Finite Group Databasebeta

← #27593698

Subgroups — #27593698

Order 13568.

1680 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283025C212yesmaximal, complemented
2#20282431C212yesmaximal, complemented
3#20282096C212yesmaximal, complemented
4#20282022C212yesmaximal, complemented
5#20281947C212yesmaximal, complemented
6#20281521C212yesmaximal, complemented
7#20281496C212yesmaximal, complemented
8#20281421C212yesmaximal, complemented
9#20281245C212yesmaximal, complemented
10#20280757C212yesmaximal, complemented
11#20280382C211yesmaximal, characteristic, complemented
12#20280130C212yesmaximal, complemented
13#20280090C211yesmaximal, characteristic, complemented
14#20278925C212yesmaximal, complemented
15#20278339C211yesmaximal, characteristic
16#20278046C211yesmaximal, characteristic
17#20277471C211yesmaximal, characteristic, complemented
18#20277315C211yesmaximal, characteristic, complemented
19C53×#2297C211yesmaximal, characteristic
20C2×#13133215C2211yescharacteristic
21C2×#13133210C2212yes—
22C2×#13133209C2212yes—
23C2×#13133204C2211yescharacteristic
24C2×#13133198C2211yescharacteristic
25C2×#13133198C2211yescharacteristic
26C2×#13133196C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28#16810565C2212yes—
29#16810564C2212yes—
30#16810564C2212yes—
31#16810563C2212yes—
32#16810557C2212yes—
33#16810557C2212yes—
34#16810556C2212yes—
35#16810555C2212yes—
36#16810553C2212yes—
37#16810551C2212yes—
38#16810551C2212yes—
39#16810551C2212yes—
40#16810551C2212yes—
41#16810548C2212yes—
42#16810546C2212yes—
43#16810546C2212yes—
44#16810546C2212yes—
45#16810546C2212yes—
46#16810546C2212yes—
47#16810544C2212yes—
48#16810542C2212yes—
49#16810537C2212yes—
50#16810537C2212yes—
51#16810537C2212yes—
52#16810530C2211yescharacteristic
53#16810527C2212yes—
54#16810526C2211yescharacteristic
55#16810521C2212yes—
56#16810521C2212yes—
57#16810521C2212yes—
58#16810520C2212yes—
59#16810520C2212yes—
60#16810518C2212yes—
61#16810517C2212yes—
62#16810516C2212yes—
63#16810516C2212yes—
64#16810516C2212yes—
65#16810511C2212yes—
66#16810510C2212yes—
67#16810510C2212yes—
68#16810508C2212yes—
69#16810507C2212yes—
70#16810507C2212yes—
71#16810507C2212yes—
72#16810507C2212yes—
73#16810507C2212yes—
74#16810507C2212yes—
75#16810505C2212yes—
76#16810505C2212yes—
77#16810504C2212yes—
78#16810503C2211yescharacteristic
79#16810503C2211yescharacteristic
80#16810498C2212yes—
81#16810498C2212yes—
82#16810496C2212yes—
83#16810496C2212yes—
84#16810496C2212yes—
85#16810496C2212yes—
86#16810496C2212yes—
87#16810496C2212yes—
88#16810489C2212yes—
89#16810486C2211yescharacteristic
90#16810484C2212yes—
91#16810483C2212yes—
92#16810483C2212yes—
93#16810481C2212yes—
94C4×#11719919C2212yes—
95C4×C22⋊Dic53C2211yescharacteristic
96C22×#41×C53C2211yescharacteristic
97C2×#117×C53C2211yescharacteristic
98C22×C42×C53C2211yescharacteristic
99C53×#391C2212yes—
100C53×#390C2212yes—
101C53×#386C2212yes—
