Finite Group Databasebeta

← #28252842

Subgroups — #28252842

Order 13568.

2214 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288457C211yesmaximal, characteristic, complemented
2#518×D53C211yesmaximal, characteristic, complemented
3#20284966C212yesmaximal, complemented
4#20284964C212yesmaximal, complemented
5#20284905C212yesmaximal, complemented
6#20284903C212yesmaximal, complemented
7#20284857C212yesmaximal, complemented
8#20284812C212yesmaximal, complemented
9#20284766C212yesmaximal, complemented
10#20284721C212yesmaximal, complemented
11#20284661C211yesmaximal, characteristic, complemented
12#20284632C211yesmaximal, characteristic, complemented
13#20284549C211yesmaximal, characteristic, complemented
14#20284548C211yesmaximal, characteristic, complemented
15#20284226C211yesmaximal, characteristic, complemented
16#20284224C211yesmaximal, characteristic, complemented
17#20283944C211yesmaximal, characteristic
18C2×#16810772C211yesmaximal, characteristic, complemented
19#20283574C211yesmaximal, characteristic, complemented
20#20283549C211yesmaximal, characteristic, complemented
21#20283547C211yesmaximal, characteristic, complemented
22#20283370C211yesmaximal, characteristic, complemented
23C53×#2949C211yesmaximal, characteristic, complemented
24C22×D4×D53C2211yescharacteristic
25C2×#13133245C2211yescharacteristic
26C2×#13133243C2211yescharacteristic
27C22×#11719924C2211yescharacteristic
28#16811346—21no—
29#16811333—21no—
30#16811314—21no—
31#16811314—21no—
32#16811306—22no—
33#16811297—22no—
34#16811251C2211yescharacteristic, complemented
35#16811245C2212yescomplemented
36#16811231C2212yescomplemented
37#16811197C2211yescharacteristic, complemented
38#16811177C2212yescomplemented
39#16811160C2212yescomplemented
40#16811135C2211yescharacteristic
41C2×#13133193C2211yescharacteristic
42#16811103C2211yescharacteristic, complemented
43#16811098C2211yescharacteristic
44#16811097C2211yescharacteristic
45#16811097C2211yescharacteristic
46#16811096—22no—
47#16811095—21no—
48#16811095—21no—
49#16811095C2212yes—
50#16811095C2212yes—
51C4×D4×D53—21no—
52C4×D4×D53—21no—
53C4×D4×D53C2212yes—
54C4×D4×D53C2212yes—
55#117×D53C2211yescharacteristic
56#117×D53C2211yescharacteristic
57C2×C22⋊C4×D53—22no—
58#16810967C2211yescharacteristic, complemented
59#16810966C2211yescharacteristic, complemented
60#16810963C2212yescomplemented
61#16810962C2212yescomplemented
62#16810960C2211yescharacteristic, complemented
63#16810957C2212yescomplemented
64#16810955C2211yescharacteristic, complemented
65#16810952C2212yescomplemented
66#16810950C2211yescharacteristic, complemented
67#16810949C2211yescharacteristic, complemented
68#16810943C2211yescharacteristic, complemented
69#16810938C2211yescharacteristic, complemented
70#16810926C2212yescomplemented
71#16810925C2212yescomplemented
72#16810922C2212yescomplemented
73#16810921C2212yescomplemented
74#16810912C2212yescomplemented
75#16810911C2212yescomplemented
76#16810902C2212yescomplemented
77#16810901C2212yescomplemented
78#16810841C2212yescomplemented
79#16810841C2212yescomplemented
80#16810840C2212yescomplemented
81#16810840C2212yescomplemented
82#16810827C2212yescomplemented
83#16810827C2212yescomplemented
84#16810826C2212yescomplemented
85#16810826C2212yescomplemented
86#16810775C2212yes—
87#16810775C2212yes—
88#16810772C2212yes—
89#16810772C2212yes—
90#16810772C2212yes—
91#16810772C2212yes—
92#16810758C2212yes—
93#16810758C2212yes—
94#16810736C2212yescomplemented
95#16810733C2212yescomplemented
96#16810725C2212yescomplemented
97#16810723C2212yescomplemented
98#16810721C2212yescomplemented
99#16810721C2212yescomplemented
100C4×#11719913C2212yescomplemented
101C4×#11719924C2212yescomplemented
102C4×#11719924C2212yescomplemented
103C4×#11719923C2212yescomplemented
104C4×D424C2212yescomplemented
105C4×#11719922C2212yescomplemented
106#16810685C2212yescomplemented
107#16810682C2212yescomplemented
108#16810678C2212yescomplemented
