Finite Group Databasebeta

← #28329502

Subgroups — #28329502

Order 13568.

2814 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133305C211yesmaximal, characteristic, complemented
2C2×D53⋊#131C211yesmaximal, characteristic, complemented
3#20291460C213yesmaximal, complemented
4#20291454C213yesmaximal, complemented
5#20291450C213yesmaximal, complemented
6#20291445C213yesmaximal, complemented
7#20291439C213yesmaximal, complemented
8#20291431C213yesmaximal, complemented
9#20291429C213yesmaximal, complemented
10D4×D53⋊C8C213yesmaximal, complemented
11#20291363C211yesmaximal, characteristic, complemented
12#20291306C211yesmaximal, characteristic, complemented
13#20291304C211yesmaximal, characteristic, complemented
14C4×#13133305C211yesmaximal, characteristic, complemented
15#20288204C211yesmaximal, characteristic
16C2×#13133305—28no—
17C2×#13133305C2211yescharacteristic
18C2×#13133305C2211yescharacteristic
19C2×#13133305C2211yescharacteristic
20C2×#13133305C2211yescharacteristic
21C2×#13133305C2213yescomplemented
22C2×#13133305C2213yescomplemented
23D53⋊#131—28no—
24C2×#13133304C2213yescomplemented
25C2×#13133304C2213yescomplemented
26C22×#11719936C2213yescomplemented
27C2×D53⋊M16C2213yescomplemented
28C22×D53⋊C8C2213yescomplemented
29C22×D53⋊C8C2213yescomplemented
30#16811656C2216yescomplemented
31#16811656C2216yescomplemented
32#16811655C2216yescomplemented
33#16811654C2216yescomplemented
34#16811653C2216yescomplemented
35#16811652C2216yescomplemented
36#16811651C2213yescomplemented
37#16811651C2213yescomplemented
38#16811650C2211yescharacteristic
39#16811650C2213yes—
40#16811650C2213yescomplemented
41#16811650C2213yescomplemented
42#16811650C2216yescomplemented
43D4×#88324C2213yescomplemented
44D4×#88324C2213yescomplemented
45#16811630C2213yescomplemented
46#16811630C2213yescomplemented
47#16811628C2213yescomplemented
48D53⋊(C4⋊C8)C2213yescomplemented
49#16811598C2213yescomplemented
50#16811598C2213yescomplemented
51#16811597C2213yescomplemented
52#16811597C2213yescomplemented
53#16811594C2213yescomplemented
54#16811594C2213yescomplemented
55D53⋊(C22⋊C8)C2213yescomplemented
56D53⋊(C22⋊C8)C2213yescomplemented
57#16811588C2213yescomplemented
58#16811588C2213yescomplemented
59C4×#11719936C2213yescomplemented
60C4×D53⋊C8C2213yescomplemented
61C22×#11719949C2211yescharacteristic
62C2×#41×D53C2211yescharacteristic
63#16811292C411yescharacteristic
64Q8×C22⋊D53C411yescharacteristic
65#16811285C411yescharacteristic
66#16811275C413yes—
67#16811269C413yes—
68#16811266C413yes—
69#16811257C413yes—
70#16811172C2213yes—