102C53×#386C2212yes—
103C4×C22⋊C4×C53C2211yescharacteristic
104C4×C22⋊C4×C53C2211yescharacteristic
105C4×C22⋊C4×C53C2211yescharacteristic
106C4×C22⋊C4×C53C2211yescharacteristic
107C22×Dic106C2311yescharacteristic
108C23×Dic53C2311yescharacteristic
109C23×Dic53C2311yescharacteristic
110#13133215—42no—
111#13133210—44no—
112#13133209—44no—
113#13133204—42no—
114#13133198—42no—
115#13133198—42no—
116#13133196—24no—
117C2×C4⋊Dic53C2311yescharacteristic
118C2×C4⋊Dic53C2312yes—
119C2×C4⋊Dic53C2312yes—
120C2×C4⋊Dic53C2312yes—
121C2×C4⋊Dic53C2312yes—
122C2×C4⋊Dic53C2312yes—
123C2×C4⋊Dic53C2312yes—
124C2×#11719919—24no—
125C2×#11719919C2312yes—
126C2×#11719919C2312yes—
127C2×#11719919C2312yes—
128C2×#11719919C2312yes—
129C2×#11719919C2312yes—
130C2×#11719919C2312yes—
131C2×#11719919C2312yes—
132C2×#11719919C2312yes—
133C2×#11719919C2312yes—
134C2×#11719919C2312yes—
135C2×#11719919C2312yes—
136C2×#11719919C2312yes—
137C2×#11719919C2312yes—
138C2×#11719919C2312yes—
139C2×#11719919C2312yes—
140C2×C22⋊Dic53C2312yes—
141C2×C22⋊Dic53C2312yes—
142C2×C22⋊Dic53C2312yes—
143C2×C22⋊Dic53C2312yes—
144C2×C22⋊Dic53C2312yes—
145C2×C22⋊Dic53C2312yes—
146C2×C22⋊Dic53C2312yes—
147C2×C22⋊Dic53C2312yes—
148C2×C22⋊Dic53C2312yes—
149C2×C22⋊Dic53C2311yescharacteristic
150C2×C22⋊Dic53C2311yescharacteristic
151C2×C22⋊Dic53C2312yes—
152C2×C4×Dic53C2312yes—
153C2×C4×Dic53C2311yescharacteristic
154C2×C4×Dic53C2311yescharacteristic
155C2×C4×Dic53C2312yes—
156#13133124C2312yes—
157#13133124C2312yes—
158#13133124C2312yes—
159#13133124C2312yes—
160#13133124C2312yes—
161#13133124C2312yes—
162#13133124C2312yes—
163#13133124C2312yes—
164#13133124C2312yes—
165#13133124C2312yes—
166#13133124C2312yes—
167#13133124C2312yes—
168#13133124C2312yes—
169#13133124C2312yes—
170#13133124C2312yes—
171#13133124C2312yes—
172#13133124C2312yes—
173#13133124C2312yes—
174#13133124C2312yes—
175#13133124C2312yes—
176#13133124C2312yes—
177#13133124C2312yes—
178#13133124C2312yes—
179C2×#41×C53—24no—
180C2×#41×C53—42no—
181C2×#41×C53—42no—
182C22×Q8×C53C2311yescharacteristic
183C22×D4×C53C2311yescharacteristic
184C22×D4×C53C2311yescharacteristic
185C22×D4×C53C2311yescharacteristic
186C23×C4×C53C2311yescharacteristic
187C23×C4×C53C2311yescharacteristic
188C23×C4×C53C2312yes—
189C23×C4×C53C2311yescharacteristic
190#117×C53—42no—
191C2×C4⋊C4×C53C2312yes—
192C2×C22⋊C4×C53C2312yes—
193C2×C22⋊C4×C53C2312yes—
194C2×C22⋊C4×C53C2312yes—
195C2×C22⋊C4×C53C2312yes—
196C2×C22⋊C4×C53C2312yes—
197C2×C42×C53—42no—
198C2×C42×C53C2312yes—
199C2×C42×C53C2311yescharacteristic
200C2×C42×C53C2311yescharacteristic
201C2×C42×C53C2311yescharacteristic
202C2×C42×C53C2311yescharacteristic
203#95×C53C2312yes—
204#95×C53C2312yes—
205#95×C53C2312yes—
206#95×C53C2312yes—
207C24×C53C2411yescharacteristic
208C24×C53C2411yescharacteristic
209C24×C53C2411yescharacteristic
210#41×C53—416no—
211C2×Q8×C53—22no—
212C2×Q8×C53—22no—
213C2×Q8×C53—41no—
214C2×D4×C53—22no—
