Finite Group Databasebeta

← #28271025

Subgroups — #28271025

Order 13568.

2160 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289120C211yesmaximal, characteristic, complemented
2#20286901C214yesmaximal, complemented
3#20286871C214yesmaximal, complemented
4#20286211C214yesmaximal, complemented
5#20286196C214yesmaximal, complemented
6#20285702C212yesmaximal, complemented
7#20285582C212yesmaximal, complemented
8#20285576C212yesmaximal, complemented
9#20284866C212yesmaximal, complemented
10#20284001C212yesmaximal, complemented
11#20283983C212yesmaximal, complemented
12#20283786C211yesmaximal, characteristic, complemented
13C53×#3500C211yesmaximal, characteristic, complemented
14C2×#13133242C2212yescomplemented
15C2×#13133242C2212yescomplemented
16C22×#11719924C2212yescomplemented
17C22×#11719922C2212yescomplemented
18#16811365—21no—
19#16811365—21no—
20#16811339—21no—
21#16811338C2214yescomplemented
22D4×D212C2214yescomplemented
23#16811258—21no—
24#16811189—24no—
25#16811187C2212yes—
26#16811187C2212yescomplemented
27#16811173C2212yescomplemented
28#16811013C2214yescomplemented
29#16810982C2214yescomplemented
30#16810961C2214yescomplemented
31#16810947C2214yescomplemented
32#16810944C2214yescomplemented
33#16810908C2212yescomplemented
34#16810903C2212yescomplemented
35#16810874C2214yescomplemented
36#16810871C2214yescomplemented
37#16810857C2214yescomplemented
38#16810854C2214yescomplemented
39#16810835C2214yescomplemented
40#16810835C2214yescomplemented
41#16810823C2212yescomplemented
42#16810818C2212yescomplemented
43#16810773C2214yescomplemented
44#16810768C2214yescomplemented
45#16810768C2214yescomplemented
46#16810768C2214yescomplemented
47#16810762C2214yescomplemented
48#16810762C2214yescomplemented
49#16810757C2214yescomplemented
50#16810757C2214yescomplemented
51#16810756C2214yescomplemented
52#16810733C2214yescomplemented
53#16810721C2214yescomplemented
54#16810695C2214yescomplemented
55#16810695C2214yescomplemented
56#16810680C2212yescomplemented
57#16810632C2212yescomplemented
58#16810628C2212yescomplemented
59#16810619C2212yescomplemented
60#16810619C2212yescomplemented
61#16810590C2212yescomplemented
62#16810590C2212yescomplemented
63C2×2−1+4×C53C2211yescharacteristic, complemented
64C2×H(5,𝔽2)×C53C2211yescharacteristic, complemented
65C53×#548C2214yescomplemented
66C53×#546—24no—
67C53×#546C2214yescomplemented
68C53×#536—21no—
69C53×#536C2211yescharacteristic, complemented
70C53×#535—21no—
71C53×#535C2211yescharacteristic, complemented
72C53×#532—21no—
73C53×#532C2211yescharacteristic
74C2×#124×C53—21no—
75C2×#124×C53C2211yescharacteristic, complemented
76C4×#41×C53C2211yescharacteristic, complemented
77C2×#11719945—22no—
78C22×D212C2312yes—
79C22×D212C2312yes—
