Finite Group Databasebeta

← C23×C42×D47 #27122826

Subgroups — C23×C42×D47 #27122826

Order 12032.

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×D47C213yesmaximal
2C23×C4×Dic47C213yesmaximal, complemented
3C22×C42×D47C2156yesmaximal, direct product factor
4C23×C42×C47C211yesmaximal, characteristic, complemented
5C25×D47C2211yescharacteristic
6C24×Dic47C2213yes—
7C23×C4×D47C4196yesdirect product factor
8C23×C4×D47C22184yes—
9C22×C4×Dic47C22184yescomplemented
10C2×C42×D47C221448yesdirect product factor
11C24×C4×C47C2213yes—
12C22×C42×C47C22128yescomplemented
13C24×D47C2×C4148yes—
14C24×D47C23114yes—
15C23×Dic47C2×C4148yescomplemented
16C23×Dic47C23142yes—
17C22×C4×D47C2×C411344yesdirect product factor
18C22×C4×D47C231336yes—
19C2×C4×Dic47C231336yescomplemented
20C42×D47C231512yesdirect product factor
21C25×C47C2311yescharacteristic
22C23×C4×C47C2×C4148yescomplemented
23C23×C4×C47C23142yes—
24C2×C42×C47C231112yescomplemented
25C24×C47C22×C4124yes—
26C24×C47C2417yes—
27C23×D47C421256yesdirect product factor
28C23×D47C22×C41336yes—
29C23×D47C24128yes—
30C22×C4×C47C22×C41336yescomplemented
31C22×C4×C47C24184yes—
32C22×Dic47C22×C41336yescomplemented
33C22×Dic47C24184yes—
34C2×C4×D47C22×C412688yesdirect product factor
35C2×C4×D47C241192yes—
36C42×C47C24164yescomplemented
37C4×Dic47C241192yescomplemented
38C23×C47C2×C42164yescomplemented
39C23×C47C23×C4184yes—
40C23×C47C2517yes—
41C22×D47C2×C421896yesdirect product factor
42C22×D47C23×C41336yes—
43C22×D47C2518yes—
44C2×C4×C47C23×C41336yescomplemented
45C2×C4×C47C25124yes—
46C2×Dic47C23×C41336yescomplemented
47C2×Dic47C25124yes—
48C4×D47C23×C41768yesdirect product factor
49C24×C42—471nomaximal, Sylow
50C22×C47C22×C421112yescomplemented
51C22×C47C24×C4142yes—
52C22×C47C2611yescharacteristic
53C2×D47C22×C421448yesdirect product factor
54C2×D47C24×C4148yes—
55C4×C47C24×C4148yescomplemented
56Dic47C24×C4148yescomplemented
57C25×C4—473no—
58C23×C42—4756no—
59C23×C42—473no—
60C23×C42D4711yescharacteristic, direct product factor
61C2×C47C23×C42128yescomplemented
62C2×C47C25×C413yes—
63D47C23×C42132yesdirect product factor
64C26—471no—
65C24×C4—473no—
66C24×C4—4796no—
67C24×C4—4784no—
68C24×C4C2×D4713yes—
69C22×C42—4784no—
70C22×C42—47448no—
71C22×C42C2×D47128yesdirect product factor
72C47C24×C4211yescharacteristic, complemented, Sylow
73C25—4748no—
74C25—4714no—
75C25C22×D4711yescharacteristic
76C23×C4—4748no—
77C23×C4—4742no—
78C23×C4—471344no—
79C23×C4—47336no—
80C23×C4C4×D47148yesdirect product factor
81C23×C4C22×D47142yes—
82C2×C42—47336no—
83C2×C42—47512no—
84C2×C42C22×D471112yesdirect product factor
85C24—47256no—
86C24—47336no—
87C24—4728no—
88C24C2×C4×D47124yes—
89C24C23×D4717yes—
90C22×C4—47336no—
91C22×C4—4784no—
92C22×C4—472688no—
93C22×C4—47192no—
94C22×C4C2×C4×D471336yesdirect product factor
95C22×C4C23×D47184yes—
96C42—47192no—
97C42C23×D47164yesdirect product factor
98C23—47896no—
99C23—47336no—
100C23—478no—
101C23C42×D47164yesdirect product factor
102C23C22×C4×D47184yes—
103C23C24×D4717yes—
104C2×C4—47336no—
105C2×C4—4724no—
106C2×C4—47768no—
107C2×C4C22×C4×D471336yesdirect product factor
108C2×C4C24×D47124yes—
109C22—47448no—
110C22—4748no—
111C22C2×C42×D471112yesdirect product factor
112C22C23×C4×D47142yes—
113C22C25×D4711yescharacteristic
114C4—4748no—
115C4C23×C4×D47148yesdirect product factor
116C2—4732no—
117C2C22×C42×D47128yesdirect product factor
118C2C24×C4×D4713yes—
subgroupG/H
center, hypercenterC23×C42D47
commutator, hypocenterC47C24×C42
FrattiniC22C25×D47
FittingC23×C42×C47C2
socleC25×C47C23
prime radicalC25×D47C22
cosocleC22×C47C26
LCSG ▷ C47
UCSC1 ◁ C23×C42

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic47C2semidirect
3. C22×C42×D47C2direct (N × H)
4. C23×C42×C47C2semidirect
7. C23×C4×D47C4direct (N × H)
9. C22×C4×Dic47C22semidirect
10. C2×C42×D47C22direct (N × H)
12. C22×C42×C47C22semidirect
15. C23×Dic47C2×C4semidirect
17. C22×C4×D47C2×C4direct (N × H)
19. C2×C4×Dic47C23semidirect
20. C42×D47C23direct (N × H)
22. C23×C4×C47C2×C4semidirect
24. C2×C42×C47C23semidirect
27. C23×D47C42direct (N × H)
30. C22×C4×C47C22×C4semidirect
32. C22×Dic47C22×C4semidirect
34. C2×C4×D47C22×C4direct (N × H)
36. C42×C47C24semidirect
37. C4×Dic47C24semidirect
38. C23×C47C2×C42semidirect
41. C22×D47C2×C42direct (N × H)
44. C2×C4×C47C23×C4semidirect
46. C2×Dic47C23×C4semidirect
48. C4×D47C23×C4direct (N × H)
50. C22×C47C22×C42semidirect
53. C2×D47C22×C42direct (N × H)
55. C4×C47C24×C4semidirect
56. Dic47C24×C4semidirect
60. C23×C42D47direct (N × H)
61. C2×C47C23×C42semidirect
63. D47C23×C42direct (N × H)
71. C22×C42C2×D47direct (N × H)
72. C47C24×C42semidirect
80. C23×C4C4×D47direct (N × H)
84. C2×C42C22×D47direct (N × H)
94. C22×C4C2×C4×D47direct (N × H)
97. C42C23×D47direct (N × H)
101. C23C42×D47direct (N × H)
107. C2×C4C22×C4×D47direct (N × H)
111. C22C2×C42×D47direct (N × H)
115. C4C23×C4×D47direct (N × H)
117. C2C22×C42×D47direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D472
C23×C4×Dic472
C22×C42×D472
C23×C42×C472
C24×C4247