Finite Group Databasebeta

← #28253757

Subgroups — #28253757

Order 13568.

1798 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288118C211yesmaximal, characteristic
2C2×#16811250C211yesmaximal, characteristic
3#20285268C211yesmaximal, characteristic, complemented
4#20285267C211yesmaximal, characteristic, complemented
5#20285265C212yesmaximal, complemented
6#20285259C212yesmaximal, complemented
7#20285257C211yesmaximal, characteristic, complemented
8#20285250C214yesmaximal, complemented
9#20285248C214yesmaximal, complemented
10#20285242C214yesmaximal, complemented
11#20285240C214yesmaximal, complemented
12#20283302C212yesmaximal
13#428×D53C212yesmaximal
14#20283132C211yesmaximal, characteristic
15C53×#3165C211yesmaximal, characteristic, complemented
16C2×M16×D53C2212yes—
17#16811253C2212yes—
18#16811253C2212yes—
19#16811252—21no—
20#16811252—21no—
21#16811250—22no—
22#16811250—22no—
23#16811250C2212yes—
24#16811250C2214yes—
25#16811250C2214yes—
26#16811250C2212yes—
27#16811248—21no—
28#16811248—21no—
29#16811180C2211yescharacteristic
30#16811177—22no—
31#16811177—22no—
32#16811176C2212yes—
33C2×#13133216C2211yescharacteristic
34C2×#13133215—21no—
35C2×#13133209C2211yescharacteristic
36C2×#13133208C2211yescharacteristic
37C2×#13133207—21no—
38C2×#13133195—21no—
39C2×#13133193—21no—
40C2×#13133175C2211yescharacteristic
41C2×#13133174C2211yescharacteristic
42#117×D53C2212yes—
43C2×C4⋊C4×D53C2211yescharacteristic
44#16811032C2212yescomplemented
45#16811032C2212yescomplemented
46#16811031C2214yescomplemented
47#16811031C2214yescomplemented
48#16811030C2214yescomplemented
49#16811030C2214yescomplemented
50#16811029C2212yescomplemented
51#16811029C2214yescomplemented
52#16811029C2212yescomplemented
53#16811027C2214yescomplemented
54#16811026C2212yescomplemented
55#16811025C2214yescomplemented
56#16811024C2214yescomplemented
57#16811023C2214yescomplemented
58#16811022C2214yescomplemented
59#16811020C2214yescomplemented
60#16811019C2212yescomplemented
61#16810666C2212yes—
62#16810666C2212yes—
63#16810665C2212yes—
64#16810665C2212yes—
65#16810664C2214yes—
66#16810664C2214yes—
67#16810663C2212yes—
68#16810663C2212yes—
69#16810662C2214yes—
70#16810662C2214yes—
71#16810660C2214yes—
72#16810658C2214yes—
73#107×D53C2214yes—
74#106×D53C2214yes—
75#16810580C2214yes—
76#16810577C2214yes—
77C4×#11719917C2211yescharacteristic
78M16×Dic53C2212yes—
79C53×#533C2211yescharacteristic
80C2×C4⋊Q8×C53C2211yescharacteristic
81C53×#501C2214yescomplemented
82C53×#500C2212yescomplemented
83C53×#498C2212yescomplemented
84C53×#428C2212yes—
85C53×#428C2212yes—
86C4×M16×C53C2211yescharacteristic
87C22×Dic106—21no—
88C22×C4×D53—21no—
89C22×C4×D53C2311yescharacteristic
90C2×#11719917C2312yes—
91C2×#11719912C2314yes—
92M16×D53Q8116yescomplemented
93C2×C8×D53C2314yes—
94#13133217C2311yescharacteristic
95#13133217C2311yescharacteristic
96#13133216—22no—
97#13133216—22no—
