Finite Group Databasebeta

← C3×C22⋊#1057 #11928357

Subgroups — C3×C22⋊#1057 #11928357

Order 1248.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic13C211yesmaximal, characteristic
2C2×C3×#1057C212yesmaximal, complemented
3C22⋊#1057C311yesmaximal, characteristic, direct product factor, Hall
4C23×C3×C13C411yescharacteristic
5C2×C3×Dic13—22no—
6C2×C3×Dic13C411yescharacteristic
7C2×C3×Dic13C2211yescharacteristic
8C3×#1057—22no—
9C22×Dic13C2×C311yescharacteristic
10C2×#1057C2×C312yescomplemented
11C22×C3×C13—21no—
12C22×C3×C13—21no—
13C22×C3×C13C812yescomplemented
14C22×C3×C13C2×C411yescharacteristic
15C3×Dic13—21no—
16C3×Dic13D412yes—
17C23×C13C3×C411yescharacteristic
18C2×Dic13—22no—
19C2×Dic13C3×C411yescharacteristic
20C2×Dic13C22×C311yescharacteristic
21#1057—22no—
22C3×C22⋊C8—131nomaximal, Hall
23C2×C3×C13—22no—
24C2×C3×C13C22⋊C411yescharacteristic
25C2×C3×C13C2×C811yescharacteristic
26C2×C3×C13M1611yescharacteristic
27C22×C13—21no—
28C22×C13—21no—
29C22×C13C3×C812yescomplemented
30C22×C13C2×C3×C411yescharacteristic
31Dic13—21no—
32Dic13C3×D412yes—
33C22×C3×C4—131no—
34C2×C3×C8—132no—
35C3×C13C22⋊C811yescharacteristic, complemented, Hall
36C22⋊C8—131noSylow
37C2×C13—22no—
38C2×C13C3×C22⋊C411yescharacteristic
39C2×C13C2×C3×C811yescharacteristic
40C2×C13C3×M1611yescharacteristic
41C23×C3#26111yescharacteristic
42C2×C3×C4—131no—
43C2×C3×C4—131no—
44C2×C3×C4—262no—
45C3×C8—262no—
46C22×C4—131no—
47C2×C8—132no—
48C13C3×C22⋊C811yescharacteristic, complemented, Sylow
49C22×C3—21no—
50C22×C3—21no—
51C22×C3#105712yescomplemented
52C22×C3C2×#26111yescharacteristic
53C3×C4—132no—
54C3×C4—261no—
55C23C3×#26111yescharacteristic
56C2×C4—131no—
57C2×C4—131no—
58C2×C4—262no—
59C8—262no—
60C2×C3—22no—
61C2×C3C2×#105711yescharacteristic
62C2×C3#612211yescharacteristic
63C2×C3C22⋊#26111yescharacteristic
64C22—21no—
65C22—21no—
66C22C3×#105712yescomplemented
67C22C2×C3×#26111yescharacteristic
68C4—132no—
69C4—261no—
70C3C22⋊#105711yescharacteristic, direct product factor, Sylow
71C2—22no—
72C2C2×C3×#105711yescharacteristic
73C2C3×#612211yescharacteristic
74C2C3×C22⋊#26111yescharacteristic
subgroupG/H
centerC22×C3C2×#261
commutatorC2×C13C2×C3×C8
FrattiniC22C2×C3×#261
Fitting, prime radicalC23×C3×C13C4
socleC22×C3×C13C2×C4
cosocleC2×Dic13C22×C3
hypercenterC23×C3#261
hypocenterC13C3×C22⋊C8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×#1057C2semidirect
3. C22⋊#1057C3direct (N × H)
10. C2×#1057C2×C3semidirect
13. C22×C3×C13C8semidirect
29. C22×C13C3×C8semidirect
35. C3×C13C22⋊C8semidirect
48. C13C3×C22⋊C8semidirect
51. C22×C3#1057semidirect
66. C22C3×#1057semidirect
70. C3C22⋊#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
C3×C22⋊C813