Finite Group Databasebeta

← C24×C3×Dic9 #13164963

Subgroups — C24×C3×Dic9 #13164963

Order 1728.

4834 conjugacy classes of subgroups; only the 2858 normal subgroups are shown.

normal subgroups only

This group has 4834 conjugacy classes of subgroups — too many to draw. Only its 2858 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
1C25×C3×C9C211yesmaximal, characteristic
2C23×C3×Dic9C2130yesmaximal, direct product factor
3C24×C3×Dic3—31nomaximal
4C24×Dic9C311yesmaximal, characteristic, direct product factor
5C24×C3×C9C4116yescomplemented
6C24×C3×C9C22115yes—
7C22×C3×Dic9C221140yesdirect product factor
8C25×C32D311yescharacteristic
9C23×C3×Dic3—330no—
10C25×C9—21no—
11C25×C9C2×C311yescharacteristic
12C23×Dic9C2×C3130yesdirect product factor
13C23×C3×C9C2×C41120yescomplemented
14C23×C3×C9C23135yes—
15C2×C3×Dic9C231120yesdirect product factor
16C24×C3×C4—91no—
17C24×Dic3—31no—
18C24×C32Dic3116yes—
19C24×C32C2×D3115yes—
20C22×C3×Dic3—3140no—
21C24×C9—216no—
22C24×C9—215no—
23C24×C9C3×C4116yescomplemented
24C24×C9C22×C3115yes—
25C22×Dic9C22×C31140yesdirect product factor
26C22×C3×C9C22×C41140yescomplemented
27C22×C3×C9C24115yes—
28C3×Dic9C24116yesdirect product factor
29C25×C3—21no—
30C25×C3D911yescharacteristic
31C25×C3C3×D311yescharacteristic
32C23×C3×C4—930no—
33C23×Dic3—330no—
34C23×C32C2×Dic31120yes—
35C23×C32C22×D3135yes—
36C2×C3×Dic3—3120no—
37C23×C9—2120no—
38C23×C9—235no—
39C23×C9C2×C3×C41120yescomplemented
40C23×C9C23×C3135yes—
41C2×Dic9C23×C31120yesdirect product factor
42C24×C4—91noSylow
43C2×C3×C9C23×C4130yescomplemented
44C2×C3×C9C2511yescharacteristic
45C24×C3—216no—
46C24×C3—215no—
47C24×C3Dic9116yesdirect product factor
48C24×C3C2×D9115yes—
49C24×C3C3×Dic3116yes—
50C24×C3C2×C3×D3115yes—
51C22×C3×C4—9140no—
52C22×Dic3—3140no—
53C22×C32C22×Dic31140yes—
54C22×C32C23×D3115yes—
55C3×Dic3—316no—
56C22×C9—215no—
57C22×C9—2140no—
58C22×C9C22×C3×C41140yescomplemented
59C22×C9C24×C3115yes—
60Dic9C24×C3116yesdirect product factor
61C25C3×D911yescharacteristic
62C23×C4—930no—
63C3×C9C24×C411yescharacteristic, complemented, Sylow
64C23×C3—2120no—
65C23×C3—235no—
66C23×C3C2×Dic91120yesdirect product factor
67C23×C3C22×D9135yes—
68C23×C3C2×C3×Dic31120yes—
69C23×C3C22×C3×D3135yes—
70C2×C3×C4—9120no—
71C2×Dic3—3120no—
72C2×C32C23×Dic3130yes—
73C2×C32C24×D311yescharacteristic
74C2×C9—230no—
75C2×C9—21no—
76C2×C9C23×C3×C4130yescomplemented
77C2×C9C25×C311yescharacteristic
78C24C3×Dic9116yesdirect product factor
79C24C2×C3×D9115yes—
80C22×C4—9140no—
81C22×C3—215no—
82C22×C3—2140no—
83C22×C3C22×Dic91140yesdirect product factor
84C22×C3C23×D9115yes—
85C22×C3C22×C3×Dic31140yes—
86C22×C3C23×C3×D3115yes—
87C3×C4—916no—
88Dic3—316no—
89C32C24×Dic311yescharacteristic
90C9—21no—
91C9C24×C3×C411yescharacteristic, complemented
92C23C2×C3×Dic91120yesdirect product factor
93C23C22×C3×D9135yes—
94C2×C4—9120no—
95C2×C3—21no—
96C2×C3—230no—
97C2×C3C23×Dic9130yesdirect product factor
98C2×C3C24×D911yescharacteristic
99C2×C3C23×C3×Dic3130yes—
100C2×C3C24×C3×D311yescharacteristic
101C22C22×C3×Dic91140yesdirect product factor
102C22C23×C3×D9115yes—
103C4—916no—
104C3—21no—
105C3C24×Dic911yescharacteristic, direct product factor
106C3C24×C3×Dic311yescharacteristic
107C2C23×C3×Dic9130yesdirect product factor
108C2C24×C3×D911yescharacteristic
subgroupG/H
center, hypercenterC25×C3D9
commutator, hypocenterC9C24×C3×C4
FrattiniC2×C3C24×C3×D3
FittingC25×C3×C9C2
socle, prime radicalC25×C32D3
cosocleC2×C9C25×C3
LCSG ▷ C9
UCSC1 ◁ C25×C3

Complements

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

NH ≅ G/Ntype
2. C23×C3×Dic9C2direct (N × H)
4. C24×Dic9C3direct (N × H)
5. C24×C3×C9C4semidirect
7. C22×C3×Dic9C22direct (N × H)
12. C23×Dic9C2×C3direct (N × H)
13. C23×C3×C9C2×C4semidirect
15. C2×C3×Dic9C23direct (N × H)
23. C24×C9C3×C4semidirect
25. C22×Dic9C22×C3direct (N × H)
26. C22×C3×C9C22×C4semidirect
28. C3×Dic9C24direct (N × H)
39. C23×C9C2×C3×C4semidirect
41. C2×Dic9C23×C3direct (N × H)
43. C2×C3×C9C23×C4semidirect
47. C24×C3Dic9direct (N × H)
58. C22×C9C22×C3×C4semidirect
60. Dic9C24×C3direct (N × H)
63. C3×C9C24×C4semidirect
66. C23×C3C2×Dic9direct (N × H)
76. C2×C9C23×C3×C4semidirect
78. C24C3×Dic9direct (N × H)
83. C22×C3C22×Dic9direct (N × H)
91. C9C24×C3×C4semidirect
92. C23C2×C3×Dic9direct (N × H)
97. C2×C3C23×Dic9direct (N × H)
101. C22C22×C3×Dic9direct (N × H)
105. C3C24×Dic9direct (N × H)
107. C2C23×C3×Dic9direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C3×C92
C23×C3×Dic92
C24×C3×Dic33
C24×Dic93