98#13133216—22no—
99#13133216C2312yes—
100#13133216C2314yes—
101#13133216C2312yes—
102#13133215—24no—
103#13133215—24no—
104#13133215—22no—
105#13133215—22no—
106#13133209—21no—
107#13133209—21no—
108#13133209C2312yes—
109#13133209C2312yes—
110#13133209C2312yes—
111#13133208—22no—
112#13133208C2312yes—
113#13133208C2314yes—
114#13133208C2312yes—
115#13133207—24no—
116#13133207—24no—
117#13133207—22no—
118#13133207—22no—
119#13133207—22no—
120#13133207—22no—
121#13133197—22no—
122#13133197—22no—
123#13133196—21no—
124#13133196—21no—
125#13133195—24no—
126#13133195—24no—
127#13133195—22no—
128#13133195—22no—
129#13133195—22no—
130#13133195—22no—
131#13133194—22no—
132#13133194—22no—
133#13133193—24no—
134#13133193—24no—
135#13133193—22no—
136#13133193—22no—
137C4×Dic106—21no—
138C4×Dic106—21no—
139C4×Dic106—22no—
140C4×Dic106—22no—
141#13133176C2312yes—
142#13133175—22no—
143#13133175C2312yes—
144#13133175C2312yes—
145#13133175C2314yes—
146#13133174—22no—
147#13133174D412yes—
148#13133174D412yes—
149#13133174C2312yes—
150#13133174C2312yes—
151#13133173—22no—
152C2×C4⋊Dic53—21no—
153C2×C4⋊Dic53C2311yescharacteristic
154C2×C4⋊Dic53C2311yescharacteristic
155C2×#11719919—21no—
156C2×#11719919—21no—
157C2×#11719919—21no—
158C2×#11719919—21no—
159C2×#11719919—21no—
160C2×#11719919D411yescharacteristic
161C2×#11719919D411yescharacteristic
162C4⋊C4×D53—22no—
163C4⋊C4×D53C2314yes—
164C4⋊C4×D53C2312yes—
165C4⋊C4×D53C2312yes—
166C2×#11719921—21no—
167C2×#11719921D411yescharacteristic
168C2×#11719921D411yescharacteristic
169C22⋊C4×D53—22no—
170C2×C4×Dic53—21no—
171C2×C4×Dic53C2311yescharacteristic
172C42×D53—22no—
173#13133151C2314yes—
174#13133151C2314yes—
175#13133150C2314yes—
176#13133150C2314yes—
177#13133150C2314yes—
178#13133150C2314yes—
179#13133149C2314yes—
180#13133149C2314yes—
181#13133148C2314yes—
182#13133148C2314yes—
183#13133148C2314yes—
184#13133148C2314yes—
185#13133128C2312yes—
186#13133127C2314yes—
187C4×#88322C2312yes—
188C8×Dic53C2314yes—
189C22×Q8×C53—21no—
190C2×M16×C53C2312yes—
191C4⋊Q8×C53—21no—
192C4⋊Q8×C53—21no—
193C4⋊Q8×C53C2312yes—
194C4⋊Q8×C53C2311yescharacteristic
195C4⋊Q8×C53C2312yes—
196C4⋊Q8×C53C2311yescharacteristic
197#125×C53C2312yes—
198C22⋊Q8×C53—21no—
199C22⋊Q8×C53—21no—
200C4×Q8×C53—21no—
201C4×Q8×C53—21no—
202#117×C53C2312yes—
203C2×C4⋊C4×C53—21no—
204C2×C4⋊C4×C53C2311yescharacteristic
205C2×C4⋊C4×C53C2311yescharacteristic
206C2×C42×C53C2311yescharacteristic
207#107×C53C2314yes—
208#107×C53C2314yes—
209#106×C53C2314yes—
210#106×C53C2314yes—
211#97×C53C2312yes—
212C4×C8×C53C2312yes—
213C23×D53C2×D411yescharacteristic
214C2×Q8×C53—21no—
215C2×Q8×C53—21no—
216C2×Q8×C53—22no—
217C2×Q8×C53—22no—
218C2×Q8×C53—82no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2411yescharacteristic
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53C2×D411yescharacteristic
227C22×Dic53C2×D411yescharacteristic
