Finite Group Databasebeta

← C3×C3⋊(C5⋊(C7⋊D7)) #17984409

Subgroups — C3×C3⋊(C5⋊(C7⋊D7)) #17984409

Order 4410.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C72C211yesmaximal, characteristic, complemented, Hall
2C3⋊(C5⋊(C7⋊D7))C311yesmaximal, characteristic, direct product factor
3C3×C5⋊(C7⋊D7)—31nomaximal
4C3×C3⋊(C7⋊D7)—51nomaximal, Hall
5C3×C5×C72—21no—
6C3×C5×C72D311yescharacteristic, complemented
7C3×C5×C72C2×C311yescharacteristic, complemented
8C3×D105—78nomaximal
9C5⋊(C7⋊D7)—31noHall
10C32×C72D511yescharacteristic, complemented, Hall
11C32×C5×C7D718yescomplemented
12C3⋊(C7⋊D7)—51no—
13C3×C7⋊D7—151no—
14C5×C72C3×D311yescharacteristic, complemented, Hall
15D105—78no—
16C3×D35—218no—
17C3×C72—21no—
18C3×C72C3×D511yescharacteristic, complemented
19C3×C72D1511yescharacteristic, complemented
20C3×D21—358no—
21C3×C5×C7—28no—
22C3×C5×C7C3×D718yescomplemented
23C3×C5×C7D2118yescomplemented
24C7⋊D7—151noHall
25C3×D15—491noHall
26D35—218no—
27C32×C7D3518yescomplemented
28C72C3×D1511yescharacteristic, complemented, Sylow
29C32×C5C7⋊D711yescharacteristic, complemented, Hall
30D21—358no—
31C3×D7—1058no—
32C5×C7C3×D2118yescomplemented
33D15—491no—
34C3×D5—1471no—
35C3×C7—28no—
36C3×C7C3×D3518yescomplemented
37C3×C7D10518yescomplemented
38C3×D3—2451noHall
39C3×C5—21no—
40C3×C5C3×C7⋊D711yescharacteristic, complemented
41C3×C5C3⋊(C7⋊D7)11yescharacteristic, complemented
42D7—1058no—
43D5—1471noHall
44C32C5⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
45C7C3×D10518yescomplemented
46C2×C3—7351no—
47D3—2451no—
48C5C3×C3⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
49C3—21no—
50C3C3×C5⋊(C7⋊D7)11yescharacteristic, complemented
51C3C3⋊(C5⋊(C7⋊D7))11yescharacteristic, direct product factor
52C2—7351noSylow
subgroupG/H
center, hypercenterC3C3⋊(C5⋊(C7⋊D7))
commutator, cosocle, hypocenterC3×C5×C72C2×C3
FrattiniC1G
Fitting, socleC32×C5×C72C2
LCSG ▷ C3×C5×C72
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5×C72C2semidirect
2. C3⋊(C5⋊(C7⋊D7))C3direct (N × H)
6. C3×C5×C72D3semidirect
7. C3×C5×C72C2×C3semidirect
10. C32×C72D5semidirect
11. C32×C5×C7D7semidirect
14. C5×C72C3×D3semidirect
18. C3×C72C3×D5semidirect
19. C3×C72D15semidirect
22. C3×C5×C7C3×D7semidirect
23. C3×C5×C7D21semidirect
27. C32×C7D35semidirect
28. C72C3×D15semidirect
29. C32×C5C7⋊D7semidirect
32. C5×C7C3×D21semidirect
36. C3×C7C3×D35semidirect
37. C3×C7D105semidirect
40. C3×C5C3×C7⋊D7semidirect
41. C3×C5C3⋊(C7⋊D7)semidirect
44. C32C5⋊(C7⋊D7)semidirect
45. C7C3×D105semidirect
48. C5C3×C3⋊(C7⋊D7)semidirect
50. C3C3×C5⋊(C7⋊D7)semidirect
51. C3C3⋊(C5⋊(C7⋊D7))direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C722
C3⋊(C5⋊(C7⋊D7))3
C3×C5⋊(C7⋊D7)3
C3×C3⋊(C7⋊D7)5
C3×D1057