Finite Group Databasebeta

← #27383781

Subgroups — #27383781

Order 13568.

1330 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811388C211yesmaximal, characteristic
2C2×#16810670C211yesmaximal, characteristic, complemented
3C2×#16810662C211yesmaximal, characteristic, complemented
4#20283231C211yesmaximal, characteristic
5#417×D53C211yesmaximal, characteristic
6#20274779C211yesmaximal, characteristic, complemented
7#20274778C211yesmaximal, characteristic, complemented
8#20274777C211yesmaximal, characteristic, complemented
9#20274776C211yesmaximal, characteristic, complemented
10#20274775C211yesmaximal, characteristic, complemented
11#20274773C211yesmaximal, characteristic, complemented
12#20274772C211yesmaximal, characteristic, complemented
13#20274452C211yesmaximal, characteristic, complemented
14#343×D53C211yesmaximal, characteristic, complemented
15C53×#1815C211yesmaximal, characteristic, complemented
16C2×#41×D53C2211yescharacteristic
17#16811388—24no—
18#16811388C418yescomplemented
19C2×#13133225—21no—
20C2×#13133225C2211yescharacteristic
21C2×#13133224C2211yescharacteristic
22C2×#13133223—21no—
23C2×#13133223C2211yescharacteristic
24C22×#11719912—21no—
25C22×#11719912C2211yescharacteristic
26C2×M16×D53—21no—
27C2×M16×D53C2211yescharacteristic
28C2×M16×D53C2211yescharacteristic
29C2×M16×D53C2211yescharacteristic
30C2×#13133175C2211yescharacteristic
31C2×C4⋊C4×D53C2211yescharacteristic
32#16810670—24no—
33C2×#13133153C2211yescharacteristic, complemented
34C2×#13133152C2211yescharacteristic, complemented
35C2×#13133152C2211yescharacteristic, complemented
36#16810662—21no—
37#16810662—21no—
38#16810662—21no—
39#16810662—21no—
40C2×#13133151C2211yescharacteristic, complemented
41C2×#13133150C2211yescharacteristic, complemented
42C2×#13133148C2211yescharacteristic, complemented
43#16810630—21no—
44#16810626—21no—
45#16810625C2211yescharacteristic
46#16810625C2211yescharacteristic
47#16810624C2211yescharacteristic
48#16810624C2211yescharacteristic
49#16810623—21no—
50#16810622C2211yescharacteristic
51#16810622C2211yescharacteristic
52#16810621—21no—
53#16810618—21no—
54#16810616—21no—
55#103×D53—21no—
56#102×D53—21no—
57#16810392C2211yescharacteristic, complemented
58#16810392C2211yescharacteristic, complemented
59#16810391C2211yescharacteristic, complemented
60#16810391C2211yescharacteristic, complemented
61#16810391C2211yescharacteristic, complemented
62#16810391C2211yescharacteristic, complemented
63C2×#131×C53C2211yescharacteristic
64C2×#108×C53C2211yescharacteristic, complemented
65C2×#106×C53C2211yescharacteristic, complemented
66C53×#417C2211yescharacteristic
67C53×#417C2211yescharacteristic
68C53×#343C2211yescharacteristic, complemented
69C53×#343C2211yescharacteristic, complemented
70C2×#11719949D411yescharacteristic
71C2×#11719945—21no—
72C2×#11719945C2311yescharacteristic
73C2×#11719947—21no—
74C2×#11719947D411yescharacteristic
75#41×D53—22no—
76#41×D53—22no—
77#41×D53C2×C414yes—
78#41×D53Q814yes—
79C2×Q8×D53D411yescharacteristic
80C2×D4×D53—21no—
81C2×D4×D53D411yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85#13133225—22no—
86#13133225—28no—
87#13133225C2×C414yescomplemented
88#13133224—22no—
