Finite Group Databasebeta

← C9×A4×C3⋊D3 #14519250

Subgroups — C9×A4×C3⋊D3 #14519250

Order 1944.

664 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C32×C9×A4C211yesmaximal, characteristic, complemented
2C3×A4×C3⋊D3C311yesmaximal, characteristic
3C22×C9×C3⋊D3C311yesmaximal, characteristic, complemented
4C3⋊D3×C22⋊C9C312yesmaximal, complemented
5D3×C9×A4—34nomaximal
6C3×C9×C3⋊D3—41nomaximal
7C33×A4C2×C311yescharacteristic
8C22×C32×C9C2×C311yescharacteristic, complemented
9C2×C9×C3⋊D3—31no—
10C2×C9×C3⋊D3—31no—
11C32×C22⋊C9C2×C312yescomplemented
12C3×C9×A4—24no—
13C3×C9×A4—24no—
14C3×C9×A4—28no—
15C3×C9×A4D314yescomplemented
16C33×C9—41noSylow
17C22×C3×C3⋊D3C3211yescharacteristic
18A4×C3⋊D3C913yesdirect product factor
19C3×D3×A4—34no—
20C22×D3×C9—34no—
21C2×C9×A4—91no—
22D3×C22⋊C9—38no—
23C32×C3⋊D3—41no—
24C2×C32×C9—31no—
25C9×C3⋊D3—31no—
26C9×C3⋊D3—42no—
27C9×C3⋊D3A411yescharacteristic, direct product factor
28C3×D3×C9—124no—
29C22×C33C2×C3211yescharacteristic
30C2×C3×C3⋊D3—31no—
31C2×C3×C3⋊D3—31no—
32C32×A4—24no—
33C32×A4—212no—
34C32×A4C2×C913yescomplemented
35C32×A4C3×D314yes—
36C22×C3×C9—24no—
37C22×C3×C9C3×D314yescomplemented
38C2×D3×C9—94no—
39C2×D3×C9—94no—
40C3×C22⋊C9—28no—
41C3×C22⋊C9C3×D318yescomplemented
42C9×A4—224no—
43C9×A4—24no—
44C9×A4—24no—
45C9×A4—28no—
46C9×A4C3⋊D311yescharacteristic, direct product factor
47C34—41no—
48C32×C9—42no—
49C32×C9—44no—
50C32×C9—88no—
51C32×C9—84no—
52C32×C9—84no—
53C32×C9C2×A411yescharacteristic, complemented
54C22×C3⋊D3C3×C911yescharacteristic, complemented
55C22×C3×D3—34no—
56C2×C3×A4—91no—
57D3×A4—312no—
58C23×C9—91no—
59C2×C22⋊C9—92no—
60C2×C33—31no—
61C3×C3⋊D3—31no—
62C3×C3⋊D3—43no—
63C3×C3⋊D3C3×A411yescharacteristic
64C32×D3—124no—
65C2×C3×C9—34no—
66C2×C3×C9—64no—
67C2×C3×C9—361no—
68D3×C9—34no—
69D3×C9—94no—
70D3×C9—128no—
71C22×C32—24no—
72C22×C32C2×C3×C911yescharacteristic, complemented
73C22×C32C32×D314yes—
74C2×C3⋊D3—31no—
75C2×C3⋊D3—31no—
76C2×C3×D3—94no—
77C2×C3×D3—94no—
78C3×A4—224no—
79C3×A4—212no—
80C3×A4—24no—
81C3×A4—212no—
82C3×A4D3×C9112yescomplemented
83C3×A4C3×C3⋊D311yescharacteristic
84C22×C9—24no—
85C22×C9—271no—
86C22×C9—271no—
87C22×C9C3×C3⋊D311yescharacteristic, complemented
88C22⋊C9—28no—
89C22⋊C9C3×C3⋊D312yescomplemented
90C33—43no—
91C33—44no—
92C33—812no—
93C33—84no—
94C33C2×C3×A411yescharacteristic
95C3×C9—24no—
96C3×C9—41no—
97C3×C9—48no—
98C3×C9—88no—
99C3×C9—84no—
100C3×C9—824no—
101C3×C9—88no—
102C3×C9—84no—
103C3×C9D3×A414yescomplemented
104C23×C3—91no—
105C22×D3—34no—
106C2×A4—93no—
107C2×C32—31no—
108C2×C32—34no—
109C2×C32—64no—
110C2×C32—361no—
111C3⋊D3—31no—
112C3⋊D3C9×A411yescharacteristic, direct product factor
113C3×D3—34no—
114C3×D3—94no—
115C3×D3—1212no—
116C2×C9—31no—
117C2×C9—64no—
118C2×C9—91no—
119C2×C9—271no—
120C2×C9—362no—
121C22×C3—24no—
122C22×C3—271no—
123C22×C3—271no—
124C22×C3C3×D3×C914yescomplemented
125C22×C3C32×C3⋊D311yescharacteristic
126C2×D3—94no—
127C2×D3—94no—
128A4—212no—
129A4C9×C3⋊D313yesdirect product factor
130C32—24no—
131C32—41no—
132C32—412no—
133C32—812no—
134C32—824no—
135C32—84no—
136C32—812no—
137C32C2×C9×A411yescharacteristic, complemented
138C32C3×D3×A414yes—
139C9—24no—
140C9—42no—
141C9—88no—
142C9A4×C3⋊D311yescharacteristic, direct product factor
143C23—91noSylow
144C2×C3—31no—
145C2×C3—34no—
146C2×C3—64no—
147C2×C3—91no—
148C2×C3—271no—
149C2×C3—363no—
150D3—34no—
151D3—94no—
152C22—271no—
153C22—271no—
154C22C3×C9×C3⋊D311yescharacteristic, complemented
155C3—24no—
156C3—43no—
157C3—812no—
158C3D3×C9×A414yescomplemented
159C3C3×A4×C3⋊D311yescharacteristic
160C2—31no—
161C2—91no—
162C2—271no—
subgroupG/H
center, hypercenterC9A4×C3⋊D3
commutator, hypocenterC22×C32C2×C3×C9
FrattiniC3C3×A4×C3⋊D3
FittingC22×C32×C9C2×C3
socle, cosocleC22×C33C2×C32
prime radicalC3×A4×C3⋊D3C3
LCSG ▷ C22×C32
UCSC1 ◁ C9

