Finite Group Databasebeta

← D12×C3⋊D9 #13048651

Subgroups — D12×C3⋊D9 #13048651

Order 1296.

660 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 108 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×D3×C3⋊D9C212yesmaximal, complemented
2C4⋊(C3⋊(C3⋊D9))C211yesmaximal, characteristic, complemented
3C3×C4×C3⋊D9C211yesmaximal, characteristic, complemented
4C3×C9×D12C211yesmaximal, characteristic, complemented
5#10619880C212yesmaximal, complemented
6C3⋊D3×D12—31nomaximal
7D4×C3⋊D9—31nomaximal
8D9×D12—33nomaximal
9C2×C3⋊(C3⋊D9)C2212yescomplemented
10C2×C3×C3⋊D9C2211yescharacteristic
11C2×C3×D3×C9C2212yescomplemented
12D3×C3⋊D9—24no—
13C32×C4×C9C2211yescharacteristic, complemented
14C3×C3⋊Dic9C2211yescharacteristic, complemented
15C2×D3×C3⋊D3—32no—
16C4⋊(C3⋊(C3⋊D3))—31no—
17C3×C4×C3⋊D3—31no—
18C32×D12D311yescharacteristic
19#6291—32no—
20C22×C3⋊D9—32no—
21C2×D3×D9—36no—
22C3×D4×C9—31no—
23#6233—32no—
24C4⋊(C3⋊D9)—31no—
25C4⋊(C3⋊D9)—33no—
26C4⋊(C3⋊D9)—63no—
27C4⋊(C3⋊D9)—61no—
28C4×C3⋊D9D311yescharacteristic, complemented
29C9×D12D313yescomplemented
30C3×C4×D9—33no—
31#6195—36no—
32C2×C32×C9C2311yescharacteristic
33C3⋊(C3⋊D9)—22no—
34C3×C3⋊D9D412yescomplemented
35C3×D3×C9—22no—
36D4×C3⋊D3—91no—
37D3×D12—93no—
38D3×D12—91no—
39D4×D9—93no—
40C2×C3⋊(C3⋊D3)—32no—
41C2×C3×C3⋊D3—31no—
42C2×C32×D3C2×D312yes—
43D3×C3⋊D3—64no—
44C33×C4C2×D311yescharacteristic
45C3×C3⋊Dic3—31no—
46C22×C3×C9—32no—
47C2×C3⋊D9—32no—
48C2×C3⋊D9—36no—
49C2×C3⋊D9—64no—
50C2×C3⋊D9—66no—
51C2×C3⋊D9—62no—
52C2×C3⋊D9C2×D311yescharacteristic
53C2×D3×C9C2×D316yescomplemented
54C2×C3×D9—33no—
55D3×D9—612no—
56C3×C4×C9—21no—
57C3×C4×C9—23no—
58C3×C4×C9C2×D313yescomplemented
59C3×C4×C9C2×D311yescharacteristic, complemented
60C3⋊Dic9C2×D311yescharacteristic, complemented
61C3×Dic9—33no—
62C32×C9C2×D411yescharacteristic, complemented, Sylow
63C22×C3⋊D3—92no—
64C2×D32—96no—
65C2×D32—92no—
66C32×D4—31no—
67#638—92no—
68C4⋊(C3⋊D3)—91no—
69C4⋊(C3⋊D3)—93no—
70C4⋊(C3⋊D3)—91no—
71C4⋊(C3⋊D3)—181no—
72C4⋊(C3⋊D3)—183no—
73C4×C3⋊D3—31no—
74C3×D12D913yescomplemented
75C3×D12C3⋊D311yescharacteristic
76C3×C4×D3—93no—
77C3×C4×D3—91no—
78#626—96no—
79#626—92no—
80C22×D9—96no—
81D4×C9—33no—
82#611—96no—
83D36—93no—
84D36—183no—
85C4×D9—33no—
86C2×C33C22×D311yescharacteristic
87C3⋊(C3⋊D3)—62no—
88C3×C3⋊D3—32no—
89C32×D3—22no—
90C2×C3×C9—21no—
91C2×C3×C9—23no—
92C2×C3×C9—62no—
93C2×C3×C9C22×D313yes—
94C2×C3×C9C22×D311yescharacteristic
95C3⋊D9—62no—
96C3⋊D9—66no—
97C3⋊D9—126no—
98C3⋊D9—122no—
99C3⋊D9D1212yesdirect product factor
100D3×C9—26no—
101C3×D9—36no—
102D3×D4—271no—
103D3×D4—273no—
104C2×D12—271no—
105C22×C32—32no—
106C2×C3⋊D3—31no—
107C2×C3⋊D3—92no—
108C2×C3⋊D3—96no—
109C2×C3⋊D3—92no—
110C2×C3⋊D3—182no—
111C2×C3⋊D3—186no—
112C2×C3⋊D3—184no—
113C2×C3×D3—93no—
114C2×C3×D3—91no—
115C2×C3×D3C2×D916yescomplemented
116C2×C3×D3C2×C3⋊D312yes—
117D32—184no—
118D32—1812no—
119C32×C4—23no—
120C32×C4—21no—
121C32×C4C2×D913yescomplemented
122C32×C4D3211yescharacteristic
123C32×C4C2×C3⋊D311yescharacteristic
124C3⋊Dic3—31no—
125C3×Dic3—93no—
126C3×Dic3—91no—
127C22×C9—36no—
128C2×D9—33no—
129C2×D9—96no—
130C2×D9—186no—
131C2×D9—1812no—
132C4×C9—23no—
133C4×C9D3213yescomplemented
134Dic9—33no—
135C33D3×D411yescharacteristic
136C3×C9—21no—
137C3×C9—23no—