89#13133224C2×C414yescomplemented
90#13133223—22no—
91#13133223—28no—
92#13133223C2×C414yescomplemented
93C2×#11719917—21no—
94C2×#11719917C2311yescharacteristic
95C2×#11719917C2311yescharacteristic
96C2×#11719917C2311yescharacteristic
97C2×#11719912—21no—
98C2×#11719912—21no—
99C2×#11719912—28no—
100C2×#11719912—21no—
101C2×#11719912—21no—
102C2×#11719912—21no—
103C2×#11719912C2×C414yes—
104C2×#11719912D411yescharacteristic
105C2×#11719912D411yescharacteristic
106C2×#11719912D411yescharacteristic
107C2×#11719912D411yescharacteristic
108C2×#11719912D414yes—
109M16×D53—28no—
110M16×D53—22no—
111M16×D53—22no—
112M16×D53—22no—
113M16×D53—22no—
114M16×D53—22no—
115M16×D53C2×C414yes—
116C22×#88322—21no—
117C22×#88322C2311yescharacteristic
118C2×C8×D53—21no—
119C2×C8×D53—21no—
120C2×C8×D53—21no—
121C2×C8×D53—21no—
122C2×C8×D53—21no—
123#13133175—21no—
124#13133175—21no—
125#13133175—21no—
126#13133175—21no—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C4⋊C4×D53—21no—
131C4⋊C4×D53—21no—
132C4⋊C4×D53—21no—
133C4⋊C4×D53—21no—
134C2×#11719921—21no—
135C2×C4×Dic53—21no—
136#13133153—22no—
137#13133152—22no—
138#13133152—22no—
139#13133151—21no—
140#13133151—21no—
141#13133150—21no—
142#13133150—21no—
143#13133148—21no—
144#13133148—21no—
145#13133142—21no—
146#13133142—21no—
147#13133141—21no—
148#13133141—21no—
149#13133140—21no—
150#13133140—21no—
151#13133139—21no—
152#13133139—21no—
153#13133138—21no—
154#13133138—21no—
155#13133137—21no—
156#13133137—21no—
157C2×#41×C53C2311yescharacteristic
158#131×C53—22no—
159#131×C53C2×C414yescomplemented
160C2×M16×C53—21no—
161C2×M16×C53C2311yescharacteristic
162C2×M16×C53C2311yescharacteristic
163C2×M16×C53C2311yescharacteristic
164C22×C8×C53—21no—
165C22×C8×C53C2311yescharacteristic
166C2×C4⋊C4×C53C2311yescharacteristic
167C2×C4⋊C4×C53C2311yescharacteristic
168#108×C53—22no—
169#106×C53—21no—
170#106×C53—21no—
171#103×C53—21no—
172#103×C53—21no—
173#102×C53—21no—
174#102×C53—21no—
175C23×D53—21no—
176C23×D53#4111yescharacteristic
177#41×C53—21no—
178#41×C53—21no—
179#41×C53C22×C412yes—
180#41×C53C2×Q812yes—
181C2×Q8×C53C2×D411yescharacteristic
182C2×D4×C53—21no—
183C2×D4×C53C2×D411yescharacteristic
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53C2411yescharacteristic
188C2×C22⋊D53—21no—
189C2×C22⋊D53—21no—
190C2×C22⋊D53—21no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53#4111yescharacteristic
195#11719949—22no—
196#11719949C4⋊C414yes—
197Q8×D53—22no—
198Q8×D53C4⋊C414yes—
199#11719947—24no—
200#11719947—24no—
201#11719947—22no—
202#11719947C4⋊C414yes—
203D4×D53—24no—
204D4×D53—24no—
205D4×D53—22no—
206D4×D53C4⋊C414yes—
207#11719945—21no—
208#11719945—21no—
209#11719945—24no—
210#11719945—24no—
211#11719945C22×C412yes—
212#11719945C2×Q812yes—
213C2×D212—21no—
214C2×D212C2×D411yescharacteristic
215C2×C4×D53—21no—
216C2×C4×D53—21no—
217C2×C4×D53—21no—
218C2×C4×D53—24no—
219C2×C4×D53—24no—
220C2×C4×D53—41no—
221C2×C4×D53—41no—
222C2×C4×D53—82no—
223C2×C4×D53C22×C412yes—
224C2×C4×D53C2×D412yes—
225C2×C4×D53C2×D411yescharacteristic
226C2×C4×D53C2×D411yescharacteristic
227C2×C4×D53C2×D411yescharacteristic
228C2×C4×D53C2×D411yescharacteristic