215C2×D4×C53—22no—
216C2×D4×C53—22no—
217C2×D4×C53—22no—
218C2×D4×C53—22no—
219C2×D4×C53—22no—
220C2×D4×C53—41no—
221C2×D4×C53—41no—
222C2×D4×C53—41no—
223C22×C4×C53—22no—
224C22×C4×C53—22no—
225C22×C4×C53—22no—
226C22×C4×C53—22no—
227C22×C4×C53—24no—
228C22×C4×C53—42no—
229C22×C4×C53—42no—
230C22×C4×C53—41no—
231C22×C4×C53—41no—
232C22×C4×C53—41no—
233C22×C4×C53—41no—
234C22×C4×C53#4114yes—
235C22×C4×C53C2411yescharacteristic
236C22×C4×C53C2412yes—
237C22×C4×C53C2412yes—
238C22×C4×C53C2412yes—
239C22×C4×C53C2411yescharacteristic
240C22×C4×C53C2411yescharacteristic
241C22×C4×C53C2411yescharacteristic
242C22×C4×C53C2412yes—
243C22×Dic53—22no—
244C22×Dic53—22no—
245C22×Dic53—42no—
246C22×Dic53—41no—
247C22×Dic53—41no—
248C22×Dic53C2412yes—
249C22×Dic53C2412yes—
250C22×Dic53C2412yes—
251C22×Dic53C2412yes—
252C22×Dic53C2412yes—
253C22×Dic53C2412yes—
254C22×Dic53C2412yes—
255C22×Dic53C2412yes—
256C2×Dic106—22no—
257C2×Dic106—41no—
258C2×Dic106—41no—
259C4⋊C4×C53—42no—
260C22⋊C4×C53—24no—
261C22⋊C4×C53—24no—
262C22⋊C4×C53—24no—
263C22⋊C4×C53—42no—
264C22⋊C4×C53—42no—
265C42×C53—24no—
266C42×C53—41no—
267C42×C53—41no—
268C42×C53—41no—
269C42×C53—41no—
270C22⋊Dic53—24no—
271C22⋊Dic53—24no—
272C22⋊Dic53—24no—
273C22⋊Dic53—42no—
274C22⋊Dic53—42no—
275C22⋊Dic53—42no—
276C22⋊Dic53—42no—
277C22⋊Dic53—42no—
278C22⋊Dic53—42no—
279C22⋊Dic53—41no—
280C22⋊Dic53—41no—
281C22⋊Dic53—42no—
282C4⋊Dic53—22no—
283C4⋊Dic53—42no—
284C4⋊Dic53—42no—
285C4⋊Dic53—42no—
286C4⋊Dic53—42no—
287C4⋊Dic53—42no—
288C4⋊Dic53—42no—
289#11719919—24no—
290#11719919—24no—
291#11719919—24no—
292#11719919—24no—
293#11719919—24no—
294#11719919—24no—
295#11719919—24no—
296#11719919—42no—
297#11719919—42no—
298#11719919—42no—
299#11719919—42no—
300#11719919—42no—
301#11719919—42no—
302#11719919—42no—
303#11719919—42no—
304C4×Dic53—42no—
305C4×Dic53—41no—
306C4×Dic53—42no—
307C4×Dic53—41no—
308C23×C53—21no—
309C23×C53—21no—
310C23×C53—21no—
311C23×C53—21no—
312C23×C53—22no—
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53—21no—
317C23×C53—21no—
318C23×C53—21no—
319C23×C53—22no—
320C23×C53—22no—
321C23×C53C2×#4112yes—
322C23×C53H(5,𝔽2)12yes—
323C23×C53C2511yescharacteristic
324Q8×C53—44no—
325D4×C53—44no—
326D4×C53—44no—
327D4×C53—44no—
328C2×C4×C53—28no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—44no—
350C2×C4×C53—48no—
351C2×C4×C53—44no—
352C2×C4×C53C2×#4112yes—
353C2×C4×C53C2×#4112yes—
354C2×C4×C53H(5,𝔽2)12yes—
355C2×C4×C532−1+414yes—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—22no—
363C2×Dic53—22no—
364C2×Dic53—22no—
365C2×Dic53—22no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—22no—
380C2×Dic53—44no—
381C2×Dic53—82no—
382Dic106—82no—
383#36819—531nomaximal, Sylow
384C22×C53—22no—
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—22no—
388C22×C53—24no—
389C22×C53—41no—
390C22×C53—41no—
391C22×C53—42no—
392C22×C53—42no—
