Finite Group Databasebeta

← #564×D251 #44564507

Subgroups — #564×D251 #44564507

Order 32128.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C251⋊#564C2115yesmaximal, complemented
2#125×D251C2115yesmaximal
3#564×C251C211yesmaximal, characteristic, complemented
4#22548707C22115yes—
5#22548706C22130yes—
6#22548705C22160yes—
7C4⋊C4×D251C22130yes—
8C42×D251C2215yes—
9#125×C251C22115yes—
10C2×C4×D251C23115yes—
11C4⋊Dic251C23130yes—
12Dic251⋊C4C23160yes—
13C4×Dic251C23115yes—
14C4⋊C4×C251C23130yes—
15C42×C251C2315yes—
16C22×D251C2411yescharacteristic
17C2×Dic251C24115yes—
18C4×D251—230no—
19C2×C4×C251C24115yes—
20C22×C251C2511yescharacteristic
21C2×D2512−1+416yes—
22C4×C251—215no—
23Dic251—215no—
24C2×C251C2×2−1+413yes—
25D251#56414yesdirect product factor
26C251C2×#56411yescharacteristic, complemented, Sylow
27C2×#564—2511nomaximal, Sylow
28#564—25115no—
29#564D25111yescharacteristic, direct product factor
30C2×#125—25115no—
31#125—25160no—
32#125—25130no—
33#125—25115no—
34#125C2×D251115yes—
35C2×C4⋊C4—25130no—
36C2×C42—2515no—
37C22×C4—25115no—
38C4⋊C4—25160no—
39C4⋊C4—25130no—
40C4⋊C4C22×D251130yes—
41C42—25115no—
42C42C22×D25115yes—
43C23—2511no—
44C2×C4—50230no—
45C2×C4—25115no—
46C2×C4C23×D251115yes—
47C22—2516no—
48C22C24×D25111yescharacteristic
49C4—215no—
50C4—50215no—
51C2—2514no—
52C22−1+4×D25113yes—
subgroupG/H
center, FrattiniC22C24×D251
commutator, socle, cosocleC22×C251C25
Fitting#564×C251C2
prime radicalC22×D251C24
hypercenter#564D251
hypocenterC251C2×#564
LCSG ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C251⋊#564C2semidirect
3. #564×C251C2semidirect
25. D251#564direct (N × H)
26. C251C2×#564semidirect
29. #564D251direct (N × H)

Maximal subgroups

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

subgroupindex
C251⋊#5642
#125×D2512
#564×C2512
C2×#564251