229C2×C4×D53C2×Q812yes—
230C2×C4×D53#4112yes—
231C2×Dic106—21no—
232C2×Dic106C2×D411yescharacteristic
233M16×C53—21no—
234M16×C53—24no—
235M16×C53—21no—
236M16×C53—21no—
237M16×C53—21no—
238M16×C53—21no—
239M16×C53C22×C412yes—
240C2×C8×C53—21no—
241C2×C8×C53—24no—
242C2×C8×C53—21no—
243C2×C8×C53—21no—
244C2×C8×C53C22×C412yes—
245C2×C8×C53C2×D411yescharacteristic
246C2×C8×C53C2×D411yescharacteristic
247C2×C8×C53C2×D412yes—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252#11719921—41no—
253#11719921—41no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258#11719919—41no—
259#11719919—41no—
260C4×Dic53—41no—
261C4×Dic53—41no—
262#11719917—21no—
263#11719917—24no—
264#11719917—21no—
265#11719917—21no—
266#11719917—21no—
267#11719917—21no—
268#11719917C22×C412yes—
269C2×#88322—21no—
270C2×#88322—24no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322C22×C412yes—
274C2×#88322C2×D411yescharacteristic
275C2×#88322C2×D411yescharacteristic
276C2×#88322C2×D412yes—
277#11719912—24no—
278#11719912—24no—
279#11719912—24no—
280#11719912—42no—
281#11719912—42no—
282#11719912C22⋊C414yes—
283#11719912C22⋊C414yes—
284#11719912C22⋊C414yes—
285#11719912C22⋊C414yes—
286C8×D53—24no—
287C8×D53—24no—
288C8×D53—24no—
289C8×D53—42no—
290C8×D53—42no—
291C23×C53—21no—
292C23×C53C2×#4111yescharacteristic
293C22×D53—21no—
294C22×D53—24no—
295C22×D53—41no—
296C22×D53—41no—
297C22×D53—81no—
298C22×D53—81no—
299C22×D53#11712yes—
300C22×D53#12111yescharacteristic
301C22×D53#12111yescharacteristic
302C22×D53C22⋊Q812yes—
303Q8×C53—21no—
304Q8×C53C2×C4⋊C412yes—
305D4×C53—22no—
306D4×C53—22no—
307D4×C53—21no—
308D4×C53C2×C4⋊C412yes—
309C2×C4×C53—21no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—81no—
315C2×C4×C53—81no—
316C2×C4×C53C23×C411yescharacteristic
317C2×C4×C53C22×D411yescharacteristic
318C2×C4×C53C22×D411yescharacteristic
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53C22×Q811yescharacteristic
321C2×C4×C53C2×#4111yescharacteristic
322C22⋊D53—22no—
323C22⋊D53—22no—
324C22⋊D53—24no—
325C22⋊D53—24no—
326C2×Dic53—21no—
327C2×Dic53—24no—
328C2×Dic53—41no—
329C2×Dic53—41no—
330C2×Dic53—81no—
331C2×Dic53—81no—
332C2×Dic53#11712yes—
333C2×Dic53#12111yescharacteristic
334C2×Dic53#12111yescharacteristic
335C2×Dic53C22⋊Q812yes—
336D212—24no—
337D212—21no—
338D212C2×C4⋊C412yes—
339C4×D53—24no—
340C4×D53—22no—
341C4×D53—22no—
342C4×D53—24no—
343C4×D53—82no—
344C4×D53—82no—
345C4×D53C2×C22⋊C412yes—
346C4×D53C2×C22⋊C412yes—
347C4×D53C2×C4⋊C412yes—
348C4×D53C2×C4⋊C412yes—
349C4×D53#12112yes—
350C4×D53#12112yes—
351C4×D53C22⋊Q812yes—
352C4×D53C22⋊Q812yes—
353Dic106—21no—
354Dic106—24no—
355Dic106C2×C4⋊C412yes—
356C8×C53—22no—
357C8×C53—41no—
358C8×C53—41no—
359C8×C53C2×C22⋊C412yes—
360C8×C53C2×C22⋊C412yes—
361#88322—22no—
362#88322—41no—
363#88322—41no—
364#88322C2×C22⋊C412yes—
365#88322C2×C22⋊C412yes—
366#20679—531nomaximal, Sylow
367C22×C53—21no—
368C22×C53—21no—
369C22×C53—22no—
370C22×C53—41no—
371C22×C53—41no—
372C22×C53C2×#11711yescharacteristic
373C22×C53C2×#12111yescharacteristic
374C22×C53C2×C22⋊Q811yescharacteristic
375C2×D53—21no—
376C2×D53—21no—
377C2×D53—21no—
378C2×D53—21no—
379C2×D53—22no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—41no—
