Finite Group Databasebeta

← C11×C7⋊(C9⋊#261) #49114473

Subgroups — C11×C7⋊(C9⋊#261) #49114473

Order 36036.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C9×C11×D13C211yesmaximal, characteristic
2C11×C3⋊(C7⋊#261)—31nomaximal
3C7×C9×C11×C13C411yescharacteristic, complemented, Hall
4C3×C7×C11×D13D311yescharacteristic
5C11×C9⋊#261—71nomaximal, Hall
6C11×C7⋊#261—91noHall
7C7⋊(C9⋊#261)C1111yesmaximal, characteristic, direct product factor, Hall
8C3×C7×C11×C13Dic311yescharacteristic
9C11×Dic63—131nomaximal, Hall
10C9×C11×D13D711yescharacteristic
11C7×C11×D13D911yescharacteristic
12C11×C3⋊#261—211no—
13C7×C9×D13C2×C1111yescharacteristic
14C2×C7×C9×C11—131no—
15C9×C11×C13Dic711yescharacteristic, complemented, Hall
16C3⋊(C7⋊#261)—31no—
17C7×C11×C13Dic911yescharacteristic, complemented, Hall
18C11×Dic21—391no—
19C3×C11×D13D2111yescharacteristic
20C7×C9×C13C4×C1111yescharacteristic, complemented, Hall
21C7×C9×C11#26111yescharacteristic, complemented, Hall
22C11×#261—631noHall
23C3×C7×D13D3×C1111yescharacteristic
24C9⋊#261—71noHall
25C2×C3×C7×C11—131no—
26C3×C11×C13Dic2111yescharacteristic
27C11×Dic9—911noHall
28C7⋊#261—91noHall
29C11×Dic7—1171noHall
30C11×D13D6311yescharacteristic
31C3×C7×C13C11×Dic311yescharacteristic
32Dic63—131noHall
33C9×D13C11×D711yescharacteristic
34C3×C7×C11C3⋊#26111yescharacteristic
35C2×C9×C11—131no—
36C7×D13C11×D911yescharacteristic
37C3⋊#261—211no—
38C2×C7×C11—131no—
39C11×C13Dic6311yescharacteristic, complemented, Hall
40C11×Dic3—2731no—
41C2×C7×C9—131no—
42C9×C13C11×Dic711yescharacteristic, complemented, Hall
43C9×C11C7⋊#26111yescharacteristic, complemented, Hall
44C7×C13C11×Dic911yescharacteristic, complemented, Hall
45Dic21—391no—
46C3×D13C11×D2111yescharacteristic
47C7×C11C9⋊#26111yescharacteristic, complemented, Hall
48C2×C3×C11—131no—
49C7×C9C11×#26111yescharacteristic, complemented, Hall
50#261—631noHall
51C4×C11—8191noHall
52C2×C3×C7—131no—
53C3×C13C11×Dic2111yescharacteristic
54Dic9—911noHall
55C3×C11C3⋊(C7⋊#261)11yescharacteristic
56Dic7—1171noHall
57D13C11×D6311yescharacteristic
58C2×C11—131no—
59C3×C7C11×C3⋊#26111yescharacteristic
60C2×C9—131no—
61C2×C7—131no—
62C13C11×Dic6311yescharacteristic, complemented, Sylow
63Dic3—2731no—
64C11C7⋊(C9⋊#261)11yescharacteristic, direct product factor, Sylow
65C9C11×C7⋊#26111yescharacteristic, complemented, Sylow
66C7C11×C9⋊#26111yescharacteristic, complemented, Sylow
67C2×C3—131no—
68C4—8191noSylow
69C3C11×C3⋊(C7⋊#261)11yescharacteristic
70C2—131no—
subgroupG/H
center, hypercenterC11C7⋊(C9⋊#261)
commutator, hypocenterC7×C9×C13C4×C11
FrattiniC3C11×C3⋊(C7⋊#261)
FittingC7×C9×C11×C13C4
socleC3×C7×C11×C13Dic3
prime radicalC3×C7×C11×D13D3
cosocleC7×C9×D13C2×C11
LCSG ▷ C7×C9×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
3. C7×C9×C11×C13C4semidirect
7. C7⋊(C9⋊#261)C11direct (N × H)
15. C9×C11×C13Dic7semidirect
17. C7×C11×C13Dic9semidirect
20. C7×C9×C13C4×C11semidirect
21. C7×C9×C11#261semidirect
39. C11×C13Dic63semidirect
42. C9×C13C11×Dic7semidirect
43. C9×C11C7⋊#261semidirect
44. C7×C13C11×Dic9semidirect
47. C7×C11C9⋊#261semidirect
49. C7×C9C11×#261semidirect
62. C13C11×Dic63semidirect
64. C11C7⋊(C9⋊#261)direct (N × H)
65. C9C11×C7⋊#261semidirect
66. C7C11×C9⋊#261semidirect

Maximal subgroups

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

subgroupindex
C7×C9×C11×D132
C11×C3⋊(C7⋊#261)3
C11×C9⋊#2617
C7⋊(C9⋊#261)11
C11×Dic6313