Finite Group Databasebeta

← C22×C3×#1057 #11929177

Subgroups — C22×C3×#1057 #11929177

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic13C211yesmaximal, characteristic
2C2×C3×#1057C216yesmaximal, direct product factor
3C22×#1057C311yesmaximal, characteristic, direct product factor, Hall
4C23×C3×C13C411yescharacteristic
5C2×C3×Dic13C413yes—
6C2×C3×Dic13C2213yes—
7C3×#1057C2214yesdirect product factor
8C22×Dic13C2×C311yescharacteristic
9C2×#1057C2×C316yesdirect product factor
10C22×C3×C13C814yescomplemented
11C22×C3×C13C2×C413yes—
12C3×Dic13C2×C413yes—
13C3×Dic13C2311yescharacteristic
14C23×C13C3×C411yescharacteristic
15C2×Dic13C3×C413yes—
16C2×Dic13C22×C313yes—
17#1057C22×C314yesdirect product factor
18C22×C3×C8—131nomaximal, Hall
19C2×C3×C13C2×C816yescomplemented
20C2×C3×C13C22×C411yescharacteristic
21C22×C13C3×C814yescomplemented
22C22×C13C2×C3×C413yes—
23Dic13C2×C3×C413yes—
24Dic13C23×C311yescharacteristic
25C22×C3×C4—131no—
26C2×C3×C8—136no—
27C3×C13C22×C811yescharacteristic, complemented, Hall
28C22×C8—131noSylow
29C2×C13C2×C3×C816yescomplemented
30C2×C13C22×C3×C411yescharacteristic
31C23×C3#26111yescharacteristic
32C2×C3×C4—133no—
33C2×C3×C4—133no—
34C3×C8—134no—
35C22×C4—131no—
36C2×C8—136no—
37C13C22×C3×C811yescharacteristic, complemented, Sylow
38C22×C3#105714yesdirect product factor
39C22×C3C2×#26113yes—
40C3×C4—131no—
41C3×C4—133no—
42C23C3×#26111yescharacteristic
43C2×C4—133no—
44C2×C4—133no—
45C8—134no—
46C2×C3C2×#105716yesdirect product factor
47C2×C3C22×#26111yescharacteristic
48C22C3×#105714yesdirect product factor
49C22C2×C3×#26113yes—
50C4—133no—
51C4—131no—
52C3C22×#105711yescharacteristic, direct product factor, Sylow
53C2C2×C3×#105716yesdirect product factor
54C2C22×C3×#26111yescharacteristic
subgroupG/H
center, hypercenterC23×C3#261
commutator, hypocenterC13C22×C3×C8
FrattiniC2C22×C3×#261
Fitting, socle, prime radicalC23×C3×C13C4
cosocleDic13C23×C3
LCSG ▷ C13
UCSC1 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×#1057C2direct (N × H)
3. C22×#1057C3direct (N × H)
7. C3×#1057C22direct (N × H)
9. C2×#1057C2×C3direct (N × H)
10. C22×C3×C13C8semidirect
17. #1057C22×C3direct (N × H)
19. C2×C3×C13C2×C8semidirect
21. C22×C13C3×C8semidirect
27. C3×C13C22×C8semidirect
29. C2×C13C2×C3×C8semidirect
37. C13C22×C3×C8semidirect
38. C22×C3#1057direct (N × H)
46. C2×C3C2×#1057direct (N × H)
48. C22C3×#1057direct (N × H)
52. C3C22×#1057direct (N × H)
53. C2C2×C3×#1057direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Dic132
C2×C3×#10572
C22×#10573
C22×C3×C813