Finite Group Databasebeta

← C22×C3×C11×#63271 #49115008

Subgroups — C22×C3×C11×#63271 #49115008

Order 36036.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C11×#63271C213yesmaximal, direct product factor
2C22×C11×#63271C313yesmaximal, direct product factor
3C22×C3×C7×C11×C13C311yesmaximal, characteristic, complemented
4C3×C11×#63271C2211yescharacteristic, direct product factor, Hall
5C2×C11×#63271C2×C319yesdirect product factor
6C2×C3×C7×C11×C13C2×C313yescomplemented
7C22×C3×C11×C13⋊C3—71nomaximal, Hall
8C22×C7×C11×C13C3211yescharacteristic, complemented, Hall
9C22×C3×#63271C1111yesmaximal, characteristic, direct product factor, Hall
10C11×#63271C22×C313yesdirect product factor
11C3×C7×C11×C13C22×C311yescharacteristic, complemented
12C22×C3×C11×ΓL(1,𝔽8)—131nomaximal, Hall
13C2×C3×C11×C13⋊C3—73no—
14C2×C7×C11×C13C2×C3213yescomplemented
15C22×C3×C11×C13ΓL(1,𝔽8)11yescharacteristic, complemented
16C22×C11×C13⋊C3—73no—
17C2×C3×#63271C2×C1113yesdirect product factor
18C2×C3×C11×ΓL(1,𝔽8)—133no—
19C3×C11×C13⋊C3—71noHall
20C22×C3×C7×C13C3×C1111yescharacteristic, complemented
21C22×#63271C3×C1113yesdirect product factor
22C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
23C22×C3×C7×C11C13⋊C311yescharacteristic, complemented
24C22×C11×ΓL(1,𝔽8)—133no—
25C2×C3×C11×C13C2×ΓL(1,𝔽8)13yescomplemented
26C2×C11×C13⋊C3—79no—
27C3×#63271C22×C1111yescharacteristic, direct product factor, Hall
28C3×C11×ΓL(1,𝔽8)—131noHall
29C22×C11×C13C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
30C2×C3×C7×C13C2×C3×C1113yescomplemented
31C2×#63271C2×C3×C1119yesdirect product factor
32C22×C3×C13⋊C3—71noHall
33C2×C3×C7×C11C2×C13⋊C313yescomplemented
34C2×C11×ΓL(1,𝔽8)—139no—
35C3×C11×C13C22×ΓL(1,𝔽8)11yescharacteristic, complemented
36C11×C13⋊C3—73no—
37C22×C32×C11—911noHall
38C22×C7×C13C32×C1111yescharacteristic, complemented, Hall
39C22×C7×C11C3×C13⋊C311yescharacteristic, complemented, Hall
40C2×C11×C13C2×C3×ΓL(1,𝔽8)13yescomplemented
41C3×C7×C13C22×C3×C1111yescharacteristic, complemented
42#63271C22×C3×C1113yesdirect product factor
43C22×C3×ΓL(1,𝔽8)—131noHall
44C2×C3×C13⋊C3—73no—
45C3×C7×C11C22×C13⋊C311yescharacteristic, complemented
46C11×ΓL(1,𝔽8)—133no—
47C2×C32×C11—913no—
48C2×C7×C13C2×C32×C1113yescomplemented
49C22×C3×C13C11×ΓL(1,𝔽8)11yescharacteristic, complemented
50C22×C13⋊C3—73no—
51C2×C7×C11C2×C3×C13⋊C313yescomplemented
52C11×C13C22×C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
53C22×C3×C11—913no—
54C22×C3×C11#6327111yescharacteristic, direct product factor
55C2×C3×ΓL(1,𝔽8)—133no—
56C3×C13⋊C3—71noHall
57C32×C11—911noHall
58C7×C13C22×C32×C1111yescharacteristic, complemented, Hall
59C22×C3×C7C11×C13⋊C311yescharacteristic, complemented
60C22×ΓL(1,𝔽8)—133no—
61C2×C3×C13C2×C11×ΓL(1,𝔽8)13yescomplemented
62C2×C13⋊C3—79no—
63C7×C11C22×C3×C13⋊C311yescharacteristic, complemented, Hall
64C2×C3×C11—919no—
65C2×C3×C11C2×#6327113yesdirect product factor
66C3×ΓL(1,𝔽8)—131noHall
67C22×C13C3×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
68C22×C11C3×#6327111yescharacteristic, direct product factor, Hall
69C2×C3×C7C2×C11×C13⋊C313yescomplemented
70C2×ΓL(1,𝔽8)—139no—
71C3×C13C22×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
72C13⋊C3—73no—
73C22×C32—911noHall
74C3×C11—913no—
75C3×C11C22×#6327111yescharacteristic, direct product factor
76C22×C7C3×C11×C13⋊C311yescharacteristic, complemented, Hall
77C2×C13C2×C3×C11×ΓL(1,𝔽8)13yescomplemented
78C2×C11C2×C3×#6327113yesdirect product factor
79C3×C7C22×C11×C13⋊C311yescharacteristic, complemented
80ΓL(1,𝔽8)—133no—
81C2×C32—913no—
82C2×C7C2×C3×C11×C13⋊C313yescomplemented
83C13C22×C3×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
84C22×C3—913no—
85C22×C3C11×#6327111yescharacteristic, direct product factor
86C11C22×C3×#6327111yescharacteristic, direct product factor, Sylow
87C32—911noSylow
88C7C22×C3×C11×C13⋊C311yescharacteristic, complemented, Sylow
89C2×C3—919no—
90C2×C3C2×C11×#6327113yesdirect product factor
91C22C3×C11×#6327111yescharacteristic, direct product factor, Sylow
92C3—913no—
93C3C22×C11×#6327111yescharacteristic, direct product factor
94C2C2×C3×C11×#6327113yesdirect product factor
subgroupG/H
center, hypercenterC22×C3×C11#63271
commutator, cosocle, hypocenterC7×C13C22×C32×C11
FrattiniC1G
Fitting, socleC22×C3×C7×C11×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C22×C3×C11

