Finite Group Databasebeta

← C22×C3×C3⋊Dic9 #13048937

Subgroups — C22×C3×C3⋊Dic9 #13048937

Order 1296.

780 conjugacy classes of subgroups; only the 342 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 342 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
1C23×C32×C9C211yesmaximal, characteristic
2C2×C3×C3⋊Dic9C216yesmaximal, direct product factor
3C22×C3×C3⋊Dic3—31nomaximal
4C22×C3⋊Dic9C311yesmaximal, characteristic, direct product factor
5C22×C3×Dic9—33nomaximal
6C22×C32×C9C414yescomplemented
7C22×C32×C9C2213yes—
8C3×C3⋊Dic9C2214yesdirect product factor
9C23×C33D311yescharacteristic
10C2×C3×C3⋊Dic3—36no—
11C23×C3×C9—21no—
12C23×C3×C9—23no—
13C23×C3×C9D313yes—
14C23×C3×C9C2×C311yescharacteristic
15C2×C3⋊Dic9C2×C316yesdirect product factor
16C2×C3×Dic9—318no—
17C2×C32×C9C2×C416yescomplemented
18C2×C32×C9C2311yescharacteristic
19C22×C3⋊Dic3—31no—
20C22×C3×Dic3—93no—
21C22×C3×Dic3—91no—
22C22×Dic9—33no—
23C22×C33Dic314yes—
24C22×C33C2×D313yes—
25C3×C3⋊Dic3—34no—
26C22×C3×C9—24no—
27C22×C3×C9—23no—
28C22×C3×C9—212no—
29C22×C3×C9—29no—
30C22×C3×C9Dic3112yescomplemented
31C22×C3×C9C3×C414yescomplemented
32C22×C3×C9C2×D319yes—
33C22×C3×C9C22×C313yes—
34C3⋊Dic9C22×C314yesdirect product factor
35C3×Dic9—312no—
36C32×C9C22×C411yescharacteristic, complemented, Sylow
37C23×C32—23no—
38C23×C32—21no—
39C23×C32D913yes—
40C23×C32C3×D311yescharacteristic
41C23×C32C3⋊D311yescharacteristic
42C2×C3⋊Dic3—36no—
43C2×C3×Dic3—918no—
44C2×C3×Dic3—96no—
45C23×C9—23no—
46C23×C9C3×D313yes—
47C2×Dic9—318no—
48C2×C33C2×Dic316yes—
49C2×C33C22×D311yescharacteristic
50C2×C3×C9—26no—
51C2×C3×C9—21no—
52C2×C3×C9—218no—
53C2×C3×C9—23no—
54C2×C3×C9C2×Dic3118yescomplemented
55C2×C3×C9C2×C3×C416yescomplemented
56C2×C3×C9C22×D313yes—
57C2×C3×C9C23×C311yescharacteristic
58C22×C3×C4—271no—
59C22×Dic3—93no—
60C22×Dic3—91no—
61C22×C32—212no—
62C22×C32—29no—
63C22×C32—24no—
64C22×C32—23no—
65C22×C32Dic9112yescomplemented
66C22×C32C2×D919yes—
67C22×C32C3×Dic314yes—
68C22×C32C3⋊Dic314yes—
69C22×C32C2×C3×D313yes—
70C22×C32C2×C3⋊D313yes—
71C3⋊Dic3—34no—
72C3×Dic3—912no—
73C3×Dic3—94no—
74C22×C9—212no—
75C22×C9—29no—
76C22×C9C3×Dic3112yescomplemented
77C22×C9C2×C3×D319yes—
78Dic9—312no—
79C33C22×Dic311yescharacteristic
80C3×C9—21no—
81C3×C9—23no—
82C3×C9C22×Dic313yescomplemented
83C3×C9C22×C3×C411yescharacteristic, complemented
84C23×C3—23no—
85C23×C3—21no—
86C23×C3C3×D913yes—
87C23×C3C3⋊D911yescharacteristic
88C23×C3C3×C3⋊D311yescharacteristic
89C2×C3×C4—276no—
90C2×Dic3—918no—
91C2×Dic3—96no—
92C2×C32—218no—
93C2×C32—23no—
94C2×C32—26no—
95C2×C32—21no—
