Finite Group Databasebeta

← #28280644

Subgroups — #28280644

Order 13568.

1700 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288601C211yesmaximal, characteristic, complemented
2#20287602C212yesmaximal, complemented
3#20287396C212yesmaximal, complemented
4#20287299C212yesmaximal, complemented
5#20287284C214yesmaximal, complemented
6#20286998C212yesmaximal, complemented
7#20286983C214yesmaximal, complemented
8#20286106C211yesmaximal, characteristic, complemented
9#20286088C212yesmaximal, complemented
10#20285890C212yesmaximal, complemented
11#20285863C211yesmaximal, characteristic, complemented
12#20284786C211yesmaximal, characteristic, complemented
13#20284754C212yesmaximal, complemented
14#20284530C211yesmaximal, characteristic, complemented
15#20284520C212yesmaximal, complemented
16#20283847C211yesmaximal, characteristic, complemented
17C53×#3482C211yesmaximal, characteristic
18#16811351—21no—
19#16811351C2212yes—
20#16811343—21no—
21#16811343C2212yes—
22#16811313—22no—
23#16811313C2214yes—
24#16811235—22no—
25#16811194—21no—
26#16811180C2212yes—
27#16811180C2211yescharacteristic
28#16811180C2212yes—
29C2×#13133217C2211yescharacteristic
30#16811100—21no—
31#16811026C2212yes—
32#16811022C2214yes—
33#16810977C2214yes—
34#16810973C2212yes—
35#16810964C2212yes—
36#16810961C2214yes—
37#16810958C2214yes—
38#16810956C2214yes—
39#16810944C2214yes—
40#16810930C2214yes—
41#16810930C2214yes—
42#16810927C2214yes—
43#16810918C2212yes—
44#16810918C2212yes—
45#16810918C2212yes—
46#16810913C2212yes—
47#16810908C2212yes—
48#16810908C2211yescharacteristic
49#16810908C2212yes—
50#16810905C2212yes—
51#16810903C2212yes—
52#16810903C2211yescharacteristic
53#16810879C2214yes—
54#16810879C2214yes—
55#16810867C2214yes—
56#16810842C2214yes—
57#16810833C2211yescharacteristic
58#16810833C2212yes—
59#16810830C2212yes—
60#16810828C2211yescharacteristic
61#16810785C2212yes—
62#16810779C2214yes—
63Q8×#88322C2212yes—
64C4×#11719925C2214yes—
65C4×#11719925C2212yes—
66C4×#11719925C2214yes—
67C4×#11719923C2212yes—
68#16810701C2214yes—
69#16810701C2212yes—
70#16810676C2212yes—
71#16810676C2211yescharacteristic
72#16810666C2212yes—
73#16810663C2214yes—
74#16810647C2212yes—
75#16810647C2211yescharacteristic
76#16810632C2214yes—
77#16810624C2212yes—
78C53×#557C2211yescharacteristic
79C53×#556—21no—
80C53×#556C2211yescharacteristic
81C53×#552—22no—
82C53×#552C2212yes—
83D4×Q8×C53C2211yescharacteristic
84C53×#548C2212yes—
85C53×#547—21no—
86C53×#547C2211yescharacteristic
87C53×#533—21no—
88C53×#533C2211yescharacteristic
89C53×#529—22no—
90C53×#529C2212yes—
91C4×#41×C53—21no—
92C4×#41×C53C2211yescharacteristic
93C4×#41×C53C2211yescharacteristic
94C2×C4×Q8×C53C2212yes—
95C22×Dic106—21no—
96C2×#11719925C2312yes—
97C2×#11719925C2314yes—
98C2×#11719923C2312yes—
99C2×#11719917C2314yes—
100C2×#11719917C2312yes—
101#13133217—21no—
102#13133217—21no—
103#13133217C2312yes—
104#13133217C2311yescharacteristic
105#13133217C2312yes—
106#13133217C2311yescharacteristic
107#13133215—22no—
108#13133210—24no—
109#13133210—24no—