71#16811136C2213yes—
72#16811133C2213yes—
73C4×#11719949C2211yescharacteristic
74C4×D4×D53C2213yes—
75C53×#548C411yescharacteristic
76#13133305—212no—
77#13133305—24no—
78#13133305—24no—
79#13133305—24no—
80#13133305—212no—
81#13133305D418yescomplemented
82#13133304—212no—
83#13133304—212no—
84C2×#11719936—212no—
85C2×#11719936C2313yes—
86C2×#11719936C2313yes—
87C2×#11719936C2313yes—
88C2×#11719936C2316yes—
89C2×#11719936C2313yes—
90D53⋊M16—212no—
91C2×#11719940C2316yes—
92C2×D53⋊C8—212no—
93C2×D53⋊C8—212no—
94C2×D53⋊C8C2313yes—
95C2×D53⋊C8C2313yes—
96C2×D53⋊C8C2313yes—
97C2×D53⋊C8C2311yescharacteristic
98C2×D53⋊C8C2313yes—
99C2×D53⋊C8C2313yes—
100C2×D53⋊C8C2313yes—
101C2×D53⋊C8C2313yes—
102C22×#88324C2311yescharacteristic
103C22×#88324C2313yes—
104C22×#88324C2313yes—
105C22×#88324C2313yes—
106#13133284C2311yescharacteristic
107#13133284C2313yes—
108#13133284C2316yes—
109C4⋊#88324C2313yes—
110C4⋊#88324C2313yes—
111#13133274C2311yescharacteristic
112#13133274C2313yes—
113#13133274C2313yes—
114#13133274C2313yes—
115#13133274C2316yes—
116C22⋊#88324C2311yescharacteristic
117C22⋊#88324C2313yes—
118C22⋊#88324C2313yes—
119C22⋊#88324C2313yes—
120C22⋊#88324C2316yes—
121#13133272C2316yes—
122C4×#88324C2311yescharacteristic
123C4×#88324C2313yes—
124C4×#88324C2313yes—
125C4×#88324C2313yes—
126C2×#11719949—24no—
127C2×#11719949—24no—
128C2×#11719949C2×C413yes—
129C2×#11719949C2×C411yescharacteristic
130C2×#11719949C2313yes—
131C2×#11719949C2311yescharacteristic
132C2×#11719945C2×C413yes—
133C2×#11719947C2313yes—
134#41×D53—24no—
135#41×D53—24no—
136C2×Q8×D53C2×C411yescharacteristic
137C22×D212C2×C413yes—
138C2×D4×D53C2×C413yes—
139C2×D4×D53C2×C413yes—
140C22×C4×D53C2313yes—
141C22×C4×D53C2313yes—
142#13133215C2×C413yes—
143#13133213C2×C413yes—
144#13133205C2×C413yes—
145#13133202C2×C416yes—
146#13133199C2×C416yes—
147#13133197C2×C413yes—
148#13133196C2×C413yes—
149#13133193C2×C413yes—
150#13133192C2×C413yes—
151#13133191C2×C413yes—
152#13133190C2×C416yes—
153#13133190C2×C416yes—
154#13133188C2×C413yes—
155#13133187C2×C416yes—
156#13133185C2×C416yes—
157Q8×Dic53C2×C411yescharacteristic
158C4×D212C2×C413yes—
159C4×D212C2×C413yes—
160D4×Dic53C2313yes—
161#13133179C2×C413yes—
162#13133179C2313yes—
163C4×C22⋊D53C2×C413yes—
164C4×C22⋊D53C2×C413yes—
165#13133177C2311yescharacteristic
166#13133177C2313yes—
167#13133177C2316yes—
168#13133175C2313yes—
169C4⋊C4×D53C2×C413yes—
170C22⋊C4×D53C2×C413yes—
171C22⋊C4×D53C2×C413yes—
172C42×D53C2313yes—
173C2×#41×C53C2×C411yescharacteristic
174C22×Q8×C53C2×C411yescharacteristic
175#124×C53C2×C413yes—
