Finite Group Databasebeta

← C3×2−1+4⋊C3 #64337

Subgroups — C3×2−1+4⋊C3 #64337

Order 288.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#41⋊C3C211yesmaximal, characteristic, complemented
2C2×C3×SL(2,𝔽3)C212yesmaximal, complemented
3C3×2−1+4C311yesmaximal, characteristic, complemented
42−1+4⋊C3C313yesmaximal, direct product factor
5C32×D4—41nomaximal
6C3×SL(2,𝔽3)C2211yescharacteristic
7C3×#41—31no—
8C3×#41—32no—
9C3×#41C2×C311yescharacteristic, complemented
10C2×C3×Q8—31no—
11C2×C3×Q8C2×C312yescomplemented
12#41⋊C3C2×C313yescomplemented
13C2×SL(2,𝔽3)C2×C316yescomplemented
14C22×C32—42no—
15C32×C4—41no—
162−1+4C3211yescharacteristic, complemented, Sylow
17C3×Q8—32no—
18C3×Q8—31no—
19C3×Q8C22×C311yescharacteristic
20C3×D4—31no—
21C3×D4—32no—
22C3×D4—43no—
23C3×D4A411yescharacteristic
24C2×C3×C4—32no—
25C2×C3×C4—32no—
26C2×C3×C4—31no—
27SL(2,𝔽3)C22×C313yes—
28C2×C32—41no—
29C2×C32—82no—
30#41—31no—
31#41—32no—
32#41C2×C3211yescharacteristic, complemented
33C2×Q8—31no—
34C2×Q8C2×C3212yescomplemented
35C22×C3—31no—
36C22×C3—46no—
37C22×C3C2×A412yes—
38C3×C4—32no—
39C3×C4—31no—
40C3×C4—43no—
41C3×C4C2×A411yescharacteristic
42C32—41noSylow
43Q8—32no—
44Q8—31no—
45Q8C22×C3211yescharacteristic
46D4—31no—
47D4—32no—
48D4C3×A411yescharacteristic
49C2×C4—32no—
50C2×C4—32no—
51C2×C4—31no—
52C2×C3—22no—
53C2×C3—43no—
54C2×C3—61no—
55C2×C3—86no—
56C2×C3C22×A411yescharacteristic
57C22—31no—
58C22C2×C3×A412yes—
59C4—31no—
60C4—32no—
61C4C2×C3×A411yescharacteristic
62C3—43no—
63C32−1+4⋊C311yescharacteristic, direct product factor
64C2—22no—
65C2—61no—
66C2C22×C3×A411yescharacteristic
subgroupG/H
center, socleC2×C3C22×A4
commutator, cosocle, hypocenterQ8C22×C32
FrattiniC2C22×C3×A4
FittingC3×2−1+4C3
hypercenterC3×D4A4
LCSG ▷ Q8
UCSC1 ◁ C2×C3 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
1. C3×#41⋊C3C2semidirect
2. C2×C3×SL(2,𝔽3)C2semidirect
3. C3×2−1+4C3semidirect
4. 2−1+4⋊C3C3direct (N × H)
9. C3×#41C2×C3semidirect
11. C2×C3×Q8C2×C3semidirect
12. #41⋊C3C2×C3semidirect
13. C2×SL(2,𝔽3)C2×C3semidirect
16. 2−1+4C32semidirect
32. #41C2×C32semidirect
34. C2×Q8C2×C32semidirect
63. C32−1+4⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#41⋊C32
C2×C3×SL(2,𝔽3)2
C3×2−1+43
2−1+4⋊C33
C32×D44