393C22×C53—42no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—42no—
398C22×C53—42no—
399C22×C53C22×#4111yescharacteristic
400C22×C53C2×H(5,𝔽2)11yescharacteristic
401C22×C53C2×H(5,𝔽2)11yescharacteristic
402C22×C53C2×2−1+412yes—
403C22×C53#58512yes—
404C4×C53—22no—
405C4×C53—22no—
406C4×C53—22no—
407C4×C53—24no—
408C4×C53—41no—
409C4×C53—42no—
410C4×C53—42no—
411C4×C53—42no—
412Dic53—42no—
413Dic53—42no—
414Dic53—42no—
415Dic53—42no—
416Dic53—42no—
417Dic53—42no—
418Dic53—42no—
419Dic53—42no—
420#2851—532no—
421#2786—532no—
422#2761—532no—
423#2755—532no—
424#2750—532no—
425#2715—532no—
426#2713—532no—
427#2707—532no—
428#2695—532no—
429#2652—532no—
430#2608—531no—
431#2587—532no—
432#2583—531no—
433#2478—532no—
434#2432—531no—
435#2406—531no—
436#2332—531no—
437#2313—531no—
438#2297D5311yescharacteristic
439C2×C53—42no—
440C2×C53—42no—
441C2×C53—81no—
442C2×C53#345511yescharacteristic
443C2×C53#349011yescharacteristic
444C2×C53#350911yescharacteristic
445C2×C53#354112yes—
446C2×C53#355912yes—
447C22×#41C2×D5311yescharacteristic
448C2×C4⋊Q8—531no—
449C2×#126—532no—
450C2×#125—532no—
451C2×#124—531no—
452C2×#123—531no—
453C2×#123—531no—
454C2×C22⋊Q8—531no—
455C2×#117C2×D5311yescharacteristic
456C22×C4⋊C4—531no—
457C22×C42C2×D5311yescharacteristic
458#400—532no—
459#400—532no—
460#400—532no—
461#400—532no—
462#398—532no—
463#398—532no—
464#398—532no—
465#398—532no—
466#398—532no—
467#397—532no—
468#397—532no—
469#397—532no—
470#397—532no—
471#397—532no—
472#396—532no—
473#396—532no—
474#396—532no—
475#396—532no—
476#396—532no—
477#395—532no—
478#395—532no—
479#394—532no—
480#394—532no—
481#394—532no—
482#391—531no—
483#391—532no—
484#391C2×D5312yes—
485#390—531no—
486#390C2×D5312yes—
487#389—532no—
488#389—532no—
489#389—532no—
490#389—532no—
491#389—532no—
492#389—532no—
493#388—532no—
494#388—532no—
495#388—532no—
496#388—532no—
497#388—532no—
498#387—532no—
499#387—532no—
500#387—532no—
501#387—532no—
502#387—532no—
503#387—532no—
504#387—532no—
505#387—532no—
506#387—532no—
507#387—532no—
508#387—532no—
509#387—532no—
510#386—531no—
511#386—531no—
512#386C2×D5312yes—
513#386C2×D5312yes—
514#385—532no—
515#385—532no—
516#385—532no—
517#385—532no—
518#385—532no—
519#385—532no—
520#385—532no—
521#385—532no—
522#382—532no—
523#381—531no—
524#381—532no—
525#380—532no—
526#380—532no—
527#380—532no—
528C4×C4⋊C4—532no—
529C4×C22⋊C4—531no—
530C4×C22⋊C4C2×D5311yescharacteristic
531C4×C22⋊C4C2×D5311yescharacteristic
532C4×C22⋊C4C2×D5311yescharacteristic
533C4×C22⋊C4C2×D5311yescharacteristic
534C53#3681911yescharacteristic, complemented, Sylow
535C2×#41—24no—
536C2×#41—42no—
537C2×#41—42no—
538C22×Q8—531no—
539C22×Q8C22×D5311yescharacteristic
540C22×D4C22×D5311yescharacteristic
541C22×D4C22×D5311yescharacteristic
542C22×D4C22×D5311yescharacteristic
543C23×C4—531no—
544C23×C4—531no—
545C23×C4C22×D5311yescharacteristic
546C23×C4C22×D5311yescharacteristic
547C23×C4C22×D5312yes—
