Finite Group Databasebeta

← #560×#64408 #34030878

Subgroups — #560×#64408 #34030878

Order 18688.

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#22626478C212yesmaximal, complemented
2#22626475C211yesmaximal, characteristic, complemented
3#22626472C216yesmaximal, complemented
4#22626471C213yesmaximal, complemented
5#22626470C213yesmaximal, complemented
6#127×#64408C211yesmaximal, characteristic, complemented
7#126×#64408C212yesmaximal, complemented
8#123×#64408C213yesmaximal, complemented
9#121×#64408C216yesmaximal, complemented
10#120×#64408C213yesmaximal, complemented
11#560×D73C211yesmaximal, characteristic
12C24×#64408C2211yescharacteristic
13C2×D4×#64408C2216yes—
14C2×D4×#64408C2213yes—
15C2×D4×#64408C2213yescomplemented
16C22×C4×#64408C2213yescomplemented
17#17989539C2216yes—
18#17989539C2213yes—
19#17989539C2213yescomplemented
20#17989538C2216yescomplemented
21#17989537C2216yes—
22#17989537C2216yes—
23#17989537C2216yes—
24#17989537C2216yescomplemented
25#17989536C2216yescomplemented
26#17989536C2216yescomplemented
27#17989535C2213yes—
28#17989535C2216yes—
29#17989535C2216yes—
30#17989535C2213yes—
31#17989535C2216yescomplemented
32#17989534C2213yes—
33#17989534C2216yes—
34#17989534C2213yescomplemented
35#17989533C2211yescharacteristic, complemented
36#17989532C2212yescomplemented
37#17989530C2213yescomplemented
38#17989529C2216yescomplemented
39#17989528C2213yes—
40C4⋊C4×#64408C2216yescomplemented
41C22⋊C4×#64408C2216yes—
42C22⋊C4×#64408C2213yes—
43C22⋊C4×#64408C2213yescomplemented
44C42×#64408C2211yescharacteristic, complemented
45#17989328C412yescomplemented
46#17989327C413yescomplemented
47#17989326C413yescomplemented
48#17989325C416yescomplemented
49#17989324C411yescharacteristic, complemented
50#127×D73C2211yescharacteristic
51#126×D73C2212yes—
52#123×D73C2213yes—
53#121×D73C2216yes—
54#120×D73C2213yes—
55#560×C73C411yescharacteristic, complemented
56C23×#64408—46no—
57C23×#64408C2313yes—
58C23×#64408C2312yes—
59C23×#64408C2311yescharacteristic
60C23×#64408C2313yes—
61C23×#64408C2311yescharacteristic
62C23×#64408C2312yes—
63D4×#64408—412no—
64D4×#64408—46no—
65D4×#64408—46no—
66C2×C4⋊#64408C2316yes—
67C2×C4⋊#64408C2313yes—
68C2×C4⋊#64408C2313yes—
69C2×C4⋊#64408C2316yes—
70C2×C22⋊#64408C2316yes—
71C2×C22⋊#64408C2313yes—
72C2×C22⋊#64408C2316yes—
73C2×C22⋊#64408C2313yes—
74C2×C22⋊#64408C2316yes—
75C2×C22⋊#64408C2313yes—
76C2×C22⋊#64408C2316yes—
77C2×C22⋊#64408C2313yes—
78C2×C4×#64408—46no—
79C2×C4×#64408C2316yes—
80C2×C4×#64408C2313yes—
81C2×C4×#64408C2316yes—
82C2×C4×#64408C2313yes—
83(C2×#64408)⋊C4C2316yes—
84(C2×#64408)⋊C4C2316yes—
85(C2×#64408)⋊C4C2316yes—
86(C2×#64408)⋊C4C2316yes—
87(C2×#64408)⋊C4C2316yes—
88(C2×#64408)⋊C4C2316yes—