Complements

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

NH ≅ G/Ntype
1. C32×C9×A4C2semidirect
3. C22×C9×C3⋊D3C3semidirect
4. C3⋊D3×C22⋊C9C3semidirect
8. C22×C32×C9C2×C3semidirect
11. C32×C22⋊C9C2×C3semidirect
15. C3×C9×A4D3semidirect
18. A4×C3⋊D3C9direct (N × H)
27. C9×C3⋊D3A4direct (N × H)
34. C32×A4C2×C9semidirect
37. C22×C3×C9C3×D3semidirect
41. C3×C22⋊C9C3×D3semidirect
46. C9×A4C3⋊D3direct (N × H)
53. C32×C9C2×A4semidirect
54. C22×C3⋊D3C3×C9semidirect
72. C22×C32C2×C3×C9semidirect
82. C3×A4D3×C9semidirect
87. C22×C9C3×C3⋊D3semidirect
89. C22⋊C9C3×C3⋊D3semidirect
103. C3×C9D3×A4semidirect
112. C3⋊D3C9×A4direct (N × H)
124. C22×C3C3×D3×C9semidirect
129. A4C9×C3⋊D3direct (N × H)
137. C32C2×C9×A4semidirect
142. C9A4×C3⋊D3direct (N × H)
154. C22C3×C9×C3⋊D3semidirect
158. C3D3×C9×A4semidirect

Maximal subgroups

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

subgroupindex
C32×C9×A42
C3×A4×C3⋊D33
C22×C9×C3⋊D33
C3⋊D3×C22⋊C93
D3×C9×A43
C3×C9×C3⋊D34