Finite Group Databasebeta

← #28252581

Subgroups — #28252581

Order 13568.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288105C211yesmaximal, characteristic, complemented
2#20284992C214yesmaximal, complemented
3#20284977C214yesmaximal, complemented
4#20284929C214yesmaximal, complemented
5#20284914C214yesmaximal, complemented
6#20284638C212yesmaximal, complemented
7#20284520C211yesmaximal, characteristic, complemented
8#20284512C211yesmaximal, characteristic, complemented
9#20284187C211yesmaximal, characteristic, complemented
10#20284179C211yesmaximal, characteristic, complemented
11#20283957C212yesmaximal, complemented
12C4×#13133248C212yesmaximal, complemented
13C4×#13133243C212yesmaximal, complemented
14#20283353C211yesmaximal, characteristic, complemented
15C2×C53×#520C211yesmaximal, characteristic, complemented
16C2×#13133248C2212yes—
17C2×#13133243C2212yes—
18#16811244C2212yescomplemented
19#16811244C2212yescomplemented
20#16811235C2212yescomplemented
21#16811228C2212yescomplemented
22#16811220—21no—
23#16811220—21no—
24#16811211—21no—
25#16811211—21no—
26#16811180C2211yescharacteristic
27#16811173C2211yescharacteristic
28#16811151—22no—
29#16811151—22no—
30#16811134C2212yes—
31C4×#11719945C2212yes—
32#16810958C2214yescomplemented
33#16810953C2214yescomplemented
34#16810941C2214yescomplemented
35#16810936C2214yescomplemented
36#16810930C2214yescomplemented
37#16810923C2214yescomplemented
38#16810918C2212yescomplemented
39#16810913C2212yescomplemented
40#16810908C2212yescomplemented
41#16810903C2212yescomplemented
42#16810845C2214yescomplemented
43#16810838C2214yescomplemented
44#16810833C2212yescomplemented
45#16810828C2212yescomplemented
46#16810823C2212yescomplemented
47#16810818C2212yescomplemented
48#16810785C2214yes—
49#16810785C2214yes—
50#16810768C2214yes—
51#16810768C2214yes—
52#16810733C2214yescomplemented
53#16810728C2214yescomplemented
54#16810723C2214yescomplemented
55#16810721C2214yescomplemented
56C4×#11719925C2214yescomplemented
57C4×#11719924C2214yescomplemented
58C4×#11719923C2214yescomplemented
59C4×#11719922C2214yescomplemented
60#16810684C2214yescomplemented
61#16810684C2214yescomplemented
62#16810663C2212yes—
63#16810663C2212yes—
64#16810647C2211yescharacteristic
65#16810647C2211yescharacteristic
66#16810632C2212yes—
67#16810628C2212yes—
68#16810622C2212yes—
69#16810622C2212yes—
70#16810587C2212yes—
71C4×#11719917C2212yes—
72C22×#41×C53C2211yescharacteristic
73C53×#520—22no—
74C53×#520—22no—
75C53×#520C2214yes—
76C53×#520C2214yes—
77C2×C4×Q8×C53C2211yescharacteristic
78C2×C4×Q8×C53C2211yescharacteristic
79C2×C4×D4×C53—21no—
80C2×C4×D4×C53—21no—
81C2×C4×D4×C53C2211yescharacteristic
82C2×C4×D4×C53C2211yescharacteristic
83C2×#117×C53—21no—
84C2×#117×C53C2211yescharacteristic
85C22×C4⋊C4×C53—21no—
