Finite Group Databasebeta

← C3×#64223 #11724278

Subgroups — C3×#64223 #11724278

Order 864.

236 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 46 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×#3798C212yesmaximal, complemented
2C3×#3787C211yesmaximal, characteristic, complemented
3C3×#3776C211yesmaximal, characteristic, complemented
4C3×#3775C212yesmaximal, complemented
5C3×#3774C211yesmaximal, characteristic, complemented
6#64223C311yesmaximal, characteristic, direct product factor
7C3×C4×C3⋊D3C2211yescharacteristic
8C32×C4×D3—22no—
9C3×#627C2212yes—
10C3×#626—22no—
11C3×#625C2212yes—
12C3×#622C2211yescharacteristic
13C3×#622C2211yescharacteristic
14C3×#235—62no—
15#3798C2×C312yescomplemented
16#3787C2×C311yescharacteristic, complemented
17#3776C2×C311yescharacteristic, complemented
18#3775C2×C312yescomplemented
19#3774C2×C311yescharacteristic, complemented
20C2×C3×C3⋊D3D411yescharacteristic
21C2×C32×D3—22no—
22C33×C4D411yescharacteristic
23C3×C3⋊Dic3C2311yescharacteristic
24C32×Dic3—22no—
25C3×#135—91nomaximal
26C2×C32×C4—62no—
27C4×C3⋊D3C22×C311yescharacteristic
28C3×#67—62no—
29C3×#67—62no—
30C3×D12—62no—
31C3×C4×D3—22no—
32C3×C4×D3—22no—
33C3×C4×D3—42no—
34C3×C4×D3—62no—
35C3×Dic6—62no—
36#627C22×C312yes—
37#626—22no—
38#625C22×C312yes—
39#622C22×C311yescharacteristic
40#622C22×C311yescharacteristic
41C2×C33C2×D411yescharacteristic
42C3×C3⋊D3—21no—
43C32×D3—42no—
44C3×#41—92no—
45#235—62no—
46C3×Q16—91no—
47C3×SD16—92no—
48C3×D8—91no—
49C2×C3×C8—91no—
50C22×C32—62no—
51C2×C3⋊D3C3×D411yescharacteristic
52C2×C3×D3—22no—
53C2×C3×D3—22no—
54C2×C3×D3—42no—
55C2×C3×D3—62no—
56C32×C4—22no—
57C32×C4—42no—
58C32×C4—62no—
59C32×C4C3×D411yescharacteristic
60C3⋊Dic3C23×C311yescharacteristic
61C3×Dic3—22no—
62C3×Dic3—22no—
63C3×Dic3—42no—
64C3×Dic3—62no—
65#135—91noSylow
66C33#13511yescharacteristic, complemented, Sylow
67C3×Q8—92no—
68C3×D4—92no—
69C3×D4—182no—
70C2×C3×C4—62no—
71C2×C3×C4—62no—
72C2×C3×C4—91no—
73C2×C3×C4—122no—
74#67—62no—
75#67—62no—
76D12—62no—
77C4×D3—22no—
78C4×D3—62no—
79Dic6—62no—
80C3×C8—91no—
81C3×C8—91no—
82C2×C32—22no—
83C2×C32—42no—
84C2×C32—122no—
85C2×C32C2×C3×D411yescharacteristic
86C3⋊D3—21no—
87C3×D3—42no—
88C3×D3—44no—
89C3×D3—42no—
90C3×D3—122no—
91#41—92no—
92Q16—91no—
93SD16—92no—
94D8—91no—
95C2×C8—91no—
96C22×C3—62no—
97C22×C3—62no—
98C22×C3—91no—
99C22×C3—122no—
100C2×D3—22no—
101C2×D3—62no—
102C3×C4—22no—
103C3×C4—42no—
104C3×C4—62no—
105C3×C4—62no—
106C3×C4—91no—
107C3×C4—122no—
108C3×C4GO+(4,𝔽2)11yescharacteristic
109Dic3—22no—
110Dic3—62no—
111C32—22no—
112C32—42no—
113C32C3×#13511yescharacteristic, complemented
114Q8—92no—
115D4—92no—
116D4—182no—
117C2×C4—62no—
118C2×C4—91no—
119C8—91no—
120C8—91no—
121C2×C3—22no—
122C2×C3—42no—
123C2×C3—122no—
124C2×C3—124no—
125C2×C3—122no—
126C2×C3—181no—
127C2×C3C2×GO+(4,𝔽2)11yescharacteristic
128D3—42no—
129D3—122no—
130C22—62no—
131C22—91no—
132C4—62no—
133C4—91no—
134C4C3×GO+(4,𝔽2)11yescharacteristic
135C3—22no—
136C3—42no—
137C3#6422311yescharacteristic, direct product factor
138C2—122no—
139C2—181no—
140C2C2×C3×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, hypercenterC3×C4GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C23×C3
FrattiniC2C2×C3×GO+(4,𝔽2)
FittingC33×C4D4
socleC2×C33C2×D4
hypocenterC32C3×#135
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×#3798C2semidirect
2. C3×#3787C2semidirect
3. C3×#3776C2semidirect
4. C3×#3775C2semidirect
5. C3×#3774C2semidirect
6. #64223C3direct (N × H)
15. #3798C2×C3semidirect
16. #3787C2×C3semidirect
17. #3776C2×C3semidirect
18. #3775C2×C3semidirect
19. #3774C2×C3semidirect
66. C33#135semidirect
113. C32C3×#135semidirect
137. C3#64223direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#37982
C3×#37872
C3×#37762
C3×#37752
C3×#37742
#642233
C3×#1359