89C24×D73C2311yescharacteristic
90C2×D4×D73C2313yes—
91C2×D4×D73C2316yes—
92C2×D4×D73C2313yes—
93C22×C4×D73C2313yes—
94#14556588C2×C411yescharacteristic, complemented
95#14556587C2×C413yescomplemented
96#14556587C2×C413yescomplemented
97#14556586C2×C416yescomplemented
98#14556585C2×C412yescomplemented
99#14556584C2×C416yescomplemented
100#14556576C2×C416yescomplemented
101#14556575C2×C413yescomplemented
102#14556574C2×C413yescomplemented
103#14556573C2×C416yescomplemented
104#14556572C2×C413yescomplemented
105#14556566C2×C416yescomplemented
106#14556565C2×C416yescomplemented
107#14556564C2×C416yescomplemented
108#14556564C2×C416yescomplemented
109#14556563C2×C416yescomplemented
110#14556563C2×C416yescomplemented
111#14556562C2×C416yescomplemented
112#14556561C2×C416yescomplemented
113#14556561C2×C413yescomplemented
114#14556560C2×C413yescomplemented
115#14556559C2×C413yescomplemented
116#14556559C2×C416yescomplemented
117C4⋊C4×D73C2316yes—
118C22⋊C4×D73C2316yes—
119C22⋊C4×D73C2313yes—
120C22⋊C4×D73C2313yes—
121C42×D73C2311yescharacteristic
122#127×C73C2×C411yescharacteristic, complemented
123#126×C73C2×C412yescomplemented
124#123×C73C2×C413yescomplemented
125#121×C73C2×C416yescomplemented
126#120×C73C2×C413yescomplemented
127C22×#64408—212no—
128C22×#64408—26no—
129C22×#64408—26no—
130C22×#64408—212no—
131C22×#64408—43no—
132C22×#64408—46no—
133C22×#64408—46no—
134C22×#64408—43no—
135C22×#64408—416no—
136C22×#64408C2412yes—
137C22×#64408C2411yescharacteristic
138C22×#64408C2416yes—
139C22×#64408C2413yes—
140C22×#64408C2413yes—
141C22×#64408C2411yescharacteristic
142C4⋊#64408—46no—
143C4⋊#64408—46no—
144C4⋊#64408—43no—
145C4⋊#64408—43no—
146C22⋊#64408—46no—
147C22⋊#64408—43no—
148C22⋊#64408—43no—
149C22⋊#64408—46no—
150C22⋊#64408—46no—
151C22⋊#64408—43no—
152C22⋊#64408—46no—
153C22⋊#64408—43no—
154C4×#64408—212no—
155C4×#64408—26no—
156C4×#64408—46no—
157C4×#64408—43no—
158C23×D73—43no—
159C23×D73—43no—
160C23×D73C22×C411yescharacteristic
161C23×D73C22×C412yes—
162C23×D73C2412yes—
163C23×D73C2411yescharacteristic
164C23×D73C2413yes—
165C2×D292C22×C416yes—
166C2×D292C22×C413yes—
167C2×D292C22×C413yescomplemented
168C2×C22⋊D73C22×C416yes—
169C2×C22⋊D73C22×C413yes—
170C2×C22⋊D73C22×C416yes—
171C2×C22⋊D73C22×C413yes—
172C2×C22⋊D73C22×C416yescomplemented
173D4×D73—46no—
174D4×D73—43no—
175D4×D73—43no—
176D4×D73—46no—
177D4×D73—43no—
178D4×D73—43no—
179C22×Dic73C22×C413yescomplemented
180C2×C4×D73—43no—
181C2×C4×D73—43no—
182C2×C4×D73C22×C416yescomplemented
183C2×C4×D73C2413yes—
184C2×C4×D73C2416yes—
185C4⋊Dic73C22×C416yescomplemented
186#11924007C22×C416yescomplemented
187#11924007C22×C416yescomplemented
188C22⋊Dic73C22×C416yes—
189C22⋊Dic73C22×C413yes—
