Finite Group Databasebeta

← D53×#3444 #28290799

Subgroups — D53×#3444 #28290799

Order 13568.

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#20288012C213yesmaximal, complemented
2#20288011C211yesmaximal, characteristic, complemented
3#20288010C213yesmaximal, complemented
4#20288009C2112yesmaximal, complemented
5#20288008C216yesmaximal, complemented
6#20288007C216yesmaximal, complemented
7#533×D53C213yesmaximal, complemented
8#532×D53C213yesmaximal, complemented
9#529×D53C2112yesmaximal, complemented
10#525×D53C216yesmaximal, complemented
11C4×#41×D53C216yesmaximal, complemented
12C22×C42×D53C211yesmaximal, characteristic, complemented
13C53×#3444C211yesmaximal, characteristic, complemented
14C2×#41×D53C2216yes—
15C23×C4×D53C2213yes—
16#16811180C2213yescomplemented
17#16811179C2216yescomplemented
18#16811178C2216yescomplemented
19#16811177C22112yescomplemented
20#16811176C2216yescomplemented
21#16811175C22112yescomplemented
22#16811174C2213yescomplemented
23#16811173C2213yescomplemented
24#16811172C2216yescomplemented
25#16811171C2213yescomplemented
26#16811170C22112yescomplemented
27#16811169C2216yescomplemented
28#16811168C22112yescomplemented
29C4⋊Q8×D53C2213yescomplemented
30#127×D53C2211yescharacteristic, complemented
31#16811160C22112yescomplemented
32#16811159C22112yescomplemented
33#16811158C22112yescomplemented
34#16811157C22112yescomplemented
35#16811156C22124yescomplemented
36#16811155C22112yescomplemented
37#16811154C22112yescomplemented
38#16811153C22124yescomplemented
39#16811152C22112yescomplemented
40#16811151C22124yescomplemented
41#16811150C22124yescomplemented
42#126×D53C2218yescomplemented
43#125×D53C2216yescomplemented
44#124×D53C2216yescomplemented
45#16811136C22112yescomplemented
46#16811135C2216yescomplemented
47#16811134C2216yescomplemented
48#16811133C22112yescomplemented
49#16811132C22124yescomplemented
50#16811131C22112yescomplemented
51#16811130C2216yescomplemented
52#16811129C22112yescomplemented
53#123×D53C22112yes—
54C22⋊Q8×D53C22112yes—
55#121×D53C22112yes—
56#120×D53C2214yes—
57#41×Dic53C2216yescomplemented
58C4×#11719949C22112yescomplemented
59C4×#11719945C2216yescomplemented
60C4×#11719945C22112yescomplemented
61#16811091C2216yescomplemented
62#16811091C22112yescomplemented
63C4×#11719947C22124yescomplemented
64C4×#11719947C22112yescomplemented
65C4×Q8×D53C22112yescomplemented
66C4×D4×D53C22124yes—
67C4×D4×D53C22112yescomplemented
68#117×D53C2216yes—
69#117×D53C22112yescomplemented
70C22×C4×Dic53C2213yescomplemented
71C2×C42×D53C2213yes—
72C2×C42×D53C2213yes—
73C2×C42×D53C2216yes—
74C2×C42×D53C2213yescomplemented
75C2×C42×D53C2216yescomplemented