228C22×Dic53C2×D411yescharacteristic
229C2×C4×D53—22no—
230C2×C4×D53—22no—
231C2×C4×D53—24no—
232C2×C4×D53—82no—
233C2×C4×D53C2×D412yes—
234C2×C4×D53C2×Q818yes—
235C2×C4×D53C2412yes—
236C2×Dic106—21no—
237C2×Dic106—21no—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—24no—
241C2×Dic106—82no—
242M16×C53C2×Q818yes—
243C2×C8×C53C2414yes—
244C4⋊C4×C53—22no—
245C4⋊C4×C53—22no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—22no—
249C4⋊C4×C53—22no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53C2412yes—
253C4⋊C4×C53C2412yes—
254C4⋊C4×C53C2412yes—
255C4⋊C4×C53C2412yes—
256C22⋊C4×C53—22no—
257C42×C53—22no—
258C42×C53C2×D411yescharacteristic
259C42×C53C2×D411yescharacteristic
260C42×C53C2411yescharacteristic
261C42×C53C2411yescharacteristic
262C22⋊Dic53—22no—
263#11719921—22no—
264#11719921—22no—
265#11719921—24no—
266#11719921C2×D412yes—
267#11719921C2×D412yes—
268#11719921C2×D412yes—
269#11719921C2×D412yes—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—21no—
273C4⋊Dic53—21no—
274C4⋊Dic53—24no—
275C4⋊Dic53—22no—
276C4⋊Dic53—22no—
277C4⋊Dic53C2412yes—
278C4⋊Dic53C2412yes—
279C4⋊Dic53C2412yes—
280C4⋊Dic53C2412yes—
281#11719919—22no—
282#11719919—22no—
283#11719919—22no—
284#11719919—22no—
285#11719919—22no—
286#11719919—22no—
287#11719919—24no—
288#11719919—22no—
289#11719919—22no—
290#11719919—24no—
291#11719919—24no—
292#11719919—22no—
293#11719919—22no—
294#11719919—22no—
295#11719919—22no—
296#11719919C2×D412yes—
297#11719919C2×D412yes—
298#11719919C2×D412yes—
299#11719919C2×D412yes—
300C4×Dic53—22no—
301C4×Dic53—22no—
302C4×Dic53—22no—
303C4×Dic53—24no—
304C4×Dic53C2×D412yes—
305C4×Dic53C2412yes—
306#11719917C2×Q818yes—
307C2×#88322C2414yes—
308#11719912C2×Q8116yescomplemented
309C8×D53C2×Q8116yescomplemented
310C23×C53C22×D411yescharacteristic
311C22×D53—41no—
312C22×D53—41no—
313C22×D53C4⋊Q814yes—
314C22×D53C22×D412yes—
315Q8×C53—81no—
316Q8×C53—81no—
317Q8×C53—82no—
318Q8×C53—82no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—41no—
324C2×C4×C53—41no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53C22×D411yescharacteristic
328C2×C4×C53C22×D411yescharacteristic
329C2×C4×C53C22×D411yescharacteristic
330C2×C4×C53C22×D411yescharacteristic
331C2×C4×C53C22×D411yescharacteristic
332C2×C4×C53C22×Q814yes—
333C2×C4×C53C2511yescharacteristic
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53C4⋊Q814yes—
343C2×Dic53C22×D412yes—
344C2×Dic53C22×D412yes—
345C2×Dic53C22×D412yes—
346C4×D53—82no—
347C4×D53—82no—
348C4×D53—84no—
349C4×D53C4⋊Q818yes—
350C4×D53C22×Q814yes—
351C4×D53C22×Q814yes—
352Dic106—82no—
353Dic106—82no—
354Dic106—84no—
355Dic106—81no—
356Dic106—81no—
357C8×C53C22×Q818yes—
358#88322C22×Q818yes—
359#60664—531nomaximal, Sylow
360C22×C53—21no—
361C22×C53—21no—
362C22×C53C2×C4⋊Q812yes—
363C22×C53C23×D411yescharacteristic
364C2×D53—22no—
365C2×D53—22no—
366C2×D53—44no—
367C2×D53C2×C4⋊Q814yes—
368C4×C53—21no—
