Finite Group Databasebeta

← D59×#3444 #29495396

Subgroups — D59×#3444 #29495396

Order 15104.

8518 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437393C213yesmaximal, complemented
2#21437392C211yesmaximal, characteristic, complemented
3#21437391C213yesmaximal, complemented
4#21437390C2112yesmaximal, complemented
5#21437389C216yesmaximal, complemented
6#21437388C216yesmaximal, complemented
7#533×D59C213yesmaximal, complemented
8#532×D59C213yesmaximal, complemented
9#529×D59C2112yesmaximal, complemented
10#525×D59C216yesmaximal, complemented
11C4×#41×D59C216yesmaximal, complemented
12C22×C42×D59C211yesmaximal, characteristic, complemented
13C59×#3444C211yesmaximal, characteristic, complemented
14C2×#41×D59C2216yes—
15C23×C4×D59C2213yes—
16#16837959C2213yescomplemented
17#16837958C2216yescomplemented
18#16837957C2216yescomplemented
19#16837956C22112yescomplemented
20#16837955C2216yescomplemented
21#16837954C22112yescomplemented
22#16837953C2213yescomplemented
23#16837952C2213yescomplemented
24#16837951C2216yescomplemented
25#16837950C2213yescomplemented
26#16837949C22112yescomplemented
27#16837948C2216yescomplemented
28#16837947C22112yescomplemented
29C4⋊Q8×D59C2213yescomplemented
30#127×D59C2211yescharacteristic, complemented
31#16837939C22112yescomplemented
32#16837938C22112yescomplemented
33#16837937C22112yescomplemented
34#16837936C22112yescomplemented
35#16837935C22124yescomplemented
36#16837934C22112yescomplemented
37#16837933C22112yescomplemented
38#16837932C22124yescomplemented
39#16837931C22112yescomplemented
40#16837930C22124yescomplemented
41#16837929C22124yescomplemented
42#126×D59C2218yescomplemented
43#125×D59C2216yescomplemented
44#124×D59C2216yescomplemented
45#16837915C22112yescomplemented
46#16837914C2216yescomplemented
47#16837913C2216yescomplemented
48#16837912C22112yescomplemented
49#16837911C22124yescomplemented
50#16837910C22112yescomplemented
51#16837909C2216yescomplemented
52#16837908C22112yescomplemented
53#123×D59C22112yes—
54C22⋊Q8×D59C22112yes—
55#121×D59C22112yes—
56#120×D59C2214yes—
57#41×Dic59C2216yescomplemented
58C4×#11745689C22112yescomplemented
59C4×#11745685C2216yescomplemented
60C4×#11745685C22112yescomplemented
61#16837870C2216yescomplemented
62#16837870C22112yescomplemented
63C4×#11745687C22124yescomplemented
64C4×#11745687C22112yescomplemented
65C4×Q8×D59C22112yescomplemented
66C4×D4×D59C22124yes—
67C4×D4×D59C22112yescomplemented
68#117×D59C2216yes—
69#117×D59C22112yescomplemented
70C22×C4×Dic59C2213yescomplemented
71C2×C42×D59C2213yes—
72C2×C42×D59C2216yes—
73C2×C42×D59C2213yes—
74C2×C42×D59C2213yescomplemented
75C2×C42×D59C2216yescomplemented
