Finite Group Databasebeta

← #564×D283 #49135403

Subgroups — #564×D283 #49135403

Order 36224.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C283⋊#564C2115yesmaximal, complemented
2#125×D283C2115yesmaximal
3#564×C283C211yesmaximal, characteristic, complemented
4#22583602C22115yes—
5#22583601C22130yes—
6#22583600C22160yes—
7C4⋊C4×D283C22130yes—
8C42×D283C2215yes—
9#125×C283C22115yes—
10C2×C4×D283C23115yes—
11C4⋊Dic283C23130yes—
12Dic283⋊C4C23160yes—
13C4×Dic283C23115yes—
14C4⋊C4×C283C23130yes—
15C42×C283C2315yes—
16C22×D283C2411yescharacteristic
17C2×Dic283C24115yes—
18C4×D283—230no—
19C2×C4×C283C24115yes—
20C22×C283C2511yescharacteristic
21C2×D2832−1+416yes—
22C4×C283—215no—
23Dic283—215no—
24C2×C283C2×2−1+413yes—
25D283#56414yesdirect product factor
26C283C2×#56411yescharacteristic, complemented, Sylow
27C2×#564—2831nomaximal, Sylow
28#564—28315no—
29#564D28311yescharacteristic, direct product factor
30C2×#125—28315no—
31#125—28360no—
32#125—28330no—
33#125—28315no—
34#125C2×D283115yes—
35C2×C4⋊C4—28330no—
36C2×C42—2835no—
37C22×C4—28315no—
38C4⋊C4—28360no—
39C4⋊C4—28330no—
40C4⋊C4C22×D283130yes—
41C42—28315no—
42C42C22×D28315yes—
43C23—2831no—
44C2×C4—28315no—
45C2×C4—56630no—
46C2×C4C23×D283115yes—
47C22—2836no—
48C22C24×D28311yescharacteristic
49C4—215no—
50C4—56615no—
51C2—2834no—
52C22−1+4×D28313yes—
subgroupG/H
center, FrattiniC22C24×D283
commutator, socle, cosocleC22×C283C25
Fitting#564×C283C2
prime radicalC22×D283C24
hypercenter#564D283
hypocenterC283C2×#564
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C283⋊#564C2semidirect
3. #564×C283C2semidirect
25. D283#564direct (N × H)
26. C283C2×#564semidirect
29. #564D283direct (N × H)

Maximal subgroups

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

subgroupindex
C283⋊#5642
#125×D2832
#564×C2832
C2×#564283