80C2×D4×D53—24no—
81#13133242—44no—
82#13133242—44no—
83C2×#11719924—44no—
84C2×#11719924C2314yes—
85C2×#11719924C2314yes—
86C2×#11719924C2314yes—
87C2×#11719922—44no—
88C2×#11719922C2314yes—
89C2×#11719922C2314yes—
90C2×#11719922C2314yes—
91C2×#11719917C2312yes—
92C2×#11719917C2312yes—
93C22×#88322C2312yes—
94C22×#88322C2312yes—
95#13133217C2312yes—
96#13133214C2312yes—
97#13133213—22no—
98#13133213—22no—
99#13133206—22no—
100#13133206—22no—
101#13133205—22no—
102#13133203—24no—
103#13133203—24no—
104#13133192—24no—
105#13133191—22no—
106#13133191C2314yes—
107#13133191C2314yes—
108#13133191C2314yes—
109#13133188—24no—
110#13133187—24no—
111#13133187—24no—
112#13133185—22no—
113#13133185—22no—
114#13133185—22no—
115#13133185—22no—
116C4×D212—22no—
117C4×D212C2314yes—
118#13133176C2312yes—
119#13133176C2312yes—
120#13133175—24no—
121#13133150C2314yes—
122#13133148C2314yes—
123C4⋊#88322C2312yes—
124C4⋊#88322C2312yes—
125#13133141C2314yes—
126#13133141C2314yes—
127#13133141C2314yes—
128#13133138C2314yes—
129#13133138C2314yes—
130#13133138C2314yes—
131#13133137C2314yes—
132#13133137C2314yes—
133C22⋊#88322C2314yes—
134C22⋊#88322C2314yes—
135C22⋊#88322C2314yes—
136#13133128C2314yes—
1372−1+4×C53—42no—
1382−1+4×C53—42no—
139H(5,𝔽2)×C53—42no—
140H(5,𝔽2)×C53—42no—
141C2×#41×C53—21no—
142C2×#41×C53—21no—
143C2×#41×C53—22no—
144C2×#41×C53C2311yescharacteristic
145C2×#41×C53C2312yes—
146C2×#41×C53C2312yes—
147C2×#41×C53C2311yescharacteristic
148C2×#41×C53C2311yescharacteristic
149C22×Q8×C53—21no—
150C22×Q8×C53C2312yes—
151C22×Q8×C53C2311yescharacteristic
152C22×D4×C53—21no—
153C22×D4×C53—22no—
154C22×D4×C53C2312yes—
155C22×D4×C53C2311yescharacteristic
156C4⋊Q8×C53—21no—
157C4⋊Q8×C53D411yescharacteristic
158#127×C53—21no—
159#127×C53D411yescharacteristic
160#124×C53—24no—
161#124×C53—21no—
162#124×C53—21no—
163#124×C53—21no—
164#124×C53—21no—
165#124×C53D411yescharacteristic
166#124×C53D411yescharacteristic
167#124×C53C2314yes—
168#123×C53—24no—
169#123×C53—22no—
170C22⋊Q8×C53—24no—
171C22⋊Q8×C53C2314yes—
172#121×C53—24no—
173#121×C53—24no—
174#121×C53D414yes—
175#121×C53C2314yes—
176#120×C53—24no—
177#120×C53—22no—
178C4×Q8×C53C2312yes—
179C4×D4×C53—24no—
180C4×D4×C53—22no—
181C4×D4×C53C2312yes—
182C4×D4×C53C2314yes—
183#117×C53—21no—
184#117×C53C2311yescharacteristic
185C2×C22⋊C4×C53—24no—
186C2×C22⋊C4×C53—22no—
187C2×C42×C53—21no—
188C2×C42×C53C2311yescharacteristic
189C24×C53—22no—
190C24×C53—21no—
191C23×D53—22no—
192C23×D53—22no—
193#41×C53—22no—
194#41×C53—22no—
195#41×C53—24no—
196#41×C53—24no—
197#41×C53—41no—
198#41×C53—41no—
199#41×C53—41no—
200#41×C53—41no—
201#41×C53—42no—
202#41×C53—42no—
203#41×C53—44no—
204#41×C53—44no—
205#41×C53—48no—
206C2×Q8×C53—22no—
207C2×Q8×C53—21no—
