Finite Group Databasebeta

← D12×#713 #14483217

Subgroups — D12×#713 #14483217

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#713C212yesmaximal, complemented
2#11756336C211yesmaximal, characteristic, complemented
3C5×Q8×D12C211yesmaximal, characteristic, complemented
4C3×C4×#713C211yesmaximal, characteristic, complemented
5#11755131C212yesmaximal, complemented
6#11753876C216yesmaximal, complemented
7#11753874C216yesmaximal, complemented
8D12×D20C213yesmaximal, complemented
9C4×D5×D12C213yesmaximal, complemented
10#11752674C213yesmaximal, complemented
11#11752533C213yesmaximal, complemented
12D4×#713—31nomaximal, Hall
13C2×#6821C2212yescomplemented
14C2×C5×D3×Q8C2212yescomplemented
15C2×C3×#713C2211yescharacteristic
16D3×#713—216no—
17C2×D3×D20C2216yescomplemented
18C2×D5×D12C2213yes—
19C2×C4×D3×D5C2216yescomplemented
20C2×#6773C2216yescomplemented
21C2×#6766C2216yescomplemented
22C3×C4×C5×Q8C2211yescharacteristic, complemented
23#91784C2216yescomplemented
24#91763C2213yescomplemented
25C4×D60C2213yescomplemented
26C5×#897C2216yescomplemented
27C4×C5×D12C2213yes—
28C5×#869C2213yescomplemented
29C3×Q8×Dic5C2211yescharacteristic, complemented
30C3×#4039C2213yescomplemented
31C3×#4038C2213yescomplemented
32C3×C4×D20C2213yescomplemented
33C3×C42×D5C2213yescomplemented
34#91476C22112yescomplemented
35D5×(C2×D3)⋊C4C2216yescomplemented
36#91460C2216yescomplemented
37#91450C2216yescomplemented
38#91450C2216yescomplemented
39C4×#1203C2216yescomplemented
40#91418C2213yescomplemented
41#91418C2216yescomplemented
42Dic5×D12C2211yescharacteristic
43#91413C22112yescomplemented
44D5×C4⋊Dic3C2213yescomplemented
45#91405C2216yescomplemented
46#91383C2216yescomplemented
47#91375C2216yescomplemented
48#41×D12—51nomaximal, Hall
49C22×#713—32no—
50C5×D4×Q8—31no—
51#66151—32no—
52#66060—33no—
53#66059—33no—
54#65964—36no—
55#65961—36no—
56#65911—31no—
57C4×#713D311yescharacteristic, complemented
58D4×D20—33no—
59C4×D4×D5—33no—
60C22×D3×D5C2316yes—
61C2×C3×C5×Q8C2311yescharacteristic
62#6821—28no—
63C2×D60C2313yes—
64C2×D60C2316yes—
65C2×D60C2316yes—
66C2×C4×D15C2316yes—
67C5×D3×Q8—28no—
68C2×C5×D12C2311yescharacteristic
69C2×C4×C5×D3C2316yes—
70C2×C5×Dic6C2316yes—
71C3×#713D418yescomplemented
72C2×C3×D20C2313yes—
73C2×C3×C4×D5C2313yes—
74C2×C3×C4×D5C2313yes—
75C2×C3×C4×D5C2313yes—
76C2×#1203C2316yes—
77C2×#1202C23112yes—
78C2×#1200C2316yes—
79C2×D3×Dic5C2312yes—
80C2×D5×Dic3C2316yes—
81D3×D20—224no—
82D5×D12—212no—
83C4×D3×D5—224no—
84#6773—224no—
85#6766—224no—
86C3×C5×C4⋊C4C2313yes—
87C3×C42×C5C2313yes—
88#6714C2316yes—
89C4⋊Dic15C2311yescharacteristic
90C5×(C2×D3)⋊C4C2316yes—
91C5×C4⋊Dic3C2313yes—
92C5×C4⋊Dic3C2316yes—
93C3×#685C2316yes—
94C3×C4⋊Dic5C2313yes—
95C3×C4×Dic5C2313yes—
96C3×C4×Dic5C2313yes—
97C3×C4×Dic5C2311yescharacteristic
98#6668C2316yes—
99#6667C23112yes—
100#6667C2316yes—
101(C2×D3)⋊Dic5C2312yes—
102C2×D3×#41—52no—
