Finite Group Databasebeta

← #28257138

Subgroups — #28257138

Order 13568.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288105C211yesmaximal, characteristic, complemented
2#20286180C214yesmaximal, complemented
3#20286171C214yesmaximal, complemented
4#20286141C214yesmaximal, complemented
5#20286126C214yesmaximal, complemented
6#20284524C212yesmaximal, complemented
7#20284520C211yesmaximal, characteristic, complemented
8#20284512C211yesmaximal, characteristic, complemented
9#20284341C212yesmaximal, complemented
10#20284330C212yesmaximal, complemented
11#20284205C212yesmaximal, complemented
12#20284187C211yesmaximal, characteristic, complemented
13#20284179C211yesmaximal, characteristic, complemented
14#20283279C211yesmaximal, characteristic, complemented
15C2×C53×#542C211yesmaximal, characteristic, complemented
16C2×#13133248C2212yes—
17C2×#13133243C2212yes—
18C22×#11719917C2212yes—
19#16811244C2212yescomplemented
20#16811244C2212yescomplemented
21#16811235C2212yescomplemented
22#16811228C2212yescomplemented
23#16811220—21no—
24#16811220—21no—
25#16811211—21no—
26#16811211—21no—
27#16811180C2211yescharacteristic
28#16811173C2211yescharacteristic
29#16811151—22no—
30#16811151—22no—
31#16811134C2212yes—
32C4×#11719945C2212yes—
33#16810930C2214yescomplemented
34#16810923C2214yescomplemented
35#16810918C2212yescomplemented
36#16810915C2214yescomplemented
37#16810913C2212yescomplemented
38#16810910C2214yescomplemented
39#16810908C2212yescomplemented
40#16810905C2214yescomplemented
41#16810903C2212yescomplemented
42#16810900C2214yescomplemented
43#16810879C2214yescomplemented
44#16810874C2214yes—
45#16810871C2214yescomplemented
46#16810867C2214yes—
47#16810862C2214yescomplemented
48#16810857C2214yes—
49#16810854C2214yescomplemented
50#16810850C2214yes—
51#16810845C2214yescomplemented
52#16810842C2214yescomplemented
53#16810842C2214yescomplemented
54#16810838C2214yescomplemented
55#16810835C2214yescomplemented
56#16810835C2214yescomplemented
57#16810833C2212yescomplemented
58#16810828C2212yescomplemented
59#16810823C2212yescomplemented
60#16810818C2212yescomplemented
61#16810663C2212yes—
62#16810663C2212yes—
63#16810650C2214yescomplemented
64#16810650C2214yescomplemented
65#16810647C2211yescharacteristic
66#16810647C2211yescharacteristic
67#16810647C2212yes—
68#16810632C2212yes—
69#16810628C2212yes—
70#16810622C2212yes—
71#16810622C2212yes—
72C53×#542—22no—
73C53×#542—22no—
74C53×#542C2214yes—
75C53×#542C2214yes—
76C2×C4⋊Q8×C53C2211yescharacteristic
77C2×#126×C53—21no—
78C2×#124×C53—21no—
79C2×#124×C53C2211yescharacteristic
80C2×#123×C53—21no—
81C2×C22⋊Q8×C53—21no—
82C2×C22⋊Q8×C53C2211yescharacteristic
83C2×#121×C53C2211yescharacteristic