548C23×C4C22×D5311yescharacteristic
549C4⋊Q8—2122no—
550#126—2124no—
551#125—2124no—
552#124—2122no—
553#123—2122no—
554#123—2122no—
555C22⋊Q8—1064no—
556#117—42no—
557C2×C4⋊C4—532no—
558C2×C4⋊C4—532no—
559C2×C4⋊C4—532no—
560C2×C4⋊C4—531no—
561C2×C4⋊C4—532no—
562C2×C4⋊C4—532no—
563C2×C4⋊C4—532no—
564C2×C4⋊C4—532no—
565C2×C4⋊C4—532no—
566C2×C4⋊C4—532no—
567C2×C4⋊C4—532no—
568C2×C4⋊C4—532no—
569C2×C4⋊C4—532no—
570C2×C4⋊C4—532no—
571C2×C4⋊C4—532no—
572C2×C4⋊C4—532no—
573C2×C4⋊C4—532no—
574C2×C4⋊C4—532no—
575C2×C4⋊C4—532no—
576C2×C4⋊C4—532no—
577C2×C4⋊C4—532no—
578C2×C4⋊C4—532no—
579C2×C4⋊C4—1064no—
580C2×C4⋊C4C22×D5312yes—
581C2×C22⋊C4—532no—
582C2×C22⋊C4—532no—
583C2×C22⋊C4—532no—
584C2×C22⋊C4—531no—
585C2×C22⋊C4—531no—
586C2×C22⋊C4—532no—
587C2×C22⋊C4—532no—
588C2×C22⋊C4—532no—
589C2×C22⋊C4—532no—
590C2×C22⋊C4—532no—
591C2×C22⋊C4—532no—
592C2×C22⋊C4—532no—
593C2×C22⋊C4C22×D5312yes—
594C2×C22⋊C4C22×D5312yes—
595C2×C22⋊C4C22×D5312yes—
596C2×C22⋊C4C22×D5312yes—
597C2×C22⋊C4C22×D5312yes—
598C2×C42—42no—
599C2×C42—531no—
600C2×C42—532no—
601C2×C42—531no—
602C2×C42—532no—
603C2×C42C22×D5312yes—
604C2×C42C22×D5311yescharacteristic
605C2×C42C22×D5311yescharacteristic
606C2×C42C22×D5311yescharacteristic
607C2×C42C22×D5311yescharacteristic
608#95—532no—
609#95—532no—
610#95—532no—
611#95—532no—
612#95—532no—
613#95—532no—
614#95—532no—
615#95—532no—
616#95—532no—
617#95—532no—
618#95—532no—
619#95—532no—
620#95—532no—
621#95—532no—
622#95—532no—
623#95—532no—
624#95—532no—
625#95—532no—
626#95—532no—
627#95—532no—
628#95—532no—
629#95—532no—
630#95—532no—
631#95C22×D5312yes—
632#95C22×D5312yes—
633#95C22×D5312yes—
634#95C22×D5312yes—
635C24C23×D5311yescharacteristic
636C24C23×D5311yescharacteristic
637C24C23×D5311yescharacteristic
638#41—416no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—41no—
642C2×Q8—1062no—
643C2×Q8—2121no—
644C2×Q8—2121no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—41no—
652C2×D4—41no—
653C2×D4—41no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—24no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—532no—
666C22×C4—532no—
667C22×C4—532no—
668C22×C4—532no—
669C22×C4—532no—
670C22×C4—532no—
671C22×C4—532no—
672C22×C4—532no—
673C22×C4—1062no—
674C22×C4—1062no—
675C22×C4—2121no—
676C22×C4—2121no—
677C22×C4—2122no—
678C22×C4#1171994514yes—
679C22×C4C23×D5312yes—
680C22×C4C23×D5311yescharacteristic
681C22×C4C23×D5312yes—
682C22×C4C23×D5312yes—
683C22×C4C23×D5311yescharacteristic
684C22×C4C23×D5311yescharacteristic
685C22×C4C23×D5311yescharacteristic
686C22×C4C23×D5312yes—
687C4⋊C4—42no—
688C4⋊C4—1064no—
689C4⋊C4—1064no—
690C4⋊C4—1064no—
691C4⋊C4—1062no—
692C4⋊C4—1064no—
693C4⋊C4—1064no—
694C4⋊C4—1064no—
695C4⋊C4—1064no—
696C4⋊C4—2122no—
697C4⋊C4—2122no—
698C4⋊C4—2122no—
699C4⋊C4—2122no—
700C4⋊C4—2122no—
701C4⋊C4—2122no—
702C4⋊C4—2122no—
703C4⋊C4—2122no—
704C4⋊C4—2122no—
705C4⋊C4—2122no—
706C4⋊C4—2122no—
707C4⋊C4—2122no—
708C4⋊C4—2122no—