190C22⋊Dic73C22×C413yescomplemented
191#11924005C22×C416yes—
192#11924005C22×C416yes—
193#11924005C22×C416yes—
194#11924005C22×C416yescomplemented
195C4×Dic73C22×C413yescomplemented
196C24×C73C22×C411yescharacteristic
197C2×D4×C73C22×C416yes—
198C2×D4×C73C22×C413yes—
199C2×D4×C73C22×C413yescomplemented
200C22×C4×C73C22×C413yescomplemented
201C4⋊C4×C73C22×C416yescomplemented
202C22⋊C4×C73C22×C416yes—
203C22⋊C4×C73C22×C413yes—
204C22⋊C4×C73C22×C413yescomplemented
205C42×C73C22×C411yescharacteristic, complemented
206C23×C73—43no—
207C23×C73C23×C412yes—
208C23×C73C23×C411yescharacteristic
209C23×C73C23×C413yes—
210C22×D73—23no—
211C22×D73—26no—
212C22×D73—26no—
213C22×D73—23no—
214C22×D73—23no—
215C22×D73—26no—
216C22×D73—26no—
217C22×D73—23no—
218C22×D73—43no—
219C22×D73—46no—
220C22×D73—412no—
221C22×D73—44no—
222C22×D73C23×C412yes—
223C22×D73C23×C411yescharacteristic
224C22×D73C23×C413yes—
225C22×D73C2511yescharacteristic
226C2×#64408—26no—
227C2×#64408—23no—
228C2×#64408—23no—
229C2×#64408—26no—
230C2×#64408—26no—
231C2×#64408—23no—
232C2×#64408—26no—
233C2×#64408—26no—
234C2×#64408—26no—
235C2×#64408—412no—
236C2×#64408—44no—
237C2×#64408—48no—
238C2×#64408—412no—
239C2×#64408—48no—
240C2×#64408—44no—
241C2×#64408H(5,𝔽2)16yes—
242D4×C73—46no—
243D4×C73—43no—
244D4×C73—43no—
245C2×C4×C73—43no—
246C2×C4×C73C23×C413yes—
247C2×C4×C73C23×C416yes—
248C22⋊D73—46no—
249C22⋊D73—46no—
250C22⋊D73—43no—
251C22⋊D73—43no—
252C22⋊D73—46no—
253C2×Dic73—43no—
254C2×Dic73C23×C413yes—
255C2×Dic73C23×C416yes—
256D292—46no—
257D292—43no—
258D292—43no—
259C4×D73—26no—
260C4×D73—23no—
261C4×D73—26no—
262C4×D73—23no—
263C4×D73—46no—
264C22×C73—23no—
265C22×C73—26no—
266C22×C73—26no—
267C22×C73—23no—
268C22×C73—44no—
269C22×C73C24×C411yescharacteristic
270C2×D73—23no—
271C2×D73—26no—
272C2×D73—26no—
273C2×D73—23no—
274C2×D73—44no—
275C2×D73—48no—
276C2×D73—42no—
277C2×D73—41no—
278C2×D73—43no—
279C2×D73—43no—
280C2×D73—46no—
281C2×D73—46no—
282C2×D73—43no—
283C2×D73C2×H(5,𝔽2)13yes—
284C2×D73#58513yes—
285#64408—43no—
286#64408—42no—
287#64408—41no—
288#64408—43no—
289#64408—46no—
290#64408#56014yesdirect product factor
291C4×C73—26no—
292C4×C73—23no—
293Dic73—26no—
294Dic73—23no—
295C4×#560—731nomaximal, Sylow
296C2×C73—42no—
297C2×C73—41no—
298C2×C73—43no—
299C2×C73C4×H(5,𝔽2)13yes—
300D73—43no—
301D73—42no—
302D73—41no—
303D73C2×#56011yescharacteristic
304D73#352913yes—
305C2×#560—731no—
306#2383—732no—
307#2380—731no—
308#2377—736no—
309#2376—733no—
310#2375—733no—
311C4×#127—731no—
312C4×#126—732no—
313C4×#123—733no—
314C4×#121—736no—
315C4×#120—733no—
316C73C4×#56011yescharacteristic, complemented, Sylow
317C24×C4—731no—
318#560—731no—
319#560—732no—
320#560—733no—
