Finite Group Databasebeta

← C2×C3⋊D3×Dic9 #13048696

Subgroups — C2×C3⋊D3×Dic9 #13048696

Order 1296.

614 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 149 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×C9×C3⋊D3C211yesmaximal, characteristic
2C2×C3⋊(C3⋊Dic9)C211yesmaximal, characteristic, complemented
3C2×C32×Dic9C211yesmaximal, characteristic, complemented
4C3⋊D3×Dic9C214yesmaximal, direct product factor
5C2×Dic3×C3⋊D3—31nomaximal
6C2×D3×Dic9—34nomaximal
7C22×C32×C9C2211yescharacteristic
8C2×C9×C3⋊D3C414yescomplemented
9C2×C9×C3⋊D3C2212yes—
10C3⋊(C3⋊Dic9)C2212yescomplemented
11C32×Dic9C2212yescomplemented
12C22×C3×C3⋊D3D311yescharacteristic
13C2×C3⋊(C3⋊Dic3)—31no—
14C2×C32×Dic3—31no—
15Dic3×C3⋊D3—34no—
16C22×D3×C9—34no—
17C2×C3⋊Dic9—34no—
18C2×C3⋊Dic9—64no—
19C2×C3×Dic9D314yescomplemented
20D3×Dic9—316no—
21C2×C32×C9C2×C412yescomplemented
22C2×C32×C9C2311yescharacteristic
23C9×C3⋊D3C2×C414yescomplemented
24C2×C4×C3⋊D3—91no—
25C2×D3×Dic3—94no—
26C22×Dic9—91no—
27C22×C33C2×D311yescharacteristic
28C2×C3×C3⋊D3Dic314yes—
29C2×C3×C3⋊D3C2×D312yes—
30C3⋊(C3⋊Dic3)—32no—
31C32×Dic3—32no—
32C22×C3×C9—24no—
33C22×C3×C9C2×D314yes—
34C2×D3×C9—316no—
35C2×D3×C9—38no—
36C3⋊Dic9—38no—
37C3⋊Dic9—68no—
38C3×Dic9C2×D318yescomplemented
39C32×C9C22×C411yescharacteristic, complemented, Sylow
40C22×C3⋊D3D911yescharacteristic
41C22×C3×D3—34no—
42C2×C32×C4—91no—
43C2×C3⋊Dic3—91no—
44C2×C3⋊Dic3—94no—
45C2×C3⋊Dic3—184no—
46C4×C3⋊D3—94no—
47C2×C3×Dic3—34no—
48D3×Dic3—916no—
49C23×C9—91no—
50C2×Dic9—91no—
51C2×Dic9—94no—
52C2×Dic9—184no—
53C2×Dic9C3⋊D311yescharacteristic, direct product factor
54C2×C33C2×Dic312yes—
55C2×C33C22×D311yescharacteristic
56C3×C3⋊D3C2×Dic314yes—
57C2×C3×C9—28no—
58C2×C3×C9—24no—
59C2×C3×C9C4×D318yescomplemented
60C2×C3×C9C22×D314yes—
61D3×C9—316no—
62C22×Dic3—271no—
63C2×C4×D3—274no—
64C22×C32—24no—
65C22×C32C2×D911yescharacteristic
66C22×C32D3214yes—
67C2×C3⋊D3Dic914yesdirect product factor
68C2×C3⋊D3C2×D912yes—
69C2×C3×D3—316no—
70C2×C3×D3—38no—
71C32×C4—92no—
72C3⋊Dic3—92no—
73C3⋊Dic3—98no—
74C3⋊Dic3—188no—
75C3×Dic3—38no—
76C22×C9—24no—
77C22×C9—94no—
78C22×C9—92no—
79C22×C9C2×C3⋊D311yescharacteristic
80Dic9—92no—
81Dic9—188no—
82Dic9C2×C3⋊D312yesdirect product factor
83C33C22×Dic311yescharacteristic
84C3×C9—24no—
85C3×C9C2×C4×D314yescomplemented
86C23×C3—91no—
87C22×D3—34no—
88C2×C3×C4—94no—
