Finite Group Databasebeta

← C2×C3×#4715 #11874383

Subgroups — C2×C3×#4715 #11874383

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic12C212yesmaximal, complemented
2C22×C3×#204C212yesmaximal
3C2×C3×#875C211yesmaximal, characteristic
4C2×C3×#869C211yesmaximal, characteristic, complemented
5C2×C32×#97C211yesmaximal, characteristic, complemented
6C3×#4715C218yesmaximal, direct product factor
7C2×C3×#497—31nomaximal
8C2×#4715C311yesmaximal, characteristic, direct product factor
9C22×C3×D12C2211yescharacteristic
10C22×C3×Dic6C2212yes—
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×C4⋊Dic3—22no—
16C2×C3×Dic12—28no—
17C2×C3×Dic12C2218yescomplemented
18C2×C3×#204—28no—
19C2×C3×#204C2218yes—
20C3×#875—22no—
21C3×#875C2214yes—
22C3×#869—22no—
23C3×#869C2214yescomplemented
24C32×#97C2214yescomplemented
25C22×C3×Q16—32no—
26C22×C3×SD16—32no—
27C2×C3×C4⋊Q8—31no—
28C2×C3×#124—31no—
29C22×Dic12C2×C312yescomplemented
30C22×#204C2×C312yes—
31C2×#875C2×C311yescharacteristic
32C2×#869C2×C311yescharacteristic, complemented
33C3×#497—38no—
34C2×C3×#97—21no—
35C2×C3×#97D311yescharacteristic, complemented
36C2×C3×#97C2×C311yescharacteristic, complemented
37#4715C2×C318yesdirect product factor
38C23×C3×D3—21no—
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3×Dic3—22no—
42C22×C3×Dic3—21no—
43C2×C3×D12—24no—
44C2×C3×D12—21no—
45C2×C3×D12C2312yes—
46C2×C3×Dic6—24no—
47C2×C3×Dic6—24no—
48C2×C3×Dic6—24no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6—21no—
51C2×C3×Dic6C2314yes—
52C2×C3×Dic6C2312yes—
53C2×C32×C8D418yes—
54C2×C32×C8C2314yes—
55C32×C42D412yes—
56C32×C42C2312yes—
57C3×(C2×D3)⋊C4—28no—
58C3×C4⋊Dic3—28no—
59C3×Dic12—216no—
60C3×#204—216no—
61C2×#497—31noSylow
62C22×C3×Q8—32no—
63C22×C3×Q8—31no—
64C22×C3×D4—31no—
65C22×D12C22×C311yescharacteristic
66C22×Dic6C22×C312yes—
67C22×Dic6C22×C311yescharacteristic
68C2×C3×Q16—38no—
69C2×C3×Q16—68no—
70C2×C3×SD16—38no—
71C2×C3×SD16—68no—
72C22×C3×C8—22no—
73C22×C3×C8C2×D312yes—
74C22×C3×C8C22×C312yes—
75C3×C4⋊Q8—34no—
76C3×C4⋊Q8—62no—
77C3×#124—34no—
78C3×#124—62no—
79C2×C3×C4⋊C4—62no—
80C2×C3×C22⋊C4—62no—
81C2×C3×C42—21no—
82C2×C3×C42C2×D311yescharacteristic
83C2×C3×C42C22×C311yescharacteristic
84C2×(C2×D3)⋊C4—22no—
85C2×C4⋊Dic3—22no—
86C2×Dic12—28no—
87C2×Dic12C22×C318yescomplemented
88C2×#204—28no—
89C2×#204C22×C318yes—
90#875—22no—
91#875C22×C314yes—
92#869—22no—
93#869C22×C314yescomplemented
94C3×#97—24no—
95C3×#97C2×D314yescomplemented
96C3×#97C22×C314yescomplemented
97C23×C32C2×D411yescharacteristic
98C22×C3×D3—22no—
99C22×C3×D3—42no—
100C22×C3×D3—44no—
101C2×C32×C4—24no—
102C2×C32×C4C2×D414yes—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D414yes—
105C2×C32×C4C2411yescharacteristic
106C2×C3×Dic3—24no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—44no—
109C2×C3×Dic3—42no—
110C3×D12—24no—
111C3×D12—42no—
112C3×Dic6—24no—
113C3×Dic6—24no—
114C3×Dic6—24no—
115C3×Dic6—44no—
116C3×Dic6—42no—
117C32×C8C2×D418yes—
118C22×Q16—32no—
119C22×SD16—32no—
120C2×C4⋊Q8—31no—
121C2×#124—31no—
122#497—38no—
123C2×#97C3×D311yescharacteristic, complemented
124C24×C3—61no—
125C23×D3—21no—
126C2×C3×Q8—32no—
127C2×C3×Q8—34no—
128C2×C3×Q8—61no—
129C2×C3×Q8—62no—
130C2×C3×Q8—64no—
131C2×C3×Q8—64no—
132C2×C3×Q8—64no—
133C2×C3×D4—32no—
134C2×C3×D4—64no—
135C2×C3×D4—61no—
136C22×C3×C4—22no—
137C22×C3×C4—21no—
138C22×C3×C4—61no—
139C22×C3×C4—62no—
140C22×C3×C4D1212yes—
141C22×C3×C4C3×D412yes—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C23×C311yescharacteristic
144C22×Dic3—22no—
145C22×Dic3—21no—
146C2×D12—24no—
147C2×D12—21no—
148C2×D12C23×C312yes—
149C2×Dic6—24no—
150C2×Dic6—24no—
151C2×Dic6—24no—
152C2×Dic6—22no—
153C2×Dic6—21no—
154C2×Dic6C23×C314yes—
155C2×Dic6C23×C312yes—
156C3×Q16—616no—
157C3×SD16—616no—
158C2×C3×C8—28no—
159C2×C3×C8—24no—
160C2×C3×C8D1218yes—
161C2×C3×C8C3×D418yes—
162C2×C3×C8C22×D314yes—
163C2×C3×C8C23×C314yes—
164C3×C4⋊C4—68no—
165C3×C22⋊C4—68no—
166C3×C42—22no—
167C3×C42—22no—
