Finite Group Databasebeta

← C7×C11⋊(#1043⋊C3) #37528508

Subgroups — C7×C11⋊(#1043⋊C3) #37528508

Order 23100.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C11×(C5⋊D5)⋊C3C211yesmaximal, characteristic
2C7×C11⋊#1043C311yesmaximal, characteristic, complemented, Hall
3C7×C11×C52⋊C3C411yescharacteristic, complemented, Hall
4C7×C11×C5⋊D5C2×C311yescharacteristic
5C11⋊(#1043⋊C3)C711yesmaximal, characteristic, direct product factor, Hall
6C7×#1043⋊C3—111nomaximal, Hall
7C52×C7×C11C3×C411yescharacteristic, complemented, Hall
8C11×(C5⋊D5)⋊C3C2×C711yescharacteristic
9C7×C11⋊AGL(1,𝔽5)—152no—
10C11⋊#1043C3×C711yescharacteristic, complemented, Hall
11C7×(C5⋊D5)⋊C3D1111yescharacteristic
12C3×C7×Dic11—251nomaximal, Hall
13C11×C52⋊C3C4×C711yescharacteristic, complemented, Hall
14C7×D5×C11—152no—
15C7×#1043—111noHall
16C11×C5⋊D5C2×C3×C711yescharacteristic
17C7×C52⋊C3Dic1111yescharacteristic, complemented, Hall
18C2×C3×C7×C11—251no—
19C5×C7×C11—32no—
20C7×C5⋊D5C3×D1111yescharacteristic
21C7×Dic11—251noHall
22#1043⋊C3—111noHall
23C52×C11C3×C4×C711yescharacteristic, complemented, Hall
24C3×C7×C11—251noHall
25C11⋊AGL(1,𝔽5)—152no—
26C52×C7C3×Dic1111yescharacteristic, complemented, Hall
27C2×C7×C11—251no—
28(C5⋊D5)⋊C3C7×D1111yescharacteristic
29C7×AGL(1,𝔽5)—1652no—
30C3×Dic11—251noHall
31D5×C11—152no—
32#1043—111noHall
33C3×C4×C7—2751noHall
34C7×C11#1043⋊C311yescharacteristic, complemented, Hall
35C52⋊C3C7×Dic1111yescharacteristic, complemented, Hall
36C7×D5—152no—
37C2×C3×C11—251no—
38C5×C11—32no—
39C5⋊D5C3×C7×D1111yescharacteristic
40Dic11—251noHall
41C2×C3×C7—251no—
42C5×C7—32no—
43C3×C11—251noHall
44C4×C7—2751noHall
45C52C3×C7×Dic1111yescharacteristic, complemented, Sylow
46C2×C11—251no—
47C3×C7—251noHall
48AGL(1,𝔽5)—1652no—
49C2×C7—251no—
50C3×C4—2751noHall
51C11C7×#1043⋊C311yescharacteristic, complemented, Sylow
52D5—152no—
53C7C11⋊(#1043⋊C3)11yescharacteristic, direct product factor, Sylow
54C2×C3—251no—
55C5—32no—
56C4—2751noSylow
57C3—251noSylow
58C2—251no—
subgroupG/H
center, hypercenterC7C11⋊(#1043⋊C3)
commutator, hypocenterC52×C11C3×C4×C7
FrattiniC1G
Fitting, socleC52×C7×C11C3×C4
prime radicalC7×C11×(C5⋊D5)⋊C3C2
cosocleC11×C5⋊D5C2×C3×C7
LCSG ▷ C52×C11
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
2. C7×C11⋊#1043C3semidirect
3. C7×C11×C52⋊C3C4semidirect
5. C11⋊(#1043⋊C3)C7direct (N × H)
7. C52×C7×C11C3×C4semidirect
10. C11⋊#1043C3×C7semidirect
13. C11×C52⋊C3C4×C7semidirect
17. C7×C52⋊C3Dic11semidirect
23. C52×C11C3×C4×C7semidirect
26. C52×C7C3×Dic11semidirect
34. C7×C11#1043⋊C3semidirect
35. C52⋊C3C7×Dic11semidirect
45. C52C3×C7×Dic11semidirect
51. C11C7×#1043⋊C3semidirect
53. C7C11⋊(#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
C7×C11×(C5⋊D5)⋊C32
C7×C11⋊#10433
C11⋊(#1043⋊C3)7
C7×#1043⋊C311
C3×C7×Dic1125