Finite Group Databasebeta

← C2×C3×D3×C3⋊Dic3 #13049639

Subgroups — C2×C3×D3×C3⋊Dic3 #13049639

Order 1296.

1220 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 280 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
1C22×C33×D3C211yesmaximal, characteristic
2C2×C3×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C2×C32×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×D3×C3⋊Dic3C214yesmaximal, direct product factor
5C22×C3×C3⋊Dic3—31nomaximal
6C2×D3×C3⋊Dic3C311yesmaximal, characteristic, direct product factor
7C2×C3×D3×Dic3—34nomaximal
8C22×C34C2211yescharacteristic
9C2×C33×D3C414yescomplemented
10C2×C33×D3C2212yes—
11C3×C3⋊(C3⋊Dic3)C2212yescomplemented
12C32×C3⋊Dic3C2212yescomplemented
13C23×C33—31no—
14C22×C32×D3—24no—
15C22×C32×D3D314yes—
16C22×C32×D3C2×C311yescharacteristic
17C2×C3⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
18C2×C3×C3⋊Dic3—21no—
19C2×C3×C3⋊Dic3—31no—
20C2×C3×C3⋊Dic3—34no—
21C2×C3×C3⋊Dic3—34no—
22C2×C3×C3⋊Dic3—64no—
23C2×C3×C3⋊Dic3D311yescharacteristic, direct product factor
24C2×C3×C3⋊Dic3C2×C311yescharacteristic, complemented
25C2×C32×Dic3—34no—
26D3×C3⋊Dic3C2×C314yesdirect product factor
27C3×D3×Dic3—316no—
28C2×C34C2×C412yescomplemented
29C2×C34C2311yescharacteristic
30C33×D3C2×C414yescomplemented
31C22×C3⋊Dic3—31no—
32C22×C3×Dic3—94no—
33C2×C3×C4×D3—91no—
34C2×D3×Dic3—34no—
35C22×C33—24no—
36C22×C33—21no—
37C22×C33—24no—
38C22×C33—34no—
39C22×C33—32no—
40C22×C33—44no—
41C22×C33C2×D311yescharacteristic
42C22×C33C2×D314yes—
43C22×C33C22×C311yescharacteristic
44C2×C32×D3—216no—
45C2×C32×D3—28no—
46C2×C32×D3Dic3116yescomplemented
47C2×C32×D3C3×C414yescomplemented
48C2×C32×D3C2×D318yes—
49C2×C32×D3C22×C312yes—
50C3⋊(C3⋊Dic3)C22×C312yescomplemented
51C3×C3⋊Dic3—22no—
52C3×C3⋊Dic3—32no—
53C3×C3⋊Dic3—38no—
54C3×C3⋊Dic3—68no—
55C3×C3⋊Dic3C2×D312yesdirect product factor
56C3×C3⋊Dic3C22×C312yescomplemented
57C32×Dic3—38no—
58C34C22×C411yescharacteristic, complemented, Sylow
59C23×C32—31no—
60C23×C32—34no—
61C23×C32—64no—
62C22×C3×D3—24no—
63C22×C3×D3C3×D314yes—
64C22×C3×D3C3⋊D311yescharacteristic
65C2×C32×C4—91no—
66C2×C3⋊Dic3—31no—
67C2×C3⋊Dic3—34no—
68C2×C3⋊Dic3—34no—
69C2×C3⋊Dic3—64no—
70C2×C3⋊Dic3C3×D311yescharacteristic, direct product factor
71C2×C3×Dic3—34no—
72C2×C3×Dic3—34no—
73C2×C3×Dic3—64no—
74C2×C3×Dic3—916no—
75C2×C3×Dic3—94no—
76C2×C3×Dic3—91no—
77C2×C3×Dic3—184no—
78C3×C4×D3—94no—
79D3×Dic3—316no—
80C2×C33—28no—
81C2×C33—22no—
82C2×C33—28no—
83C2×C33—24no—
84C2×C33—21no—
85C2×C33—24no—
86C2×C33—34no—
87C2×C33—48no—
88C2×C33—44no—
89C2×C33C4×D312yescomplemented
90C2×C33C2×Dic318yescomplemented
91C2×C33C2×C3×C412yescomplemented
92C2×C33C22×D311yescharacteristic
93C2×C33C22×D314yes—
94C2×C33C23×C311yescharacteristic
95C32×D3—216no—
96C32×D3C2×Dic3116yescomplemented