76C2×C42×D59C2213yescomplemented
77C2×C42×D59C2214yescomplemented
78C59×#533C2213yescomplemented
79C59×#532C2213yescomplemented
80C59×#529C22112yescomplemented
81C59×#525C2216yescomplemented
82C4×#41×C59C2216yescomplemented
83C22×C42×C59C2211yescharacteristic, complemented
84C24×D59C2311yescharacteristic
85C2×#11745689C2316yes—
86C2×#11745685C23112yes—
87C2×#11745685C2316yes—
88C2×#11745687C23112yes—
89C2×#11745687C2316yes—
90#41×D59—248no—
91C2×Q8×D59C2316yes—
92C2×D4×D59C23112yes—
93C2×D4×D59C2316yes—
94C23×Dic59C2313yes—
95C22×C4×D59—224no—
96C22×C4×D59C2316yes—
97C22×C4×D59C2313yes—
98C22×C4×D59C2313yes—
99C22×C4×D59C2313yes—
100C22×C4×D59C2316yes—
101C22×C4×D59C2316yes—
102C22×C4×D59C2316yes—
103C22×C4×D59C23112yes—
104C22×C4×D59C2313yes—
105#14273727C2313yescomplemented
106#14273726C23112yescomplemented
107#14273725C2316yescomplemented
108#14273724C2311yescharacteristic, complemented
109#14273723C2316yescomplemented
110#14273722C23124yescomplemented
111#14273721C2318yescomplemented
112#14273720C23124yescomplemented
113#14273719C2316yescomplemented
114#14273718C23112yescomplemented
115#14273717C23124yescomplemented
116#14273716C2316yescomplemented
117#14273715C2316yescomplemented
118#14273714C2316yescomplemented
119#14273713C23124yescomplemented
120#14273712C23124yes—
121#14273711C23112yes—
122#14273710C23112yes—
123#14273709C23124yes—
124#14273708C23112yes—
125#14273707C23112yes—
126#14273706C23112yes—
127#14273705C23124yes—
128#14273704C23124yes—
129#14273703C23112yes—
130#14273702C23112yes—
131#14273701C23112yes—
132#14273700C23124yes—
133#14273699C23124yes—
134#14273698C23112yes—
135#14273697C23112yes—
136#14273696C2314yes—
137#14273695C23112yes—
138Q8×Dic59C23112yescomplemented
139C4×Dic118C23124yescomplemented
140C4×Dic118C23112yescomplemented
141#14273692C23124yescomplemented
142#14273692C23112yescomplemented
143C4×D236C23124yes—
144C4×D236C23112yescomplemented
145D4×Dic59C23124yes—
146D4×Dic59C23112yescomplemented
147#14273689C23124yes—
148#14273689C23112yescomplemented
149C4×C22⋊D59C23124yes—
150C4×C22⋊D59C23124yes—
151C4×C22⋊D59C23124yescomplemented
152(C22⋊D59)⋊C4C23124yes—
153(C22⋊D59)⋊C4C23124yes—
154(C22⋊D59)⋊C4C23124yescomplemented
155#14273686C2316yes—
156#14273686C23112yescomplemented
157#14273685C23112yes—
158#14273685C23124yescomplemented
159#14273684C23112yes—
160#14273684C23112yescomplemented
161#14273684C23112yescomplemented
162#14273683C23112yes—
163#14273683C23124yescomplemented
164C4⋊C4×D59C23112yes—
165C4⋊C4×D59C23124yes—
166C22⋊C4×D59C23124yes—
167C22⋊C4×D59C23112yes—
168C2×C4×Dic59C2316yes—
169C2×C4×Dic59C2316yes—
170C2×C4×Dic59C2316yes—
171C2×C4×Dic59C2316yes—
172C2×C4×Dic59C2313yes—