86C22×C4⋊C4×C53C2211yescharacteristic
87C2×#11719945C2312yes—
88#13133248—28no—
89#13133243—28no—
90C2×#11719925C2314yes—
91C2×#11719923C2314yes—
92C2×#11719924C2314yes—
93C2×#11719922C2314yes—
94C2×#11719917C2312yes—
95C2×#11719917C2312yes—
96#13133217C2311yescharacteristic
97#13133217C2311yescharacteristic
98#13133217C2311yescharacteristic
99#13133214C2311yescharacteristic
100#13133212—22no—
101#13133212—22no—
102#13133210—22no—
103#13133210—22no—
104#13133209C2312yes—
105#13133207—22no—
106#13133207—22no—
107#13133205C2312yes—
108#13133203—22no—
109#13133203—22no—
110#13133202—22no—
111#13133202—22no—
112#13133200—22no—
113#13133199—22no—
114#13133199—22no—
115#13133196—21no—
116#13133196—21no—
117#13133196C2312yes—
118#13133196C2312yes—
119#13133195—22no—
120#13133195—22no—
121#13133191—21no—
122#13133191—21no—
123#13133191C2312yes—
124#13133191C2312yes—
125#13133190—22no—
126#13133190—22no—
127#13133186—22no—
128C4×Dic106—21no—
129C4×Dic106—21no—
130C4×Dic106C2312yes—
131C4×Dic106C2312yes—
132C4×D212—21no—
133C4×D212—21no—
134C4×D212C2312yes—
135C4×D212C2312yes—
136C4×C22⋊D53—22no—
137C4×C22⋊D53—22no—
138C4×C22⋊D53—22no—
139C4×C22⋊D53—22no—
140#13133176C2312yes—
141#13133174—22no—
142C42×D53—22no—
143#13133150C2314yes—
144#13133150C2314yes—
145#13133148C2314yes—
146#13133148C2314yes—
147C4⋊#88322C2312yes—
148C4⋊#88322C2312yes—
149C4⋊#88322C2312yes—
150C4⋊#88322C2312yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133140C2314yes—
154#13133140C2314yes—
155#13133138C2314yes—
156#13133138C2314yes—
157#13133137C2314yes—
158#13133137C2314yes—
159C22⋊#88322C2314yes—
160C22⋊#88322C2314yes—
161#13133128C2314yes—
162C4×#88322C2314yes—
163C2×#41×C53—24no—
164C2×#41×C53—24no—
165C2×#41×C53—22no—
166C2×#41×C53C2314yes—
167C22×Q8×C53C2311yescharacteristic
168C22×D4×C53—21no—
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53—21no—
171C23×C4×C53—21no—
172C23×C4×C53—21no—
173C23×C4×C53—21no—
174C23×C4×C53C2311yescharacteristic
175C4×Q8×C53—22no—
176C4×Q8×C53—21no—
177C4×Q8×C53—21no—
178C4×Q8×C53C2312yes—
179C4×Q8×C53C2312yes—
180C4×Q8×C53C2314yes—
181C4×D4×C53—24no—
182C4×D4×C53—24no—
183C4×D4×C53—24no—
184C4×D4×C53—24no—
185C4×D4×C53—22no—
186C4×D4×C53—21no—
187C4×D4×C53—21no—
188C4×D4×C53C2312yes—
189C4×D4×C53C2312yes—
190C4×D4×C53C2314yes—
191#117×C53—24no—
192#117×C53—24no—
193#117×C53D412yes—
194#117×C53D412yes—
195#117×C53C2312yes—
196#117×C53C2312yes—
197C2×C4⋊C4×C53—24no—
198C2×C4⋊C4×C53—24no—
199C2×C4⋊C4×C53—21no—
200C2×C4⋊C4×C53—21no—
201C2×C4⋊C4×C53—21no—
202C2×C4⋊C4×C53—22no—
203C2×C4⋊C4×C53D411yescharacteristic
204C2×C4⋊C4×C53D411yescharacteristic
205C2×C4⋊C4×C53C2311yescharacteristic
206C2×C4⋊C4×C53C2311yescharacteristic
207C2×C4⋊C4×C53C2314yes—
208C2×C22⋊C4×C53—21no—
209C2×C22⋊C4×C53—21no—
