Finite Group Databasebeta

← #564×D163 #35228678

Subgroups — #564×D163 #35228678

Order 20864.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C163⋊#564C2115yesmaximal, complemented
2#125×D163C2115yesmaximal
3#564×C163C211yesmaximal, characteristic, complemented
4#19104727C22115yes—
5#19104726C22130yes—
6#19104725C22160yes—
7C4⋊C4×D163C22130yes—
8C42×D163C2215yes—
9#125×C163C22115yes—
10C2×C4×D163C23115yes—
11C4⋊Dic163C23130yes—
12Dic163⋊C4C23160yes—
13C4×Dic163C23115yes—
14C4⋊C4×C163C23130yes—
15C42×C163C2315yes—
16C22×D163C2411yescharacteristic
17C2×Dic163C24115yes—
18C4×D163—230no—
19C2×C4×C163C24115yes—
20C22×C163C2511yescharacteristic
21C2×D1632−1+416yes—
22C4×C163—215no—
23Dic163—215no—
24C2×C163C2×2−1+413yes—
25D163#56414yesdirect product factor
26C163C2×#56411yescharacteristic, complemented, Sylow
27C2×#564—1631nomaximal, Sylow
28#564—16315no—
29#564D16311yescharacteristic, direct product factor
30C2×#125—16315no—
31#125—16360no—
32#125—16330no—
33#125—16315no—
34#125C2×D163115yes—
35C2×C4⋊C4—16330no—
36C2×C42—1635no—
37C22×C4—16315no—
38C4⋊C4—16360no—
39C4⋊C4—16330no—
40C4⋊C4C22×D163130yes—
41C42—16315no—
42C42C22×D16315yes—
43C23—1631no—
44C2×C4—32630no—
45C2×C4—16315no—
46C2×C4C23×D163115yes—
47C22—1636no—
48C22C24×D16311yescharacteristic
49C4—215no—
50C4—32615no—
51C2—1634no—
52C22−1+4×D16313yes—
subgroupG/H
center, FrattiniC22C24×D163
commutator, socle, cosocleC22×C163C25
Fitting#564×C163C2
prime radicalC22×D163C24
hypercenter#564D163
hypocenterC163C2×#564
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C163⋊#564C2semidirect
3. #564×C163C2semidirect
25. D163#564direct (N × H)
26. C163C2×#564semidirect
29. #564D163direct (N × H)

Maximal subgroups

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

subgroupindex
C163⋊#5642
#125×D1632
#564×C1632
C2×#564163