709C4⋊C4—2122no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—1064no—
716C22⋊C4—1064no—
717C22⋊C4—1064no—
718C22⋊C4—2121no—
719C22⋊C4—2121no—
720C22⋊C4—2122no—
721C22⋊C4—2122no—
722C22⋊C4—2122no—
723C22⋊C4—2122no—
724C22⋊C4—2122no—
725C22⋊C4—2122no—
726C22⋊C4—2122no—
727C42—24no—
728C42—41no—
729C42—41no—
730C42—41no—
731C42—41no—
732C42—2121no—
733C42—2122no—
734C42—2121no—
735C42—2122no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—22no—
748C23—22no—
749C23C2×#1171994512yes—
750C23#1313326212yes—
751C23C24×D5311yescharacteristic
752Q8—44no—
753Q8—4242no—
754D4—44no—
755D4—44no—
756D4—44no—
757C2×C4—28no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—44no—
779C2×C4—48no—
780C2×C4—44no—
781C2×C4—1062no—
782C2×C4—1062no—
783C2×C4—1062no—
784C2×C4—1062no—
785C2×C4—1062no—
786C2×C4—1062no—
787C2×C4—1062no—
788C2×C4—1062no—
789C2×C4—1062no—
790C2×C4—1062no—
791C2×C4—1062no—
792C2×C4—1062no—
793C2×C4—1062no—
794C2×C4—1062no—
795C2×C4—1062no—
796C2×C4—1062no—
797C2×C4—1062no—
798C2×C4—1062no—
799C2×C4—1062no—
800C2×C4—1062no—
801C2×C4—1062no—
802C2×C4—1062no—
803C2×C4—1062no—
804C2×C4—1062no—
805C2×C4—4242no—
806C2×C4—2124no—
807C2×C4C2×#1171994512yes—
808C2×C4C2×#1171994512yes—
809C2×C4#1313326212yes—
810C2×C4#1313326414yes—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—24no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—42no—
826C22C22×#1171994511yescharacteristic
827C22C2×#1313326211yescharacteristic
828C22C2×#1313326211yescharacteristic
829C22C2×#1313326412yes—
830C22#1681145912yes—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—24no—
835C4—41no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—2122no—
840C4—2122no—
841C4—2122no—
842C4—2122no—
843C4—2122no—
844C4—2122no—
845C4—2122no—
846C4—2122no—
847C2—42no—
848C2—42no—
849C2—81no—
850C2#2028810011yescharacteristic
851C2#2028840411yescharacteristic
852C2#2028860111yescharacteristic
853C2#2028900012yes—
854C2#2028925312yes—
subgroupG/H
center, FrattiniC23C24×D53
commutator, socle, cosocleC23×C53C25
FittingC53×#2297C2
prime radicalC22×#41×C53C22
hypercenter#2297D53
hypocenterC53#36819
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. #20283025C2semidirect
2. #20282431C2semidirect
3. #20282096C2semidirect
4. #20282022C2semidirect
5. #20281947C2semidirect
6. #20281521C2semidirect
7. #20281496C2semidirect
8. #20281421C2semidirect
9. #20281245C2semidirect
10. #20280757C2semidirect
11. #20280382C2semidirect
12. #20280130C2semidirect
13. #20280090C2semidirect
14. #20278925C2semidirect
17. #20277471C2semidirect
18. #20277315C2semidirect
534. C53#36819semidirect

Maximal subgroups

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

subgroupindex
#202830252
#202824312
#202820962
#202820222
#202819472
#202815212
#202814962
#202814212
#202812452
#202807572
#202803822
#202801302
#202800902
#202789252
#202783392
#202780462
#202774712
#202773152
C53×#22972
#3681953