109#16810674C2212yescomplemented
110#16810666C2211yescharacteristic, complemented
111#16810665C2211yescharacteristic, complemented
112#16810659C2211yescharacteristic, complemented
113#16810651C2211yescharacteristic, complemented
114#16810649C2211yescharacteristic, complemented
115#16810632C2211yescharacteristic, complemented
116#16810627C2211yescharacteristic
117#16810620C2211yescharacteristic, complemented
118#16810617C2211yescharacteristic, complemented
119C2×#13133139C2211yescharacteristic
120C2×#13133138C2211yescharacteristic
121#16810586C2211yescharacteristic
122C2×#13133129C2211yescharacteristic
123#16810579C2211yescharacteristic, complemented
124C22×SD16×C53C2211yescharacteristic
125C53×#519C2211yescharacteristic, complemented
126C53×#518C2211yescharacteristic
127C53×#440C2212yescomplemented
128C53×#440C2212yescomplemented
129C4×SD16×C53C2212yescomplemented
130C4×SD16×C53C2212yescomplemented
131C53×#427C2211yescharacteristic, complemented
132C53×#419C2211yescharacteristic, complemented
133C53×#418C2211yescharacteristic
134C53×#405C2211yescharacteristic, complemented
135C24×D53—21no—
136C2×#11719945C2311yescharacteristic
137C22×D212C2311yescharacteristic
138C22×C22⋊D53—21no—
139C2×D4×D53—24no—
140C2×D4×D53—24no—
141C2×D4×D53—21no—
142C2×D4×D53—21no—
143C2×D4×D53C2312yes—
144C2×D4×D53C2312yes—
145C22×C4×D53—22no—
146C22×C4×D53—22no—
147C22×C4×D53C2311yescharacteristic
148#13133245—24no—
149#13133243—24no—
150C2×#11719913C2312yes—
151C2×#11719923C2312yes—
152C2×#11719924—24no—
153C2×#11719924C2312yes—
154C2×#11719924C2312yes—
155C2×D424C2312yes—
156C2×#11719922C2312yes—
157C2×#11719917C2311yescharacteristic
158C22×#88322C2311yescharacteristic
159#13133217—21no—
160#13133216C2312yescomplemented
161#13133215C2312yescomplemented
162#13133212—22no—
163#13133212—22no—
164#13133211—22no—
165#13133211—22no—
166#13133209—21no—
167#13133209—22no—
168#13133208C2312yescomplemented
169#13133207—22no—
170#13133207—22no—
171#13133206C2312yescomplemented
172#13133205—22no—
173#13133202—22no—
174#13133202—22no—
175#13133201—21no—
176#13133200—22no—
177#13133197C2311yescharacteristic
178#13133197C2311yescharacteristic
179#13133195—22no—
180#13133195—22no—
181#13133194—22no—
182#13133193—21no—
183#13133193—21no—
184#13133193—21no—
185#13133193—21no—
186#13133193C2312yes—
187#13133193C2312yes—
188#13133192C2311yescharacteristic
189#13133192C2311yescharacteristic
190#13133187—21no—
191C4×Dic106—22no—
192C4×Dic106C2312yescomplemented
193C4×D212—21no—
194C4×D212—21no—
195C4×D212—22no—
196C4×D212—21no—
197C4×D212—21no—
198C4×D212C2312yes—
199C4×D212C2312yes—
200C4×D212C2312yescomplemented
201D4×Dic53—21no—
202D4×Dic53—21no—
203D4×Dic53C2312yes—
204D4×Dic53C2312yes—
205#13133179—21no—
206#13133179—21no—
207#13133179C2312yes—
208#13133179C2312yes—
209C4×C22⋊D53—22no—
210C4×C22⋊D53—22no—
211C4×C22⋊D53—22no—
212C4×C22⋊D53—22no—
213#13133177—22no—
214#13133177—22no—
215#13133177—22no—
216#13133177—22no—
217#13133177—22no—
218#13133176C2311yescharacteristic
219#13133176C2311yescharacteristic
220#13133175—21no—
221#13133175D411yescharacteristic
222#13133175D411yescharacteristic
223#13133175C2311yescharacteristic
224#13133175C2311yescharacteristic
225#13133174—22no—
226#13133174—22no—
227#13133174—21no—
228#13133174C2312yes—
229#13133173—21no—
230#13133173D412yes—
231C2×C4⋊Dic53C2311yescharacteristic
232C2×#11719919—21no—
233C4⋊C4×D53—21no—
234C4⋊C4×D53D411yescharacteristic
235C4⋊C4×D53D411yescharacteristic
236C4⋊C4×D53C2311yescharacteristic
237C4⋊C4×D53C2311yescharacteristic
238C2×C22⋊Dic53—22no—
239C2×#11719921—22no—
240C2×#11719921—22no—
241C2×#11719921—21no—
242C22⋊C4×D53—22no—
243C22⋊C4×D53—22no—
244C22⋊C4×D53—22no—
245C22⋊C4×D53—22no—
246C22⋊C4×D53—21no—
247C22⋊C4×D53—22no—
248C22⋊C4×D53—22no—
249C22⋊C4×D53D412yes—
250C42×D53—21no—
251C42×D53C2312yes—
252#13133151C2312yescomplemented
253#13133150C2311yescharacteristic, complemented
254#13133150C2312yescomplemented
255#13133150C2311yescharacteristic, complemented
