Finite Group Databasebeta

← C3×C52×C11×D21 #46831664

Subgroups — C3×C52×C11×D21 #46831664

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×C11×D7—31nomaximal
3C52×C11×D21C311yesmaximal, characteristic, direct product factor
4C3×C5×C11×D21C516yesmaximal, direct product factor
5C3×C52×C7×C11—21no—
6C3×C52×C7×C11D311yescharacteristic, complemented
7C3×C52×C7×C11C2×C311yescharacteristic, complemented
8C3×C52×D3×C11—71nomaximal, Hall
9C52×C11×D7—31noHall
10C32×C5×C7×C11C2×C516yescomplemented
11C3×C52×D21C1111yesmaximal, characteristic, direct product factor, Hall
12C32×C52×C11D711yescharacteristic, complemented, Hall
13C5×C11×D21C3×C516yesdirect product factor
14C3×C5×C11×D7—36no—
15C52×C7×C11C3×D311yescharacteristic, complemented, Hall
16C2×C3×C52×C11—211no—
17C52×D3×C11—71no—
18C32×C52×C7C2×C1111yescharacteristic, complemented, Hall
19C3×C11×D21C5211yescharacteristic, direct product factor, Hall
20C3×C5×C7×C11—26no—
21C3×C5×C7×C11C5×D316yescomplemented
22C3×C5×C7×C11C2×C3×C516yescomplemented
23C52×D21C3×C1111yescharacteristic, direct product factor
24C3×C52×D7—31no—
25C3×C5×D3×C11—76no—
26C3×C52×C11—21no—
27C3×C52×C11C3×D711yescharacteristic, complemented
28C3×C52×C11D2111yescharacteristic, direct product factor
29C5×C11×D7—36no—
30C32×C7×C11C2×C5211yescharacteristic, complemented, Hall
31C3×C5×D21C5×C1116yesdirect product factor
32C2×C52×C11—211noHall
33C3×C52×C7—21no—
34C3×C52×C7D3×C1111yescharacteristic, complemented
35C3×C52×C7C2×C3×C1111yescharacteristic, complemented
36C32×C5×C11C5×D716yescomplemented
37C11×D21C3×C5211yescharacteristic, direct product factor
38C3×C11×D7—31no—
39C3×C52×D3—71noHall
40C5×C7×C11C3×C5×D316yescomplemented
41C52×D7—31noHall
42C2×C3×C5×C11—216no—
43C5×D3×C11—76no—
44C32×C5×C7C2×C5×C1116yescomplemented
45C52×C11C3×D2111yescharacteristic, direct product factor, Hall
46C3×C7×C11—21no—
47C3×C7×C11C52×D311yescharacteristic, complemented
48C3×C7×C11C2×C3×C5211yescharacteristic, complemented
49C32×C52C11×D711yescharacteristic, complemented, Hall
50C5×D21C3×C5×C1116yesdirect product factor
51C3×C5×D7—36no—
52C3×D3×C11—71noHall
53C52×C7C3×D3×C1111yescharacteristic, complemented, Hall
54C3×C5×C11—26no—
55C3×C5×C11C3×C5×D716yescomplemented
56C3×C5×C11C5×D2116yesdirect product factor
57C11×D7—31noHall
58C2×C3×C52—211no—
59C52×D3—71no—
60C3×D21C52×C1111yescharacteristic, direct product factor, Hall
61C2×C5×C11—216no—
62C3×C5×C7—26no—
63C3×C5×C7C5×D3×C1116yescomplemented
64C3×C5×C7C2×C3×C5×C1116yescomplemented
65C32×C11C52×D711yescharacteristic, complemented, Hall
66C3×C5×D3—76no—
67C7×C11C3×C52×D311yescharacteristic, complemented, Hall
68C3×C52—21no—
69C3×C52C3×C11×D711yescharacteristic, complemented
70C3×C52C11×D2111yescharacteristic, direct product factor
71C5×D7—36no—
72C2×C3×C11—211no—
73D3×C11—71no—
74C32×C7C2×C52×C1111yescharacteristic, complemented, Hall
75C5×C11C3×C5×D2116yesdirect product factor
76C2×C52—211noHall
77C32×C5C5×C11×D716yescomplemented
78D21C3×C52×C1111yescharacteristic, direct product factor
79C3×D7—31no—
80C5×C7C3×C5×D3×C1116yescomplemented
81C3×C11—21no—
82C3×C11C3×C52×D711yescharacteristic, complemented
83C3×C11C52×D2111yescharacteristic, direct product factor
84C2×C3×C5—216no—
85C5×D3—76no—
86C52C3×C11×D2111yescharacteristic, direct product factor, Sylow
87C2×C11—211noHall
88C3×C7—21no—
89C3×C7C52×D3×C1111yescharacteristic, complemented
90C3×C7C2×C3×C52×C1111yescharacteristic, complemented
91C3×D3—71noHall
92C3×C5—26no—
93C3×C5C3×C5×C11×D716yescomplemented
94C3×C5C5×C11×D2116yesdirect product factor
95D7—31noHall
96C11C3×C52×D2111yescharacteristic, direct product factor, Sylow
97C2×C5—216no—
98C32C52×C11×D711yescharacteristic, complemented, Sylow
99C7C3×C52×D3×C1111yescharacteristic, complemented, Sylow
100C2×C3—211no—
101D3—71no—
102C5C3×C5×C11×D2116yesdirect product factor
103C3—21no—
104C3C52×C11×D2111yescharacteristic, direct product factor
105C3C3×C52×C11×D711yescharacteristic, complemented
106C2—211noSylow
subgroupG/H
center, hypercenterC3×C52×C11D21
commutator, cosocle, hypocenterC3×C7C2×C3×C52×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3×C7
UCSC1 ◁ C3×C52×C11

