Finite Group Databasebeta

← C24×C3×C3⋊C8 #11918423

Subgroups — C24×C3×C3⋊C8 #11918423

Order 1152.

4633 conjugacy classes of subgroups; only the 3338 normal subgroups are shown.

normal subgroups only

This group has 4633 conjugacy classes of subgroups — too many to draw. Only its 3338 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×C32×C4C211yesmaximal, characteristic
2C23×C3×C3⋊C8C2130yesmaximal, direct product factor
3C24×C3×C8—31nomaximal
4C24×C3⋊C8C311yesmaximal, characteristic, direct product factor
5C25×C32C411yescharacteristic
6C23×C32×C4C4115yes—
7C23×C32×C4C22115yes—
8C22×C3×C3⋊C8C221140yesdirect product factor
9C24×C3×C4—21no—
10C24×C3×C4D311yescharacteristic
11C24×C3×C4C2×C311yescharacteristic
12C23×C3×C8—330no—
13C23×C3⋊C8C2×C3130yesdirect product factor
14C24×C32C8116yescomplemented
15C24×C32C2×C4115yes—
16C22×C32×C4C2×C41105yes—
17C22×C32×C4C23135yes—
18C2×C3×C3⋊C8C231120yesdirect product factor
19C24×C8—31noSylow
20C25×C3—21no—
21C25×C3Dic311yescharacteristic
22C25×C3C3×C411yescharacteristic
23C23×C3×C4—215no—
24C23×C3×C4—215no—
25C23×C3×C4Dic3115yes—
26C23×C3×C4C3×C4115yes—
27C23×C3×C4C2×D3115yes—
28C23×C3×C4C22×C3115yes—
29C22×C3×C8—3140no—
30C22×C3⋊C8C22×C31140yesdirect product factor
31C23×C32C2×C81120yescomplemented
32C23×C32C22×C4135yes—
33C2×C32×C4C22×C41105yes—
34C2×C32×C4C24115yes—
35C3×C3⋊C8C24116yesdirect product factor
36C24×C4C3×D311yescharacteristic
37C23×C8—330no—
38C24×C3—216no—
39C24×C3—215no—
40C24×C3C3⋊C8116yesdirect product factor
41C24×C3C3×C8116yescomplemented
42C24×C3C2×Dic3115yes—
43C24×C3C2×C3×C4115yes—
44C22×C3×C4—2105no—
45C22×C3×C4—235no—
46C22×C3×C4C2×Dic31105yes—
47C22×C3×C4C2×C3×C41105yes—
48C22×C3×C4C22×D3135yes—
49C22×C3×C4C23×C3135yes—
50C2×C3×C8—3120no—
51C2×C3⋊C8C23×C31120yesdirect product factor
52C22×C32C22×C81140yescomplemented
53C22×C32C23×C4115yes—
54C32×C4C23×C4115yes—
55C32×C4C2511yescharacteristic
56C25C3×Dic311yescharacteristic
57C23×C4C3×Dic3115yes—
58C23×C4C2×C3×D3115yes—
59C22×C8—3140no—
60C23×C3—2120no—
61C23×C3—235no—
62C23×C3C2×C3⋊C81120yesdirect product factor
63C23×C3C2×C3×C81120yescomplemented
64C23×C3C22×Dic3135yes—
65C23×C3C22×C3×C4135yes—
66C2×C3×C4—215no—
67C2×C3×C4—2105no—
68C2×C3×C4C22×Dic31105yes—
69C2×C3×C4C22×C3×C41105yes—
70C2×C3×C4C23×D3115yes—
71C2×C3×C4C24×C3115yes—
72C3×C8—316no—
73C3⋊C8C24×C3116yesdirect product factor
74C2×C32C23×C8130yescomplemented
75C2×C32C24×C411yescharacteristic
76C24C3×C3⋊C8116yesdirect product factor
77C24C2×C3×Dic3115yes—
78C22×C4C2×C3×Dic31105yes—
79C22×C4C22×C3×D3135yes—
80C2×C8—3120no—
81C22×C3—2140no—
82C22×C3—215no—
83C22×C3C22×C3⋊C81140yesdirect product factor
84C22×C3C22×C3×C81140yescomplemented
85C22×C3C23×Dic3115yes—
86C22×C3C23×C3×C4115yes—
87C3×C4—215no—
88C3×C4—21no—
89C3×C4C23×Dic3115yes—
90C3×C4C23×C3×C4115yes—
91C3×C4C24×D311yescharacteristic
92C3×C4C25×C311yescharacteristic
93C32C24×C811yescharacteristic, complemented, Sylow
94C23C2×C3×C3⋊C81120yesdirect product factor
95C23C22×C3×Dic3135yes—
96C2×C4C22×C3×Dic31105yes—
97C2×C4C23×C3×D3115yes—
98C8—316no—
99C2×C3—230no—
100C2×C3—21no—
101C2×C3C23×C3⋊C8130yesdirect product factor
102C2×C3C23×C3×C8130yescomplemented
103C2×C3C24×Dic311yescharacteristic
104C2×C3C24×C3×C411yescharacteristic
105C22C22×C3×C3⋊C81140yesdirect product factor
106C22C23×C3×Dic3115yes—
107C4C23×C3×Dic3115yes—
108C4C24×C3×D311yescharacteristic
109C3—21no—
110C3C24×C3⋊C811yescharacteristic, direct product factor
111C3C24×C3×C811yescharacteristic, complemented
112C2C23×C3×C3⋊C8130yesdirect product factor
113C2C24×C3×Dic311yescharacteristic
subgroupG/H
center, hypercenterC24×C3×C4D3
commutator, hypocenterC3C24×C3×C8
FrattiniC4C24×C3×D3
FittingC24×C32×C4C2
socle, prime radicalC25×C32C4
cosocleC3×C4C25×C3
LCSG ▷ C3
UCSC1 ◁ C24×C3×C4

Complements

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

NH ≅ G/Ntype
2. C23×C3×C3⋊C8C2direct (N × H)
4. C24×C3⋊C8C3direct (N × H)
8. C22×C3×C3⋊C8C22direct (N × H)
13. C23×C3⋊C8C2×C3direct (N × H)
14. C24×C32C8semidirect
18. C2×C3×C3⋊C8C23direct (N × H)
30. C22×C3⋊C8C22×C3direct (N × H)
31. C23×C32C2×C8semidirect
35. C3×C3⋊C8C24direct (N × H)
40. C24×C3C3⋊C8direct (N × H)
41. C24×C3C3×C8semidirect
51. C2×C3⋊C8C23×C3direct (N × H)
52. C22×C32C22×C8semidirect
62. C23×C3C2×C3⋊C8direct (N × H)
63. C23×C3C2×C3×C8semidirect
73. C3⋊C8C24×C3direct (N × H)
74. C2×C32C23×C8semidirect
76. C24C3×C3⋊C8direct (N × H)
83. C22×C3C22×C3⋊C8direct (N × H)
84. C22×C3C22×C3×C8semidirect
93. C32C24×C8semidirect
94. C23C2×C3×C3⋊C8direct (N × H)
101. C2×C3C23×C3⋊C8direct (N × H)
102. C2×C3C23×C3×C8semidirect
105. C22C22×C3×C3⋊C8direct (N × H)
110. C3C24×C3⋊C8direct (N × H)
111. C3C24×C3×C8semidirect
112. C2C23×C3×C3⋊C8direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C32×C42
C23×C3×C3⋊C82
C24×C3×C83
C24×C3⋊C83