173C2×C4×Dic59C2316yes—
174C2×C4×Dic59C2313yes—
175C2×C4×Dic59C23112yescomplemented
176C42×D59C2313yes—
177C42×D59C2312yes—
178C42×D59C2316yes—
179C42×D59C2316yes—
180C42×D59C2316yes—
181C42×D59C2316yes—
182C42×D59C2311yescharacteristic
183C42×D59C2316yes—
184C42×D59C2313yes—
185C42×D59C2313yes—
186C42×D59C2311yescharacteristic
187C42×D59C2313yes—
188C42×D59C2316yes—
189C42×D59C2316yes—
190C42×D59C2313yes—
191C42×D59C2313yes—
192C42×D59C23112yes—
193C42×D59C23112yescomplemented
194C42×D59C2314yescomplemented
195C2×#41×C59C2316yes—
196C23×C4×C59C2313yes—
197C4⋊Q8×C59C2313yescomplemented
198#127×C59C2311yescharacteristic, complemented
199#126×C59C2318yescomplemented
200#125×C59C2316yescomplemented
201#124×C59C2316yescomplemented
202#123×C59C23112yes—
203C22⋊Q8×C59C23112yes—
204#121×C59C23112yes—
205#120×C59C2314yes—
206C4×Q8×C59C23112yescomplemented
207C4×D4×C59C23124yes—
208C4×D4×C59C23112yescomplemented
209#117×C59C2316yes—
210#117×C59C23112yescomplemented
211C2×C42×C59C2316yes—
212C2×C42×C59C2313yes—
213C2×C42×C59C2313yes—
214C2×C42×C59C2314yescomplemented
215C24×C59C2411yescharacteristic
216C23×D59—212no—
217C23×D59C2414yes—
218C23×D59C2413yes—
219C23×D59C2413yes—
220#41×C59—224no—
221C2×Q8×C59C2416yes—
222C2×D4×C59C24112yes—
223C2×D4×C59C2416yes—
224C22×C4×C59—212no—
225C22×C4×C59C2416yes—
226C22×C4×C59C2416yes—
227C22×C4×C59C2413yes—
228C22×C4×C59C24112yes—
229C22×C4×C59C2413yes—
230C2×C22⋊D59C24112yes—
231C2×C22⋊D59C24112yes—
232C2×C22⋊D59C24112yes—
233C22×Dic59—212no—
234C22×Dic59C2416yes—
235C22×Dic59C2416yes—
236C22×Dic59C2413yes—
237C22×Dic59C24112yes—
238C22×Dic59C2413yes—
239#11745689—224no—
240Q8×D59—224no—
241#11745687—248no—
242#11745687—224no—
243D4×D59—248no—
244D4×D59—224no—
245#11745685—224no—
246#11745685—248no—
247C2×D236C24112yes—
248C2×D236C2416yes—
249C2×C4×D59—212no—
250C2×C4×D59—212no—
251C2×C4×D59—212no—
252C2×C4×D59—224no—
253C2×C4×D59—224no—
254C2×C4×D59—248no—
255C2×C4×D59—224no—
256C2×C4×D59—224no—
257C2×C4×D59#41124yescomplemented
258C2×C4×D59C2416yes—
259C2×C4×D59C2416yes—
260C2×C4×D59C2416yes—
261C2×C4×D59C2416yes—
262C2×C4×D59C2416yes—
263C2×C4×D59C2416yes—
264C2×C4×D59C24112yes—
265C2×C4×D59C24112yes—
266C2×C4×D59C24112yes—
267C2×C4×D59C2413yes—
268C2×C4×D59C2413yes—
269C2×C4×D59C2413yes—
270C2×C4×D59C2413yes—
271C2×Dic118C24112yes—
272C2×Dic118C2416yes—
273C4⋊C4×C59C24112yes—
274C4⋊C4×C59C24124yes—
275C22⋊C4×C59C24112yes—
276C22⋊C4×C59C24124yes—
277C42×C59C2413yes—
278C42×C59C2416yes—
279C42×C59C2413yes—
280C42×C59C2412yes—
281C42×C59C2411yescharacteristic
282C42×C59C24112yes—
283C42×C59C2411yescharacteristic
284C22⋊Dic59C24112yes—
285C22⋊Dic59C24124yes—
286(C2×D59)⋊C4C24124yes—