110#13133209—22no—
111#13133209—21no—
112#13133209C2314yes—
113#13133207—24no—
114#13133207—24no—
115#13133204—22no—
116#13133198—24no—
117#13133196—21no—
118#13133196—22no—
119#13133196—22no—
120#13133196—22no—
121#13133196C2314yes—
122#13133196C2312yes—
123C4×Dic106—22no—
124C4×Dic106—21no—
125C4×Dic106—22no—
126C4×Dic106—22no—
127C4×Dic106C2314yes—
128C4×Dic106C2312yes—
129#13133182—22no—
130#13133182—22no—
131#13133176—22no—
132#13133176—21no—
133#13133176C2314yes—
134#13133173—24no—
135C2×C4⋊Dic53—21no—
136C2×C4⋊Dic53C2312yes—
137#13133150C2312yes—
138#13133150C2314yes—
139#13133150C2314yes—
140#13133150C2314yes—
141#13133148C2314yes—
142#13133148C2314yes—
143#13133148C2312yes—
144C4⋊#88322C2311yescharacteristic
145C4⋊#88322C2312yes—
146C4⋊#88322C2312yes—
147C4⋊#88322C2311yescharacteristic
148C4⋊#88322C2314yes—
149#13133141C2314yes—
150#13133141C2314yes—
151#13133141C2312yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133140C2312yes—
155#13133140C2314yes—
156#13133140C2312yes—
157#13133138C2312yes—
158#13133138C2314yes—
159C22⋊#88322C2314yes—
160C22⋊#88322C2312yes—
161C4×#88322C2314yes—
162C4×#88322C2312yes—
163C2×#41×C53—21no—
164C2×#41×C53D411yescharacteristic
165C2×#41×C53C2311yescharacteristic
166C22×Q8×C53C2312yes—
167C4⋊Q8×C53—21no—
168C4⋊Q8×C53—21no—
169C4⋊Q8×C53C2311yescharacteristic
170C4⋊Q8×C53C2311yescharacteristic
171#126×C53—22no—
172#126×C53—22no—
173#126×C53—22no—
174#125×C53—22no—
175#125×C53—22no—
176#125×C53—21no—
177#125×C53C2312yes—
178#124×C53—22no—
179#124×C53C2312yes—
180#123×C53—22no—
181#123×C53—22no—
182#123×C53—22no—
183C22⋊Q8×C53—21no—
184C22⋊Q8×C53—22no—
185C22⋊Q8×C53—22no—
186C22⋊Q8×C53—21no—
187C22⋊Q8×C53—21no—
188C22⋊Q8×C53C2312yes—
189C22⋊Q8×C53C2312yes—
190#121×C53—22no—
191#121×C53C2312yes—
192C4×Q8×C53—21no—
193C4×Q8×C53—22no—
194C4×Q8×C53—22no—
195C4×Q8×C53—21no—
196C4×Q8×C53D411yescharacteristic
197C4×Q8×C53C2311yescharacteristic
198C4×Q8×C53C2311yescharacteristic
199C4×Q8×C53C2312yes—
200C4×Q8×C53C2312yes—
201C4×Q8×C53C2312yes—
202C4×Q8×C53C2311yescharacteristic
203C4×D4×C53—22no—
204C4×D4×C53—21no—
205C4×D4×C53—22no—
206C4×D4×C53—21no—
207C4×D4×C53—21no—
208C4×D4×C53D411yescharacteristic
209C4×D4×C53D412yes—
210C4×D4×C53C2311yescharacteristic
211C4×D4×C53C2311yescharacteristic
212C4×D4×C53C2312yes—
213C4×D4×C53C2311yescharacteristic
214#117×C53—21no—
215#117×C53—22no—
216#117×C53—21no—
217#117×C53—22no—
218#117×C53—21no—
219#117×C53D412yes—
220#117×C53D411yescharacteristic
221#117×C53C2311yescharacteristic
222C2×C4⋊C4×C53—22no—
223C2×C4⋊C4×C53C2312yes—
224C2×C42×C53—21no—
225C2×C42×C53—22no—
226C2×C42×C53C2312yes—
227C2×C42×C53C2311yescharacteristic
228#41×C53—22no—
229#41×C53—42no—
230#41×C53—41no—
231#41×C53—44no—
232C2×Q8×C53—22no—
233C2×Q8×C53—21no—
234C2×Q8×C53—24no—
235C2×Q8×C53—42no—
236C2×Q8×C53C2×D411yescharacteristic
237C2×Q8×C53C2412yes—
238C2×Q8×C53C2411yescharacteristic
239C2×D4×C53—21no—
240C2×D4×C53—22no—
241C2×D4×C53C2×D411yescharacteristic
242C2×D4×C53C2×D412yes—
243C2×D4×C53C2411yescharacteristic
244C22×C4×C53—22no—