256#13133149C2312yescomplemented
257#13133148C2311yescharacteristic, complemented
258#13133148C2312yescomplemented
259#13133148C2311yescharacteristic, complemented
260#13133146C2312yescomplemented
261#13133146C2312yescomplemented
262#13133146C2312yescomplemented
263#13133146C2312yescomplemented
264#13133142C2311yescharacteristic, complemented
265#13133142C2311yescharacteristic, complemented
266#13133141C2312yescomplemented
267#13133141C2312yescomplemented
268#13133140C2311yescharacteristic, complemented
269#13133140C2311yescharacteristic, complemented
270#13133139C2312yes—
271#13133139C2312yes—
272#13133139C2311yescharacteristic, complemented
273#13133139C2311yescharacteristic, complemented
274#13133138C2312yes—
275#13133138C2312yes—
276#13133137C2312yes—
277#13133137C2312yes—
278#13133137C2311yescharacteristic, complemented
279#13133137C2311yescharacteristic, complemented
280#13133129C2312yes—
281#13133129C2312yes—
282#13133129C2311yescharacteristic
283#13133129C2311yescharacteristic
284#13133129C2311yescharacteristic
285#13133129C2311yescharacteristic
286#13133128C2312yescomplemented
287C4×#88322C2312yescomplemented
288C22×Q8×C53C2311yescharacteristic
289C22×D4×C53C2311yescharacteristic
290C2×SD16×C53—24no—
291C2×SD16×C53C2312yes—
292C2×SD16×C53C2312yes—
293C2×M16×C53C2311yescharacteristic
294C22×C8×C53C2311yescharacteristic
295C4×Q8×C53—21no—
296C4×Q8×C53—21no—
297C4×Q8×C53C2312yescomplemented
298C4×Q8×C53C2312yescomplemented
299C4×D4×C53—21no—
300C4×D4×C53—21no—
301C4×D4×C53C2312yes—
302C4×D4×C53C2312yes—
303#117×C53—22no—
304#117×C53C2311yescharacteristic
305#117×C53C2311yescharacteristic
306#117×C53C2311yescharacteristic
307C2×C22⋊C4×C53—22no—
308#107×C53C2311yescharacteristic, complemented
309#107×C53C2311yescharacteristic, complemented
310#106×C53C2311yescharacteristic, complemented
311#106×C53C2311yescharacteristic, complemented
312#103×C53C2312yescomplemented
313#103×C53C2312yescomplemented
314#102×C53C2312yes—
315#102×C53C2312yes—
316#97×C53C2312yescomplemented
317C4×C8×C53C2312yescomplemented
318C24×C53—21no—
319C23×D53—28no—
320C23×D53—21no—
321C23×D53—22no—
322C23×D53—22no—
323C23×D53—82no—
324C23×D53—82no—
325C23×D53C2×D411yescharacteristic
326C2×Q8×C53—21no—
327C2×Q8×C53—22no—
328C2×Q8×C53—22no—
329C2×Q8×C53C2412yes—
330C2×D4×C53—21no—
331C2×D4×C53—22no—
332C2×D4×C53#4114yes—
333C2×D4×C53C2412yes—
334C22×C4×C53—21no—
335C22×C4×C53—22no—
336C22×C4×C53—22no—
337C22×C4×C53C2411yescharacteristic
338C2×C22⋊D53—28no—
339C2×C22⋊D53—21no—
340C2×C22⋊D53—22no—
341C2×C22⋊D53—22no—
342C22×Dic53—21no—
343C22×Dic53—22no—
344C22×Dic53—22no—
345C22×Dic53C2×D411yescharacteristic
346D4×D53—28no—
347D4×D53—28no—
348D4×D53—24no—
349D4×D53—24no—
350D4×D53—24no—
351D4×D53—24no—
352#11719945—22no—
353#11719945—22no—
354C2×D212—21no—
355C2×D212—22no—
356C2×D212—21no—
357C2×D212—21no—
358C2×D212#4114yes—
359C2×D212C2411yescharacteristic
360C2×D212C2412yes—
361C2×C4×D53—22no—
362C2×C4×D53—22no—
363C2×C4×D53—21no—
364C2×C4×D53—21no—
365C2×C4×D53—21no—
366C2×C4×D53—22no—
367C2×C4×D53—22no—
368C2×C4×D53—22no—
369C2×C4×D53—22no—
370C2×C4×D53—22no—
371C2×C4×D53—84no—
372C2×C4×D53—84no—
373C2×C4×D53C2×D411yescharacteristic
374C2×C4×D53C2×D412yes—
375C2×C4×D53C2×D411yescharacteristic
376C2×C4×D53C2×D412yes—
377C2×C4×D53C2411yescharacteristic
378C2×C4×D53C2411yescharacteristic
379C2×Dic106—22no—
380C2×Dic106C2411yescharacteristic
381SD16×C53—24no—
382SD16×C53—24no—
383M16×C53—22no—
384C2×C8×C53—22no—
385C2×C8×C53C2411yescharacteristic
386C2×C8×C53C2412yes—
387C2×C8×C53C2411yescharacteristic
388C4⋊C4×C53—22no—
389C4⋊C4×C53—22no—
390C4⋊C4×C53C2×D411yescharacteristic
391C4⋊C4×C53C2×D411yescharacteristic
392C4⋊C4×C53C2411yescharacteristic
393C4⋊C4×C53C2411yescharacteristic
394C4⋊C4×C53C2411yescharacteristic
395C4⋊C4×C53C2411yescharacteristic
396C22⋊C4×C53—21no—
397C22⋊C4×C53—21no—
398C22⋊C4×C53—22no—
399C22⋊C4×C53—22no—
400C22⋊C4×C53C2×D412yes—
401C42×C53—22no—
402C42×C53—22no—
