Finite Group Databasebeta

← C3×C52×D3×C7×C11 #46831662

Subgroups — C3×C52×D3×C7×C11 #46831662

Order 34650.

288 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 192 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
2C52×D3×C7×C11C311yesmaximal, characteristic, direct product factor
3C2×C3×C52×C7×C11—31nomaximal
4C3×C5×D3×C7×C11C516yesmaximal, direct product factor
5C3×C52×C7×C11—21no—
6C3×C52×C7×C11D311yescharacteristic, direct product factor
7C3×C52×C7×C11C2×C311yescharacteristic, complemented
8C3×C52×D3×C11C711yesmaximal, characteristic, direct product factor, Hall
9C2×C52×C7×C11—31noHall
10C32×C5×C7×C11C2×C516yescomplemented
11C3×C52×D3×C7C1111yesmaximal, characteristic, direct product factor, Hall
12C32×C52×C11C2×C711yescharacteristic, complemented, Hall
13C5×D3×C7×C11C3×C516yesdirect product factor
14C2×C3×C5×C7×C11—36no—
15C52×C7×C11C3×D311yescharacteristic, direct product factor, Hall
16C2×C3×C52×C11—31no—
17C52×D3×C11C3×C711yescharacteristic, direct product factor
18C32×C52×C7C2×C1111yescharacteristic, complemented, Hall
19C3×D3×C7×C11C5211yescharacteristic, direct product factor, Hall
20C3×C5×C7×C11—26no—
21C3×C5×C7×C11C5×D316yesdirect product factor
22C3×C5×C7×C11C2×C3×C516yescomplemented
23C2×C3×C52×C7—31no—
24C52×D3×C7C3×C1111yescharacteristic, direct product factor
25C3×C5×D3×C11C5×C716yesdirect product factor
26C3×C52×C11—21no—
27C3×C52×C11D3×C711yescharacteristic, direct product factor
28C3×C52×C11C2×C3×C711yescharacteristic, complemented
29C2×C5×C7×C11—36no—
30C32×C7×C11C2×C5211yescharacteristic, complemented, Hall
31C3×C5×D3×C7C5×C1116yesdirect product factor
32C2×C52×C11—31noHall
33C3×C52×C7—21no—
34C3×C52×C7D3×C1111yescharacteristic, direct product factor
35C3×C52×C7C2×C3×C1111yescharacteristic, complemented
36C32×C5×C11C2×C5×C716yescomplemented
37C2×C3×C7×C11—31no—
38D3×C7×C11C3×C5211yescharacteristic, direct product factor
39C3×C52×D3C7×C1111yescharacteristic, direct product factor, Hall
40C5×C7×C11C3×C5×D316yesdirect product factor
41C2×C52×C7—31noHall
42C2×C3×C5×C11—36no—
43C5×D3×C11C3×C5×C716yesdirect product factor
44C32×C5×C7C2×C5×C1116yescomplemented
45C52×C11C3×D3×C711yescharacteristic, direct product factor, Hall
46C3×C7×C11—21no—
47C3×C7×C11C52×D311yescharacteristic, direct product factor
48C3×C7×C11C2×C3×C5211yescharacteristic, complemented
49C32×C52C2×C7×C1111yescharacteristic, complemented, Hall
50C2×C3×C5×C7—36no—
51C5×D3×C7C3×C5×C1116yesdirect product factor
52C3×D3×C11C52×C711yescharacteristic, direct product factor, Hall
53C52×C7C3×D3×C1111yescharacteristic, direct product factor, Hall
54C3×C5×C11—26no—
55C3×C5×C11C5×D3×C716yesdirect product factor
56C3×C5×C11C2×C3×C5×C716yescomplemented
57C2×C7×C11—31noHall
58C2×C3×C52—31no—
59C52×D3C3×C7×C1111yescharacteristic, direct product factor
60C3×D3×C7C52×C1111yescharacteristic, direct product factor, Hall
61C2×C5×C11—36no—
62C3×C5×C7—26no—
63C3×C5×C7C5×D3×C1116yesdirect product factor
64C3×C5×C7C2×C3×C5×C1116yescomplemented
65C32×C11C2×C52×C711yescharacteristic, complemented, Hall
66C3×C5×D3C5×C7×C1116yesdirect product factor
67C7×C11C3×C52×D311yescharacteristic, direct product factor, Hall
68C3×C52—21no—
69C3×C52D3×C7×C1111yescharacteristic, direct product factor
70C3×C52C2×C3×C7×C1111yescharacteristic, complemented
71C2×C5×C7—36no—
72C2×C3×C11—31no—
73D3×C11C3×C52×C711yescharacteristic, direct product factor
74C32×C7C2×C52×C1111yescharacteristic, complemented, Hall
75C5×C11C3×C5×D3×C716yesdirect product factor
76C2×C52—31noHall
77C32×C5C2×C5×C7×C1116yescomplemented
78C2×C3×C7—31no—
79D3×C7C3×C52×C1111yescharacteristic, direct product factor
80C5×C7C3×C5×D3×C1116yesdirect product factor
81C3×C11—21no—
82C3×C11C52×D3×C711yescharacteristic, direct product factor
83C3×C11C2×C3×C52×C711yescharacteristic, complemented
84C2×C3×C5—36no—
85C5×D3C3×C5×C7×C1116yesdirect product factor
86C52C3×D3×C7×C1111yescharacteristic, direct product factor, Sylow
87C2×C11—31noHall
88C3×C7—21no—
89C3×C7C52×D3×C1111yescharacteristic, direct product factor
90C3×C7C2×C3×C52×C1111yescharacteristic, complemented
91C3×D3C52×C7×C1111yescharacteristic, direct product factor, Hall
92C3×C5—26no—
93C3×C5C2×C3×C5×C7×C1116yescomplemented
94C3×C5C5×D3×C7×C1116yesdirect product factor
95C2×C7—31noHall
96C11C3×C52×D3×C711yescharacteristic, direct product factor, Sylow
97C2×C5—36no—
98C32C2×C52×C7×C1111yescharacteristic, complemented, Sylow
99C7C3×C52×D3×C1111yescharacteristic, direct product factor, Sylow
100C2×C3—31no—
101D3C3×C52×C7×C1111yescharacteristic, direct product factor
102C5C3×C5×D3×C7×C1116yesdirect product factor
103C3—21no—
104C3C2×C3×C52×C7×C1111yescharacteristic, complemented
105C3C52×D3×C7×C1111yescharacteristic, direct product factor
106C2—31noSylow
subgroupG/H
center, hypercenterC3×C52×C7×C11D3
commutator, cosocle, hypocenterC3C2×C3×C52×C7×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3
UCSC1 ◁ C3×C52×C7×C11