176C22⋊Q8×C53C2×C413yes—
177#121×C53C2×C413yes—
178C4×Q8×C53C2×C411yescharacteristic
179C4×D4×C53C2×C413yes—
180C23×D53C22×C413yes—
181C23×D53C22×C413yes—
182#41×C53—24no—
183C2×Q8×C53—24no—
184C2×Q8×C53C22×C413yes—
185C2×Q8×C53C22×C411yescharacteristic
186C2×D4×C53C22×C413yes—
187C2×D4×C53C22×C413yes—
188C22×C4×C53C22×C413yes—
189C22×C4×C53C22×C413yes—
190C2×C22⋊D53C22×C413yes—
191C2×C22⋊D53C22×C416yes—
192C2×C22⋊D53C22×C416yes—
193C2×C22⋊D53C22×C411yescharacteristic
194C22×Dic53C2413yes—
195C22×Dic53C2411yescharacteristic
196#11719949—24no—
197#11719949—212no—
198#11719949—26no—
199#11719949—26no—
200#11719949C2×D414yes—
201#11719949#4114yes—
202Q8×D53—24no—
203#11719947—26no—
204#11719947—26no—
205D4×D53—212no—
206D4×D53—212no—
207#11719945—212no—
208C2×D212—212no—
209C2×D212C22×C413yes—
210C2×D212C22×C416yes—
211C2×D212C22×C413yes—
212C2×D212C22×C413yes—
213C2×C4×D53—26no—
214C2×C4×D53—26no—
215C2×C4×D53—26no—
216C2×C4×D53—26no—
217C2×C4×D53C22×C413yes—
218C2×C4×D53C22×C413yes—
219C2×C4×D53C22×C413yes—
220C2×C4×D53C22×C413yes—
221C2×C4×D53C22×C413yes—
222C2×C4×D53C22×C413yes—
223C2×C4×D53C2413yes—
224C2×C4×D53C2411yescharacteristic
225C2×C4×D53C2413yes—
226C2×Dic106C22×C413yes—
227#11719940—212no—
228C2×#88324—22no—
229C2×#88324—26no—
230C2×#88324—26no—
231C2×#88324—26no—
232C2×#88324C2411yescharacteristic
233C2×#88324C2413yes—
234C2×#88324C2411yescharacteristic
235C2×#88324C2413yes—
236C2×#88324C2411yescharacteristic
237C2×#88324C2413yes—
238C2×#88324C2411yescharacteristic
239C2×#88324C2413yes—
240#11719936—26no—
241#11719936—26no—
242#11719936—26no—
243#11719936—212no—
244#11719936C2×D4112yescomplemented
245D53⋊C8—26no—
246D53⋊C8—26no—
247D53⋊C8—26no—
248D53⋊C8—22no—
249D53⋊C8—26no—
250D53⋊C8—26no—
251D53⋊C8—26no—
252D53⋊C8C2×D4112yescomplemented
253C4⋊C4×C53C22×C413yes—
254C4⋊C4×C53C22×C413yes—
255C22⋊C4×C53C22×C411yescharacteristic
256C22⋊C4×C53C22×C413yes—
257C22⋊C4×C53C22×C416yes—
258C42×C53C22×C413yes—
259C22⋊Dic53C22×C413yes—
260C22⋊Dic53C22×C413yes—
261#11719921C22×C411yescharacteristic
262#11719921C22×C413yes—
263#11719921C22×C413yes—
264#11719921C22×C413yes—
265#11719921C22×C416yes—
266#11719921C22×C416yes—
267C4⋊Dic53C22×C413yes—
268C4⋊Dic53C22×C413yes—
269#11719919C22×C411yescharacteristic
270#11719919C22×C413yes—
271#11719919C22×C416yes—
272C4×Dic53C22×C413yes—
273C4×Dic53C2411yescharacteristic
274C4×Dic53C2413yes—
275C23×C53C23×C413yes—
276C23×C53C23×C411yescharacteristic
277C22×D53—26no—
278C22×D53—26no—
279C22×D53—26no—
280C22×D53—26no—
281C22×D53—43no—
282C22×D53—43no—
283C22×D53C23×C413yes—
284C22×D53C23×C413yes—
