Finite Group Databasebeta

← #519×C97 #20260386

Subgroups — #519×C97 #20260386

Order 6208.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C97C211yesmaximal, characteristic
2C4×Q8×C97C218yesmaximal, complemented
3#117×C97C216yesmaximal
4C2×Q8×C97C418yescomplemented
5C2×Q8×C97C2214yes—
6C22×C4×C97C2213yes—
7C4⋊C4×C97C22112yes—
8C22⋊C4×C97C2214yes—
9C42×C97C22112yes—
10C23×C97C2311yescharacteristic
11Q8×C97C2×C4116yes—
12C2×C4×C97C2×C4112yes—
13C2×C4×C97C2318yes—
14C2×C4×C97C2316yes—
15C22×C97—22no—
16C22×C97C22×C412yes—
17C22×C97C2411yescharacteristic
18C4×C97—28no—
19C4×C97C22×C4112yes—
20C2×C97—22no—
21C2×C97C23×C411yescharacteristic
22C2×C972−1+412yes—
23C97#51911yescharacteristic, direct product factor, Sylow
24#519C9711yesmaximal, characteristic, direct product factor, Sylow
25C22×Q8C2×C9711yescharacteristic
26C4×Q8C2×C9718yescomplemented
27#117C2×C9716yes—
28C2×Q8C4×C9718yescomplemented
29C2×Q8C22×C9714yes—
30C22×C4C22×C9713yes—
31C4⋊C4C22×C97112yes—
32C22⋊C4C22×C9714yes—
33C42C22×C97112yes—
34C23C23×C9711yescharacteristic
35Q8C2×C4×C97116yes—
36C2×C4C2×C4×C97112yes—
37C2×C4C23×C9718yes—
38C2×C4C23×C9716yes—
39C22—22no—
40C22C22×C4×C9712yes—
41C22C24×C9711yescharacteristic
42C4—28no—
43C4C22×C4×C97112yes—
44C2—22no—
45C2C23×C4×C9711yescharacteristic
46C22−1+4×C9712yes—
subgroupG/H
center, socleC22×C97C24
commutatorC2C23×C4×C97
Frattini, cosocleC22C24×C97
prime radicalC23×C97C23
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C97 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×Q8×C97C2semidirect
4. C2×Q8×C97C4semidirect
23. C97#519direct (N × H)
24. #519C97direct (N × H)
26. C4×Q8C2×C97semidirect
28. C2×Q8C4×C97semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C972
C4×Q8×C972
#117×C972
#51997