369C4×C53—21no—
370C4×C53—21no—
371C4×C53—21no—
372C4×C53—42no—
373C4×C53—42no—
374C4×C53—42no—
375C4×C53—42no—
376C4×C53C2×C4⋊Q812yes—
377C4×C53C23×Q812yes—
378Dic53—22no—
379Dic53—22no—
380Dic53—42no—
381Dic53—42no—
382Dic53—42no—
383Dic53—42no—
384Dic53C2×C4⋊Q814yes—
385#3458—531no—
386C2×#544—531no—
387#3166—532no—
388#3166—531no—
389#3166—531no—
390#3165—532no—
391#3165—531no—
392#3165D5311yescharacteristic, complemented
393#3164—534no—
394#3164—534no—
395#3163—534no—
396#3163—534no—
397#2911—532no—
398C2×#428—532no—
399#2873—531no—
400C2×C53—22no—
401C2×C53C22×C4⋊Q811yescharacteristic
402C2×C53#358511yescharacteristic
403C2×C53#358611yescharacteristic
404D53—24no—
405C22×M16—532no—
406#544—532no—
407#544—534no—
408#544—534no—
409#544—532no—
410#544—532no—
411#544—532no—
412#544—1061no—
413#544—1061no—
414#544—1062no—
415#544—1062no—
416#543—1061no—
417#543—1061no—
418#533—532no—
419#533—531no—
420#533—1062no—
421#533—1062no—
422#533C2×D5311yescharacteristic
423C2×C4⋊Q8—531no—
424C2×C4⋊Q8—1061no—
425C2×C4⋊Q8C2×D5311yescharacteristic
426C2×#125—531no—
427C2×#125—531no—
428C2×#125—1061no—
429C2×C22⋊Q8—1061no—
430C2×C22⋊Q8—1061no—
431C2×#117—531no—
432C2×#117—532no—
433C2×#117—531no—
434C22×C4⋊C4—531no—
435#501—532no—
436#501—534no—
437#501—532no—
438#501—534no—
439#501—534no—
440#501—534no—
441#501—534no—
442#501—532no—
443#501—532no—
444#501C2×D5314yescomplemented
445#500—532no—
446#500—534no—
447#500C2×D5312yescomplemented
448#499—534no—
449#499—534no—
450#499—534no—
451#499—534no—
452#498—532no—
453#498—534no—
454#498C2×D5312yescomplemented
455#428—532no—
456#428—532no—
457#428—532no—
458#428—532no—
459#428—532no—
460#428—532no—
461#428—534no—
462#428—534no—
463#428—534no—
464#428—534no—
465#428C2×D5312yes—
466#428C2×D5312yes—
467#427—534no—
468#427—534no—
469C2×#107—534no—
470C2×#106—534no—
471#405—534no—
472#405—534no—
473C4×M16—532no—
474C4×M16—531no—
475C4×M16C2×D5311yescharacteristic
476C53#6066411yescharacteristic, complemented, Sylow
477C22×Q8—21no—
478C22×Q8—1061no—
479C23×C4—531no—
480C23×C4—1061no—
481C2×M16—532no—
482C2×M16—5316no—
483C2×M16—534no—
484C2×M16C22×D5312yes—
485C22×C8—534no—
486C4⋊Q8—21no—
487C4⋊Q8—21no—
488C4⋊Q8—534no—
489C4⋊Q8—532no—
490C4⋊Q8—532no—
491C4⋊Q8—531no—
492C4⋊Q8—531no—
493C4⋊Q8—1062no—
494C4⋊Q8—1062no—
495C4⋊Q8—1062no—
496C4⋊Q8—1064no—
497C4⋊Q8—1064no—
498C4⋊Q8—1062no—
499C4⋊Q8—1062no—
500C4⋊Q8C22×D5312yes—
501C4⋊Q8C22×D5312yes—
502C4⋊Q8C22×D5311yescharacteristic
503C4⋊Q8C22×D5311yescharacteristic
504#125—534no—
505#125—532no—
506#125—532no—
507#125—532no—
508#125—532no—
509#125—532no—
510#125—1062no—
511#125—1064no—
512#125—1064no—
513#125—1062no—
514#125—1062no—
515#125—1062no—
516#125—1062no—
517#125—1061no—
518#125—1061no—
519#125C22×D5312yes—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—1062no—
523C22⋊Q8—1062no—
524C22⋊Q8—1064no—
525C22⋊Q8—1064no—
526C22⋊Q8—1062no—
527C22⋊Q8—1062no—