96C2×C32C2×Dic9118yescomplemented
97C2×C32C22×D913yes—
98C2×C32C2×C3×Dic316yes—
99C2×C32C2×C3⋊Dic316yes—
100C2×C32C22×C3×D311yescharacteristic
101C2×C32C22×C3⋊D311yescharacteristic
102C2×C9—218no—
103C2×C9—23no—
104C2×C9C2×C3×Dic3118yescomplemented
105C2×C9C22×C3×D313yes—
106C22×C4—271noSylow
107C22×C3—212no—
108C22×C3—24no—
109C22×C3—29no—
110C22×C3—23no—
111C22×C3C3×Dic9112yescomplemented
112C22×C3C3⋊Dic914yesdirect product factor
113C22×C3C2×C3×D919yes—
114C22×C3C2×C3⋊D913yes—
115C22×C3C3×C3⋊Dic314yes—
116C22×C3C2×C3×C3⋊D313yes—
117C3×C4—274no—
118Dic3—912no—
119Dic3—94no—
120C32—23no—
121C32—21no—
122C32C22×Dic913yescomplemented
123C32C22×C3×Dic311yescharacteristic
124C32C22×C3⋊Dic311yescharacteristic
125C9—23no—
126C9C22×C3×Dic313yescomplemented
127C23C3×C3⋊D911yescharacteristic
128C2×C4—276no—
129C2×C3—218no—
130C2×C3—26no—
131C2×C3—23no—
132C2×C3—21no—
133C2×C3C2×C3×Dic9118yescomplemented
134C2×C3C2×C3⋊Dic916yesdirect product factor
135C2×C3C22×C3×D913yes—
136C2×C3C22×C3⋊D911yescharacteristic
137C2×C3C2×C3×C3⋊Dic316yes—
138C2×C3C22×C3×C3⋊D311yescharacteristic
139C22C3×C3⋊Dic914yesdirect product factor
140C22C2×C3×C3⋊D913yes—
141C4—274no—
142C3—23no—
143C3—21no—
144C3C22×C3×Dic913yescomplemented
145C3C22×C3⋊Dic911yescharacteristic, direct product factor
146C3C22×C3×C3⋊Dic311yescharacteristic
147C2C2×C3×C3⋊Dic916yesdirect product factor
148C2C22×C3×C3⋊D911yescharacteristic
subgroupG/H
center, hypercenterC23×C3C3⋊D9
commutator, hypocenterC3×C9C22×C3×C4
FrattiniC2×C3C22×C3×C3⋊D3
FittingC23×C32×C9C2
socle, prime radicalC23×C33D3
cosocleC2×C3×C9C23×C3
LCSG ▷ C3×C9
UCSC1 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×C3⋊Dic9C2direct (N × H)
4. C22×C3⋊Dic9C3direct (N × H)
6. C22×C32×C9C4semidirect
8. C3×C3⋊Dic9C22direct (N × H)
15. C2×C3⋊Dic9C2×C3direct (N × H)
17. C2×C32×C9C2×C4semidirect
30. C22×C3×C9Dic3semidirect
31. C22×C3×C9C3×C4semidirect
34. C3⋊Dic9C22×C3direct (N × H)
36. C32×C9C22×C4semidirect
54. C2×C3×C9C2×Dic3semidirect
55. C2×C3×C9C2×C3×C4semidirect
65. C22×C32Dic9semidirect
76. C22×C9C3×Dic3semidirect
82. C3×C9C22×Dic3semidirect
83. C3×C9C22×C3×C4semidirect
96. C2×C32C2×Dic9semidirect
104. C2×C9C2×C3×Dic3semidirect
111. C22×C3C3×Dic9semidirect
112. C22×C3C3⋊Dic9direct (N × H)
122. C32C22×Dic9semidirect
126. C9C22×C3×Dic3semidirect
133. C2×C3C2×C3×Dic9semidirect
134. C2×C3C2×C3⋊Dic9direct (N × H)
139. C22C3×C3⋊Dic9direct (N × H)
144. C3C22×C3×Dic9semidirect
145. C3C22×C3⋊Dic9direct (N × H)
147. C2C2×C3×C3⋊Dic9direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×C92
C2×C3×C3⋊Dic92
C22×C3×C3⋊Dic33
C22×C3⋊Dic93
C22×C3×Dic93