Finite Group Databasebeta

← C2×C3×D3×#106 #11858372

Subgroups — C2×C3×D3×#106 #11858372

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic
2C2×C3×D3×C4⋊C4C212yesmaximal
3C2×C32×#106C211yesmaximal, characteristic, complemented
4C2×C3×#817C211yesmaximal, characteristic, complemented
5C2×C3×#808C212yesmaximal, complemented
6C3×D3×#106C218yesmaximal, direct product factor
7C22×C3×#106—31nomaximal
8C2×D3×#106C311yesmaximal, characteristic, direct product factor
9C22×C3×C4×D3—22no—
10C22×C3×C4×D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2212yes—
13C2×C3×C4⋊Dic3C2212yes—
14C2×C3×Dic3⋊C4—22no—
15C22×C3×C3⋊C8C2211yescharacteristic
16C2×C3×D3×C8C418yescomplemented
17C2×C3×D3×C8C2214yes—
18C3×D3×C4⋊C4—24no—
19C3×D3×C4⋊C4C2218yes—
20C32×#106C2214yescomplemented
21C3×#817C2214yescomplemented
22C3×#808C2218yescomplemented
23C23×C3×C8—31no—
24C22×C3×C4⋊C4—32no—
25C22×D3×C8C2×C311yescharacteristic
26C2×D3×C4⋊C4C2×C312yes—
27C2×C3×#106—21no—
28C2×C3×#106—31no—
29C2×C3×#106—32no—
30C2×C3×#106—38no—
31C2×C3×#106D311yescharacteristic, direct product factor
32C2×C3×#106C2×C311yescharacteristic, complemented
33C2×#817C2×C311yescharacteristic, complemented
34C2×#808C2×C312yescomplemented
35D3×#106C2×C318yesdirect product factor
36C23×C3×D3D411yescharacteristic
37C22×C32×C4—22no—
38C22×C32×C4C2311yescharacteristic
39C22×C3×Dic3—22no—
40C22×C3×Dic3D411yescharacteristic
41C2×C3×C4×D3—28no—
42C2×C3×C4×D3—48no—
43C2×C3×C4×D3C2×C414yes—
44C2×C3×C4×D3D412yes—
45C2×C3×C4×D3Q814yes—
46C2×C3×C4×D3C2312yes—
47C2×C32×C8C2×C414yescomplemented
48C2×C32×C8C2312yes—
49C32×C4⋊C4—22no—
50C32×C4⋊C4C2314yes—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3C2314yes—
53C3×Dic3⋊C4—28no—
54C2×C3×C3⋊C8C2×C414yescomplemented
55C2×C3×C3⋊C8C2312yes—
56C3×D3×C8C2×C4116yescomplemented
57C22×#106—31noSylow
58C23×C3×C4—31no—
59C23×C3×C4—62no—
60C22×C4×D3—22no—
61C22×C4×D3C22×C311yescharacteristic
62C22×C3×C8—21no—
63C22×C3×C8—31no—
64C22×C3×C8—38no—
65C22×C3×C8—34no—
66C22×C3×C8C2×D311yescharacteristic
67C22×C3×C8C22×C311yescharacteristic
68C2×C3×C4⋊C4—22no—
69C2×C3×C4⋊C4—32no—
70C2×C3×C4⋊C4—38no—
71C2×C3×C4⋊C4—64no—
72C2×C3×C4⋊C4—62no—
73C2×C3×C4⋊C4C2×D312yes—
74C2×C3×C4⋊C4C22×C312yes—
75C2×C4⋊Dic3C22×C312yes—
76C2×Dic3⋊C4—22no—
77C22×C3⋊C8C22×C311yescharacteristic
78C2×D3×C8C3×C418yescomplemented
79C2×D3×C8C22×C314yes—
80D3×C4⋊C4—24no—
81D3×C4⋊C4C22×C318yes—
82C3×#106—24no—
83C3×#106—34no—
84C3×#106—38no—
85C3×#106C2×D314yesdirect product factor
86C3×#106C22×C314yescomplemented
87#817C22×C314yescomplemented
88#808C22×C318yescomplemented
89C23×C32C2×D411yescharacteristic
