Finite Group Databasebeta

← #519×C197 #27160730

Subgroups — #519×C197 #27160730

Order 12608.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C197C211yesmaximal, characteristic
2C4×Q8×C197C218yesmaximal, complemented
3#117×C197C216yesmaximal
4C2×Q8×C197C418yescomplemented
5C2×Q8×C197C2214yes—
6C22×C4×C197C2213yes—
7C4⋊C4×C197C22112yes—
8C22⋊C4×C197C2214yes—
9C42×C197C22112yes—
10C23×C197C2311yescharacteristic
11Q8×C197C2×C4116yes—
12C2×C4×C197C2×C4112yes—
13C2×C4×C197C2318yes—
14C2×C4×C197C2316yes—
15C22×C197—22no—
16C22×C197C22×C412yes—
17C22×C197C2411yescharacteristic
18C4×C197—28no—
19C4×C197C22×C4112yes—
20C2×C197—22no—
21C2×C197C23×C411yescharacteristic
22C2×C1972−1+412yes—
23C197#51911yescharacteristic, direct product factor, Sylow
24#519C19711yesmaximal, characteristic, direct product factor, Sylow
25C22×Q8C2×C19711yescharacteristic
26C4×Q8C2×C19718yescomplemented
27#117C2×C19716yes—
28C2×Q8C4×C19718yescomplemented
29C2×Q8C22×C19714yes—
30C22×C4C22×C19713yes—
31C4⋊C4C22×C197112yes—
32C22⋊C4C22×C19714yes—
33C42C22×C197112yes—
34C23C23×C19711yescharacteristic
35Q8C2×C4×C197116yes—
36C2×C4C2×C4×C197112yes—
37C2×C4C23×C19718yes—
38C2×C4C23×C19716yes—
39C22—22no—
40C22C22×C4×C19712yes—
41C22C24×C19711yescharacteristic
42C4—28no—
43C4C22×C4×C197112yes—
44C2—22no—
45C2C23×C4×C19711yescharacteristic
46C22−1+4×C19712yes—
subgroupG/H
center, socleC22×C197C24
commutatorC2C23×C4×C197
Frattini, cosocleC22C24×C197
prime radicalC23×C197C23
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C197 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×Q8×C197C2semidirect
4. C2×Q8×C197C4semidirect
23. C197#519direct (N × H)
24. #519C197direct (N × H)
26. C4×Q8C2×C197semidirect
28. C2×Q8C4×C197semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C1972
C4×Q8×C1972
#117×C1972
#519197