76C2×C42×D53C2213yescomplemented
77C2×C42×D53C2214yescomplemented
78C53×#533C2213yescomplemented
79C53×#532C2213yescomplemented
80C53×#529C22112yescomplemented
81C53×#525C2216yescomplemented
82C4×#41×C53C2216yescomplemented
83C22×C42×C53C2211yescharacteristic, complemented
84C24×D53C2311yescharacteristic
85C2×#11719949C2316yes—
86C2×#11719945C23112yes—
87C2×#11719945C2316yes—
88C2×#11719947C23112yes—
89C2×#11719947C2316yes—
90#41×D53—248no—
91C2×Q8×D53C2316yes—
92C2×D4×D53C23112yes—
93C2×D4×D53C2316yes—
94C23×Dic53C2313yes—
95C22×C4×D53—224no—
96C22×C4×D53C2316yes—
97C22×C4×D53C2316yes—
98C22×C4×D53C2313yes—
99C22×C4×D53C2313yes—
100C22×C4×D53C2313yes—
101C22×C4×D53C2316yes—
102C22×C4×D53C2316yes—
103C22×C4×D53C23112yes—
104C22×C4×D53C2313yes—
105#13133217C2313yescomplemented
106#13133216C23112yescomplemented
107#13133215C2316yescomplemented
108#13133214C2311yescharacteristic, complemented
109#13133213C2316yescomplemented
110#13133212C23124yescomplemented
111#13133211C2318yescomplemented
112#13133210C23124yescomplemented
113#13133209C2316yescomplemented
114#13133208C23112yescomplemented
115#13133207C23124yescomplemented
116#13133206C2316yescomplemented
117#13133205C2316yescomplemented
118#13133204C2316yescomplemented
119#13133203C23124yescomplemented
120#13133202C23124yes—
121#13133201C23112yes—
122#13133200C23112yes—
123#13133199C23124yes—
124#13133198C23112yes—
125#13133197C23112yes—
126#13133196C23112yes—
127#13133195C23124yes—
128#13133194C23124yes—
129#13133193C23112yes—
130#13133192C23112yes—
131#13133191C23112yes—
132#13133190C23124yes—
133#13133189C23124yes—
134#13133188C23112yes—
135#13133187C23112yes—
136#13133186C2314yes—
137#13133185C23112yes—
138Q8×Dic53C23112yescomplemented
139C4×Dic106C23124yescomplemented
140C4×Dic106C23112yescomplemented
141#13133182C23124yescomplemented
142#13133182C23112yescomplemented
143C4×D212C23124yes—
144C4×D212C23112yescomplemented
145D4×Dic53C23124yes—
146D4×Dic53C23112yescomplemented
147#13133179C23124yes—
148#13133179C23112yescomplemented
149C4×C22⋊D53C23124yes—
150C4×C22⋊D53C23124yes—
151C4×C22⋊D53C23124yescomplemented
152#13133177C23124yes—
153#13133177C23124yes—
154#13133177C23124yescomplemented
155#13133176C2316yes—
156#13133176C23112yescomplemented
157#13133175C23112yes—
158#13133175C23124yescomplemented
159#13133174C23112yes—
160#13133174C23112yescomplemented
161#13133174C23112yescomplemented
162#13133173C23112yes—
163#13133173C23124yescomplemented
164C4⋊C4×D53C23112yes—
165C4⋊C4×D53C23124yes—
166C22⋊C4×D53C23112yes—
167C22⋊C4×D53C23124yes—
168C2×C4×Dic53C2316yes—
169C2×C4×Dic53C2313yes—
170C2×C4×Dic53C2316yes—
171C2×C4×Dic53C2316yes—
172C2×C4×Dic53C2316yes—
173C2×C4×Dic53C2316yes—
