Finite Group Databasebeta

← C3×C52×C7×D33 #46831663

Subgroups — C3×C52×C7×D33 #46831663

Order 34650.

288 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 160 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
1C32×C52×C7×C11C211yesmaximal, characteristic, complemented, Hall
2C3×C52×C7×D11—31nomaximal
3C52×C7×D33C311yesmaximal, characteristic, direct product factor
4C3×C5×C7×D33C516yesmaximal, direct product factor
5C3×C52×C7×C11—21no—
6C3×C52×C7×C11D311yescharacteristic, complemented
7C3×C52×C7×C11C2×C311yescharacteristic, complemented
8C3×C52×D33C711yesmaximal, characteristic, direct product factor, Hall
9C52×C7×D11—31noHall
10C32×C5×C7×C11C2×C516yescomplemented
11C3×C52×D3×C7—111nomaximal, Hall
12C32×C52×C11C2×C711yescharacteristic, complemented, Hall
13C5×C7×D33C3×C516yesdirect product factor
14C3×C5×C7×D11—36no—
15C52×C7×C11C3×D311yescharacteristic, complemented, Hall
16C52×D33C3×C711yescharacteristic, direct product factor
17C3×C52×D11—31no—
18C32×C52×C7D1111yescharacteristic, complemented, Hall
19C3×C7×D33C5211yescharacteristic, direct product factor, Hall
20C3×C5×C7×C11—26no—
21C3×C5×C7×C11C5×D316yescomplemented
22C3×C5×C7×C11C2×C3×C516yescomplemented
23C2×C3×C52×C7—331no—
24C52×D3×C7—111no—
25C3×C5×D33C5×C716yesdirect product factor
26C3×C52×C11—21no—
27C3×C52×C11D3×C711yescharacteristic, complemented
28C3×C52×C11C2×C3×C711yescharacteristic, complemented
29C5×C7×D11—36no—
30C32×C7×C11C2×C5211yescharacteristic, complemented, Hall
31C3×C5×D3×C7—116no—
32C52×D11—31noHall
33C3×C52×C7—21no—
34C3×C52×C7C3×D1111yescharacteristic, complemented
35C3×C52×C7D3311yescharacteristic, direct product factor
36C32×C5×C11C2×C5×C716yescomplemented
37C7×D33C3×C5211yescharacteristic, direct product factor
38C3×C7×D11—31no—
39C3×C52×D3—111noHall
40C5×C7×C11C3×C5×D316yescomplemented
41C2×C52×C7—331noHall
42C5×D33C3×C5×C716yesdirect product factor
43C3×C5×D11—36no—
44C32×C5×C7C5×D1116yescomplemented
45C52×C11C3×D3×C711yescharacteristic, complemented, Hall
46C3×C7×C11—21no—
47C3×C7×C11C52×D311yescharacteristic, complemented
48C3×C7×C11C2×C3×C5211yescharacteristic, complemented
49C32×C52C7×D1111yescharacteristic, complemented, Hall
50C2×C3×C5×C7—336no—
51C5×D3×C7—116no—
52C3×D33C52×C711yescharacteristic, direct product factor, Hall
53C52×C7C3×D3311yescharacteristic, direct product factor, Hall
54C3×C5×C11—26no—
55C3×C5×C11C5×D3×C716yescomplemented
56C3×C5×C11C2×C3×C5×C716yescomplemented
57C7×D11—31noHall
58C2×C3×C52—331no—
59C52×D3—111no—
60C3×D3×C7—111noHall
61C5×D11—36no—
62C3×C5×C7—26no—
63C3×C5×C7C3×C5×D1116yescomplemented
64C3×C5×C7C5×D3316yesdirect product factor
65C32×C11C2×C52×C711yescharacteristic, complemented, Hall
66C3×C5×D3—116no—
67C7×C11C3×C52×D311yescharacteristic, complemented, Hall
68C3×C52—21no—
69C3×C52C3×C7×D1111yescharacteristic, complemented
70C3×C52C7×D3311yescharacteristic, direct product factor
71C2×C5×C7—336no—
72D33C3×C52×C711yescharacteristic, direct product factor
73C3×D11—31no—
74C32×C7C52×D1111yescharacteristic, complemented, Hall
75C5×C11C3×C5×D3×C716yescomplemented
76C2×C52—331noHall
77C32×C5C5×C7×D1116yescomplemented
78C2×C3×C7—331no—
79D3×C7—111no—
