Finite Group Databasebeta

← C2×C3×D3×Dic3 #89004

Subgroups — C2×C3×D3×Dic3 #89004

Order 432.

290 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C22×C32×D3C211yesmaximal, characteristic
2C2×C3×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C32×Dic3C211yesmaximal, characteristic, complemented
4C3×D3×Dic3C214yesmaximal, direct product factor
5C22×C3×Dic3—31nomaximal
6C2×C3×C4×D3—31nomaximal
7C2×D3×Dic3C311yesmaximal, characteristic, direct product factor
8C22×C33C2211yescharacteristic
9C2×C32×D3C414yescomplemented
10C2×C32×D3C2212yes—
11C3×C3⋊Dic3C2212yescomplemented
12C32×Dic3C2212yescomplemented
13C23×C32—31no—
14C22×C3×D3—21no—
15C22×C3×D3D311yescharacteristic
16C22×C3×D3C2×C311yescharacteristic
17C2×C32×C4—31no—
18C2×C3⋊Dic3C2×C311yescharacteristic, complemented
19C2×C3×Dic3—21no—
20C2×C3×Dic3—31no—
21C2×C3×Dic3—31no—
22C2×C3×Dic3—34no—
23C2×C3×Dic3—61no—
24C2×C3×Dic3D311yescharacteristic, direct product factor
25C2×C3×Dic3C2×C311yescharacteristic, complemented
26C3×C4×D3—34no—
27D3×Dic3C2×C314yesdirect product factor
28C2×C33C2×C412yescomplemented
29C2×C33C2311yescharacteristic
30C32×D3C2×C414yescomplemented
31C22×C3×C4—91no—
32C22×Dic3—31no—
33C2×C4×D3—31no—
34C22×C32—21no—
35C22×C32—21no—
36C22×C32—21no—
37C22×C32—34no—
38C22×C32—32no—
39C22×C32—41no—
40C22×C32C2×D311yescharacteristic
41C22×C32C2×D311yescharacteristic
42C22×C32C22×C311yescharacteristic
43C2×C3×D3—24no—
44C2×C3×D3—22no—
45C2×C3×D3Dic314yesdirect product factor
46C2×C3×D3C3×C414yescomplemented
47C2×C3×D3C2×D312yes—
48C2×C3×D3C22×C312yes—
49C32×C4—32no—
50C3⋊Dic3C22×C312yescomplemented
51C3×Dic3—22no—
52C3×Dic3—32no—
53C3×Dic3—32no—
54C3×Dic3—62no—
55C3×Dic3C2×D312yesdirect product factor
56C3×Dic3C22×C312yescomplemented
57C33C22×C411yescharacteristic, complemented, Sylow
58C23×C3—31no—
59C23×C3—31no—
60C23×C3—61no—
61C22×D3C3×D311yescharacteristic
62C2×C3×C4—31no—
63C2×C3×C4—31no—
64C2×C3×C4—61no—
65C2×C3×C4—94no—
66C2×C3×C4—91no—
67C2×Dic3—31no—
68C2×Dic3—31no—
69C2×Dic3—34no—
70C2×Dic3—61no—
71C2×Dic3C3×D311yescharacteristic, direct product factor
72C4×D3—34no—
73C2×C32—22no—
74C2×C32—22no—
75C2×C32—22no—
76C2×C32—21no—
77C2×C32—21no—
78C2×C32—21no—
79C2×C32—34no—
80C2×C32—42no—
81C2×C32—41no—
82C2×C32C4×D312yescomplemented
83C2×C32C2×Dic312yescomplemented
84C2×C32C2×C3×C412yescomplemented
85C2×C32C22×D311yescharacteristic
86C2×C32C22×D311yescharacteristic
87C2×C32C23×C311yescharacteristic
88C3×D3—24no—
89C3×D3C2×Dic314yesdirect product factor
90C3×D3C2×C3×C414yescomplemented
91C22×C4—91noSylow
92C22×C3—21no—
93C22×C3—21no—
94C22×C3—21no—
95C22×C3—34no—
96C22×C3—34no—
97C22×C3—32no—
98C22×C3—32no—
99C22×C3—41no—
100C22×C3—64no—
101C22×C3—62no—
102C22×C3D3211yescharacteristic
103C22×C3C2×C3×D311yescharacteristic
