Finite Group Databasebeta

← D3×#564 #87142

Subgroups — D3×#564 #87142

Order 384.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#564C211yesmaximal, characteristic, complemented
2D3×#125C2115yesmaximal
3C3⋊#564C2115yesmaximal, complemented
4C2×#564—31nomaximal, Sylow
5C3×#125C22115yes—
6D3×C4⋊C4C22130yes—
7#890C22130yes—
8#889C22160yes—
9C42×D3C2215yes—
10#870C22115yes—
11#564—315no—
12#564D311yescharacteristic, direct product factor
13C2×#125—315no—
14C2×C4×D3C23115yes—
15C3×C4⋊C4C23130yes—
16C3×C42C2315yes—
17C4⋊Dic3C23130yes—
18Dic3⋊C4C23160yes—
19C4×Dic3C23115yes—
20#125—360no—
21#125—330no—
22#125—315no—
23#125C2×D3115yes—
24C2×C4⋊C4—330no—
25C2×C42—35no—
26C22×D3C2411yescharacteristic
27C2×C3×C4C24115yes—
28C2×Dic3C24115yes—
29C4×D3—230no—
30C22×C4—315no—
31C4⋊C4—360no—
32C4⋊C4—330no—
33C4⋊C4C22×D3130yes—
34C42—315no—
35C42C22×D315yes—
36C22×C3C2511yescharacteristic
37C2×D32−1+416yes—
38C3×C4—215no—
39Dic3—215no—
40C23—31no—
41C2×C4—315no—
42C2×C4—630no—
43C2×C4C23×D3115yes—
44C2×C3C2×2−1+413yes—
45D3#56414yesdirect product factor
46C22—36no—
47C22C24×D311yescharacteristic
48C4—215no—
49C4—615no—
50C3C2×#56411yescharacteristic, complemented, Sylow
51C2—34no—
52C2D3×2−1+413yes—
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#564C2
prime radicalC22×D3C24
hypercenter#564D3
hypocenterC3C2×#564
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C3×#564C2semidirect
3. C3⋊#564C2semidirect
12. #564D3direct (N × H)
45. D3#564direct (N × H)
50. C3C2×#564semidirect

Maximal subgroups

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

subgroupindex
C3×#5642
D3×#1252
C3⋊#5642
C2×#5643