Finite Group Databasebeta

← C3×C3⋊(#127⋊C3) #11723050

Subgroups — C3×C3⋊(#127⋊C3) #11723050

Order 864.

164 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 28 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×#874C311yesmaximal, characteristic, complemented
3C3×#127⋊C3—31nomaximal
4C3⋊(#127⋊C3)C313yesmaximal, direct product factor
5C3×D3×A4—41nomaximal
6C2×C3×D12—31no—
7C2×C3×D12—31no—
8C32×C42C2×C311yescharacteristic, complemented
9C3×C42⋊C3—21no—
10C3×C42⋊C3—23no—
11C3×C42⋊C3D311yescharacteristic, complemented
12C3×C42⋊C3C2×C313yescomplemented
13C32×A4—41no—
14C3×#127—31no—
15#874C3211yescharacteristic, complemented
16#127⋊C3—33no—
17C22×C3×D3—31no—
18C22×C3×D3A411yescharacteristic
19C2×C3×A4—121no—
20D3×A4—43no—
21C2×C32×C4—31no—
22C3×D12—62no—
23C3×D12—62no—
24C32×D3—161no—
25C2×C3×D4—91no—
26C2×C3×D4—91no—
27C2×D12—31no—
28C2×D12—31no—
29C3×C42—21no—
30C3×C42C3×D311yescharacteristic, complemented
31C3×C42C2×C3211yescharacteristic, complemented
32C42⋊C3—23no—
33C42⋊C3C3×D313yescomplemented
34C22×C32C2×A411yescharacteristic
35C2×C3×D3—61no—
36C2×C3×D3—61no—
37C2×C3×D3—62no—
38C3×A4—41no—
39C3×A4—43no—
40C3×A4—83no—
41C3×A4—81no—
42C32×C4—32no—
43#127—31noSylow
44C33—161noSylow
45C23×C3—31no—
46C23×C3—91no—
47C22×D3—31no—
48C22×D3C3×A411yescharacteristic
49C2×A4—123no—
50C3×D4—182no—
51C3×D4—182no—
52C2×C3×C4—31no—
53C2×C3×C4—31no—
54C2×C3×C4—61no—
55D12—62no—
56D12—62no—
57C2×C32—31no—
58C2×C32—481no—
59C3×D3—41no—
60C3×D3—121no—
61C3×D3—163no—
62C2×D4—91no—
63C2×D4—91no—
64C42C32×D311yescharacteristic, complemented
65C22×C3—21no—
66C22×C3—181no—
67C22×C3—181no—
68C22×C3—182no—
69C22×C3D3×A411yescharacteristic
70C22×C3C2×C3×A411yescharacteristic
71C2×D3—61no—
72C2×D3—61no—
73C2×D3—62no—
74A4—43no—
75A4—83no—
76C3×C4—32no—
77C3×C4—32no—
78C3×C4—62no—
79C32—161no—
80C32—163no—
81C32—323no—
82C32—321no—
83C32#127⋊C311yescharacteristic, complemented
84C23—31no—
85C23—91no—
86D4—182no—
87D4—182no—
88C2×C4—31no—
89C2×C3—31no—
90C2×C3—31no—
91C2×C3—61no—
92C2×C3—121no—
93C2×C3—361no—
94C2×C3—483no—
95D3—41no—
96D3—121no—
97C22—181no—
98C22—181no—
99C22—182no—
100C22C3×D3×A411yescharacteristic
101C4—32no—
102C3—21no—
103C3—163no—
104C3—323no—
105C3C3⋊(#127⋊C3)11yescharacteristic, direct product factor
106C3C3×#127⋊C311yescharacteristic, complemented
107C2—31no—
108C2—121no—
109C2—361no—
subgroupG/H
center, hypercenterC3C3⋊(#127⋊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×#874C3semidirect
4. C3⋊(#127⋊C3)C3direct (N × H)
8. C32×C42C2×C3semidirect
11. C3×C42⋊C3D3semidirect
12. C3×C42⋊C3C2×C3semidirect
15. #874C32semidirect
30. C3×C42C3×D3semidirect
31. C3×C42C2×C32semidirect
33. C42⋊C3C3×D3semidirect
64. C42C32×D3semidirect
83. C32#127⋊C3semidirect
105. C3C3⋊(#127⋊C3)direct (N × H)
106. C3C3×#127⋊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×#8743
C3×#127⋊C33
C3⋊(#127⋊C3)3
C3×D3×A44