Complements

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

NH ≅ G/Ntype
1. C32×C52×C7×C11C2semidirect
3. C52×C11×D21C3direct (N × H)
4. C3×C5×C11×D21C5direct (N × H)
6. C3×C52×C7×C11D3semidirect
7. C3×C52×C7×C11C2×C3semidirect
10. C32×C5×C7×C11C2×C5semidirect
11. C3×C52×D21C11direct (N × H)
12. C32×C52×C11D7semidirect
13. C5×C11×D21C3×C5direct (N × H)
15. C52×C7×C11C3×D3semidirect
18. C32×C52×C7C2×C11semidirect
19. C3×C11×D21C52direct (N × H)
21. C3×C5×C7×C11C5×D3semidirect
22. C3×C5×C7×C11C2×C3×C5semidirect
23. C52×D21C3×C11direct (N × H)
27. C3×C52×C11C3×D7semidirect
28. C3×C52×C11D21direct (N × H)
30. C32×C7×C11C2×C52semidirect
31. C3×C5×D21C5×C11direct (N × H)
34. C3×C52×C7D3×C11semidirect
35. C3×C52×C7C2×C3×C11semidirect
36. C32×C5×C11C5×D7semidirect
37. C11×D21C3×C52direct (N × H)
40. C5×C7×C11C3×C5×D3semidirect
44. C32×C5×C7C2×C5×C11semidirect
45. C52×C11C3×D21direct (N × H)
47. C3×C7×C11C52×D3semidirect
48. C3×C7×C11C2×C3×C52semidirect
49. C32×C52C11×D7semidirect
50. C5×D21C3×C5×C11direct (N × H)
53. C52×C7C3×D3×C11semidirect
55. C3×C5×C11C3×C5×D7semidirect
56. C3×C5×C11C5×D21direct (N × H)
60. C3×D21C52×C11direct (N × H)
63. C3×C5×C7C5×D3×C11semidirect
64. C3×C5×C7C2×C3×C5×C11semidirect
65. C32×C11C52×D7semidirect
67. C7×C11C3×C52×D3semidirect
69. C3×C52C3×C11×D7semidirect
70. C3×C52C11×D21direct (N × H)
74. C32×C7C2×C52×C11semidirect
75. C5×C11C3×C5×D21direct (N × H)
77. C32×C5C5×C11×D7semidirect
78. D21C3×C52×C11direct (N × H)
80. C5×C7C3×C5×D3×C11semidirect
82. C3×C11C3×C52×D7semidirect
83. C3×C11C52×D21direct (N × H)
86. C52C3×C11×D21direct (N × H)
89. C3×C7C52×D3×C11semidirect
90. C3×C7C2×C3×C52×C11semidirect
93. C3×C5C3×C5×C11×D7semidirect
94. C3×C5C5×C11×D21direct (N × H)
96. C11C3×C52×D21direct (N × H)
98. C32C52×C11×D7semidirect
99. C7C3×C52×D3×C11semidirect
102. C5C3×C5×C11×D21direct (N × H)
104. C3C52×C11×D21direct (N × H)
105. C3C3×C52×C11×D7semidirect

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×C11×D73
C52×C11×D213
C3×C5×C11×D215
C3×C52×D3×C117
C3×C52×D2111