403C42×C53—21no—
404C42×C53—21no—
405C42×C53C2412yes—
406C22⋊Dic53—21no—
407C22⋊Dic53—22no—
408C22⋊Dic53—22no—
409C22⋊Dic53C2×D412yes—
410#11719924—24no—
411#11719924—24no—
412#11719923—24no—
413#11719922—24no—
414#11719921—21no—
415#11719921—21no—
416#11719921—22no—
417#11719921—22no—
418#11719921—21no—
419#11719921—21no—
420#11719921—22no—
421#11719921—22no—
422#11719921—22no—
423#11719921—22no—
424#11719921—22no—
425#11719921—21no—
426#11719921—22no—
427#11719921—21no—
428#11719921—22no—
429#11719921C2×D412yes—
430#11719921C2×D412yes—
431C4⋊Dic53—21no—
432C4⋊Dic53—21no—
433C4⋊Dic53—22no—
434C4⋊Dic53—21no—
435C4⋊Dic53C2×D411yescharacteristic
436C4⋊Dic53C2×D411yescharacteristic
437C4⋊Dic53C2412yes—
438C4⋊Dic53C2411yescharacteristic
439C4⋊Dic53C2411yescharacteristic
440#11719919—22no—
441#11719919—21no—
442#11719919—21no—
443#11719919—22no—
444#11719919—22no—
445#11719919—22no—
446#11719919—22no—
447#11719919—22no—
448#11719919—22no—
449#11719919C2×D412yes—
450#11719919C2×D412yes—
451C4×Dic53—21no—
452C4×Dic53—22no—
453C4×Dic53—21no—
454C4×Dic53—21no—
455C4×Dic53C2×D412yes—
456C4×Dic53C2×D412yes—
457C4×Dic53C2412yes—
458#11719917—22no—
459C2×#88322—22no—
460C2×#88322C2411yescharacteristic
461C2×#88322C2412yes—
462C2×#88322C2411yescharacteristic
463D424—24no—
464#11719913—24no—
465C23×C53—22no—
466C23×C53—24no—
467C23×C53—81no—
468C23×C53—81no—
469C23×C53C22×D411yescharacteristic
470C22×D53—28no—
471C22×D53—22no—
472C22×D53—22no—
473C22×D53—28no—
474C22×D53—24no—
475C22×D53—22no—
476C22×D53—21no—
477C22×D53—41no—
478C22×D53—44no—
479C22×D53—44no—
480C22×D53—82no—
481C22×D53—82no—
482C22×D53—816no—
483C22×D53—81no—
484C22×D53—81no—
485C22×D53C22×D411yescharacteristic
486C22×D53C22×D411yescharacteristic
487Q8×C53—22no—
488Q8×C53—22no—
489Q8×C53—42no—
490D4×C53—24no—
491D4×C53—22no—
492D4×C53C2×#4114yes—
493C2×C4×C53—21no—
494C2×C4×C53—21no—
495C2×C4×C53—21no—
496C2×C4×C53—21no—
497C2×C4×C53—22no—
498C2×C4×C53—42no—
499C2×C4×C53—82no—
500C2×C4×C53—82no—
501C2×C4×C53C22×D412yes—
502C2×C4×C53C22×D412yes—
503C2×C4×C53C22×D411yescharacteristic
504C2×C4×C53C2×#4112yes—
505C2×C4×C53C2×#4112yes—
506C2×C4×C53C2511yescharacteristic
507C22⋊D53—28no—
508C22⋊D53—28no—
509C22⋊D53—42no—
510C2×Dic53—22no—
511C2×Dic53—22no—
512C2×Dic53—21no—
513C2×Dic53—21no—
514C2×Dic53—21no—
515C2×Dic53—82no—
516C2×Dic53—82no—
517C2×Dic53—81no—
518C2×Dic53C22×D412yes—
519C2×Dic53C22×D412yes—
520C2×Dic53C22×D411yescharacteristic
521C2×Dic53C22×D411yescharacteristic
522D212—24no—
523D212—22no—
524D212—21no—
525D212—21no—
526D212—42no—
527D212—81no—
528D212C2×#4114yes—
529C4×D53—24no—
530C4×D53—22no—
531C4×D53—22no—
532C4×D53—21no—
533C4×D53—21no—
534C4×D53—21no—
535C4×D53—21no—
536C4×D53—42no—
537C4×D53—42no—
538C4×D53—42no—
539C4×D53—42no—
540C4×D53—82no—
541C4×D53—82no—
542C4×D53—82no—
543C4×D53—82no—
544C4×D53—82no—
545Dic106—21no—
546Dic106—21no—
547Dic106—82no—
548C8×C53—22no—
549C8×C53—21no—
550C8×C53—21no—
551#88322—21no—
552#88322—21no—
553#88322—22no—
554#60579—531nomaximal, Sylow
555C22×C53—21no—
556C22×C53—21no—
557C22×C53—24no—
558C22×C53—42no—
559C22×C53—42no—
560C22×C53—84no—
561C22×C53#52512yes—
562C22×C53C23×D411yescharacteristic
563C2×D53—21no—
564C2×D53—21no—
565C2×D53—21no—
566C2×D53—21no—
567C2×D53—24no—
568C2×D53—21no—
569C2×D53—44no—
570C2×D53—416no—
571C2×D53—42no—
572C2×D53—42no—
573C2×D53—41no—
574C2×D53—41no—
575C2×D53—41no—
576C2×D53—84no—
577C2×D53—88no—
578C2×D53#57712yes—
579C4×C53—22no—
580C4×C53—22no—
581C4×C53—41no—
582C4×C53—41no—
583C4×C53—42no—
584C4×C53—41no—
585C4×C53—41no—
586C4×C53#52512yes—
587C4×C53C22×#4111yescharacteristic
588C4×C53C22×#4111yescharacteristic
589Dic53—22no—
590Dic53—21no—
591Dic53—21no—
592Dic53—22no—
593Dic53—42no—
594Dic53—41no—
595Dic53—41no—
596Dic53—41no—
597#3495—531no—
598C2×#518—531no—
599#3123—532no—
600#3123—532no—
601#3118—532no—
602#3118—532no—
603#3114—532no—
604#3110—532no—
605#3105—532no—
606#3101—532no—
607#3095—531no—
