Finite Group Databasebeta

← C101×#6911 #37589445

Subgroups — C101×#6911 #37589445

Order 24543.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×3−1+2×C101C311yesmaximal, characteristic, complemented
2C3×H(3,𝔽3)×C101C313yesmaximal, complemented
3#732×C101C319yesmaximal, complemented
4C33×C101—33no—
5C33×C101C3211yescharacteristic
63−1+2×C101—33no—
7H(3,𝔽3)×C101—36no—
8H(3,𝔽3)×C101C3219yescomplemented
9C3×C9×C101C3213yescomplemented
10C32×C101—39no—
11C32×C101—91no—
12C32×C101—99no—
13C32×C101H(3,𝔽3)13yes—
14C32×C101C3311yescharacteristic
15C9×C101—33no—
16C3×C101—33no—
17C3×C101—31no—
18C3×C101—99no—
19C3×C101C3×H(3,𝔽3)11yescharacteristic
20#6911C10111yesmaximal, characteristic, direct product factor, Sylow
21C101#691111yescharacteristic, direct product factor, Sylow
22C3×3−1+2C3×C10111yescharacteristic, complemented
23C3×H(3,𝔽3)C3×C10113yescomplemented
24#732C3×C10119yescomplemented
25C33—33no—
26C33C32×C10111yescharacteristic
273−1+2—33no—
28H(3,𝔽3)—36no—
29H(3,𝔽3)C32×C10119yescomplemented
30C3×C9C32×C10113yescomplemented
31C32—39no—
32C32—91no—
33C32—99no—
34C32H(3,𝔽3)×C10113yes—
35C32C33×C10111yescharacteristic
36C9—33no—
37C3—33no—
38C3—31no—
39C3—99no—
40C3C3×H(3,𝔽3)×C10111yescharacteristic
subgroupG/H
center, socleC3×C101C3×H(3,𝔽3)
commutator, Frattini, cosocleC32C33×C101
LCSG ▷ C32 ▷ C3 ▷ C1
UCSC1 ◁ C3×C101 ◁ C33×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×3−1+2×C101C3semidirect
2. C3×H(3,𝔽3)×C101C3semidirect
3. #732×C101C3semidirect
8. H(3,𝔽3)×C101C32semidirect
9. C3×C9×C101C32semidirect
20. #6911C101direct (N × H)
21. C101#6911direct (N × H)
22. C3×3−1+2C3×C101semidirect
23. C3×H(3,𝔽3)C3×C101semidirect
24. #732C3×C101semidirect
29. H(3,𝔽3)C32×C101semidirect
30. C3×C9C32×C101semidirect

Maximal subgroups

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

subgroupindex
C3×3−1+2×C1013
C3×H(3,𝔽3)×C1013
#732×C1013
#6911101