174C2×C4×Dic53C2313yes—
175C2×C4×Dic53C23112yescomplemented
176C42×D53C2311yescharacteristic
177C42×D53C2313yes—
178C42×D53C2316yes—
179C42×D53C2313yes—
180C42×D53C2312yes—
181C42×D53C2311yescharacteristic
182C42×D53C2316yes—
183C42×D53C2313yes—
184C42×D53C2313yes—
185C42×D53C2316yes—
186C42×D53C2316yes—
187C42×D53C2316yes—
188C42×D53C2316yes—
189C42×D53C2316yes—
190C42×D53C2313yes—
191C42×D53C2313yes—
192C42×D53C23112yes—
193C42×D53C23112yescomplemented
194C42×D53C2314yescomplemented
195C2×#41×C53C2316yes—
196C23×C4×C53C2313yes—
197C4⋊Q8×C53C2313yescomplemented
198#127×C53C2311yescharacteristic, complemented
199#126×C53C2318yescomplemented
200#125×C53C2316yescomplemented
201#124×C53C2316yescomplemented
202#123×C53C23112yes—
203C22⋊Q8×C53C23112yes—
204#121×C53C23112yes—
205#120×C53C2314yes—
206C4×Q8×C53C23112yescomplemented
207C4×D4×C53C23124yes—
208C4×D4×C53C23112yescomplemented
209#117×C53C2316yes—
210#117×C53C23112yescomplemented
211C2×C42×C53C2313yes—
212C2×C42×C53C2316yes—
213C2×C42×C53C2313yes—
214C2×C42×C53C2314yescomplemented
215C24×C53C2411yescharacteristic
216C23×D53—212no—
217C23×D53C2414yes—
218C23×D53C2413yes—
219C23×D53C2413yes—
220#41×C53—224no—
221C2×Q8×C53C2416yes—
222C2×D4×C53C24112yes—
223C2×D4×C53C2416yes—
224C22×C4×C53—212no—
225C22×C4×C53C2416yes—
226C22×C4×C53C2416yes—
227C22×C4×C53C2413yes—
228C22×C4×C53C24112yes—
229C22×C4×C53C2413yes—
230C2×C22⋊D53C24112yes—
231C2×C22⋊D53C24112yes—
232C2×C22⋊D53C24112yes—
233C22×Dic53—212no—
234C22×Dic53C2416yes—
235C22×Dic53C2416yes—
236C22×Dic53C2413yes—
237C22×Dic53C24112yes—
238C22×Dic53C2413yes—
239#11719949—224no—
240Q8×D53—224no—
241#11719947—248no—
242#11719947—224no—
243D4×D53—248no—
244D4×D53—224no—
245#11719945—224no—
246#11719945—248no—
247C2×D212C24112yes—
248C2×D212C2416yes—
249C2×C4×D53—212no—
250C2×C4×D53—212no—
251C2×C4×D53—212no—
252C2×C4×D53—224no—
253C2×C4×D53—224no—
254C2×C4×D53—248no—
255C2×C4×D53—224no—
256C2×C4×D53—224no—
257C2×C4×D53#41124yescomplemented
258C2×C4×D53C2416yes—
259C2×C4×D53C2416yes—
260C2×C4×D53C2416yes—
261C2×C4×D53C2416yes—
262C2×C4×D53C2416yes—
263C2×C4×D53C2416yes—
264C2×C4×D53C24112yes—
265C2×C4×D53C24112yes—
266C2×C4×D53C24112yes—
267C2×C4×D53C2413yes—
268C2×C4×D53C2413yes—
269C2×C4×D53C2413yes—
270C2×C4×D53C2413yes—
271C2×Dic106C24112yes—
272C2×Dic106C2416yes—
273C4⋊C4×C53C24112yes—
274C4⋊C4×C53C24124yes—
275C22⋊C4×C53C24112yes—
276C22⋊C4×C53C24124yes—
277C42×C53C2413yes—
278C42×C53C2416yes—
279C42×C53C2413yes—
280C42×C53C2412yes—
281C42×C53C2411yescharacteristic
282C42×C53C24112yes—
283C42×C53C2411yescharacteristic
284C22⋊Dic53C24112yes—
285C22⋊Dic53C24124yes—
286#11719921C24124yes—
