Finite Group Databasebeta

← C22×C3×C3⋊(C3⋊D9) #14519372

Subgroups — C22×C3×C3⋊(C3⋊D9) #14519372

Order 1944.

2340 conjugacy classes of subgroups; only the 522 normal subgroups are shown.

normal subgroups only

This group has 2340 conjugacy classes of subgroups — too many to draw. Only its 522 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×C33×C9C211yesmaximal, characteristic, complemented
2C2×C3×C3⋊(C3⋊D9)C216yesmaximal, direct product factor
3C22×C3×C3⋊(C3⋊D3)—31nomaximal
4C22×C3⋊(C3⋊D9)C311yesmaximal, characteristic, direct product factor
5C22×C3×C3⋊D9—312nomaximal
6C2×C33×C9C2213yescomplemented
7C3×C3⋊(C3⋊D9)C2214yesdirect product factor
8C22×C34D311yescharacteristic
9C2×C3×C3⋊(C3⋊D3)—36no—
10C22×C32×C9—21no—
11C22×C32×C9—212no—
12C22×C32×C9D3112yescomplemented
13C22×C32×C9C2×C311yescharacteristic, complemented
14C2×C3⋊(C3⋊D9)C2×C316yesdirect product factor
15C2×C3×C3⋊D9—372no—
16C33×C9C2311yescharacteristic, complemented, Sylow
17C22×C3⋊(C3⋊D3)—31no—
18C22×C3×C3⋊D3—99no—
19C22×C3×C3⋊D3—94no—
20C22×C3⋊D9—312no—
21C22×C3×D9—99no—
22C2×C34C2×D313yes—
23C3×C3⋊(C3⋊D3)—34no—
24C2×C32×C9—23no—
25C2×C32×C9—236no—
26C2×C32×C9C2×D3136yescomplemented
27C2×C32×C9C22×C313yescomplemented
28C3⋊(C3⋊D9)C22×C314yesdirect product factor
29C3×C3⋊D9—348no—
30C22×C33—29no—
31C22×C33—24no—
32C22×C33D919yescomplemented
33C22×C33C3×D311yescharacteristic
34C22×C33C3⋊D314yes—
35C2×C3⋊(C3⋊D3)—36no—
36C2×C3×C3⋊D3—954no—
37C2×C3×C3⋊D3—924no—
38C22×C3×C9—212no—
39C22×C3×C9—236no—
40C22×C3×C9C3×D3112yescomplemented
41C22×C3×C9C3⋊D319yescomplemented
42C2×C3⋊D9—372no—
43C2×C3×D9—954no—
44C34C22×D311yescharacteristic
45C32×C9—21no—
46C32×C9—212no—
47C32×C9C22×D3112yescomplemented
48C32×C9C23×C311yescharacteristic, complemented
49C22×C3⋊D3—99no—
50C22×C3⋊D3—94no—
51C22×C3×D3—2712no—
52C22×C3×D3—271no—
53C22×D9—99no—
54C2×C33—227no—
55C2×C33—212no—
56C2×C33C2×D9127yescomplemented
57C2×C33C2×C3×D313yes—
58C2×C33C2×C3⋊D3112yes—
59C3⋊(C3⋊D3)—34no—
60C3×C3⋊D3—936no—
61C3×C3⋊D3—916no—
62C2×C3×C9—236no—
63C2×C3×C9—2108no—
64C2×C3×C9C2×C3×D3136yescomplemented
65C2×C3×C9C2×C3⋊D3127yescomplemented
66C3⋊D9—348no—
67C3×D9—936no—
68C22×C32—236no—
69C22×C32—212no—
70C22×C32—24no—
71C22×C32C3×D919yescomplemented
72C22×C32C3⋊D9112yescomplemented
73C22×C32C3×C3⋊D314yes—
74C22×C32C3⋊(C3⋊D3)11yescharacteristic
75C2×C3⋊D3—954no—
76C2×C3⋊D3—924no—
77C2×C3×D3—2772no—
78C2×C3×D3—276no—
79C22×C9—29no—
80C22×C9C3×C3⋊D319yescomplemented
81C2×D9—954no—
82C33—29no—
83C33—24no—
84C33C22×D919yescomplemented
85C33C22×C3×D311yescharacteristic
86C33C22×C3⋊D314yes—
87C3×C9—212no—
88C3×C9—236no—
89C3×C9C22×C3×D3112yescomplemented
90C3×C9C22×C3⋊D319yescomplemented
91C23×C3—811no—
92C22×D3—2712no—
93C22×D3—271no—
94C2×C32—2108no—
95C2×C32—236no—
96C2×C32—212no—