287(C2×D59)⋊C4C24124yes—
288(C2×D59)⋊C4C24124yes—
289C4⋊Dic59C24112yes—
290C4⋊Dic59C24124yes—
291Dic59⋊C4C24124yes—
292Dic59⋊C4C24124yes—
293Dic59⋊C4C24124yes—
294C4×Dic59C2413yes—
295C4×Dic59C2416yes—
296C4×Dic59C2413yes—
297C4×Dic59C2416yes—
298C4×Dic59C2416yes—
299C4×Dic59C2416yes—
300C4×Dic59C2416yes—
301C4×Dic59C2413yes—
302C4×Dic59C2416yes—
303C4×Dic59C2413yes—
304C4×Dic59C24124yes—
305C4×Dic59C24112yes—
306C23×C59—26no—
307C23×C59C2514yes—
308C23×C59C2513yes—
309C22×D59—232no—
310C22×D59—26no—
311C22×D59—212no—
312C22×D59—212no—
313C22×D59—224no—
314C22×D59C2×#41112yes—
315C22×D59C2514yes—
316C22×D59C2513yes—
317C22×D59C2511yescharacteristic
318Q8×C59—212no—
319D4×C59—224no—
320D4×C59—212no—
321C2×C4×C59—26no—
322C2×C4×C59—212no—
323C2×C4×C59—212no—
324C2×C4×C59—224no—
325C2×C4×C59C2×#41112yescomplemented
326C2×C4×C59C2516yes—
327C2×C4×C59C25112yes—
328C2×C4×C59C2513yes—
329C2×C4×C59C2513yes—
330C22⋊D59—224no—
331C22⋊D59—224no—
332C22⋊D59—224no—
333C2×Dic59—26no—
334C2×Dic59—212no—
335C2×Dic59—212no—
336C2×Dic59—224no—
337C2×Dic59C2×#41112yescomplemented
338C2×Dic59C2516yes—
339C2×Dic59C25112yes—
340C2×Dic59C2513yes—
341C2×Dic59C2513yes—
342D236—224no—
343D236—212no—
344C4×D59—212no—
345C4×D59—212no—
346C4×D59—224no—
347C4×D59—212no—
348C4×D59—212no—
349C4×D59—224no—
350C4×D59—212no—
351C4×D59—212no—
352C4×D59—224no—
353C4×D59C2×#41112yes—
354C4×D59C2×#41112yes—
355C4×D59C2×#41112yescomplemented
356C4×D59C2×#41112yescomplemented
357Dic118—212no—
358Dic118—224no—
359C2×#3444—591nomaximal, Sylow
360C22×C59—28no—
361C22×C59—26no—
362C22×C59—212no—
363C22×C59C22×#4116yes—
364C22×C59C2611yescharacteristic
365C2×D59—224no—
366C2×D59—26no—
367C2×D59—224no—
368C2×D59—212no—
369C2×D59—416no—
370C2×D59C22×#4116yes—
371C2×D59C22×#4116yes—
372C4×C59—212no—
373C4×C59—26no—
374C4×C59C22×#4116yes—
375C4×C59C22×#4116yes—
376Dic59—212no—
377Dic59—26no—
378Dic59C22×#4116yes—
379Dic59C22×#4116yes—
380#3444—591no—
381#3444—593no—
382#3444—593no—
383#3444—5912no—
384#3444—596no—
385#3444—596no—
386#3444D5911yescharacteristic, direct product factor
387C2×#533—593no—
388C2×#532—593no—
389C2×#529—5912no—
390C2×#525—596no—
391C2×C4×#41—596no—
392C23×C42—591no—
393C2×C59—26no—
394C2×C59—44no—
395C2×C59C23×#4113yes—
396D59—26no—
397D59—44no—
398D59#344414yesdirect product factor
399C22×#41—596no—
400C24×C4—593no—
401#533—596no—
402#533—596no—
403#533—5912no—
404#533—5912no—
405#533—596no—
406#533—593no—
407#533C2×D5913yescomplemented
408#532—596no—
409#532—593no—
410#532—593no—
411#532—596no—
412#532—5912no—
413#532—5912no—
414#532—593no—
415#532C2×D5913yescomplemented
416C2×C4⋊Q8—593no—
417C2×#127—591no—
418#529—5924no—
