Finite Group Databasebeta

← C3×#88107 #11928344

Subgroups — C3×#88107 #11928344

Order 1248.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D52C211yesmaximal, characteristic
2C3×C22⋊#261C212yesmaximal, complemented
3#88107C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×D13C411yescharacteristic, complemented
5C22×C3×D13C2211yescharacteristic
6C2×C3×#261—22no—
7C2×C3×C4×C13C411yescharacteristic, complemented
8C3×D52—22no—
9C2×D52C2×C311yescharacteristic
10C22⋊#261C2×C312yescomplemented
11C22×C3×C13C2×C411yescharacteristic
12C2×C3×D13—21no—
13C2×C3×D13—41no—
14C2×C3×D13—41no—
15C2×C3×D13D412yes—
16C3×#261—42no—
17C3×C4×C13—21no—
18C22×D13C3×C411yescharacteristic, complemented
19C22×D13C22×C311yescharacteristic
20C2×#261—22no—
21C2×C4×C13C3×C411yescharacteristic, complemented
22D52—22no—
23C3×#99—131nomaximal, Hall
24C2×C3×C13—21no—
25C2×C3×C13C22⋊C411yescharacteristic
26C3×D13—22no—
27C3×D13—41no—
28C22×C13C2×C3×C411yescharacteristic
29C2×D13—21no—
30C2×D13—41no—
31C2×D13—41no—
32C2×D13C3×D412yes—
33#261—42no—
34C4×C13—21no—
35C2×C3×D4—131no—
36C3×C22⋊C4—132no—
37C3×C13#9911yescharacteristic, complemented, Hall
38#99—131noSylow
39C2×C13—21no—
40C2×C13C3×C22⋊C411yescharacteristic
41D13—22no—
42D13—41no—
43C23×C3—131no—
44C23×C3—131no—
45C3×D4—262no—
46C2×C3×C4—262no—
47C2×C3×C4#26111yescharacteristic, complemented
48C2×D4—131no—
49C22⋊C4—132no—
50C13C3×#9911yescharacteristic, complemented, Sylow
51C22×C3—132no—
52C22×C3—261no—
53C22×C3—521no—
54C22×C3—521no—
55C22×C3C2×#26111yescharacteristic
56C3×C4—21no—
57C3×C4—522no—
58C23—131no—
59C23—131no—
60D4—262no—
61C2×C4—262no—
62C2×C4C3×#26111yescharacteristic, complemented
63C2×C3—21no—
64C2×C3—262no—
65C2×C3—521no—
66C2×C3C22⋊#26111yescharacteristic
67C22—132no—
68C22—261no—
69C22—521no—
70C22—521no—
71C22C2×C3×#26111yescharacteristic
72C4—21no—
73C4—522no—
74C3#8810711yescharacteristic, direct product factor, Sylow
75C2—21no—
76C2—262no—
77C2—521no—
78C2C3×C22⋊#26111yescharacteristic
subgroupG/H
centerC2×C3C22⋊#261
commutatorC22×C13C2×C3×C4
FrattiniC22C2×C3×#261
FittingC2×C3×C4×C13C4
socleC2×C3×C13C22⋊C4
prime radicalC2×C3×D52C2
cosocleC22×D13C22×C3
hypercenterC2×C3×C4#261
hypocenterC13C3×#99
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×C22⋊#261C2semidirect
3. #88107C3direct (N × H)
4. C22×C3×D13C4semidirect
7. C2×C3×C4×C13C4semidirect
10. C22⋊#261C2×C3semidirect
18. C22×D13C3×C4semidirect
21. C2×C4×C13C3×C4semidirect
37. C3×C13#99semidirect
47. C2×C3×C4#261semidirect
50. C13C3×#99semidirect
62. C2×C4C3×#261semidirect
74. C3#88107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D522
C3×C22⋊#2612
#881073
C3×#9913