Complements

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

NH ≅ G/Ntype
1. C32×C52×C7×C11C2semidirect
2. C52×D3×C7×C11C3direct (N × H)
4. C3×C5×D3×C7×C11C5direct (N × H)
6. C3×C52×C7×C11D3direct (N × H)
7. C3×C52×C7×C11C2×C3semidirect
8. C3×C52×D3×C11C7direct (N × H)
10. C32×C5×C7×C11C2×C5semidirect
11. C3×C52×D3×C7C11direct (N × H)
12. C32×C52×C11C2×C7semidirect
13. C5×D3×C7×C11C3×C5direct (N × H)
15. C52×C7×C11C3×D3direct (N × H)
17. C52×D3×C11C3×C7direct (N × H)
18. C32×C52×C7C2×C11semidirect
19. C3×D3×C7×C11C52direct (N × H)
21. C3×C5×C7×C11C5×D3direct (N × H)
22. C3×C5×C7×C11C2×C3×C5semidirect
24. C52×D3×C7C3×C11direct (N × H)
25. C3×C5×D3×C11C5×C7direct (N × H)
27. C3×C52×C11D3×C7direct (N × H)
28. C3×C52×C11C2×C3×C7semidirect
30. C32×C7×C11C2×C52semidirect
31. C3×C5×D3×C7C5×C11direct (N × H)
34. C3×C52×C7D3×C11direct (N × H)
35. C3×C52×C7C2×C3×C11semidirect
36. C32×C5×C11C2×C5×C7semidirect
38. D3×C7×C11C3×C52direct (N × H)
39. C3×C52×D3C7×C11direct (N × H)
40. C5×C7×C11C3×C5×D3direct (N × H)
43. C5×D3×C11C3×C5×C7direct (N × H)
44. C32×C5×C7C2×C5×C11semidirect
45. C52×C11C3×D3×C7direct (N × H)
47. C3×C7×C11C52×D3direct (N × H)
48. C3×C7×C11C2×C3×C52semidirect
49. C32×C52C2×C7×C11semidirect
51. C5×D3×C7C3×C5×C11direct (N × H)
52. C3×D3×C11C52×C7direct (N × H)
53. C52×C7C3×D3×C11direct (N × H)
55. C3×C5×C11C5×D3×C7direct (N × H)
56. C3×C5×C11C2×C3×C5×C7semidirect
59. C52×D3C3×C7×C11direct (N × H)
60. C3×D3×C7C52×C11direct (N × H)
63. C3×C5×C7C5×D3×C11direct (N × H)
64. C3×C5×C7C2×C3×C5×C11semidirect
65. C32×C11C2×C52×C7semidirect
66. C3×C5×D3C5×C7×C11direct (N × H)
67. C7×C11C3×C52×D3direct (N × H)
69. C3×C52D3×C7×C11direct (N × H)
70. C3×C52C2×C3×C7×C11semidirect
73. D3×C11C3×C52×C7direct (N × H)
74. C32×C7C2×C52×C11semidirect
75. C5×C11C3×C5×D3×C7direct (N × H)
77. C32×C5C2×C5×C7×C11semidirect
79. D3×C7C3×C52×C11direct (N × H)
80. C5×C7C3×C5×D3×C11direct (N × H)
82. C3×C11C52×D3×C7direct (N × H)
83. C3×C11C2×C3×C52×C7semidirect
85. C5×D3C3×C5×C7×C11direct (N × H)
86. C52C3×D3×C7×C11direct (N × H)
89. C3×C7C52×D3×C11direct (N × H)
90. C3×C7C2×C3×C52×C11semidirect
91. C3×D3C52×C7×C11direct (N × H)
93. C3×C5C2×C3×C5×C7×C11semidirect
94. C3×C5C5×D3×C7×C11direct (N × H)
96. C11C3×C52×D3×C7direct (N × H)
98. C32C2×C52×C7×C11semidirect
99. C7C3×C52×D3×C11direct (N × H)
101. D3C3×C52×C7×C11direct (N × H)
102. C5C3×C5×D3×C7×C11direct (N × H)
104. C3C2×C3×C52×C7×C11semidirect
105. C3C52×D3×C7×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C52×C7×C112
C52×D3×C7×C113
C2×C3×C52×C7×C113
C3×C5×D3×C7×C115
C3×C52×D3×C117
C3×C52×D3×C711