287#11719921C24124yes—
288#11719921C24124yes—
289C4⋊Dic53C24112yes—
290C4⋊Dic53C24124yes—
291#11719919C24124yes—
292#11719919C24124yes—
293#11719919C24124yes—
294C4×Dic53C2413yes—
295C4×Dic53C2416yes—
296C4×Dic53C2413yes—
297C4×Dic53C2416yes—
298C4×Dic53C2416yes—
299C4×Dic53C2416yes—
300C4×Dic53C2416yes—
301C4×Dic53C2413yes—
302C4×Dic53C2416yes—
303C4×Dic53C2413yes—
304C4×Dic53C24124yes—
305C4×Dic53C24112yes—
306C23×C53—26no—
307C23×C53C2514yes—
308C23×C53C2513yes—
309C22×D53—232no—
310C22×D53—26no—
311C22×D53—212no—
312C22×D53—212no—
313C22×D53—224no—
314C22×D53C2×#41112yes—
315C22×D53C2514yes—
316C22×D53C2513yes—
317C22×D53C2511yescharacteristic
318Q8×C53—212no—
319D4×C53—224no—
320D4×C53—212no—
321C2×C4×C53—26no—
322C2×C4×C53—212no—
323C2×C4×C53—212no—
324C2×C4×C53—224no—
325C2×C4×C53C2×#41112yescomplemented
326C2×C4×C53C25112yes—
327C2×C4×C53C2516yes—
328C2×C4×C53C2513yes—
329C2×C4×C53C2513yes—
330C22⋊D53—224no—
331C22⋊D53—224no—
332C22⋊D53—224no—
333C2×Dic53—26no—
334C2×Dic53—212no—
335C2×Dic53—212no—
336C2×Dic53—224no—
337C2×Dic53C2×#41112yescomplemented
338C2×Dic53C25112yes—
339C2×Dic53C2516yes—
340C2×Dic53C2513yes—
341C2×Dic53C2513yes—
342D212—224no—
343D212—212no—
344C4×D53—212no—
345C4×D53—212no—
346C4×D53—224no—
347C4×D53—212no—
348C4×D53—212no—
349C4×D53—224no—
350C4×D53—212no—
351C4×D53—212no—
352C4×D53—224no—
353C4×D53C2×#41112yes—
354C4×D53C2×#41112yes—
355C4×D53C2×#41112yescomplemented
356C4×D53C2×#41112yescomplemented
357Dic106—212no—
358Dic106—224no—
359C2×#3444—531nomaximal, Sylow
360C22×C53—28no—
361C22×C53—26no—
362C22×C53—212no—
363C22×C53C22×#4116yes—
364C22×C53C2611yescharacteristic
365C2×D53—224no—
366C2×D53—26no—
367C2×D53—224no—
368C2×D53—212no—
369C2×D53—416no—
370C2×D53C22×#4116yes—
371C2×D53C22×#4116yes—
372C4×C53—212no—
373C4×C53—26no—
374C4×C53C22×#4116yes—
375C4×C53C22×#4116yes—
376Dic53—212no—
377Dic53—26no—
378Dic53C22×#4116yes—
379Dic53C22×#4116yes—
380#3444—531no—
381#3444—533no—
382#3444—533no—
383#3444—5312no—
384#3444—536no—
385#3444—536no—
386#3444D5311yescharacteristic, direct product factor
387C2×#533—533no—
388C2×#532—533no—
389C2×#529—5312no—
390C2×#525—536no—
391C2×C4×#41—536no—
392C23×C42—531no—
393C2×C53—26no—
394C2×C53—44no—
395C2×C53C23×#4113yes—
396D53—26no—
397D53—44no—
398D53#344414yesdirect product factor
399C22×#41—536no—
400C24×C4—533no—
401#533—536no—
402#533—536no—
403#533—5312no—
404#533—5312no—
405#533—536no—
406#533—533no—
407#533C2×D5313yescomplemented
408#532—536no—
409#532—533no—
410#532—533no—
411#532—536no—
412#532—5312no—
413#532—5312no—
414#532—533no—
415#532C2×D5313yescomplemented
416C2×C4⋊Q8—533no—
417C2×#127—531no—
418#529—5324no—
419#529—5312no—
