Finite Group Databasebeta

← C23×C42×D43 #26003145

Subgroups — C23×C42×D43 #26003145

Order 11008.

24030 conjugacy classes of subgroups; only the 13515 normal subgroups are shown.

normal subgroups only

This group has 24030 conjugacy classes of subgroups — too many to draw. Only its 13515 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
1C24×C4×D43C213yesmaximal
2C23×C4×Dic43C213yesmaximal, complemented
3C22×C42×D43C2156yesmaximal, direct product factor
4C23×C42×C43C211yesmaximal, characteristic, complemented
5C25×D43C2211yescharacteristic
6C24×Dic43C2213yes—
7C23×C4×D43C4196yesdirect product factor
8C23×C4×D43C22184yes—
9C22×C4×Dic43C22184yescomplemented
10C2×C42×D43C221448yesdirect product factor
11C24×C4×C43C2213yes—
12C22×C42×C43C22128yescomplemented
13C24×D43C2×C4148yes—
14C24×D43C23114yes—
15C23×Dic43C2×C4148yescomplemented
16C23×Dic43C23142yes—
17C22×C4×D43C2×C411344yesdirect product factor
18C22×C4×D43C231336yes—
19C2×C4×Dic43C231336yescomplemented
20C42×D43C231512yesdirect product factor
21C25×C43C2311yescharacteristic
22C23×C4×C43C2×C4148yescomplemented
23C23×C4×C43C23142yes—
24C2×C42×C43C231112yescomplemented
25C24×C43C22×C4124yes—
26C24×C43C2417yes—
27C23×D43C421256yesdirect product factor
28C23×D43C22×C41336yes—
29C23×D43C24128yes—
30C22×C4×C43C22×C41336yescomplemented
31C22×C4×C43C24184yes—
32C22×Dic43C22×C41336yescomplemented
33C22×Dic43C24184yes—
34C2×C4×D43C22×C412688yesdirect product factor
35C2×C4×D43C241192yes—
36C42×C43C24164yescomplemented
37C4×Dic43C241192yescomplemented
38C23×C43C2×C42164yescomplemented
39C23×C43C23×C4184yes—
40C23×C43C2517yes—
41C22×D43C2×C421896yesdirect product factor
42C22×D43C23×C41336yes—
43C22×D43C2518yes—
44C2×C4×C43C23×C41336yescomplemented
45C2×C4×C43C25124yes—
46C2×Dic43C23×C41336yescomplemented
47C2×Dic43C25124yes—
48C4×D43C23×C41768yesdirect product factor
49C24×C42—431nomaximal, Sylow
50C22×C43C22×C421112yescomplemented
51C22×C43C24×C4142yes—
52C22×C43C2611yescharacteristic
53C2×D43C22×C421448yesdirect product factor
54C2×D43C24×C4148yes—
55C4×C43C24×C4148yescomplemented
56Dic43C24×C4148yescomplemented
57C25×C4—433no—
58C23×C42—4356no—
59C23×C42—433no—
60C23×C42D4311yescharacteristic, direct product factor
61C2×C43C23×C42128yescomplemented
62C2×C43C25×C413yes—
63D43C23×C42132yesdirect product factor
64C26—431no—
65C24×C4—433no—
66C24×C4—4384no—
67C24×C4—4396no—
68C24×C4C2×D4313yes—
69C22×C42—4384no—
70C22×C42—43448no—
71C22×C42C2×D43128yesdirect product factor
72C43C24×C4211yescharacteristic, complemented, Sylow
73C25—4348no—
74C25—4314no—
75C25C22×D4311yescharacteristic
76C23×C4—4348no—
77C23×C4—4342no—
78C23×C4—431344no—
79C23×C4—43336no—
80C23×C4C4×D43148yesdirect product factor
81C23×C4C22×D43142yes—
82C2×C42—43336no—
83C2×C42—43512no—
84C2×C42C22×D431112yesdirect product factor
85C24—43256no—
86C24—43336no—
87C24—4328no—
88C24C2×C4×D43124yes—
89C24C23×D4317yes—
90C22×C4—43336no—
91C22×C4—4384no—
92C22×C4—432688no—
93C22×C4—43192no—
94C22×C4C2×C4×D431336yesdirect product factor
95C22×C4C23×D43184yes—
96C42—43192no—
97C42C23×D43164yesdirect product factor
98C23—43896no—
99C23—43336no—
100C23—438no—
101C23C42×D43164yesdirect product factor
102C23C22×C4×D43184yes—
103C23C24×D4317yes—
104C2×C4—43336no—
105C2×C4—4324no—
106C2×C4—43768no—
107C2×C4C22×C4×D431336yesdirect product factor
108C2×C4C24×D43124yes—
109C22—4348no—
110C22—43448no—
111C22C2×C42×D431112yesdirect product factor
112C22C23×C4×D43142yes—
113C22C25×D4311yescharacteristic
114C4—4348no—
115C4C23×C4×D43148yesdirect product factor
116C2—4332no—
117C2C22×C42×D43128yesdirect product factor
118C2C24×C4×D4313yes—
subgroupG/H
center, hypercenterC23×C42D43
commutator, hypocenterC43C24×C42
FrattiniC22C25×D43
FittingC23×C42×C43C2
socleC25×C43C23
prime radicalC25×D43C22
cosocleC22×C43C26
LCSG ▷ C43
UCSC1 ◁ C23×C42

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic43C2semidirect
3. C22×C42×D43C2direct (N × H)
4. C23×C42×C43C2semidirect
7. C23×C4×D43C4direct (N × H)
9. C22×C4×Dic43C22semidirect
10. C2×C42×D43C22direct (N × H)
12. C22×C42×C43C22semidirect
15. C23×Dic43C2×C4semidirect
17. C22×C4×D43C2×C4direct (N × H)
19. C2×C4×Dic43C23semidirect
20. C42×D43C23direct (N × H)
22. C23×C4×C43C2×C4semidirect
24. C2×C42×C43C23semidirect
27. C23×D43C42direct (N × H)
30. C22×C4×C43C22×C4semidirect
32. C22×Dic43C22×C4semidirect
34. C2×C4×D43C22×C4direct (N × H)
36. C42×C43C24semidirect
37. C4×Dic43C24semidirect
38. C23×C43C2×C42semidirect
41. C22×D43C2×C42direct (N × H)
44. C2×C4×C43C23×C4semidirect
46. C2×Dic43C23×C4semidirect
48. C4×D43C23×C4direct (N × H)
50. C22×C43C22×C42semidirect
53. C2×D43C22×C42direct (N × H)
55. C4×C43C24×C4semidirect
56. Dic43C24×C4semidirect
60. C23×C42D43direct (N × H)
61. C2×C43C23×C42semidirect
63. D43C23×C42direct (N × H)
71. C22×C42C2×D43direct (N × H)
72. C43C24×C42semidirect
80. C23×C4C4×D43direct (N × H)
84. C2×C42C22×D43direct (N × H)
94. C22×C4C2×C4×D43direct (N × H)
97. C42C23×D43direct (N × H)
101. C23C42×D43direct (N × H)
107. C2×C4C22×C4×D43direct (N × H)
111. C22C2×C42×D43direct (N × H)
115. C4C23×C4×D43direct (N × H)
117. C2C22×C42×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D432
C23×C4×Dic432
C22×C42×D432
C23×C42×C432
C24×C4243