Finite Group Databasebeta

← #564×D83 #24921605

Subgroups — #564×D83 #24921605

Order 10624.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83⋊#564C2115yesmaximal, complemented
2#125×D83C2115yesmaximal
3#564×C83C211yesmaximal, characteristic, complemented
4#14581784C22115yes—
5#14581783C22130yes—
6#14581782C22160yes—
7C4⋊C4×D83C22130yes—
8C42×D83C2215yes—
9#125×C83C22115yes—
10C2×C4×D83C23115yes—
11C4⋊Dic83C23130yes—
12Dic83⋊C4C23160yes—
13C4×Dic83C23115yes—
14C4⋊C4×C83C23130yes—
15C42×C83C2315yes—
16C22×D83C2411yescharacteristic
17C2×C4×C83C24115yes—
18C2×Dic83C24115yes—
19C4×D83—230no—
20C22×C83C2511yescharacteristic
21C2×D832−1+416yes—
22C4×C83—215no—
23Dic83—215no—
24C2×C83C2×2−1+413yes—
25D83#56414yesdirect product factor
26C2×#564—831nomaximal, Sylow
27C83C2×#56411yescharacteristic, complemented, Sylow
28#564—8315no—
29#564D8311yescharacteristic, direct product factor
30C2×#125—8315no—
31#125—8360no—
32#125—8330no—
33#125—8315no—
34#125C2×D83115yes—
35C2×C4⋊C4—8330no—
36C2×C42—835no—
37C22×C4—8315no—
38C4⋊C4—8360no—
39C4⋊C4—8330no—
40C4⋊C4C22×D83130yes—
41C42—8315no—
42C42C22×D8315yes—
43C23—831no—
44C2×C4—8315no—
45C2×C4—16630no—
46C2×C4C23×D83115yes—
47C22—836no—
48C22C24×D8311yescharacteristic
49C4—215no—
50C4—16615no—
51C2—834no—
52C22−1+4×D8313yes—
subgroupG/H
center, FrattiniC22C24×D83
commutator, socle, cosocleC22×C83C25
Fitting#564×C83C2
prime radicalC22×D83C24
hypercenter#564D83
hypocenterC83C2×#564
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C83⋊#564C2semidirect
3. #564×C83C2semidirect
25. D83#564direct (N × H)
27. C83C2×#564semidirect
29. #564D83direct (N × H)

Maximal subgroups

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

subgroupindex
C83⋊#5642
#125×D832
#564×C832
C2×#56483