Finite Group Databasebeta

← C3×C3⋊(C7⋊#92150) #44479191

Subgroups — C3×C3⋊(C7⋊#92150) #44479191

Order 30492.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11⋊D11C211yesmaximal, characteristic
2C3⋊(C7⋊#92150)C311yesmaximal, characteristic, direct product factor
3C3×C7⋊#92150—31nomaximal
4C32×C7×C112C411yescharacteristic, complemented, Hall
5C3×C7×C11⋊D11—21no—
6C3×C7×C11⋊D11D311yescharacteristic
7C3×C7×C11⋊D11C2×C311yescharacteristic
8C3×C3⋊#92150—71nomaximal, Hall
9C7⋊#92150—31noHall
10C3×C7×C112—21no—
11C3×C7×C112Dic311yescharacteristic, complemented
12C3×C7×C112C3×C411yescharacteristic, complemented
13C32×C11⋊D11D711yescharacteristic
14C7×C11⋊D11C3×D311yescharacteristic
15C3⋊#92150—71no—
16C3×#92150—211no—
17C32×C7×D11—226no—
18C32×C112Dic711yescharacteristic, complemented, Hall
19C7×C112C3×Dic311yescharacteristic, complemented, Hall
20C3×C11⋊D11—21no—
21C3×C11⋊D11C3×D711yescharacteristic
22C3×C11⋊D11D2111yescharacteristic
23C32×C7×C11—26no—
24#92150—211noHall
25C3×C7×D11—226no—
26C3×C7×D11—226no—
27C3×C7×D11—2212no—
28C3×C112—21no—
29C3×C112C3×Dic711yescharacteristic, complemented
30C3×C112Dic2111yescharacteristic, complemented
31C3×Dic21—1211nomaximal, Hall
32C11⋊D11C3×D2111yescharacteristic
33C3×C7×C11—212no—
34C3×C7×C11—26no—
35C3×C7×C11—26no—
36C32×D11—226no—
37C7×D11—226no—
38C2×C32×C7—1211no—
39C112C3×Dic2111yescharacteristic, complemented, Sylow
40C32×C11—26no—
41Dic21—1211no—
42C3×Dic7—3631no—
43C7×C11—26no—
44C3×D11—226no—
45C3×D11—226no—
46C3×D11—2212no—
47C32×C7#9215011yescharacteristic, complemented, Hall
48C2×C3×C7—1211no—
49C2×C3×C7—1211no—
50C2×C3×C7—2421no—
51C3×Dic3—8471noHall
52C3×C11—212no—
53C3×C11—26no—
54C3×C11—26no—
55Dic7—3631noHall
56D11—226no—
57C3×C7—21no—
58C3×C7C3×#9215011yescharacteristic, complemented
59C3×C7C3⋊#9215011yescharacteristic, complemented
60C2×C32—1211no—
61C2×C7—1211no—
62C3×C4—25411no—
63Dic3—8471no—
64C11—26no—
65C32C7⋊#9215011yescharacteristic, complemented, Sylow
66C7C3×C3⋊#9215011yescharacteristic, complemented, Sylow
67C2×C3—1211no—
68C2×C3—1211no—
69C2×C3—2421no—
70C4—25411noSylow
71C3—21no—
72C3C3×C7⋊#9215011yescharacteristic, complemented
73C3C3⋊(C7⋊#92150)11yescharacteristic, direct product factor
74C2—1211no—
subgroupG/H
center, hypercenterC3C3⋊(C7⋊#92150)
commutator, hypocenterC3×C7×C112C3×C4
FrattiniC1G
Fitting, socleC32×C7×C112C4
prime radicalC32×C7×C11⋊D11C2
cosocleC3×C7×C11⋊D11C2×C3
LCSG ▷ C3×C7×C112
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3⋊(C7⋊#92150)C3direct (N × H)
4. C32×C7×C112C4semidirect
11. C3×C7×C112Dic3semidirect
12. C3×C7×C112C3×C4semidirect
18. C32×C112Dic7semidirect
19. C7×C112C3×Dic3semidirect
29. C3×C112C3×Dic7semidirect
30. C3×C112Dic21semidirect
39. C112C3×Dic21semidirect
47. C32×C7#92150semidirect
58. C3×C7C3×#92150semidirect
59. C3×C7C3⋊#92150semidirect
65. C32C7⋊#92150semidirect
66. C7C3×C3⋊#92150semidirect
72. C3C3×C7⋊#92150semidirect
73. C3C3⋊(C7⋊#92150)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C11⋊D112
C3⋊(C7⋊#92150)3
C3×C7⋊#921503
C3×C3⋊#921507
C3×Dic21121