Finite Group Databasebeta

← #560×#6923 #30624907

Subgroups — #560×#6923 #30624907

Order 15616.

2568 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462366C212yesmaximal, complemented
2#21462363C211yesmaximal, characteristic, complemented
3#21462360C216yesmaximal, complemented
4#21462359C213yesmaximal, complemented
5#21462358C213yesmaximal, complemented
6#127×#6923C211yesmaximal, characteristic, complemented
7#126×#6923C212yesmaximal, complemented
8#123×#6923C213yesmaximal, complemented
9#121×#6923C216yesmaximal, complemented
10#120×#6923C213yesmaximal, complemented
11#560×D61C211yesmaximal, characteristic
12C24×#6923C2211yescharacteristic
13C2×D4×#6923C2216yes—
14C2×D4×#6923C2213yes—
15C2×D4×#6923C2213yescomplemented
16C22×C4×#6923C2213yescomplemented
17#16840714C2216yes—
18#16840714C2213yes—
19#16840714C2213yescomplemented
20#16840713C2216yescomplemented
21#16840712C2216yes—
22#16840712C2216yes—
23#16840712C2216yes—
24#16840712C2216yescomplemented
25#16840711C2216yescomplemented
26#16840711C2216yescomplemented
27#16840710C2213yes—
28#16840710C2216yes—
29#16840710C2216yes—
30#16840710C2213yes—
31#16840710C2216yescomplemented
32#16840709C2213yes—
33#16840709C2216yes—
34#16840709C2213yescomplemented
35#16840708C2211yescharacteristic, complemented
36#16840707C2212yescomplemented
37#16840705C2213yescomplemented
38#16840704C2216yescomplemented
39#16840703C2213yes—
40C4⋊C4×#6923C2216yescomplemented
41C22⋊C4×#6923C2216yes—
42C22⋊C4×#6923C2213yes—
43C22⋊C4×#6923C2213yescomplemented
44C42×#6923C2211yescharacteristic, complemented
45#16840503C412yescomplemented
46#16840502C413yescomplemented
47#16840501C413yescomplemented
48#16840500C416yescomplemented
49#16840499C411yescharacteristic, complemented
50#127×D61C2211yescharacteristic
51#126×D61C2212yes—
52#123×D61C2213yes—
53#121×D61C2216yes—
54#120×D61C2213yes—
55C61×#560C411yescharacteristic, complemented
56C23×#6923—46no—
57C23×#6923C2313yes—
58C23×#6923C2312yes—
59C23×#6923C2311yescharacteristic
60C23×#6923C2311yescharacteristic
61C23×#6923C2312yes—
62C23×#6923C2313yes—
63D4×#6923—412no—
64D4×#6923—46no—
65D4×#6923—46no—
66C2×C4⋊#6923C2316yes—
67C2×C4⋊#6923C2316yes—
68C2×C4⋊#6923C2313yes—
69C2×C4⋊#6923C2313yes—
70C2×C22⋊#6923C2316yes—
71C2×C22⋊#6923C2316yes—
72C2×C22⋊#6923C2313yes—
73C2×C22⋊#6923C2313yes—
74C2×C22⋊#6923C2316yes—
75C2×C22⋊#6923C2313yes—
76C2×C22⋊#6923C2313yes—
77C2×C22⋊#6923C2316yes—
78C2×C4×#6923—46no—
79C2×C4×#6923C2316yes—
80C2×C4×#6923C2313yes—
81C2×C4×#6923C2313yes—
82C2×C4×#6923C2316yes—
83(C2×#6923)⋊C4C2316yes—
84(C2×#6923)⋊C4C2316yes—
85(C2×#6923)⋊C4C2316yes—
86(C2×#6923)⋊C4C2316yes—
87(C2×#6923)⋊C4C2316yes—
88(C2×#6923)⋊C4C2316yes—