245C22×C4×C53—22no—
246C22×C4×C53—21no—
247C22×C4×C53—21no—
248C22×C4×C53—21no—
249C22×C4×C53C2×D412yes—
250C22×C4×C53C2×D411yescharacteristic
251C22×C4×C53C2×D411yescharacteristic
252C22×C4×C53C2×D412yes—
253C22×C4×C53C2412yes—
254C22×C4×C53C2411yescharacteristic
255C22×Dic53—22no—
256C2×Dic106—22no—
257C2×Dic106—21no—
258C2×Dic106—22no—
259C2×Dic106—44no—
260C2×Dic106C2412yes—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—22no—
263C4⋊C4×C53—22no—
264C4⋊C4×C53—22no—
265C4⋊C4×C53—22no—
266C4⋊C4×C53—21no—
267C4⋊C4×C53—22no—
268C4⋊C4×C53—22no—
269C4⋊C4×C53—21no—
270C4⋊C4×C53—21no—
271C4⋊C4×C53—22no—
272C4⋊C4×C53—21no—
273C4⋊C4×C53—22no—
274C4⋊C4×C53C2×D411yescharacteristic
275C4⋊C4×C53C2×D412yes—
276C4⋊C4×C53C2×D412yes—
277C4⋊C4×C53C2×D411yescharacteristic
278C4⋊C4×C53C2411yescharacteristic
279C4⋊C4×C53C2412yes—
280C4⋊C4×C53C2411yescharacteristic
281C22⋊C4×C53—22no—
282C22⋊C4×C53—22no—
283C22⋊C4×C53—21no—
284C22⋊C4×C53—22no—
285C22⋊C4×C53—21no—
286C22⋊C4×C53—21no—
287C22⋊C4×C53—22no—
288C22⋊C4×C53—22no—
289C22⋊C4×C53C2×D412yes—
290C22⋊C4×C53C2×D412yes—
291C22⋊C4×C53C2×D412yes—
292C42×C53—21no—
293C42×C53—21no—
294C42×C53—22no—
295C42×C53—22no—
296C42×C53—21no—
297C42×C53—22no—
298C42×C53C2×D411yescharacteristic
299C42×C53C2×D411yescharacteristic
300C42×C53C2×D412yes—
301C42×C53C2×D412yes—
302C42×C53C2411yescharacteristic
303C42×C53C2411yescharacteristic
304C42×C53C2412yes—
305C22⋊Dic53—22no—
306C22⋊Dic53—24no—
307C22⋊Dic53—24no—
308#11719925—24no—
309#11719925—44no—
310#11719923—42no—
311C4⋊Dic53—22no—
312C4⋊Dic53—22no—
313C4⋊Dic53—22no—
314C4⋊Dic53—21no—
315C4⋊Dic53—21no—
316C4⋊Dic53—21no—
317C4⋊Dic53C2412yes—
318C4⋊Dic53C2414yes—
319#11719919—24no—
320#11719919—24no—
321#11719919—24no—
322#11719919—22no—
323#11719919—24no—
324#11719919—22no—
325C4×Dic53—24no—
326C4×Dic53—24no—
327C4×Dic53—22no—
328#11719917—44no—
329#11719917—42no—
330C2×#88322C2412yes—
331C2×#88322C2414yes—
332C2×#88322C2412yes—
333C23×C53—21no—
334C23×C53C22×D411yescharacteristic
335C23×C53C22×D412yes—
336Q8×C53—22no—
337Q8×C53—21no—
338Q8×C53—22no—
339Q8×C53—22no—
340Q8×C53—44no—
341Q8×C53—42no—
342Q8×C532−1+412yes—
343D4×C53—22no—
344D4×C53—21no—
345D4×C53—21no—
346D4×C53—42no—
347D4×C53—42no—
348D4×C53—44no—
349C2×C4×C53—21no—
350C2×C4×C53—22no—
351C2×C4×C53—24no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—21no—
355C2×C4×C53—22no—
356C2×C4×C53—21no—
357C2×C4×C53—21no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—21no—
361C2×C4×C53—42no—
362C2×C4×C53—42no—
363C2×C4×C53—44no—
364C2×C4×C53—44no—
365C2×C4×C53—42no—
366C2×C4×C53—42no—
367C2×C4×C53C22×D411yescharacteristic
368C2×C4×C53C22×D411yescharacteristic
369C2×C4×C53C22×D412yes—
370C2×C4×C53C22×D412yes—
371C2×C4×C53C22×D411yescharacteristic
372C2×C4×C53C22×D412yes—
373C2×C4×C53C22×D411yescharacteristic
374C2×C4×C53C22×D411yescharacteristic
375C2×C4×C53C2511yescharacteristic
376C2×Dic53—24no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—44no—
380Dic106—22no—
381Dic106—22no—
382Dic106—44no—
383Dic106—44no—
384Dic106—42no—
