Finite Group Databasebeta

← D29×#564 #16833634

Subgroups — D29×#564 #16833634

Order 3712.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29⋊#564C2115yesmaximal, complemented
2#125×D29C2115yesmaximal
3C29×#564C211yesmaximal, characteristic, complemented
4C29×#125C22115yes—
5C4⋊C4×D29C22130yes—
6#11745252C22130yes—
7#11745251C22160yes—
8C42×D29C2215yes—
9#11745232C22115yes—
10C2×C4×D29C23115yes—
11C4⋊C4×C29C23130yes—
12C42×C29C2315yes—
13C4⋊Dic29C23130yes—
14#90779C23160yes—
15C4×Dic29C23115yes—
16C22×D29C2411yescharacteristic
17C2×C4×C29C24115yes—
18C2×Dic29C24115yes—
19C4×D29—230no—
20C2×#564—291nomaximal, Sylow
21C22×C29C2511yescharacteristic
22C2×D292−1+416yes—
23C4×C29—215no—
24Dic29—215no—
25#564—2915no—
26#564D2911yescharacteristic, direct product factor
27C2×#125—2915no—
28C2×C29C2×2−1+413yes—
29D29#56414yesdirect product factor
30#125—2960no—
31#125—2930no—
32#125—2915no—
33#125C2×D29115yes—
34C2×C4⋊C4—2930no—
35C2×C42—295no—
36C29C2×#56411yescharacteristic, complemented, Sylow
37C22×C4—2915no—
38C4⋊C4—2960no—
39C4⋊C4—2930no—
40C4⋊C4C22×D29130yes—
41C42—2915no—
42C42C22×D2915yes—
43C23—291no—
44C2×C4—2915no—
45C2×C4—5830no—
46C2×C4C23×D29115yes—
47C22—296no—
48C22C24×D2911yescharacteristic
49C4—215no—
50C4—5815no—
51C2—294no—
52C22−1+4×D2913yes—
subgroupG/H
center, FrattiniC22C24×D29
commutator, socle, cosocleC22×C29C25
FittingC29×#564C2
prime radicalC22×D29C24
hypercenter#564D29
hypocenterC29C2×#564
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C29⋊#564C2semidirect
3. C29×#564C2semidirect
26. #564D29direct (N × H)
29. D29#564direct (N × H)
36. C29C2×#564semidirect

Maximal subgroups

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

subgroupindex
C29⋊#5642
#125×D292
C29×#5642
C2×#56429