420#529—5312no—
421#529—5324no—
422#529—5312no—
423#529—5312no—
424#529—5312no—
425#529—5324no—
426#529—5312no—
427#529—5324no—
428#529—5312no—
429#529C2×D53112yescomplemented
430C2×#126—538no—
431C2×#125—536no—
432C2×#124—536no—
433#525—536no—
434#525—536no—
435#525—5312no—
436#525—5312no—
437#525—5312no—
438#525—5312no—
439#525—5324no—
440#525—536no—
441#525C2×D5316yescomplemented
442C2×#123—5312no—
443C2×C22⋊Q8—5312no—
444C2×#121—5312no—
445C2×#120—534no—
446C4×#41—536no—
447C4×#41—5312no—
448C4×#41—5324no—
449C4×#41—5312no—
450C4×#41—536no—
451C4×#41—5312no—
452C4×#41—536no—
453C4×#41—5312no—
454C4×#41C2×D5316yescomplemented
455C2×C4×Q8—5312no—
456C2×C4×D4—5324no—
457C2×C4×D4—5312no—
458C2×#117—536no—
459C2×#117—5312no—
460C22×C42—533no—
461C22×C42—533no—
462C22×C42—536no—
463C22×C42—533no—
464C22×C42—533no—
465C22×C42—536no—
466C22×C42—533no—
467C22×C42—534no—
468C22×C42C2×D5311yescharacteristic, complemented
469C53C2×#344411yescharacteristic, complemented, Sylow
470C25—531no—
471C2×#41—536no—
472C2×#41—5312no—
473C2×#41—536no—
474C2×#41—5312no—
475C2×#41—536no—
476C2×#41—10648no—
477C2×#41C22×D5316yes—
478C22×Q8—536no—
479C22×D4—5312no—
480C22×D4—536no—
481C23×C4—533no—
482C23×C4—533no—
483C23×C4—5312no—
484C23×C4—536no—
485C23×C4—536no—
486C23×C4—533no—
487C23×C4—533no—
488C23×C4—536no—
489C23×C4—536no—
490C23×C4—533no—
491C23×C4—10624no—
492C23×C4C22×D5313yes—
493C4⋊Q8—536no—
494C4⋊Q8—5312no—
495C4⋊Q8—533no—
496C4⋊Q8C22×D5313yescomplemented
497#127—536no—
498#127—531no—
499#127C22×D5311yescharacteristic, complemented
500#126—5324no—
501#126—5324no—
502#126—538no—
503#126C22×D5318yescomplemented
504#125—5324no—
505#125—5312no—
506#125—536no—
507#125C22×D5316yescomplemented
508#124—536no—
509#124—536no—
510#124—5324no—
511#124—536no—
512#124C22×D5316yescomplemented
513#123—5312no—
514#123—5312no—
515#123—5324no—
516#123—5324no—
517#123—5312no—
518#123C22×D53112yes—
519C22⋊Q8—5312no—
520C22⋊Q8—5312no—
521C22⋊Q8—5324no—
522C22⋊Q8—5312no—
523C22⋊Q8—5324no—
524C22⋊Q8C22×D53112yes—
525#121—5312no—
526#121—5324no—
527#121—5312no—
528#121—5312no—
529#121—5324no—
530#121C22×D53112yes—
531#120—534no—
532#120—5312no—
533#120—5312no—
534#120C22×D5314yes—
535C4×Q8—5312no—
536C4×Q8—5324no—
537C4×Q8—5312no—
538C4×Q8—5324no—
539C4×Q8—5312no—
540C4×Q8C22×D53112yescomplemented
541C4×D4—5324no—
542C4×D4—5312no—
543C4×D4—5324no—
544C4×D4—5324no—
545C4×D4—5324no—
546C4×D4—5324no—
547C4×D4—5312no—
548C4×D4—5324no—
549C4×D4—5324no—
550C4×D4—5324no—
551C4×D4—5324no—
552C4×D4—5312no—
553C4×D4C22×D53124yes—
554C4×D4C22×D53112yescomplemented
555#117—536no—
556#117—5312no—
557#117—5312no—
558#117—5324no—
559#117—5312no—