385#88322—22no—
386#88322—22no—
387#88322—24no—
388#62146—531nomaximal, Sylow
389C22×C53—22no—
390C22×C53—21no—
391C22×C53—21no—
392C22×C53—22no—
393C22×C53—21no—
394C22×C53—22no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—41no—
398C22×C53C23×D411yescharacteristic
399C4×C53—21no—
400C4×C53—22no—
401C4×C53—22no—
402C4×C53—21no—
403C4×C53—22no—
404C4×C53—22no—
405C4×C53—21no—
406C4×C53—42no—
407C4×C53—41no—
408C4×C53—42no—
409C4×C53—41no—
410C4×C53#57512yes—
411C4×C53#57812yes—
412C4×C53C2×2−1+411yescharacteristic
413C4×C53#58511yescharacteristic
414Dic53—42no—
415Dic53—44no—
416Dic53—42no—
417#3509—531no—
418#3482D5311yescharacteristic
419#3383—532no—
420#3364—532no—
421#3353—532no—
422#3352—534no—
423#3328—532no—
424#3327—534no—
425#3255—531no—
426#3252—532no—
427#3233—532no—
428#3230—531no—
429#3107—531no—
430#3104—532no—
431#3079—531no—
432#3078—532no—
433#2991—531no—
434C2×C53—42no—
435C2×C53—41no—
436C2×C53—81no—
437C2×C53#348911yescharacteristic
438C2×C53C2×#57511yescharacteristic
439C2×C53C2×#57811yescharacteristic
440#557—532no—
441#557—1061no—
442#557C2×D5311yescharacteristic
443#556—21no—
444#556—532no—
445#556—1061no—
446#556C2×D5311yescharacteristic
447#552—22no—
448#552—534no—
449#552—1062no—
450#552C2×D5312yes—
451D4×Q8C2×D5311yescharacteristic
452#548C2×D5312yes—
453#547—21no—
454#547C2×D5311yescharacteristic
455#541—1062no—
456#536—1061no—
457#533—21no—
458#533—532no—
459#533—532no—
460#533—531no—
461#533C2×D5311yescharacteristic
462C2×C4⋊Q8—531no—
463#529—22no—
464#529C2×D5312yes—
465#519—1061no—
466C4×#41—21no—
467C4×#41C2×D5311yescharacteristic
468C4×#41C2×D5311yescharacteristic
469C2×C4×Q8C2×D5312yes—
470#500—532no—
471#499—534no—
472#488—534no—
473#487—532no—
474#485—534no—
475#485—532no—
476#484—534no—
477#484—534no—
478#482—534no—
479#479—534no—
480#479—534no—
481#479—534no—
482#477—532no—
483#477—532no—
484#477—532no—
485#476—532no—
486#475—532no—
487#475—532no—
488#475—531no—
489#475—532no—
490#474—532no—
491#474—531no—
492#470—534no—
493#470—534no—
494#468—534no—
495#464—534no—
496#462—532no—
497#462—531no—
498#462—532no—
499#461—531no—
500#452—532no—
501#451—534no—
502C8×Q8—532no—
503C4×Q16—532no—
504C4×Q16—534no—
505C4×Q16—534no—
506C4×SD16—532no—
507#436—532no—
508#436—534no—
509#431—532no—
510#431—531no—
511#428—532no—
512#428—534no—
513#423—532no—
514#423—531no—
515#419—534no—
516#417—532no—
517C53#6214611yescharacteristic, complemented, Sylow
518C2×#41—21no—
519C2×#41C22⋊D5311yescharacteristic
520C2×#41C22×D5311yescharacteristic
521C22×Q8—1061no—
522C22×Q8C22×D5312yes—
523C2×Q16—532no—
524C2×Q16—534no—
525C2×SD16—532no—
526C2×M16—532no—
527C2×M16—534no—
528C4⋊Q8—21no—
529C4⋊Q8—21no—
530C4⋊Q8—532no—
531C4⋊Q8—532no—
532C4⋊Q8—531no—
533C4⋊Q8—531no—
534C4⋊Q8—1062no—
535C4⋊Q8—1061no—
536C4⋊Q8—1061no—
537C4⋊Q8C22×D5311yescharacteristic
538C4⋊Q8C22×D5311yescharacteristic
539#126—22no—
540#126—22no—
541#126—22no—
542#126—1064no—
543#126—1064no—
544#125—22no—
545#125—22no—
546#125—21no—
547#125—534no—
548#125—1064no—
549#125—1064no—
550#125—1061no—
