Finite Group Databasebeta

← (C22⋊(C52⋊C3))⋊(C31⋊C3) #42124837

Subgroups — (C22⋊(C52⋊C3))⋊(C31⋊C3) #42124837

Order 27900.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C52⋊(C31⋊C3)C311yesmaximal, characteristic, complemented
2C52×C22⋊(C31⋊C3)C311yesmaximal, characteristic, complemented
3C31×C22⋊(C52⋊C3)C311yesmaximal, characteristic, complemented
4C22⋊(C52⋊(C31⋊C3))C311yesmaximal, characteristic, complemented
5C52⋊C3×C31⋊C3—41nomaximal, Hall
6C2×C52⋊(C31⋊C3)—31no—
7C22×C52×C31C3211yescharacteristic, complemented, Hall
8C52⋊(C31⋊C3)—41no—
9C52⋊(C31⋊C3)A411yescharacteristic, complemented
10C31×C52⋊C3—41no—
11C52×C31⋊C3—41no—
12C5×C22⋊(C31⋊C3)—32no—
13C2×C52×C31—31no—
14A4×C31⋊C3—251nomaximal, Hall
15A4×C52⋊C3—311nomaximal, Hall
16C52×C31C3×A411yescharacteristic, complemented, Hall
17C22×C5×C31—32no—
18C5×C31⋊C3—122no—
19C22⋊(C31⋊C3)—251no—
20C22⋊(C31⋊C3)C52⋊C311yescharacteristic, complemented
21A4×C31—251no—
22C22×C31⋊C3—251no—
23C2×C5×C31—92no—
24C22⋊(C52⋊C3)—311no—
25C22⋊(C52⋊C3)C31⋊C311yescharacteristic, complemented
26C52×A4—311no—
27C22×C52⋊C3—311no—
28C3×C31⋊C3—1001noHall
29C3×C52⋊C3—1241noHall
30C2×C31⋊C3—751no—
31C5×C31—32no—
32C2×C52⋊C3—931no—
33C22×C31C3×C52⋊C311yescharacteristic, complemented, Hall
34C22×C52C3×C31⋊C311yescharacteristic, complemented, Hall
35C3×C31—1001no—
36C31⋊C3—41no—
37C31⋊C3—251no—
38C31⋊C3—1001no—
39C3×C52—1241no—
40C52⋊C3—41no—
41C52⋊C3—311no—
42C52⋊C3—1241no—
43C2×C31—31no—
44C5×A4—932no—
45C2×C52—31no—
46C3×A4—7751noHall
47C31A4×C52⋊C311yescharacteristic, complemented, Sylow
48C52A4×C31⋊C311yescharacteristic, complemented, Sylow
49C22×C5—32no—
50C3×C5—3722no—
51C22×C3—7751no—
52A4—7751no—
53A4—251no—
54A4—311no—
55C2×C5—92no—
56C32—31001noSylow
57C2×C3—23251no—
58C5—32no—
59C22C52⋊C3×C31⋊C311yescharacteristic, complemented, Sylow
60C3—7751no—
61C3—31001no—
62C3—1001no—
63C3—1241no—
64C2—31no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C52×C31C32
LCSG ▷ C22×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C22×C52⋊(C31⋊C3)C3semidirect
2. C52×C22⋊(C31⋊C3)C3semidirect
3. C31×C22⋊(C52⋊C3)C3semidirect
4. C22⋊(C52⋊(C31⋊C3))C3semidirect
7. C22×C52×C31C32semidirect
9. C52⋊(C31⋊C3)A4semidirect
16. C52×C31C3×A4semidirect
20. C22⋊(C31⋊C3)C52⋊C3semidirect
25. C22⋊(C52⋊C3)C31⋊C3semidirect
33. C22×C31C3×C52⋊C3semidirect
34. C22×C52C3×C31⋊C3semidirect
47. C31A4×C52⋊C3semidirect
48. C52A4×C31⋊C3semidirect
59. C22C52⋊C3×C31⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C52⋊(C31⋊C3)3
C52×C22⋊(C31⋊C3)3
C31×C22⋊(C52⋊C3)3
C22⋊(C52⋊(C31⋊C3))3
C52⋊C3×C31⋊C34
A4×C31⋊C325
A4×C52⋊C331