210C2×C22⋊C4×C53D411yescharacteristic
211C2×C22⋊C4×C53D411yescharacteristic
212C2×C42×C53—21no—
213C2×C42×C53—21no—
214C2×C42×C53C2311yescharacteristic
215C2×C42×C53C2311yescharacteristic
216C24×C53—21no—
217C24×C53C2×D411yescharacteristic
218#41×C53—216no—
219#41×C53—28no—
220#41×C53—28no—
221C2×Q8×C53—21no—
222C2×Q8×C53—22no—
223C2×Q8×C53#4114yes—
224C2×Q8×C53C2412yes—
225C2×D4×C53—28no—
226C2×D4×C53—24no—
227C2×D4×C53—21no—
228C2×D4×C53—22no—
229C2×D4×C53#4114yes—
230C2×D4×C53C2412yes—
231C22×C4×C53—28no—
232C22×C4×C53—21no—
233C22×C4×C53—24no—
234C22×C4×C53—22no—
235C22×C4×C53—22no—
236C22×C4×C53—21no—
237C22×C4×C53—21no—
238C22×C4×C53—24no—
239C22×C4×C53—22no—
240C22×C4×C53—24no—
241C22×C4×C53—22no—
242C22×C4×C53—82no—
243C22×C4×C53—82no—
244C22×C4×C53—82no—
245C22×C4×C53C2×D411yescharacteristic
246C22×C4×C53C2×D412yes—
247C22×C4×C53C2×D411yescharacteristic
248C22×C4×C53C2×D411yescharacteristic
249C22×C4×C53C2×D411yescharacteristic
250C22×C4×C53C2×D411yescharacteristic
251C22×C4×C53C2412yes—
252C22×C4×C53C2411yescharacteristic
253C2×C22⋊D53—22no—
254C2×C22⋊D53—22no—
255C2×C22⋊D53—22no—
256#11719945—24no—
257#11719945—24no—
258C2×D212—21no—
259C2×D212—21no—
260C2×D212C2412yes—
261C2×C4×D53—22no—
262C2×C4×D53—22no—
263C2×C4×D53—22no—
264C2×Dic106—21no—
265C2×Dic106—21no—
266C2×Dic106C2412yes—
267C4⋊C4×C53—24no—
268C4⋊C4×C53—22no—
269C4⋊C4×C53—24no—
270C4⋊C4×C53—22no—
271C4⋊C4×C53—21no—
272C4⋊C4×C53—21no—
273C4⋊C4×C53C2×D412yes—
274C4⋊C4×C53C2×D412yes—
275C4⋊C4×C53C2×D412yes—
276C4⋊C4×C53C2×D412yes—
277C4⋊C4×C53C2412yes—
278C4⋊C4×C53C2412yes—
279C22⋊C4×C53—22no—
280C22⋊C4×C53—24no—
281C22⋊C4×C53—22no—
282C22⋊C4×C53C2×D412yes—
283C22⋊C4×C53C2×D412yes—
284C22⋊C4×C53C2×D412yes—
285C22⋊C4×C53C2×D412yes—
286C42×C53—22no—
287C42×C53—24no—
288C42×C53—22no—
289C42×C53C2×D412yes—
290C42×C53C2×D411yescharacteristic
291C42×C53C2×D411yescharacteristic
292C42×C53C2412yes—
293C42×C53C2411yescharacteristic
294C42×C53C2411yescharacteristic
295C22⋊Dic53—22no—
296C22⋊Dic53—22no—
297C22⋊Dic53—22no—
298#11719925—28no—
299#11719924—28no—
300#11719923—28no—
301#11719922—28no—
302#11719921—22no—
303#11719921—22no—
304#11719921—22no—
305#11719921—22no—
306#11719921—22no—
307#11719921—22no—
308C4⋊Dic53—21no—
309C4⋊Dic53—21no—
310C4⋊Dic53—21no—
311C4⋊Dic53—21no—
312C4⋊Dic53C2412yes—
313C4⋊Dic53C2412yes—
314#11719919—22no—
315#11719919—22no—
316#11719919—22no—
317#11719919—22no—
318#11719919—22no—
319#11719919—22no—
320C4×Dic53—22no—
321C4×Dic53—22no—
322C4×Dic53—22no—
323#11719917—24no—
324#11719917—24no—
325C2×#88322C2414yes—
326C2×#88322C2414yes—
327C23×C53—22no—
328C23×C53—24no—
329C23×C53—22no—
330C23×C53—41no—
331C23×C53—41no—
332C23×C53—42no—
333C23×C53—42no—
334C23×C53C22×D412yes—
335C23×C53C22×D411yescharacteristic
336C22×D53—22no—
337Q8×C53—24no—