383C2×D53—41no—
384C2×D53—84no—
385C2×D53#38012yes—
386C2×D53#38012yes—
387C4×C53—22no—
388C4×C53—81no—
389C4×C53—81no—
390C4×C53C22×C22⋊C411yescharacteristic
391C4×C53C22×C4⋊C411yescharacteristic
392C4×C53C2×#12111yescharacteristic
393C4×C53C2×C22⋊Q811yescharacteristic
394Dic53—22no—
395Dic53—81no—
396Dic53—81no—
397Dic53#38012yes—
398Dic53#38012yes—
399C2×#568—531no—
400C2×#430—531no—
401C2×#428—531no—
402#2896—531no—
403C2×#417—531no—
404#1816—531no—
405#1816—531no—
406#1816—531no—
407#1816—531no—
408#1815—531no—
409#1815—531no—
410#1815—531no—
411#1815D5311yescharacteristic, complemented
412#1742—531no—
413C2×#343—531no—
414C2×C53—21no—
415C2×C53—21no—
416C2×C53—42no—
417C2×C53C2×#38011yescharacteristic
418C2×C53#306811yescharacteristic
419C2×C53#306911yescharacteristic
420D53—22no—
421D53—22no—
422D53—42no—
423C22×#41—531no—
424#568—538no—
425#568—1064no—
426C2×#131—531no—
427C2×#131—531no—
428C2×#131—531no—
429C2×#131—1061no—
430C2×#131—1061no—
431C2×#131C2×D5311yescharacteristic
432C22×M16—531no—
433C22×M16—531no—
434C22×M16—531no—
435C22×M16—531no—
436C22×M16—1061no—
437C22×M16—1061no—
438C2×#117—531no—
439C22×C4⋊C4—531no—
440#430—1064no—
441C2×#108—531no—
442C2×#108—531no—
443C2×#108—531no—
444C2×#108C2×D5311yescharacteristic, complemented
445#428—1061no—
446#428—1061no—
447#428—1061no—
448#428—1061no—
449C2×#107—531no—
450C2×#107—531no—
451C2×#106—531no—
452C2×#106C2×D5311yescharacteristic, complemented
453#419—1061no—
454#418—1061no—
455#417—531no—
456#417—531no—
457#417—531no—
458#417—531no—
459#417—531no—
460#417—531no—
461#417—1061no—
462#417—1061no—
463#417C2×D5311yescharacteristic
464#417C2×D5311yescharacteristic
465#416—1061no—
466#416—1061no—
467C2×#103—1061no—
468C2×#102—1061no—
469#343—531no—
470#343—531no—
471#343—531no—
472#343—531no—
473#343—531no—
474#343—531no—
475#343C2×D5311yescharacteristic, complemented
476#343C2×D5311yescharacteristic, complemented
477C53#2067911yescharacteristic, complemented, Sylow
478C2×#41—534no—
479C2×#41—534no—
480C2×#41—531no—
481C2×#41—531no—
482C2×#41—531no—
483C2×#41—1061no—
484C2×#41—1061no—
485C2×#41—1062no—
486C2×#41—1062no—
487C2×#41C22×D5311yescharacteristic
488C22×Q8—531no—
489C22×D4—531no—
490C22×D4—1061no—
491C23×C4—531no—
492C23×C4—1061no—
493C23×C4—1061no—
494#131—22no—
495#131—534no—
496#131—534no—
497#131—534no—
498#131—1068no—
499#131—1062no—
500#131—1062no—
501#131—1068no—
502#131—1062no—
503#131C4×D5314yescomplemented
504C2×M16—21no—
505C2×M16—534no—
506C2×M16—531no—
507C2×M16—531no—
508C2×M16—531no—
509C2×M16—531no—
510C2×M16—534no—
511C2×M16—531no—
512C2×M16—534no—
513C2×M16—531no—
514C2×M16—531no—
515C2×M16—1061no—
516C2×M16—1068no—
517C2×M16—1061no—
518C2×M16—1061no—
519C2×M16—1061no—
520C2×M16—1061no—
521C2×M16—1068no—
522C2×M16—1062no—
523C2×M16—1061no—
524C2×M16—1062no—
525C2×M16—1062no—
526C2×M16—1062no—
527C2×M16—1062no—
528C2×M16C22×D5311yescharacteristic
529C2×M16C22×D5311yescharacteristic
530C2×M16C22×D5311yescharacteristic
531C22×C8—21no—
532C22×C8—531no—
533C22×C8—1061no—
534C22×C8—1061no—
535C22×C8—1061no—
536C22×C8—1061no—
537C22×C8—1061no—
538C22×C8—1061no—
539C22×C8C22×D5311yescharacteristic