168C3×C42D1212yes—
169C3×C42C3×D412yes—
170C3×C42C22×D312yes—
171C3×C42C23×C312yes—
172(C2×D3)⋊C4—28no—
173C4⋊Dic3—28no—
174Dic12—216no—
175#204—216no—
176C22×C32#12712yes—
177C22×C32#13714yes—
178C22×C32C22×D411yescharacteristic
179C2×C3×D3—42no—
180C2×C3×D3—44no—
181C2×C3×D3—84no—
182C32×C4—24no—
183C32×C4#12712yes—
184C32×C4C22×D412yes—
185C3×Dic3—44no—
186C3×Dic3—42no—
187C22×Q8—31no—
188C22×Q8—32no—
189C22×D4—31no—
190C2×Q16—38no—
191C2×Q16—68no—
192C2×SD16—38no—
193C2×SD16—68no—
194C22×C8C2×C3×D312yes—
195C4⋊Q8—34no—
196C4⋊Q8—62no—
197#124—34no—
198#124—62no—
199C2×C4⋊C4—62no—
200C2×C22⋊C4—62no—
201C2×C42C2×C3×D311yescharacteristic
202#97C2×C3×D314yescomplemented
203C23×C3—21no—
204C23×C3—62no—
205C23×C3—122no—
206C23×C3—124no—
207C23×C3C2×D1211yescharacteristic
208C23×C3C2×C3×D411yescharacteristic
209C22×D3—22no—
210C22×D3—42no—
211C22×D3—44no—
212C3×Q8—64no—
213C3×Q8—64no—
214C3×Q8—64no—
215C3×Q8—122no—
216C3×Q8—124no—
217C3×D4—64no—
218C3×D4—122no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—44no—
226C2×C3×C4—62no—
227C2×C3×C4—64no—
228C2×C3×C4—122no—
229C2×C3×C4—124no—
230C2×C3×C4C2×D1214yes—
231C2×C3×C4C2×D1211yescharacteristic
232C2×C3×C4C2×D1214yes—
233C2×C3×C4C2×C3×D414yes—
234C2×C3×C4C2×C3×D411yescharacteristic
235C2×C3×C4C2×C3×D414yes—
236C2×C3×C4C23×D311yescharacteristic
237C2×C3×C4C24×C311yescharacteristic
238C2×Dic3—24no—
239C2×Dic3—22no—
240C2×Dic3—44no—
241C2×Dic3—42no—
242D12—24no—
243D12—42no—
244Dic6—24no—
245Dic6—24no—
246Dic6—24no—
247Dic6—44no—
248Dic6—42no—
249C3×C8—28no—
250C3×C8C2×D1218yes—
251C3×C8C2×C3×D418yes—
252C2×C32#49714yescomplemented
253C2×C32C2×#12711yescharacteristic
254C2×C32C2×#13712yes—
255C3×D3—82no—
256C24—61no—
257C2×Q8—32no—
258C2×Q8—34no—
259C2×Q8—61no—
260C2×Q8—62no—
261C2×Q8—64no—
262C2×Q8—64no—
263C2×Q8—64no—
264C2×D4—32no—
265C2×D4—64no—
266C2×D4—61no—
267C22×C4—61no—
268C22×C4—62no—
269C22×C4C3×D1212yes—
270C22×C4C22×C3×D311yescharacteristic
271Q16—616no—
272SD16—616no—
273C2×C8C3×D1218yes—
274C2×C8C22×C3×D314yes—
275C4⋊C4—68no—
276C22⋊C4—68no—
277C42C3×D1212yes—
278C42C22×C3×D312yes—
279C22×C3—24no—
280C22×C3—21no—
281C22×C3—22no—
282C22×C3—122no—
283C22×C3—124no—
284C22×C3—244no—
285C22×C3#87412yes—
286C22×C3#90914yes—
287C22×C3C3×#12712yes—
288C22×C3C3×#13714yes—
289C22×C3C22×D1211yescharacteristic
290C22×C3C22×C3×D411yescharacteristic
291C2×D3—44no—
292C2×D3—42no—
293C2×D3—84no—
294C3×C4—24no—
295C3×C4—24no—
296C3×C4—22no—
297C3×C4—22no—
298C3×C4—44no—
299C3×C4—122no—
300C3×C4—124no—
301C3×C4#87412yes—
302C3×C4C3×#12712yes—
303C3×C4C22×D1212yes—
304C3×C4C22×C3×D412yes—
305Dic3—44no—
306Dic3—42no—
307C32C2×#49711yescharacteristic, complemented, Sylow
308C23—62no—
309C23—124no—
310C23—122no—
311C23C2×C3×D1211yescharacteristic
312Q8—64no—
313Q8—64no—
314Q8—64no—
315Q8—122no—
316Q8—124no—
317D4—64no—
318D4—122no—
319C2×C4—24no—
320C2×C4—62no—
321C2×C4—64no—
322C2×C4—122no—
323C2×C4—124no—
324C2×C4C2×C3×D1214yes—
325C2×C4C2×C3×D1214yes—
326C2×C4C2×C3×D1211yescharacteristic
327C2×C4C23×C3×D311yescharacteristic
328C8C2×C3×D1218yes—
329C2×C3—22no—
330C2×C3—24no—
331C2×C3—21no—
332C2×C3—242no—
333C2×C3#471514yesdirect product factor
334C2×C3C3×#49714yescomplemented
335C2×C3C2×#87411yescharacteristic
336C2×C3C2×#90912yes—
337C2×C3C2×C3×#12711yescharacteristic
338C2×C3C2×C3×#13712yes—
339D3—82no—
340C22—124no—
341C22—122no—
342C22—244no—
343C22C3×#87412yes—
344C22C3×#90914yes—
345C22C22×C3×D1211yescharacteristic
346C4—24no—
347C4—122no—
348C4—124no—
349C4C3×#87412yes—
350C4C22×C3×D1212yes—
351C3—21no—
352C3C2×#471511yescharacteristic, direct product factor
353C3C2×C3×#49711yescharacteristic, complemented
354C2—242no—
355C2C3×#471514yesdirect product factor
356C2C2×C3×#87411yescharacteristic
357C2C2×C3×#90912yes—
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#97C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C3×#97D3
hypocenterC3C2×C3×#497
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×#97

