Finite Group Databasebeta

← C3×#826 #63612

Subgroups — C3×#826 #63612

Order 288.

67 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D8C211yesmaximal, characteristic, complemented
2C3×D24C211yesmaximal, characteristic, complemented
3C3×C3⋊C16C211yesmaximal, characteristic, complemented
4C3×D16—31nomaximal
5#826C311yesmaximal, characteristic, direct product factor
6C32×D4—21no—
7C3×D12—21no—
8C32×C8C2211yescharacteristic
9C3×D8—21no—
10C3×D8—31no—
11C3×D8D311yescharacteristic, complemented
12C3×D8C2×C311yescharacteristic, complemented
13D24C2×C311yescharacteristic, complemented
14C3×C16—31no—
15C3⋊C16C2×C311yescharacteristic, complemented
16C22×C32—41no—
17C2×C3×D3—41no—
18C32×C4D411yescharacteristic
19D16—31noSylow
20C3×D4—22no—
21C3×D4—21no—
22C3×D4—21no—
23C3×D4—61no—
24D12—21no—
25C3×C8—21no—
26C3×C8C2×D311yescharacteristic
27C3×C8C22×C311yescharacteristic
28C2×C32—81no—
29C2×C32D811yescharacteristic
30C3×D3—81no—
31D8—31no—
32D8C3×D311yescharacteristic, complemented
33C16—31no—
34C22×C3—42no—
35C22×C3—41no—
36C22×C3—41no—
37C22×C3—121no—
38C2×D3—41no—
39C3×C4—21no—
40C3×C4#6711yescharacteristic
41C3×C4C3×D411yescharacteristic
42C32D1611yescharacteristic, complemented, Sylow
43D4—21no—
44D4—61no—
45C8C2×C3×D311yescharacteristic
46C2×C3—21no—
47C2×C3—82no—
48C2×C3—81no—
49C2×C3—81no—
50C2×C3—241no—
51C2×C3#21311yescharacteristic
52C2×C3C3×D811yescharacteristic
53D3—81no—
54C22—41no—
55C22—121no—
56C4C3×#6711yescharacteristic
57C3—21no—
58C3#82611yescharacteristic, direct product factor
59C3C3×D1611yescharacteristic, complemented
60C2—81no—
61C2—241no—
62C2C3×#21311yescharacteristic
subgroupG/H
centerC2×C3#213
commutator, cosocleC3×C8C22×C3
FrattiniC8C2×C3×D3
FittingC32×D8C2
socleC2×C32D8
hypercenterC3×D8D3
hypocenterC3C3×D16
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×D8

Complements

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

NH ≅ G/Ntype
1. C32×D8C2semidirect
2. C3×D24C2semidirect
3. C3×C3⋊C16C2semidirect
5. #826C3direct (N × H)
11. C3×D8D3semidirect
12. C3×D8C2×C3semidirect
13. D24C2×C3semidirect
15. C3⋊C16C2×C3semidirect
32. D8C3×D3semidirect
42. C32D16semidirect
58. C3#826direct (N × H)
59. C3C3×D16semidirect

Maximal subgroups

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

subgroupindex
C32×D82
C3×D242
C3×C3⋊C162
C3×D163
#8263