Finite Group Databasebeta

← #519×C503 #44565932

Subgroups — #519×C503 #44565932

Order 32192.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C503C211yesmaximal, characteristic
2C4×Q8×C503C218yesmaximal, complemented
3#117×C503C216yesmaximal
4C2×Q8×C503C418yescomplemented
5C2×Q8×C503C2214yes—
6C22×C4×C503C2213yes—
7C4⋊C4×C503C22112yes—
8C22⋊C4×C503C2214yes—
9C42×C503C22112yes—
10C23×C503C2311yescharacteristic
11Q8×C503C2×C4116yes—
12C2×C4×C503C2×C4112yes—
13C2×C4×C503C2318yes—
14C2×C4×C503C2316yes—
15C22×C503—22no—
16C22×C503C22×C412yes—
17C22×C503C2411yescharacteristic
18C4×C503—28no—
19C4×C503C22×C4112yes—
20C2×C503—22no—
21C2×C503C23×C411yescharacteristic
22C2×C5032−1+412yes—
23C503#51911yescharacteristic, direct product factor, Sylow
24#519C50311yesmaximal, characteristic, direct product factor, Sylow
25C22×Q8C2×C50311yescharacteristic
26C4×Q8C2×C50318yescomplemented
27#117C2×C50316yes—
28C2×Q8C4×C50318yescomplemented
29C2×Q8C22×C50314yes—
30C22×C4C22×C50313yes—
31C4⋊C4C22×C503112yes—
32C22⋊C4C22×C50314yes—
33C42C22×C503112yes—
34C23C23×C50311yescharacteristic
35Q8C2×C4×C503116yes—
36C2×C4C2×C4×C503112yes—
37C2×C4C23×C50318yes—
38C2×C4C23×C50316yes—
39C22—22no—
40C22C22×C4×C50312yes—
41C22C24×C50311yescharacteristic
42C4—28no—
43C4C22×C4×C503112yes—
44C2—22no—
45C2C23×C4×C50311yescharacteristic
46C22−1+4×C50312yes—
subgroupG/H
center, socleC22×C503C24
commutatorC2C23×C4×C503
Frattini, cosocleC22C24×C503
prime radicalC23×C503C23
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C503 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×Q8×C503C2semidirect
4. C2×Q8×C503C4semidirect
23. C503#519direct (N × H)
24. #519C503direct (N × H)
26. C4×Q8C2×C503semidirect
28. C2×Q8C4×C503semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C5032
C4×Q8×C5032
#117×C5032
#519503