608#3091—531no—
609#3081—531no—
610#3081—531no—
611#3042—531no—
612#3042—531no—
613#3003—531no—
614C2×#450—531no—
615#2949—531no—
616#2949D5311yescharacteristic, complemented
617#2946—531no—
618#2946—531no—
619#2924—531no—
620C2×C53—22no—
621C2×C53—44no—
622C2×C53C2×#52511yescharacteristic
623C2×C53C2×#57711yescharacteristic
624C2×C53#358511yescharacteristic
625D53—22no—
626D53—41no—
627D53—44no—
628D53—81no—
629C23×D4—531no—
630C2×AGL(1,ℤ/8)—531no—
631C2×AGL(1,ℤ/8)—531no—
632C22×SD16—531no—
633C22×SD16C2×D5311yescharacteristic
634#556—1061no—
635#554—1061no—
636#552—1061no—
637#552—1062no—
638#552—1061no—
639#551—1062no—
640#544—531no—
641#542—532no—
642#541—532no—
643#536—531no—
644#533—532no—
645#529—532no—
646#525—531no—
647C2×C22⋊Q8—531no—
648#520—531no—
649#519C2×D5311yescharacteristic, complemented
650#518—531no—
651#518—532no—
652#518—532no—
653#518—531no—
654#518—531no—
655#518—1062no—
656#518—1061no—
657#518—1061no—
658#518C2×D5311yescharacteristic
659C2×C4×D4—532no—
660C2×C4×D4—532no—
661C2×C4×D4—1061no—
662C2×C4×D4—1061no—
663C2×#117—531no—
664C2×#117—531no—
665C22×C22⋊C4—1062no—
666#485—531no—
667#485—531no—
668#485—532no—
669#485—532no—
670#484—531no—
671#484—532no—
672#483—531no—
673#483—532no—
674#482—531no—
675#482—531no—
676#481—531no—
677#480—531no—
678#478—532no—
679#478—532no—
680#478—532no—
681#478—532no—
682#476—532no—
683#476—532no—
684#474—532no—
685#474—532no—
686#463—532no—
687#463—532no—
688#463—532no—
689#463—532no—
690#461—532no—
691#461—532no—
692#461—532no—
693#461—532no—
694#450—532no—
695#450—532no—
696#450—532no—
697#450—532no—
698#450—532no—
699#450—532no—
700#447—532no—
701#447—532no—
702#442—532no—
703#442—532no—
704#440—532no—
705#440—532no—
706#440—532no—
707#440—532no—
708#440C2×D5312yescomplemented
709#440C2×D5312yescomplemented
710C4×SD16—532no—
711C4×SD16—532no—
712C4×SD16—532no—
713C4×SD16—532no—
714C4×SD16C2×D5312yescomplemented
715C4×SD16C2×D5312yescomplemented
716C4×D8—532no—
717C4×D8—532no—
718#433—532no—
719#433—532no—
720#432—532no—
721#431—532no—
722#428—531no—
723#428—531no—
724#427—531no—
725#427C2×D5311yescharacteristic, complemented
726#424—531no—
727#424—531no—
728#419—531no—
729#419C2×D5311yescharacteristic, complemented
730#418—531no—
731#418C2×D5311yescharacteristic
732#416—531no—
733#416—531no—
734C2×#102—531no—
735C2×#102—531no—
736#407—531no—
737C2×C22⋊C8—531no—
738#405—531no—
739#405C2×D5311yescharacteristic, complemented
740C53#6057911yescharacteristic, complemented, Sylow
741C25—1061no—
742C2×#41—531no—
743C22×Q8C22×D5311yescharacteristic
744C22×D4—532no—
745C22×D4—532no—
746C22×D4—531no—
747C22×D4—1061no—
748C22×D4—1061no—
749C22×D4—1061no—
750C22×D4—1064no—
751C22×D4—1064no—
752C22×D4C22×D5311yescharacteristic
753C23×C4—531no—
754C23×C4—1062no—
755C23×C4—1062no—
756AGL(1,ℤ/8)—1064no—
757AGL(1,ℤ/8)—1064no—
758C2×SD16—24no—
759C2×SD16—532no—
760C2×SD16—532no—
761C2×SD16—532no—
762C2×SD16—532no—
763C2×SD16—1064no—
764C2×SD16C22×D5312yes—
765C2×SD16C22×D5312yes—
766C2×D8—532no—
767C2×D8—532no—
768C2×M16—531no—
769C2×M16C22×D5311yescharacteristic
770C22×C8—531no—
771C22×C8C22×D5311yescharacteristic
772C4⋊Q8—532no—
773C4⋊Q8—532no—
774C4⋊Q8—1061no—
775#126—1062no—
776#126—1062no—
777#126—1062no—
778#126—1062no—
779#125—532no—
780#125—1062no—
781#125—1061no—
782#125—1062no—
783#125—1062no—
784#124—532no—
785#124—1062no—
786#123—1061no—
787#123—1062no—
788#123—1062no—
789#123—1062no—
790C22⋊Q8—532no—
791C22⋊Q8—532no—
792C22⋊Q8—531no—
793C22⋊Q8—531no—
794C22⋊Q8—1062no—
795C22⋊Q8—1062no—
796C22⋊Q8—1062no—
797C22⋊Q8—1061no—
798C22⋊Q8—1061no—
799C22⋊Q8—1061no—
800C22⋊Q8—1061no—
801#121—531no—
802#121—531no—
803#120—1061no—
804C4×Q8—21no—
805C4×Q8—21no—
806C4×Q8—532no—
807C4×Q8—1062no—
808C4×Q8C22×D5312yescomplemented
809C4×Q8C22×D5312yescomplemented
810C4×D4—21no—
811C4×D4—21no—
812C4×D4—532no—
813C4×D4—532no—
814C4×D4—532no—
815C4×D4—532no—
816C4×D4—532no—
817C4×D4—532no—
818C4×D4—532no—
819C4×D4—1061no—