338Q8×C53—22no—
339Q8×C53C2×#4114yes—
340D4×C53—216no—
341D4×C53—24no—
342D4×C53—22no—
343D4×C53C2×#4114yes—
344C2×C4×C53—216no—
345C2×C4×C53—22no—
346C2×C4×C53—24no—
347C2×C4×C53—22no—
348C2×C4×C53—24no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—42no—
358C2×C4×C53—42no—
359C2×C4×C53—82no—
360C2×C4×C53—84no—
361C2×C4×C53—82no—
362C2×C4×C53—84no—
363C2×C4×C53C22×D411yescharacteristic
364C2×C4×C53C22×D411yescharacteristic
365C2×C4×C53C22×D412yes—
366C2×C4×C53C22×D412yes—
367C2×C4×C53C22×D411yescharacteristic
368C2×C4×C53C22×D411yescharacteristic
369C2×C4×C53C22×D412yes—
370C2×C4×C53C22×D411yescharacteristic
371C2×C4×C53C2×#4112yes—
372C2×C4×C53C2×#4112yes—
373C2×C4×C53C2511yescharacteristic
374C22⋊D53—44no—
375C22⋊D53—82no—
376C22⋊D53—82no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—22no—
380D212—22no—
381D212—22no—
382D212—81no—
383D212—81no—
384C4×D53—44no—
385C4×D53—82no—
386C4×D53—82no—
387Dic106—22no—
388Dic106—22no—
389Dic106—81no—
390Dic106—81no—
391#88322—24no—
392#88322—24no—
393#60565—531nomaximal, Sylow
394C22×C53—21no—
395C22×C53—21no—
396C22×C53—22no—
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—24no—
400C22×C53—44no—
401C22×C53—48no—
402C22×C53—42no—
403C22×C53—42no—
404C22×C53#52512yes—
405C22×C53C23×D411yescharacteristic
406C2×D53—42no—
407C2×D53—42no—
408C2×D53—42no—
409C4×C53—21no—
410C4×C53—22no—
411C4×C53—21no—
412C4×C53—21no—
413C4×C53—22no—
414C4×C53—21no—
415C4×C53—22no—
416C4×C53—24no—
417C4×C53—42no—
418C4×C53—42no—
419C4×C53#52512yes—
420C4×C53C22×#4111yescharacteristic
421C4×C53C22×#4111yescharacteristic
422Dic53—42no—
423Dic53—42no—
424Dic53—42no—
425#3455—531no—
426C2×#520D5311yescharacteristic, complemented
427#3125—534no—
428#3124—534no—
429#3120—534no—
430#3119—534no—
431#3092—532no—
432#3078—531no—
433#3077—531no—
434#3037—531no—
435#3036—531no—
436#3005—532no—
437C4×#137—532no—
438C4×AGL(1,ℤ/8)—532no—
439#2921—531no—
440C2×C53—22no—
441C2×C53—42no—
442C2×C53—44no—
443C2×C53C2×#52511yescharacteristic
444C2×C53#358511yescharacteristic
445C2×C53#358611yescharacteristic
446D53—82no—
447C22×#41C2×D5311yescharacteristic
448C2×#137—532no—
449C2×AGL(1,ℤ/8)—532no—
450#542—532no—
451#542—532no—
452#541—532no—
453#540—532no—
454#539—1061no—
455#539—1061no—
456#538—1061no—
457#538—1061no—
458#533—531no—
459#532—531no—
460#529—1062no—
461#529—1062no—
462#525—532no—
463#520—22no—
464#520—22no—
465#520C2×D5314yes—
466#520C2×D5314yes—
467C4×#41—532no—
468C2×C4×Q8C2×D5311yescharacteristic
469C2×C4×Q8C2×D5311yescharacteristic
470C2×C4×D4—21no—
471C2×C4×D4—21no—
472C2×C4×D4C2×D5311yescharacteristic
473C2×C4×D4C2×D5311yescharacteristic
474C2×#117—21no—
475C2×#117C2×D5311yescharacteristic
476C22×C4⋊C4—21no—
477C22×C4⋊C4C2×D5311yescharacteristic
478#484—534no—
479#483—534no—