540#117—1061no—
541#117—1061no—
542#117—1061no—
543#117—1061no—
544C2×C4⋊C4—531no—
545C2×C4⋊C4—531no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4—1061no—
550C2×C4⋊C4—1061no—
551C2×C4⋊C4C22×D5311yescharacteristic
552C2×C4⋊C4C22×D5311yescharacteristic
553C2×C22⋊C4—1061no—
554C2×C42—1061no—
555#108—22no—
556#108—1062no—
557#108—1062no—
558#108—1062no—
559#107—1061no—
560#107—1061no—
561#107—1061no—
562#107—1061no—
563#106—21no—
564#106—21no—
565#106—1061no—
566#106—1061no—
567#103—21no—
568#103—21no—
569#103—1061no—
570#103—1061no—
571#103—1061no—
572#103—1061no—
573#103—1061no—
574#103—1061no—
575#102—21no—
576#102—21no—
577#102—1061no—
578#102—1061no—
579#102—1061no—
580#102—1061no—
581#102—1061no—
582#102—1061no—
583C24—531no—
584C24—1061no—
585#41—21no—
586#41—21no—
587#41—534no—
588#41—534no—
589#41—532no—
590#41—532no—
591#41—1064no—
592#41—1064no—
593#41—1064no—
594#41—1064no—
595#41—1062no—
596#41—1062no—
597#41—1061no—
598#41—1061no—
599#41C2×C4×D5312yes—
600#41Q8×D5312yes—
601C2×Q8—534no—
602C2×Q8—531no—
603C2×Q8—1061no—
604C2×Q8—1062no—
605C2×Q8D4×D5311yescharacteristic
606C2×D4—21no—
607C2×D4—534no—
608C2×D4—531no—
609C2×D4—1061no—
610C2×D4—1062no—
611C2×D4—1061no—
612C2×D4—1064no—
613C2×D4—1064no—
614C2×D4—1061no—
615C2×D4—1061no—
616C2×D4D4×D5311yescharacteristic
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—531no—
621C22×C4—532no—
622C22×C4—531no—
623C22×C4—531no—
624C22×C4—531no—
625C22×C4—531no—
626C22×C4—532no—
627C22×C4—532no—
628C22×C4—532no—
629C22×C4—1064no—
630C22×C4—1061no—
631C22×C4—1064no—
632C22×C4—1061no—
633C22×C4—1061no—
634C22×C4—1061no—
635C22×C4—1061no—
636C22×C4—1061no—
637C22×C4—4242no—
638C22×C4—2121no—
639C22×C4—2121no—
640C22×C4C23×D5311yescharacteristic
641M16—21no—
642M16—24no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—21no—
647M16—534no—
648M16—534no—
649M16—534no—
650M16—534no—
651M16—532no—
652M16—1064no—
653M16—1064no—
654M16—1064no—
655M16—1061no—
656M16—1064no—
657M16—1061no—
658M16—1061no—
659M16—1061no—
660M16—1061no—
661M16—2122no—
662M16—2122no—
663M16C2×C4×D5312yes—
664C2×C8—21no—
665C2×C8—24no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—532no—
669C2×C8—531no—
670C2×C8—531no—
671C2×C8—532no—
672C2×C8—1064no—
673C2×C8—1064no—
674C2×C8—1064no—
675C2×C8—1061no—
676C2×C8—1064no—
677C2×C8—1061no—
678C2×C8—1061no—
679C2×C8—2122no—
680C2×C8—2122no—
681C2×C8C2×C4×D5312yes—
682C2×C8D4×D5311yescharacteristic
683C2×C8D4×D5311yescharacteristic
684C2×C8D4×D5312yes—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—1061no—
690C4⋊C4—1061no—
691C4⋊C4—1061no—
692C4⋊C4—1061no—
693C4⋊C4—2121no—
694C4⋊C4—2121no—
695C22⋊C4—2121no—
696C22⋊C4—2121no—
697C42—2121no—
698C42—2121no—
699C23—21no—
700C23—531no—
701C23—531no—
702C23—532no—
703C23—532no—
704C23—1064no—
705C23—1061no—
706C23—4241no—
707C23—4241no—
708C23—2121no—
709C23—2121no—
710C23#41×D5311yescharacteristic
711Q8—21no—
712Q8—532no—
713Q8—1064no—
714Q8—1061no—
715Q8C4⋊C4×D5312yes—
716D4—22no—
717D4—22no—
718D4—21no—
719D4—532no—
720D4—1064no—
721D4—1064no—
722D4—1064no—
723D4—1062no—
724D4—1062no—
725D4—1061no—
726D4C4⋊C4×D5312yes—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—532no—