560#117—5324no—
561#117—5312no—
562#117—5312no—
563#117—5312no—
564#117C22×D5316yes—
565#117C22×D53112yescomplemented
566C2×C4⋊C4—5312no—
567C2×C4⋊C4—5324no—
568C2×C22⋊C4—5312no—
569C2×C22⋊C4—5324no—
570C2×C42—5312no—
571C2×C42—536no—
572C2×C42—533no—
573C2×C42—536no—
574C2×C42—536no—
575C2×C42—536no—
576C2×C42—536no—
577C2×C42—533no—
578C2×C42—533no—
579C2×C42—5312no—
580C2×C42—536no—
581C2×C42—5312no—
582C2×C42—536no—
583C2×C42—533no—
584C2×C42—533no—
585C2×C42—532no—
586C2×C42—536no—
587C2×C42—536no—
588C2×C42—536no—
589C2×C42—536no—
590C2×C42—531no—
591C2×C42—533no—
592C2×C42—533no—
593C2×C42—536no—
594C2×C42—534no—
595C2×C42—533no—
596C2×C42—531no—
597C2×C42C22×D5316yes—
598C2×C42C22×D5313yes—
599C2×C42C22×D5313yes—
600C2×C42C22×D5314yescomplemented
601C24—533no—
602C24—534no—
603C24—533no—
604C24—10612no—
605C24C23×D5311yescharacteristic
606#41—224no—
607#41—10648no—
608#41—10648no—
609#41—10624no—
610#41—10624no—
611#41—10624no—
612C2×Q8—5312no—
613C2×Q8—536no—
614C2×Q8—10624no—
615C2×Q8C23×D5316yes—
616C2×D4—5312no—
617C2×D4—5312no—
618C2×D4—5312no—
619C2×D4—5312no—
620C2×D4—536no—
621C2×D4—10624no—
622C2×D4—10648no—
623C2×D4C23×D53112yes—
624C2×D4C23×D5316yes—
625C22×C4—212no—
626C22×C4—533no—
627C22×C4—5324no—
628C22×C4—533no—
629C22×C4—533no—
630C22×C4—533no—
631C22×C4—533no—
632C22×C4—536no—
633C22×C4—536no—
634C22×C4—533no—
635C22×C4—5312no—
636C22×C4—536no—
637C22×C4—536no—
638C22×C4—536no—
639C22×C4—536no—
640C22×C4—536no—
641C22×C4—536no—
642C22×C4—5312no—
643C22×C4—5312no—
644C22×C4—5312no—
645C22×C4—10612no—
646C22×C4—10624no—
647C22×C4—10624no—
648C22×C4—10624no—
649C22×C4—10624no—
650C22×C4—10648no—
651C22×C4—10612no—
652C22×C4—10612no—
653C22×C4—10612no—
654C22×C4C23×D5316yes—
655C22×C4C23×D5316yes—
656C22×C4C23×D5313yes—
657C22×C4C23×D53112yes—
658C22×C4C23×D5313yes—
659C4⋊C4—5324no—
660C4⋊C4—5312no—
661C4⋊C4—5324no—
662C4⋊C4—5324no—
663C4⋊C4—5324no—
664C4⋊C4C23×D53112yes—
665C4⋊C4C23×D53124yes—
666C22⋊C4—5312no—
667C22⋊C4—5324no—
668C22⋊C4—5324no—
669C22⋊C4—5324no—
670C22⋊C4—5324no—
671C22⋊C4C23×D53112yes—
672C22⋊C4C23×D53124yes—
673C42—533no—
674C42—536no—
675C42—533no—
676C42—536no—
677C42—536no—
678C42—536no—
679C42—536no—
680C42—533no—
681C42—536no—
682C42—533no—
683C42—5324no—
684C42—5312no—
685C42C23×D5313yes—
686C42C23×D5316yes—
687C42C23×D5313yes—
688C42C23×D5312yes—
689C42C23×D5311yescharacteristic
690C42C23×D53112yes—
691C42C23×D5311yescharacteristic
692C23—26no—
693C23—531no—
694C23—5312no—
695C23—533no—
696C23—534no—
697C23—10612no—
698C23—10612no—
699C23—10624no—
700C23—10632no—
701C23—1066no—
702C23C24×D5314yes—
703C23C24×D5313yes—
704Q8—212no—
705Q8—10624no—
706Q8—10612no—