528C22⋊Q8—1062no—
529C22⋊Q8—1062no—
530C22⋊Q8—1062no—
531C22⋊Q8—1062no—
532C22⋊Q8—1064no—
533C22⋊Q8—1064no—
534C22⋊Q8—1062no—
535C22⋊Q8—1062no—
536C22⋊Q8—1061no—
537C22⋊Q8—1061no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—1062no—
541C4×Q8—1062no—
542C4×Q8—1061no—
543C4×Q8—1061no—
544#117—532no—
545#117—532no—
546#117—532no—
547#117—532no—
548#117—532no—
549#117—532no—
550#117—534no—
551#117—532no—
552#117—1062no—
553#117—1062no—
554#117—1062no—
555#117C22×D5312yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—531no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—531no—
560C2×C4⋊C4—531no—
561C2×C4⋊C4—534no—
562C2×C4⋊C4—532no—
563C2×C4⋊C4—532no—
564C2×C4⋊C4—1062no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—1061no—
568C2×C4⋊C4—1061no—
569C2×C4⋊C4—1061no—
570C2×C4⋊C4—1061no—
571C2×C4⋊C4C22×D5311yescharacteristic
572C2×C4⋊C4C22×D5311yescharacteristic
573C2×C22⋊C4—531no—
574C2×C22⋊C4—531no—
575C2×C22⋊C4—1062no—
576C2×C22⋊C4—1061no—
577C2×C42—531no—
578C2×C42—1062no—
579C2×C42—1061no—
580C2×C42C22×D5311yescharacteristic
581#107—534no—
582#107—534no—
583#107—534no—
584#107—534no—
585#107—534no—
586#107—534no—
587#107C22×D5314yes—
588#107C22×D5314yes—
589#106—534no—
590#106—534no—
591#106—534no—
592#106—534no—
593#106—534no—
594#106—534no—
595#106C22×D5314yes—
596#106C22×D5314yes—
597#97—534no—
598#97—532no—
599#97C22×D5312yes—
600C4×C8—534no—
601C4×C8—532no—
602C4×C8C22×D5312yes—
603C24—531no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—82no—
609C2×Q8—1062no—
610C2×Q8—1062no—
611C2×Q8—1064no—
612C2×Q8—1061no—
613C2×Q8—1061no—
614C2×Q8—4242no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—531no—
618C22×C4—532no—
619C22×C4—538no—
620C22×C4—532no—
621C22×C4—531no—
622C22×C4—531no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1064no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4—4242no—
629C22×C4D4×D5311yescharacteristic
630C22×C4D4×D5311yescharacteristic
631C22×C4C23×D5311yescharacteristic
632M16—538no—
633M16—5316no—
634M16Q8×D5318yes—
635C2×C8—534no—
636C2×C8—5316no—
637C2×C8C23×D5314yes—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—532no—
647C4⋊C4—532no—
648C4⋊C4—532no—
649C4⋊C4—532no—
650C4⋊C4—532no—
651C4⋊C4—532no—
652C4⋊C4—532no—
653C4⋊C4—532no—
654C4⋊C4—1064no—
655C4⋊C4—1062no—
656C4⋊C4—1062no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1062no—
661C4⋊C4—1062no—
662C4⋊C4—1062no—
663C4⋊C4—1062no—
664C4⋊C4—1062no—
665C4⋊C4—1062no—
666C4⋊C4—1061no—
667C4⋊C4—1061no—
668C4⋊C4—1062no—
669C4⋊C4—1062no—
670C4⋊C4—1062no—
671C4⋊C4—1062no—
672C4⋊C4—1062no—
673C4⋊C4—1062no—
674C4⋊C4—1061no—
675C4⋊C4—1061no—
676C4⋊C4C23×D5312yes—
677C4⋊C4C23×D5312yes—
678C4⋊C4C23×D5312yes—
679C4⋊C4C23×D5312yes—
680C22⋊C4—22no—
681C22⋊C4—532no—
682C22⋊C4—532no—
683C22⋊C4—532no—
684C22⋊C4—532no—
685C22⋊C4—1062no—
686C22⋊C4—1062no—
687C22⋊C4—1064no—
688C22⋊C4—1062no—
689C42—22no—
690C42—532no—
691C42—532no—
