Finite Group Databasebeta

← #564×D127 #30652872

Subgroups — #564×D127 #30652872

Order 16256.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127⋊#564C2115yesmaximal, complemented
2#125×D127C2115yesmaximal
3#564×C127C211yesmaximal, characteristic, complemented
4#16861201C22115yes—
5#16861200C22130yes—
6#16861199C22160yes—
7C4⋊C4×D127C22130yes—
8C42×D127C2215yes—
9#125×C127C22115yes—
10C2×C4×D127C23115yes—
11C4⋊Dic127C23130yes—
12Dic127⋊C4C23160yes—
13C4×Dic127C23115yes—
14C4⋊C4×C127C23130yes—
15C42×C127C2315yes—
16C22×D127C2411yescharacteristic
17C2×Dic127C24115yes—
18C4×D127—230no—
19C2×C4×C127C24115yes—
20C22×C127C2511yescharacteristic
21C2×D1272−1+416yes—
22C4×C127—215no—
23Dic127—215no—
24C2×C127C2×2−1+413yes—
25D127#56414yesdirect product factor
26C2×#564—1271nomaximal, Sylow
27C127C2×#56411yescharacteristic, complemented, Sylow
28#564—12715no—
29#564D12711yescharacteristic, direct product factor
30C2×#125—12715no—
31#125—12760no—
32#125—12730no—
33#125—12715no—
34#125C2×D127115yes—
35C2×C4⋊C4—12730no—
36C2×C42—1275no—
37C22×C4—12715no—
38C4⋊C4—12760no—
39C4⋊C4—12730no—
40C4⋊C4C22×D127130yes—
41C42—12715no—
42C42C22×D12715yes—
43C23—1271no—
44C2×C4—12715no—
45C2×C4—25430no—
46C2×C4C23×D127115yes—
47C22—1276no—
48C22C24×D12711yescharacteristic
49C4—215no—
50C4—25415no—
51C2—1274no—
52C22−1+4×D12713yes—
subgroupG/H
center, FrattiniC22C24×D127
commutator, socle, cosocleC22×C127C25
Fitting#564×C127C2
prime radicalC22×D127C24
hypercenter#564D127
hypocenterC127C2×#564
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C127⋊#564C2semidirect
3. #564×C127C2semidirect
25. D127#564direct (N × H)
27. C127C2×#564semidirect
29. #564D127direct (N × H)

Maximal subgroups

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

subgroupindex
C127⋊#5642
#125×D1272
#564×C1272
C2×#564127