90C22×C3×D3C4⋊C414yes—
91C22×C3×D3SD1618yes—
92C22×C3×D3C2×D412yes—
93C2×C32×C4—24no—
94C2×C32×C4—44no—
95C2×C32×C4C22×C412yes—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×Q812yes—
98C2×C32×C4C2411yescharacteristic
99C2×C3×Dic3—24no—
100C2×C3×Dic3—44no—
101C2×C3×Dic3C4⋊C414yes—
102C2×C3×Dic3C2×D412yes—
103C3×C4×D3—416no—
104C3×C4×D3C4⋊C418yes—
105C3×C4×D3C22×C414yes—
106C3×C4×D3C2×Q814yes—
107C32×C8C22×C414yescomplemented
108C3×C3⋊C8C22×C414yescomplemented
109C23×C8—31no—
110C22×C4⋊C4—32no—
111C2×#106—31no—
112C2×#106—32no—
113C2×#106—38no—
114C2×#106C3×D311yescharacteristic, direct product factor
115C24×C3—31no—
116C23×D3C3×D411yescharacteristic
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—31no—
121C22×C3×C4—34no—
122C22×C3×C4—32no—
123C22×C3×C4—34no—
124C22×C3×C4—32no—
125C22×C3×C4—42no—
126C22×C3×C4—68no—
127C22×C3×C4—62no—
128C22×C3×C4—128no—
129C22×C3×C4C22×D311yescharacteristic
130C22×C3×C4C23×C311yescharacteristic
131C22×Dic3—22no—
132C22×Dic3C3×D411yescharacteristic
133C2×C4×D3—28no—
134C2×C4×D3—48no—
135C2×C4×D3C2×C3×C414yes—
136C2×C4×D3C3×D412yes—
137C2×C4×D3C3×Q814yes—
138C2×C4×D3C23×C312yes—
139C2×C3×C8—24no—
140C2×C3×C8—22no—
141C2×C3×C8—34no—
142C2×C3×C8—32no—
143C2×C3×C8—316no—
144C2×C3×C8C4×D314yescomplemented
145C2×C3×C8C2×C3×C414yescomplemented
146C2×C3×C8C22×D312yes—
147C2×C3×C8C23×C312yes—
148C3×C4⋊C4—22no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—24no—
151C3×C4⋊C4—34no—
152C3×C4⋊C4—42no—
153C3×C4⋊C4—68no—
154C3×C4⋊C4—62no—
155C3×C4⋊C4C22×D314yes—
156C3×C4⋊C4C23×C314yes—
157C4⋊Dic3—22no—
158C4⋊Dic3C23×C314yes—
159Dic3⋊C4—28no—
160C2×C3⋊C8C2×C3×C414yescomplemented
161C2×C3⋊C8C23×C312yes—
162D3×C8C2×C3×C4116yescomplemented
163C22×C32C2×C4⋊C412yes—
164C22×C32C2×SD1614yes—
165C22×C32C22×D411yescharacteristic
166C2×C3×D3#106116yesdirect product factor
167C2×C3×D3C2×C4⋊C414yes—
168C2×C3×D3C2×SD1618yes—
169C32×C4—44no—
170C32×C4C2×C4⋊C412yes—
171C32×C4C23×C411yescharacteristic
172C32×C4C22×Q811yescharacteristic
173C3×Dic3—44no—
174C3×Dic3C2×C4⋊C414yes—
175C23×C4—31no—
176C23×C4—62no—
177C22×C8—31no—
178C22×C8—38no—
179C22×C8—34no—
180C22×C8C2×C3×D311yescharacteristic
181C2×C4⋊C4—32no—
182C2×C4⋊C4—38no—
183C2×C4⋊C4—64no—
184C2×C4⋊C4—62no—
185C2×C4⋊C4C2×C3×D312yes—
186#106—34no—
187#106—38no—
188#106C2×C3×D314yesdirect product factor
189C23×C3—21no—
190C23×C3—34no—
191C23×C3—38no—
192C23×C3—32no—
193C23×C3D3×D411yescharacteristic
194C23×C3C2×C3×D411yescharacteristic
195C22×D3C3×C4⋊C414yes—
196C22×D3C3×SD1618yes—
197C22×D3C2×C3×D412yes—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—21no—