89C24×D61C2311yescharacteristic
90C2×D4×D61C2316yes—
91C2×D4×D61C2313yes—
92C2×D4×D61C2313yes—
93C22×C4×D61C2313yes—
94#14519774C2×C411yescharacteristic, complemented
95#14519773C2×C413yescomplemented
96#14519773C2×C413yescomplemented
97#14519772C2×C416yescomplemented
98#14519771C2×C412yescomplemented
99#14519770C2×C416yescomplemented
100#14519762C2×C416yescomplemented
101#14519761C2×C413yescomplemented
102#14519760C2×C413yescomplemented
103#14519759C2×C416yescomplemented
104#14519758C2×C413yescomplemented
105#14519752C2×C416yescomplemented
106#14519751C2×C416yescomplemented
107#14519750C2×C416yescomplemented
108#14519750C2×C416yescomplemented
109#14519749C2×C416yescomplemented
110#14519749C2×C416yescomplemented
111#14519748C2×C416yescomplemented
112#14519747C2×C416yescomplemented
113#14519747C2×C413yescomplemented
114#14519746C2×C413yescomplemented
115#14519745C2×C413yescomplemented
116#14519745C2×C416yescomplemented
117C4⋊C4×D61C2316yes—
118C22⋊C4×D61C2316yes—
119C22⋊C4×D61C2313yes—
120C22⋊C4×D61C2313yes—
121C42×D61C2311yescharacteristic
122#127×C61C2×C411yescharacteristic, complemented
123#126×C61C2×C412yescomplemented
124#123×C61C2×C413yescomplemented
125#121×C61C2×C416yescomplemented
126#120×C61C2×C413yescomplemented
127C24×C61C22×C411yescharacteristic
128C23×D61—43no—
129C23×D61—43no—
130C23×D61C22×C411yescharacteristic
131C23×D61C22×C412yes—
132C23×D61C2413yes—
133C23×D61C2412yes—
134C23×D61C2411yescharacteristic
135C22×#6923—26no—
136C22×#6923—212no—
137C22×#6923—212no—
138C22×#6923—26no—
139C22×#6923—43no—
140C22×#6923—43no—
141C22×#6923—46no—
142C22×#6923—46no—
143C22×#6923—416no—
144C22×#6923C2416yes—
145C22×#6923C2412yes—
146C22×#6923C2411yescharacteristic
147C22×#6923C2413yes—
148C22×#6923C2413yes—
149C22×#6923C2411yescharacteristic
150C2×D4×C61C22×C416yes—
151C2×D4×C61C22×C413yes—
152C2×D4×C61C22×C413yescomplemented
153C22×C4×C61C22×C413yescomplemented
154C2×C22⋊D61C22×C416yes—
155C2×C22⋊D61C22×C413yes—
156C2×C22⋊D61C22×C416yes—
157C2×C22⋊D61C22×C413yes—
158C2×C22⋊D61C22×C416yescomplemented
159C22×Dic61C22×C413yescomplemented
160D4×D61—43no—
161D4×D61—43no—
162D4×D61—46no—
163D4×D61—46no—
164D4×D61—43no—
165D4×D61—43no—
166C2×D244C22×C416yes—
167C2×D244C22×C413yes—
168C2×D244C22×C413yescomplemented
169C2×C4×D61—43no—
170C2×C4×D61—43no—
171C2×C4×D61C22×C416yescomplemented
172C2×C4×D61C2416yes—
173C2×C4×D61C2413yes—
174C22⋊#6923—46no—
175C22⋊#6923—43no—
176C22⋊#6923—43no—
177C22⋊#6923—46no—
178C22⋊#6923—46no—
179C22⋊#6923—43no—
180C22⋊#6923—46no—
181C22⋊#6923—43no—
182C4⋊#6923—46no—
183C4⋊#6923—46no—
184C4⋊#6923—43no—
185C4⋊#6923—43no—
186C4×#6923—212no—
187C4×#6923—26no—
188C4×#6923—46no—
189C4×#6923—43no—