84C2×C4×Q8×C53C2211yescharacteristic
85C2×C4×D4×C53C2211yescharacteristic
86C2×#117×C53C2211yescharacteristic
87C2×#11719945C2312yes—
88#13133248—44no—
89#13133243—44no—
90C2×#11719925C2314yes—
91C2×#11719923C2314yes—
92C2×#11719924C2314yes—
93C2×#11719922C2314yes—
94C2×#11719917—44no—
95C2×#11719917C2312yes—
96C2×#11719917C2312yes—
97C2×#11719917C2314yes—
98C22×#88322C2314yes—
99#13133217C2311yescharacteristic
100#13133217C2311yescharacteristic
101#13133217C2311yescharacteristic
102#13133214C2311yescharacteristic
103#13133212—22no—
104#13133212—22no—
105#13133210—22no—
106#13133210—22no—
107#13133209C2312yes—
108#13133207—22no—
109#13133207—22no—
110#13133205C2312yes—
111#13133203—22no—
112#13133203—22no—
113#13133202—22no—
114#13133202—22no—
115#13133200—22no—
116#13133199—22no—
117#13133199—22no—
118#13133196—21no—
119#13133196—21no—
120#13133196C2312yes—
121#13133196C2312yes—
122#13133195—22no—
123#13133195—22no—
124#13133191—21no—
125#13133191—21no—
126#13133191C2312yes—
127#13133191C2312yes—
128#13133190—22no—
129#13133190—22no—
130#13133186—22no—
131C4×Dic106—21no—
132C4×Dic106—21no—
133C4×Dic106C2312yes—
134C4×Dic106C2312yes—
135C4×D212—21no—
136C4×D212—21no—
137C4×D212C2312yes—
138C4×D212C2312yes—
139C4×C22⋊D53—22no—
140C4×C22⋊D53—22no—
141C4×C22⋊D53—22no—
142C4×C22⋊D53—22no—
143#13133176C2312yes—
144#13133174—22no—
145C42×D53—22no—
146#13133150C2314yes—
147#13133150C2314yes—
148#13133148C2314yes—
149#13133148C2314yes—
150C4⋊#88322C2312yes—
151C4⋊#88322C2312yes—
152C4⋊#88322C2314yes—
153C4⋊#88322C2314yes—
154C4⋊#88322C2312yes—
155C4⋊#88322C2312yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133138C2314yes—
161#13133138C2314yes—
162#13133137C2314yes—
163#13133137C2314yes—
164C22×Q8×C53—21no—
165C22×Q8×C53C2311yescharacteristic
166C22×D4×C53—21no—
167C22×D4×C53C2311yescharacteristic
168C23×C4×C53—21no—
169C23×C4×C53C2311yescharacteristic
170C4⋊Q8×C53—22no—
171C4⋊Q8×C53C2314yes—
172#126×C53—24no—
173#126×C53—24no—
174#124×C53—24no—
175#124×C53—24no—
176#124×C53—22no—
177#124×C53C2314yes—
178#123×C53—24no—
179#123×C53—24no—
180C22⋊Q8×C53—24no—
181C22⋊Q8×C53—24no—
182C22⋊Q8×C53—22no—
183C22⋊Q8×C53C2314yes—
184#121×C53—22no—
185#121×C53C2314yes—
186C4×Q8×C53—21no—
187C4×Q8×C53—21no—
188C4×Q8×C53C2312yes—
189C4×Q8×C53C2312yes—
190C4×D4×C53—21no—
191C4×D4×C53—21no—
192C4×D4×C53C2312yes—
193C4×D4×C53C2312yes—
194#117×C53D412yes—
195#117×C53D412yes—
196#117×C53C2312yes—
197#117×C53C2312yes—
198C2×C4⋊C4×C53—21no—
199C2×C4⋊C4×C53—21no—
200C2×C4⋊C4×C53—21no—
201C2×C4⋊C4×C53D411yescharacteristic
202C2×C4⋊C4×C53D411yescharacteristic
203C2×C4⋊C4×C53C2311yescharacteristic
204C2×C4⋊C4×C53C2311yescharacteristic
205C2×C22⋊C4×C53—21no—
206C2×C22⋊C4×C53—21no—