201C2×C3×C4—22no—
202C2×C3×C4—21no—
203C2×C3×C4—22no—
204C2×C3×C4—34no—
205C2×C3×C4—32no—
206C2×C3×C4—38no—
207C2×C3×C4—34no—
208C2×C3×C4—34no—
209C2×C3×C4—44no—
210C2×C3×C4—44no—
211C2×C3×C4—44no—
212C2×C3×C4—64no—
213C2×C3×C4—84no—
214C2×C3×C4—1216no—
215C2×C3×C4—124no—
216C2×C3×C4C2×C4×D312yes—
217C2×C3×C4D3×D411yescharacteristic
218C2×C3×C4D3×Q812yes—
219C2×C3×C4C22×C3×C412yes—
220C2×C3×C4C2×C3×D411yescharacteristic
221C2×C3×C4C2×C3×Q812yes—
222C2×C3×C4C23×D311yescharacteristic
223C2×C3×C4C24×C311yescharacteristic
224C2×Dic3—24no—
225C2×Dic3—44no—
226C2×Dic3C3×C4⋊C414yes—
227C2×Dic3C2×C3×D412yes—
228C4×D3—416no—
229C4×D3C3×C4⋊C418yes—
230C4×D3C22×C3×C414yes—
231C4×D3C2×C3×Q814yes—
232C3×C8—24no—
233C3×C8—34no—
234C3×C8C2×C4×D314yescomplemented
235C3×C8C22×C3×C414yescomplemented
236C3⋊C8C22×C3×C414yescomplemented
237C2×C32C2×#10614yescomplemented
238C2×C32C22×C4⋊C411yescharacteristic
239C2×C32C22×SD1612yes—
240C3×D3C2×#10618yesdirect product factor
241C24—31no—
242C22×C4—22no—
243C22×C4—31no—
244C22×C4—32no—
245C22×C4—34no—
246C22×C4—32no—
247C22×C4—34no—
248C22×C4—68no—
249C22×C4—62no—
250C22×C4—128no—
251C22×C4C22×C3×D311yescharacteristic
252C2×C8—32no—
253C2×C8—34no—
254C2×C8—316no—
255C2×C8C3×C4×D314yescomplemented
256C2×C8C22×C3×D312yes—
257C4⋊C4—22no—
258C4⋊C4—34no—
259C4⋊C4—68no—
260C4⋊C4—62no—
261C4⋊C4C22×C3×D314yes—
262C22×C3—22no—
263C22×C3—24no—
264C22×C3—21no—
265C22×C3—34no—
266C22×C3—38no—
267C22×C3—316no—
268C22×C3D3×C4⋊C412yes—
269C22×C3D3×SD1614yes—
270C22×C3C2×C3×C4⋊C412yes—
271C22×C3C2×C3×SD1614yes—
272C22×C3C2×D3×D411yescharacteristic
273C22×C3C22×C3×D411yescharacteristic
274C2×D3C3×#106116yesdirect product factor
275C2×D3C2×C3×C4⋊C414yes—
276C2×D3C2×C3×SD1618yes—
277C3×C4—22no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—34no—
281C3×C4—44no—
282C3×C4—44no—
283C3×C4—84no—
284C3×C4—124no—
285C3×C4D3×C4⋊C412yes—
286C3×C4C2×C3×C4⋊C412yes—
287C3×C4C22×C4×D311yescharacteristic
288C3×C4C2×D3×Q811yescharacteristic
289C3×C4C23×C3×C411yescharacteristic
290C3×C4C22×C3×Q811yescharacteristic
291Dic3—44no—
292Dic3C2×C3×C4⋊C414yes—
293C32C22×#10611yescharacteristic, complemented, Sylow
294C23—34no—
295C23—38no—
296C23—32no—
297C23C3×D3×D411yescharacteristic
298C2×C4—24no—
299C2×C4—34no—
300C2×C4—32no—
301C2×C4—38no—
302C2×C4—34no—
303C2×C4—34no—
304C2×C4—44no—
305C2×C4—64no—
306C2×C4—1216no—
307C2×C4—124no—
308C2×C4C2×C3×C4×D312yes—
309C2×C4C3×D3×D411yescharacteristic
310C2×C4C3×D3×Q812yes—
311C2×C4C23×C3×D311yescharacteristic
312C8—34no—
313C8C2×C3×C4×D314yescomplemented
314C2×C3—21no—
