Finite Group Databasebeta

← C3×C7×C22⋊(C112⋊C3) #44479250

Subgroups — C3×C7×C22⋊(C112⋊C3) #44479250

Order 30492.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C22⋊(C112⋊C3)C313yesmaximal, direct product factor
2C22×C3×C7×C112C311yesmaximal, characteristic, complemented
3C3×C7×C112⋊C3—41nomaximal, Hall
4C2×C3×C7×C112—31no—
5C3×C22⋊(C112⋊C3)C711yesmaximal, characteristic, direct product factor, Hall
6C22×C7×C112C3211yescharacteristic, complemented, Hall
7C7×C112⋊C3—43no—
8C3×C7×C112A411yescharacteristic, complemented
9C2×C7×C112—31no—
10C22×C3×C112C3×C711yescharacteristic, complemented
11C22⋊(C112⋊C3)C3×C713yesdirect product factor
12C3×C112⋊C3—41noHall
13C22×C3×C7×C11—34no—
14C7×C112C3×A411yescharacteristic, complemented, Hall
15C2×C3×C112—31no—
16C22×C112C32×C711yescharacteristic, complemented, Hall
17C2×C3×C7×C11—312no—
18C3×C112C7×A411yescharacteristic, complemented
19C112⋊C3—43no—
20C22×C7×C11—34no—
21C3×C7×A4—1211nomaximal, Hall
22C2×C112—31no—
23C3×C7×C11—34no—
24C2×C7×C11—312no—
25C22×C3×C11—34no—
26C112C3×C7×A411yescharacteristic, complemented, Sylow
27C22×C3×C7C112⋊C311yescharacteristic, complemented
28C7×A4—1213no—
29C7×C11—34no—
30C2×C3×C11—312no—
31C32×C7—4841noHall
32C22×C11—34no—
33C2×C3×C7—31no—
34C3×A4—1211noHall
35C3×C11—34no—
36C22×C7C3×C112⋊C311yescharacteristic, complemented, Hall
37C2×C11—312no—
38C3×C7—4843no—
39C3×C7C22⋊(C112⋊C3)11yescharacteristic, direct product factor
40C2×C7—31no—
41C22×C3C7×C112⋊C311yescharacteristic, complemented
42A4—1213no—
43C11—34no—
44C32—4841noSylow
45C7C3×C22⋊(C112⋊C3)11yescharacteristic, direct product factor, Sylow
46C2×C3—31no—
47C22C3×C7×C112⋊C311yescharacteristic, complemented, Sylow
48C3—4843no—
49C3C7×C22⋊(C112⋊C3)11yescharacteristic, direct product factor
50C2—31no—
subgroupG/H
center, hypercenterC3×C7C22⋊(C112⋊C3)
commutator, cosocle, hypocenterC22×C112C32×C7
FrattiniC1G
Fitting, socleC22×C3×C7×C112C3
LCSG ▷ C22×C112
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C7×C22⋊(C112⋊C3)C3direct (N × H)
2. C22×C3×C7×C112C3semidirect
5. C3×C22⋊(C112⋊C3)C7direct (N × H)
6. C22×C7×C112C32semidirect
8. C3×C7×C112A4semidirect
10. C22×C3×C112C3×C7semidirect
11. C22⋊(C112⋊C3)C3×C7direct (N × H)
14. C7×C112C3×A4semidirect
16. C22×C112C32×C7semidirect
18. C3×C112C7×A4semidirect
26. C112C3×C7×A4semidirect
27. C22×C3×C7C112⋊C3semidirect
36. C22×C7C3×C112⋊C3semidirect
39. C3×C7C22⋊(C112⋊C3)direct (N × H)
41. C22×C3C7×C112⋊C3semidirect
45. C7C3×C22⋊(C112⋊C3)direct (N × H)
47. C22C3×C7×C112⋊C3semidirect
49. C3C7×C22⋊(C112⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C22⋊(C112⋊C3)3
C22×C3×C7×C1123
C3×C7×C112⋊C34
C3×C22⋊(C112⋊C3)7
C3×C7×A4121