Finite Group Databasebeta

← C3×C4×C9×C3⋊D3 #14518911

Subgroups — C3×C4×C9×C3⋊D3 #14518911

Order 1944.

984 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 230 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
1C2×C3×C9×C3⋊D3C211yesmaximal, characteristic
2C33×C4×C9C211yesmaximal, characteristic, complemented
3C3×C9×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C32×C4×C3⋊D3C311yesmaximal, characteristic
5C4×C9×C3⋊D3C313yesmaximal, direct product factor
6C3×C4×D3×C9—34nomaximal
7C2×C33×C9C2211yescharacteristic
8C3×C9×C3⋊D3C412yesdirect product factor
9C2×C32×C3⋊D3C2×C311yescharacteristic
10C34×C4C2×C311yescharacteristic
11C32×C3⋊Dic3C2×C311yescharacteristic
12C2×C9×C3⋊D3C2×C313yes—
13C2×C3×D3×C9—34no—
14C32×C4×C9—24no—
15C32×C4×C9—212no—
16C32×C4×C9D314yescomplemented
17C32×C4×C9C2×C313yescomplemented
18C9×C3⋊Dic3C2×C313yescomplemented
19C3×C9×Dic3—34no—
20C33×C9C2×C411yescharacteristic, complemented, Sylow
21C3×C4×C3⋊D3C913yesdirect product factor
22C3×C4×C3⋊D3C3211yescharacteristic
23C32×C4×D3—34no—
24C2×C3×C4×C9—91no—
25C4×D3×C9—312no—
26C2×C34C22×C311yescharacteristic
27C32×C3⋊D3C3×C412yes—
28C2×C32×C9—24no—
29C2×C32×C9—212no—
30C2×C32×C9C2×D314yes—
31C2×C32×C9C22×C313yes—
32C9×C3⋊D3C3×C416yesdirect product factor
33C3×D3×C9—38no—
34C2×C3×C3⋊D3C2×C913yes—
35C2×C3×C3⋊D3C2×C3211yescharacteristic
36C2×C32×D3—34no—
37C33×C4—212no—
38C33×C4—24no—
39C33×C4C2×C913yescomplemented
40C33×C4C3×D314yes—
41C33×C4C2×C3211yescharacteristic
42C3×C3⋊Dic3C2×C913yescomplemented
43C3×C3⋊Dic3C2×C3211yescharacteristic
44C32×Dic3—34no—
45C22×C3×C9—91no—
46C2×D3×C9—312no—
47C3×C4×C9—224no—
48C3×C4×C9—212no—
49C3×C4×C9—24no—
50C3×C4×C9—212no—
51C3×C4×C9—91no—
52C3×C4×C9C3×D3112yescomplemented
53C3×C4×C9C3⋊D311yescharacteristic, direct product factor
54C9×Dic3—312no—
55C34C2×C3×C411yescharacteristic
56C32×C9—24no—
57C32×C9—212no—
58C32×C9C4×D314yescomplemented
59C32×C9C2×C3×C413yescomplemented
60C2×C32×C4—91no—
61C4×C3⋊D3C3×C911yescharacteristic, direct product factor
62C3×C4×D3—312no—
63C3×C4×D3—34no—
64C2×C4×C9—93no—
65C2×C33—212no—
66C2×C33—24no—
67C2×C33C22×C913yes—
68C2×C33C2×C3×D314yes—
69C2×C33C22×C3211yescharacteristic
70C3×C3⋊D3C4×C916yesdirect product factor
71C3×C3⋊D3C32×C412yes—
72C32×D3—38no—
73C2×C3×C9—224no—
74C2×C3×C9—212no—
75C2×C3×C9—24no—
76C2×C3×C9—212no—
77C2×C3×C9—92no—
78C2×C3×C9C2×C3×D3112yes—
79C2×C3×C9C2×C3⋊D311yescharacteristic
80D3×C9—324no—
81C22×C32—91no—
82C2×C3⋊D3C2×C3×C911yescharacteristic
83C2×C3×D3—312no—
84C2×C3×D3—34no—
85C32×C4—224no—
86C32×C4—212no—
87C32×C4—24no—
88C32×C4—212no—
89C32×C4—24no—
90C32×C4—91no—
91C32×C4D3×C9112yescomplemented
92C32×C4C2×C3×C911yescharacteristic, complemented
93C32×C4C32×D314yes—
94C32×C4C3×C3⋊D311yescharacteristic
95C3⋊Dic3C2×C3×C911yescharacteristic, complemented
96C3×Dic3—312no—
97C3×Dic3—34no—
98C22×C9—93no—
99C4×C9—212no—
100C4×C9—93no—
101C4×C9C3×C3⋊D313yesdirect product factor
102C33—212no—
103C33—24no—
104C33C2×C4×C913yescomplemented
105C33C3×C4×D314yes—
106C33C2×C32×C411yescharacteristic
107C3×C9—224no—
108C3×C9—212no—
109C3×C9—24no—
110C3×C9—212no—
111C3×C9C3×C4×D3112yescomplemented
112C3×C9C4×C3⋊D311yescharacteristic, direct product factor
113C2×C3×C4—93no—
114C2×C3×C4—91no—
115C4×D3—34no—
116C2×C32—224no—
117C2×C32—212no—
118C2×C32—24no—
119C2×C32—212no—
120C2×C32—24no—
121C2×C32—92no—
122C2×C32C2×D3×C9112yes—
123C2×C32C22×C3×C911yescharacteristic
124C2×C32C2×C32×D314yes—
125C2×C32C2×C3×C3⋊D311yescharacteristic
126C3⋊D3C3×C4×C912yesdirect product factor
127C3×D3—324no—
128C3×D3—38no—
129C2×C9—212no—
130C2×C9—96no—
131C2×C9C2×C3×C3⋊D313yes—
132C22×C3—93no—
133C22×C3—91no—
134C2×D3—34no—
135C3×C4—212no—
136C3×C4—24no—
137C3×C4—93no—
138C3×C4—91no—
139C3×C4C3×D3×C914yescomplemented
140C3×C4C9×C3⋊D313yesdirect product factor
141C3×C4C32×C3⋊D311yescharacteristic
142Dic3—34no—
143C32—224no—
144C32—24no—
145C32—212no—
146C32—24no—
147C32—212no—
148C32C4×D3×C9112yescomplemented
149C32C2×C3×C4×C911yescharacteristic, complemented
150C32C32×C4×D314yes—
151C32C3×C4×C3⋊D311yescharacteristic
152C9—212no—
153C9C3×C4×C3⋊D313yesdirect product factor
154C2×C4—91noSylow
155C2×C3—212no—
156C2×C3—24no—
157C2×C3—92no—
158C2×C3—96no—
159C2×C3C2×C3×D3×C914yes—
160C2×C3C2×C9×C3⋊D313yes—
161C2×C3C2×C32×C3⋊D311yescharacteristic
162D3—38no—
163C22—91no—
164C4—91no—
165C4C3×C9×C3⋊D311yescharacteristic, direct product factor
166C3—212no—
167C3—24no—
168C3C3×C4×D3×C914yescomplemented
169C3C4×C9×C3⋊D313yesdirect product factor
170C3C32×C4×C3⋊D311yescharacteristic
171C2—92no—
172C2C2×C3×C9×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC3×C4×C9C3⋊D3
commutator, hypocenterC32C2×C3×C4×C9
FrattiniC2×C3C2×C32×C3⋊D3
FittingC33×C4×C9C2
socleC2×C34C22×C3
prime radicalC2×C32×C3⋊D3C2×C3
cosocleC2×C33C22×C32
LCSG ▷ C32
UCSC1 ◁ C3×C4×C9