419#529—5912no—
420#529—5912no—
421#529—5924no—
422#529—5912no—
423#529—5912no—
424#529—5912no—
425#529—5924no—
426#529—5912no—
427#529—5924no—
428#529—5912no—
429#529C2×D59112yescomplemented
430C2×#126—598no—
431C2×#125—596no—
432C2×#124—596no—
433#525—596no—
434#525—596no—
435#525—5912no—
436#525—5912no—
437#525—5912no—
438#525—5912no—
439#525—5924no—
440#525—596no—
441#525C2×D5916yescomplemented
442C2×#123—5912no—
443C2×C22⋊Q8—5912no—
444C2×#121—5912no—
445C2×#120—594no—
446C4×#41—596no—
447C4×#41—5912no—
448C4×#41—5924no—
449C4×#41—5912no—
450C4×#41—596no—
451C4×#41—5912no—
452C4×#41—596no—
453C4×#41—5912no—
454C4×#41C2×D5916yescomplemented
455C2×C4×Q8—5912no—
456C2×C4×D4—5924no—
457C2×C4×D4—5912no—
458C2×#117—596no—
459C2×#117—5912no—
460C22×C42—593no—
461C22×C42—593no—
462C22×C42—596no—
463C22×C42—593no—
464C22×C42—593no—
465C22×C42—596no—
466C22×C42—593no—
467C22×C42—594no—
468C22×C42C2×D5911yescharacteristic, complemented
469C59C2×#344411yescharacteristic, complemented, Sylow
470C25—591no—
471C2×#41—596no—
472C2×#41—5912no—
473C2×#41—596no—
474C2×#41—5912no—
475C2×#41—596no—
476C2×#41—11848no—
477C2×#41C22×D5916yes—
478C22×Q8—596no—
479C22×D4—5912no—
480C22×D4—596no—
481C23×C4—593no—
482C23×C4—593no—
483C23×C4—5912no—
484C23×C4—596no—
485C23×C4—596no—
486C23×C4—593no—
487C23×C4—593no—
488C23×C4—596no—
489C23×C4—596no—
490C23×C4—593no—
491C23×C4—11824no—
492C23×C4C22×D5913yes—
493C4⋊Q8—596no—
494C4⋊Q8—5912no—
495C4⋊Q8—593no—
496C4⋊Q8C22×D5913yescomplemented
497#127—596no—
498#127—591no—
499#127C22×D5911yescharacteristic, complemented
500#126—5924no—
501#126—5924no—
502#126—598no—
503#126C22×D5918yescomplemented
504#125—5924no—
505#125—5912no—
506#125—596no—
507#125C22×D5916yescomplemented
508#124—596no—
509#124—596no—
510#124—5924no—
511#124—596no—
512#124C22×D5916yescomplemented
513#123—5912no—
514#123—5912no—
515#123—5924no—
516#123—5924no—
517#123—5912no—
518#123C22×D59112yes—
519C22⋊Q8—5912no—
520C22⋊Q8—5912no—
521C22⋊Q8—5924no—
522C22⋊Q8—5912no—
523C22⋊Q8—5924no—
524C22⋊Q8C22×D59112yes—
525#121—5912no—
526#121—5924no—
527#121—5912no—
528#121—5912no—
529#121—5924no—
530#121C22×D59112yes—
531#120—594no—
532#120—5912no—
533#120—5912no—
534#120C22×D5914yes—
535C4×Q8—5912no—
536C4×Q8—5924no—
537C4×Q8—5912no—
538C4×Q8—5924no—
539C4×Q8—5912no—
540C4×Q8C22×D59112yescomplemented
541C4×D4—5924no—
542C4×D4—5912no—
543C4×D4—5924no—
544C4×D4—5924no—
545C4×D4—5924no—
546C4×D4—5924no—
547C4×D4—5912no—
548C4×D4—5924no—
549C4×D4—5924no—
550C4×D4—5924no—
551C4×D4—5924no—
552C4×D4—5912no—
553C4×D4C22×D59124yes—
554C4×D4C22×D59112yescomplemented
555#117—596no—
556#117—5912no—
557#117—5912no—
558#117—5924no—
559#117—5912no—
