Finite Group Databasebeta

← C4×D9×C3⋊D3 #13048650

Subgroups — C4×D9×C3⋊D3 #13048650

Order 1296.

614 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 113 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×D9×C3⋊D3C211yesmaximal, characteristic
2C4×C3⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
3C4×C9×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×C4×D9C211yesmaximal, characteristic, complemented
5C3⋊D3×Dic9C211yesmaximal, characteristic, complemented
6#10619870C211yesmaximal, characteristic, complemented
7D9×C3⋊Dic3C211yesmaximal, characteristic, complemented
8C4×D3×C3⋊D3—31nomaximal
9C4×D3×D9—34nomaximal
10C2×C3⋊(C3⋊D9)C2211yescharacteristic
11C2×C9×C3⋊D3C2211yescharacteristic
12C2×C32×D9C2211yescharacteristic
13D9×C3⋊D3C414yesdirect product factor
14C32×C4×C9C2211yescharacteristic, complemented
15C3⋊(C3⋊Dic9)C2211yescharacteristic, complemented
16C9×C3⋊Dic3C2211yescharacteristic, complemented
17C32×Dic9C2211yescharacteristic, complemented
18C2×D3×C3⋊D3—31no—
19C4×C3⋊(C3⋊D3)—31no—
20C3×C4×C3⋊D3D311yescharacteristic
21C32×C4×D3—31no—
22#6289—31no—
23Dic3×C3⋊D3—31no—
24D3×C3⋊Dic3—31no—
25C2×D3×D9—34no—
26C4×C3⋊D9—34no—
27C4×C3⋊D9—64no—
28C4×D3×C9—34no—
29C3×C4×D9D314yescomplemented
30D3×Dic9—34no—
31(C3⋊D9)⋊C4—34no—
32Dic3×D9—34no—
33C2×C32×C9C2311yescharacteristic
34C3⋊(C3⋊D9)C2×C412yescomplemented
35C9×C3⋊D3C2×C412yescomplemented
36C32×D9C2×C412yescomplemented
37C2×C4×C3⋊D3—91no—
38C4×D32—94no—
39C2×C4×D9—91no—
40C2×C3⋊(C3⋊D3)—31no—
41C2×C3×C3⋊D3C2×D311yescharacteristic
42C2×C32×D3—31no—
43D3×C3⋊D3—34no—
44C33×C4C2×D311yescharacteristic
45C3⋊(C3⋊Dic3)—31no—
46C3×C3⋊Dic3C2×D311yescharacteristic
47C32×Dic3—31no—
48C2×C3⋊D9—34no—
49C2×C3⋊D9—64no—
50C2×D3×C9—34no—
51C2×C3×D9C2×D314yes—
52D3×D9—316no—
53C3×C4×C9—24no—
54C3×C4×C9C2×D314yescomplemented
55C3⋊Dic9—34no—
56C3⋊Dic9—64no—
57C9×Dic3—34no—
58C3×Dic9C2×D314yescomplemented
59C32×C9C22×C411yescharacteristic, complemented, Sylow
60C22×C3⋊D3—91no—
61C2×D32—94no—
62C2×C32×C4—91no—
63C2×C3⋊Dic3—91no—
64C4×C3⋊D3—91no—
65C4×C3⋊D3—91no—
66C4×C3⋊D3—91no—
67C4×C3⋊D3—94no—
68C4×C3⋊D3—184no—
69C4×C3⋊D3D911yescharacteristic, direct product factor
70C3×C4×D3—34no—
71C3×C4×D3—34no—
72#624—94no—
73D3×Dic3—94no—
74D3×Dic3—94no—
75C22×D9—91no—
76C2×C4×C9—91no—
77C2×Dic9—91no—
78C4×D9—91no—
79C4×D9—91no—
80C4×D9—91no—
81C4×D9—184no—
82C4×D9C3⋊D311yescharacteristic, direct product factor
83C2×C33C22×D311yescharacteristic
84C3⋊(C3⋊D3)—32no—
85C3×C3⋊D3C4×D312yes—
86C32×D3—32no—
87C2×C3×C9—24no—
88C2×C3×C9C22×D314yes—
89C3⋊D9—38no—
90C3⋊D9—68no—
91D3×C9—38no—
92C3×D9C4×D318yescomplemented
93C2×C4×D3—271no—
94C2×C4×D3—274no—
95C22×C32—91no—
96C2×C3⋊D3—91no—
97C2×C3⋊D3—94no—
98C2×C3⋊D3—94no—
99C2×C3⋊D3—184no—
100C2×C3⋊D3C2×D911yescharacteristic
101C2×C3×D3—34no—
102C2×C3×D3—34no—
103D32—916no—
104C32×C4—24no—
105C32×C4—91no—
106C32×C4C2×D911yescharacteristic, complemented
107C32×C4D3214yes—
108C3⋊Dic3—91no—
109C3⋊Dic3—94no—
110C3⋊Dic3—184no—
111C3⋊Dic3C2×D911yescharacteristic, complemented
112C3×Dic3—34no—
113C3×Dic3—34no—
114C22×C9—91no—
115C2×D9—91no—
116C2×D9—94no—
117C2×D9—184no—
118C2×D9C2×C3⋊D311yescharacteristic
119C4×C9—24no—
120C4×C9—91no—
121C4×C9C2×C3⋊D311yescharacteristic, complemented