208C2×Q8×C53—24no—
209C2×Q8×C53—42no—
210C2×Q8×C53—41no—
211C2×Q8×C53—41no—
212C2×Q8×C53—44no—
213C2×Q8×C53C2×D411yescharacteristic
214C2×Q8×C53C2×D411yescharacteristic
215C2×Q8×C53C2412yes—
216C2×Q8×C53C2411yescharacteristic
217C2×D4×C53—21no—
218C2×D4×C53—24no—
219C2×D4×C53—22no—
220C2×D4×C53—22no—
221C2×D4×C53—24no—
222C2×D4×C53—22no—
223C2×D4×C53—21no—
224C2×D4×C53—42no—
225C2×D4×C53—41no—
226C2×D4×C53—41no—
227C2×D4×C53—44no—
228C2×D4×C53—48no—
229C2×D4×C53C2×D414yes—
230C2×D4×C53C2×D412yes—
231C2×D4×C53C2×D412yes—
232C2×D4×C53C2×D411yescharacteristic
233C2×D4×C53C2×D411yescharacteristic
234C2×D4×C53C2412yes—
235C2×D4×C53C2411yescharacteristic
236C22×C4×C53—21no—
237C22×C4×C53—21no—
238C22×C4×C53—22no—
239C22×C4×C53—22no—
240C22×C4×C53—22no—
241C22×C4×C53—22no—
242C22×C4×C53C2×D412yes—
243C22×C4×C53C2411yescharacteristic
244C22×C4×C53C2412yes—
245C22×C4×C53C2412yes—
246C2×C22⋊D53—24no—
247C2×C22⋊D53—24no—
248C2×C22⋊D53—24no—
249D4×D53—88no—
250#11719945—84no—
251C2×D212—22no—
252C2×D212—22no—
253C2×D212—22no—
254C2×D212—22no—
255C2×D212—42no—
256C2×D212—42no—
257C2×D212—42no—
258C2×D212—42no—
259C2×D212C2414yes—
260C2×C4×D53—24no—
261C2×Dic106—22no—
262C4⋊C4×C53—22no—
263C4⋊C4×C53—24no—
264C4⋊C4×C53C2×D414yes—
265C4⋊C4×C53C2412yes—
266C22⋊C4×C53—24no—
267C22⋊C4×C53—21no—
268C22⋊C4×C53—24no—
269C22⋊C4×C53—24no—
270C22⋊C4×C53—24no—
271C22⋊C4×C53—22no—
272C22⋊C4×C53C2×D414yes—
273C22⋊C4×C53C2×D414yes—
274C42×C53—21no—
275C42×C53—22no—
276C42×C53C2×D411yescharacteristic
277C42×C53C2×D411yescharacteristic
278C42×C53C2412yes—
279C22⋊Dic53—22no—
280C22⋊Dic53—22no—
281#11719924—28no—
282#11719924—44no—
283#11719924—44no—
284#11719922—28no—
285#11719922—44no—
286#11719922—44no—
287#11719921—24no—
288#11719921—24no—
289#11719921—24no—
290#11719921—24no—
291C4⋊Dic53—22no—
292C4⋊Dic53C2414yes—
293C4×Dic53—22no—
294C4×Dic53—22no—
295#11719917—42no—
296#11719917—42no—
297C2×#88322—42no—
298C2×#88322—42no—
299C2×#88322C2414yes—
300C2×#88322C2414yes—
301C23×C53—21no—
302C23×C53—22no—
303C23×C53—44no—
304C23×C53—42no—
305C23×C53—82no—
306C23×C53—84no—
307C23×C53C22×D411yescharacteristic
308C23×C53C22×D412yes—
309C23×C53C22×D412yes—
310C22×D53—24no—
311C22×D53—82no—
312C22×D53—82no—
313C22×D53—84no—
314C22×D53—84no—
315Q8×C53—21no—
316Q8×C53—22no—
317Q8×C53—22no—
318Q8×C53—41no—
319Q8×C53—41no—
320Q8×C53—44no—
321Q8×C53—42no—
322Q8×C53H(5,𝔽2)12yes—
323D4×C53—24no—
324D4×C53—21no—
325D4×C53—22no—
326D4×C53—22no—
327D4×C53—44no—
328D4×C53—42no—
329D4×C53—41no—
330D4×C53—42no—
331D4×C53—41no—
332D4×C53—44no—
333D4×C53—44no—
334D4×C53—42no—
335D4×C53—44no—
336D4×C53—84no—
337D4×C53H(5,𝔽2)12yes—
338C2×C4×C53—24no—
339C2×C4×C53—21no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—21no—