551#125—1062no—
552#125C22×D5312yes—
553#124—22no—
554#124—1062no—
555#124C22×D5312yes—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—1064no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—532no—
566C22⋊Q8—534no—
567C22⋊Q8—1062no—
568C22⋊Q8—1062no—
569C22⋊Q8—1061no—
570C22⋊Q8—1062no—
571C22⋊Q8C22×D5312yes—
572C22⋊Q8C22×D5312yes—
573#121—22no—
574#121C22×D5312yes—
575C4×Q8—21no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×Q8—21no—
579C4×Q8—534no—
580C4×Q8—532no—
581C4×Q8—1062no—
582C4×Q8—1062no—
583C4×Q8—1062no—
584C4×Q8—1062no—
585C4×Q8—1062no—
586C4×Q8—1061no—
587C4×Q8C22⋊D5311yescharacteristic
588C4×Q8C22×D5311yescharacteristic
589C4×Q8C22×D5312yes—
590C4×Q8C22×D5312yes—
591C4×Q8C22×D5312yes—
592C4×Q8C22×D5311yescharacteristic
593C4×Q8C22×D5311yescharacteristic
594C4×D4—21no—
595C4×D4—22no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—22no—
599C4×D4C22⋊D5311yescharacteristic
600C4×D4C22⋊D5312yes—
601C4×D4C22×D5311yescharacteristic
602C4×D4C22×D5311yescharacteristic
603C4×D4C22×D5311yescharacteristic
604C4×D4C22×D5312yes—
605#117—21no—
606#117—21no—
607#117—22no—
608#117—21no—
609#117—22no—
610#117—534no—
611#117—1061no—
612#117—1062no—
613#117—1064no—
614#117C22⋊D5311yescharacteristic
615#117C22⋊D5312yes—
616#117C22×D5311yescharacteristic
617C2×C4⋊C4—22no—
618C2×C4⋊C4—532no—
619C2×C4⋊C4—1061no—
620C2×C4⋊C4C22×D5312yes—
621C2×C42—22no—
622C2×C42—21no—
623C2×C42C22×D5312yes—
624C2×C42C22×D5311yescharacteristic
625#107—534no—
626#107—534no—
627#107—532no—
628#107—534no—
629#106—532no—
630#106—534no—
631#106—534no—
632C4⋊C8—531no—
633C4⋊C8—532no—
634C4⋊C8—532no—
635C4⋊C8—534no—
636C4⋊C8—531no—
637#103—534no—
638#103—532no—
639#103—534no—
640#103—534no—
641#103—534no—
642#103—532no—
643#103—532no—
644#103—534no—
645#102—534no—
646#102—532no—
647C22⋊C8—534no—
648C22⋊C8—532no—
649C4×C8—532no—
650C4×C8—534no—
651#41—22no—
652#41—42no—
653#41—41no—
654#41—44no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—24no—
658C2×Q8—42no—
659C2×Q8—532no—
660C2×Q8—1061no—
661C2×Q8—1062no—
662C2×Q8—1062no—
663C2×Q8—2124no—
664C2×Q8C2×C22⋊D5311yescharacteristic
665C2×Q8C23×D5312yes—
666C2×Q8C23×D5311yescharacteristic
667C2×D4—21no—
668C2×D4—22no—
669C2×D4C2×C22⋊D5311yescharacteristic
670C2×D4C2×C22⋊D5312yes—
671C2×D4C23×D5311yescharacteristic
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—1062no—
678C22×C4C2×C22⋊D5312yes—
679C22×C4C2×C22⋊D5311yescharacteristic
680C22×C4C2×C22⋊D5311yescharacteristic
681C22×C4C2×C22⋊D5312yes—
682C22×C4C23×D5311yescharacteristic
683C22×C4C23×D5312yes—
684Q16—1064no—
685Q16—2124no—
686SD16—2122no—
687M16—2124no—
688M16—2122no—
689C2×C8—532no—
690C2×C8—534no—
691C2×C8—532no—
692C4⋊C4—21no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—22no—
703C4⋊C4—21no—
704C4⋊C4—22no—
705C4⋊C4—532no—
706C4⋊C4—534no—
707C4⋊C4—1062no—
708C4⋊C4—1062no—
709C4⋊C4—1062no—
710C4⋊C4—1061no—
711C4⋊C4—1064no—
712C4⋊C4—1061no—
713C4⋊C4—1061no—
714C4⋊C4—1064no—
715C4⋊C4—1064no—
716C4⋊C4—1062no—
717C4⋊C4—1062no—
718C4⋊C4—1064no—
719C4⋊C4C2×C22⋊D5311yescharacteristic