207C2×C22⋊C4×C53—21no—
208C2×C22⋊C4×C53—21no—
209C2×C22⋊C4×C53—21no—
210C2×C22⋊C4×C53D411yescharacteristic
211C2×C22⋊C4×C53D411yescharacteristic
212C2×C42×C53—21no—
213C2×C42×C53C2311yescharacteristic
214C2×C42×C53C2311yescharacteristic
215C24×C53—21no—
216C24×C53C2×D411yescharacteristic
217C2×Q8×C53—21no—
218C2×Q8×C53—24no—
219C2×Q8×C53—22no—
220C2×Q8×C53—22no—
221C2×Q8×C53—82no—
222C2×Q8×C53C2412yes—
223C2×D4×C53—24no—
224C2×D4×C53—21no—
225C2×D4×C53—22no—
226C2×D4×C53—22no—
227C2×D4×C53—82no—
228C2×D4×C53C2412yes—
229C22×C4×C53—22no—
230C22×C4×C53—22no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—22no—
235C22×C4×C53—22no—
236C22×C4×C53—82no—
237C22×C4×C53C2×D411yescharacteristic
238C22×C4×C53C2×D412yes—
239C22×C4×C53C2×D411yescharacteristic
240C22×C4×C53C2×D411yescharacteristic
241C22×C4×C53C2×D411yescharacteristic
242C22×C4×C53C2×D411yescharacteristic
243C22×C4×C53C2412yes—
244C22×C4×C53C2411yescharacteristic
245C2×C22⋊D53—22no—
246C2×C22⋊D53—22no—
247C2×C22⋊D53—22no—
248#11719945—24no—
249#11719945—24no—
250C2×D212—21no—
251C2×D212—21no—
252C2×D212C2412yes—
253C2×C4×D53—22no—
254C2×C4×D53—22no—
255C2×C4×D53—22no—
256C2×Dic106—21no—
257C2×Dic106—21no—
258C2×Dic106C2412yes—
259C4⋊C4×C53—22no—
260C4⋊C4×C53—22no—
261C4⋊C4×C53—24no—
262C4⋊C4×C53—24no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53—21no—
265C4⋊C4×C53C2×D412yes—
266C4⋊C4×C53C2×D412yes—
267C4⋊C4×C53C2×D412yes—
268C4⋊C4×C53C2×D412yes—
269C4⋊C4×C53C2412yes—
270C4⋊C4×C53C2412yes—
271C22⋊C4×C53—24no—
272C22⋊C4×C53—22no—
273C22⋊C4×C53—22no—
274C22⋊C4×C53—24no—
275C22⋊C4×C53—24no—
276C22⋊C4×C53—24no—
277C22⋊C4×C53C2×D412yes—
278C22⋊C4×C53C2×D412yes—
279C22⋊C4×C53C2×D412yes—
280C22⋊C4×C53C2×D412yes—
281C42×C53—22no—
282C42×C53—22no—
283C42×C53C2×D411yescharacteristic
284C42×C53C2×D411yescharacteristic
285C42×C53C2×D412yes—
286C42×C53C2411yescharacteristic
287C42×C53C2411yescharacteristic
288C42×C53C2412yes—
289C22⋊Dic53—22no—
290C22⋊Dic53—22no—
291C22⋊Dic53—22no—
292#11719925—44no—
293#11719924—44no—
294#11719923—44no—
295#11719922—44no—
296#11719921—22no—
297#11719921—22no—
298#11719921—22no—
299#11719921—22no—
300#11719921—22no—
301#11719921—22no—
302C4⋊Dic53—21no—
303C4⋊Dic53—21no—
304C4⋊Dic53—21no—
305C4⋊Dic53—21no—
306C4⋊Dic53C2412yes—
307C4⋊Dic53C2412yes—
308#11719919—22no—
309#11719919—22no—
310#11719919—22no—
311#11719919—22no—
312#11719919—22no—
313#11719919—22no—
314C4×Dic53—22no—
315C4×Dic53—22no—
316C4×Dic53—22no—
317#11719917—24no—
318#11719917—24no—
319#11719917—44no—
320C2×#88322—44no—
321C2×#88322C2414yes—
322C2×#88322C2414yes—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—41no—
326C23×C53—41no—
327C23×C53—42no—
328C23×C53—42no—
329C23×C53—42no—
330C23×C53C22×D412yes—