285C22×D53C23×C411yescharacteristic
286Q8×C53—26no—
287Q8×C53C4×D414yes—
288D4×C53—26no—
289D4×C53—26no—
290C2×C4×C53—26no—
291C2×C4×C53—26no—
292C2×C4×C53C23×C411yescharacteristic
293C2×C4×C53C23×C411yescharacteristic
294C2×C4×C53C23×C413yes—
295C2×C4×C53C23×C413yes—
296C2×C4×C53C23×C413yes—
297C22⋊D53—212no—
298C22⋊D53—26no—
299C22⋊D53—46no—
300C22⋊D53#13114yescomplemented
301C2×Dic53—21no—
302C2×Dic53—23no—
303C2×Dic53—21no—
304C2×Dic53—23no—
305C2×Dic53C23×C413yes—
306C2×Dic53C23×C411yescharacteristic
307C2×Dic53C23×C413yes—
308C2×Dic53C23×C411yescharacteristic
309C2×Dic53C2511yescharacteristic
310D212—212no—
311D212—26no—
312D212—26no—
313D212C4×D4112yes—
314C4×D53—26no—
315C4×D53—26no—
316C4×D53—26no—
317C4×D53—26no—
318C4×D53—26no—
319C4×D53—23no—
320C4×D53—21no—
321C4×D53—21no—
322C4×D53—23no—
323C4×D53—43no—
324C4×D53C22×D416yes—
325C4×D53C2×#4116yes—
326Dic106—26no—
327#88324—23no—
328#88324—23no—
329#88324—21no—
330#88324—21no—
331#88324—23no—
332#88324—21no—
333#88324C22×D416yes—
334#88324C22×D412yes—
335D4×#131—531nomaximal, Sylow
336C22×C53—21no—
337C22×C53—21no—
338C22×C53—23no—
339C22×C53—23no—
340C22×C53—23no—
341C22×C53C2×#13112yescomplemented
342C22×C53C24×C411yescharacteristic
343C2×D53—21no—
344C2×D53—23no—
345C2×D53—23no—
346C2×D53—21no—
347C2×D53—23no—
348C2×D53—23no—
349C2×D53—23no—
350C2×D53—412no—
351C2×D53—412no—
352C2×D53C2×C4×D416yes—
353C2×D53C2×#13112yescomplemented
354C4×C53—21no—
355C4×C53—23no—
356C4×C53—23no—
357C4×C53—21no—
358C4×C53C2×C4×D416yes—
359Dic53—23no—
360Dic53—21no—
361Dic53—23no—
362Dic53C2×#13112yescomplemented
363Dic53C23×D411yescharacteristic
364Dic53C22×#4111yescharacteristic
365C22×#131—531no—
366C22×#131—531no—
367D4×#41—531no—
368#2935—533no—
369D4×M16—533no—
370#2933—533no—
371#2933—533no—
372#2931—533no—
373#2929—533no—
374#2929—533no—
375C2×C8×D4—533no—
376#2906—531no—
377#2880—531no—
378#2880—531no—
379C4×#131—531no—
380C2×C53—22no—
381C2×C53—43no—
382C2×C53C22×C4×D411yescharacteristic
383C2×C53C22×#13111yescharacteristic
384C2×C53#357311yescharacteristic
385D53—22no—
386D53—26no—
387D53—43no—
388C22×#41—531no—
389C22×#41—531no—
390C2×#131—531no—
391C2×#131—531no—
392C2×#131—531no—
393C2×#131—531no—
394C2×#131—533no—
395C2×#131—533no—
396C2×#131—533no—
397C2×#131—533no—
398C2×#131—1068no—
399C2×#131—1068no—
400C22×M16—533no—
401C22×M16—533no—
402C23×C8—533no—
403C23×C8—533no—
404#550—531no—
405D4×Q8—531no—
406#548—531no—
407#548#615711yescharacteristic
408#547—533no—
409#546—533no—
410#546—533no—
411D42—533no—
412#532—533no—
413#525—533no—
414#525—533no—