190C4⋊C4×C61C22×C416yescomplemented
191C22⋊C4×C61C22×C416yes—
192C22⋊C4×C61C22×C413yes—
193C22⋊C4×C61C22×C413yescomplemented
194C42×C61C22×C411yescharacteristic, complemented
195C22⋊Dic61C22×C416yes—
196C22⋊Dic61C22×C413yes—
197C22⋊Dic61C22×C413yescomplemented
198#11758198C22×C416yes—
199#11758198C22×C416yes—
200#11758198C22×C416yes—
201#11758198C22×C416yescomplemented
202C4⋊Dic61C22×C416yescomplemented
203#11758196C22×C416yescomplemented
204#11758196C22×C416yescomplemented
205C4×Dic61C22×C413yescomplemented
206C23×C61—43no—
207C23×C61C23×C412yes—
208C23×C61C23×C411yescharacteristic
209C23×C61C23×C413yes—
210C22×D61—26no—
211C22×D61—23no—
212C22×D61—26no—
213C22×D61—23no—
214C22×D61—23no—
215C22×D61—26no—
216C22×D61—23no—
217C22×D61—26no—
218C22×D61—43no—
219C22×D61—46no—
220C22×D61—44no—
221C22×D61—412no—
222C22×D61C23×C412yes—
223C22×D61C23×C411yescharacteristic
224C22×D61C23×C413yes—
225C22×D61C2511yescharacteristic
226C2×#6923—26no—
227C2×#6923—23no—
228C2×#6923—23no—
229C2×#6923—26no—
230C2×#6923—26no—
231C2×#6923—23no—
232C2×#6923—26no—
233C2×#6923—26no—
234C2×#6923—26no—
235C2×#6923—412no—
236C2×#6923—44no—
237C2×#6923—48no—
238C2×#6923—412no—
239C2×#6923—48no—
240C2×#6923—44no—
241C2×#6923H(5,𝔽2)16yes—
242D4×C61—46no—
243D4×C61—43no—
244D4×C61—43no—
245C2×C4×C61—43no—
246C2×C4×C61C23×C413yes—
247C2×C4×C61C23×C416yes—
248C22⋊D61—46no—
249C22⋊D61—46no—
250C22⋊D61—43no—
251C22⋊D61—43no—
252C22⋊D61—46no—
253C2×Dic61—43no—
254C2×Dic61C23×C413yes—
255C2×Dic61C23×C416yes—
256D244—46no—
257D244—43no—
258D244—43no—
259C4×D61—26no—
260C4×D61—23no—
261C4×D61—23no—
262C4×D61—26no—
263C4×D61—46no—
264C4×#560—611nomaximal, Sylow
265C22×C61—23no—
266C22×C61—26no—
267C22×C61—26no—
268C22×C61—23no—
269C22×C61—44no—
270C22×C61C24×C411yescharacteristic
271C2×D61—23no—
272C2×D61—26no—
273C2×D61—26no—
274C2×D61—23no—
275C2×D61—44no—
276C2×D61—48no—
277C2×D61—42no—
278C2×D61—41no—
279C2×D61—43no—
280C2×D61—43no—
281C2×D61—46no—
282C2×D61—46no—
283C2×D61—43no—
284C2×D61C2×H(5,𝔽2)13yes—
285C2×D61#58513yes—
286#6923—43no—
287#6923—42no—
288#6923—41no—
289#6923—43no—
290#6923—46no—
291#6923#56014yesdirect product factor
292C4×C61—26no—
293C4×C61—23no—
294Dic61—26no—
295Dic61—23no—
296C2×#560—611no—
297#2383—612no—
298#2380—611no—
299#2377—616no—
300#2376—613no—
301#2375—613no—
302C4×#127—611no—
303C4×#126—612no—
304C4×#123—613no—
305C4×#121—616no—
306C4×#120—613no—
307C2×C61—42no—
308C2×C61—41no—
309C2×C61—43no—
310C2×C61C4×H(5,𝔽2)13yes—
311D61—43no—
312D61—42no—
313D61—41no—
314D61C2×#56011yescharacteristic
315D61#352913yes—
316C24×C4—611no—
317#560—611no—
318#560—612no—
319#560—613no—
320#560—616no—
321#560—613no—