331C23×C53C22×D411yescharacteristic
332C22×D53—22no—
333Q8×C53—22no—
334Q8×C53—22no—
335Q8×C53—42no—
336Q8×C53—84no—
337D4×C53—22no—
338D4×C53—22no—
339D4×C53—42no—
340D4×C53—84no—
341C2×C4×C53—22no—
342C2×C4×C53—24no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—42no—
353C2×C4×C53—42no—
354C2×C4×C53—42no—
355C2×C4×C53—82no—
356C2×C4×C53—82no—
357C2×C4×C53C22×D411yescharacteristic
358C2×C4×C53C22×D411yescharacteristic
359C2×C4×C53C22×D412yes—
360C2×C4×C53C22×D412yes—
361C2×C4×C53C22×D411yescharacteristic
362C2×C4×C53C22×D411yescharacteristic
363C2×C4×C53C22×D412yes—
364C2×C4×C53C22×D411yescharacteristic
365C2×C4×C53H(5,𝔽2)12yes—
366C2×C4×C532−1+412yes—
367C2×C4×C53C2511yescharacteristic
368C22⋊D53—44no—
369C22⋊D53—82no—
370C22⋊D53—82no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—22no—
374D212—22no—
375D212—22no—
376D212—81no—
377D212—81no—
378C4×D53—44no—
379C4×D53—82no—
380C4×D53—82no—
381Dic106—22no—
382Dic106—22no—
383Dic106—81no—
384Dic106—81no—
385#88322—24no—
386#88322—24no—
387#60919—531nomaximal, Sylow
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—22no—
391C22×C53—22no—
392C22×C53—22no—
393C22×C53—42no—
394C22×C53—42no—
395C22×C53—42no—
396C22×C53—82no—
397C22×C53—84no—
398C22×C53#53712yes—
399C22×C53C23×D411yescharacteristic
400C2×D53—42no—
401C2×D53—42no—
402C2×D53—42no—
403C4×C53—21no—
404C4×C53—22no—
405C4×C53—21no—
406C4×C53—21no—
407C4×C53—22no—
408C4×C53—21no—
409C4×C53—22no—
410C4×C53—42no—
411C4×C53—42no—
412C4×C53—42no—
413C4×C53#53712yes—
414C4×C53C2×H(5,𝔽2)11yescharacteristic
415C4×C53C2×2−1+411yescharacteristic
416Dic53—42no—
417Dic53—42no—
418Dic53—42no—
419#3455—531no—
420C2×#542D5311yescharacteristic, complemented
421#3263—534no—
422#3262—534no—
423#3258—534no—
424#3257—534no—
425#3079—532no—
426#3078—531no—
427#3077—531no—
428#3056—532no—
429#3055—532no—
430#3040—532no—
431#3037—531no—
432#3036—531no—
433#2905—531no—
434C2×C53—22no—
435C2×C53—42no—
436C2×C53—82no—
437C2×C53C2×#53711yescharacteristic
438C2×C53#358511yescharacteristic
439C2×C53#358611yescharacteristic
440D53—82no—
441C2×#137—532no—
442C2×AGL(1,ℤ/8)—532no—
443C22×M16—532no—
444#542—22no—
445#542—22no—
446#542—532no—
447#542—532no—
448#542C2×D5314yes—
449#542C2×D5314yes—
450#541—532no—
451#540—532no—
452#539—1061no—
453#539—1061no—
454#538—1061no—
455#538—1061no—
456#533—531no—
457#532—531no—
458C2×C4⋊Q8C2×D5311yescharacteristic
459#529—1062no—
460#529—1062no—
461C2×#126—21no—
462C2×#124—21no—
463C2×#124C2×D5311yescharacteristic
464#525—532no—
465C2×#123—21no—
466C2×C22⋊Q8—21no—
467C2×C22⋊Q8C2×D5311yescharacteristic
468C2×#121C2×D5311yescharacteristic
469C4×#41—532no—
470C2×C4×Q8C2×D5311yescharacteristic
471C2×C4×D4C2×D5311yescharacteristic
