Finite Group Databasebeta

← C2×C3×C72×D5×C11 #44568937

Subgroups — C2×C3×C72×D5×C11 #44568937

Order 32340.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C72×D5×C11C212yesmaximal, direct product factor
2C2×C3×C5×C72×C11C211yesmaximal, characteristic, complemented
3C2×C72×D5×C11C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C22×C3×C72×C11—51nomaximal, Hall
6C72×D5×C11C2×C312yesdirect product factor
7C2×C5×C72×C11C2×C311yescharacteristic, complemented
8C2×C3×C7×D5×C11C718yesmaximal, direct product factor
9C2×C3×C72×C11—52no—
10C2×C3×C72×C11D511yescharacteristic, direct product factor
11C2×C3×C72×D5C1111yesmaximal, characteristic, direct product factor, Hall
12C5×C72×C11C22×C311yescharacteristic, complemented, Hall
13C3×C7×D5×C11C2×C7116yesdirect product factor
14C2×C3×C5×C7×C11C2×C718yescomplemented
15C22×C72×C11—51noHall
16C3×C72×C11C2×D511yescharacteristic, direct product factor, Hall
17C2×C7×D5×C11C3×C718yesdirect product factor
18C2×C3×C5×C72C2×C1111yescharacteristic, complemented
19C3×C72×D5C2×C1112yesdirect product factor
20C3×C5×C7×C11C22×C718yescomplemented
21C2×C72×C11—52no—
22C2×C72×C11C3×D511yescharacteristic, direct product factor
23C2×C72×D5C3×C1111yescharacteristic, direct product factor, Hall
24C22×C3×C7×C11—58no—
25C2×C5×C7×C11C2×C3×C718yescomplemented
26C7×D5×C11C2×C3×C7116yesdirect product factor
27C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
28C2×C3×D5×C11C7211yescharacteristic, direct product factor, Hall
29C22×C3×C72—51noHall
30C72×C11C2×C3×D511yescharacteristic, direct product factor, Hall
31C2×C5×C72C2×C3×C1111yescharacteristic, complemented
32C72×D5C2×C3×C1112yesdirect product factor
33C2×C3×C7×C11—516no—
34C2×C3×C7×C11C7×D518yesdirect product factor
35C2×C3×C7×D5C7×C1118yesdirect product factor
36C5×C7×C11C22×C3×C718yescomplemented
37C2×C3×C5×C11C2×C7211yescharacteristic, complemented
38C3×D5×C11C2×C7212yesdirect product factor
39C22×C7×C11—58no—
40C2×C3×C72—52no—
41C2×C3×C72D5×C1111yescharacteristic, direct product factor
42C5×C72C22×C3×C1111yescharacteristic, complemented, Hall
43C3×C7×C11C2×C7×D518yesdirect product factor
44C2×D5×C11C3×C7211yescharacteristic, direct product factor, Hall
45C2×C3×C5×C7C2×C7×C1118yescomplemented
46C3×C7×D5C2×C7×C11116yesdirect product factor
47C22×C72—51noHall
48C3×C5×C11C22×C7211yescharacteristic, complemented, Hall
49C2×C7×C11—516no—
50C2×C7×C11C3×C7×D518yesdirect product factor
51C3×C72C2×D5×C1111yescharacteristic, direct product factor, Hall
52C2×C7×D5C3×C7×C1118yesdirect product factor
53C22×C3×C11—51noHall
54C2×C5×C11C2×C3×C7211yescharacteristic, complemented
55D5×C11C2×C3×C7212yesdirect product factor
56C3×C5×C7C22×C7×C1118yescomplemented
57C2×C72—52no—
58C2×C72C3×D5×C1111yescharacteristic, direct product factor
59C22×C3×C7—58no—
60C7×C11C2×C3×C7×D518yesdirect product factor
61C2×C5×C7C2×C3×C7×C1118yescomplemented
62C7×D5C2×C3×C7×C11116yesdirect product factor
63C2×C3×C11—52no—
64C2×C3×C11C72×D511yescharacteristic, direct product factor
65C2×C3×D5C72×C1111yescharacteristic, direct product factor, Hall
66C5×C11C22×C3×C7211yescharacteristic, complemented, Hall
67C72C2×C3×D5×C1111yescharacteristic, direct product factor, Sylow
68C22×C11—51noHall
69C2×C3×C7—516no—
70C2×C3×C7C7×D5×C1118yesdirect product factor
71C5×C7C22×C3×C7×C1118yescomplemented
72C3×C11C2×C72×D511yescharacteristic, direct product factor, Hall
73C2×C3×C5C2×C72×C1111yescharacteristic, complemented
74C3×D5C2×C72×C1112yesdirect product factor
75C22×C7—58no—
76C2×C11—52no—
77C2×C11C3×C72×D511yescharacteristic, direct product factor
78C3×C7C2×C7×D5×C1118yesdirect product factor
79C2×D5C3×C72×C1111yescharacteristic, direct product factor, Hall
80C3×C5C22×C72×C1111yescharacteristic, complemented, Hall
81C2×C7—516no—
82C2×C7C3×C7×D5×C1118yesdirect product factor
83C22×C3—51noHall
84C11C2×C3×C72×D511yescharacteristic, direct product factor, Sylow
85C2×C5C2×C3×C72×C1111yescharacteristic, complemented
86D5C2×C3×C72×C1112yesdirect product factor
87C7C2×C3×C7×D5×C1118yesdirect product factor
88C2×C3—52no—
89C2×C3C72×D5×C1111yescharacteristic, direct product factor
90C5C22×C3×C72×C1111yescharacteristic, complemented, Sylow
91C22—51noSylow
92C3C2×C72×D5×C1111yescharacteristic, direct product factor, Sylow
93C2—52no—
94C2C3×C72×D5×C1111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C72×C11D5
commutator, cosocle, hypocenterC5C22×C3×C72×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C72×C11