103C3×C4×#41—51no—
104#5577—51no—
105#5576—52no—
106Q8×D12D511yescharacteristic, complemented
107#5555—53no—
108#5554—56no—
109D4×D12—53no—
110#5524—56no—
111#5477—53no—
112C2×C4×D12—53no—
113C22×C5×Q8—32no—
114C2×#713—32no—
115C2×#713—36no—
116C2×#713—36no—
117C2×#713—616no—
118C2×#713C2×D311yescharacteristic
119C2×D4×D5—33no—
120C22×D20—36no—
121C22×C4×D5—36no—
122C5×C4⋊Q8—33no—
123C5×C22⋊Q8—36no—
124C4×C5×Q8C2×D311yescharacteristic, complemented
125C4×C5×D4—33no—
126#4093—36no—
127#4092—36no—
128Q8×Dic5C2×D311yescharacteristic, complemented
129D4×Dic5—31no—
130#4076—36no—
131C4×C22⋊D5—36no—
132#4041—36no—
133#4041—36no—
134#4041—36no—
135#4040—312no—
136#4039—33no—
137#4039—36no—
138#4039C2×D313yescomplemented
139#4038C2×D313yescomplemented
140D5×C4⋊C4—33no—
141#4028—312no—
142#4027—36no—
143D5×C22⋊C4—36no—
144#4020—33no—
145C4×D20—33no—
146C4×D20C2×D313yescomplemented
147C42×D5C2×D313yescomplemented
148D4×#41—151noSylow
149C22×D15C2416yes—
150C22×C5×D3C2412yes—
151C22×C3×D5C2413yes—
152C2×D3×D5—212no—
153C2×D3×D5—212no—
154C2×D3×D5—46no—
155C3×C5×Q8C2×D414yescomplemented
156C2×C3×C4×C5C2413yes—
157C2×C3×C4×C5C2413yes—
158C2×C3×C4×C5C2411yescharacteristic
159C2×Dic15C2412yes—
160D60—212no—
161D60—26no—
162D60—46no—
163C4×D15—212no—
164C2×C5×Dic3C2416yes—
165C5×D12#4114yescomplemented
166C4×C5×D3—212no—
167C5×Dic6—212no—
168C2×C3×Dic5C2411yescharacteristic
169C2×C3×Dic5C2413yes—
170C2×C3×Dic5C2411yescharacteristic
171C3×D20C2×D4112yescomplemented
172C3×C4×D5—26no—
173C3×C4×D5—43no—
174C3×C4×D5C2×D4112yescomplemented
175#1203—212no—
176#1202—224no—
177#1200—212no—
178D3×Dic5—24no—
179D5×Dic3—212no—
180C2×C3×#41—51no—
181D3×#41—1016no—
182C2×#239—52no—
183C2×D3×Q8C2×D512yescomplemented
184C2×#237—56no—
185C2×D3×D4—56no—
186C2×#235—56no—
187C22×D12—53no—
188C22×C4×D3—56no—
189C3×C4×Q8—51no—
190C3×C4×Q8C2×D511yescharacteristic, complemented
191C3×C4×D4—53no—
192C3×C4×D4—53no—
193C3×#117—53no—
194C2×C3×C42—53no—
195#930—56no—
196#930—56no—
197C2×(C2×D3)⋊C4—56no—
198C2×C4⋊Dic3—53no—
199#897—56no—
200#897C2×D516yescomplemented
201#895—56no—
202#895—56no—
203#886—512no—
204#882—512no—
205#875—56no—
206#874—53no—
207C4×D12—51no—
208C4×D12—56no—
209C4×D12—53no—
210C4×D12—56no—
211C4×D12—53no—
212C4×D12—56no—
213C4×D12C2×D513yes—
214#869C2×D513yescomplemented
215C23×D5—36no—
216C2×C5×Q8—36no—
217C2×C5×Q8—68no—
218C2×C5×Q8C22×D311yescharacteristic
219C2×C5×D4—31no—
220C22×C4×C5—36no—
221C2×C22⋊D5—36no—
222C22×Dic5—32no—
223#713—68no—
224#713—624no—
225#713—624no—
226#713D1218yesdirect product factor
227D4×D5—612no—
228C2×D20—312no—
229C2×D20—36no—
230C2×D20—33no—
231C2×D20—36no—
232C2×D20—624no—
233C2×D20C22×D313yes—
234C2×C4×D5—36no—
235C2×C4×D5—36no—
236C2×C4×D5—36no—
237C2×C4×D5—624no—
238C2×C4×D5C22×D313yes—
239C2×C4×D5C22×D313yes—
240C2×C4×D5C22×D313yes—
241C5×C4⋊C4—33no—
242C5×C4⋊C4—36no—
243C5×C4⋊C4C22×D313yes—
244C5×C22⋊C4—36no—
