Finite Group Databasebeta

← #3556×C197 #38740490

Subgroups — #3556×C197 #38740490

Order 25216.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#564×C197C214yesmaximal, complemented
2#557×C197C2112yesmaximal, complemented
3#541×C197C2112yesmaximal
4#533×C197C213yesmaximal
5C4⋊Q8×C197C2216yes—
6C4⋊Q8×C197C22112yes—
7#126×C197C22116yes—
8#125×C197C2216yes—
9#125×C197C22112yes—
10#125×C197C22148yes—
11C22⋊Q8×C197C22112yes—
12C4×Q8×C197C22112yes—
13C4×Q8×C197C22124yes—
14#117×C197C2216yes—
15C2×C42×C197C2211yescharacteristic
16C2×Q8×C197C23112yes—
17C22×C4×C197C2313yes—
18C4⋊C4×C197C23112yes—
19C4⋊C4×C197C23112yes—
20C4⋊C4×C197C23124yes—
21C4⋊C4×C197C23148yes—
22C22⋊C4×C197C23112yes—
23C42×C197C2313yes—
24C42×C197C2311yescharacteristic
25C42×C197C23112yes—
26C42×C197C23116yes—
27C23×C197C2411yescharacteristic
28Q8×C197—224no—
29C2×C4×C197—26no—
30C2×C4×C197C24124yes—
31C2×C4×C197C2413yes—
32C2×C4×C197C2413yes—
33C22×C197—23no—
34C22×C197C2511yescharacteristic
35C4×C197—23no—
36C4×C197—224no—
37C4×C1972−1+416yes—
38C2×C197—41no—
39C2×C197C2×2−1+413yes—
40C197#355611yescharacteristic, direct product factor, Sylow
41#3556C19711yesmaximal, characteristic, direct product factor, Sylow
42#564C2×C19714yescomplemented
43#557C2×C197112yescomplemented
44#541C2×C197112yes—
45#533C2×C19713yes—
46C4⋊Q8C22×C19716yes—
47C4⋊Q8C22×C197112yes—
48#126C22×C197116yes—
49#125C22×C19716yes—
50#125C22×C197112yes—
51#125C22×C197148yes—
52C22⋊Q8C22×C197112yes—
53C4×Q8C22×C197112yes—
54C4×Q8C22×C197124yes—
55#117C22×C19716yes—
56C2×C42C22×C19711yescharacteristic
57C2×Q8C23×C197112yes—
58C22×C4C23×C19713yes—
59C4⋊C4C23×C197112yes—
60C4⋊C4C23×C197112yes—
61C4⋊C4C23×C197124yes—
62C4⋊C4C23×C197148yes—
63C22⋊C4C23×C197112yes—
64C42C23×C19713yes—
65C42C23×C19711yescharacteristic
66C42C23×C197112yes—
67C42C23×C197116yes—
68C23C24×C19711yescharacteristic
69Q8—224no—
70C2×C4—26no—
71C2×C4C24×C197124yes—
72C2×C4C24×C19713yes—
73C2×C4C24×C19713yes—
74C22—23no—
75C22C25×C19711yescharacteristic
76C4—23no—
77C4—224no—
78C42−1+4×C19716yes—
79C2—41no—
80C2C2×2−1+4×C19713yes—
subgroupG/H
center, socleC22×C197C25
commutator, Frattini, cosocleC22C25×C197
prime radicalC23×C197C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C197 ◁ G

Complements

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

NH ≅ G/Ntype
1. #564×C197C2semidirect
2. #557×C197C2semidirect
40. C197#3556direct (N × H)
41. #3556C197direct (N × H)
42. #564C2×C197semidirect
43. #557C2×C197semidirect

Maximal subgroups

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

subgroupindex
#564×C1972
#557×C1972
#541×C1972
#533×C1972
#3556197