321#560—736no—
322#560—733no—
323#560#6440811yescharacteristic, direct product factor
324C2×#127—731no—
325C2×#126—732no—
326C2×#123—733no—
327C2×#121—736no—
328C2×#120—733no—
329C2×C4×D4—733no—
330C2×C4×D4—733no—
331C2×C4×D4—736no—
332C22×C42—733no—
333#390—733no—
334#390—733no—
335#390—736no—
336#389—736no—
337#388—736no—
338#388—736no—
339#388—736no—
340#388—736no—
341#387—736no—
342#387—736no—
343#386—736no—
344#386—733no—
345#386—733no—
346#386—736no—
347#386—736no—
348#385—733no—
349#385—733no—
350#385—736no—
351#384—731no—
352#383—732no—
353#381—733no—
354#380—736no—
355#379—733no—
356C4×C4⋊C4—736no—
357C4×C22⋊C4—736no—
358C4×C22⋊C4—733no—
359C4×C22⋊C4—733no—
360C43—731no—
361C25—731no—
362C22×D4—736no—
363C22×D4—733no—
364C22×D4—733no—
365C23×C4—2926no—
366C23×C4—731no—
367C23×C4—732no—
368C23×C4—733no—
369C23×C4—733no—
370C23×C4—733no—
371C23×C4—731no—
372C23×C4—732no—
373#127—733no—
374#127—733no—
375#127—731no—
376#127C2×#6440811yescharacteristic, complemented
377#126—736no—
378#126—736no—
379#126—732no—
380#126C2×#6440812yescomplemented
381#123—733no—
382#123—733no—
383#123—736no—
384#123—736no—
385#123—733no—
386#123C2×#6440813yescomplemented
387#121—736no—
388#121—736no—
389#121—736no—
390#121—736no—
391#121—736no—
392#121—736no—
393#121—736no—
394#121C2×#6440816yescomplemented
395#120—733no—
396#120—736no—
397#120—733no—
398#120—733no—
399#120—736no—
400#120C2×#6440813yescomplemented
401C4×D4—29212no—
402C4×D4—2926no—
403C4×D4—2926no—
404C2×C4⋊C4—736no—
405C2×C4⋊C4—733no—
406C2×C4⋊C4—733no—
407C2×C4⋊C4—736no—
408C2×C4⋊C4—736no—
409C2×C22⋊C4—736no—
410C2×C22⋊C4—733no—
411C2×C22⋊C4—736no—
412C2×C22⋊C4—736no—
413C2×C22⋊C4—733no—
414C2×C22⋊C4—733no—
415C2×C22⋊C4—736no—
416C2×C22⋊C4—733no—
417C2×C22⋊C4—736no—
418C2×C22⋊C4—733no—
419C2×C22⋊C4—733no—
420C2×C42—2926no—
421C2×C42—733no—
422C2×C42—736no—
423C2×C42—731no—
424C2×C42—733no—
425C2×C42—736no—
426#95—736no—
427#95—736no—
428#95—736no—
429#95—736no—
430#95—736no—
431#95—736no—
432C24—2923no—
433C24—2923no—
434C24—731no—
435C24—732no—
436C24—732no—
437C24—731no—
438C24—733no—
439C24C22×#6440811yescharacteristic
440C2×D4—2926no—
441C2×D4—2923no—
442C2×D4—2923no—
443C2×D4—2923no—
444C2×D4—2923no—
445C2×D4—2926no—
446C2×D4—736no—
447C2×D4—736no—
448C2×D4—733no—
449C2×D4—733no—
450C2×D4—736no—
451C2×D4—736no—
452C2×D4—733no—
453C2×D4—733no—
454C2×D4C22×#6440816yes—
455C2×D4C22×#6440813yes—
456C2×D4C22×#6440813yescomplemented
457C22×C4—2923no—
458C22×C4—2923no—
459C22×C4—29216no—
460C22×C4—2923no—
461C22×C4—2923no—
462C22×C4—2926no—
463C22×C4—2926no—
464C22×C4—733no—
465C22×C4—736no—
466C22×C4—731no—
467C22×C4—733no—
468C22×C4—736no—
469C22×C4—736no—
470C22×C4—732no—
471C22×C4—731no—