245C42×C5C22×D313yes—
246C22⋊Dic5—32no—
247#685—36no—
248#685—36no—
249#685—312no—
250#685C22×D316yes—
251C4⋊Dic5—31no—
252C4⋊Dic5C22×D313yes—
253#683—36no—
254C4×Dic5C22×D311yescharacteristic
255C4×Dic5C22×D313yes—
256C4×Dic5C22×D313yes—
257C22×#41—152no—
258#550—151no—
259D4×Q8—31no—
260#548—152no—
261#547—153no—
262#546—156no—
263D42—153no—
264#532—153no—
265#525—156no—
266C4×#41—51no—
267C2×C4×D4—153no—
268C22×C3×C5C2511yescharacteristic
269C2×D15—26no—
270C2×D15—26no—
271C2×D15—26no—
272C2×C5×D3—22no—
273C2×C5×D3—22no—
274C2×C5×D3C2×#4114yescomplemented
275C2×C3×D5—23no—
276C2×C3×D5—23no—
277C2×C3×D5C22×D416yes—
278D3×D5—424no—
279C3×C4×C5—23no—
280C3×C4×C5C22×D416yes—
281C3×C4×C5C2×#4112yescomplemented
282Dic15—22no—
283C3×Dic5—23no—
284C3×Dic5—21no—
285C3×Dic5C22×D412yes—
286C5×Dic3—26no—
287C23×D3—56no—
288C3×#41—58no—
289C2×C3×Q8C22×D511yescharacteristic
290C2×C3×D4—53no—
291C22×C3×C4—53no—
292C22×C3×C4—53no—
293C22×C3×C4—53no—
294C2×#67—512no—
295C22×Dic3—56no—
296#239—108no—
297D3×Q8—28no—
298#237—1024no—
299D3×D4—1024no—
300#235—1024no—
301C2×D12—56no—
302C2×D12—53no—
303C2×D12—56no—
304C2×D12—56no—
305C2×D12—1012no—
306C2×D12C22×D511yescharacteristic
307C2×C4×D3—52no—
308C2×C4×D3—56no—
309C2×C4×D3—56no—
310C2×C4×D3—1024no—
311C2×C4×D3C22×D516yes—
312C2×Dic6C22×D516yes—
313C3×C4⋊C4—53no—
314C3×C4⋊C4C22×D513yes—
315C3×C22⋊C4—56no—
316C3×C42—51no—
317C3×C42—53no—
318C3×C42—53no—
319C3×C42C22×D513yes—
320(C2×D3)⋊C4—52no—
321(C2×D3)⋊C4—56no—
322(C2×D3)⋊C4—56no—
323(C2×D3)⋊C4—512no—
324(C2×D3)⋊C4C22×D516yes—
325C4⋊Dic3—51no—
326C4⋊Dic3—56no—
327C4⋊Dic3C22×D513yes—
328C4⋊Dic3C22×D516yes—
329C23×C5—32no—
330C22×D5—36no—
331C22×D5—612no—
332C22×D5—612no—
333C22×D5—126no—
334C22×D5C23×D313yes—
335C5×Q8—612no—
336C5×Q8C2×D1214yescomplemented
337C5×D4—34no—
338C2×C4×C5—36no—
339C2×C4×C5—612no—
340C2×C4×C5C23×D313yes—
341C2×C4×C5C23×D313yes—
342C2×C4×C5C23×D311yescharacteristic
343C22⋊D5—612no—
344C2×Dic5—32no—
345C2×Dic5—64no—
346C2×Dic5C23×D311yescharacteristic
347C2×Dic5C23×D313yes—
348C2×Dic5C23×D311yescharacteristic
349D20—624no—
350D20—612no—
351D20—66no—
352D20—126no—
353D20C2×D12112yescomplemented
354C4×D5—26no—
355C4×D5—43no—
356C4×D5—612no—
357C4×D5—612no—
358C4×D5—612no—
359C4×D5C2×D12112yescomplemented
360C2×#41—51no—
361C2×#41—156no—
362C2×#41—156no—
363C2×#41—152no—
364C2×#41—3016no—
365C22×Q8—32no—
366C22×D4—156no—
367C22×D4—153no—
368C23×C4—156no—
369C4⋊Q8—33no—
370#127—153no—
371#124—156no—
372#123—1512no—
373C22⋊Q8—36no—
374C22⋊Q8—156no—
375#121—156no—
376#121—156no—
377#121—156no—
378#121—156no—
379#120—1512no—
380C4×Q8—51no—
381C4×Q8D3×D511yescharacteristic, complemented
382C4×D4—33no—
383C4×D4—53no—
384C4×D4—53no—
385C4×D4—156no—
386C4×D4—153no—
387C4×D4—156no—
388C4×D4—156no—
389C4×D4—151no—
390C4×D4—153no—
391#117—53no—
392C2×C4⋊C4—153no—
393C2×C22⋊C4—156no—
394C2×C42—53no—
395C2×C3×C5C23×D411yescharacteristic
