Finite Group Databasebeta

← #8813⋊C3 #11709136

Subgroups — #8813⋊C3 #11709136

Order 768.

101 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C82⋊C3C211yesmaximal, characteristic
2#8813C311yesmaximal, characteristic, complemented, Sylow
3#384⋊C3—41nomaximal
4C82⋊C3C411yescharacteristic, complemented
5#1844—31no—
6#1844—31no—
7C2×C82C2×C311yescharacteristic
8C2×C42⋊C3—41no—
9C2×#106—62no—
10C2×#106—62no—
11C2×C4×C8—31no—
12#384—31no—
13#384A411yescharacteristic
14C82—31no—
15C82C3×C411yescharacteristic, complemented
16C4×A4—161no—
17C42⋊C3—41no—
18C22×C8—32no—
19C2×C4⋊C4—61no—
20C2×C4⋊C4—61no—
21C2×C4⋊C4—62no—
22C2×C42C2×A411yescharacteristic
23#106—124no—
24#106—124no—
25C4×C8—32no—
26C4×C8—31no—
27C4×C8—31no—
28C2×A4—161no—
29C22×C4—31no—
30C22×C4—41no—
31C22×C4—121no—
32C2×C8—32no—
33C2×C8—32no—
34C2×C8—34no—
35C2×C8—34no—
36C4⋊C4—122no—
37C4⋊C4—124no—
38C4⋊C4—122no—
39C42—31no—
40C42C4×A411yescharacteristic
41A4—161no—
42C3×C4—641no—
43C23#127⋊C311yescharacteristic
44C2×C4—32no—
45C2×C4—32no—
46C2×C4—31no—
47C2×C4—31no—
48C2×C4—241no—
49C2×C4—242no—
50C2×C4—241no—
51C8—34no—
52C8—34no—
53C2×C3—641no—
54C22—31no—
55C22—31no—
56C22#384⋊C311yescharacteristic
57C4—32no—
58C4—32no—
59C4—161no—
60C4—481no—
61C3—641noSylow
62C2—31no—
63C2—31no—
64C2#1705⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#1705⋊C3
commutator, hypocenterC82C3×C4
FrattiniC2×C42C2×A4
Fitting#8813C3
socleC23#127⋊C3
prime radicalC2×C82⋊C3C2
cosocleC2×C82C2×C3
LCSG ▷ C82
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #8813C3semidirect
4. C82⋊C3C4semidirect
15. C82C3×C4semidirect

Maximal subgroups

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

subgroupindex
C2×C82⋊C32
#88133
#384⋊C34