Finite Group Databasebeta

← C9×#3958 #13083787

Subgroups — C9×#3958 #13083787

Order 1440.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C9×D8C211yesmaximal, characteristic, complemented
2C9×D40C211yesmaximal, characteristic, complemented
3C9×#672C211yesmaximal, characteristic, complemented
4C3×#3958C311yesmaximal, characteristic
5C5×D4×C9—21no—
6C9×D20—21no—
7C5×C8×C9C2211yescharacteristic
8C9×D16—51nomaximal, Hall
9C3×C5×D8C2×C311yescharacteristic
10C3×D40C2×C311yescharacteristic
11C3×#672C2×C311yescharacteristic
12C22×C5×C9—41no—
13C2×C9×D5—41no—
14C4×C5×C9D411yescharacteristic
15#3958C911yescharacteristic, direct product factor, Hall
16C9×D8—51no—
17C9×D8D511yescharacteristic, complemented
18C9×C16—51no—
19C3×C5×D4—21no—
20C3×D20—21no—
21C3×C5×C8C22×C311yescharacteristic
22C3×D16—51no—
23C2×C5×C9—81no—
24C2×C5×C9D811yescharacteristic
25C9×D5—81no—
26C5×D8C2×C911yescharacteristic, complemented
27D40C2×C911yescharacteristic, complemented
28#672C2×C911yescharacteristic, complemented
29D4×C9—21no—
30D4×C9—101no—
31C8×C9C2×D511yescharacteristic
32C22×C3×C5—41no—
33C2×C3×D5—41no—
34C3×C4×C5C3×D411yescharacteristic
35C3×D8—51no—
36C3×D8C3×D511yescharacteristic
37C3×C16—51no—
38C5×C9D1611yescharacteristic, complemented, Hall
39C5×D4—21no—
40D20—21no—
41C5×C8C22×C911yescharacteristic
42C22×C9—41no—
43C22×C9—201no—
44C4×C9C22⋊D511yescharacteristic
45D16—51noSylow
46C2×C3×C5—81no—
47C2×C3×C5C3×D811yescharacteristic
48C3×D5—81no—
49C3×D4—21no—
50C3×D4—101no—
51C3×C8C2×C3×D511yescharacteristic
52C22×C5—41no—
53C2×D5—41no—
54C4×C5D4×C911yescharacteristic
55C2×C9—81no—
56C2×C9—401no—
57C2×C9#68611yescharacteristic
58D8—51no—
59D8C9×D511yescharacteristic, complemented
60C16—51no—
61C3×C5C3×D1611yescharacteristic
62C22×C3—41no—
63C22×C3—201no—
64C3×C4C3×C22⋊D511yescharacteristic
65C2×C5—81no—
66C2×C5C9×D811yescharacteristic
67D5—81no—
68C9#395811yescharacteristic, direct product factor, Sylow
69D4—21no—
70D4—101no—
71C8C2×C9×D511yescharacteristic
72C2×C3—81no—
73C2×C3—401no—
74C2×C3C3×#68611yescharacteristic
75C5C9×D1611yescharacteristic, complemented, Sylow
76C22—41no—
77C22—201no—
78C4C9×C22⋊D511yescharacteristic
79C3C3×#395811yescharacteristic
80C2—81no—
81C2—401no—
82C2C9×#68611yescharacteristic
subgroupG/H
centerC2×C9#686
commutatorC5×C8C22×C9
FrattiniC3×C8C2×C3×D5
FittingC5×C9×D8C2
socleC2×C3×C5C3×D8
prime radicalC3×#3958C3
cosocleC3×C5×C8C22×C3
hypercenterC9×D8D5
hypocenterC5C9×D16
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ C8×C9 ◁ C9×D8

Complements

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

NH ≅ G/Ntype
1. C5×C9×D8C2semidirect
2. C9×D40C2semidirect
3. C9×#672C2semidirect
15. #3958C9direct (N × H)
17. C9×D8D5semidirect
26. C5×D8C2×C9semidirect
27. D40C2×C9semidirect
28. #672C2×C9semidirect
38. C5×C9D16semidirect
59. D8C9×D5semidirect
68. C9#3958direct (N × H)
75. C5C9×D16semidirect

Maximal subgroups

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

subgroupindex
C5×C9×D82
C9×D402
C9×#6722
C3×#39583
C9×D165