415C4×#41—531no—
416C2×C4×D4—533no—
417#436—536no—
418#436—536no—
419#435—536no—
420#435—536no—
421#435—536no—
422#435—536no—
423C8×D4—531no—
424C8×D4—533no—
425C8×D4—533no—
426C8×D4—533no—
427C8×D4—533no—
428C8×D4—533no—
429C8×D4—533no—
430C8×D4—533no—
431C8×D4—536no—
432#424—533no—
433#424—533no—
434#423—533no—
435C2×C4⋊C8—533no—
436#408—533no—
437#408—533no—
438#408—533no—
439#408—533no—
440#407—533no—
441#407—533no—
442C2×C22⋊C8—533no—
443C2×C22⋊C8—533no—
444#405—533no—
445#405—533no—
446C4×M16—533no—
447C2×C4×C8—533no—
448C53D4×#13111yescharacteristic, complemented, Sylow
449C2×#41—531no—
450C2×#41—533no—
451C2×#41—533no—
452C2×#41—531no—
453C2×#41—533no—
454C2×#41—533no—
455C2×#41—1064no—
456C2×#41—1064no—
457C2×#41—1064no—
458C2×#41—1064no—
459C2×#41C2×#615711yescharacteristic
460C22×Q8—531no—
461C22×Q8C2×#615711yescharacteristic
462C22×D4—533no—
463C22×D4—533no—
464C22×D4—533no—
465C23×C4—533no—
466C23×C4—533no—
467#131—538no—
468#131—10612no—
469#131—10612no—
470#131—10612no—
471#131—10612no—
472#131—1064no—
473#131—1064no—
474#131—1064no—
475C2×M16—533no—
476C2×M16—533no—
477C2×M16—533no—
478C2×M16—536no—
479C2×M16—536no—
480C2×M16—533no—
481C2×M16—10612no—
482C2×M16—10612no—
483C22×C8—533no—
484C22×C8—531no—
485C22×C8—531no—
486C22×C8—533no—
487C22×C8—533no—
488C22×C8—533no—
489C22×C8—533no—
490C22×C8—533no—
491C22×C8—533no—
492C22×C8—533no—
493C22×C8—533no—
494C22×C8—533no—
495C22×C8—10612no—
496C22×C8—10612no—
497C4⋊Q8—533no—
498#127—533no—
499#124—533no—
500#124C2×#615713yes—
501#123—536no—
502#123—536no—
503C22⋊Q8—533no—
504C22⋊Q8—533no—
505C22⋊Q8—533no—
506C22⋊Q8C2×#615713yes—
507#121—533no—
508#121—533no—
509#121—533no—
510#121—536no—
511#121—536no—
512#121C2×#615713yes—
513#120—536no—
514#120—536no—
515C4×Q8—531no—
516C4×Q8C2×#615711yescharacteristic
517C4×D4—533no—
518C4×D4—533no—
519C4×D4—533no—
520C4×D4—533no—
521C4×D4—533no—
522C4×D4—531no—
523C4×D4—533no—
524C4×D4—536no—
525C4×D4—533no—
526C4×D4—533no—
527C4×D4C2×#615713yes—
528#117—533no—
529C2×C4⋊C4—533no—
530C2×C22⋊C4—533no—
531C2×C22⋊C4—533no—
532C2×C42—533no—
533C4⋊C8—531no—
534C4⋊C8—533no—
535C4⋊C8—533no—
536C4⋊C8—533no—
537C4⋊C8—536no—
538C22⋊C8—531no—
539C22⋊C8—531no—
540C22⋊C8—533no—
541C22⋊C8—533no—
542C22⋊C8—533no—
543C22⋊C8—533no—
544C22⋊C8—533no—
545C22⋊C8—533no—
546C22⋊C8—536no—
547C22⋊C8—536no—
548#97—536no—
549C4×C8—531no—
550C4×C8—533no—
551C4×C8—533no—
552C4×C8—533no—
553C24—533no—
554C24—533no—
555#41—24no—
556#41—534no—
557#41—534no—
558#41—10612no—
559#41—1066no—
560#41—1066no—
561#41—1066no—
562#41—1066no—
563#41—10612no—