Complements

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

NH ≅ G/Ntype
1. C2×C3×C11×#63271C2direct (N × H)
2. C22×C11×#63271C3direct (N × H)
3. C22×C3×C7×C11×C13C3semidirect
4. C3×C11×#63271C22direct (N × H)
5. C2×C11×#63271C2×C3direct (N × H)
6. C2×C3×C7×C11×C13C2×C3semidirect
8. C22×C7×C11×C13C32semidirect
9. C22×C3×#63271C11direct (N × H)
10. C11×#63271C22×C3direct (N × H)
11. C3×C7×C11×C13C22×C3semidirect
14. C2×C7×C11×C13C2×C32semidirect
15. C22×C3×C11×C13ΓL(1,𝔽8)semidirect
17. C2×C3×#63271C2×C11direct (N × H)
20. C22×C3×C7×C13C3×C11semidirect
21. C22×#63271C3×C11direct (N × H)
22. C7×C11×C13C22×C32semidirect
23. C22×C3×C7×C11C13⋊C3semidirect
25. C2×C3×C11×C13C2×ΓL(1,𝔽8)semidirect
27. C3×#63271C22×C11direct (N × H)
29. C22×C11×C13C3×ΓL(1,𝔽8)semidirect
30. C2×C3×C7×C13C2×C3×C11semidirect
31. C2×#63271C2×C3×C11direct (N × H)
33. C2×C3×C7×C11C2×C13⋊C3semidirect
35. C3×C11×C13C22×ΓL(1,𝔽8)semidirect
38. C22×C7×C13C32×C11semidirect
39. C22×C7×C11C3×C13⋊C3semidirect
40. C2×C11×C13C2×C3×ΓL(1,𝔽8)semidirect
41. C3×C7×C13C22×C3×C11semidirect
42. #63271C22×C3×C11direct (N × H)
45. C3×C7×C11C22×C13⋊C3semidirect
48. C2×C7×C13C2×C32×C11semidirect
49. C22×C3×C13C11×ΓL(1,𝔽8)semidirect
51. C2×C7×C11C2×C3×C13⋊C3semidirect
52. C11×C13C22×C3×ΓL(1,𝔽8)semidirect
54. C22×C3×C11#63271direct (N × H)
58. C7×C13C22×C32×C11semidirect
59. C22×C3×C7C11×C13⋊C3semidirect
61. C2×C3×C13C2×C11×ΓL(1,𝔽8)semidirect
63. C7×C11C22×C3×C13⋊C3semidirect
65. C2×C3×C11C2×#63271direct (N × H)
67. C22×C13C3×C11×ΓL(1,𝔽8)semidirect
68. C22×C11C3×#63271direct (N × H)
69. C2×C3×C7C2×C11×C13⋊C3semidirect
71. C3×C13C22×C11×ΓL(1,𝔽8)semidirect
75. C3×C11C22×#63271direct (N × H)
76. C22×C7C3×C11×C13⋊C3semidirect
77. C2×C13C2×C3×C11×ΓL(1,𝔽8)semidirect
78. C2×C11C2×C3×#63271direct (N × H)
79. C3×C7C22×C11×C13⋊C3semidirect
82. C2×C7C2×C3×C11×C13⋊C3semidirect
83. C13C22×C3×C11×ΓL(1,𝔽8)semidirect
85. C22×C3C11×#63271direct (N × H)
86. C11C22×C3×#63271direct (N × H)
88. C7C22×C3×C11×C13⋊C3semidirect
90. C2×C3C2×C11×#63271direct (N × H)
91. C22C3×C11×#63271direct (N × H)
93. C3C22×C11×#63271direct (N × H)
94. C2C2×C3×C11×#63271direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C11×#632712
C22×C11×#632713
C22×C3×C7×C11×C133
C22×C3×C11×C13⋊C37
C22×C3×#6327111
C22×C3×C11×ΓL(1,𝔽8)13