472C22×C4—733no—
473C22×C4—733no—
474C22×C4—1466no—
475C22×C4—14612no—
476C22×C4—14612no—
477C22×C4—1466no—
478C22×C4C22×#6440813yescomplemented
479C4⋊C4—2926no—
480C4⋊C4—2926no—
481C4⋊C4—2923no—
482C4⋊C4—2923no—
483C4⋊C4—736no—
484C4⋊C4—736no—
485C4⋊C4—736no—
486C4⋊C4C22×#6440816yescomplemented
487C22⋊C4—2926no—
488C22⋊C4—2923no—
489C22⋊C4—2923no—
490C22⋊C4—2923no—
491C22⋊C4—2926no—
492C22⋊C4—2926no—
493C22⋊C4—2926no—
494C22⋊C4—2923no—
495C22⋊C4—736no—
496C22⋊C4—733no—
497C22⋊C4—733no—
498C22⋊C4—736no—
499C22⋊C4—736no—
500C22⋊C4—736no—
501C22⋊C4—736no—
502C22⋊C4C22×#6440816yes—
503C22⋊C4C22×#6440813yes—
504C22⋊C4C22×#6440813yescomplemented
505C42—2926no—
506C42—2923no—
507C42—733no—
508C42—14612no—
509C42—1466no—
510C42C22×#6440811yescharacteristic, complemented
511C23—43no—
512C23—2926no—
513C23—2923no—
514C23—2924no—
515C23—29212no—
516C23—731no—
517C23—732no—
518C23—731no—
519C23—733no—
520C23—1466no—
521C23—1463no—
522C23—1463no—
523C23—1466no—
524C23—1463no—
525C23—1466no—
526C23—1463no—
527C23—1466no—
528C23C23×#6440812yes—
529C23C23×#6440811yescharacteristic
530C23C23×#6440813yes—
531D4—46no—
532D4—43no—
533D4—43no—
534D4—2926no—
535D4—2923no—
536D4—2923no—
537D4—2926no—
538D4—2926no—
539D4—2923no—
540D4—2926no—
541D4—2923no—
542C2×C4—43no—
543C2×C4—2926no—
544C2×C4—2924no—
545C2×C4—2928no—
546C2×C4—29212no—
547C2×C4—2928no—
548C2×C4—2924no—
549C2×C4—29212no—
550C2×C4—2923no—
551C2×C4—736no—
552C2×C4—733no—
553C2×C4—736no—
554C2×C4—1466no—
555C2×C4—1463no—
556C2×C4—1463no—
557C2×C4—1466no—
558C2×C4—1463no—
559C2×C4—1466no—
560C2×C4—1466no—
561C2×C4—1463no—
562C2×C4—1466no—
563C2×C4—1466no—
564C2×C4—1466no—
565C2×C4—1463no—
566C2×C4—1466no—
567C2×C4C23×#6440813yes—
568C2×C4C23×#6440816yes—
569C22—23no—
570C22—26no—
571C22—26no—
572C22—23no—
573C22—44no—
574C22—2928no—
575C22—2924no—
576C22—2921no—
577C22—2922no—
578C22—2923no—
579C22—2923no—
580C22—2923no—
581C22—2926no—
582C22—2926no—
583C22—733no—
584C22—733no—
585C22—1463no—
586C22—1466no—
587C22—1466no—
588C22—1463no—
589C22C24×#6440811yescharacteristic
590C4—26no—
591C4—23no—
592C4—2922no—
593C4—2921no—
594C4—2923no—
595C4—2926no—
596C4—2923no—
597C4—734no—
598C4—1466no—
599C4—1463no—
600C2—42no—
601C2—41no—
602C2—43no—
603C2—2922no—
604C2—2921no—
605C2—2923no—
606C2—731no—
607C2—733no—
608C2H(5,𝔽2)×#6440813yes—
subgroupG/H
center, FrattiniC22C24×#64408
commutator, socleC22×C73C24×C4
Fitting#560×C73C4
prime radical#560×D73C2
cosocleC22×D73C25
hypercenter#560#64408
hypocenterC73C4×#560
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #560

Complements

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

NH ≅ G/Ntype
1. #22626478C2semidirect
2. #22626475C2semidirect
3. #22626472C2semidirect