Complements

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

NH ≅ G/Ntype
2. C33×C4×C9C2semidirect
3. C3×C9×C3⋊Dic3C2semidirect
5. C4×C9×C3⋊D3C3direct (N × H)
8. C3×C9×C3⋊D3C4direct (N × H)
16. C32×C4×C9D3semidirect
17. C32×C4×C9C2×C3semidirect
18. C9×C3⋊Dic3C2×C3semidirect
20. C33×C9C2×C4semidirect
21. C3×C4×C3⋊D3C9direct (N × H)
32. C9×C3⋊D3C3×C4direct (N × H)
39. C33×C4C2×C9semidirect
42. C3×C3⋊Dic3C2×C9semidirect
52. C3×C4×C9C3×D3semidirect
53. C3×C4×C9C3⋊D3direct (N × H)
58. C32×C9C4×D3semidirect
59. C32×C9C2×C3×C4semidirect
61. C4×C3⋊D3C3×C9direct (N × H)
70. C3×C3⋊D3C4×C9direct (N × H)
91. C32×C4D3×C9semidirect
92. C32×C4C2×C3×C9semidirect
95. C3⋊Dic3C2×C3×C9semidirect
101. C4×C9C3×C3⋊D3direct (N × H)
104. C33C2×C4×C9semidirect
111. C3×C9C3×C4×D3semidirect
112. C3×C9C4×C3⋊D3direct (N × H)
126. C3⋊D3C3×C4×C9direct (N × H)
139. C3×C4C3×D3×C9semidirect
140. C3×C4C9×C3⋊D3direct (N × H)
148. C32C4×D3×C9semidirect
149. C32C2×C3×C4×C9semidirect
153. C9C3×C4×C3⋊D3direct (N × H)
165. C4C3×C9×C3⋊D3direct (N × H)
168. C3C3×C4×D3×C9semidirect
169. C3C4×C9×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C9×C3⋊D32
C33×C4×C92
C3×C9×C3⋊Dic32
C32×C4×C3⋊D33
C4×C9×C3⋊D33
C3×C4×D3×C93