Finite Group Databasebeta

← #519×C163 #23781316

Subgroups — #519×C163 #23781316

Order 10432.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C163C211yesmaximal, characteristic
2C4×Q8×C163C218yesmaximal, complemented
3#117×C163C216yesmaximal
4C2×Q8×C163C418yescomplemented
5C2×Q8×C163C2214yes—
6C22×C4×C163C2213yes—
7C4⋊C4×C163C22112yes—
8C22⋊C4×C163C2214yes—
9C42×C163C22112yes—
10C23×C163C2311yescharacteristic
11Q8×C163C2×C4116yes—
12C2×C4×C163C2×C4112yes—
13C2×C4×C163C2318yes—
14C2×C4×C163C2316yes—
15C22×C163—22no—
16C22×C163C22×C412yes—
17C22×C163C2411yescharacteristic
18C4×C163—28no—
19C4×C163C22×C4112yes—
20C2×C163—22no—
21C2×C163C23×C411yescharacteristic
22C2×C1632−1+412yes—
23C163#51911yescharacteristic, direct product factor, Sylow
24#519C16311yesmaximal, characteristic, direct product factor, Sylow
25C22×Q8C2×C16311yescharacteristic
26C4×Q8C2×C16318yescomplemented
27#117C2×C16316yes—
28C2×Q8C4×C16318yescomplemented
29C2×Q8C22×C16314yes—
30C22×C4C22×C16313yes—
31C4⋊C4C22×C163112yes—
32C22⋊C4C22×C16314yes—
33C42C22×C163112yes—
34C23C23×C16311yescharacteristic
35Q8C2×C4×C163116yes—
36C2×C4C2×C4×C163112yes—
37C2×C4C23×C16318yes—
38C2×C4C23×C16316yes—
39C22—22no—
40C22C22×C4×C16312yes—
41C22C24×C16311yescharacteristic
42C4—28no—
43C4C22×C4×C163112yes—
44C2—22no—
45C2C23×C4×C16311yescharacteristic
46C22−1+4×C16312yes—
subgroupG/H
center, socleC22×C163C24
commutatorC2C23×C4×C163
Frattini, cosocleC22C24×C163
prime radicalC23×C163C23
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C163 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×Q8×C163C2semidirect
4. C2×Q8×C163C4semidirect
23. C163#519direct (N × H)
24. #519C163direct (N × H)
26. C4×Q8C2×C163semidirect
28. C2×Q8C4×C163semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C1632
C4×Q8×C1632
#117×C1632
#519163