820C4×D4—1061no—
821C4×D4—1061no—
822C4×D4—1061no—
823C4×D4—1062no—
824C4×D4—1062no—
825C4×D4—1062no—
826C4×D4—1062no—
827C4×D4—1062no—
828C4×D4—1062no—
829C4×D4—1062no—
830C4×D4—1062no—
831C4×D4—1062no—
832C4×D4—1061no—
833C4×D4—1061no—
834C4×D4—1061no—
835C4×D4—1061no—
836C4×D4—1062no—
837C4×D4C22×D5312yes—
838C4×D4C22×D5312yes—
839#117—22no—
840#117—531no—
841#117—531no—
842#117—531no—
843#117—532no—
844#117—532no—
845#117—531no—
846#117—531no—
847#117—531no—
848#117—1062no—
849#117—1061no—
850#117—1062no—
851#117—1061no—
852#117—1061no—
853#117C22×D5311yescharacteristic
854#117C22×D5311yescharacteristic
855#117C22×D5311yescharacteristic
856C2×C4⋊C4—531no—
857C2×C4⋊C4—531no—
858C2×C4⋊C4—531no—
859C2×C4⋊C4—531no—
860C2×C4⋊C4—531no—
861C2×C4⋊C4—1061no—
862C2×C4⋊C4—1061no—
863C2×C22⋊C4—22no—
864C2×C22⋊C4—532no—
865C2×C22⋊C4—1062no—
866C2×C22⋊C4—1062no—
867C2×C22⋊C4—1062no—
868C2×C22⋊C4—1062no—
869C2×C22⋊C4—1062no—
870C2×C22⋊C4—1061no—
871C2×C22⋊C4—1062no—
872C2×C22⋊C4—1062no—
873C2×C22⋊C4—1062no—
874C2×C22⋊C4—1061no—
875C2×C22⋊C4—1062no—
876C2×C42—532no—
877C2×C42—1061no—
878#107—532no—
879#107—531no—
880#107—531no—
881#107—532no—
882#107C22×D5311yescharacteristic, complemented
883#107C22×D5311yescharacteristic, complemented
884#106—532no—
885#106—531no—
886#106—531no—
887#106—532no—
888#106C22×D5311yescharacteristic, complemented
889#106C22×D5311yescharacteristic, complemented
890C4⋊C8—532no—
891C4⋊C8—532no—
892C4⋊C8—532no—
893C4⋊C8—532no—
894#103—532no—
895#103—532no—
896#103—531no—
897#103—531no—
898#103—531no—
899#103—531no—
900#103C22×D5312yescomplemented
901#103C22×D5312yescomplemented
902#102—532no—
903#102—532no—
904#102—532no—
905#102—532no—
906#102—531no—
907#102—531no—
908#102—532no—
909#102—532no—
910#102—531no—
911#102—531no—
912#102C22×D5312yes—
913#102C22×D5312yes—
914C22⋊C8—531no—
915C22⋊C8—531no—
916C22⋊C8—531no—
917C22⋊C8—531no—
918C22⋊C8—532no—
919C22⋊C8—532no—
920#97—532no—
921#97C22×D5312yescomplemented
922C4×C8—532no—
923C4×C8C22×D5312yescomplemented
924C24—21no—
925C24—531no—
926C24—1062no—
927C24—1062no—
928C24—1068no—
929C24—1061no—
930C24—4242no—
931C24—4242no—
932#41—1062no—
933#41—1062no—
934C2×Q8—21no—
935C2×Q8—22no—
936C2×Q8—22no—
937C2×Q8—531no—
938C2×Q8—1062no—
939C2×Q8C23×D5312yes—
940C2×D4—21no—
941C2×D4—22no—
942C2×D4—534no—
943C2×D4—532no—
944C2×D4—531no—
945C2×D4—1061no—
946C2×D4—1061no—
947C2×D4—1062no—
948C2×D4—1062no—
949C2×D4—1064no—
950C2×D4—1064no—
951C2×D4—1068no—
952C2×D4—1068no—
953C2×D4—1068no—
954C2×D4—1064no—
955C2×D4—1064no—
956C2×D4—1061no—
957C2×D4—1061no—
958C2×D4—1062no—
959C2×D4#1171994514yes—
960C2×D4C23×D5312yes—
961C22×C4—21no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—531no—
965C22×C4—532no—
966C22×C4—531no—
967C22×C4—531no—
968C22×C4—531no—
969C22×C4—531no—
970C22×C4—532no—
971C22×C4—1062no—
972C22×C4—1062no—
973C22×C4—1061no—
974C22×C4—1061no—
975C22×C4—1062no—
976C22×C4—1062no—
977C22×C4—1062no—
978C22×C4—1062no—
979C22×C4—1061no—
980C22×C4—1062no—
981C22×C4—1062no—
982C22×C4—1062no—
983C22×C4—1061no—
984C22×C4—4244no—
985C22×C4—4244no—
986C22×C4C23×D5311yescharacteristic
987SD16—24no—
988SD16—24no—
989SD16—1064no—
990SD16—1064no—
991SD16—1064no—
992SD16—1064no—
993D8—1064no—
994D8—1064no—
995M16—22no—
996M16—1062no—
997C2×C8—22no—
998C2×C8—531no—
999C2×C8—532no—
1000C2×C8—531no—
1001C2×C8—1062no—
1002C2×C8C23×D5311yescharacteristic
1003C2×C8C23×D5312yes—
1004C2×C8C23×D5311yescharacteristic
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—532no—
1008C4⋊C4—531no—
1009C4⋊C4—531no—
1010C4⋊C4—532no—
1011C4⋊C4—532no—
1012C4⋊C4—531no—
1013C4⋊C4—531no—
1014C4⋊C4—1061no—
1015C4⋊C4—1061no—
1016C4⋊C4—1062no—
1017C4⋊C4—1062no—
1018C4⋊C4—1062no—
1019C4⋊C4—1062no—
1020C4⋊C4—1062no—
1021C4⋊C4—1061no—
1022C4⋊C4—1061no—
1023C4⋊C4—1062no—
1024C4⋊C4—1062no—
1025C4⋊C4—1061no—
1026C4⋊C4—1062no—
1027C4⋊C4D4×D5311yescharacteristic
1028C4⋊C4D4×D5311yescharacteristic
1029C4⋊C4C23×D5311yescharacteristic
