Finite Group Databasebeta

← C23×#239 #87559

Subgroups — C23×#239 #87559

Order 384.

6520 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Q8C211yesmaximal, characteristic, complemented
2C22×#239C2156yesmaximal, direct product factor
3C23×D12C213yesmaximal, complemented
4C23×C4×D3C213yesmaximal, complemented
5C23×#41—31nomaximal, Sylow
6C24×D3C2213yes—
7C22×C3×Q8C22128yescomplemented
8C23×C3×C4C2213yes—
9C23×Dic3C2211yescharacteristic
10C2×#239C221448yesdirect product factor
11C22×D12C22184yescomplemented
12C22×C4×D3C22184yescomplemented
13C22×#41—356no—
14C23×Q8D311yescharacteristic, complemented
15C23×D4—33no—
16C24×C4—33no—
17C24×C3C2311yescharacteristic
18C23×D3—224no—
19C23×D3C23142yes—
20C2×C3×Q8C231112yescomplemented
21C22×C3×C4C23142yes—
22C22×Dic3C23114yes—
23#239C231512yesdirect product factor
24C2×D12C231336yescomplemented
25C2×C4×D3C231336yescomplemented
26C25—33no—
27C2×#41—3448no—
28C22×Q8C2×D3128yescomplemented
29C22×D4—384no—
30C23×C4—31no—
31C23×C4—384no—
32C23×C4C2×D313yes—
33C23×C3#4118yescomplemented
34C23×C3C2417yes—
35C22×D3—2168no—
36C22×D3C24184yes—
37C3×Q8C24164yescomplemented
38C2×C3×C4C24184yes—
39C2×Dic3C24128yes—
40D12C241192yescomplemented
41C4×D3C241192yescomplemented
42C24—342no—
43C24—624no—
44C24C22×D311yescharacteristic
45#41—3512no—
46C2×Q8C22×D31112yescomplemented
47C2×D4—3336no—
48C22×C4—314no—
49C22×C4—3336no—
50C22×C4C22×D3142yes—
51C22×C3C2×#41128yescomplemented
52C22×C3C2517yes—
53C2×D3—2168no—
54C2×D3C25124yes—
55C3×C4C25124yes—
56Dic3C2518yes—
57C23—384no—
58C23—6168no—
59C23#23918yesdirect product factor
60C23C23×D317yes—
61Q8C23×D3164yescomplemented
62D4—3192no—
63C2×C4—328no—
64C2×C4—3192no—
65C2×C4C23×D3184yes—
66C2×C3C22×#41114yescomplemented
67C2×C3C2611yescharacteristic
68D3—224no—
69C22—324no—
70C22—6168no—
71C22C2×#239128yesdirect product factor
72C22C24×D317yes—
73C4—38no—
74C4C24×D3124yes—
75C3C23×#4111yescharacteristic, complemented, Sylow
76C2—624no—
77C2C22×#239114yesdirect product factor
78C2C25×D311yescharacteristic
subgroupG/H
centerC24C22×D3
commutator, cosocleC2×C3C26
FrattiniC2C25×D3
FittingC23×C3×Q8C2
socleC24×C3C23
hypercenterC23×Q8D3
hypocenterC3C23×#41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
1. C23×C3×Q8C2semidirect
2. C22×#239C2direct (N × H)
3. C23×D12C2semidirect
4. C23×C4×D3C2semidirect
7. C22×C3×Q8C22semidirect
10. C2×#239C22direct (N × H)
11. C22×D12C22semidirect
12. C22×C4×D3C22semidirect
14. C23×Q8D3semidirect
20. C2×C3×Q8C23semidirect
23. #239C23direct (N × H)
24. C2×D12C23semidirect
25. C2×C4×D3C23semidirect
28. C22×Q8C2×D3semidirect
33. C23×C3#41semidirect
37. C3×Q8C24semidirect
40. D12C24semidirect
41. C4×D3C24semidirect
46. C2×Q8C22×D3semidirect
51. C22×C3C2×#41semidirect
59. C23#239direct (N × H)
61. Q8C23×D3semidirect
66. C2×C3C22×#41semidirect
71. C22C2×#239direct (N × H)
75. C3C23×#41semidirect
77. C2C22×#239direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Q82
C22×#2392
C23×D122
C23×C4×D32
C23×#413