Finite Group Databasebeta

← C2×C3×#4889 #11860040

Subgroups — C2×C3×#4889 #11860040

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×C3×#893C211yesmaximal, characteristic
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C2×C32×#107C211yesmaximal, characteristic, complemented
5C2×C3×#815C211yesmaximal, characteristic, complemented
6C2×C3×#810C211yesmaximal, characteristic, complemented
7C2×C3×#809C211yesmaximal, characteristic
8C3×#4889C218yesmaximal, direct product factor
9C2×C3×#440—31nomaximal
10C2×#4889C311yesmaximal, characteristic, direct product factor
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×Dic3⋊C4—21no—
19C2×C3×C4×Dic3—21no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×C3×#204C418yescomplemented
23C2×C3×#204C2214yes—
24C3×#893—22no—
25C3×#893C2214yes—
26C3×#887—22no—
27C3×#887C2214yescomplemented
28C32×#107C2214yescomplemented
29C3×#815C2214yescomplemented
30C3×#810C2214yescomplemented
31C3×#809C2214yes—
32C22×C3×SD16—31no—
33C2×C3×C4×Q8—31no—
34C2×C3×C4×D4—31no—
35C22×#204C2×C311yescharacteristic
36C2×#893C2×C311yescharacteristic
37C2×#887C2×C311yescharacteristic, complemented
38C3×#440—38no—
39C2×C3×#107—21no—
40C2×C3×#107D311yescharacteristic, complemented
41C2×C3×#107C2×C311yescharacteristic, complemented
42C2×C3×#103—31no—
43C2×C3×#102—31no—
44C2×C3×#97—31no—
45C2×#815C2×C311yescharacteristic, complemented
46C2×#810C2×C311yescharacteristic, complemented
47C2×#809C2×C311yescharacteristic
48#4889C2×C318yesdirect product factor
49C23×C3×D3—21no—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×C4×D3—24no—
61C2×C3×C4×D3—44no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6C2×C414yescomplemented
65C2×C3×Dic6C2312yes—
66C2×C32×C8C2×C414yescomplemented
67C2×C32×C8C2312yes—
68C32×C4⋊C4—21no—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C32×C4⋊C4C2312yes—
72C3×(C2×D3)⋊C4—24no—
73C3×Dic3⋊C4—24no—
74C3×C4×Dic3—24no—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79C3×#204C2×C4116yescomplemented
80C2×#440—31noSylow
81C22×C3×Q8—31no—
82C22×C3×D4—31no—
83C23×C3×C4—61no—
84C22×D12C22×C311yescharacteristic
85C22×C4×D3—21no—
86C22×Dic6C22×C311yescharacteristic
87C2×C3×SD16—38no—
88C2×C3×SD16—34no—
89C22×C3×C8—21no—
90C22×C3×C8—31no—
91C22×C3×C8C2×D311yescharacteristic
92C22×C3×C8C22×C311yescharacteristic
93C3×C4×Q8—34no—
94C3×C4×Q8—62no—
95C3×C4×D4—34no—
96C3×C4×D4—62no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—61no—
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C4⋊C4C22×C311yescharacteristic
103C2×C3×C4⋊C4C22×C311yescharacteristic
104C2×C3×C22⋊C4—61no—
105C2×C3×C42—31no—
106C2×C3×C42—61no—
107C2×(C2×D3)⋊C4—21no—
108C2×Dic3⋊C4—21no—
109C2×C4×Dic3—21no—
110C2×C4×Dic3C22×C311yescharacteristic
111C22×C3⋊C8C22×C311yescharacteristic
112C2×#204C3×C418yescomplemented
113C2×#204C22×C314yes—
114#893—22no—
115#893C22×C314yes—
116#887—22no—
117#887C22×C314yescomplemented
118C3×#107—24no—
119C3×#107C2×D314yescomplemented
120C3×#107C22×C314yescomplemented
121C3×#103—34no—
