Finite Group Databasebeta

← C2×D3×D8 #5754

Subgroups — C2×D3×D8 #5754

Order 192.

338 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D4C212yesmaximal, complemented
2C2×C3×D8C211yesmaximal, characteristic, complemented
3C2×#213C212yesmaximal, complemented
4D3×D8C218yesmaximal, direct product factor
5C2×D24C211yesmaximal, characteristic, complemented
6C2×D3×C8C211yesmaximal, characteristic, complemented
7C22×D8—31nomaximal, Sylow
8C23×D3—22no—
9C2×C3×D4C2212yescomplemented
10C2×#67—22no—
11D3×D4—24no—
12D3×D4C2218yescomplemented
13C2×D12C2212yescomplemented
14C2×C4×D3C2211yescharacteristic
15C3×D8C2214yescomplemented
16C2×C3×C8C2211yescharacteristic, complemented
17#213C2218yescomplemented
18C2×C3⋊C8C2211yescharacteristic, complemented
19D24C2214yescomplemented
20D3×C8C2214yescomplemented
21C22×D4—32no—
22C2×D8—32no—
23C2×D8—38no—
24C2×D8—31no—
25C2×D8D311yescharacteristic, direct product factor
26C22×C8—31no—
27C23×C3—22no—
28C22×D3—22no—
29C22×D3—28no—
30C22×D3—48no—
31C22×D3D411yescharacteristic
32C3×D4—22no—
33C3×D4C2314yescomplemented
34C2×C3×C4C2311yescharacteristic
35#67—28no—
36C2×Dic3D411yescharacteristic
37D12—22no—
38D12C2314yescomplemented
39C4×D3D412yes—
40C4×D3C2312yes—
41C3×C8C2312yescomplemented
42C3⋊C8C2312yescomplemented
43C24—62no—
44C2×D4—38no—
45C2×D4—32no—
46C2×D4—64no—
47C2×D4—62no—
48C2×D4C2×D312yescomplemented
49C22×C4—31no—
50D8—38no—
51D8—34no—
52D8C2×D314yesdirect product factor
53C2×C8—31no—
54C2×C8—34no—
55C2×C8C2×D311yescharacteristic, complemented
56C22×C3—24no—
57C22×C3—44no—
58C22×C3C2×D411yescharacteristic
59C2×D3—24no—
60C2×D3—44no—
61C2×D3—416no—
62C2×D3D814yesdirect product factor
63C2×D3C2×D412yes—
64C3×C4C2×D411yescharacteristic
65C3×C4C2411yescharacteristic
66Dic3C2×D412yes—
67C23—22no—
68C23—31no—
69C23—68no—
70C23—62no—
71C23—128no—
72D4—22no—
73D4—34no—
74D4—68no—
75D4—62no—
76D4C22×D314yescomplemented
77C2×C4—31no—
78C2×C4—32no—
79C2×C4—32no—
80C2×C4C22×D311yescharacteristic
81C8—32no—
82C8C22×D312yescomplemented
83C2×C3—44no—
84C2×C3C2×D812yescomplemented
85C2×C3C22×D411yescharacteristic
86D3—44no—
87D3C2×D814yesdirect product factor
88C22—24no—
89C22—34no—
90C22—32no—
91C22—44no—
92C22—64no—
93C22—1216no—
94C22—124no—
95C22D3×D411yescharacteristic
96C4—32no—
97C4D3×D411yescharacteristic
98C4C23×D311yescharacteristic
99C3C22×D811yescharacteristic, complemented, Sylow
100C2—34no—
101C2—44no—
102C2—124no—
103C2D3×D812yesdirect product factor
104C2C2×D3×D411yescharacteristic
subgroupG/H
centerC22D3×D4
commutator, cosocleC3×C4C24
FrattiniC4C23×D3
FittingC2×C3×D8C2
socleC22×C3C2×D4
hypercenterC2×D8D3
hypocenterC3C22×D8
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D3×D4C2semidirect
2. C2×C3×D8C2semidirect
3. C2×#213C2semidirect
4. D3×D8C2direct (N × H)
5. C2×D24C2semidirect
6. C2×D3×C8C2semidirect
9. C2×C3×D4C22semidirect
12. D3×D4C22semidirect
13. C2×D12C22semidirect
15. C3×D8C22semidirect
16. C2×C3×C8C22semidirect
17. #213C22semidirect
18. C2×C3⋊C8C22semidirect
19. D24C22semidirect
20. D3×C8C22semidirect
25. C2×D8D3direct (N × H)
33. C3×D4C23semidirect
38. D12C23semidirect
41. C3×C8C23semidirect
42. C3⋊C8C23semidirect
48. C2×D4C2×D3semidirect
52. D8C2×D3direct (N × H)
55. C2×C8C2×D3semidirect
62. C2×D3D8direct (N × H)
76. D4C22×D3semidirect
82. C8C22×D3semidirect
84. C2×C3C2×D8semidirect
87. D3C2×D8direct (N × H)
99. C3C22×D8semidirect
103. C2D3×D8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×D42
C2×C3×D82
C2×#2132
D3×D82
C2×D242
C2×D3×C82
C22×D83