735C2×C4—531no—
736C2×C4—531no—
737C2×C4—532no—
738C2×C4—532no—
739C2×C4—532no—
740C2×C4—532no—
741C2×C4—532no—
742C2×C4—532no—
743C2×C4—532no—
744C2×C4—532no—
745C2×C4—532no—
746C2×C4—1064no—
747C2×C4—1064no—
748C2×C4—1064no—
749C2×C4—1061no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—4242no—
753C2×C4—4242no—
754C2×C4—4241no—
755C2×C4—4241no—
756C2×C4—2121no—
757C2×C4—2121no—
758C2×C4C22×C4×D5311yescharacteristic
759C2×C4C2×D4×D5311yescharacteristic
760C2×C4C2×D4×D5311yescharacteristic
761C2×C4C2×D4×D5311yescharacteristic
762C2×C4C2×Q8×D5311yescharacteristic
763C2×C4#41×D5311yescharacteristic
764C8—22no—
765C8—41no—
766C8—41no—
767C8—532no—
768C8—532no—
769C8—1062no—
770C8—2121no—
771C8—2121no—
772C8C22⋊C4×D5312yes—
773C8C22⋊C4×D5312yes—
774C22—21no—
775C22—21no—
776C22—22no—
777C22—41no—
778C22—41no—
779C22—532no—
780C22—532no—
781C22—1061no—
782C22—1061no—
783C22—1061no—
784C22—1061no—
785C22—1062no—
786C22—4244no—
787C22—2122no—
788C22—2122no—
789C22—2121no—
790C22—2121no—
791C22#117×D5311yescharacteristic
792C22#121×D5311yescharacteristic
793C22C22⋊Q8×D5311yescharacteristic
794C4—22no—
795C4—81no—
796C4—81no—
797C4—532no—
798C4—532no—
799C4—1062no—
800C4—4241no—
801C4—4241no—
802C4C2×C22⋊C4×D5311yescharacteristic
803C4C2×C4⋊C4×D5311yescharacteristic
804C4#121×D5311yescharacteristic
805C4C22⋊Q8×D5311yescharacteristic
806C2—21no—
807C2—21no—
808C2—42no—
809C2—1062no—
810C2—1062no—
811C2—2122no—
812C2#380×D5311yescharacteristic
813C2#2028443811yescharacteristic
814C2#2028444711yescharacteristic
subgroupG/H
centerC22#121×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1815C2
socleC22×C53C2×#121
prime radicalC2×#41×D53C22
cosocleC22×C4×C53C24
hypercenter#1815D53
hypocenterC53#20679
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1815

Complements

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

NH ≅ G/Ntype
2. C2×#16810670C2semidirect
3. C2×#16810662C2semidirect
6. #20274779C2semidirect
7. #20274778C2semidirect
8. #20274777C2semidirect
9. #20274776C2semidirect
10. #20274775C2semidirect
11. #20274773C2semidirect
12. #20274772C2semidirect
13. #20274452C2semidirect
14. #343×D53C2semidirect
15. C53×#1815C2semidirect
18. #16811388C4semidirect
33. C2×#13133153C22semidirect
34. C2×#13133152C22semidirect
35. C2×#13133152C22semidirect
40. C2×#13133151C22semidirect
41. C2×#13133150C22semidirect
42. C2×#13133148C22semidirect
57. #16810392C22semidirect
58. #16810392C22semidirect
59. #16810391C22semidirect
60. #16810391C22semidirect
61. #16810391C22semidirect
62. #16810391C22semidirect
64. C2×#108×C53C22semidirect
65. C2×#106×C53C22semidirect
68. C53×#343C22semidirect
69. C53×#343C22semidirect
87. #13133225C2×C4semidirect
89. #13133224C2×C4semidirect
92. #13133223C2×C4semidirect
159. #131×C53C2×C4semidirect
411. #1815D53semidirect
444. C2×#108C2×D53semidirect
452. C2×#106C2×D53semidirect
475. #343C2×D53semidirect
476. #343C2×D53semidirect
477. C53#20679semidirect
503. #131C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168113882
C2×#168106702
C2×#168106622
#202832312
#417×D532
#202747792
#202747782
#202747772
#202747762
#202747752
#202747732
#202747722
#202744522
#343×D532
C53×#18152
#2067953