692C42—1062no—
693C42—1062no—
694C42—1064no—
695C42—1062no—
696C42D4×D5311yescharacteristic
697C42D4×D5311yescharacteristic
698C42C23×D5311yescharacteristic
699C42C23×D5311yescharacteristic
700C23—532no—
701C23—534no—
702C23—2121no—
703C23—2121no—
704C23C2×D4×D5311yescharacteristic
705Q8—81no—
706Q8—81no—
707Q8—82no—
708Q8—82no—
709Q8—4241no—
710Q8—4241no—
711Q8—4242no—
712Q8—4242no—
713Q8—4244no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—534no—
723C2×C4—532no—
724C2×C4—538no—
725C2×C4—534no—
726C2×C4—534no—
727C2×C4—532no—
728C2×C4—532no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—4242no—
734C2×C4—4242no—
735C2×C4—4244no—
736C2×C4—2121no—
737C2×C4—2121no—
738C2×C4—2122no—
739C2×C4—2122no—
740C2×C4C2×D4×D5311yescharacteristic
741C2×C4C2×D4×D5311yescharacteristic
742C2×C4C2×D4×D5311yescharacteristic
743C2×C4C2×D4×D5311yescharacteristic
744C2×C4C2×D4×D5311yescharacteristic
745C2×C4C2×Q8×D5314yes—
746C2×C4C24×D5311yescharacteristic
747C8—538no—
748C8C2×Q8×D5318yes—
749C22—21no—
750C22—21no—
751C22—534no—
752C22—1062no—
753C22—1062no—
754C22—2124no—
755C22C4⋊Q8×D5312yes—
756C22C22×D4×D5311yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—534no—
766C4—1062no—
767C4—1062no—
768C4—2122no—
769C4—2122no—
770C4—2122no—
771C4—2122no—
772C4C4⋊Q8×D5312yes—
773C4C22×Q8×D5312yes—
774C2—22no—
775C2—1064no—
776C2C2×C4⋊Q8×D5311yescharacteristic
777C2#2028949111yescharacteristic
778C2#2028949811yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3165C2
socleC22×C53C23×D4
prime radicalC23×D53C2×D4
hypercenter#3165D53
hypocenterC53#60664
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. #20285268C2semidirect
4. #20285267C2semidirect
5. #20285265C2semidirect
6. #20285259C2semidirect
7. #20285257C2semidirect
8. #20285250C2semidirect
9. #20285248C2semidirect
10. #20285242C2semidirect
11. #20285240C2semidirect
15. C53×#3165C2semidirect
44. #16811032C22semidirect
45. #16811032C22semidirect
46. #16811031C22semidirect
47. #16811031C22semidirect
48. #16811030C22semidirect
49. #16811030C22semidirect
50. #16811029C22semidirect
51. #16811029C22semidirect
52. #16811029C22semidirect
53. #16811027C22semidirect
54. #16811026C22semidirect
55. #16811025C22semidirect
56. #16811024C22semidirect
57. #16811023C22semidirect
58. #16811022C22semidirect
59. #16811020C22semidirect
60. #16811019C22semidirect
81. C53×#501C22semidirect
82. C53×#500C22semidirect
83. C53×#498C22semidirect
92. M16×D53Q8semidirect
308. #11719912C2×Q8semidirect
309. C8×D53C2×Q8semidirect
392. #3165D53semidirect
444. #501C2×D53semidirect
447. #500C2×D53semidirect
454. #498C2×D53semidirect
476. C53#60664semidirect

Maximal subgroups

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

subgroupindex
#202881182
C2×#168112502
#202852682
#202852672
#202852652
#202852592
#202852572
#202852502
#202852482
#202852422
#202852402
#202833022
#428×D532
#202831322
C53×#31652
#6066453