Finite Group Databasebeta

← #564×D101 #27185274

Subgroups — #564×D101 #27185274

Order 12928.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101⋊#564C2115yesmaximal, complemented
2#125×D101C2115yesmaximal
3#564×C101C211yesmaximal, characteristic, complemented
4#15692247C22115yes—
5#15692246C22130yes—
6#15692245C22160yes—
7C4⋊C4×D101C22130yes—
8C42×D101C2215yes—
9#125×C101C22115yes—
10C2×C4×D101C23115yes—
11C4⋊Dic101C23130yes—
12#13108053C23160yes—
13C4×Dic101C23115yes—
14C4⋊C4×C101C23130yes—
15C42×C101C2315yes—
16C22×D101C2411yescharacteristic
17C2×C4×C101C24115yes—
18C2×Dic101C24115yes—
19C4×D101—230no—
20C22×C101C2511yescharacteristic
21C2×D1012−1+416yes—
22C4×C101—215no—
23Dic101—215no—
24C2×C101C2×2−1+413yes—
25D101#56414yesdirect product factor
26C2×#564—1011nomaximal, Sylow
27C101C2×#56411yescharacteristic, complemented, Sylow
28#564—10115no—
29#564D10111yescharacteristic, direct product factor
30C2×#125—10115no—
31#125—10160no—
32#125—10130no—
33#125—10115no—
34#125C2×D101115yes—
35C2×C4⋊C4—10130no—
36C2×C42—1015no—
37C22×C4—10115no—
38C4⋊C4—10160no—
39C4⋊C4—10130no—
40C4⋊C4C22×D101130yes—
41C42—10115no—
42C42C22×D10115yes—
43C23—1011no—
44C2×C4—10115no—
45C2×C4—20230no—
46C2×C4C23×D101115yes—
47C22—1016no—
48C22C24×D10111yescharacteristic
49C4—215no—
50C4—20215no—
51C2—1014no—
52C22−1+4×D10113yes—
subgroupG/H
center, FrattiniC22C24×D101
commutator, socle, cosocleC22×C101C25
Fitting#564×C101C2
prime radicalC22×D101C24
hypercenter#564D101
hypocenterC101C2×#564
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C101⋊#564C2semidirect
3. #564×C101C2semidirect
25. D101#564direct (N × H)
27. C101C2×#564semidirect
29. #564D101direct (N × H)

Maximal subgroups

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

subgroupindex
C101⋊#5642
#125×D1012
#564×C1012
C2×#564101