Finite Group Databasebeta

← #564×D61 #21459961

Subgroups — #564×D61 #21459961

Order 7808.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61⋊#564C2115yesmaximal, complemented
2#125×D61C2115yesmaximal
3C61×#564C211yesmaximal, characteristic, complemented
4#14519769C22115yes—
5#14519768C22130yes—
6#14519767C22160yes—
7C4⋊C4×D61C22130yes—
8C42×D61C2215yes—
9#125×C61C22115yes—
10C2×C4×D61C23115yes—
11C4⋊C4×C61C23130yes—
12C42×C61C2315yes—
13C4⋊Dic61C23130yes—
14#11758196C23160yes—
15C4×Dic61C23115yes—
16C22×D61C2411yescharacteristic
17C2×C4×C61C24115yes—
18C2×Dic61C24115yes—
19C4×D61—230no—
20C22×C61C2511yescharacteristic
21C2×D612−1+416yes—
22C4×C61—215no—
23Dic61—215no—
24C2×#564—611nomaximal, Sylow
25C2×C61C2×2−1+413yes—
26D61#56414yesdirect product factor
27#564—6115no—
28#564D6111yescharacteristic, direct product factor
29C2×#125—6115no—
30C61C2×#56411yescharacteristic, complemented, Sylow
31#125—6160no—
32#125—6130no—
33#125—6115no—
34#125C2×D61115yes—
35C2×C4⋊C4—6130no—
36C2×C42—615no—
37C22×C4—6115no—
38C4⋊C4—6160no—
39C4⋊C4—6130no—
40C4⋊C4C22×D61130yes—
41C42—6115no—
42C42C22×D6115yes—
43C23—611no—
44C2×C4—6115no—
45C2×C4—12230no—
46C2×C4C23×D61115yes—
47C22—616no—
48C22C24×D6111yescharacteristic
49C4—215no—
50C4—12215no—
51C2—614no—
52C22−1+4×D6113yes—
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC61×#564C2
hypercenter#564D61
hypocenterC61C2×#564
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C61⋊#564C2semidirect
3. C61×#564C2semidirect
26. D61#564direct (N × H)
28. #564D61direct (N × H)
30. C61C2×#564semidirect