Finite Group Databasebeta

← D23×#564 #15687539

Subgroups — D23×#564 #15687539

Order 2944.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23⋊#564C2115yesmaximal, complemented
2#125×D23C2115yesmaximal
3C23×#564C211yesmaximal, characteristic, complemented
4C23×#125C22115yes—
5C4⋊C4×D23C22130yes—
6#10625061C22130yes—
7#10625060C22160yes—
8C42×D23C2215yes—
9#10625041C22115yes—
10C2×C4×D23C23115yes—
11C4⋊C4×C23C23130yes—
12C42×C23C2315yes—
13C4⋊Dic23C23130yes—
14Dic23⋊C4C23160yes—
15C4×Dic23C23115yes—
16C22×D23C2411yescharacteristic
17C2×C4×C23C24115yes—
18C2×Dic23C24115yes—
19C4×D23—230no—
20C2×#564—231nomaximal, Sylow
21C22×C23C2511yescharacteristic
22C2×D232−1+416yes—
23C4×C23—215no—
24Dic23—215no—
25#564—2315no—
26#564D2311yescharacteristic, direct product factor
27C2×#125—2315no—
28C2×C23C2×2−1+413yes—
29D23#56414yesdirect product factor
30#125—2360no—
31#125—2330no—
32#125—2315no—
33#125C2×D23115yes—
34C2×C4⋊C4—2330no—
35C2×C42—235no—
36C23C2×#56411yescharacteristic, complemented, Sylow
37C22×C4—2315no—
38C4⋊C4—2360no—
39C4⋊C4—2330no—
40C4⋊C4C22×D23130yes—
41C42—2315no—
42C42C22×D2315yes—
43C23—231no—
44C2×C4—2315no—
45C2×C4—4630no—
46C2×C4C23×D23115yes—
47C22—236no—
48C22C24×D2311yescharacteristic
49C4—215no—
50C4—4615no—
51C2—234no—
52C22−1+4×D2313yes—
subgroupG/H
center, FrattiniC22C24×D23
commutator, socle, cosocleC22×C23C25
FittingC23×#564C2
prime radicalC22×D23C24
hypercenter#564D23
hypocenterC23C2×#564
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C23⋊#564C2semidirect
3. C23×#564C2semidirect
26. #564D23direct (N × H)
29. D23#564direct (N × H)
36. C23C2×#564semidirect

Maximal subgroups

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

subgroupindex
C23⋊#5642
#125×D232
C23×#5642
C2×#56423