Finite Group Databasebeta

← C22×C17×C7⋊(C52⋊C3) #49088038

Subgroups — C22×C17×C7⋊(C52⋊C3) #49088038

Order 35700.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×C7⋊(C52⋊C3)C213yesmaximal, direct product factor
2C22×C52×C7×C17C311yesmaximal, characteristic, complemented, Hall
3C17×C7⋊(C52⋊C3)C2211yescharacteristic, direct product factor, Hall
4C2×C52×C7×C17C2×C313yescomplemented
5C22×C17×C52⋊C3—71nomaximal, Hall
6C52×C7×C17C22×C311yescharacteristic, complemented, Hall
7C2×C17×C52⋊C3—73no—
8C22×C5×C7×C17—32no—
9C22×C7⋊(C52⋊C3)C1711yesmaximal, characteristic, direct product factor, Hall
10C22×C52×C17ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
11C22×C17×ΓL(1,𝔽8)—251nomaximal, Hall
12C17×C52⋊C3—71noHall
13C2×C5×C7×C17—36no—
14C2×C7⋊(C52⋊C3)C2×C1713yesdirect product factor
15C2×C52×C17C2×ΓL(1,𝔽8)13yescomplemented
16C2×C17×ΓL(1,𝔽8)—253no—
17C22×C52×C7C3×C1711yescharacteristic, complemented, Hall
18C5×C7×C17—32no—
19C7⋊(C52⋊C3)C22×C1711yescharacteristic, direct product factor, Hall
20C22×C7×C17C52⋊C311yescharacteristic, complemented, Hall
21C52×C17C22×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
22C17×ΓL(1,𝔽8)—251noHall
23C2×C52×C7C2×C3×C1713yescomplemented
24C22×C5×C17—32no—
25C22×C52⋊C3—71noHall
26C2×C7×C17C2×C52⋊C313yescomplemented
27C22×C3×C17—1751noHall
28C52×C7C22×C3×C1711yescharacteristic, complemented, Hall
29C2×C5×C17—36no—
30C2×C52⋊C3—73no—
31C22×C5×C7—32no—
32C7×C17C22×C52⋊C311yescharacteristic, complemented, Hall
33C2×C3×C17—1753no—
34C22×C52C17×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
35C5×C17—32no—
36C22×ΓL(1,𝔽8)—251noHall
37C52⋊C3—71noHall
38C2×C5×C7—36no—
39C22×C17C7⋊(C52⋊C3)11yescharacteristic, direct product factor, Hall
40C3×C17—1751noHall
41C2×C52C2×C17×ΓL(1,𝔽8)13yescomplemented
42C2×ΓL(1,𝔽8)—253no—
43C5×C7—32no—
44C2×C17C2×C7⋊(C52⋊C3)13yesdirect product factor
45C22×C7C17×C52⋊C311yescharacteristic, complemented, Hall
46C52C22×C17×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
47ΓL(1,𝔽8)—251noHall
48C22×C5—32no—
49C17C22×C7⋊(C52⋊C3)11yescharacteristic, direct product factor, Sylow
50C2×C7C2×C17×C52⋊C313yescomplemented
51C22×C3—1751noHall
52C2×C5—36no—
53C7C22×C17×C52⋊C311yescharacteristic, complemented, Sylow
54C2×C3—1753no—
55C5—32no—
56C22C17×C7⋊(C52⋊C3)11yescharacteristic, direct product factor, Sylow
57C3—1751noSylow
58C2C2×C17×C7⋊(C52⋊C3)13yesdirect product factor
subgroupG/H
center, hypercenterC22×C17C7⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C7C22×C3×C17
FrattiniC1G
Fitting, socleC22×C52×C7×C17C3
LCSG ▷ C52×C7
UCSC1 ◁ C22×C17

Complements

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

NH ≅ G/Ntype
1. C2×C17×C7⋊(C52⋊C3)C2direct (N × H)
2. C22×C52×C7×C17C3semidirect
3. C17×C7⋊(C52⋊C3)C22direct (N × H)
4. C2×C52×C7×C17C2×C3semidirect
6. C52×C7×C17C22×C3semidirect
9. C22×C7⋊(C52⋊C3)C17direct (N × H)
10. C22×C52×C17ΓL(1,𝔽8)semidirect
14. C2×C7⋊(C52⋊C3)C2×C17direct (N × H)
15. C2×C52×C17C2×ΓL(1,𝔽8)semidirect
17. C22×C52×C7C3×C17semidirect
19. C7⋊(C52⋊C3)C22×C17direct (N × H)
20. C22×C7×C17C52⋊C3semidirect
21. C52×C17C22×ΓL(1,𝔽8)semidirect
23. C2×C52×C7C2×C3×C17semidirect
26. C2×C7×C17C2×C52⋊C3semidirect
28. C52×C7C22×C3×C17semidirect
32. C7×C17C22×C52⋊C3semidirect
34. C22×C52C17×ΓL(1,𝔽8)semidirect
39. C22×C17C7⋊(C52⋊C3)direct (N × H)
41. C2×C52C2×C17×ΓL(1,𝔽8)semidirect
44. C2×C17C2×C7⋊(C52⋊C3)direct (N × H)
45. C22×C7C17×C52⋊C3semidirect
46. C52C22×C17×ΓL(1,𝔽8)semidirect
49. C17C22×C7⋊(C52⋊C3)direct (N × H)
50. C2×C7C2×C17×C52⋊C3semidirect
53. C7C22×C17×C52⋊C3semidirect
56. C22C17×C7⋊(C52⋊C3)direct (N × H)
58. C2C2×C17×C7⋊(C52⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×C7⋊(C52⋊C3)2
C22×C52×C7×C173
C22×C17×C52⋊C37
C22×C7⋊(C52⋊C3)17
C22×C17×ΓL(1,𝔽8)25