138C3×C9C2×D1211yescharacteristic, complemented
139C3×C9D3×D413yescomplemented
140C22×D3—272no—
141C22×D3—276no—
142C22×D3—272no—
143C3×D4—33no—
144C3×D4—31no—
145C2×C3×C4—271no—
146#67—272no—
147#67—276no—
148D12—272no—
149D12—273no—
150D12—271no—
151D12—271no—
152D12—543no—
153D12—541no—
154D12C3⋊D911yescharacteristic, direct product factor
155C4×D3—93no—
156C4×D3—91no—
157C2×C32—23no—
158C2×C32—21no—
159C2×C32—62no—
160C2×C32C22×D913yes—
161C2×C32C2×D3211yescharacteristic
162C2×C32C22×C3⋊D311yescharacteristic
163C3⋊D3—32no—
164C3⋊D3—182no—
165C3⋊D3—186no—
166C3⋊D3—182no—
167C3⋊D3—362no—
168C3⋊D3—366no—
169C3×D3—26no—
170C3×D3—22no—
171C3×D3—96no—
172C3×D3—92no—
173C2×C9—23no—
174C2×C9—66no—
175C2×C9C2×D3213yes—
176D9—36no—
177D9—186no—
178D9—366no—
179C2×D4—811noSylow
180C22×C3—36no—
181C22×C3—32no—
182C22×C3—271no—
183C2×D3—93no—
184C2×D3—91no—
185C2×D3—276no—
186C2×D3—272no—
187C2×D3—272no—
188C2×D3—546no—
189C2×D3—542no—
190C2×D3—544no—
191C2×D3—544no—
192C2×D3—5412no—
193C2×D3C2×C3⋊D912yescomplemented
194C3×C4—23no—
195C3×C4—21no—
196C3×C4—271no—
197C3×C4D3×D913yescomplemented
198C3×C4C2×C3⋊D911yescharacteristic, complemented
199C3×C4D3×C3⋊D311yescharacteristic
200Dic3—93no—
201Dic3—91no—
202C32—23no—
203C32—21no—
204C32D4×D913yescomplemented
205C32D3×D1211yescharacteristic
206C32D4×C3⋊D311yescharacteristic
207C9—23no—
208C9D3×D1213yescomplemented
209C23—812no—
210D4—31no—
211D4—812no—
212D4—811no—
213C2×C4—271no—
214C2×C3—23no—
215C2×C3—21no—
216C2×C3—66no—
217C2×C3—62no—
218C2×C3—272no—
219C2×C3C2×D3×D913yes—
220C2×C3C22×C3⋊D911yescharacteristic
221C2×C3C2×D3×C3⋊D311yescharacteristic
222D3—22no—
223D3—96no—
224D3—92no—
225D3—546no—
226D3—542no—
227D3—542no—
228D3—1086no—
229D3—1082no—
230C22—32no—
231C22—271no—
232C22—812no—
233C22—1624no—
234C4—271no—
235C4D3×C3⋊D911yescharacteristic, complemented
236C3—23no—
237C3—21no—
238C3D9×D1213yescomplemented
239C3D4×C3⋊D911yescharacteristic, complemented
240C3C3⋊D3×D1211yescharacteristic
241C2—62no—
242C2—272no—
243C2—1622no—
244C2C2×D3×C3⋊D911yescharacteristic
subgroupG/H
centerC2C2×D3×C3⋊D9
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×D3×C3⋊D3
FittingC32×C4×C9C22
socleC2×C33C22×D3
hypercenterC4D3×C3⋊D9
hypocenterC32×C9C2×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×C3⋊D9C2semidirect
2. C4⋊(C3⋊(C3⋊D9))C2semidirect
3. C3×C4×C3⋊D9C2semidirect
4. C3×C9×D12C2semidirect
5. #10619880C2semidirect
9. C2×C3⋊(C3⋊D9)C22semidirect
11. C2×C3×D3×C9C22semidirect
13. C32×C4×C9C22semidirect
14. C3×C3⋊Dic9C22semidirect
28. C4×C3⋊D9D3semidirect
29. C9×D12D3semidirect
34. C3×C3⋊D9D4semidirect
53. C2×D3×C9C2×D3semidirect
58. C3×C4×C9C2×D3semidirect
59. C3×C4×C9C2×D3semidirect
60. C3⋊Dic9C2×D3semidirect
62. C32×C9C2×D4semidirect
74. C3×D12D9semidirect
99. C3⋊D9D12direct (N × H)
115. C2×C3×D3C2×D9semidirect
121. C32×C4C2×D9semidirect
133. C4×C9D32semidirect
138. C3×C9C2×D12semidirect
139. C3×C9D3×D4semidirect
154. D12C3⋊D9direct (N × H)
193. C2×D3C2×C3⋊D9semidirect
197. C3×C4D3×D9semidirect
198. C3×C4C2×C3⋊D9semidirect
204. C32D4×D9semidirect
208. C9D3×D12semidirect
235. C4D3×C3⋊D9semidirect
238. C3D9×D12semidirect
239. C3D4×C3⋊D9semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C3⋊D92
C4⋊(C3⋊(C3⋊D9))2
C3×C4×C3⋊D92
C3×C9×D122
#106198802
C3⋊D3×D123
D4×C3⋊D93
D9×D123