Finite Group Databasebeta

← C2×D19×#89204 #45691648

Subgroups — C2×D19×#89204 #45691648

Order 33516.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#89204C211yesmaximal, characteristic, complemented
2D19×#89204C212yesmaximal, direct product factor
3C2×C3×C72×D19C311yesmaximal, characteristic
4C19×#89204C2211yescharacteristic, complemented, Hall
5C3×C72×D19C2×C312yes—
6C2×C3×C72×C19C2×C311yescharacteristic
7C2×D19×C7⋊C9—78nomaximal
8C2×C72×D19C911yescharacteristic, complemented, Hall
9C3×C72×C19C22×C311yescharacteristic
10C2×C19×C7⋊C9—78no—
11D19×C7⋊C9—716no—
12C2×C72×C19C2×C911yescharacteristic, complemented
13C72×D19C2×C912yescomplemented
14C22×#89204—191nomaximal, Hall
15C2×C3×C7×D19ΓL(1,𝔽8)18yes—
16C19×C7⋊C9—78no—
17C72×C19C22×C911yescharacteristic, complemented, Hall
18C2×#89204—192no—
19C2×#89204D1911yescharacteristic, direct product factor
20C2×C3×C7×C19C2×ΓL(1,𝔽8)18yes—
21C3×C7×D19C2×ΓL(1,𝔽8)116yes—
22C2×C9×D19—491noHall
23C22×C3×C72—191no—
24C2×C7×D19C7⋊C918yescomplemented
25#89204C2×D1911yescharacteristic, direct product factor, Hall
26C3×C7×C19C22×ΓL(1,𝔽8)18yes—
27C2×C9×C19—491no—
28C9×D19—492no—
29C2×C3×C72—192no—
30C2×C3×C72C3×D1911yescharacteristic
31C2×C7×C19C2×C7⋊C918yescomplemented
32C7×D19C2×C7⋊C9116yescomplemented
33C22×C7⋊C9—1338no—
34C2×C3×D19#386111yescharacteristic
35C22×C72—191noHall
36C9×C19—491noHall
37C3×C72C2×C3×D1911yescharacteristic
38C7×C19C22×C7⋊C918yescomplemented
39C2×C7⋊C9—78no—
40C2×C7⋊C9—13316no—
41C2×C3×C19C2×#386111yescharacteristic
42C3×D19C2×#386112yes—
43C2×C72—192no—
44C2×C72C9×D1911yescharacteristic, complemented
45C22×C3×C7—198no—
46C2×D19#8920411yescharacteristic, direct product factor, Hall
47C7⋊C9—78no—
48C3×C19C22×#386111yescharacteristic
49C72C2×C9×D1911yescharacteristic, complemented, Sylow
50C2×C3×C7—1916no—
51C2×C3×C7ΓL(1,𝔽8)×D1918yes—
52C2×C19C2×#8920411yescharacteristic, complemented
53D19C2×#8920412yesdirect product factor
54C22×C9—9311noHall
55C22×C7—198no—
56C3×C7C2×ΓL(1,𝔽8)×D1918yes—
57C19C22×#8920411yescharacteristic, complemented, Sylow
58C2×C9—491no—
59C2×C9—9312no—
60C2×C7—1916no—
61C2×C7D19×C7⋊C918yescomplemented
62C22×C3—191no—
63C9—491noSylow
64C7C2×D19×C7⋊C918yescomplemented
65C2×C3—192no—
66C2×C3D19×#386111yescharacteristic
67C22—191noSylow
68C3C2×D19×#386111yescharacteristic
69C2—192no—
70C2D19×#8920411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D19×#3861
commutator, hypocenterC72×C19C22×C9
FrattiniC3C2×D19×#3861
Fitting, socleC2×C3×C72×C19C2×C3
prime radicalC2×C3×C72×D19C3
cosocleC3×C72×C19C22×C3
LCSG ▷ C72×C19
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C19×#89204C2semidirect
2. D19×#89204C2direct (N × H)
4. C19×#89204C22semidirect
8. C2×C72×D19C9semidirect
12. C2×C72×C19C2×C9semidirect
13. C72×D19C2×C9semidirect
17. C72×C19C22×C9semidirect
19. C2×#89204D19direct (N × H)
24. C2×C7×D19C7⋊C9semidirect
25. #89204C2×D19direct (N × H)
31. C2×C7×C19C2×C7⋊C9semidirect
32. C7×D19C2×C7⋊C9semidirect
38. C7×C19C22×C7⋊C9semidirect
44. C2×C72C9×D19semidirect
46. C2×D19#89204direct (N × H)
49. C72C2×C9×D19semidirect
52. C2×C19C2×#89204semidirect
53. D19C2×#89204direct (N × H)
57. C19C22×#89204semidirect
61. C2×C7D19×C7⋊C9semidirect
64. C7C2×D19×C7⋊C9semidirect
70. C2D19×#89204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#892042
D19×#892042
C2×C3×C72×D193
C2×D19×C7⋊C97
C22×#8920419