Finite Group Databasebeta

← C3⋊D3×C9⋊A4 #14519251

Subgroups — C3⋊D3×C9⋊A4 #14519251

Order 1944.

520 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 70 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⋊D3×3−1+2—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
16C32×3−1+2—41noSylow
17C22×C3×C3⋊D3C3211yescharacteristic
18A4×C3⋊D3—31no—
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, complemented
28D3×3−1+2—124no—
29C22×C33C2×C3211yescharacteristic
30C2×C3×C3⋊D3—31no—
31C2×C3×C3⋊D3—31no—
32C32×A4—24no—
33C32×A4—31no—
34C32×A4—64no—
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—
48C3×3−1+2—44no—
49C3×3−1+2—88no—
50C3×3−1+2—84no—
51C3×3−1+2—84no—
52C32×C9—42no—
53C32×C9C2×A411yescharacteristic, complemented
54C22×C3⋊D33−1+211yescharacteristic, complemented
55C22×C3×D3—34no—
56C2×C3×A4—91no—
57D3×A4—94no—
58C23×C9—91no—
59C2×C22⋊C9—92no—
60C2×C33—31no—
61C3×C3⋊D3—31no—
62C3×C3⋊D3—121no—
63C3×C3⋊D3C3×A411yescharacteristic
64C32×D3—124no—
65C2×3−1+2—361no—
66C2×C3×C9—34no—
67C2×C3×C9—64no—
68D3×C9—34no—
69D3×C9—94no—
70D3×C9—128no—
71C22×C32—24no—
72C22×C32C2×3−1+211yescharacteristic, complemented
73C22×C32C32×D314yes—
74C2×C3⋊D3—31no—
75C2×C3⋊D3—31no—
76C2×C3×D3—94no—
77C2×C3×D3—94no—
78C3×A4—24no—
79C3×A4—34no—
80C3×A4—64no—
81C3×A4—68no—
82C3×A4—64no—
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—44no—
91C33—84no—
92C33—121no—
93C33—244no—
94C33C2×C3×A411yescharacteristic
953−1+2—41no—
963−1+2—88no—
973−1+2—84no—
983−1+2—824no—
993−1+2—84no—
100C3×C9—24no—
101C3×C9—48no—
102C3×C9—88no—
103C3×C9D3×A414yescomplemented
104C23×C3—91no—
105C22×D3—34no—
106C2×A4—271no—
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—364no—
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×C3D3×3−1+214yescomplemented
125C22×C3C32×C3⋊D311yescharacteristic
126C2×D3—94no—
127C2×D3—94no—
128A4—31no—
129A4—64no—
130C32—24no—
131C32—41no—
132C32—84no—
133C32—124no—
134C32—244no—
135C32—248no—
136C32—244no—
137C32C2×C9⋊A411yescharacteristic, complemented
138C32C3×D3×A414yes—
139C9—24no—
140C9—42no—
141C9—88no—
142C9A4×C3⋊D311yescharacteristic, complemented
143C23—91noSylow
144C2×C3—31no—
145C2×C3—34no—
146C2×C3—64no—
147C2×C3—91no—
148C2×C3—271no—
149C2×C3—1081no—
150D3—34no—
151D3—94no—
152C22—271no—
153C22—271no—
154C22C3⋊D3×3−1+211yescharacteristic, complemented
155C3—24no—
156C3—121no—
157C3—244no—
158C3D3×C9⋊A414yescomplemented
159C3C3×A4×C3⋊D311yescharacteristic
160C2—31no—
161C2—91no—
162C2—271no—
subgroupG/H
center, FrattiniC3C3×A4×C3⋊D3
commutator, socle, cosocleC22×C33C2×C32
FittingC22×C32×C9C2×C3
prime radicalC3×A4×C3⋊D3C3
hypercenterC9A4×C3⋊D3
hypocenterC22×C32C2×3−1+2
LCSG ▷ C22×C33 ▷ C22×C32
UCSC1 ◁ C3 ◁ 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
27. C9×C3⋊D3A4semidirect
37. C22×C3×C9C3×D3semidirect
41. C3×C22⋊C9C3×D3semidirect
46. C9⋊A4C3⋊D3direct (N × H)
53. C32×C9C2×A4semidirect
54. C22×C3⋊D33−1+2semidirect
72. C22×C32C2×3−1+2semidirect
87. C22×C9C3×C3⋊D3semidirect
89. C22⋊C9C3×C3⋊D3semidirect
103. C3×C9D3×A4semidirect
112. C3⋊D3C9⋊A4direct (N × H)
124. C22×C3D3×3−1+2semidirect
137. C32C2×C9⋊A4semidirect
142. C9A4×C3⋊D3semidirect
154. C22C3⋊D3×3−1+2semidirect
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⋊D3×3−1+24