345C2×C4×C53—21no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—42no—
349C2×C4×C53—44no—
350C2×C4×C53—44no—
351C2×C4×C53—44no—
352C2×C4×C53—42no—
353C2×C4×C53—82no—
354C2×C4×C53C22×D412yes—
355C2×C4×C53C22×D412yes—
356C2×C4×C53C22×D412yes—
357C2×C4×C53C22×D412yes—
358C2×C4×C53C22×D411yescharacteristic
359C2×C4×C53C2511yescharacteristic
360C22⋊D53—84no—
361C22⋊D53—84no—
362C22⋊D53—84no—
363C2×Dic53—24no—
364D212—24no—
365D212—24no—
366D212—44no—
367D212—82no—
368D212—82no—
369D212—82no—
370C4×D53—48no—
371Dic106—82no—
372#88322—24no—
373#88322—24no—
374#61673—531nomaximal, Sylow
375C22×C53—22no—
376C22×C53—24no—
377C22×C53—24no—
378C22×C53—21no—
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—42no—
383C22×C53—44no—
384C22×C53—42no—
385C22×C53—164no—
386C22×C53—162no—
387C22×C53C23×D411yescharacteristic
388C2×D53—44no—
389C2×D53—44no—
390C2×D53—44no—
391C2×D53—164no—
392C2×D53—164no—
393C4×C53—22no—
394C4×C53—22no—
395C4×C53—22no—
396C4×C53—22no—
397C4×C53—21no—
398C4×C53—22no—
399C4×C53—42no—
400C4×C53—42no—
401C4×C53C2×H(5,𝔽2)11yescharacteristic
402C4×C53C2×H(5,𝔽2)11yescharacteristic
403Dic53—44no—
404#3549—531no—
405#3500D5311yescharacteristic, complemented
406#3321—534no—
407#3319—534no—
408#3265—534no—
409#3264—534no—
410#3213—532no—
411#3200—532no—
412#3199—532no—
413#3115—532no—
414#3010—532no—
415#3008—532no—
416#2980—531no—
417C2×C53—42no—
418C2×C53—42no—
419C2×C53—41no—
420C2×C53—42no—
421C2×C53—82no—
422C2×C53#348411yescharacteristic
423C2×C53#358512yes—
424D53—84no—
425C2×2−1+4C2×D5311yescharacteristic, complemented
426C2×H(5,𝔽2)C2×D5311yescharacteristic, complemented
427C2×AGL(1,ℤ/8)—532no—
428C2×AGL(1,ℤ/8)—532no—
429C22×SD16—532no—
430C22×D8—532no—
431H(3,𝔽4)—1061no—
432H(3,𝔽4)—1061no—
433#555—534no—
434#555—1061no—
435#548C2×D5314yescomplemented
436#546—24no—
437#546C2×D5314yescomplemented
438D42—534no—
439D42—1061no—
440#536—21no—
441#536C2×D5311yescharacteristic, complemented
442#535—21no—
443#535—532no—
444#535—532no—
445#535—1064no—
446#535C2×D5311yescharacteristic, complemented
447#532—21no—
448#532—532no—
449#532C2×D5311yescharacteristic
450C2×#124—21no—
451C2×#124C2×D5311yescharacteristic, complemented
452C4×#41C2×D5311yescharacteristic, complemented
453#496—534no—
454#489—534no—
455#485—534no—
456#482—534no—
457#482—534no—
458#475—532no—
459#474—532no—
460#469—534no—
461#468—534no—
462#466—534no—
463#465—534no—
464#463—534no—
465#463—534no—
466#460—532no—
467#459—532no—
468#450—534no—
469#449—534no—
470#449—534no—
471#449—534no—
472#448—534no—
473#448—534no—
474#447—534no—
475#447—534no—
476#447—534no—
477#442—534no—
478#440—534no—
479#435—534no—
480#435—534no—
481#432—532no—
482#419—532no—
483#418—532no—
484#416—532no—
485#416—532no—