97C32×D3C2×C3×C414yescomplemented
98C22×C3×C4—271no—
99C22×Dic3—94no—
100C2×C4×D3—91no—
101C22×C32—24no—
102C22×C32—24no—
103C22×C32—24no—
104C22×C32—24no—
105C22×C32—24no—
106C22×C32—34no—
107C22×C32—32no—
108C22×C32—316no—
109C22×C32—38no—
110C22×C32—44no—
111C22×C32—412no—
112C22×C32—44no—
113C22×C32—616no—
114C22×C32—68no—
115C22×C32D3214yes—
116C22×C32C2×C3×D314yes—
117C22×C32C2×C3×D311yescharacteristic
118C22×C32C2×C3⋊D311yescharacteristic
119C2×C3×D3—216no—
120C2×C3×D3—28no—
121C2×C3×D3C3×Dic3116yescomplemented
122C2×C3×D3C3⋊Dic314yesdirect product factor
123C2×C3×D3C2×C3×D318yes—
124C2×C3×D3C2×C3⋊D312yes—
125C32×C4—92no—
126C3⋊Dic3—32no—
127C3⋊Dic3—38no—
128C3⋊Dic3—68no—
129C3⋊Dic3C2×C3×D312yesdirect product factor
130C3×Dic3—38no—
131C3×Dic3—38no—
132C3×Dic3—68no—
133C3×Dic3—98no—
134C3×Dic3—92no—
135C3×Dic3—188no—
136C33—24no—
137C33—21no—
138C33—24no—
139C33—44no—
140C33C2×C4×D311yescharacteristic, complemented
141C33C22×Dic314yescomplemented
142C33C22×C3×C411yescharacteristic, complemented
143C23×C3—34no—
144C23×C3—31no—
145C23×C3—64no—
146C22×D3C3×C3⋊D311yescharacteristic
147C2×C3×C4—91no—
148C2×C3×C4—91no—
149C2×C3×C4—181no—
150C2×C3×C4—274no—
151C2×C3×C4—271no—
152C2×Dic3—34no—
153C2×Dic3—916no—
154C2×Dic3—94no—
155C2×Dic3—91no—
156C2×Dic3—184no—
157C4×D3—94no—
158C2×C32—28no—
159C2×C32—28no—
160C2×C32—24no—
161C2×C32—24no—
162C2×C32—28no—
163C2×C32—28no—
164C2×C32—28no—
165C2×C32—24no—
166C2×C32—24no—
167C2×C32—24no—
168C2×C32—34no—
169C2×C32—316no—
170C2×C32—48no—
171C2×C32—44no—
172C2×C32—412no—
173C2×C32—424no—
174C2×C32—48no—
175C2×C32—44no—
176C2×C32—616no—
177C2×C32D3×Dic318yescomplemented
178C2×C32C3×C4×D312yescomplemented
179C2×C32C2×C3×Dic318yescomplemented
180C2×C32C2×C3⋊Dic312yescomplemented
181C2×C32C2×D3214yes—
182C2×C32C22×C3×D314yes—
183C2×C32C22×C3×D311yescharacteristic
184C2×C32C22×C3⋊D311yescharacteristic
185C3×D3—216no—
186C3×D3C2×C3×Dic3116yescomplemented
187C3×D3C2×C3⋊Dic314yesdirect product factor
188C22×C4—271noSylow
189C22×C3—24no—
190C22×C3—21no—
191C22×C3—24no—
192C22×C3—316no—
193C22×C3—34no—
194C22×C3—38no—
195C22×C3—32no—
196C22×C3—44no—
197C22×C3—68no—
198C22×C3—616no—
199C22×C3C3×D3214yes—
200C22×C3D3×C3⋊D311yescharacteristic
201C22×C3C2×C3×C3⋊D311yescharacteristic
202C2×D3C3×C3⋊Dic314yesdirect product factor
203C2×D3C2×C3×C3⋊D312yes—
204C3×C4—92no—
205C3×C4—92no—
206C3×C4—182no—
207C3×C4—272no—
208Dic3—38no—
209Dic3—98no—
210Dic3—92no—
211Dic3—188no—
212C32—24no—
213C32—24no—
214C32—24no—
215C32—24no—
216C32—24no—
217C32—44no—
218C32—412no—
219C32—44no—
220C32C2×D3×Dic314yescomplemented
221C32C2×C3×C4×D311yescharacteristic, complemented
222C32C22×C3×Dic314yescomplemented
223C32C22×C3⋊Dic311yescharacteristic, complemented
224C23—31no—
225C2×C4—91no—
226C2×C4—274no—
