Finite Group Databasebeta

← C11×C11⋊(#1043⋊C3) #49137573

Subgroups — C11×C11⋊(#1043⋊C3) #49137573

Order 36300.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C112×(C5⋊D5)⋊C3C211yesmaximal, characteristic
2C11×C11⋊#1043C311yesmaximal, characteristic, complemented, Hall
3C112×C52⋊C3C411yescharacteristic, complemented, Hall
4C112×C5⋊D5C2×C311yescharacteristic
5C11⋊(#1043⋊C3)C1111yesmaximal, characteristic, direct product factor
6C11×#1043⋊C3—111nomaximal
7C52×C112C3×C411yescharacteristic, complemented, Hall
8C11×C11⋊AGL(1,𝔽5)—152no—
9C11×(C5⋊D5)⋊C3—21no—
10C11×(C5⋊D5)⋊C3—24no—
11C11×(C5⋊D5)⋊C3D1111yescharacteristic
12C11×(C5⋊D5)⋊C3C2×C1111yescharacteristic
13C3×C11×Dic11—251nomaximal, Hall
14D5×C112—152no—
15C11⋊#1043C3×C1111yescharacteristic, complemented
16C11×#1043—111no—
17C11×C52⋊C3—21no—
18C11×C52⋊C3—24no—
19C11×C52⋊C3Dic1111yescharacteristic, complemented
20C11×C52⋊C3C4×C1111yescharacteristic, complemented
21C2×C3×C112—251no—
22C5×C112—32no—
23C11×C5⋊D5—21no—
24C11×C5⋊D5—24no—
25C11×C5⋊D5C3×D1111yescharacteristic
26C11×C5⋊D5C2×C3×C1111yescharacteristic
27C11×Dic11—251noHall
28C3×C112—1001noHall
29#1043⋊C3—111noHall
30C52×C11—21no—
31C52×C11—24no—
32C52×C11C3×Dic1111yescharacteristic, complemented
33C52×C11C3×C4×C1111yescharacteristic, complemented
34C2×C112—251no—
35C11⋊AGL(1,𝔽5)—152no—
36C11×AGL(1,𝔽5)—1652no—
37(C5⋊D5)⋊C3C11×D1111yescharacteristic
38C3×C4×C11—2751no—
39C3×Dic11—251no—
40C112#1043⋊C311yescharacteristic, complemented, Sylow
41D5×C11—152no—
42D5×C11—152no—
43D5×C11—302no—
44D5×C11—308no—
45#1043—111noHall
46C52⋊C3C11×Dic1111yescharacteristic, complemented, Hall
47C2×C3×C11—251no—
48C2×C3×C11—251no—
49C2×C3×C11—501no—
50C2×C3×C11—504no—
51C5×C11—32no—
52C5×C11—32no—
53C5×C11—62no—
54C5×C11—68no—
55C5⋊D5C3×C11×D1111yescharacteristic
56C4×C11—2751no—
57Dic11—251no—
58C3×C11—501no—
59C3×C11—1004no—
60C3×C11—1001no—
61C3×C11—1001no—
62C52C3×C11×Dic1111yescharacteristic, complemented, Sylow
63C2×C11—251no—
64C2×C11—251no—
65C2×C11—501no—
66C2×C11—504no—
67AGL(1,𝔽5)—1652no—
68C3×C4—2751noHall
69C11—21no—
70C11—24no—
71C11C11×#1043⋊C311yescharacteristic, complemented
72C11C11⋊(#1043⋊C3)11yescharacteristic, direct product factor
73D5—152no—
74C2×C3—251no—
75C5—32no—
76C4—2751noSylow
77C3—1001noSylow
78C2—251no—
subgroupG/H
center, hypercenterC11C11⋊(#1043⋊C3)
commutator, hypocenterC52×C11C3×C4×C11
FrattiniC1G
Fitting, socleC52×C112C3×C4
prime radicalC112×(C5⋊D5)⋊C3C2
cosocleC11×C5⋊D5C2×C3×C11
LCSG ▷ C52×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
2. C11×C11⋊#1043C3semidirect
3. C112×C52⋊C3C4semidirect
5. C11⋊(#1043⋊C3)C11direct (N × H)
7. C52×C112C3×C4semidirect
15. C11⋊#1043C3×C11semidirect
19. C11×C52⋊C3Dic11semidirect
20. C11×C52⋊C3C4×C11semidirect
32. C52×C11C3×Dic11semidirect
33. C52×C11C3×C4×C11semidirect
40. C112#1043⋊C3semidirect
46. C52⋊C3C11×Dic11semidirect
62. C52C3×C11×Dic11semidirect
71. C11C11×#1043⋊C3semidirect
72. C11C11⋊(#1043⋊C3)direct (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⋊#10433
C11⋊(#1043⋊C3)11
C11×#1043⋊C311
C3×C11×Dic1125