322#560#692311yescharacteristic, direct product factor
323C2×#127—611no—
324C2×#126—612no—
325C2×#123—613no—
326C2×#121—616no—
327C2×#120—613no—
328C2×C4×D4—613no—
329C2×C4×D4—613no—
330C2×C4×D4—616no—
331C22×C42—613no—
332#390—613no—
333#390—613no—
334#390—616no—
335#389—616no—
336#388—616no—
337#388—616no—
338#388—616no—
339#388—616no—
340#387—616no—
341#387—616no—
342#386—616no—
343#386—613no—
344#386—613no—
345#386—616no—
346#386—616no—
347#385—613no—
348#385—616no—
349#385—613no—
350#384—611no—
351#383—612no—
352#381—613no—
353#380—616no—
354#379—613no—
355C4×C4⋊C4—616no—
356C4×C22⋊C4—616no—
357C4×C22⋊C4—613no—
358C4×C22⋊C4—613no—
359C43—611no—
360C61C4×#56011yescharacteristic, complemented, Sylow
361C25—611no—
362C22×D4—616no—
363C22×D4—613no—
364C22×D4—613no—
365C23×C4—613no—
366C23×C4—613no—
367C23×C4—611no—
368C23×C4—612no—
369C23×C4—611no—
370C23×C4—612no—
371C23×C4—613no—
372C23×C4—2446no—
373#127—613no—
374#127—613no—
375#127—611no—
376#127C2×#692311yescharacteristic, complemented
377#126—616no—
378#126—616no—
379#126—612no—
380#126C2×#692312yescomplemented
381#123—613no—
382#123—613no—
383#123—616no—
384#123—616no—
385#123—613no—
386#123C2×#692313yescomplemented
387#121—616no—
388#121—616no—
389#121—616no—
390#121—616no—
391#121—616no—
392#121—616no—
393#121—616no—
394#121C2×#692316yescomplemented
395#120—613no—
396#120—616no—
397#120—613no—
398#120—613no—
399#120—616no—
400#120C2×#692313yescomplemented
401C4×D4—24412no—
402C4×D4—2446no—
403C4×D4—2446no—
404C2×C4⋊C4—616no—
405C2×C4⋊C4—616no—
406C2×C4⋊C4—613no—
407C2×C4⋊C4—613no—
408C2×C4⋊C4—616no—
409C2×C22⋊C4—616no—
410C2×C22⋊C4—613no—
411C2×C22⋊C4—613no—
412C2×C22⋊C4—616no—
413C2×C22⋊C4—613no—
414C2×C22⋊C4—616no—
415C2×C22⋊C4—616no—
416C2×C22⋊C4—613no—
417C2×C22⋊C4—613no—
418C2×C22⋊C4—616no—
419C2×C22⋊C4—613no—
420C2×C42—611no—
421C2×C42—613no—
422C2×C42—616no—
423C2×C42—613no—
424C2×C42—616no—
425C2×C42—2446no—
426#95—616no—
427#95—616no—
428#95—616no—
429#95—616no—
430#95—616no—
431#95—616no—
432C24—612no—
433C24—611no—
434C24—613no—
435C24—611no—
436C24—612no—
437C24—2443no—
438C24—2443no—
439C24C22×#692311yescharacteristic
440C2×D4—616no—
441C2×D4—616no—
442C2×D4—613no—
443C2×D4—613no—
444C2×D4—616no—
445C2×D4—616no—
446C2×D4—613no—
447C2×D4—613no—
448C2×D4—2446no—
449C2×D4—2443no—
450C2×D4—2443no—
451C2×D4—2443no—
452C2×D4—2443no—
453C2×D4—2446no—
454C2×D4C22×#692316yes—
455C2×D4C22×#692313yes—
456C2×D4C22×#692313yescomplemented
457C22×C4—611no—
458C22×C4—613no—
459C22×C4—613no—
460C22×C4—616no—
461C22×C4—616no—
462C22×C4—616no—
463C22×C4—612no—
464C22×C4—611no—
465C22×C4—613no—
466C22×C4—613no—
467C22×C4—1226no—
468C22×C4—12212no—
469C22×C4—12212no—
470C22×C4—1226no—