89C2×Dic3—31no—
90C2×Dic3—274no—
91C2×Dic3—274no—
92C2×Dic3—271no—
93C2×Dic3—544no—
94C4×D3—2716no—
95C2×C32—28no—
96C2×C32—24no—
97C2×C32C2×Dic912yescomplemented
98C2×C32C22×D911yescharacteristic
99C2×C32D3×Dic318yes—
100C2×C32C2×D3214yes—
101C3⋊D3C2×Dic914yesdirect product factor
102C3×D3—316no—
103C2×C9—28no—
104C2×C9—24no—
105C2×C9—94no—
106C2×C9C4×C3⋊D312yescomplemented
107C2×C9C22×C3⋊D311yescharacteristic
108C22×C4—811noSylow
109C22×C3—24no—
110C22×C3—94no—
111C22×C3—92no—
112C22×C3D3×D914yes—
113C22×C3D3×C3⋊D311yescharacteristic
114C2×D3—316no—
115C2×D3—38no—
116C3×C4—98no—
117Dic3—32no—
118Dic3—278no—
119Dic3—272no—
120Dic3—548no—
121C32—24no—
122C32C22×Dic911yescharacteristic, complemented
123C32C2×D3×Dic314yes—
124C9—24no—
125C9C2×C4×C3⋊D311yescharacteristic, complemented
126C23—91no—
127C2×C4—91no—
128C2×C4—814no—
129C2×C4—811no—
130C2×C3—24no—
131C2×C3—28no—
132C2×C3—94no—
133C2×C3D3×Dic918yescomplemented
134C2×C3C2×D3×D914yes—
135C2×C3Dic3×C3⋊D312yes—
136C2×C3C2×D3×C3⋊D311yescharacteristic
137D3—316no—
138C22—92no—
139C22—94no—
140C22D9×C3⋊D311yescharacteristic
141C4—92no—
142C4—812no—
143C3—24no—
144C3C2×D3×Dic914yescomplemented
145C3C2×Dic3×C3⋊D311yescharacteristic
146C2—94no—
147C2C3⋊D3×Dic912yesdirect product factor
148C2C2×D9×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC22D9×C3⋊D3
commutator, hypocenterC32×C9C22×C4
FrattiniC2×C3C2×D3×C3⋊D3
FittingC22×C32×C9C22
socleC22×C33C2×D3
prime radicalC22×C3×C3⋊D3D3
cosocleC2×C32×C9C23
LCSG ▷ C32×C9
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊(C3⋊Dic9)C2semidirect
3. C2×C32×Dic9C2semidirect
4. C3⋊D3×Dic9C2direct (N × H)
8. C2×C9×C3⋊D3C4semidirect
10. C3⋊(C3⋊Dic9)C22semidirect
11. C32×Dic9C22semidirect
19. C2×C3×Dic9D3semidirect
21. C2×C32×C9C2×C4semidirect
23. C9×C3⋊D3C2×C4semidirect
38. C3×Dic9C2×D3semidirect
39. C32×C9C22×C4semidirect
53. C2×Dic9C3⋊D3direct (N × H)
59. C2×C3×C9C4×D3semidirect
67. C2×C3⋊D3Dic9direct (N × H)
82. Dic9C2×C3⋊D3direct (N × H)
85. C3×C9C2×C4×D3semidirect
97. C2×C32C2×Dic9semidirect
101. C3⋊D3C2×Dic9direct (N × H)
106. C2×C9C4×C3⋊D3semidirect
122. C32C22×Dic9semidirect
125. C9C2×C4×C3⋊D3semidirect
133. C2×C3D3×Dic9semidirect
144. C3C2×D3×Dic9semidirect
147. C2C3⋊D3×Dic9direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C9×C3⋊D32
C2×C3⋊(C3⋊Dic9)2
C2×C32×Dic92
C3⋊D3×Dic92
C2×Dic3×C3⋊D33
C2×D3×Dic93