564#41—1064no—
565C2×Q8—24no—
566C2×Q8—533no—
567C2×Q8—1064no—
568C2×Q8C22×#615713yes—
569C2×Q8C22×#615711yescharacteristic
570C2×D4—531no—
571C2×D4—533no—
572C2×D4—536no—
573C2×D4—536no—
574C2×D4—533no—
575C2×D4—533no—
576C2×D4—536no—
577C2×D4—533no—
578C2×D4—10612no—
579C2×D4—10612no—
580C2×D4—10612no—
581C2×D4C22×#615713yes—
582C2×D4C22×#615713yes—
583C22×C4—533no—
584C22×C4—531no—
585C22×C4—533no—
586C22×C4—533no—
587C22×C4—533no—
588C22×C4—533no—
589C22×C4—533no—
590C22×C4—533no—
591C22×C4—531no—
592C22×C4—533no—
593C22×C4—533no—
594C22×C4—1066no—
595C22×C4—1066no—
596C22×C4—1066no—
597C22×C4—1066no—
598C22×C4C22×#615713yes—
599C22×C4C22×#615713yes—
600M16—5312no—
601M16—10612no—
602M16—10612no—
603M16—1066no—
604M16—1066no—
605M16—1066no—
606C2×C8—531no—
607C2×C8—533no—
608C2×C8—5312no—
609C2×C8—531no—
610C2×C8—533no—
611C2×C8—531no—
612C2×C8—531no—
613C2×C8—533no—
614C2×C8—533no—
615C2×C8—1062no—
616C2×C8—1066no—
617C2×C8—1066no—
618C2×C8—1066no—
619C2×C8—1062no—
620C2×C8—1066no—
621C2×C8—1066no—
622C2×C8—1066no—
623C2×C8—1066no—
624C2×C8—1066no—
625C2×C8—1066no—
626C4⋊C4—531no—
627C4⋊C4—533no—
628C4⋊C4—533no—
629C4⋊C4—533no—
630C4⋊C4—536no—
631C4⋊C4C22×#615713yes—
632C4⋊C4C22×#615713yes—
633C22⋊C4—533no—
634C22⋊C4—533no—
635C22⋊C4—531no—
636C22⋊C4—533no—
637C22⋊C4—533no—
638C22⋊C4—533no—
639C22⋊C4—536no—
640C22⋊C4—536no—
641C22⋊C4C22×#615711yescharacteristic
642C22⋊C4C22×#615713yes—
643C22⋊C4C22×#615716yes—
644C42—531no—
645C42—533no—
646C42—533no—
647C42C22×#615713yes—
648C23—531no—
649C23—533no—
650C23—533no—
651C23—1066no—
652C23—1066no—
653C23—1066no—
654C23—1066no—
655C23—2123no—
656C23—2123no—
657C23C23×#615713yes—
658C23C23×#615711yescharacteristic
659Q8—26no—
660Q8—1066no—
661Q8D4×#615714yes—
662D4—26no—
663D4—26no—
664D4—534no—
665D4—5312no—
666D4—1066no—
667D4—10612no—
668D4—1066no—
669D4—10612no—
670D4—1066no—
671D4—2126no—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—531no—
675C2×C4—531no—
676C2×C4—536no—
677C2×C4—536no—
678C2×C4—533no—
679C2×C4—531no—
680C2×C4—533no—
681C2×C4—1061no—
682C2×C4—1063no—
683C2×C4—1061no—
684C2×C4—1063no—
685C2×C4—1066no—
686C2×C4—1066no—
687C2×C4—1066no—
688C2×C4—1061no—
689C2×C4—1063no—
690C2×C4—1061no—
691C2×C4—1063no—
692C2×C4—1066no—
693C2×C4—1066no—
694C2×C4—2123no—
695C2×C4C23×#615711yescharacteristic
696C2×C4C23×#615713yes—
697C2×C4C23×#615711yescharacteristic
698C2×C4C23×#615713yes—
699C2×C4C23×#615713yes—
700C8—532no—
701C8—536no—
702C8—1061no—
703C8—1061no—
704C8—1061no—
705C8—1063no—
706C8—1063no—
707C8—1063no—
708C22—21no—
709C22—21no—