560#117—5924no—
561#117—5912no—
562#117—5912no—
563#117—5912no—
564#117C22×D5916yes—
565#117C22×D59112yescomplemented
566C2×C4⋊C4—5912no—
567C2×C4⋊C4—5924no—
568C2×C22⋊C4—5912no—
569C2×C22⋊C4—5924no—
570C2×C42—5912no—
571C2×C42—596no—
572C2×C42—593no—
573C2×C42—596no—
574C2×C42—596no—
575C2×C42—596no—
576C2×C42—596no—
577C2×C42—593no—
578C2×C42—593no—
579C2×C42—5912no—
580C2×C42—596no—
581C2×C42—5912no—
582C2×C42—596no—
583C2×C42—593no—
584C2×C42—593no—
585C2×C42—592no—
586C2×C42—596no—
587C2×C42—596no—
588C2×C42—596no—
589C2×C42—596no—
590C2×C42—591no—
591C2×C42—593no—
592C2×C42—593no—
593C2×C42—596no—
594C2×C42—594no—
595C2×C42—593no—
596C2×C42—591no—
597C2×C42C22×D5916yes—
598C2×C42C22×D5913yes—
599C2×C42C22×D5913yes—
600C2×C42C22×D5914yescomplemented
601C24—593no—
602C24—594no—
603C24—593no—
604C24—11812no—
605C24C23×D5911yescharacteristic
606#41—224no—
607#41—11848no—
608#41—11848no—
609#41—11824no—
610#41—11824no—
611#41—11824no—
612C2×Q8—5912no—
613C2×Q8—596no—
614C2×Q8—11824no—
615C2×Q8C23×D5916yes—
616C2×D4—5912no—
617C2×D4—5912no—
618C2×D4—5912no—
619C2×D4—5912no—
620C2×D4—596no—
621C2×D4—11824no—
622C2×D4—11848no—
623C2×D4C23×D59112yes—
624C2×D4C23×D5916yes—
625C22×C4—212no—
626C22×C4—593no—
627C22×C4—5924no—
628C22×C4—593no—
629C22×C4—593no—
630C22×C4—593no—
631C22×C4—593no—
632C22×C4—596no—
633C22×C4—596no—
634C22×C4—593no—
635C22×C4—5912no—
636C22×C4—596no—
637C22×C4—596no—
638C22×C4—596no—
639C22×C4—596no—
640C22×C4—596no—
641C22×C4—596no—
642C22×C4—5912no—
643C22×C4—5912no—
644C22×C4—5912no—
645C22×C4—11812no—
646C22×C4—11824no—
647C22×C4—11824no—
648C22×C4—11824no—
649C22×C4—11824no—
650C22×C4—11848no—
651C22×C4—11812no—
652C22×C4—11812no—
653C22×C4—11812no—
654C22×C4C23×D5916yes—
655C22×C4C23×D5916yes—
656C22×C4C23×D5913yes—
657C22×C4C23×D59112yes—
658C22×C4C23×D5913yes—
659C4⋊C4—5924no—
660C4⋊C4—5912no—
661C4⋊C4—5924no—
662C4⋊C4—5924no—
663C4⋊C4—5924no—
664C4⋊C4C23×D59112yes—
665C4⋊C4C23×D59124yes—
666C22⋊C4—5912no—
667C22⋊C4—5924no—
668C22⋊C4—5924no—
669C22⋊C4—5924no—
670C22⋊C4—5924no—
671C22⋊C4C23×D59112yes—
672C22⋊C4C23×D59124yes—
673C42—593no—
674C42—596no—
675C42—593no—
676C42—596no—
677C42—596no—
678C42—596no—
679C42—596no—
680C42—593no—
681C42—596no—
682C42—593no—
683C42—5924no—
684C42—5912no—
685C42C23×D5913yes—
686C42C23×D5916yes—
687C42C23×D5913yes—
688C42C23×D5912yes—
689C42C23×D5911yescharacteristic
690C42C23×D59112yes—
691C42C23×D5911yescharacteristic
692C23—26no—
693C23—591no—
694C23—5912no—
695C23—593no—
696C23—594no—
697C23—11812no—
698C23—11812no—
699C23—11824no—
700C23—11832no—
701C23—1186no—
702C23C24×D5914yes—
703C23C24×D5913yes—
704Q8—212no—
705Q8—11824no—