80C5×C7C3×C5×D3316yesdirect product factor
81C3×C11—21no—
82C3×C11C52×D3×C711yescharacteristic, complemented
83C3×C11C2×C3×C52×C711yescharacteristic, complemented
84C2×C3×C5—336no—
85C5×D3—116no—
86C52C3×C7×D3311yescharacteristic, direct product factor, Sylow
87D11—31noHall
88C3×C7—21no—
89C3×C7C3×C52×D1111yescharacteristic, complemented
90C3×C7C52×D3311yescharacteristic, direct product factor
91C3×D3—111noHall
92C3×C5—26no—
93C3×C5C3×C5×C7×D1116yescomplemented
94C3×C5C5×C7×D3316yesdirect product factor
95C2×C7—331noHall
96C11C3×C52×D3×C711yescharacteristic, complemented, Sylow
97C2×C5—336no—
98C32C52×C7×D1111yescharacteristic, complemented, Sylow
99C7C3×C52×D3311yescharacteristic, direct product factor, Sylow
100C2×C3—331no—
101D3—111no—
102C5C3×C5×C7×D3316yesdirect product factor
103C3—21no—
104C3C52×C7×D3311yescharacteristic, direct product factor
105C3C3×C52×C7×D1111yescharacteristic, complemented
106C2—331noSylow
subgroupG/H
center, hypercenterC3×C52×C7D33
commutator, cosocle, hypocenterC3×C11C2×C3×C52×C7
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3×C11
UCSC1 ◁ C3×C52×C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C7×C11C2semidirect
3. C52×C7×D33C3direct (N × H)
4. C3×C5×C7×D33C5direct (N × H)
6. C3×C52×C7×C11D3semidirect
7. C3×C52×C7×C11C2×C3semidirect
8. C3×C52×D33C7direct (N × H)
10. C32×C5×C7×C11C2×C5semidirect
12. C32×C52×C11C2×C7semidirect
13. C5×C7×D33C3×C5direct (N × H)
15. C52×C7×C11C3×D3semidirect
16. C52×D33C3×C7direct (N × H)
18. C32×C52×C7D11semidirect
19. C3×C7×D33C52direct (N × H)
21. C3×C5×C7×C11C5×D3semidirect
22. C3×C5×C7×C11C2×C3×C5semidirect
25. C3×C5×D33C5×C7direct (N × H)
27. C3×C52×C11D3×C7semidirect
28. C3×C52×C11C2×C3×C7semidirect
30. C32×C7×C11C2×C52semidirect
34. C3×C52×C7C3×D11semidirect
35. C3×C52×C7D33direct (N × H)
36. C32×C5×C11C2×C5×C7semidirect
37. C7×D33C3×C52direct (N × H)
40. C5×C7×C11C3×C5×D3semidirect
42. C5×D33C3×C5×C7direct (N × H)
44. C32×C5×C7C5×D11semidirect
45. C52×C11C3×D3×C7semidirect
47. C3×C7×C11C52×D3semidirect
48. C3×C7×C11C2×C3×C52semidirect
49. C32×C52C7×D11semidirect
52. C3×D33C52×C7direct (N × H)
53. C52×C7C3×D33direct (N × H)
55. C3×C5×C11C5×D3×C7semidirect
56. C3×C5×C11C2×C3×C5×C7semidirect
63. C3×C5×C7C3×C5×D11semidirect
64. C3×C5×C7C5×D33direct (N × H)
65. C32×C11C2×C52×C7semidirect
67. C7×C11C3×C52×D3semidirect
69. C3×C52C3×C7×D11semidirect
70. C3×C52C7×D33direct (N × H)
72. D33C3×C52×C7direct (N × H)
74. C32×C7C52×D11semidirect
75. C5×C11C3×C5×D3×C7semidirect
77. C32×C5C5×C7×D11semidirect
80. C5×C7C3×C5×D33direct (N × H)
82. C3×C11C52×D3×C7semidirect
83. C3×C11C2×C3×C52×C7semidirect
86. C52C3×C7×D33direct (N × H)
89. C3×C7C3×C52×D11semidirect
90. C3×C7C52×D33direct (N × H)
93. C3×C5C3×C5×C7×D11semidirect
94. C3×C5C5×C7×D33direct (N × H)
96. C11C3×C52×D3×C7semidirect
98. C32C52×C7×D11semidirect
99. C7C3×C52×D33direct (N × H)
102. C5C3×C5×C7×D33direct (N × H)
104. C3C52×C7×D33direct (N × H)
105. C3C3×C52×C7×D11semidirect

Maximal subgroups

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

subgroupindex
C32×C52×C7×C112
C3×C52×C7×D113
C52×C7×D333
C3×C5×C7×D335
C3×C52×D337
C3×C52×D3×C711