1030C4⋊C4C23×D5311yescharacteristic
1031C4⋊C4C23×D5311yescharacteristic
1032C4⋊C4C23×D5311yescharacteristic
1033C22⋊C4—21no—
1034C22⋊C4—21no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—532no—
1038C22⋊C4—532no—
1039C22⋊C4—532no—
1040C22⋊C4—1062no—
1041C22⋊C4—1062no—
1042C22⋊C4—1061no—
1043C22⋊C4—1062no—
1044C22⋊C4—1061no—
1045C22⋊C4—1062no—
1046C22⋊C4—1061no—
1047C22⋊C4—1061no—
1048C22⋊C4—1062no—
1049C22⋊C4—1062no—
1050C22⋊C4—1061no—
1051C22⋊C4—1061no—
1052C22⋊C4—1062no—
1053C22⋊C4—1062no—
1054C22⋊C4—1061no—
1055C22⋊C4—1062no—
1056C22⋊C4—1062no—
1057C22⋊C4—1062no—
1058C22⋊C4D4×D5312yes—
1059C42—21no—
1060C42—22no—
1061C42—22no—
1062C42—21no—
1063C42—532no—
1064C42—532no—
1065C42—532no—
1066C42—1061no—
1067C42—1061no—
1068C42—1061no—
1069C42—1062no—
1070C42C23×D5312yes—
1071C23—22no—
1072C23—24no—
1073C23—81no—
1074C23—81no—
1075C23—531no—
1076C23—531no—
1077C23—1062no—
1078C23—1068no—
1079C23—1068no—
1080C23—1064no—
1081C23—1062no—
1082C23—1062no—
1083C23—1061no—
1084C23—4241no—
1085C23—4241no—
1086C23—4242no—
1087C23—4242no—
1088C23—42416no—
1089C23—2121no—
1090C23—2124no—
1091C23—2124no—
1092C23C2×D4×D5311yescharacteristic
1093Q8—22no—
1094Q8—22no—
1095Q8—42no—
1096Q8—1061no—
1097Q8—1061no—
1098Q8—4242no—
1099D4—24no—
1100D4—22no—
1101D4—534no—
1102D4—1068no—
1103D4—1068no—
1104D4—1064no—
1105D4—1061no—
1106D4—1062no—
1107D4—1061no—
1108D4—4241no—
1109D4—2122no—
1110D4—2122no—
1111D4C2×#1171994514yes—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—42no—
1118C2×C4—82no—
1119C2×C4—82no—
1120C2×C4—531no—
1121C2×C4—532no—
1122C2×C4—532no—
1123C2×C4—531no—
1124C2×C4—1064no—
1125C2×C4—1062no—
1126C2×C4—1062no—
1127C2×C4—1062no—
1128C2×C4—1061no—
1129C2×C4—1061no—
1130C2×C4—1061no—
1131C2×C4—1061no—
1132C2×C4—1061no—
1133C2×C4—1061no—
1134C2×C4—1061no—
1135C2×C4—1062no—
1136C2×C4—4242no—
1137C2×C4—4242no—
1138C2×C4—4242no—
1139C2×C4—4242no—
1140C2×C4—4242no—
1141C2×C4—4242no—
1142C2×C4—4242no—
1143C2×C4—4241no—
1144C2×C4—2122no—
1145C2×C4—2122no—
1146C2×C4—2122no—
1147C2×C4—2122no—
1148C2×C4C2×D4×D5312yes—
1149C2×C4C2×D4×D5312yes—
1150C2×C4C2×D4×D5311yescharacteristic
1151C2×C4#41×D5312yes—
1152C2×C4C2×#1171994512yes—
1153C2×C4C24×D5311yescharacteristic
1154C8—22no—
1155C8—21no—
1156C8—21no—
1157C8—1061no—
1158C8—1061no—
1159C8—1062no—
1160C22—21no—
1161C22—21no—
1162C22—24no—
1163C22—42no—
1164C22—42no—
1165C22—84no—
1166C22—532no—
1167C22—1061no—
1168C22—1061no—
1169C22—1061no—
1170C22—1061no—
1171C22—1064no—
1172C22—1061no—
1173C22—4244no—
1174C22—4248no—
1175C22—2124no—
1176C22—21216no—
1177C22—2121no—
1178C22—2121no—
1179C22—2121no—
1180C22—2122no—
1181C22—2122no—
1182C22#1681113212yes—
1183C22C22×D4×D5311yescharacteristic
1184C4—22no—
1185C4—22no—
1186C4—41no—
1187C4—41no—
1188C4—42no—
1189C4—41no—
1190C4—41no—
1191C4—1062no—
1192C4—1061no—
1193C4—1061no—
1194C4—1062no—
1195C4—2121no—
1196C4—2121no—
1197C4—2121no—
1198C4—2122no—
1199C4#1681113212yes—
1200C4C2×#41×D5311yescharacteristic
1201C4C22×#1171994511yescharacteristic
1202C2—22no—
1203C2—44no—
1204C2—1062no—
1205C2—4241no—
1206C2—2121no—
1207C2—2124no—
1208C2C2×#1681113211yescharacteristic
1209C2#577×D5311yescharacteristic
1210C2#2028949311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#2949C2
socleC22×C53C23×D4
prime radical#20283944C2
hypercenter#2949D53
hypocenterC53#60579
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #2949

Complements

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

NH ≅ G/Ntype
1. #20288457C2semidirect
2. #518×D53C2semidirect
3. #20284966C2semidirect
4. #20284964C2semidirect
5. #20284905C2semidirect
6. #20284903C2semidirect
7. #20284857C2semidirect
8. #20284812C2semidirect
9. #20284766C2semidirect
10. #20284721C2semidirect
11. #20284661C2semidirect
12. #20284632C2semidirect
13. #20284549C2semidirect
14. #20284548C2semidirect
15. #20284226C2semidirect
16. #20284224C2semidirect
18. C2×#16810772C2semidirect
19. #20283574C2semidirect
20. #20283549C2semidirect