480#481—534no—
481#480—534no—
482#479—534no—
483#478—534no—
484#477—532no—
485#476—532no—
486#475—532no—
487#474—532no—
488#464—534no—
489#463—534no—
490#462—532no—
491#461—532no—
492#460—532no—
493#459—532no—
494#452—534no—
495#452—534no—
496#449—534no—
497#449—534no—
498#442—534no—
499#441—534no—
500#440—534no—
501#440—534no—
502C4×Q16—534no—
503C4×SD16—534no—
504C4×SD16—534no—
505C4×D8—534no—
506#433—534no—
507#433—534no—
508#428—532no—
509#428—532no—
510#423—531no—
511#423—531no—
512#419—532no—
513#418—532no—
514#417—532no—
515#417—532no—
516#407—532no—
517C4×M16—532no—
518C53#6056511yescharacteristic, complemented, Sylow
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—22no—
522C2×#41—532no—
523C2×#41C22×D5314yes—
524C22×Q8C22×D5311yescharacteristic
525C22×D4—21no—
526C22×D4C22×D5311yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D5311yescharacteristic
532#137—1068no—
533AGL(1,ℤ/8)—1068no—
534C2×Q16—534no—
535C2×SD16—534no—
536C2×SD16—534no—
537C2×D8—534no—
538C2×M16—532no—
539C2×M16—532no—
540C4⋊Q8—531no—
541C4⋊Q8—531no—
542C4⋊Q8—531no—
543#127—531no—
544#126—1062no—
545#126—1062no—
546#126—1062no—
547#126—1062no—
548#125—532no—
549#125—1062no—
550#125—1062no—
551#124—532no—
552#124—1062no—
553#124—1062no—
554#123—1062no—
555#123—1062no—
556#123—1062no—
557#123—1062no—
558#123—1062no—
559C22⋊Q8—532no—
560C22⋊Q8—532no—
561C22⋊Q8—1061no—
562C22⋊Q8—1061no—
563C22⋊Q8—1062no—
564C22⋊Q8—1062no—
565#121—532no—
566#121—532no—
567#121—1061no—
568#121—1061no—
569#121—1062no—
570#121—1062no—
571#120—1062no—
572C4×Q8—22no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—532no—
576C4×Q8—532no—
577C4×Q8—1061no—
578C4×Q8—1061no—
579C4×Q8C22×D5314yes—
580C4×Q8C22×D5312yes—
581C4×Q8C22×D5312yes—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—22no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—532no—
590C4×D4—532no—
591C4×D4—1062no—
592C4×D4—1062no—
593C4×D4—1062no—
594C4×D4—1062no—
595C4×D4—1061no—
596C4×D4—1061no—
597C4×D4C22×D5314yes—
598C4×D4C22×D5312yes—
599C4×D4C22×D5312yes—
600#117—24no—
601#117—24no—
602#117—532no—
603#117—1062no—
604#117C22⋊D5312yes—
605#117C22⋊D5312yes—
606#117C22×D5312yes—
607#117C22×D5312yes—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4C22⋊D5311yescharacteristic
615C2×C4⋊C4C22⋊D5311yescharacteristic
616C2×C4⋊C4C22×D5311yescharacteristic
617C2×C4⋊C4C22×D5311yescharacteristic
618C2×C4⋊C4C22×D5314yes—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4C22⋊D5311yescharacteristic
622C2×C22⋊C4C22⋊D5311yescharacteristic
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—1062no—
626C2×C42C22×D5311yescharacteristic
627C2×C42C22×D5311yescharacteristic
628#107—534no—
629#107—534no—
630#106—534no—
631#106—534no—
632C4⋊C8—532no—
633C4⋊C8—532no—
634C4⋊C8—532no—
635C4⋊C8—532no—