472C2×#117C2×D5311yescharacteristic
473#479—534no—
474#478—534no—
475#477—534no—
476#477—532no—
477#476—534no—
478#476—532no—
479#475—534no—
480#475—532no—
481#474—534no—
482#474—532no—
483#470—534no—
484#469—534no—
485#468—534no—
486#468—534no—
487#467—534no—
488#466—534no—
489#465—534no—
490#465—534no—
491#464—534no—
492#464—534no—
493#464—534no—
494#463—534no—
495#463—534no—
496#463—534no—
497#462—532no—
498#461—532no—
499#460—532no—
500#459—532no—
501#428—532no—
502#428—532no—
503#424—534no—
504#424—534no—
505#423—531no—
506#423—531no—
507#423—532no—
508#419—532no—
509#418—532no—
510#417—532no—
511#417—532no—
512C53#6091911yescharacteristic, complemented, Sylow
513C2×#41—532no—
514C22×Q8—21no—
515C22×Q8C22×D5311yescharacteristic
516C22×D4—21no—
517C22×D4C22×D5311yescharacteristic
518C23×C4—21no—
519C23×C4C22×D5311yescharacteristic
520#137—2124no—
521AGL(1,ℤ/8)—2124no—
522C2×Q16—534no—
523C2×SD16—534no—
524C2×SD16—534no—
525C2×D8—534no—
526C2×M16—532no—
527C2×M16—532no—
528C2×M16—534no—
529C2×M16—2124no—
530C22×C8—534no—
531C4⋊Q8—22no—
532C4⋊Q8—531no—
533C4⋊Q8—531no—
534C4⋊Q8—531no—
535C4⋊Q8C22×D5314yes—
536#127—531no—
537#126—24no—
538#126—24no—
539#126—1062no—
540#126—1062no—
541#126—1062no—
542#126—1062no—
543#125—532no—
544#125—1062no—
545#125—1062no—
546#124—24no—
547#124—24no—
548#124—22no—
549#124—532no—
550#124—1062no—
551#124—1062no—
552#124C22×D5314yes—
553#123—24no—
554#123—24no—
555#123—1062no—
556#123—1062no—
557#123—1062no—
558#123—1062no—
559#123—1062no—
560C22⋊Q8—22no—
561C22⋊Q8—24no—
562C22⋊Q8—24no—
563C22⋊Q8—532no—
564C22⋊Q8—532no—
565C22⋊Q8—1061no—
566C22⋊Q8—1061no—
567C22⋊Q8—1062no—
568C22⋊Q8—1062no—
569C22⋊Q8C22×D5314yes—
570#121—22no—
571#121—532no—
572#121—532no—
573#121—1061no—
574#121—1061no—
575#121—1062no—
576#121—1062no—
577#121C22×D5314yes—
578#120—1062no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—532no—
582C4×Q8—532no—
583C4×Q8—1061no—
584C4×Q8—1061no—
585C4×Q8C22×D5312yes—
586C4×Q8C22×D5312yes—
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×D5312yes—
598C4×D4C22×D5312yes—
599#117—532no—
600#117—1062no—
601#117C22⋊D5312yes—
602#117C22⋊D5312yes—
603#117C22×D5312yes—
604#117C22×D5312yes—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4C22⋊D5311yescharacteristic
609C2×C4⋊C4C22⋊D5311yescharacteristic
610C2×C4⋊C4C22×D5311yescharacteristic
611C2×C4⋊C4C22×D5311yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4C22⋊D5311yescharacteristic
618C2×C22⋊C4C22⋊D5311yescharacteristic
619C2×C42—21no—
620C2×C42—1062no—
621C2×C42C22×D5311yescharacteristic
622C2×C42C22×D5311yescharacteristic
623#107—534no—
624#107—534no—
625#106—534no—
626#106—534no—
627C4⋊C8—532no—
628C4⋊C8—532no—
629C4⋊C8—532no—