707D4—224no—
708D4—212no—
709D4—10624no—
710D4—10624no—
711D4—10624no—
712D4—10624no—
713D4—10612no—
714C2×C4—26no—
715C2×C4—212no—
716C2×C4—212no—
717C2×C4—224no—
718C2×C4—5312no—
719C2×C4—533no—
720C2×C4—533no—
721C2×C4—5312no—
722C2×C4—5312no—
723C2×C4—5312no—
724C2×C4—5312no—
725C2×C4—536no—
726C2×C4—5312no—
727C2×C4—10612no—
728C2×C4—10612no—
729C2×C4—10624no—
730C2×C4—10612no—
731C2×C4—10612no—
732C2×C4—10624no—
733C2×C4—10612no—
734C2×C4—10612no—
735C2×C4—10624no—
736C2×C4—1066no—
737C2×C4—10612no—
738C2×C4—10612no—
739C2×C4—10624no—
740C2×C4#41×D53112yescomplemented
741C2×C4C24×D5316yes—
742C2×C4C24×D53112yes—
743C2×C4C24×D5313yes—
744C2×C4C24×D5313yes—
745C22—28no—
746C22—26no—
747C22—212no—
748C22—536no—
749C22—536no—
750C22—10624no—
751C22—10624no—
752C22—1066no—
753C22—10612no—
754C22—21216no—
755C22C2×#41×D5316yes—
756C22C25×D5311yescharacteristic
757C4—26no—
758C4—212no—
759C4—536no—
760C4—536no—
761C4—1066no—
762C4—10612no—
763C4C2×#41×D5316yes—
764C4C2×#41×D5316yes—
765C2—26no—
766C2—44no—
767C2—534no—
768C2—1066no—
769C2—2124no—
770C2C22×#41×D5313yes—
subgroupG/H
centerC42C23×D53
commutator, socle, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC53×#3444C2
hypercenter#3444D53
hypocenterC53C2×#3444
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #20288012C2semidirect
2. #20288011C2semidirect
3. #20288010C2semidirect
4. #20288009C2semidirect
5. #20288008C2semidirect
6. #20288007C2semidirect
7. #533×D53C2semidirect
8. #532×D53C2semidirect
9. #529×D53C2semidirect
10. #525×D53C2semidirect
11. C4×#41×D53C2semidirect
12. C22×C42×D53C2semidirect
13. C53×#3444C2semidirect
16. #16811180C22semidirect
17. #16811179C22semidirect
18. #16811178C22semidirect
19. #16811177C22semidirect
20. #16811176C22semidirect
21. #16811175C22semidirect
22. #16811174C22semidirect
23. #16811173C22semidirect
24. #16811172C22semidirect
25. #16811171C22semidirect
26. #16811170C22semidirect
27. #16811169C22semidirect
28. #16811168C22semidirect
29. C4⋊Q8×D53C22semidirect
30. #127×D53C22semidirect
31. #16811160C22semidirect
32. #16811159C22semidirect
33. #16811158C22semidirect
34. #16811157C22semidirect
35. #16811156C22semidirect
36. #16811155C22semidirect
37. #16811154C22semidirect
38. #16811153C22semidirect
39. #16811152C22semidirect
40. #16811151C22semidirect
41. #16811150C22semidirect
42. #126×D53C22semidirect
43. #125×D53C22semidirect
44. #124×D53C22semidirect
45. #16811136C22semidirect
46. #16811135C22semidirect
47. #16811134C22semidirect
48. #16811133C22semidirect
49. #16811132C22semidirect
50. #16811131C22semidirect
51. #16811130C22semidirect
52. #16811129C22semidirect
57. #41×Dic53C22semidirect
