Finite Group Databasebeta

← #564×D157 #34114278

Subgroups — #564×D157 #34114278

Order 20096.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C157⋊#564C2115yesmaximal, complemented
2#125×D157C2115yesmaximal
3#564×C157C211yesmaximal, characteristic, complemented
4#19097763C22115yes—
5#19097762C22130yes—
6#19097761C22160yes—
7C4⋊C4×D157C22130yes—
8C42×D157C2215yes—
9#125×C157C22115yes—
10C2×C4×D157C23115yes—
11C4⋊Dic157C23130yes—
12#14578933C23160yes—
13C4×Dic157C23115yes—
14C4⋊C4×C157C23130yes—
15C42×C157C2315yes—
16C22×D157C2411yescharacteristic
17C2×Dic157C24115yes—
18C4×D157—230no—
19C2×C4×C157C24115yes—
20C22×C157C2511yescharacteristic
21C2×D1572−1+416yes—
22C4×C157—215no—
23Dic157—215no—
24C2×C157C2×2−1+413yes—
25D157#56414yesdirect product factor
26C157C2×#56411yescharacteristic, complemented, Sylow
27C2×#564—1571nomaximal, Sylow
28#564—15715no—
29#564D15711yescharacteristic, direct product factor
30C2×#125—15715no—
31#125—15760no—
32#125—15730no—
33#125—15715no—
34#125C2×D157115yes—
35C2×C4⋊C4—15730no—
36C2×C42—1575no—
37C22×C4—15715no—
38C4⋊C4—15760no—
39C4⋊C4—15730no—
40C4⋊C4C22×D157130yes—
41C42—15715no—
42C42C22×D15715yes—
43C23—1571no—
44C2×C4—31430no—
45C2×C4—15715no—
46C2×C4C23×D157115yes—
47C22—1576no—
48C22C24×D15711yescharacteristic
49C4—215no—
50C4—31415no—
51C2—1574no—
52C22−1+4×D15713yes—
subgroupG/H
center, FrattiniC22C24×D157
commutator, socle, cosocleC22×C157C25
Fitting#564×C157C2
prime radicalC22×D157C24
hypercenter#564D157
hypocenterC157C2×#564
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C157⋊#564C2semidirect
3. #564×C157C2semidirect
25. D157#564direct (N × H)
26. C157C2×#564semidirect
29. #564D157direct (N × H)

Maximal subgroups

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

subgroupindex
C157⋊#5642
#125×D1572
#564×C1572
C2×#564157