4. #22626471C2semidirect
5. #22626470C2semidirect
6. #127×#64408C2semidirect
7. #126×#64408C2semidirect
8. #123×#64408C2semidirect
9. #121×#64408C2semidirect
10. #120×#64408C2semidirect
15. C2×D4×#64408C22semidirect
16. C22×C4×#64408C22semidirect
19. #17989539C22semidirect
20. #17989538C22semidirect
24. #17989537C22semidirect
25. #17989536C22semidirect
26. #17989536C22semidirect
31. #17989535C22semidirect
34. #17989534C22semidirect
35. #17989533C22semidirect
36. #17989532C22semidirect
37. #17989530C22semidirect
38. #17989529C22semidirect
40. C4⋊C4×#64408C22semidirect
43. C22⋊C4×#64408C22semidirect
44. C42×#64408C22semidirect
45. #17989328C4semidirect
46. #17989327C4semidirect
47. #17989326C4semidirect
48. #17989325C4semidirect
49. #17989324C4semidirect
55. #560×C73C4semidirect
94. #14556588C2×C4semidirect
95. #14556587C2×C4semidirect
96. #14556587C2×C4semidirect
97. #14556586C2×C4semidirect
98. #14556585C2×C4semidirect
99. #14556584C2×C4semidirect
100. #14556576C2×C4semidirect
101. #14556575C2×C4semidirect
102. #14556574C2×C4semidirect
103. #14556573C2×C4semidirect
104. #14556572C2×C4semidirect
105. #14556566C2×C4semidirect
106. #14556565C2×C4semidirect
107. #14556564C2×C4semidirect
108. #14556564C2×C4semidirect
109. #14556563C2×C4semidirect
110. #14556563C2×C4semidirect
111. #14556562C2×C4semidirect
112. #14556561C2×C4semidirect
113. #14556561C2×C4semidirect
114. #14556560C2×C4semidirect
115. #14556559C2×C4semidirect
116. #14556559C2×C4semidirect
122. #127×C73C2×C4semidirect
123. #126×C73C2×C4semidirect
124. #123×C73C2×C4semidirect
125. #121×C73C2×C4semidirect
126. #120×C73C2×C4semidirect
167. C2×D292C22×C4semidirect
172. C2×C22⋊D73C22×C4semidirect
179. C22×Dic73C22×C4semidirect
182. C2×C4×D73C22×C4semidirect
185. C4⋊Dic73C22×C4semidirect
186. #11924007C22×C4semidirect
187. #11924007C22×C4semidirect
190. C22⋊Dic73C22×C4semidirect
194. #11924005C22×C4semidirect
195. C4×Dic73C22×C4semidirect
199. C2×D4×C73C22×C4semidirect
200. C22×C4×C73C22×C4semidirect
201. C4⋊C4×C73C22×C4semidirect
204. C22⋊C4×C73C22×C4semidirect
205. C42×C73C22×C4semidirect
290. #64408#560direct (N × H)
316. C73C4×#560semidirect
323. #560#64408direct (N × H)
376. #127C2×#64408semidirect
380. #126C2×#64408semidirect
386. #123C2×#64408semidirect
394. #121C2×#64408semidirect
400. #120C2×#64408semidirect
456. C2×D4C22×#64408semidirect
478. C22×C4C22×#64408semidirect
486. C4⋊C4C22×#64408semidirect
504. C22⋊C4C22×#64408semidirect
510. C42C22×#64408semidirect

Maximal subgroups

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

subgroupindex
#226264782
#226264752
#226264722
#226264712
#226264702
#127×#644082
#126×#644082
#123×#644082
#121×#644082
#120×#644082
#560×D732
C4×#56073