Finite Group Databasebeta

← C3×#64225 #11724280

Subgroups — C3×#64225 #11724280

Order 864.

292 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C3×#3802C212yesmaximal, complemented
2C3×#3787C211yesmaximal, characteristic, complemented
3C3×#3774C214yesmaximal, complemented
4#64225C311yesmaximal, characteristic, direct product factor
5C2×C3×D32—22no—
6C3×C4×C3⋊D3C2211yescharacteristic
7C32×D12—22no—
8C3×#625C2214yescomplemented
9C3×#622C2212yescomplemented
10C3×D3×D4—62no—
11#3802C2×C312yescomplemented
12#3787C2×C311yescharacteristic, complemented
13#3774C2×C314yescomplemented
14C2×C3×C3⋊D3D411yescharacteristic
15C2×C32×D3—24no—
16C3×D32—44no—
17C33×C4D411yescharacteristic
18C3×C3⋊Dic3C2311yescharacteristic
19C2×C3×D8—91nomaximal
20C22×C3×D3—64no—
21C2×D32—22no—
22C32×D4—62no—
23C4×C3⋊D3C22×C311yescharacteristic
24C3×#67—64no—
25C3×D12—22no—
26C3×D12—22no—
27C3×D12—42no—
28C3×C4×D3—62no—
29#625C22×C314yescomplemented
30#622C22×C312yescomplemented
31C2×C33C2×D411yescharacteristic
32C3×C3⋊D3D812yescomplemented
33C32×D3—44no—
34C2×C3×D4—92no—
35D3×D4—62no—
36C3×D8—94no—
37C2×C3×C8—91no—
38C22×C32—64no—
39C2×C3⋊D3C3×D411yescharacteristic
40C2×C3×D3—24no—
41C2×C3×D3—24no—
42C2×C3×D3—44no—
43C2×C3×D3—62no—
44C2×C3×D3—128no—
45D32—44no—
46C32×C4—22no—
47C32×C4—42no—
48C32×C4C3×D411yescharacteristic
49C3⋊Dic3C23×C311yescharacteristic
50C3×Dic3—62no—
51C2×D8—91noSylow
52C33C2×D811yescharacteristic, complemented, Sylow
53C23×C3—182no—
54C22×D3—64no—
55C3×D4—62no—
56C3×D4—62no—
57C3×D4—94no—
58C3×D4—122no—
59C2×C3×C4—91no—
60#67—64no—
61D12—22no—
62C4×D3—62no—
63C3×C8—92no—
64C2×C32—22no—
65C2×C32—42no—
66C2×C32—124no—
67C2×C32C2×C3×D411yescharacteristic
68C3⋊D3C3×D812yescomplemented
69C3×D3—44no—
70C3×D3—44no—
71C3×D3—64no—
72C3×D3—84no—
73C2×D4—92no—
74D8—94no—
75C2×C8—91no—
76C22×C3—64no—
77C22×C3—64no—
78C22×C3—91no—
79C22×C3—124no—
80C22×C3—364no—
81C2×D3—24no—
82C2×D3—62no—
83C2×D3—128no—
84C3×C4—22no—
85C3×C4—42no—
86C3×C4—91no—
87C3×C4GO+(4,𝔽2)11yescharacteristic
88Dic3—62no—
89C32—22no—
90C32—42no—
91C32C2×C3×D811yescharacteristic, complemented
92C23—182no—
93D4—62no—
94D4—94no—
95C2×C4—91no—
96C8—92no—
97C2×C3—22no—
98C2×C3—42no—
99C2×C3—92no—
100C2×C3—124no—
101C2×C3—124no—
102C2×C3—244no—
103C2×C3C2×GO+(4,𝔽2)11yescharacteristic
104D3—44no—
105D3—64no—
106C22—64no—
107C22—91no—
108C22—364no—
109C4—91no—
110C4C3×GO+(4,𝔽2)11yescharacteristic
111C3—22no—
112C3—42no—
113C3#6422511yescharacteristic, direct product factor
114C2—92no—
115C2—124no—
116C2C2×C3×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC2×C3C2×GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C23×C3
FrattiniC2C2×C3×GO+(4,𝔽2)
FittingC33×C4D4
socleC2×C33C2×D4
hypercenterC3×C4GO+(4,𝔽2)
hypocenterC32C2×C3×D8
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×#3802C2semidirect
2. C3×#3787C2semidirect
3. C3×#3774C2semidirect
4. #64225C3direct (N × H)
8. C3×#625C22semidirect
9. C3×#622C22semidirect
11. #3802C2×C3semidirect
12. #3787C2×C3semidirect
13. #3774C2×C3semidirect
29. #625C22×C3semidirect
30. #622C22×C3semidirect
32. C3×C3⋊D3D8semidirect
52. C33C2×D8semidirect
68. C3⋊D3C3×D8semidirect
91. C32C2×C3×D8semidirect
113. C3#64225direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#38022
C3×#37872
C3×#37742
#642253
C2×C3×D89