706Q8—11812no—
707D4—224no—
708D4—212no—
709D4—11824no—
710D4—11824no—
711D4—11824no—
712D4—11824no—
713D4—11812no—
714C2×C4—26no—
715C2×C4—212no—
716C2×C4—212no—
717C2×C4—224no—
718C2×C4—5912no—
719C2×C4—593no—
720C2×C4—593no—
721C2×C4—5912no—
722C2×C4—5912no—
723C2×C4—5912no—
724C2×C4—5912no—
725C2×C4—596no—
726C2×C4—5912no—
727C2×C4—11812no—
728C2×C4—11812no—
729C2×C4—11824no—
730C2×C4—11812no—
731C2×C4—11812no—
732C2×C4—11824no—
733C2×C4—11812no—
734C2×C4—11812no—
735C2×C4—11824no—
736C2×C4—1186no—
737C2×C4—11812no—
738C2×C4—11812no—
739C2×C4—11824no—
740C2×C4#41×D59112yescomplemented
741C2×C4C24×D5916yes—
742C2×C4C24×D59112yes—
743C2×C4C24×D5913yes—
744C2×C4C24×D5913yes—
745C22—28no—
746C22—26no—
747C22—212no—
748C22—596no—
749C22—596no—
750C22—11824no—
751C22—11824no—
752C22—1186no—
753C22—11812no—
754C22—23616no—
755C22C2×#41×D5916yes—
756C22C25×D5911yescharacteristic
757C4—26no—
758C4—212no—
759C4—596no—
760C4—596no—
761C4—1186no—
762C4—11812no—
763C4C2×#41×D5916yes—
764C4C2×#41×D5916yes—
765C2—26no—
766C2—44no—
767C2—594no—
768C2—1186no—
769C2—2364no—
770C2C22×#41×D5913yes—
subgroupG/H
centerC42C23×D59
commutator, socle, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC59×#3444C2
hypercenter#3444D59
hypocenterC59C2×#3444
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #21437393C2semidirect
2. #21437392C2semidirect
3. #21437391C2semidirect
4. #21437390C2semidirect
5. #21437389C2semidirect
6. #21437388C2semidirect
7. #533×D59C2semidirect
8. #532×D59C2semidirect
9. #529×D59C2semidirect
10. #525×D59C2semidirect
11. C4×#41×D59C2semidirect
12. C22×C42×D59C2semidirect
13. C59×#3444C2semidirect
16. #16837959C22semidirect
17. #16837958C22semidirect
18. #16837957C22semidirect
19. #16837956C22semidirect
20. #16837955C22semidirect
21. #16837954C22semidirect
22. #16837953C22semidirect
23. #16837952C22semidirect
24. #16837951C22semidirect
25. #16837950C22semidirect
26. #16837949C22semidirect
27. #16837948C22semidirect
28. #16837947C22semidirect
29. C4⋊Q8×D59C22semidirect
30. #127×D59C22semidirect
31. #16837939C22semidirect
32. #16837938C22semidirect
33. #16837937C22semidirect
34. #16837936C22semidirect
35. #16837935C22semidirect
36. #16837934C22semidirect
37. #16837933C22semidirect
38. #16837932C22semidirect
39. #16837931C22semidirect
40. #16837930C22semidirect
41. #16837929C22semidirect
42. #126×D59C22semidirect
43. #125×D59C22semidirect
44. #124×D59C22semidirect
45. #16837915C22semidirect
46. #16837914C22semidirect
47. #16837913C22semidirect
48. #16837912C22semidirect
49. #16837911C22semidirect
50. #16837910C22semidirect
51. #16837909C22semidirect
52. #16837908C22semidirect
57. #41×Dic59C22semidirect