630C4⋊C8—534no—
631C4⋊C8—534no—
632C4⋊C8—532no—
633#103—534no—
634#103—534no—
635#103—534no—
636#103—534no—
637#102—534no—
638#102—534no—
639#102—534no—
640#102—534no—
641C24—21no—
642C24C2×C22⋊D5311yescharacteristic
643#41—1064no—
644#41—1064no—
645C2×Q8—21no—
646C2×Q8—24no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—82no—
650C2×Q8—532no—
651C2×Q8—1061no—
652C2×Q8—1061no—
653C2×Q8C23×D5312yes—
654C2×D4—24no—
655C2×D4—21no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—82no—
659C2×D4—532no—
660C2×D4—1062no—
661C2×D4—1062no—
662C2×D4—1062no—
663C2×D4—1061no—
664C2×D4—1061no—
665C2×D4C23×D5312yes—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—82no—
674C22×C4—1062no—
675C22×C4—1062no—
676C22×C4—1062no—
677C22×C4C2×C22⋊D5311yescharacteristic
678C22×C4C2×C22⋊D5312yes—
679C22×C4C2×C22⋊D5311yescharacteristic
680C22×C4C2×C22⋊D5311yescharacteristic
681C22×C4C2×C22⋊D5311yescharacteristic
682C22×C4C2×C22⋊D5311yescharacteristic
683C22×C4C23×D5312yes—
684C22×C4C23×D5311yescharacteristic
685Q16—2124no—
686SD16—2124no—
687SD16—2124no—
688D8—2124no—
689M16—1064no—
690M16—1064no—
691M16—2124no—
692C2×C8—534no—
693C2×C8—534no—
694C2×C8—2124no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—532no—
702C4⋊C4—532no—
703C4⋊C4—1062no—
704C4⋊C4—1062no—
705C4⋊C4—1061no—
706C4⋊C4—1061no—
707C4⋊C4—1062no—
708C4⋊C4—1062no—
709C4⋊C4—1062no—
710C4⋊C4—1062no—
711C4⋊C4—1061no—
712C4⋊C4—1061no—
713C4⋊C4C2×C22⋊D5312yes—
714C4⋊C4C2×C22⋊D5312yes—
715C4⋊C4C2×C22⋊D5312yes—
716C4⋊C4C2×C22⋊D5312yes—
717C4⋊C4C23×D5312yes—
718C4⋊C4C23×D5312yes—
719C22⋊C4—24no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—1062no—
726C22⋊C4—1062no—
727C22⋊C4—1062no—
728C22⋊C4—1062no—
729C22⋊C4—1062no—
730C22⋊C4—1062no—
731C22⋊C4—1062no—
732C22⋊C4—1062no—
733C22⋊C4—1062no—
734C22⋊C4C2×C22⋊D5312yes—
735C22⋊C4C2×C22⋊D5312yes—
736C22⋊C4C2×C22⋊D5312yes—
737C22⋊C4C2×C22⋊D5312yes—
738C42—22no—
739C42—22no—
740C42—1062no—
741C42—1062no—
742C42—1062no—
743C42C2×C22⋊D5312yes—
744C42C2×C22⋊D5311yescharacteristic
745C42C2×C22⋊D5311yescharacteristic
746C42C23×D5312yes—
747C42C23×D5311yescharacteristic
748C42C23×D5311yescharacteristic
749C23—22no—
750C23—22no—
751C23—41no—
752C23—41no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—1062no—
757C23C22×C22⋊D5312yes—
758C23C22×C22⋊D5311yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—42no—
762Q8—84no—
763Q8—1062no—
764Q8—1062no—
765Q8—4241no—
766Q8—4241no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—84no—
771D4—1062no—
772D4—1062no—
773D4—4241no—
774D4—4241no—
775D4—4242no—
776D4—4242no—
777D4—2124no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—82no—
793C2×C4—82no—
794C2×C4—1062no—
795C2×C4—1062no—
796C2×C4—1062no—
