Finite Group Databasebeta

← C7×#17984618 #44527550

Subgroups — C7×#17984618 #44527550

Order 31122.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#14555736C211yesmaximal, characteristic, complemented, Hall
2C3×C7×C13×D19C311yesmaximal, characteristic
3C3×C7×C13×C19C2×C311yescharacteristic
4#17984618C711yesmaximal, characteristic, direct product factor, Hall
5C7×C13×D19C911yescharacteristic, complemented, Hall
6C7×#4294⋊C2—131nomaximal, Hall
7#14555736C2×C711yescharacteristic, complemented, Hall
8C7×C13×C19C2×C911yescharacteristic, complemented, Hall
9C2×C7×C13⋊C9—191nomaximal, Hall
10C3×C13×D19C3×C711yescharacteristic
11C7×#4294—131noHall
12C7×C13⋊C9—191noHall
13C3×C7×D19C13⋊C311yescharacteristic
14C3×C13×C19C2×C3×C711yescharacteristic
15C2×C3×C7×C13—191no—
16C13×D19C7×C911yescharacteristic, complemented, Hall
17C3×C7×C19C2×C13⋊C311yescharacteristic
18#4294⋊C2—131noHall
19C3×C7×C13D19⋊C311yescharacteristic
20C7×D19C13⋊C911yescharacteristic, complemented, Hall
21C13×C19C2×C7×C911yescharacteristic, complemented, Hall
22C2×C13⋊C9—191noHall
23C2×C7×C13—191noHall
24#4294—131noHall
25C7×C19C2×C13⋊C911yescharacteristic, complemented, Hall
26C2×C7×C9—2471noHall
27C13⋊C9—191noHall
28C3×D19C7×C13⋊C311yescharacteristic
29C7×C13#4294⋊C211yescharacteristic, complemented, Hall
30C2×C3×C13—191no—
31C7×C9—2471noHall
32C3×C19C2×C7×C13⋊C311yescharacteristic
33C2×C3×C7—191no—
34C3×C13C7×D19⋊C311yescharacteristic
35D19C7×C13⋊C911yescharacteristic, complemented, Hall
36C2×C13—191noHall
37C3×C7#1309336111yescharacteristic
38C19C2×C7×C13⋊C911yescharacteristic, complemented, Sylow
39C2×C9—2471noHall
40C2×C7—191noHall
41C13C7×#4294⋊C211yescharacteristic, complemented, Sylow
42C9—2471noSylow
43C7#1798461811yescharacteristic, direct product factor, Sylow
44C2×C3—191no—
45C3C7×#1309336111yescharacteristic
46C2—191noSylow
subgroupG/H
center, hypercenterC3×C7#13093361
commutator, hypocenterC13×C19C2×C7×C9
FrattiniC3C7×#13093361
Fitting, socleC3×C7×C13×C19C2×C3
prime radicalC3×C7×C13×D19C3
cosocleC3×C13×C19C2×C3×C7
LCSG ▷ C13×C19
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C7×#14555736C2semidirect
4. #17984618C7direct (N × H)
5. C7×C13×D19C9semidirect
7. #14555736C2×C7semidirect
8. C7×C13×C19C2×C9semidirect
16. C13×D19C7×C9semidirect
20. C7×D19C13⋊C9semidirect
21. C13×C19C2×C7×C9semidirect
25. C7×C19C2×C13⋊C9semidirect
29. C7×C13#4294⋊C2semidirect
35. D19C7×C13⋊C9semidirect
38. C19C2×C7×C13⋊C9semidirect
41. C13C7×#4294⋊C2semidirect
43. C7#17984618direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#145557362
C3×C7×C13×D193
#179846187
C7×#4294⋊C213
C2×C7×C13⋊C919