486#408—532no—
487#408—532no—
488C53#6167311yescharacteristic, complemented, Sylow
4892−1+4—42no—
4902−1+4—42no—
491H(5,𝔽2)—42no—
492H(5,𝔽2)—42no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—22no—
496C2×#41—1062no—
497C2×#41C22×D5311yescharacteristic
498C2×#41C22×D5312yes—
499C2×#41C22×D5312yes—
500C2×#41C22×D5311yescharacteristic
501C2×#41C22×D5311yescharacteristic
502C22×Q8—21no—
503C22×Q8C22×D5312yes—
504C22×Q8C22×D5311yescharacteristic
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—532no—
508C22×D4—532no—
509C22×D4—1064no—
510C22×D4C22×D5312yes—
511C22×D4C22×D5311yescharacteristic
512AGL(1,ℤ/8)—2124no—
513AGL(1,ℤ/8)—2124no—
514C2×SD16—534no—
515C2×SD16—534no—
516C2×SD16—534no—
517C2×SD16—2124no—
518C2×D8—534no—
519C2×D8—534no—
520C2×D8—534no—
521C2×D8—2124no—
522C2×M16—532no—
523C2×M16—532no—
524C22×C8—532no—
525C22×C8—532no—
526C4⋊Q8—21no—
527C4⋊Q8—532no—
528C4⋊Q8C22⋊D5311yescharacteristic
529#127—21no—
530#127—532no—
531#127—1062no—
532#127—1062no—
533#127C22⋊D5311yescharacteristic
534#124—21no—
535#124—21no—
536#124—24no—
537#124—21no—
538#124—21no—
539#124—1062no—
540#124—1062no—
541#124—1064no—
542#124—1064no—
543#124—1062no—
544#124C22⋊D5311yescharacteristic
545#124C22⋊D5311yescharacteristic
546#124C22×D5314yes—
547#123—22no—
548#123—24no—
549C22⋊Q8—24no—
550C22⋊Q8C22×D5314yes—
551#121—24no—
552#121—24no—
553#121—534no—
554#121—534no—
555#121—534no—
556#121—1064no—
557#121—1062no—
558#121—1064no—
559#121C22⋊D5314yes—
560#121C22×D5314yes—
561#120—24no—
562#120—22no—
563#120—1062no—
564#120—1062no—
565#120—1062no—
566#120—1062no—
567#120—1064no—
568#120—1064no—
569C4×Q8C22×D5312yes—
570C4×D4—22no—
571C4×D4—24no—
572C4×D4—534no—
573C4×D4—1062no—
574C4×D4C22×D5312yes—
575C4×D4C22×D5314yes—
576#117—21no—
577#117—532no—
578#117—532no—
579#117—1064no—
580#117C22×D5311yescharacteristic
581C2×C22⋊C4—22no—
582C2×C22⋊C4—24no—
583C2×C42—21no—
584C2×C42C22×D5311yescharacteristic
585#107—534no—
586#106—534no—
587C4⋊C8—532no—
588C4⋊C8—532no—
589#103—534no—
590#103—534no—
591#103—534no—
592#102—534no—
593#102—534no—
594#102—534no—
595#102—534no—
596#102—534no—
597C22⋊C8—534no—
598C22⋊C8—534no—
599C22⋊C8—534no—
600#97—534no—
601C24—22no—
602C24—21no—
603C24—1062no—
604C24—1062no—
605#41—22no—
606#41—22no—
607#41—24no—
608#41—24no—
609#41—41no—
610#41—41no—
611#41—41no—
612#41—41no—
613#41—42no—
614#41—42no—
615#41—44no—
616#41—44no—
617#41—48no—
618#41—4244no—
619C2×Q8—22no—
620C2×Q8—21no—
621C2×Q8—24no—
622C2×Q8—42no—
623C2×Q8—41no—
624C2×Q8—41no—
625C2×Q8—44no—
626C2×Q8—1062no—
627C2×Q8C2×C22⋊D5311yescharacteristic
628C2×Q8C2×C22⋊D5311yescharacteristic
629C2×Q8C23×D5312yes—
630C2×Q8C23×D5311yescharacteristic
631C2×D4—21no—