471C22×C4—2443no—
472C22×C4—2443no—
473C22×C4—2443no—
474C22×C4—2443no—
475C22×C4—2446no—
476C22×C4—2446no—
477C22×C4—24416no—
478C22×C4C22×#692313yescomplemented
479C4⋊C4—616no—
480C4⋊C4—616no—
481C4⋊C4—616no—
482C4⋊C4—2446no—
483C4⋊C4—2443no—
484C4⋊C4—2443no—
485C4⋊C4—2446no—
486C4⋊C4C22×#692316yescomplemented
487C22⋊C4—616no—
488C22⋊C4—613no—
489C22⋊C4—613no—
490C22⋊C4—616no—
491C22⋊C4—616no—
492C22⋊C4—616no—
493C22⋊C4—616no—
494C22⋊C4—2446no—
495C22⋊C4—2446no—
496C22⋊C4—2443no—
497C22⋊C4—2446no—
498C22⋊C4—2443no—
499C22⋊C4—2446no—
500C22⋊C4—2443no—
501C22⋊C4—2443no—
502C22⋊C4C22×#692316yes—
503C22⋊C4C22×#692313yes—
504C22⋊C4C22×#692313yescomplemented
505C42—613no—
506C42—12212no—
507C42—1226no—
508C42—2446no—
509C42—2443no—
510C42C22×#692311yescharacteristic, complemented
511C23—43no—
512C23—611no—
513C23—612no—
514C23—611no—
515C23—613no—
516C23—1226no—
517C23—1223no—
518C23—1226no—
519C23—1223no—
520C23—1223no—
521C23—1226no—
522C23—1223no—
523C23—1226no—
524C23—2446no—
525C23—2443no—
526C23—2444no—
527C23—24412no—
528C23C23×#692312yes—
529C23C23×#692311yescharacteristic
530C23C23×#692313yes—
531D4—46no—
532D4—43no—
533D4—43no—
534D4—2446no—
535D4—2443no—
536D4—2443no—
537D4—2446no—
538D4—2446no—
539D4—2443no—
540D4—2446no—
541D4—2443no—
542C2×C4—43no—
543C2×C4—616no—
544C2×C4—613no—
545C2×C4—616no—
546C2×C4—1226no—
547C2×C4—1223no—
548C2×C4—1223no—
549C2×C4—1226no—
550C2×C4—1226no—
551C2×C4—1223no—
552C2×C4—1223no—
553C2×C4—1226no—
554C2×C4—1226no—
555C2×C4—1226no—
556C2×C4—1226no—
557C2×C4—1223no—
558C2×C4—1226no—
559C2×C4—2446no—
560C2×C4—24412no—
561C2×C4—2448no—
562C2×C4—2444no—
563C2×C4—2443no—
564C2×C4—24412no—
565C2×C4—2444no—
566C2×C4—2448no—
567C2×C4C23×#692313yes—
568C2×C4C23×#692316yes—
569C22—23no—
570C22—26no—
571C22—26no—
572C22—23no—
573C22—44no—
574C22—613no—
575C22—613no—
576C22—1223no—
577C22—1226no—
578C22—1226no—
579C22—1223no—
580C22—2442no—
581C22—2441no—
582C22—2443no—
583C22—2443no—
584C22—2446no—
585C22—2446no—
586C22—2443no—
587C22—2448no—
588C22—2444no—
589C22C24×#692311yescharacteristic
590C4—26no—
591C4—23no—
592C4—614no—
593C4—1226no—
594C4—1223no—
595C4—2442no—
596C4—2441no—
597C4—2443no—
598C4—2446no—
599C4—2443no—
600C2—42no—
601C2—41no—
602C2—43no—
603C2—611no—
604C2—613no—
605C2—2442no—
606C2—2441no—
607C2—2443no—
608C2H(5,𝔽2)×#692313yes—
subgroupG/H
center, FrattiniC22C24×#6923
commutator, socleC22×C61C24×C4
FittingC61×#560C4
prime radical#560×D61C2
cosocleC22×D61C25
hypercenter#560#6923
hypocenterC61C4×#560
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #560

Complements

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

NH ≅ G/Ntype
1. #21462366C2semidirect