122C3×#102—34no—
123C3×#97—34no—
124#815C22×C314yescomplemented
125#810C22×C314yescomplemented
126#809C22×C314yes—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—24no—
129C22×C3×D3—22no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—42no—
135C2×C32×C4—42no—
136C2×C32×C4C22×C412yes—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4112yes—
139C2×C32×C4C2411yescharacteristic
140C2×C3×Dic3—24no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3C2×D412yes—
145C2×C3×Dic3C2×D412yes—
146C3×D12—24no—
147C3×D12—22no—
148C3×D12C22×C414yes—
149C3×C4×D3—48no—
150C3×Dic6—24no—
151C3×Dic6—22no—
152C3×Dic6C22×C414yescomplemented
153C32×C8C22×C414yescomplemented
154C3×C3⋊C8—22no—
155C22×SD16—31no—
156C2×C4×Q8—31no—
157C2×C4×D4—31no—
158#440—38no—
159C2×#107C3×D311yescharacteristic, complemented
160C2×#103—31no—
161C2×#102—31no—
162C2×#97—31no—
163C24×C3—61no—
164C23×D3—21no—
165C2×C3×Q8—34no—
166C2×C3×Q8—32no—
167C2×C3×Q8—61no—
168C2×C3×Q8—62no—
169C2×C3×D4—34no—
170C2×C3×D4—32no—
171C2×C3×D4—61no—
172C2×C3×D4—62no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—41no—
181C22×C3×C4—41no—
182C22×C3×C4—64no—
183C22×C3×C4—61no—
184C22×C3×C4—124no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C23×C311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3C3×D411yescharacteristic
189C22×Dic3C3×D411yescharacteristic
190C2×D12—21no—
191C2×D12—22no—
192C2×D12C2×C3×C414yes—
193C2×D12C23×C312yes—
194C2×C4×D3—24no—
195C2×C4×D3—44no—
196C2×Dic6—21no—
197C2×Dic6—22no—
198C2×Dic6C2×C3×C414yescomplemented
199C2×Dic6C23×C312yes—
200C3×SD16—316no—
201C2×C3×C8—24no—
202C2×C3×C8—22no—
203C2×C3×C8—32no—
204C2×C3×C8—62no—
205C2×C3×C8C4×D314yescomplemented
206C2×C3×C8C2×C3×C414yescomplemented
207C2×C3×C8C22×D312yes—
208C2×C3×C8C23×C312yes—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—22no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—41no—
216C3×C4⋊C4—41no—
217C3×C4⋊C4—64no—
218C3×C4⋊C4C22×D312yes—
219C3×C4⋊C4C22×D312yes—
220C3×C4⋊C4C23×C312yes—
221C3×C4⋊C4C23×C312yes—
222C3×C22⋊C4—64no—
223C3×C42—32no—
224C3×C42—32no—
225C3×C42—64no—
226(C2×D3)⋊C4—24no—
227Dic3⋊C4—24no—
228C4×Dic3—24no—
229C4×Dic3C3×D412yes—
230C4×Dic3C23×C312yes—
231C2×C3⋊C8—22no—
232C2×C3⋊C8C23×C312yes—
233#204C2×C3×C4116yescomplemented
234C22×C32C4×D412yes—
235C22×C32AGL(1,ℤ/8)12yes—
236C22×C32#13712yes—
237C22×C32C22×D411yescharacteristic
238C2×C3×D3—24no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—48no—
242C32×C4—42no—
243C32×C4—42no—
244C32×C4C4×D412yes—
245C32×C4C23×C411yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3×Dic3—24no—
248C3×Dic3—22no—
249C3×Dic3—22no—
250C22×Q8—31no—
251C22×D4—31no—
252C23×C4—61no—
253C2×SD16—38no—
254C2×SD16—34no—
255C22×C8—31no—
256C22×C8C2×C3×D311yescharacteristic
257C4×Q8—34no—
258C4×Q8—62no—
259C4×D4—34no—
260C4×D4—62no—
261C2×C4⋊C4—61no—
262C2×C4⋊C4C2×C3×D311yescharacteristic
263C2×C4⋊C4C2×C3×D311yescharacteristic
264C2×C22⋊C4—61no—
265C2×C42—31no—
266C2×C42—61no—
267#107C2×C3×D314yescomplemented
268#103—34no—