632C2×D4—24no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—24no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—42no—
639C2×D4—41no—
640C2×D4—41no—
641C2×D4—44no—
642C2×D4—48no—
643C2×D4—534no—
644C2×D4—1064no—
645C2×D4—1064no—
646C2×D4—1064no—
647C2×D4—1062no—
648C2×D4—1062no—
649C2×D4—1062no—
650C2×D4—1062no—
651C2×D4—4248no—
652C2×D4—2122no—
653C2×D4—2122no—
654C2×D4—2122no—
655C2×D4—2122no—
656C2×D4C2×C22⋊D5314yes—
657C2×D4C2×C22⋊D5312yes—
658C2×D4C2×C22⋊D5311yescharacteristic
659C2×D4C2×C22⋊D5311yescharacteristic
660C2×D4C2×C22⋊D5312yes—
661C2×D4C23×D5312yes—
662C2×D4C23×D5311yescharacteristic
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—1064no—
670C22×C4C2×C22⋊D5312yes—
671C22×C4C23×D5311yescharacteristic
672C22×C4C23×D5312yes—
673C22×C4C23×D5312yes—
674SD16—1068no—
675SD16—2124no—
676SD16—2124no—
677D8—1068no—
678D8—2124no—
679D8—2124no—
680M16—2122no—
681M16—2122no—
682C2×C8—534no—
683C2×C8—534no—
684C2×C8—2122no—
685C2×C8—2122no—
686C4⋊C4—22no—
687C4⋊C4—24no—
688C4⋊C4—534no—
689C4⋊C4—1062no—
690C4⋊C4C2×C22⋊D5314yes—
691C4⋊C4C23×D5312yes—
692C22⋊C4—24no—
693C22⋊C4—21no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—22no—
698C22⋊C4—1062no—
699C22⋊C4—1062no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C22⋊C4C2×C22⋊D5314yes—
705C22⋊C4C2×C22⋊D5314yes—
706C42—21no—
707C42—22no—
708C42—1062no—
709C42—1062no—
710C42C2×C22⋊D5311yescharacteristic
711C42C2×C22⋊D5311yescharacteristic
712C42C23×D5312yes—
713C23—21no—
714C23—22no—
715C23—44no—
716C23—42no—
717C23—82no—
718C23—84no—
719C23—1064no—
720C23—4244no—
721C23—4244no—
722C23—4242no—
723C23—4242no—
724C23C22×C22⋊D5312yes—
725C23C22×C22⋊D5311yescharacteristic
726C23C22×C22⋊D5312yes—
727Q8—21no—
728Q8—22no—
729Q8—22no—
730Q8—41no—
731Q8—41no—
732Q8—44no—
733Q8—42no—
734Q8—4242no—
735Q8#1313326212yes—
736D4—24no—
737D4—21no—
738D4—22no—
739D4—22no—
740D4—41no—
741D4—42no—
742D4—44no—
743D4—41no—
744D4—42no—
745D4—44no—
746D4—44no—
747D4—42no—
748D4—44no—
749D4—84no—
750D4—1064no—
751D4—1064no—
752D4—4242no—
753D4—4242no—
754D4—4242no—
755D4—4244no—
756D4—4244no—
757D4—4244no—
758D4—2124no—
759D4#1313326212yes—
760C2×C4—24no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—82no—
776C2×C4—1064no—
777C2×C4—2128no—
778C2×C4C22×C22⋊D5311yescharacteristic
779C2×C4C22×C22⋊D5312yes—
780C2×C4C22×C22⋊D5312yes—
781C2×C4C22×C22⋊D5312yes—
782C2×C4C22×C22⋊D5312yes—
783C2×C4C24×D5311yescharacteristic
784C8—1064no—
785C8—1064no—
786C22—21no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—24no—
792C22—24no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—164no—
797C22—162no—
798C22—8484no—
799C22—8484no—
800C22—2124no—
801C22—2124no—
802C22—2124no—
803C22C23×C22⋊D5311yescharacteristic
804C4—21no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—22no—