2. #21462363C2semidirect
3. #21462360C2semidirect
4. #21462359C2semidirect
5. #21462358C2semidirect
6. #127×#6923C2semidirect
7. #126×#6923C2semidirect
8. #123×#6923C2semidirect
9. #121×#6923C2semidirect
10. #120×#6923C2semidirect
15. C2×D4×#6923C22semidirect
16. C22×C4×#6923C22semidirect
19. #16840714C22semidirect
20. #16840713C22semidirect
24. #16840712C22semidirect
25. #16840711C22semidirect
26. #16840711C22semidirect
31. #16840710C22semidirect
34. #16840709C22semidirect
35. #16840708C22semidirect
36. #16840707C22semidirect
37. #16840705C22semidirect
38. #16840704C22semidirect
40. C4⋊C4×#6923C22semidirect
43. C22⋊C4×#6923C22semidirect
44. C42×#6923C22semidirect
45. #16840503C4semidirect
46. #16840502C4semidirect
47. #16840501C4semidirect
48. #16840500C4semidirect
49. #16840499C4semidirect
55. C61×#560C4semidirect
94. #14519774C2×C4semidirect
95. #14519773C2×C4semidirect
96. #14519773C2×C4semidirect
97. #14519772C2×C4semidirect
98. #14519771C2×C4semidirect
99. #14519770C2×C4semidirect
100. #14519762C2×C4semidirect
101. #14519761C2×C4semidirect
102. #14519760C2×C4semidirect
103. #14519759C2×C4semidirect
104. #14519758C2×C4semidirect
105. #14519752C2×C4semidirect
106. #14519751C2×C4semidirect
107. #14519750C2×C4semidirect
108. #14519750C2×C4semidirect
109. #14519749C2×C4semidirect
110. #14519749C2×C4semidirect
111. #14519748C2×C4semidirect
112. #14519747C2×C4semidirect
113. #14519747C2×C4semidirect
114. #14519746C2×C4semidirect
115. #14519745C2×C4semidirect
116. #14519745C2×C4semidirect
122. #127×C61C2×C4semidirect
123. #126×C61C2×C4semidirect
124. #123×C61C2×C4semidirect
125. #121×C61C2×C4semidirect
126. #120×C61C2×C4semidirect
152. C2×D4×C61C22×C4semidirect
153. C22×C4×C61C22×C4semidirect
158. C2×C22⋊D61C22×C4semidirect
159. C22×Dic61C22×C4semidirect
168. C2×D244C22×C4semidirect
171. C2×C4×D61C22×C4semidirect
190. C4⋊C4×C61C22×C4semidirect
193. C22⋊C4×C61C22×C4semidirect
194. C42×C61C22×C4semidirect
197. C22⋊Dic61C22×C4semidirect
201. #11758198C22×C4semidirect
202. C4⋊Dic61C22×C4semidirect
203. #11758196C22×C4semidirect
204. #11758196C22×C4semidirect
205. C4×Dic61C22×C4semidirect
291. #6923#560direct (N × H)
322. #560#6923direct (N × H)
360. C61C4×#560semidirect
376. #127C2×#6923semidirect
380. #126C2×#6923semidirect
386. #123C2×#6923semidirect
394. #121C2×#6923semidirect
400. #120C2×#6923semidirect
456. C2×D4C22×#6923semidirect
478. C22×C4C22×#6923semidirect
486. C4⋊C4C22×#6923semidirect
504. C22⋊C4C22×#6923semidirect
510. C42C22×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623662
#214623632
#214623602
#214623592
#214623582
#127×#69232
#126×#69232
#123×#69232
#121×#69232
#120×#69232
#560×D612
C4×#56061