Finite Group Databasebeta

← C89×#3556 #26018030

Subgroups — C89×#3556 #26018030

Order 11392.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#564×C89C214yesmaximal, complemented
2#557×C89C2112yesmaximal, complemented
3#541×C89C2112yesmaximal
4#533×C89C213yesmaximal
5C4⋊Q8×C89C2216yes—
6C4⋊Q8×C89C22112yes—
7#126×C89C22116yes—
8#125×C89C2216yes—
9#125×C89C22112yes—
10#125×C89C22148yes—
11C22⋊Q8×C89C22112yes—
12C4×Q8×C89C22112yes—
13C4×Q8×C89C22124yes—
14#117×C89C2216yes—
15C2×C42×C89C2211yescharacteristic
16C2×Q8×C89C23112yes—
17C22×C4×C89C2313yes—
18C4⋊C4×C89C23112yes—
19C4⋊C4×C89C23112yes—
20C4⋊C4×C89C23124yes—
21C4⋊C4×C89C23148yes—
22C22⋊C4×C89C23112yes—
23C42×C89C2313yes—
24C42×C89C2311yescharacteristic
25C42×C89C23112yes—
26C42×C89C23116yes—
27C23×C89C2411yescharacteristic
28Q8×C89—224no—
29C2×C4×C89—26no—
30C2×C4×C89C24124yes—
31C2×C4×C89C2413yes—
32C2×C4×C89C2413yes—
33C22×C89—23no—
34C22×C89C2511yescharacteristic
35C4×C89—23no—
36C4×C89—224no—
37C4×C892−1+416yes—
38C2×C89—41no—
39C2×C89C2×2−1+413yes—
40#3556C8911yesmaximal, characteristic, direct product factor, Sylow
41C89#355611yescharacteristic, direct product factor, Sylow
42#564C2×C8914yescomplemented
43#557C2×C89112yescomplemented
44#541C2×C89112yes—
45#533C2×C8913yes—
46C4⋊Q8C22×C8916yes—
47C4⋊Q8C22×C89112yes—
48#126C22×C89116yes—
49#125C22×C8916yes—
50#125C22×C89112yes—
51#125C22×C89148yes—
52C22⋊Q8C22×C89112yes—
53C4×Q8C22×C89112yes—
54C4×Q8C22×C89124yes—
55#117C22×C8916yes—
56C2×C42C22×C8911yescharacteristic
57C2×Q8C23×C89112yes—
58C22×C4C23×C8913yes—
59C4⋊C4C23×C89112yes—
60C4⋊C4C23×C89112yes—
61C4⋊C4C23×C89124yes—
62C4⋊C4C23×C89148yes—
63C22⋊C4C23×C89112yes—
64C42C23×C8913yes—
65C42C23×C8911yescharacteristic
66C42C23×C89112yes—
67C42C23×C89116yes—
68C23C24×C8911yescharacteristic
69Q8—224no—
70C2×C4—26no—
71C2×C4C24×C89124yes—
72C2×C4C24×C8913yes—
73C2×C4C24×C8913yes—
74C22—23no—
75C22C25×C8911yescharacteristic
76C4—23no—
77C4—224no—
78C42−1+4×C8916yes—
79C2—41no—
80C2C2×2−1+4×C8913yes—
subgroupG/H
center, socleC22×C89C25
commutator, Frattini, cosocleC22C25×C89
prime radicalC23×C89C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. #564×C89C2semidirect
2. #557×C89C2semidirect
40. #3556C89direct (N × H)
41. C89#3556direct (N × H)
42. #564C2×C89semidirect
43. #557C2×C89semidirect

Maximal subgroups

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

subgroupindex
#564×C892
#557×C892
#541×C892
#533×C892
#355689