58. C4×#11745689C22semidirect
59. C4×#11745685C22semidirect
60. C4×#11745685C22semidirect
61. #16837870C22semidirect
62. #16837870C22semidirect
63. C4×#11745687C22semidirect
64. C4×#11745687C22semidirect
65. C4×Q8×D59C22semidirect
67. C4×D4×D59C22semidirect
69. #117×D59C22semidirect
70. C22×C4×Dic59C22semidirect
74. C2×C42×D59C22semidirect
75. C2×C42×D59C22semidirect
76. C2×C42×D59C22semidirect
77. C2×C42×D59C22semidirect
78. C59×#533C22semidirect
79. C59×#532C22semidirect
80. C59×#529C22semidirect
81. C59×#525C22semidirect
82. C4×#41×C59C22semidirect
83. C22×C42×C59C22semidirect
105. #14273727C23semidirect
106. #14273726C23semidirect
107. #14273725C23semidirect
108. #14273724C23semidirect
109. #14273723C23semidirect
110. #14273722C23semidirect
111. #14273721C23semidirect
112. #14273720C23semidirect
113. #14273719C23semidirect
114. #14273718C23semidirect
115. #14273717C23semidirect
116. #14273716C23semidirect
117. #14273715C23semidirect
118. #14273714C23semidirect
119. #14273713C23semidirect
138. Q8×Dic59C23semidirect
139. C4×Dic118C23semidirect
140. C4×Dic118C23semidirect
141. #14273692C23semidirect
142. #14273692C23semidirect
144. C4×D236C23semidirect
146. D4×Dic59C23semidirect
148. #14273689C23semidirect
151. C4×C22⋊D59C23semidirect
154. (C22⋊D59)⋊C4C23semidirect
156. #14273686C23semidirect
158. #14273685C23semidirect
160. #14273684C23semidirect
161. #14273684C23semidirect
163. #14273683C23semidirect
175. C2×C4×Dic59C23semidirect
193. C42×D59C23semidirect
194. C42×D59C23semidirect
197. C4⋊Q8×C59C23semidirect
198. #127×C59C23semidirect
199. #126×C59C23semidirect
200. #125×C59C23semidirect
201. #124×C59C23semidirect
206. C4×Q8×C59C23semidirect
208. C4×D4×C59C23semidirect
210. #117×C59C23semidirect
214. C2×C42×C59C23semidirect
257. C2×C4×D59#41semidirect
325. C2×C4×C59C2×#41semidirect
337. C2×Dic59C2×#41semidirect
355. C4×D59C2×#41semidirect
356. C4×D59C2×#41semidirect
386. #3444D59direct (N × H)
398. D59#3444direct (N × H)
407. #533C2×D59semidirect
415. #532C2×D59semidirect
429. #529C2×D59semidirect
441. #525C2×D59semidirect
454. C4×#41C2×D59semidirect
468. C22×C42C2×D59semidirect
469. C59C2×#3444semidirect
496. C4⋊Q8C22×D59semidirect
499. #127C22×D59semidirect
503. #126C22×D59semidirect
507. #125C22×D59semidirect
512. #124C22×D59semidirect
540. C4×Q8C22×D59semidirect
554. C4×D4C22×D59semidirect
565. #117C22×D59semidirect
600. C2×C42C22×D59semidirect
740. C2×C4#41×D59semidirect

Maximal subgroups

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

subgroupindex
#214373932
#214373922
#214373912
#214373902
#214373892
#214373882
#533×D592
#532×D592
#529×D592
#525×D592
C4×#41×D592
C22×C42×D592
C59×#34442
C2×#344459