Finite Group Databasebeta

← #2736⋊C3 #73288

Subgroups — #2736⋊C3 #73288

Order 384.

135 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2736C311yesmaximal, characteristic, complemented, Sylow
2C2×C22⋊A4—41nomaximal
3C22⋊SL(2,𝔽3)—41nomaximal
4C2×C42⋊C3—42nomaximal
5#95⋊C3—41nomaximal
6#397—31no—
7#393—31no—
8#388—32no—
9#379—31no—
10C22⋊A4—41no—
11C42⋊C3—42no—
12C25A411yescharacteristic
13C22×Q8A411yescharacteristic, complemented
14C2×C4⋊C4—31no—
15C2×C22⋊C4—32no—
16C2×C22⋊C4—31no—
17C2×C22⋊C4—32no—
18C2×C22⋊C4—31no—
19C2×C42A412yescomplemented
20#95—31no—
21#95—32no—
22#95A411yescharacteristic, complemented
23C2×A4—164no—
24C2×A4—161no—
25SL(2,𝔽3)—164no—
26C24—31no—
27C24—41no—
28C24—62no—
29C24—121no—
30C2×Q8—121no—
31C22×C4—31no—
32C22×C4—31no—
33C22×C4—32no—
34C4⋊C4—121no—
35C22⋊C4—64no—
36C22⋊C4—122no—
37C22⋊C4—121no—
38C22⋊C4—121no—
39C42—42no—
40A4—164no—
41A4—161no—
42C23—32no—
43C23—44no—
44C23—61no—
45C23—62no—
46C23—62no—
47C23—61no—
48C23—122no—
49C23—124no—
50C23—122no—
51C23C22⋊A411yescharacteristic
52Q8—44no—
53C2×C4—62no—
54C2×C4—62no—
55C2×C4—61no—
56C2×C4—62no—
57C2×C4—62no—
58C2×C4—61no—
59C2×C4—62no—
60C2×C3—641no—
61C22—31no—
62C22—31no—
63C22—44no—
64C22—62no—
65C22—64no—
66C22—122no—
67C22—121no—
68C22—124no—
69C22—121no—
70C22#99711yescharacteristic
71C4—122no—
72C4—121no—
73C4—121no—
74C3—641noSylow
75C2—31no—
76C2—31no—
77C2—122no—
78C2#546411yescharacteristic
subgroupG/H
center, hypercenterC2#5464
commutator, Fitting, cosocle, hypocenter#2736C3
Frattini, socleC23C22⋊A4
LCSG ▷ #2736
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #2736C3semidirect
13. C22×Q8A4semidirect
19. C2×C42A4semidirect
22. #95A4semidirect

Maximal subgroups

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

subgroupindex
#27363
C2×C22⋊A44
C22⋊SL(2,𝔽3)4
C2×C42⋊C34
#95⋊C34