C11×D3314yescomplemented
91C2×C32C7×C11×D1111yescharacteristic, complemented
92C3⋊D3—112no—
93C2×C7—992no—
94C2×C7C11×C3⋊D3311yescharacteristic, direct product factor
95C2×D3—334no—
96C11—25no—
97C11C2×C7×C3⋊D3311yescharacteristic, direct product factor
98C11C2×C7×C11×C3⋊D311yescharacteristic, complemented
99C32C2×C7×C11×D1111yescharacteristic, complemented, Sylow
100C7C2×C11×C3⋊D3311yescharacteristic, direct product factor, Sylow
101C2×C3C7×C11×D3314yescomplemented
102D3—338no—
103C22—991noSylow
104C3C2×C7×C11×D3314yescomplemented
105C2—992no—
106C2C7×C11×C3⋊D3311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7×C11C3⋊D33
commutator, cosocle, hypocenterC32×C11C22×C7×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C112C2
LCSG ▷ C32×C11
UCSC1 ◁ C2×C7×C11

Complements

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

NH ≅ G/Ntype
1. C7×C11×C3⋊D33C2direct (N × H)
2. C2×C32×C7×C112C2semidirect
4. C32×C7×C112C22semidirect
6. C2×C3×C7×C112D3semidirect
7. C2×C11×C3⋊D33C7direct (N × H)
10. C2×C7×C3⋊D33C11direct (N × H)
11. C3×C7×C112C2×D3semidirect
12. C11×C3⋊D33C2×C7direct (N × H)
13. C2×C32×C112C2×C7semidirect
14. C2×C7×C112C3⋊D3semidirect
18. C2×C32×C7×C11D11semidirect
19. C2×C32×C7×C11C2×C11semidirect
20. C7×C3⋊D33C2×C11direct (N × H)
22. C32×C112C22×C7semidirect
25. C7×C112C2×C3⋊D3semidirect
26. C2×C3×C112D3×C7semidirect
29. C32×C7×C11C2×D11semidirect
30. C32×C7×C11C22×C11semidirect
33. C2×C3×C7×C11D3×C11semidirect
34. C2×C3×C7×C11D33semidirect
37. C2×C3⋊D33C7×C11direct (N × H)
39. C3×C112C2×D3×C7semidirect
43. C2×C112C7×C3⋊D3semidirect
46. C3×C7×C11C2×D3×C11semidirect
47. C3×C7×C11C2×D33semidirect
49. C2×C32×C11C7×D11semidirect
50. C2×C32×C11C2×C7×C11semidirect
51. C3⋊D33C2×C7×C11direct (N × H)
55. C2×C7×C11C11×C3⋊D3semidirect
56. C2×C7×C11C3⋊D33direct (N × H)
60. C2×C32×C7C11×D11semidirect
62. C112C2×C7×C3⋊D3semidirect
64. C32×C11C2×C7×D11semidirect
65. C32×C11C22×C7×C11semidirect
68. C7×C11C2×C11×C3⋊D3semidirect
69. C7×C11C2×C3⋊D33direct (N × H)
71. C2×C3×C11D3×C7×C11semidirect
72. C2×C3×C11C7×D33semidirect
75. C32×C7C2×C11×D11semidirect
78. C2×C3×C7C11×D33semidirect
82. C3×C11C2×D3×C7×C11semidirect
83. C3×C11C2×C7×D33semidirect
87. C2×C11C7×C11×C3⋊D3semidirect
88. C2×C11C7×C3⋊D33direct (N × H)
90. C3×C7C2×C11×D33semidirect
91. C2×C32C7×C11×D11semidirect
94. C2×C7C11×C3⋊D33direct (N × H)
97. C11C2×C7×C3⋊D33direct (N × H)
98. C11C2×C7×C11×C3⋊D3semidirect
99. C32C2×C7×C11×D11semidirect
100. C7C2×C11×C3⋊D33direct (N × H)
101. C2×C3C7×C11×D33semidirect
104. C3C2×C7×C11×D33semidirect
106. C2C7×C11×C3⋊D33direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C11×C3⋊D332
C2×C32×C7×C1122
C2×C7×C11×D333
C2×C11×C3⋊D337
C2×C7×C11×C3⋊D311
C2×C7×C3⋊D3311