Finite Group Databasebeta

← C32×C11×C7⋊#261 #49114892

Subgroups — C32×C11×C7⋊#261 #49114892

Order 36036.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11×D13C211yesmaximal, characteristic
2C3×C11×C7⋊#261C314yesmaximal, direct product factor
3C32×C7×C11×C13C411yescharacteristic, complemented, Hall
4C3×C7×C11×D13C2×C314yes—
5C32×C11×#261—71nomaximal, Hall
6C11×C7⋊#261C3211yescharacteristic, direct product factor, Hall
7C32×C7⋊#261C1111yesmaximal, characteristic, direct product factor, Hall
8C3×C7×C11×C13C3×C414yescomplemented
9C32×C11×Dic7—131nomaximal, Hall
10C32×C11×D13D711yescharacteristic
11C7×C11×D13C2×C3211yescharacteristic
12C3×C11×#261—74no—
13C32×C7×D13C2×C1111yescharacteristic
14C2×C32×C7×C11—131no—
15C32×C11×C13Dic711yescharacteristic, complemented, Hall
16C3×C7⋊#261C3×C1114yesdirect product factor
17C7×C11×C13C32×C411yescharacteristic, complemented, Hall
18C3×C11×Dic7—134no—
19C3×C11×D13C3×D714yes—
20C32×C7×C13C4×C1111yescharacteristic, complemented, Hall
21C32×C7×C11#26111yescharacteristic, complemented, Hall
22C11×#261—71noHall
23C3×C7×D13C2×C3×C1114yes—
24C32×#261—71noHall
25C2×C3×C7×C11—134no—
26C3×C11×C13C3×Dic714yescomplemented
27C32×C4×C11—911noHall
28C7⋊#261C32×C1111yescharacteristic, direct product factor, Hall
29C11×Dic7—131noHall
30C11×D13C32×D711yescharacteristic
31C3×C7×C13C3×C4×C1114yescomplemented
32C32×Dic7—131noHall
33C32×D13C11×D711yescharacteristic
34C3×C7×C11C3×#26114yescomplemented
35C2×C32×C11—131no—
36C7×D13C2×C32×C1111yescharacteristic
37C3×#261—74no—
38C2×C7×C11—131no—
39C11×C13C32×Dic711yescharacteristic, complemented, Hall
40C3×C4×C11—914no—
41C2×C32×C7—131no—
42C32×C13C11×Dic711yescharacteristic, complemented, Hall
43C32×C11C7⋊#26111yescharacteristic, direct product factor, Hall
44C7×C13C32×C4×C1111yescharacteristic, complemented, Hall
45C3×Dic7—134no—
46C3×D13C3×C11×D714yes—
47C7×C11C32×#26111yescharacteristic, complemented, Hall
48C2×C3×C11—134no—
49C32×C7C11×#26111yescharacteristic, complemented, Hall
50#261—71noHall
51C4×C11—911noHall
52C2×C3×C7—134no—
53C3×C13C3×C11×Dic714yescomplemented
54C32×C4—911noHall
55C3×C11C3×C7⋊#26114yesdirect product factor
56Dic7—131noHall
57D13C32×C11×D711yescharacteristic
58C2×C11—131no—
59C3×C7C3×C11×#26114yescomplemented
60C2×C32—131no—
61C2×C7—131no—
62C13C32×C11×Dic711yescharacteristic, complemented, Sylow
63C3×C4—914no—
64C11C32×C7⋊#26111yescharacteristic, direct product factor, Sylow
65C32C11×C7⋊#26111yescharacteristic, direct product factor, Sylow
66C7C32×C11×#26111yescharacteristic, complemented, Sylow
67C2×C3—134no—
68C4—911noSylow
69C3C3×C11×C7⋊#26114yesdirect product factor
70C2—131no—
subgroupG/H
center, hypercenterC32×C11C7⋊#261
commutator, hypocenterC7×C13C32×C4×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC32×C7×C11×D13C2
cosocleC7×D13C2×C32×C11
LCSG ▷ C7×C13
UCSC1 ◁ C32×C11

Complements

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

NH ≅ G/Ntype
2. C3×C11×C7⋊#261C3direct (N × H)
3. C32×C7×C11×C13C4semidirect
6. C11×C7⋊#261C32direct (N × H)
7. C32×C7⋊#261C11direct (N × H)
8. C3×C7×C11×C13C3×C4semidirect
15. C32×C11×C13Dic7semidirect
16. C3×C7⋊#261C3×C11direct (N × H)
17. C7×C11×C13C32×C4semidirect
20. C32×C7×C13C4×C11semidirect
21. C32×C7×C11#261semidirect
26. C3×C11×C13C3×Dic7semidirect
28. C7⋊#261C32×C11direct (N × H)
31. C3×C7×C13C3×C4×C11semidirect
34. C3×C7×C11C3×#261semidirect
39. C11×C13C32×Dic7semidirect
42. C32×C13C11×Dic7semidirect
43. C32×C11C7⋊#261direct (N × H)
44. C7×C13C32×C4×C11semidirect
47. C7×C11C32×#261semidirect
49. C32×C7C11×#261semidirect
53. C3×C13C3×C11×Dic7semidirect
55. C3×C11C3×C7⋊#261direct (N × H)
59. C3×C7C3×C11×#261semidirect
62. C13C32×C11×Dic7semidirect
64. C11C32×C7⋊#261direct (N × H)
65. C32C11×C7⋊#261direct (N × H)
66. C7C32×C11×#261semidirect
69. C3C3×C11×C7⋊#261direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C11×D132
C3×C11×C7⋊#2613
C32×C11×#2617
C32×C7⋊#26111
C32×C11×Dic713