Finite Group Databasebeta

← C31×#11763957 #46799255

Subgroups — C31×#11763957 #46799255

Order 33852.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#63270C211yesmaximal, characteristic
2C7×C31×Dic13C311yesmaximal, characteristic, complemented, Hall
3C31×#63270C411yescharacteristic, complemented, Hall
4C2×C7×C13×C31C2×C311yescharacteristic
5C31×Dic13⋊C3—71nomaximal, Hall
6C7×C13×C31C3×C411yescharacteristic, complemented, Hall
7C4×ΓL(1,𝔽8)×C31—131nomaximal, Hall
8C2×C31×C13⋊C3—71no—
9C31×Dic13ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
10C2×ΓL(1,𝔽8)×C31—131no—
11C31×C13⋊C3—71noHall
12#11763957C3111yesmaximal, characteristic, direct product factor, Hall
13C4×C7×C31—131noHall
14C2×C13×C31C2×ΓL(1,𝔽8)11yescharacteristic
15ΓL(1,𝔽8)×C31—131noHall
16C2×#63270C2×C3111yescharacteristic
17C2×C7×C31D13⋊C311yescharacteristic
18C13×C31C4×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
19C3×C4×C31—911noHall
20C7×Dic13C3×C3111yescharacteristic, complemented, Hall
21#63270C4×C3111yescharacteristic, complemented, Hall
22C7×C31Dic13⋊C311yescharacteristic, complemented, Hall
23C2×C3×C31—911no—
24C2×C7×C13C2×C3×C3111yescharacteristic
25Dic13⋊C3—71noHall
26C4×C31—131noHall
27C3×C31—911noHall
28C7×C13C3×C4×C3111yescharacteristic, complemented, Hall
29C4×ΓL(1,𝔽8)—131noHall
30C2×C13⋊C3—71no—
31C2×C31#1058771611yescharacteristic
32Dic13ΓL(1,𝔽8)×C3111yescharacteristic, complemented, Hall
33C2×ΓL(1,𝔽8)—131no—
34C13⋊C3—71noHall
35C31#1176395711yescharacteristic, direct product factor, Sylow
36C4×C7—131noHall
37C2×C13C2×ΓL(1,𝔽8)×C3111yescharacteristic
38ΓL(1,𝔽8)—131noHall
39C2×C7C31×D13⋊C311yescharacteristic
40C13C4×ΓL(1,𝔽8)×C3111yescharacteristic, complemented, Sylow
41C3×C4—911noHall
42C7C31×Dic13⋊C311yescharacteristic, complemented, Sylow
43C2×C3—911no—
44C4—131noSylow
45C3—911noSylow
46C2C31×#1058771611yescharacteristic
subgroupG/H
center, hypercenterC2×C31#10587716
commutator, hypocenterC7×C13C3×C4×C31
FrattiniC2C31×#10587716
Fitting, socleC2×C7×C13×C31C2×C3
prime radicalC2×C31×#63270C2
cosocleC2×C7×C13C2×C3×C31
LCSG ▷ C7×C13
UCSC1 ◁ C2×C31

Complements

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

NH ≅ G/Ntype
2. C7×C31×Dic13C3semidirect
3. C31×#63270C4semidirect
6. C7×C13×C31C3×C4semidirect
9. C31×Dic13ΓL(1,𝔽8)semidirect
12. #11763957C31direct (N × H)
18. C13×C31C4×ΓL(1,𝔽8)semidirect
20. C7×Dic13C3×C31semidirect
21. #63270C4×C31semidirect
22. C7×C31Dic13⋊C3semidirect
28. C7×C13C3×C4×C31semidirect
32. Dic13ΓL(1,𝔽8)×C31semidirect
35. C31#11763957direct (N × H)
40. C13C4×ΓL(1,𝔽8)×C31semidirect
42. C7C31×Dic13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#632702
C7×C31×Dic133
C31×Dic13⋊C37
C4×ΓL(1,𝔽8)×C3113
#1176395731