Finite Group Databasebeta

← #564×D181 #37547863

Subgroups — #564×D181 #37547863

Order 23168.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C181⋊#564C2115yesmaximal, complemented
2#125×D181C2115yesmaximal
3#564×C181C211yesmaximal, characteristic, complemented
4#19153808C22115yes—
5#19153807C22130yes—
6#19153806C22160yes—
7C4⋊C4×D181C22130yes—
8C42×D181C2215yes—
9#125×C181C22115yes—
10C2×C4×D181C23115yes—
11C4⋊Dic181C23130yes—
12#15668428C23160yes—
13C4×Dic181C23115yes—
14C4⋊C4×C181C23130yes—
15C42×C181C2315yes—
16C22×D181C2411yescharacteristic
17C2×Dic181C24115yes—
18C4×D181—230no—
19C2×C4×C181C24115yes—
20C22×C181C2511yescharacteristic
21C2×D1812−1+416yes—
22C4×C181—215no—
23Dic181—215no—
24C2×C181C2×2−1+413yes—
25D181#56414yesdirect product factor
26C181C2×#56411yescharacteristic, complemented, Sylow
27C2×#564—1811nomaximal, Sylow
28#564—18115no—
29#564D18111yescharacteristic, direct product factor
30C2×#125—18115no—
31#125—18160no—
32#125—18130no—
33#125—18115no—
34#125C2×D181115yes—
35C2×C4⋊C4—18130no—
36C2×C42—1815no—
37C22×C4—18115no—
38C4⋊C4—18160no—
39C4⋊C4—18130no—
40C4⋊C4C22×D181130yes—
41C42—18115no—
42C42C22×D18115yes—
43C23—1811no—
44C2×C4—36230no—
45C2×C4—18115no—
46C2×C4C23×D181115yes—
47C22—1816no—
48C22C24×D18111yescharacteristic
49C4—215no—
50C4—36215no—
51C2—1814no—
52C22−1+4×D18113yes—
subgroupG/H
center, FrattiniC22C24×D181
commutator, socle, cosocleC22×C181C25
Fitting#564×C181C2
prime radicalC22×D181C24
hypercenter#564D181
hypocenterC181C2×#564
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C181⋊#564C2semidirect
3. #564×C181C2semidirect
25. D181#564direct (N × H)
26. C181C2×#564semidirect
29. #564D181direct (N × H)

Maximal subgroups

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

subgroupindex
C181⋊#5642
#125×D1812
#564×C1812
C2×#564181