Finite Group Databasebeta

← C47×H(7,𝔽2) #20241204

Subgroups — C47×H(7,𝔽2) #20241204

Order 6016.

5992 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#585C2128yesmaximal, complemented
2C2×H(5,𝔽2)×C47C2135yesmaximal, complemented
32−1+4×C47C22156yescomplemented
4H(5,𝔽2)×C47C221280yescomplemented
5C2×#41×C47C221210yescomplemented
6C22×D4×C47C221105yescomplemented
7C24×C47C23130yescomplemented
8#41×C47C231560yescomplemented
9C2×Q8×C47C23170yescomplemented
10C2×D4×C47C231630yescomplemented
11C22×C4×C47C231105yescomplemented
12C23×C47—830no—
13C23×C47C241105yes—
14Q8×C47C24156yes—
15D4×C47C241280yes—
16C2×C4×C47C241210yes—
17C22×C47—4105no—
18C22×C47C25135yes—
19C4×C47C25128yes—
20H(7,𝔽2)C4711yesmaximal, characteristic, direct product factor, Sylow
21C2×C47—235no—
22C2×C47C2611yescharacteristic
23#585C2×C47128yescomplemented
24C2×H(5,𝔽2)C2×C47135yescomplemented
25C47H(7,𝔽2)11yescharacteristic, direct product factor, Sylow
262−1+4C22×C47156yescomplemented
27H(5,𝔽2)C22×C471280yescomplemented
28C2×#41C22×C471210yescomplemented
29C22×D4C22×C471105yescomplemented
30C24C23×C47130yescomplemented
31#41C23×C471560yescomplemented
32C2×Q8C23×C47170yescomplemented
33C2×D4C23×C471630yescomplemented
34C22×C4C23×C471105yescomplemented
35C23—830no—
36C23C24×C471105yes—
37Q8C24×C47156yes—
38D4C24×C471280yes—
39C2×C4C24×C471210yes—
40C22—4105no—
41C22C25×C47135yes—
42C4C25×C47128yes—
43C2—235no—
44C2C26×C4711yescharacteristic
subgroupG/H
center, socleC2×C47C26
commutator, Frattini, cosocleC2C26×C47
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#585C2semidirect
2. C2×H(5,𝔽2)×C47C2semidirect
3. 2−1+4×C47C22semidirect
4. H(5,𝔽2)×C47C22semidirect
5. C2×#41×C47C22semidirect
6. C22×D4×C47C22semidirect
7. C24×C47C23semidirect
8. #41×C47C23semidirect
9. C2×Q8×C47C23semidirect
10. C2×D4×C47C23semidirect
11. C22×C4×C47C23semidirect
20. H(7,𝔽2)C47direct (N × H)
23. #585C2×C47semidirect
24. C2×H(5,𝔽2)C2×C47semidirect
25. C47H(7,𝔽2)direct (N × H)
26. 2−1+4C22×C47semidirect
27. H(5,𝔽2)C22×C47semidirect
28. C2×#41C22×C47semidirect
29. C22×D4C22×C47semidirect
30. C24C23×C47semidirect
31. #41C23×C47semidirect
32. C2×Q8C23×C47semidirect
33. C2×D4C23×C47semidirect
34. C22×C4C23×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#5852
C2×H(5,𝔽2)×C472
H(7,𝔽2)47