122Dic9—91no—
123Dic9—184no—
124Dic9C2×C3⋊D311yescharacteristic, complemented
125C33C2×C4×D311yescharacteristic
126C3×C9—24no—
127C3×C9C2×C4×D314yescomplemented
128C22×D3—271no—
129C22×D3—274no—
130C2×C3×C4—94no—
131C2×C3×C4—91no—
132C2×Dic3—271no—
133C2×Dic3—274no—
134C4×D3—34no—
135C4×D3—31no—
136C4×D3—271no—
137C4×D3—274no—
138C4×D3—271no—
139C4×D3—274no—
140C4×D3—274no—
141C4×D3—271no—
142C4×D3—544no—
143C2×C32—24no—
144C2×C32—92no—
145C2×C32C22×D911yescharacteristic
146C2×C32C2×D3214yes—
147C3⋊D3—92no—
148C3⋊D3—98no—
149C3⋊D3—188no—
150C3⋊D3C4×D912yesdirect product factor
151C3×D3—38no—
152C3×D3—38no—
153C2×C9—24no—
154C2×C9—92no—
155C2×C9C22×C3⋊D311yescharacteristic
156D9—92no—
157D9—188no—
158D9C4×C3⋊D312yesdirect product factor
159C22×C4—811noSylow
160C22×C3—94no—
161C22×C3—91no—
162C2×D3—34no—
163C2×D3—31no—
164C2×D3—274no—
165C2×D3—2716no—
166C2×D3—274no—
167C2×D3—271no—
168C2×D3—544no—
169C3×C4—24no—
170C3×C4—94no—
171C3×C4—91no—
172C3×C4D3×D914yescomplemented
173C3×C4D3×C3⋊D311yescharacteristic
174Dic3—34no—
175Dic3—31no—
176Dic3—274no—
177Dic3—271no—
178Dic3—544no—
179C32—24no—
180C32C2×C4×D911yescharacteristic, complemented
181C32C4×D3214yes—
182C9—24no—
183C9C2×C4×C3⋊D311yescharacteristic, complemented
184C23—811no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—811no—
188C2×C4—811no—
189C2×C4—811no—
190C2×C4—811no—
191C2×C3—24no—
192C2×C3—98no—
193C2×C3—92no—
194C2×C3C2×D3×D914yes—
195C2×C3C2×D3×C3⋊D311yescharacteristic
196D3—38no—
197D3—32no—
198D3—278no—
199D3—272no—
200D3—548no—
201C22—91no—
202C22—91no—
203C22—814no—
204C22—811no—
205C4—91no—
206C4—91no—
207C4—811no—
208C4D9×C3⋊D311yescharacteristic, direct product factor
209C3—24no—
210C3C4×D3×D914yescomplemented
211C3C4×D3×C3⋊D311yescharacteristic
212C2—92no—
213C2—92no—
214C2—812no—
215C2C2×D9×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC4D9×C3⋊D3
commutator, hypocenterC32×C9C22×C4
FrattiniC2×C3C2×D3×C3⋊D3
FittingC32×C4×C9C22
socleC2×C33C22×D3
prime radicalC2×D9×C3⋊D3C2
cosocleC2×C32×C9C23
LCSG ▷ C32×C9
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×C3⋊(C3⋊D9)C2semidirect
3. C4×C9×C3⋊D3C2semidirect
4. C32×C4×D9C2semidirect
5. C3⋊D3×Dic9C2semidirect
6. #10619870C2semidirect
7. D9×C3⋊Dic3C2semidirect
13. D9×C3⋊D3C4direct (N × H)
14. C32×C4×C9C22semidirect
15. C3⋊(C3⋊Dic9)C22semidirect
16. C9×C3⋊Dic3C22semidirect
17. C32×Dic9C22semidirect
29. C3×C4×D9D3semidirect
34. C3⋊(C3⋊D9)C2×C4semidirect
35. C9×C3⋊D3C2×C4semidirect
36. C32×D9C2×C4semidirect
54. C3×C4×C9C2×D3semidirect
58. C3×Dic9C2×D3semidirect
59. C32×C9C22×C4semidirect
69. C4×C3⋊D3D9direct (N × H)
82. C4×D9C3⋊D3direct (N × H)
92. C3×D9C4×D3semidirect
106. C32×C4C2×D9semidirect
111. C3⋊Dic3C2×D9semidirect
121. C4×C9C2×C3⋊D3semidirect
124. Dic9C2×C3⋊D3semidirect
127. C3×C9C2×C4×D3semidirect
150. C3⋊D3C4×D9direct (N × H)
158. D9C4×C3⋊D3direct (N × H)
172. C3×C4D3×D9semidirect
180. C32C2×C4×D9semidirect
183. C9C2×C4×C3⋊D3semidirect
208. C4D9×C3⋊D3direct (N × H)
210. C3C4×D3×D9semidirect

Maximal subgroups

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

subgroupindex
C2×D9×C3⋊D32
C4×C3⋊(C3⋊D9)2
C4×C9×C3⋊D32
C32×C4×D92
C3⋊D3×Dic92
#106198702
D9×C3⋊Dic32
C4×D3×C3⋊D33
C4×D3×D93