Complements

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

NH ≅ G/Ntype
1. C3×C72×D5×C11C2direct (N × H)
2. C2×C3×C5×C72×C11C2semidirect
3. C2×C72×D5×C11C3direct (N × H)
4. C3×C5×C72×C11C22semidirect
6. C72×D5×C11C2×C3direct (N × H)
7. C2×C5×C72×C11C2×C3semidirect
8. C2×C3×C7×D5×C11C7direct (N × H)
10. C2×C3×C72×C11D5direct (N × H)
11. C2×C3×C72×D5C11direct (N × H)
12. C5×C72×C11C22×C3semidirect
13. C3×C7×D5×C11C2×C7direct (N × H)
14. C2×C3×C5×C7×C11C2×C7semidirect
16. C3×C72×C11C2×D5direct (N × H)
17. C2×C7×D5×C11C3×C7direct (N × H)
18. C2×C3×C5×C72C2×C11semidirect
19. C3×C72×D5C2×C11direct (N × H)
20. C3×C5×C7×C11C22×C7semidirect
22. C2×C72×C11C3×D5direct (N × H)
23. C2×C72×D5C3×C11direct (N × H)
25. C2×C5×C7×C11C2×C3×C7semidirect
26. C7×D5×C11C2×C3×C7direct (N × H)
27. C3×C5×C72C22×C11semidirect
28. C2×C3×D5×C11C72direct (N × H)
30. C72×C11C2×C3×D5direct (N × H)
31. C2×C5×C72C2×C3×C11semidirect
32. C72×D5C2×C3×C11direct (N × H)
34. C2×C3×C7×C11C7×D5direct (N × H)
35. C2×C3×C7×D5C7×C11direct (N × H)
36. C5×C7×C11C22×C3×C7semidirect
37. C2×C3×C5×C11C2×C72semidirect
38. C3×D5×C11C2×C72direct (N × H)
41. C2×C3×C72D5×C11direct (N × H)
42. C5×C72C22×C3×C11semidirect
43. C3×C7×C11C2×C7×D5direct (N × H)
44. C2×D5×C11C3×C72direct (N × H)
45. C2×C3×C5×C7C2×C7×C11semidirect
46. C3×C7×D5C2×C7×C11direct (N × H)
48. C3×C5×C11C22×C72semidirect
50. C2×C7×C11C3×C7×D5direct (N × H)
51. C3×C72C2×D5×C11direct (N × H)
52. C2×C7×D5C3×C7×C11direct (N × H)
54. C2×C5×C11C2×C3×C72semidirect
55. D5×C11C2×C3×C72direct (N × H)
56. C3×C5×C7C22×C7×C11semidirect
58. C2×C72C3×D5×C11direct (N × H)
60. C7×C11C2×C3×C7×D5direct (N × H)
61. C2×C5×C7C2×C3×C7×C11semidirect
62. C7×D5C2×C3×C7×C11direct (N × H)
64. C2×C3×C11C72×D5direct (N × H)
65. C2×C3×D5C72×C11direct (N × H)
66. C5×C11C22×C3×C72semidirect
67. C72C2×C3×D5×C11direct (N × H)
70. C2×C3×C7C7×D5×C11direct (N × H)
71. C5×C7C22×C3×C7×C11semidirect
72. C3×C11C2×C72×D5direct (N × H)
73. C2×C3×C5C2×C72×C11semidirect
74. C3×D5C2×C72×C11direct (N × H)
77. C2×C11C3×C72×D5direct (N × H)
78. C3×C7C2×C7×D5×C11direct (N × H)
79. C2×D5C3×C72×C11direct (N × H)
80. C3×C5C22×C72×C11semidirect
82. C2×C7C3×C7×D5×C11direct (N × H)
84. C11C2×C3×C72×D5direct (N × H)
85. C2×C5C2×C3×C72×C11semidirect
86. D5C2×C3×C72×C11direct (N × H)
87. C7C2×C3×C7×D5×C11direct (N × H)
89. C2×C3C72×D5×C11direct (N × H)
90. C5C22×C3×C72×C11semidirect
92. C3C2×C72×D5×C11direct (N × H)
94. C2C3×C72×D5×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C72×D5×C112
C2×C3×C5×C72×C112
C2×C72×D5×C113
C22×C3×C72×C115
C2×C3×C7×D5×C117
C2×C3×C72×D511