Finite Group Databasebeta

← #564×D37 #18008738

Subgroups — #564×D37 #18008738

Order 4736.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37⋊#564C2115yesmaximal, complemented
2#125×D37C2115yesmaximal
3C37×#564C211yesmaximal, characteristic, complemented
4#11924528C22115yes—
5#11924527C22130yes—
6#11924526C22160yes—
7C4⋊C4×D37C22130yes—
8C42×D37C2215yes—
9#125×C37C22115yes—
10C2×C4×D37C23115yes—
11C4⋊C4×C37C23130yes—
12C42×C37C2315yes—
13C4⋊Dic37C23130yes—
14#10596936C23160yes—
15C4×Dic37C23115yes—
16C22×D37C2411yescharacteristic
17C2×C4×C37C24115yes—
18C2×Dic37C24115yes—
19C4×D37—230no—
20C22×C37C2511yescharacteristic
21C2×D372−1+416yes—
22C4×C37—215no—
23Dic37—215no—
24C2×#564—371nomaximal, Sylow
25C2×C37C2×2−1+413yes—
26D37#56414yesdirect product factor
27#564—3715no—
28#564D3711yescharacteristic, direct product factor
29C2×#125—3715no—
30C37C2×#56411yescharacteristic, complemented, Sylow
31#125—3760no—
32#125—3730no—
33#125—3715no—
34#125C2×D37115yes—
35C2×C4⋊C4—3730no—
36C2×C42—375no—
37C22×C4—3715no—
38C4⋊C4—3760no—
39C4⋊C4—3730no—
40C4⋊C4C22×D37130yes—
41C42—3715no—
42C42C22×D3715yes—
43C23—371no—
44C2×C4—3715no—
45C2×C4—7430no—
46C2×C4C23×D37115yes—
47C22—376no—
48C22C24×D3711yescharacteristic
49C4—215no—
50C4—7415no—
51C2—374no—
52C22−1+4×D3713yes—
subgroupG/H
center, FrattiniC22C24×D37
commutator, socle, cosocleC22×C37C25
FittingC37×#564C2
prime radicalC22×D37C24
hypercenter#564D37
hypocenterC37C2×#564
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C37⋊#564C2semidirect
3. C37×#564C2semidirect
26. D37#564direct (N × H)
28. #564D37direct (N × H)
30. C37C2×#564semidirect

Maximal subgroups

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

subgroupindex
C37⋊#5642
#125×D372
C37×#5642
C2×#56437