269#102—34no—
270#97—34no—
271C23×C3—21no—
272C23×C3—64no—
273C23×C3—62no—
274C23×C3—122no—
275C23×C3—122no—
276C23×C3D3×D411yescharacteristic
277C23×C3C2×C3×D411yescharacteristic
278C22×D3—24no—
279C22×D3—22no—
280C22×D3—42no—
281C22×D3—42no—
282C3×Q8—34no—
283C3×Q8—64no—
284C3×Q8—62no—
285C3×D4—34no—
286C3×D4—64no—
287C3×D4—62no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—32no—
297C2×C3×C4—32no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—64no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—82no—
309C2×C3×C4—82no—
310C2×C3×C4—128no—
311C2×C3×C4C2×C4×D312yes—
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4#23912yes—
314C2×C3×C4C22×C3×C412yes—
315C2×C3×C4C2×C3×D411yescharacteristic
316C2×C3×C4C3×#4112yes—
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C24×C311yescharacteristic
319C2×Dic3—24no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3C2×C3×D412yes—
324C2×Dic3C2×C3×D412yes—
325D12—24no—
326D12—22no—
327D12C22×C3×C414yes—
328C4×D3—48no—
329Dic6—24no—
330Dic6—22no—
331Dic6C22×C3×C414yescomplemented
332C3×C8—24no—
333C3×C8—62no—
334C3×C8C2×C4×D314yescomplemented
335C3×C8C22×C3×C414yescomplemented
336C3⋊C8—22no—
337C2×C32#44014yescomplemented
338C2×C32C2×C4×D411yescharacteristic
339C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
340C2×C32C2×#13711yescharacteristic
341C3×D3—44no—
342C24—61no—
343C2×Q8—32no—
344C2×Q8—34no—
345C2×Q8—61no—
346C2×Q8—62no—
347C2×D4—32no—
348C2×D4—34no—
349C2×D4—61no—
350C2×D4—62no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—31no—
354C22×C4—31no—
355C22×C4—64no—
356C22×C4—61no—
357C22×C4—124no—
358C22×C4C22×C3×D311yescharacteristic
359SD16—316no—
360C2×C8—32no—
361C2×C8—62no—
362C2×C8C3×C4×D314yescomplemented
363C2×C8C22×C3×D312yes—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—64no—
367C4⋊C4C22×C3×D312yes—
368C4⋊C4C22×C3×D312yes—
369C22⋊C4—64no—
370C42—32no—
371C42—32no—
372C42—64no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—21no—
377C22×C3—64no—
378C22×C3—128no—
379C22×C3—122no—
380C22×C3—122no—
381C22×C3#89312yes—
382C22×C3#91112yes—
383C22×C3#91812yes—
384C22×C3C3×C4×D412yes—
385C22×C3C3×AGL(1,ℤ/8)12yes—
386C22×C3C3×#13712yes—
387C22×C3C2×D3×D411yescharacteristic
388C22×C3C22×C3×D411yescharacteristic
389C2×D3—24no—
390C2×D3—42no—
391C2×D3—42no—
392C2×D3—48no—
393C3×C4—22no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—42no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—62no—
401C3×C4—64no—
402C3×C4—62no—
403C3×C4—82no—
404C3×C4—82no—
405C3×C4#89312yes—
406C3×C4C3×C4×D412yes—
407C3×C4C22×C4×D311yescharacteristic
408C3×C4C2×#23911yescharacteristic
409C3×C4C23×C3×C411yescharacteristic
410C3×C4C2×C3×#4111yescharacteristic
411Dic3—22no—
412Dic3—22no—
413Dic3—24no—
414C32C2×#44011yescharacteristic, complemented, Sylow
415C23—64no—
416C23—62no—
417C23—122no—
418C23—122no—
419C23C3×D3×D411yescharacteristic
420Q8—34no—
421Q8—64no—
422Q8—62no—
423D4—34no—
424D4—64no—
425D4—62no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—32no—
