Finite Group Databasebeta

← C11×C11⋊#64480 #49137566

Subgroups — C11×C11⋊#64480 #49137566

Order 36300.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C112×(C5⋊D5)⋊C3C211yesmaximal, characteristic
2C11×C11⋊#1044—31nomaximal, Hall
3C112×C52⋊C3C411yescharacteristic, complemented, Hall
4C112×C5⋊D5D311yescharacteristic
5C11⋊#64480C1111yesmaximal, characteristic, direct product factor
6C11×#64480—111nomaximal
7C52×C112Dic311yescharacteristic, complemented, Hall
8C11×C11⋊AGL(1,𝔽5)—151no—
9C11×C11⋊AGL(1,𝔽5)—151no—
10C11×(C5⋊D5)⋊C3—25no—
11C11×(C5⋊D5)⋊C3D1111yescharacteristic
12C11×(C5⋊D5)⋊C3C2×C1111yescharacteristic
13C11×Dic33—251nomaximal, Hall
14D5×C112—151no—
15D5×C112—301no—
16C11⋊#1044—31no—
17C11×#1044—331no—
18C11×C52⋊C3—25no—
19C11×C52⋊C3Dic1111yescharacteristic, complemented
20C11×C52⋊C3C4×C1111yescharacteristic, complemented
21C2×C3×C112—251no—
22C5×C112—31no—
23C5×C112—61no—
24C11×C5⋊D5—25no—
25C11×C5⋊D5D3×C1111yescharacteristic
26C11×C5⋊D5D3311yescharacteristic
27C11×Dic11—751noHall
28C3×C112—1001noHall
29#64480—111noHall
30C52×C11—25no—
31C52×C11C11×Dic311yescharacteristic, complemented
32C52×C11Dic3311yescharacteristic, complemented
33C2×C112—251no—
34C11⋊AGL(1,𝔽5)—151no—
35C11⋊AGL(1,𝔽5)—151no—
36C11×AGL(1,𝔽5)—1651no—
37C11×AGL(1,𝔽5)—1651no—
38(C5⋊D5)⋊C3C11×D1111yescharacteristic
39Dic33—251no—
40C11×Dic3—2751no—
41C112#6448011yescharacteristic, complemented, Sylow
42D5×C11—151no—
43D5×C11—151no—
44D5×C11—301no—
45D5×C11—305no—
46D5×C11—301no—
47D5×C11—305no—
48#1044—331noHall
49C52⋊C3C11×Dic1111yescharacteristic, complemented, Hall
50C2×C3×C11—251no—
51C2×C3×C11—251no—
52C2×C3×C11—505no—
53C5×C11—31no—
54C5×C11—31no—
55C5×C11—65no—
56C5×C11—61no—
57C5×C11—65no—
58C5×C11—61no—
59C5⋊D5C11×D3311yescharacteristic
60C4×C11—8251no—
61Dic11—751no—
62C3×C11—1005no—
63C3×C11—1001no—
64C3×C11—1001no—
65C52C11×Dic3311yescharacteristic, complemented, Sylow
66C2×C11—251no—
67C2×C11—251no—
68C2×C11—505no—
69AGL(1,𝔽5)—1651no—
70AGL(1,𝔽5)—1651no—
71Dic3—2751noHall
72C11—25no—
73C11C11×#6448011yescharacteristic, complemented
74C11C11⋊#6448011yescharacteristic, direct product factor
75D5—151no—
76D5—301no—
77C2×C3—251no—
78C5—31no—
79C5—61no—
80C4—8251noSylow
81C3—1001noSylow
82C2—251no—
subgroupG/H
center, hypercenterC11C11⋊#64480
commutator, hypocenterC11×C52⋊C3C4×C11
FrattiniC1G
Fitting, socleC52×C112Dic3
prime radicalC112×(C5⋊D5)⋊C3C2
cosocleC11×(C5⋊D5)⋊C3C2×C11
LCSG ▷ C11×C52⋊C3
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
3. C112×C52⋊C3C4semidirect
5. C11⋊#64480C11direct (N × H)
7. C52×C112Dic3semidirect
19. C11×C52⋊C3Dic11semidirect
20. C11×C52⋊C3C4×C11semidirect
31. C52×C11C11×Dic3semidirect
32. C52×C11Dic33semidirect
41. C112#64480semidirect
49. C52⋊C3C11×Dic11semidirect
65. C52C11×Dic33semidirect
73. C11C11×#64480semidirect
74. C11C11⋊#64480direct (N × H)

Maximal subgroups

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

subgroupindex
C112×(C5⋊D5)⋊C32
C11×C11⋊#10443
C11⋊#6448011
C11×#6448011
C11×Dic3325