797C2×C4—4242no—
798C2×C4—4242no—
799C2×C4—2124no—
800C2×C4C22×C22⋊D5311yescharacteristic
801C2×C4C22×C22⋊D5311yescharacteristic
802C2×C4C22×C22⋊D5312yes—
803C2×C4C22×C22⋊D5312yes—
804C2×C4C22×C22⋊D5311yescharacteristic
805C2×C4C22×C22⋊D5311yescharacteristic
806C2×C4C22×C22⋊D5312yes—
807C2×C4C22×C22⋊D5311yescharacteristic
808C2×C4#1313326312yes—
809C2×C4#1313326412yes—
810C2×C4C24×D5311yescharacteristic
811C8—1064no—
812C8—1064no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—82no—
822C22—84no—
823C22—2122no—
824C22—2122no—
825C22—2122no—
826C22#1681120112yes—
827C22C23×C22⋊D5311yescharacteristic
828C4—22no—
829C4—21no—
830C4—21no—
831C4—22no—
832C4—22no—
833C4—21no—
834C4—21no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—2122no—
839C4—2122no—
840C4—2122no—
841C4#1681120112yes—
842C4C2×#1313326311yescharacteristic
843C4C2×#1313326411yescharacteristic
844C2—22no—
845C2—42no—
846C2—82no—
847C2—4242no—
848C2C2×#1681120111yescharacteristic
849C2#2028949511yescharacteristic
850C2#2028950211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#542C2
socleC22×C53C23×D4
hypercenterC2×#542D53
hypocenterC53#60919
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #20288105C2semidirect
2. #20286180C2semidirect
3. #20286171C2semidirect
4. #20286141C2semidirect
5. #20286126C2semidirect
6. #20284524C2semidirect
7. #20284520C2semidirect
8. #20284512C2semidirect
9. #20284341C2semidirect
10. #20284330C2semidirect
11. #20284205C2semidirect
12. #20284187C2semidirect
13. #20284179C2semidirect
14. #20283279C2semidirect
15. C2×C53×#542C2semidirect
19. #16811244C22semidirect
20. #16811244C22semidirect
21. #16811235C22semidirect
22. #16811228C22semidirect
33. #16810930C22semidirect
34. #16810923C22semidirect
35. #16810918C22semidirect
36. #16810915C22semidirect
37. #16810913C22semidirect
38. #16810910C22semidirect
39. #16810908C22semidirect
40. #16810905C22semidirect
41. #16810903C22semidirect
42. #16810900C22semidirect
43. #16810879C22semidirect
45. #16810871C22semidirect
47. #16810862C22semidirect
49. #16810854C22semidirect
51. #16810845C22semidirect
52. #16810842C22semidirect
53. #16810842C22semidirect
54. #16810838C22semidirect
55. #16810835C22semidirect
56. #16810835C22semidirect
57. #16810833C22semidirect
58. #16810828C22semidirect
59. #16810823C22semidirect
60. #16810818C22semidirect
63. #16810650C22semidirect
64. #16810650C22semidirect
420. C2×#542D53semidirect
512. C53#60919semidirect

Maximal subgroups

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

subgroupindex
#202881052
#202861802
#202861712
#202861412
#202861262
#202845242
#202845202
#202845122
#202843412
#202843302
#202842052
#202841872
#202841792
#202832792
C2×C53×#5422
#6091953