97C2×C32C2×C3×D9127yescomplemented
98C2×C32C2×C3⋊D9136yescomplemented
99C2×C32C2×C3×C3⋊D3112yes—
100C2×C32C2×C3⋊(C3⋊D3)13yes—
101C3⋊D3—936no—
102C3⋊D3—916no—
103C3×D3—2748no—
104C3×D3—274no—
105C2×C9—227no—
106C2×C9C2×C3×C3⋊D3127yescomplemented
107D9—936no—
108C22×C3—212no—
109C22×C3—21no—
110C22×C3—816no—
111C22×C3C3×C3⋊D9112yescomplemented
112C22×C3C3⋊(C3⋊D9)11yescharacteristic, direct product factor
113C22×C3C3×C3⋊(C3⋊D3)11yescharacteristic
114C2×D3—2772no—
115C2×D3—276no—
116C32—24no—
117C32—236no—
118C32—212no—
119C32C22×C3×D919yescomplemented
120C32C22×C3⋊D9112yescomplemented
121C32C22×C3×C3⋊D314yes—
122C32C22×C3⋊(C3⋊D3)11yescharacteristic
123C9—29no—
124C9C22×C3×C3⋊D319yescomplemented
125C23—811noSylow
126C2×C3—236no—
127C2×C3—23no—
128C2×C3—814no—
129C2×C3C2×C3×C3⋊D9136yescomplemented
130C2×C3C2×C3⋊(C3⋊D9)13yesdirect product factor
131C2×C3C2×C3×C3⋊(C3⋊D3)13yes—
132D3—274no—
133D3—2748no—
134C22—816no—
135C22C3×C3⋊(C3⋊D9)11yescharacteristic, direct product factor
136C3—212no—
137C3—21no—
138C3C22×C3×C3⋊D9112yescomplemented
139C3C22×C3⋊(C3⋊D9)11yescharacteristic, direct product factor
140C3C22×C3×C3⋊(C3⋊D3)11yescharacteristic
141C2—814no—
142C2C2×C3×C3⋊(C3⋊D9)13yesdirect product factor
subgroupG/H
center, hypercenterC22×C3C3⋊(C3⋊D9)
commutator, cosocle, hypocenterC32×C9C23×C3
FrattiniC3C22×C3×C3⋊(C3⋊D3)
FittingC22×C33×C9C2
socleC22×C34D3
LCSG ▷ C32×C9
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C33×C9C2semidirect
2. C2×C3×C3⋊(C3⋊D9)C2direct (N × H)
4. C22×C3⋊(C3⋊D9)C3direct (N × H)
6. C2×C33×C9C22semidirect
7. C3×C3⋊(C3⋊D9)C22direct (N × H)
12. C22×C32×C9D3semidirect
13. C22×C32×C9C2×C3semidirect
14. C2×C3⋊(C3⋊D9)C2×C3direct (N × H)
16. C33×C9C23semidirect
26. C2×C32×C9C2×D3semidirect
27. C2×C32×C9C22×C3semidirect
28. C3⋊(C3⋊D9)C22×C3direct (N × H)
32. C22×C33D9semidirect
40. C22×C3×C9C3×D3semidirect
41. C22×C3×C9C3⋊D3semidirect
47. C32×C9C22×D3semidirect
48. C32×C9C23×C3semidirect
56. C2×C33C2×D9semidirect
64. C2×C3×C9C2×C3×D3semidirect
65. C2×C3×C9C2×C3⋊D3semidirect
71. C22×C32C3×D9semidirect
72. C22×C32C3⋊D9semidirect
80. C22×C9C3×C3⋊D3semidirect
84. C33C22×D9semidirect
89. C3×C9C22×C3×D3semidirect
90. C3×C9C22×C3⋊D3semidirect
97. C2×C32C2×C3×D9semidirect
98. C2×C32C2×C3⋊D9semidirect
106. C2×C9C2×C3×C3⋊D3semidirect
111. C22×C3C3×C3⋊D9semidirect
112. C22×C3C3⋊(C3⋊D9)direct (N × H)
119. C32C22×C3×D9semidirect
120. C32C22×C3⋊D9semidirect
124. C9C22×C3×C3⋊D3semidirect
129. C2×C3C2×C3×C3⋊D9semidirect
130. C2×C3C2×C3⋊(C3⋊D9)direct (N × H)
135. C22C3×C3⋊(C3⋊D9)direct (N × H)
138. C3C22×C3×C3⋊D9semidirect
139. C3C22×C3⋊(C3⋊D9)direct (N × H)
142. C2C2×C3×C3⋊(C3⋊D9)direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C33×C92
C2×C3×C3⋊(C3⋊D9)2
C22×C3×C3⋊(C3⋊D3)3
C22×C3⋊(C3⋊D9)3
C22×C3×C3⋊D93