Finite Group Databasebeta

← C22×C11×#11717942 #49114503

Subgroups — C22×C11×#11717942 #49114503

Order 36036.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#11717942C213yesmaximal, direct product factor
2C22×C3×C7×C11×C13C311yesmaximal, characteristic
3C11×#11717942C2211yescharacteristic, direct product factor, Hall
4C2×C3×C7×C11×C13C2×C313yes—
5C22×C11×C13⋊C9—71nomaximal, Hall
6C22×C7×C11×C13C911yescharacteristic, complemented, Hall
7C22×#11717942C1111yesmaximal, characteristic, direct product factor, Hall
8C3×C7×C11×C13C22×C311yescharacteristic
9C22×C11×C7⋊C9—131nomaximal, Hall
10C2×C11×C13⋊C9—73no—
11C2×C7×C11×C13C2×C913yescomplemented
12C22×C3×C11×C13ΓL(1,𝔽8)11yescharacteristic
13C2×#11717942C2×C1113yesdirect product factor
14C2×C11×C7⋊C9—133no—
15C11×C13⋊C9—71noHall
16C22×C3×C7×C13C3×C1111yescharacteristic
17C7×C11×C13C22×C911yescharacteristic, complemented, Hall
18C22×C3×C7×C11C13⋊C311yescharacteristic
19C2×C3×C11×C13C2×ΓL(1,𝔽8)13yes—
20#11717942C22×C1111yescharacteristic, direct product factor, Hall
21C11×C7⋊C9—131noHall
22C22×C11×C13C7⋊C911yescharacteristic, complemented, Hall
23C2×C3×C7×C13C2×C3×C1113yes—
24C22×C13⋊C9—71noHall
25C2×C3×C7×C11C2×C13⋊C313yes—
26C3×C11×C13C22×ΓL(1,𝔽8)11yescharacteristic
27C22×C9×C11—911noHall
28C22×C7×C13C9×C1111yescharacteristic, complemented, Hall
29C22×C7×C11C13⋊C911yescharacteristic, complemented, Hall
30C2×C11×C13C2×C7⋊C913yescomplemented
31C3×C7×C13C22×C3×C1111yescharacteristic
32C22×C7⋊C9—131noHall
33C2×C13⋊C9—73no—
34C3×C7×C11C22×C13⋊C311yescharacteristic
35C2×C9×C11—913no—
36C2×C7×C13C2×C9×C1113yescomplemented
37C22×C3×C13C11×ΓL(1,𝔽8)11yescharacteristic
38C2×C7×C11C2×C13⋊C913yescomplemented
39C11×C13C22×C7⋊C911yescharacteristic, complemented, Hall
40C22×C3×C11#6327111yescharacteristic
41C2×C7⋊C9—133no—
42C13⋊C9—71noHall
43C9×C11—911noHall
44C7×C13C22×C9×C1111yescharacteristic, complemented, Hall
45C22×C3×C7C11×C13⋊C311yescharacteristic
46C2×C3×C13C2×C11×ΓL(1,𝔽8)13yes—
47C7×C11C22×C13⋊C911yescharacteristic, complemented, Hall
48C2×C3×C11C2×#6327113yes—
49C7⋊C9—131noHall
50C22×C13C11×C7⋊C911yescharacteristic, complemented, Hall
51C22×C11#1171794211yescharacteristic, direct product factor, Hall
52C2×C3×C7C2×C11×C13⋊C313yes—
53C3×C13C22×C11×ΓL(1,𝔽8)11yescharacteristic
54C22×C9—911noHall
55C3×C11C22×#6327111yescharacteristic
56C22×C7C11×C13⋊C911yescharacteristic, complemented, Hall
57C2×C13C2×C11×C7⋊C913yescomplemented
58C2×C11C2×#1171794213yesdirect product factor
59C3×C7C22×C11×C13⋊C311yescharacteristic
60C2×C9—913no—
61C2×C7C2×C11×C13⋊C913yescomplemented
62C13C22×C11×C7⋊C911yescharacteristic, complemented, Sylow
63C22×C3C11×#6327111yescharacteristic
64C11C22×#1171794211yescharacteristic, direct product factor, Sylow
65C9—911noSylow
66C7C22×C11×C13⋊C911yescharacteristic, complemented, Sylow
67C2×C3C2×C11×#6327113yes—
68C22C11×#1171794211yescharacteristic, direct product factor, Sylow
69C3C22×C11×#6327111yescharacteristic
70C2C2×C11×#1171794213yesdirect product factor
subgroupG/H
center, hypercenterC22×C3×C11#63271
commutator, hypocenterC7×C13C22×C9×C11
FrattiniC3C22×C11×#63271
Fitting, socle, prime radicalC22×C3×C7×C11×C13C3
cosocleC3×C7×C13C22×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C22×C3×C11

Complements

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

NH ≅ G/Ntype
1. C2×C11×#11717942C2direct (N × H)
3. C11×#11717942C22direct (N × H)
6. C22×C7×C11×C13C9semidirect
7. C22×#11717942C11direct (N × H)
11. C2×C7×C11×C13C2×C9semidirect
13. C2×#11717942C2×C11direct (N × H)
17. C7×C11×C13C22×C9semidirect
20. #11717942C22×C11direct (N × H)
22. C22×C11×C13C7⋊C9semidirect
28. C22×C7×C13C9×C11semidirect
29. C22×C7×C11C13⋊C9semidirect
30. C2×C11×C13C2×C7⋊C9semidirect
36. C2×C7×C13C2×C9×C11semidirect
38. C2×C7×C11C2×C13⋊C9semidirect
39. C11×C13C22×C7⋊C9semidirect
44. C7×C13C22×C9×C11semidirect
47. C7×C11C22×C13⋊C9semidirect
50. C22×C13C11×C7⋊C9semidirect
51. C22×C11#11717942direct (N × H)
56. C22×C7C11×C13⋊C9semidirect
57. C2×C13C2×C11×C7⋊C9semidirect
58. C2×C11C2×#11717942direct (N × H)
61. C2×C7C2×C11×C13⋊C9semidirect
62. C13C22×C11×C7⋊C9semidirect
64. C11C22×#11717942direct (N × H)
66. C7C22×C11×C13⋊C9semidirect
68. C22C11×#11717942direct (N × H)
70. C2C2×C11×#11717942direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#117179422
C22×C3×C7×C11×C133
C22×C11×C13⋊C97
C22×#1171794211
C22×C11×C7⋊C913