58. C4×#11719949C22semidirect
59. C4×#11719945C22semidirect
60. C4×#11719945C22semidirect
61. #16811091C22semidirect
62. #16811091C22semidirect
63. C4×#11719947C22semidirect
64. C4×#11719947C22semidirect
65. C4×Q8×D53C22semidirect
67. C4×D4×D53C22semidirect
69. #117×D53C22semidirect
70. C22×C4×Dic53C22semidirect
74. C2×C42×D53C22semidirect
75. C2×C42×D53C22semidirect
76. C2×C42×D53C22semidirect
77. C2×C42×D53C22semidirect
78. C53×#533C22semidirect
79. C53×#532C22semidirect
80. C53×#529C22semidirect
81. C53×#525C22semidirect
82. C4×#41×C53C22semidirect
83. C22×C42×C53C22semidirect
105. #13133217C23semidirect
106. #13133216C23semidirect
107. #13133215C23semidirect
108. #13133214C23semidirect
109. #13133213C23semidirect
110. #13133212C23semidirect
111. #13133211C23semidirect
112. #13133210C23semidirect
113. #13133209C23semidirect
114. #13133208C23semidirect
115. #13133207C23semidirect
116. #13133206C23semidirect
117. #13133205C23semidirect
118. #13133204C23semidirect
119. #13133203C23semidirect
138. Q8×Dic53C23semidirect
139. C4×Dic106C23semidirect
140. C4×Dic106C23semidirect
141. #13133182C23semidirect
142. #13133182C23semidirect
144. C4×D212C23semidirect
146. D4×Dic53C23semidirect
148. #13133179C23semidirect
151. C4×C22⋊D53C23semidirect
154. #13133177C23semidirect
156. #13133176C23semidirect
158. #13133175C23semidirect
160. #13133174C23semidirect
161. #13133174C23semidirect
163. #13133173C23semidirect
175. C2×C4×Dic53C23semidirect
193. C42×D53C23semidirect
194. C42×D53C23semidirect
197. C4⋊Q8×C53C23semidirect
198. #127×C53C23semidirect
199. #126×C53C23semidirect
200. #125×C53C23semidirect
201. #124×C53C23semidirect
206. C4×Q8×C53C23semidirect
208. C4×D4×C53C23semidirect
210. #117×C53C23semidirect
214. C2×C42×C53C23semidirect
257. C2×C4×D53#41semidirect
325. C2×C4×C53C2×#41semidirect
337. C2×Dic53C2×#41semidirect
355. C4×D53C2×#41semidirect
356. C4×D53C2×#41semidirect
386. #3444D53direct (N × H)
398. D53#3444direct (N × H)
407. #533C2×D53semidirect
415. #532C2×D53semidirect
429. #529C2×D53semidirect
441. #525C2×D53semidirect
454. C4×#41C2×D53semidirect
468. C22×C42C2×D53semidirect
469. C53C2×#3444semidirect
496. C4⋊Q8C22×D53semidirect
499. #127C22×D53semidirect
503. #126C22×D53semidirect
507. #125C22×D53semidirect
512. #124C22×D53semidirect
540. C4×Q8C22×D53semidirect
554. C4×D4C22×D53semidirect
565. #117C22×D53semidirect
600. C2×C42C22×D53semidirect
740. C2×C4#41×D53semidirect

Maximal subgroups

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

subgroupindex
#202880122
#202880112
#202880102
#202880092
#202880082
#202880072
#533×D532
#532×D532
#529×D532
#525×D532
C4×#41×D532
C22×C42×D532
C53×#34442
C2×#344453