315C2×C3—22no—
316C2×C3—24no—
317C2×C3—38no—
318C2×C3D3×#10614yesdirect product factor
319C2×C3C2×C3×#10614yescomplemented
320C2×C3C2×D3×C4⋊C411yescharacteristic
321C2×C3C2×D3×SD1612yes—
322C2×C3C22×C3×C4⋊C411yescharacteristic
323C2×C3C22×C3×SD1612yes—
324D3C2×C3×#10618yesdirect product factor
325C22—34no—
326C22—38no—
327C22—316no—
328C22C3×D3×C4⋊C412yes—
329C22C3×D3×SD1614yes—
330C22C2×C3×D3×D411yescharacteristic
331C4—34no—
332C4—44no—
333C4—124no—
334C4C3×D3×C4⋊C412yes—
335C4C22×C3×C4×D311yescharacteristic
336C4C2×C3×D3×Q811yescharacteristic
337C3—21no—
338C3C2×D3×#10611yescharacteristic, direct product factor
339C3C22×C3×#10611yescharacteristic, complemented
340C2—38no—
341C2C3×D3×#10614yesdirect product factor
342C2C2×C3×D3×C4⋊C411yescharacteristic
343C2C2×C3×D3×SD1612yes—
subgroupG/H
centerC23×C3D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#106C2
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×#106D3
hypocenterC3C22×C3×#106
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#106

Complements

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

NH ≅ G/Ntype
3. C2×C32×#106C2semidirect
4. C2×C3×#817C2semidirect
5. C2×C3×#808C2semidirect
6. C3×D3×#106C2direct (N × H)
8. C2×D3×#106C3direct (N × H)
16. C2×C3×D3×C8C4semidirect
20. C32×#106C22semidirect
21. C3×#817C22semidirect
22. C3×#808C22semidirect
31. C2×C3×#106D3direct (N × H)
32. C2×C3×#106C2×C3semidirect
33. C2×#817C2×C3semidirect
34. C2×#808C2×C3semidirect
35. D3×#106C2×C3direct (N × H)
47. C2×C32×C8C2×C4semidirect
54. C2×C3×C3⋊C8C2×C4semidirect
56. C3×D3×C8C2×C4semidirect
78. C2×D3×C8C3×C4semidirect
85. C3×#106C2×D3direct (N × H)
86. C3×#106C22×C3semidirect
87. #817C22×C3semidirect
88. #808C22×C3semidirect
107. C32×C8C22×C4semidirect
108. C3×C3⋊C8C22×C4semidirect
114. C2×#106C3×D3direct (N × H)
144. C2×C3×C8C4×D3semidirect
145. C2×C3×C8C2×C3×C4semidirect
160. C2×C3⋊C8C2×C3×C4semidirect
162. D3×C8C2×C3×C4semidirect
166. C2×C3×D3#106direct (N × H)
188. #106C2×C3×D3direct (N × H)
234. C3×C8C2×C4×D3semidirect
235. C3×C8C22×C3×C4semidirect
236. C3⋊C8C22×C3×C4semidirect
237. C2×C32C2×#106semidirect
240. C3×D3C2×#106direct (N × H)
255. C2×C8C3×C4×D3semidirect
274. C2×D3C3×#106direct (N × H)
293. C32C22×#106semidirect
313. C8C2×C3×C4×D3semidirect
318. C2×C3D3×#106direct (N × H)
319. C2×C3C2×C3×#106semidirect
324. D3C2×C3×#106direct (N × H)
338. C3C2×D3×#106direct (N × H)
339. C3C22×C3×#106semidirect
341. C2C3×D3×#106direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×C3×D3×C4⋊C42
C2×C32×#1062
C2×C3×#8172
C2×C3×#8082
C3×D3×#1062
C22×C3×#1063
C2×D3×#1063