636#103—534no—
637#103—534no—
638#103—534no—
639#103—534no—
640#102—534no—
641#102—534no—
642#102—534no—
643#102—534no—
644C22⋊C8—534no—
645C22⋊C8—534no—
646#97—534no—
647C4×C8—534no—
648C24—21no—
649C24C2×C22⋊D5311yescharacteristic
650#41—216no—
651#41—28no—
652#41—28no—
653#41—1064no—
654#41—1064no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—532no—
658C2×Q8—1061no—
659C2×Q8—1061no—
660C2×Q8#1171994514yes—
661C2×Q8C23×D5312yes—
662C2×D4—28no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—532no—
667C2×D4—1062no—
668C2×D4—1062no—
669C2×D4—1062no—
670C2×D4—1061no—
671C2×D4—1061no—
672C2×D4#1171994514yes—
673C2×D4C23×D5312yes—
674C22×C4—28no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—82no—
686C22×C4—82no—
687C22×C4—82no—
688C22×C4—1062no—
689C22×C4—1062no—
690C22×C4—1062no—
691C22×C4C2×C22⋊D5311yescharacteristic
692C22×C4C2×C22⋊D5312yes—
693C22×C4C2×C22⋊D5311yescharacteristic
694C22×C4C2×C22⋊D5311yescharacteristic
695C22×C4C2×C22⋊D5311yescharacteristic
696C22×C4C2×C22⋊D5311yescharacteristic
697C22×C4C23×D5312yes—
698C22×C4C23×D5311yescharacteristic
699Q16—1068no—
700SD16—1068no—
701SD16—1068no—
702D8—1068no—
703M16—1064no—
704M16—1064no—
705C2×C8—534no—
706C2×C8—534no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—532no—
714C4⋊C4—532no—
715C4⋊C4—1062no—
716C4⋊C4—1062no—
717C4⋊C4—1061no—
718C4⋊C4—1061no—
719C4⋊C4—1062no—
720C4⋊C4—1062no—
721C4⋊C4—1062no—
722C4⋊C4—1062no—
723C4⋊C4—1061no—
724C4⋊C4—1061no—
725C4⋊C4C2×C22⋊D5312yes—
726C4⋊C4C2×C22⋊D5312yes—
727C4⋊C4C2×C22⋊D5312yes—
728C4⋊C4C2×C22⋊D5312yes—
729C4⋊C4C23×D5312yes—
730C4⋊C4C23×D5312yes—
731C22⋊C4—24no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—1062no—
735C22⋊C4—1062no—
736C22⋊C4—1062no—
737C22⋊C4—1062no—
738C22⋊C4—1062no—
739C22⋊C4—1062no—
740C22⋊C4—1062no—
741C22⋊C4—1062no—
742C22⋊C4—1062no—
743C22⋊C4C2×C22⋊D5312yes—
744C22⋊C4C2×C22⋊D5312yes—
745C22⋊C4C2×C22⋊D5312yes—
746C22⋊C4C2×C22⋊D5312yes—
747C42—24no—
748C42—22no—
749C42—22no—
750C42—1062no—
751C42—1062no—
752C42—1062no—
753C42C2×C22⋊D5312yes—
754C42C2×C22⋊D5311yescharacteristic
755C42C2×C22⋊D5311yescharacteristic
756C42C23×D5312yes—
757C42C23×D5311yescharacteristic
758C42C23×D5311yescharacteristic
759C23—22no—
760C23—24no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—42no—
765C23—42no—
766C23—1062no—
767C23C22×C22⋊D5312yes—
768C23C22×C22⋊D5311yescharacteristic
769Q8—24no—
770Q8—22no—
771Q8—1062no—
772Q8—1062no—
773Q8—4241no—
774Q8—4241no—
775Q8C2×#1171994514yes—
776D4—216no—
777D4—24no—
778D4—22no—
779D4—1062no—
780D4—1062no—
781D4—4241no—
782D4—4241no—
783D4—4242no—
784D4—4242no—
785D4—2124no—
786D4C2×#1171994514yes—
787C2×C4—216no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—84no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—84no—
806C2×C4—1062no—
