Finite Group Databasebeta

← C3×D3×C42⋊C3 #11723052

Subgroups — C3×D3×C42⋊C3 #11723052

Order 864.

164 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 30 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
1C32×C42⋊C3C211yesmaximal, characteristic, complemented
2C3×C42×D3C311yesmaximal, characteristic, complemented
3C2×C3×C42⋊C3—31nomaximal
4D3×C42⋊C3C313yesmaximal, direct product factor
5C3×D3×A4—41nomaximal
6C2×C3×C4×D3—31no—
7C32×C42C2×C311yescharacteristic, complemented
8C3×C4×Dic3—31no—
9C3×C42⋊C3—21no—
10C3×C42⋊C3—23no—
11C3×C42⋊C3D311yescharacteristic, direct product factor
12C3×C42⋊C3C2×C313yescomplemented
13C32×A4—41no—
14C2×C3×C42—31no—
15C42×D3C3211yescharacteristic, complemented
16C2×C42⋊C3—33no—
17C22×C3×D3A411yescharacteristic
18C2×C3×A4—121no—
19D3×A4—43no—
20C2×C32×C4—31no—
21C2×C3×Dic3—31no—
22C3×C4×D3—32no—
23C3×C4×D3—32no—
24C32×D3—161no—
25C22×C3×C4—91no—
26C2×C4×D3—31no—
27C3×C42—21no—
28C3×C42—91no—
29C3×C42C3×D311yescharacteristic, complemented
30C3×C42C2×C3211yescharacteristic, complemented
31C4×Dic3—31no—
32C42⋊C3—23no—
33C42⋊C3C3×D313yesdirect product factor
34C22×C32C2×A411yescharacteristic
35C2×C3×D3—31no—
36C2×C3×D3—31no—
37C3×A4—41no—
38C3×A4—43no—
39C3×A4—83no—
40C3×A4—81no—
41C32×C4—32no—
42C3×Dic3—32no—
43C2×C42—31noSylow
44C33—161noSylow
45C23×C3—31no—
46C22×D3C3×A411yescharacteristic
47C2×A4—123no—
48C2×C3×C4—31no—
49C2×C3×C4—31no—
50C2×C3×C4—61no—
51C2×C3×C4—92no—
52C2×C3×C4—92no—
53C2×C3×C4—91no—
54C2×Dic3—31no—
55C4×D3—32no—
56C4×D3—32no—
57C2×C32—31no—
58C2×C32—481no—
59C3×D3—31no—
60C3×D3—163no—
61C3×D3C42⋊C311yescharacteristic, direct product factor
62C22×C4—91no—
63C42—91no—
64C42C32×D311yescharacteristic, complemented
65C22×C3—21no—
66C22×C3—91no—
67C22×C3—91no—
68C22×C3D3×A411yescharacteristic
69C22×C3C2×C3×A411yescharacteristic
70C2×D3—31no—
71C2×D3—31no—
72A4—43no—
73A4—83no—
74C3×C4—32no—
75C3×C4—32no—
76C3×C4—62no—
77C3×C4—92no—
78Dic3—32no—
79C32—161no—
80C32—163no—
81C32—323no—
82C32—321no—
83C32C2×C42⋊C311yescharacteristic, complemented
84C23—31no—
85C2×C4—31no—
86C2×C4—92no—
87C2×C4—92no—
88C2×C4—91no—
89C2×C3—31no—
90C2×C3—31no—
91C2×C3—31no—
92C2×C3—61no—
93C2×C3—91no—
94C2×C3—483no—
95D3—31no—
96D3C3×C42⋊C311yescharacteristic, direct product factor
97C22—91no—
98C22—91no—
99C22C3×D3×A411yescharacteristic
100C4—32no—
101C4—92no—
102C3—21no—
103C3—163no—
104C3—323no—
105C3D3×C42⋊C311yescharacteristic, direct product factor
106C3C2×C3×C42⋊C311yescharacteristic, complemented
107C2—31no—
108C2—31no—
109C2—91no—
subgroupG/H
center, hypercenterC3D3×C42⋊C3
commutator, cosocle, hypocenterC3×C42C2×C32
FrattiniC22C3×D3×A4
FittingC32×C42C2×C3
socleC22×C32C2×A4
LCSG ▷ C3×C42
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C42⋊C3C2semidirect
2. C3×C42×D3C3semidirect
4. D3×C42⋊C3C3direct (N × H)
7. C32×C42C2×C3semidirect
11. C3×C42⋊C3D3direct (N × H)
12. C3×C42⋊C3C2×C3semidirect
15. C42×D3C32semidirect
29. C3×C42C3×D3semidirect
30. C3×C42C2×C32semidirect
33. C42⋊C3C3×D3direct (N × H)
61. C3×D3C42⋊C3direct (N × H)
64. C42C32×D3semidirect
83. C32C2×C42⋊C3semidirect
96. D3C3×C42⋊C3direct (N × H)
105. C3D3×C42⋊C3direct (N × H)
106. C3C2×C3×C42⋊C3semidirect

Maximal subgroups

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

subgroupindex
C32×C42⋊C32
C3×C42×D33
C2×C3×C42⋊C33
D3×C42⋊C33
C3×D3×A44