227C2×C4—271no—
228C2×C3—24no—
229C2×C3—21no—
230C2×C3—24no—
231C2×C3—28no—
232C2×C3—28no—
233C2×C3—22no—
234C2×C3—316no—
235C2×C3—34no—
236C2×C3—44no—
237C2×C3—48no—
238C2×C3—616no—
239C2×C3C3×D3×Dic318yescomplemented
240C2×C3D3×C3⋊Dic312yesdirect product factor
241C2×C3C2×C3×C3⋊Dic312yescomplemented
242C2×C3C2×C3×D3214yes—
243C2×C3C2×D3×C3⋊D311yescharacteristic
244C2×C3C22×C3×C3⋊D311yescharacteristic
245D3C2×C3×C3⋊Dic314yesdirect product factor
246C22—32no—
247C22—34no—
248C22C3×D3×C3⋊D311yescharacteristic
249C4—92no—
250C4—272no—
251C3—24no—
252C3—24no—
253C3—21no—
254C3—44no—
255C3C2×C3×D3×Dic314yescomplemented
256C3C2×D3×C3⋊Dic311yescharacteristic, direct product factor
257C3C22×C3×C3⋊Dic311yescharacteristic, complemented
258C2—34no—
259C2C3×D3×C3⋊Dic312yesdirect product factor
260C2C2×C3×D3×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC22×C3D3×C3⋊D3
commutator, hypocenterC33C22×C3×C4
FrattiniC2C2×C3×D3×C3⋊D3
Fitting, socleC22×C34C22
prime radicalC22×C33×D3C2
cosocleC2×C33C23×C3
LCSG ▷ C33
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×C3⋊(C3⋊Dic3)C2semidirect
3. C2×C32×C3⋊Dic3C2semidirect
4. C3×D3×C3⋊Dic3C2direct (N × H)
6. C2×D3×C3⋊Dic3C3direct (N × H)
9. C2×C33×D3C4semidirect
11. C3×C3⋊(C3⋊Dic3)C22semidirect
12. C32×C3⋊Dic3C22semidirect
17. C2×C3⋊(C3⋊Dic3)C2×C3semidirect
23. C2×C3×C3⋊Dic3D3direct (N × H)
24. C2×C3×C3⋊Dic3C2×C3semidirect
26. D3×C3⋊Dic3C2×C3direct (N × H)
28. C2×C34C2×C4semidirect
30. C33×D3C2×C4semidirect
46. C2×C32×D3Dic3semidirect
47. C2×C32×D3C3×C4semidirect
50. C3⋊(C3⋊Dic3)C22×C3semidirect
55. C3×C3⋊Dic3C2×D3direct (N × H)
56. C3×C3⋊Dic3C22×C3semidirect
58. C34C22×C4semidirect
70. C2×C3⋊Dic3C3×D3direct (N × H)
89. C2×C33C4×D3semidirect
90. C2×C33C2×Dic3semidirect
91. C2×C33C2×C3×C4semidirect
96. C32×D3C2×Dic3semidirect
97. C32×D3C2×C3×C4semidirect
121. C2×C3×D3C3×Dic3semidirect
122. C2×C3×D3C3⋊Dic3direct (N × H)
129. C3⋊Dic3C2×C3×D3direct (N × H)
140. C33C2×C4×D3semidirect
141. C33C22×Dic3semidirect
142. C33C22×C3×C4semidirect
177. C2×C32D3×Dic3semidirect
178. C2×C32C3×C4×D3semidirect
179. C2×C32C2×C3×Dic3semidirect
180. C2×C32C2×C3⋊Dic3semidirect
186. C3×D3C2×C3×Dic3semidirect
187. C3×D3C2×C3⋊Dic3direct (N × H)
202. C2×D3C3×C3⋊Dic3direct (N × H)
220. C32C2×D3×Dic3semidirect
221. C32C2×C3×C4×D3semidirect
222. C32C22×C3×Dic3semidirect
223. C32C22×C3⋊Dic3semidirect
239. C2×C3C3×D3×Dic3semidirect
240. C2×C3D3×C3⋊Dic3direct (N × H)
241. C2×C3C2×C3×C3⋊Dic3semidirect
245. D3C2×C3×C3⋊Dic3direct (N × H)
255. C3C2×C3×D3×Dic3semidirect
256. C3C2×D3×C3⋊Dic3direct (N × H)
257. C3C22×C3×C3⋊Dic3semidirect
259. C2C3×D3×C3⋊Dic3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C33×D32
C2×C3×C3⋊(C3⋊Dic3)2
C2×C32×C3⋊Dic32
C3×D3×C3⋊Dic32
C22×C3×C3⋊Dic33
C2×D3×C3⋊Dic33
C2×C3×D3×Dic33