807C2×C4—1062no—
808C2×C4—1062no—
809C2×C4—4242no—
810C2×C4—4242no—
811C2×C4—2124no—
812C2×C4C22×C22⋊D5312yes—
813C2×C4C22×C22⋊D5311yescharacteristic
814C2×C4C22×C22⋊D5311yescharacteristic
815C2×C4C22×C22⋊D5312yes—
816C2×C4C22×C22⋊D5311yescharacteristic
817C2×C4C22×C22⋊D5311yescharacteristic
818C2×C4C22×C22⋊D5312yes—
819C2×C4C22×C22⋊D5311yescharacteristic
820C2×C4C2×#1171994512yes—
821C2×C4C2×#1171994512yes—
822C2×C4C24×D5311yescharacteristic
823C8—1064no—
824C8—1064no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—48no—
833C22—42no—
834C22—42no—
835C22—2122no—
836C22—2122no—
837C22—2122no—
838C22#1681113412yes—
839C22C23×C22⋊D5311yescharacteristic
840C4—22no—
841C4—24no—
842C4—22no—
843C4—21no—
844C4—21no—
845C4—22no—
846C4—21no—
847C4—21no—
848C4—42no—
849C4—42no—
850C4—2122no—
851C4—2122no—
852C4—2122no—
853C4#1681113412yes—
854C4C22×#1171994511yescharacteristic
855C4C22×#1171994511yescharacteristic
856C2—22no—
857C2—42no—
858C2—44no—
859C2—4242no—
860C2C2×#1681113411yescharacteristic
861C2#2028949511yescharacteristic
862C2#2028950211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#520C2
socleC22×C53C23×D4
hypercenterC2×#520D53
hypocenterC53#60565
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #20288105C2semidirect
2. #20284992C2semidirect
3. #20284977C2semidirect
4. #20284929C2semidirect
5. #20284914C2semidirect
6. #20284638C2semidirect
7. #20284520C2semidirect
8. #20284512C2semidirect
9. #20284187C2semidirect
10. #20284179C2semidirect
11. #20283957C2semidirect
12. C4×#13133248C2semidirect
13. C4×#13133243C2semidirect
14. #20283353C2semidirect
15. C2×C53×#520C2semidirect
18. #16811244C22semidirect
19. #16811244C22semidirect
20. #16811235C22semidirect
21. #16811228C22semidirect
32. #16810958C22semidirect
33. #16810953C22semidirect
34. #16810941C22semidirect
35. #16810936C22semidirect
36. #16810930C22semidirect
37. #16810923C22semidirect
38. #16810918C22semidirect
39. #16810913C22semidirect
40. #16810908C22semidirect
41. #16810903C22semidirect
42. #16810845C22semidirect
43. #16810838C22semidirect
44. #16810833C22semidirect
45. #16810828C22semidirect
46. #16810823C22semidirect
47. #16810818C22semidirect
52. #16810733C22semidirect
53. #16810728C22semidirect
54. #16810723C22semidirect
55. #16810721C22semidirect
56. C4×#11719925C22semidirect
57. C4×#11719924C22semidirect
58. C4×#11719923C22semidirect
59. C4×#11719922C22semidirect
60. #16810684C22semidirect
61. #16810684C22semidirect
426. C2×#520D53semidirect
518. C53#60565semidirect

Maximal subgroups

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

subgroupindex
#202881052
#202849922
#202849772
#202849292
#202849142
#202846382
#202845202
#202845122
#202841872
#202841792
#202839572
C4×#131332482
C4×#131332432
#202833532
C2×C53×#5202
#6056553