Complements

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

NH ≅ G/Ntype
1. C22×C3×Dic12C2semidirect
4. C2×C3×#869C2semidirect
5. C2×C32×#97C2semidirect
6. C3×#4715C2direct (N × H)
8. C2×#4715C3direct (N × H)
17. C2×C3×Dic12C22semidirect
23. C3×#869C22semidirect
24. C32×#97C22semidirect
29. C22×Dic12C2×C3semidirect
32. C2×#869C2×C3semidirect
35. C2×C3×#97D3semidirect
36. C2×C3×#97C2×C3semidirect
37. #4715C2×C3direct (N × H)
87. C2×Dic12C22×C3semidirect
93. #869C22×C3semidirect
95. C3×#97C2×D3semidirect
96. C3×#97C22×C3semidirect
123. C2×#97C3×D3semidirect
202. #97C2×C3×D3semidirect
252. C2×C32#497semidirect
307. C32C2×#497semidirect
333. C2×C3#4715direct (N × H)
334. C2×C3C3×#497semidirect
352. C3C2×#4715direct (N × H)
353. C3C2×C3×#497semidirect
355. C2C3×#4715direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Dic122
C22×C3×#2042
C2×C3×#8752
C2×C3×#8692
C2×C32×#972
C3×#47152
C2×C3×#4973
C2×#47153