396C2×C3×C5C22×#4111yescharacteristic
397C2×C3×C5#58511yescharacteristic
398D15—46no—
399C3×D5—26no—
400C5×D3—24no—
401C23×C3—53no—
402C22×D3—56no—
403C22×D3—1012no—
404C22×D3—1012no—
405C22×D3—206no—
406C22×D3C23×D512yes—
407C3×Q8D4×D514yescomplemented
408C3×D4—512no—
409C2×C3×C4—51no—
410C2×C3×C4—512no—
411C2×C3×C4—53no—
412C2×C3×C4—51no—
413C2×C3×C4—106no—
414C2×C3×C4—203no—
415C2×C3×C4C23×D513yes—
416C2×C3×C4C23×D513yes—
417C2×C3×C4C23×D511yescharacteristic
418#67—1024no—
419C2×Dic3—52no—
420C2×Dic3—1012no—
421C2×Dic3C23×D516yes—
422D12—1012no—
423D12—1012no—
424D12—106no—
425D12—206no—
426D12#71314yesdirect product factor
427C4×D3—212no—
428C4×D3—1012no—
429C4×D3—104no—
430C4×D3—1012no—
431Dic6—212no—
432C22×C5—34no—
433C22×C5—62no—
434C22×C5—62no—
435C22×C5C24×D311yescharacteristic
436C2×D5—23no—
437C2×D5—23no—
438C2×D5—66no—
439C2×D5—66no—
440C2×D5—66no—
441C2×D5—1224no—
442C2×D5C22×D1216yes—
443C4×C5—23no—
444C4×C5—66no—
445C4×C5C22×D1216yes—
446C4×C5D3×#4112yescomplemented
447Dic5—23no—
448Dic5—21no—
449Dic5—62no—
450Dic5C22×D1212yes—
451C24—156no—
452#41—58no—
453#41—3024no—
454#41—3024no—
455#41—308no—
456C2×Q8—36no—
457C2×Q8—68no—
458C2×Q8C2×D3×D511yescharacteristic
459C2×D4—31no—
460C2×D4—53no—
461C2×D4—1512no—
462C2×D4—156no—
463C2×D4—153no—
464C2×D4—156no—
465C2×D4—156no—
466C2×D4—3024no—
467C2×D4—3012no—
468C22×C4—36no—
469C22×C4—53no—
470C22×C4—53no—
471C22×C4—53no—
472C22×C4—156no—
473C22×C4—156no—
474C22×C4—152no—
475C22×C4—156no—
476C22×C4—3024no—
477C4⋊C4—33no—
478C4⋊C4—36no—
479C4⋊C4—53no—
480C4⋊C4—156no—
481C4⋊C4—151no—
482C4⋊C4C2×D3×D513yes—
483C22⋊C4—36no—
484C22⋊C4—56no—
485C22⋊C4—156no—
486C22⋊C4—1512no—
487C22⋊C4—152no—
488C22⋊C4—156no—
489C42—51no—
490C42—53no—
491C42—53no—
492C42C2×D3×D513yes—
493C3×C5D4×#4111yescharacteristic, complemented, Hall
494C22×C3—56no—
495C22×C3—103no—
496C22×C3—103no—
497C22×C3C24×D511yescharacteristic
498C2×D3—22no—
499C2×D3—22no—
500C2×D3—106no—
501C2×D3—106no—
502C2×D3—106no—
503C2×D3—2024no—
504C2×D3C2×#71314yescomplemented
505C3×C4—23no—
506C3×C4—52no—
507C3×C4—103no—
508C3×C4—101no—
509C3×C4C2×D4×D516yes—
510C3×C4C2×#71312yescomplemented
511Dic3—26no—
512Dic3—102no—
513C2×C5—64no—
514C2×C5C23×D1211yescharacteristic
515C2×C5C2×D3×#4111yescharacteristic
516C2×C5#596411yescharacteristic
517D5—26no—
518D5—126no—
519C23—32no—
520C23—53no—
521C23—156no—
522C23—3012no—
523C23—3012no—
524C23—606no—
525Q8—612no—
526Q8D5×D1214yescomplemented
527D4—34no—
528D4—512no—
529D4—3024no—
530D4—3012no—
531D4—3012no—
532D4—306no—
533D4—606no—
534C2×C4—36no—
535C2×C4—51no—
536C2×C4—512no—
537C2×C4—51no—
538C2×C4—53no—
539C2×C4—612no—
540C2×C4—106no—
541C2×C4—152no—
542C2×C4—203no—
543C2×C4—3012no—
544C2×C4—304no—
545C2×C4—3012no—
546C2×C4—3012no—
547C2×C4C22×D3×D513yes—
548C2×C4C22×D3×D513yes—
549C2×C4C22×D3×D511yescharacteristic
550C2×C3—106no—
551C2×C3C22×D4×D511yescharacteristic