720C4⋊C4C2×C22⋊D5312yes—
721C4⋊C4C2×C22⋊D5311yescharacteristic
722C4⋊C4C2×C22⋊D5312yes—
723C4⋊C4C23×D5311yescharacteristic
724C4⋊C4C23×D5311yescharacteristic
725C4⋊C4C23×D5312yes—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—21no—
729C22⋊C4—22no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—1064no—
735C22⋊C4—1062no—
736C22⋊C4—1064no—
737C22⋊C4C2×C22⋊D5312yes—
738C22⋊C4C2×C22⋊D5312yes—
739C22⋊C4C2×C22⋊D5312yes—
740C42—21no—
741C42—21no—
742C42—22no—
743C42—22no—
744C42—21no—
745C42—22no—
746C42—1064no—
747C42—1064no—
748C42—1062no—
749C42C2×C22⋊D5311yescharacteristic
750C42C2×C22⋊D5311yescharacteristic
751C42C2×C22⋊D5312yes—
752C42C2×C22⋊D5312yes—
753C42C23×D5311yescharacteristic
754C42C23×D5312yes—
755C42C23×D5311yescharacteristic
756C23—21no—
757C23C22×C22⋊D5311yescharacteristic
758C23C22×C22⋊D5312yes—
759Q8—22no—
760Q8—21no—
761Q8—22no—
762Q8—22no—
763Q8—44no—
764Q8—42no—
765Q8—1062no—
766Q8—1062no—
767Q8—2124no—
768Q8—2124no—
769Q8—2122no—
770Q8#1313326412yes—
771D4—22no—
772D4—21no—
773D4—21no—
774D4—42no—
775D4—42no—
776D4—44no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—1062no—
796C2×C4—1062no—
797C2×C4—1064no—
798C2×C4—2124no—
799C2×C4C22×C22⋊D5312yes—
800C2×C4C22×C22⋊D5311yescharacteristic
801C2×C4C22×C22⋊D5312yes—
802C2×C4C22×C22⋊D5311yescharacteristic
803C2×C4C22×C22⋊D5311yescharacteristic
804C2×C4C22×C22⋊D5312yes—
805C2×C4C22×C22⋊D5311yescharacteristic
806C2×C4C22×C22⋊D5311yescharacteristic
807C2×C4C24×D5311yescharacteristic
808C8—1062no—
809C8—1062no—
810C8—1064no—
811C22—22no—
812C22—21no—
813C22—21no—
814C22—22no—
815C22—21no—
816C22—22no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22C23×C22⋊D5311yescharacteristic
821C4—21no—
822C4—22no—
823C4—22no—
824C4—21no—
825C4—22no—
826C4—22no—
827C4—21no—
828C4—42no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—2122no—
833C4—2124no—
834C4—2122no—
835C4#1681142112yes—
836C4#1681143812yes—
837C4C2×#1313326411yescharacteristic
838C4#1681145911yescharacteristic
839C2—42no—
840C2—41no—
841C2—81no—
842C2#2028839511yescharacteristic
843C2C2×#1681142111yescharacteristic
844C2C2×#1681143811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
Fitting, prime radicalC53×#3482C2
socleC22×C53C23×D4
hypercenter#3482D53
hypocenterC53#62146
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #20288601C2semidirect
2. #20287602C2semidirect
3. #20287396C2semidirect
4. #20287299C2semidirect
5. #20287284C2semidirect
6. #20286998C2semidirect
7. #20286983C2semidirect
8. #20286106C2semidirect
9. #20286088C2semidirect
10. #20285890C2semidirect
11. #20285863C2semidirect
12. #20284786C2semidirect
13. #20284754C2semidirect
14. #20284530C2semidirect
15. #20284520C2semidirect
16. #20283847C2semidirect
517. C53#62146semidirect

Maximal subgroups

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

subgroupindex
#202886012
#202876022
#202873962
#202872992
#202872842
#202869982
#202869832
#202861062
#202860882
#202858902
#202858632
#202847862
#202847542
#202845302
#202845202
#202838472
C53×#34822
#6214653