104C22×C3C2×C3×D311yescharacteristic
105C2×D3C3×Dic314yesdirect product factor
106C2×D3C2×C3×D312yes—
107C3×C4—32no—
108C3×C4—32no—
109C3×C4—62no—
110C3×C4—92no—
111Dic3—32no—
112Dic3—32no—
113Dic3—62no—
114Dic3C2×C3×D312yesdirect product factor
115C32—21no—
116C32—21no—
117C32—21no—
118C32—41no—
119C32C2×C4×D311yescharacteristic, complemented
120C32C22×Dic311yescharacteristic, complemented
121C32C22×C3×C411yescharacteristic, complemented
122C23—31no—
123C2×C4—31no—
124C2×C4—94no—
125C2×C4—91no—
126C2×C3—22no—
127C2×C3—22no—
128C2×C3—22no—
129C2×C3—21no—
130C2×C3—21no—
131C2×C3—21no—
132C2×C3—34no—
133C2×C3—34no—
134C2×C3—42no—
135C2×C3—41no—
136C2×C3—64no—
137C2×C3D3×Dic312yesdirect product factor
138C2×C3C3×C4×D312yescomplemented
139C2×C3C2×C3×Dic312yescomplemented
140C2×C3C2×D3211yescharacteristic
141C2×C3C22×C3×D311yescharacteristic
142C2×C3C22×C3×D311yescharacteristic
143D3C2×C3×Dic314yesdirect product factor
144C22—34no—
145C22—32no—
146C22C3×D3211yescharacteristic
147C4—32no—
148C4—92no—
149C3—21no—
150C3—21no—
151C3—21no—
152C3—41no—
153C3C2×D3×Dic311yescharacteristic, direct product factor
154C3C2×C3×C4×D311yescharacteristic, complemented
155C3C22×C3×Dic311yescharacteristic, complemented
156C2—34no—
157C2C3×D3×Dic312yesdirect product factor
158C2C2×C3×D3211yescharacteristic
subgroupG/H
center, hypercenterC22×C3D32
commutator, hypocenterC32C22×C3×C4
FrattiniC2C2×C3×D32
Fitting, socleC22×C33C22
prime radicalC22×C32×D3C2
cosocleC2×C32C23×C3
LCSG ▷ C32
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×C3⋊Dic3C2semidirect
3. C2×C32×Dic3C2semidirect
4. C3×D3×Dic3C2direct (N × H)
7. C2×D3×Dic3C3direct (N × H)
9. C2×C32×D3C4semidirect
11. C3×C3⋊Dic3C22semidirect
12. C32×Dic3C22semidirect
18. C2×C3⋊Dic3C2×C3semidirect
24. C2×C3×Dic3D3direct (N × H)
25. C2×C3×Dic3C2×C3semidirect
27. D3×Dic3C2×C3direct (N × H)
28. C2×C33C2×C4semidirect
30. C32×D3C2×C4semidirect
45. C2×C3×D3Dic3direct (N × H)
46. C2×C3×D3C3×C4semidirect
50. C3⋊Dic3C22×C3semidirect
55. C3×Dic3C2×D3direct (N × H)
56. C3×Dic3C22×C3semidirect
57. C33C22×C4semidirect
71. C2×Dic3C3×D3direct (N × H)
82. C2×C32C4×D3semidirect
83. C2×C32C2×Dic3semidirect
84. C2×C32C2×C3×C4semidirect
89. C3×D3C2×Dic3direct (N × H)
90. C3×D3C2×C3×C4semidirect
105. C2×D3C3×Dic3direct (N × H)
114. Dic3C2×C3×D3direct (N × H)
119. C32C2×C4×D3semidirect
120. C32C22×Dic3semidirect
121. C32C22×C3×C4semidirect
137. C2×C3D3×Dic3direct (N × H)
138. C2×C3C3×C4×D3semidirect
139. C2×C3C2×C3×Dic3semidirect
143. D3C2×C3×Dic3direct (N × H)
153. C3C2×D3×Dic3direct (N × H)
154. C3C2×C3×C4×D3semidirect
155. C3C22×C3×Dic3semidirect
157. C2C3×D3×Dic3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×D32
C2×C3×C3⋊Dic32
C2×C32×Dic32
C3×D3×Dic32
C22×C3×Dic33
C2×C3×C4×D33
C2×D3×Dic33