552C2×C3C22×#71311yescharacteristic
553C2×C3#6628711yescharacteristic
554D3—24no—
555D3—206no—
556C5#41×D1211yescharacteristic, complemented, Sylow
557C22—34no—
558C22—56no—
559C22—62no—
560C22—62no—
561C22—103no—
562C22—103no—
563C22—306no—
564C22—306no—
565C22—306no—
566C22—6024no—
567C22C23×D3×D511yescharacteristic
568C4—23no—
569C4—52no—
570C4—66no—
571C4—101no—
572C4—103no—
573C4—302no—
574C4C2×D5×D1216yes—
575C4D3×#71312yescomplemented
576C3D4×#71311yescharacteristic, complemented, Sylow
577C2—64no—
578C2—106no—
579C2—606no—
580C2C22×D5×D1211yescharacteristic
581C2C2×D3×#71311yescharacteristic
582C2#1175706011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5D4×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#713C2semidirect
2. #11756336C2semidirect
3. C5×Q8×D12C2semidirect
4. C3×C4×#713C2semidirect
5. #11755131C2semidirect
6. #11753876C2semidirect
7. #11753874C2semidirect
8. D12×D20C2semidirect
9. C4×D5×D12C2semidirect
10. #11752674C2semidirect
11. #11752533C2semidirect
13. C2×#6821C22semidirect
14. C2×C5×D3×Q8C22semidirect
17. C2×D3×D20C22semidirect
19. C2×C4×D3×D5C22semidirect
20. C2×#6773C22semidirect
21. C2×#6766C22semidirect
22. C3×C4×C5×Q8C22semidirect
23. #91784C22semidirect
24. #91763C22semidirect
25. C4×D60C22semidirect
26. C5×#897C22semidirect
28. C5×#869C22semidirect
29. C3×Q8×Dic5C22semidirect
30. C3×#4039C22semidirect
31. C3×#4038C22semidirect
32. C3×C4×D20C22semidirect
33. C3×C42×D5C22semidirect
34. #91476C22semidirect
35. D5×(C2×D3)⋊C4C22semidirect
36. #91460C22semidirect
37. #91450C22semidirect
38. #91450C22semidirect
39. C4×#1203C22semidirect
40. #91418C22semidirect
41. #91418C22semidirect
43. #91413C22semidirect
44. D5×C4⋊Dic3C22semidirect
45. #91405C22semidirect
46. #91383C22semidirect
47. #91375C22semidirect
57. C4×#713D3semidirect
71. C3×#713D4semidirect
106. Q8×D12D5semidirect
124. C4×C5×Q8C2×D3semidirect
128. Q8×Dic5C2×D3semidirect
138. #4039C2×D3semidirect
139. #4038C2×D3semidirect
146. C4×D20C2×D3semidirect
147. C42×D5C2×D3semidirect
155. C3×C5×Q8C2×D4semidirect
165. C5×D12#41semidirect
171. C3×D20C2×D4semidirect
174. C3×C4×D5C2×D4semidirect
183. C2×D3×Q8C2×D5semidirect
190. C3×C4×Q8C2×D5semidirect
200. #897C2×D5semidirect
214. #869C2×D5semidirect
226. #713D12direct (N × H)
274. C2×C5×D3C2×#41semidirect
281. C3×C4×C5C2×#41semidirect
336. C5×Q8C2×D12semidirect
353. D20C2×D12semidirect
359. C4×D5C2×D12semidirect
381. C4×Q8D3×D5semidirect
407. C3×Q8D4×D5semidirect
426. D12#713direct (N × H)
446. C4×C5D3×#41semidirect
493. C3×C5D4×#41semidirect
504. C2×D3C2×#713semidirect
510. C3×C4C2×#713semidirect
526. Q8D5×D12semidirect
556. C5#41×D12semidirect
575. C4D3×#713semidirect
576. C3D4×#713semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7132
#117563362
C5×Q8×D122
C3×C4×#7132
#117551312
#117538762
#117538742
D12×D202
C4×D5×D122
#117526742
#117525332
D4×#7133
#41×D125