429C2×C4—32no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—64no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—128no—
437C2×C4C2×C3×C4×D312yes—
438C2×C4C3×D3×D411yescharacteristic
439C2×C4C3×#23912yes—
440C2×C4C23×C3×D311yescharacteristic
441C8—62no—
442C8C2×C3×C4×D314yescomplemented
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—24no—
447C2×C3—124no—
448C2×C3#488914yesdirect product factor
449C2×C3C3×#44014yescomplemented
450C2×C3C2×#89311yescharacteristic
451C2×C3C2×#91111yescharacteristic
452C2×C3C2×#91811yescharacteristic
453C2×C3C2×C3×C4×D411yescharacteristic
454C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
455C2×C3C2×C3×#13711yescharacteristic
456D3—44no—
457C22—64no—
458C22—122no—
459C22—122no—
460C22—128no—
461C22C3×#89312yes—
462C22C3×#91112yes—
463C22C3×#91812yes—
464C22C2×C3×D3×D411yescharacteristic
465C4—42no—
466C4—42no—
467C4—62no—
468C4—64no—
469C4—62no—
470C4C3×#89312yes—
471C4C22×C3×C4×D311yescharacteristic
472C4C2×C3×#23911yescharacteristic
473C3—21no—
474C3C2×#488911yescharacteristic, direct product factor
475C3C2×C3×#44011yescharacteristic, complemented
476C2—124no—
477C2C3×#488914yesdirect product factor
478C2C2×C3×#89311yescharacteristic
479C2C2×C3×#91111yescharacteristic
480C2C2×C3×#91811yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#107C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×#107D3
hypocenterC3C2×C3×#440
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#107

Complements

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

NH ≅ G/Ntype
3. C2×C3×#887C2semidirect
4. C2×C32×#107C2semidirect
5. C2×C3×#815C2semidirect
6. C2×C3×#810C2semidirect
8. C3×#4889C2direct (N × H)
10. C2×#4889C3direct (N × H)
22. C2×C3×#204C4semidirect
27. C3×#887C22semidirect
28. C32×#107C22semidirect
29. C3×#815C22semidirect
30. C3×#810C22semidirect
37. C2×#887C2×C3semidirect
40. C2×C3×#107D3semidirect
41. C2×C3×#107C2×C3semidirect
45. C2×#815C2×C3semidirect
46. C2×#810C2×C3semidirect
48. #4889C2×C3direct (N × H)
64. C2×C3×Dic6C2×C4semidirect
66. C2×C32×C8C2×C4semidirect
79. C3×#204C2×C4semidirect
112. C2×#204C3×C4semidirect
117. #887C22×C3semidirect
119. C3×#107C2×D3semidirect
120. C3×#107C22×C3semidirect
124. #815C22×C3semidirect
125. #810C22×C3semidirect
152. C3×Dic6C22×C4semidirect
153. C32×C8C22×C4semidirect
159. C2×#107C3×D3semidirect
198. C2×Dic6C2×C3×C4semidirect
205. C2×C3×C8C4×D3semidirect
206. C2×C3×C8C2×C3×C4semidirect
233. #204C2×C3×C4semidirect
267. #107C2×C3×D3semidirect
331. Dic6C22×C3×C4semidirect
334. C3×C8C2×C4×D3semidirect
335. C3×C8C22×C3×C4semidirect
337. C2×C32#440semidirect
362. C2×C8C3×C4×D3semidirect
414. C32C2×#440semidirect
442. C8C2×C3×C4×D3semidirect
448. C2×C3#4889direct (N × H)
449. C2×C3C3×#440semidirect
474. C3C2×#4889direct (N × H)
475. C3C2×C3×#440semidirect
477. C2C3×#4889direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×C3×#8932
C2×C3×#8872
C2×C32×#1072
C2×C3×#8152
C2×C3×#8102
C2×C3×#8092
C3×#48892
C2×C3×#4403
C2×#48893