21. #20283547C2semidirect
22. #20283370C2semidirect
23. C53×#2949C2semidirect
34. #16811251C22semidirect
35. #16811245C22semidirect
36. #16811231C22semidirect
37. #16811197C22semidirect
38. #16811177C22semidirect
39. #16811160C22semidirect
42. #16811103C22semidirect
58. #16810967C22semidirect
59. #16810966C22semidirect
60. #16810963C22semidirect
61. #16810962C22semidirect
62. #16810960C22semidirect
63. #16810957C22semidirect
64. #16810955C22semidirect
65. #16810952C22semidirect
66. #16810950C22semidirect
67. #16810949C22semidirect
68. #16810943C22semidirect
69. #16810938C22semidirect
70. #16810926C22semidirect
71. #16810925C22semidirect
72. #16810922C22semidirect
73. #16810921C22semidirect
74. #16810912C22semidirect
75. #16810911C22semidirect
76. #16810902C22semidirect
77. #16810901C22semidirect
78. #16810841C22semidirect
79. #16810841C22semidirect
80. #16810840C22semidirect
81. #16810840C22semidirect
82. #16810827C22semidirect
83. #16810827C22semidirect
84. #16810826C22semidirect
85. #16810826C22semidirect
94. #16810736C22semidirect
95. #16810733C22semidirect
96. #16810725C22semidirect
97. #16810723C22semidirect
98. #16810721C22semidirect
99. #16810721C22semidirect
100. C4×#11719913C22semidirect
101. C4×#11719924C22semidirect
102. C4×#11719924C22semidirect
103. C4×#11719923C22semidirect
104. C4×D424C22semidirect
105. C4×#11719922C22semidirect
106. #16810685C22semidirect
107. #16810682C22semidirect
108. #16810678C22semidirect
109. #16810674C22semidirect
110. #16810666C22semidirect
111. #16810665C22semidirect
112. #16810659C22semidirect
113. #16810651C22semidirect
114. #16810649C22semidirect
115. #16810632C22semidirect
117. #16810620C22semidirect
118. #16810617C22semidirect
123. #16810579C22semidirect
125. C53×#519C22semidirect
127. C53×#440C22semidirect
128. C53×#440C22semidirect
129. C4×SD16×C53C22semidirect
130. C4×SD16×C53C22semidirect
131. C53×#427C22semidirect
132. C53×#419C22semidirect
134. C53×#405C22semidirect
160. #13133216C23semidirect
161. #13133215C23semidirect
168. #13133208C23semidirect
171. #13133206C23semidirect
192. C4×Dic106C23semidirect
200. C4×D212C23semidirect
252. #13133151C23semidirect
253. #13133150C23semidirect
254. #13133150C23semidirect
255. #13133150C23semidirect
256. #13133149C23semidirect
257. #13133148C23semidirect
258. #13133148C23semidirect
259. #13133148C23semidirect
260. #13133146C23semidirect
261. #13133146C23semidirect
262. #13133146C23semidirect
263. #13133146C23semidirect
264. #13133142C23semidirect
265. #13133142C23semidirect
266. #13133141C23semidirect
267. #13133141C23semidirect
268. #13133140C23semidirect
269. #13133140C23semidirect
272. #13133139C23semidirect
273. #13133139C23semidirect
278. #13133137C23semidirect
279. #13133137C23semidirect
286. #13133128C23semidirect
287. C4×#88322C23semidirect
297. C4×Q8×C53C23semidirect
298. C4×Q8×C53C23semidirect
308. #107×C53C23semidirect
309. #107×C53C23semidirect
310. #106×C53C23semidirect
311. #106×C53C23semidirect
312. #103×C53C23semidirect
313. #103×C53C23semidirect
316. #97×C53C23semidirect
317. C4×C8×C53C23semidirect
616. #2949D53semidirect
649. #519C2×D53semidirect
708. #440C2×D53semidirect
709. #440C2×D53semidirect
714. C4×SD16C2×D53semidirect
715. C4×SD16C2×D53semidirect
725. #427C2×D53semidirect
729. #419C2×D53semidirect
739. #405C2×D53semidirect
740. C53#60579semidirect
808. C4×Q8C22×D53semidirect
809. C4×Q8C22×D53semidirect
882. #107C22×D53semidirect
883. #107C22×D53semidirect
888. #106C22×D53semidirect
889. #106C22×D53semidirect
900. #103C22×D53semidirect
901. #103C22×D53semidirect
921. #97C22×D53semidirect
923. C4×C8C22×D53semidirect

Maximal subgroups

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

subgroupindex
#202884572
#518×D532
#202849662
#202849642
#202849052
#202849032
#202848572
#202848122
#202847662
#202847212
#202846612
#202846322
#202845492
#202845482
#202842262
#202842242
#202839442
C2×#168107722
#202835742
#202835492
#202835472
#202833702
C53×#29492
#6057953