Finite Group Databasebeta

← C41×2−1+6 #19107375

Subgroups — C41×2−1+6 #19107375

Order 5248.

5796 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#585C2136yesmaximal, complemented
2C2×2−1+4×C41C2127yesmaximal, complemented
32−1+4×C41C221216yescomplemented
4H(5,𝔽2)×C41C221120yescomplemented
5C2×#41×C41C221270yescomplemented
6C22×Q8×C41C22145yescomplemented
7#41×C41C231720yes—
8C2×Q8×C41C231270yes—
9C2×D4×C41C231270yes—
10C22×C4×C41C231135yes—
11C23×C41C24145yes—
12Q8×C41C241120yes—
13D4×C41C241216yes—
14C2×C4×C41C241270yes—
15C22×C41—445no—
16C22×C41C25127yes—
17C4×C41C25136yes—
182−1+6C4111yesmaximal, characteristic, direct product factor, Sylow
19C2×C41—227no—
20C2×C41C2611yescharacteristic
21#585C2×C41136yescomplemented
22C2×2−1+4C2×C41127yescomplemented
23C412−1+611yescharacteristic, direct product factor, Sylow
242−1+4C22×C411216yescomplemented
25H(5,𝔽2)C22×C411120yescomplemented
26C2×#41C22×C411270yescomplemented
27C22×Q8C22×C41145yescomplemented
28#41C23×C411720yes—
29C2×Q8C23×C411270yes—
30C2×D4C23×C411270yes—
31C22×C4C23×C411135yes—
32C23C24×C41145yes—
33Q8C24×C411120yes—
34D4C24×C411216yes—
35C2×C4C24×C411270yes—
36C22—445no—
37C22C25×C41127yes—
38C4C25×C41136yes—
39C2—227no—
40C2C26×C4111yescharacteristic
subgroupG/H
center, socleC2×C41C26
commutator, Frattini, cosocleC2C26×C41
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#585C2semidirect
2. C2×2−1+4×C41C2semidirect
3. 2−1+4×C41C22semidirect
4. H(5,𝔽2)×C41C22semidirect
5. C2×#41×C41C22semidirect
6. C22×Q8×C41C22semidirect
18. 2−1+6C41direct (N × H)
21. #585C2×C41semidirect
22. C2×2−1+4C2×C41semidirect
23. C412−1+6direct (N × H)
24. 2−1+4C22×C41semidirect
25. H(5,𝔽2)C22×C41semidirect
26. C2×#41C22×C41semidirect
27. C22×Q8C22×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#5852
C2×2−1+4×C412
2−1+641