Finite Group Databasebeta

← #564×D103 #27209286

Subgroups — #564×D103 #27209286

Order 13184.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103⋊#564C2115yesmaximal, complemented
2#125×D103C2115yesmaximal
3#564×C103C211yesmaximal, characteristic, complemented
4#15693013C22115yes—
5#15693012C22130yes—
6#15693011C22160yes—
7C4⋊C4×D103C22130yes—
8C42×D103C2215yes—
9#125×C103C22115yes—
10C2×C4×D103C23115yes—
11C4⋊Dic103C23130yes—
12Dic103⋊C4C23160yes—
13C4×Dic103C23115yes—
14C4⋊C4×C103C23130yes—
15C42×C103C2315yes—
16C22×D103C2411yescharacteristic
17C2×C4×C103C24115yes—
18C2×Dic103C24115yes—
19C4×D103—230no—
20C22×C103C2511yescharacteristic
21C2×D1032−1+416yes—
22C4×C103—215no—
23Dic103—215no—
24C2×C103C2×2−1+413yes—
25D103#56414yesdirect product factor
26C2×#564—1031nomaximal, Sylow
27C103C2×#56411yescharacteristic, complemented, Sylow
28#564—10315no—
29#564D10311yescharacteristic, direct product factor
30C2×#125—10315no—
31#125—10360no—
32#125—10330no—
33#125—10315no—
34#125C2×D103115yes—
35C2×C4⋊C4—10330no—
36C2×C42—1035no—
37C22×C4—10315no—
38C4⋊C4—10360no—
39C4⋊C4—10330no—
40C4⋊C4C22×D103130yes—
41C42—10315no—
42C42C22×D10315yes—
43C23—1031no—
44C2×C4—10315no—
45C2×C4—20630no—
46C2×C4C23×D103115yes—
47C22—1036no—
48C22C24×D10311yescharacteristic
49C4—215no—
50C4—20615no—
51C2—1034no—
52C22−1+4×D10313yes—
subgroupG/H
center, FrattiniC22C24×D103
commutator, socle, cosocleC22×C103C25
Fitting#564×C103C2
prime radicalC22×D103C24
hypercenter#564D103
hypocenterC103C2×#564
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C103⋊#564C2semidirect
3. #564×C103C2semidirect
25. D103#564direct (N × H)
27. C103C2×#564semidirect
29. #564D103direct (N × H)

Maximal subgroups

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

subgroupindex
C103⋊#5642
#125×D1032
#564×C1032
C2×#564103