809C4—22no—
810C4—42no—
811C4—42no—
812C4—2124no—
813C4C2×#1313326211yescharacteristic
814C4C2×#1313326211yescharacteristic
815C2—42no—
816C2—41no—
817C2—42no—
818C2—42no—
819C2—82no—
820C2—4244no—
821C2#2028835011yescharacteristic
822C2#2028949412yes—
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3500C2
socleC22×C53C23×D4
hypercenter#3500D53
hypocenterC53#61673
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #532 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. #20289120C2semidirect
2. #20286901C2semidirect
3. #20286871C2semidirect
4. #20286211C2semidirect
5. #20286196C2semidirect
6. #20285702C2semidirect
7. #20285582C2semidirect
8. #20285576C2semidirect
9. #20284866C2semidirect
10. #20284001C2semidirect
11. #20283983C2semidirect
12. #20283786C2semidirect
13. C53×#3500C2semidirect
14. C2×#13133242C22semidirect
15. C2×#13133242C22semidirect
16. C22×#11719924C22semidirect
17. C22×#11719922C22semidirect
21. #16811338C22semidirect
22. D4×D212C22semidirect
26. #16811187C22semidirect
27. #16811173C22semidirect
28. #16811013C22semidirect
29. #16810982C22semidirect
30. #16810961C22semidirect
31. #16810947C22semidirect
32. #16810944C22semidirect
33. #16810908C22semidirect
34. #16810903C22semidirect
35. #16810874C22semidirect
36. #16810871C22semidirect
37. #16810857C22semidirect
38. #16810854C22semidirect
39. #16810835C22semidirect
40. #16810835C22semidirect
41. #16810823C22semidirect
42. #16810818C22semidirect
43. #16810773C22semidirect
44. #16810768C22semidirect
45. #16810768C22semidirect
46. #16810768C22semidirect
47. #16810762C22semidirect
48. #16810762C22semidirect
49. #16810757C22semidirect
50. #16810757C22semidirect
51. #16810756C22semidirect
52. #16810733C22semidirect
53. #16810721C22semidirect
54. #16810695C22semidirect
55. #16810695C22semidirect
56. #16810680C22semidirect
57. #16810632C22semidirect
58. #16810628C22semidirect
59. #16810619C22semidirect
60. #16810619C22semidirect
61. #16810590C22semidirect
62. #16810590C22semidirect
63. C2×2−1+4×C53C22semidirect
64. C2×H(5,𝔽2)×C53C22semidirect
65. C53×#548C22semidirect
67. C53×#546C22semidirect
69. C53×#536C22semidirect
71. C53×#535C22semidirect
75. C2×#124×C53C22semidirect
76. C4×#41×C53C22semidirect
405. #3500D53semidirect
425. C2×2−1+4C2×D53semidirect
426. C2×H(5,𝔽2)C2×D53semidirect
435. #548C2×D53semidirect
437. #546C2×D53semidirect
441. #536C2×D53semidirect
446. #535C2×D53semidirect
451. C2×#124C2×D53semidirect
452. C4×#41C2×D53semidirect
488. C53#61673semidirect

Maximal subgroups

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

subgroupindex
#202891202
#202869012
#202868712
#202862112
#202861962
#202857022
#202855822
#202855762
#202848662
#202840012
#202839832
#202837862
C53×#35002
#6167353