710C22—23no—
711C22—23no—
712C22—23no—
713C22—536no—
714C22—532no—
715C22—1061no—
716C22—1063no—
717C22—1063no—
718C22—1061no—
719C22—1063no—
720C22—1063no—
721C22—1063no—
722C22—21212no—
723C22—21212no—
724C22D53⋊#13112yescomplemented
725C22C24×#615711yescharacteristic
726C4—21no—
727C4—23no—
728C4—23no—
729C4—21no—
730C4—531no—
731C4—531no—
732C4—532no—
733C4—1061no—
734C4—1063no—
735C4—1063no—
736C4C2×D4×#615716yes—
737C2—22no—
738C2—43no—
739C2—1062no—
740C2—1066no—
741C2—2123no—
742C2C22×D4×#615711yescharacteristic
743C2C2×D53⋊#13111yescharacteristic
744C2#2029171111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6157
commutator, socleC22×C53C24×C4
FittingC53×#548C4
prime radical#20288204C2
cosocleC2×Dic53C25
hypercenter#548#6157
hypocenterC53D4×#131
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C22×#13133305C2semidirect
2. C2×D53⋊#131C2semidirect
3. #20291460C2semidirect
4. #20291454C2semidirect
5. #20291450C2semidirect
6. #20291445C2semidirect
7. #20291439C2semidirect
8. #20291431C2semidirect
9. #20291429C2semidirect
10. D4×D53⋊C8C2semidirect
11. #20291363C2semidirect
12. #20291306C2semidirect
13. #20291304C2semidirect
14. C4×#13133305C2semidirect
21. C2×#13133305C22semidirect
22. C2×#13133305C22semidirect
24. C2×#13133304C22semidirect
25. C2×#13133304C22semidirect
26. C22×#11719936C22semidirect
27. C2×D53⋊M16C22semidirect
28. C22×D53⋊C8C22semidirect
29. C22×D53⋊C8C22semidirect
30. #16811656C22semidirect
31. #16811656C22semidirect
32. #16811655C22semidirect
33. #16811654C22semidirect
34. #16811653C22semidirect
35. #16811652C22semidirect
36. #16811651C22semidirect
37. #16811651C22semidirect
40. #16811650C22semidirect
41. #16811650C22semidirect
42. #16811650C22semidirect
43. D4×#88324C22semidirect
44. D4×#88324C22semidirect
45. #16811630C22semidirect
46. #16811630C22semidirect
47. #16811628C22semidirect
48. D53⋊(C4⋊C8)C22semidirect
49. #16811598C22semidirect
50. #16811598C22semidirect
51. #16811597C22semidirect
52. #16811597C22semidirect
53. #16811594C22semidirect
54. #16811594C22semidirect
55. D53⋊(C22⋊C8)C22semidirect
56. D53⋊(C22⋊C8)C22semidirect
57. #16811588C22semidirect
58. #16811588C22semidirect
59. C4×#11719936C22semidirect
60. C4×D53⋊C8C22semidirect
81. #13133305D4semidirect
244. #11719936C2×D4semidirect
252. D53⋊C8C2×D4semidirect
300. C22⋊D53#131semidirect
341. C22×C53C2×#131semidirect
353. C2×D53C2×#131semidirect
362. Dic53C2×#131semidirect
448. C53D4×#131semidirect
724. C22D53⋊#131semidirect

Maximal subgroups

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

subgroupindex
C22×#131333052
C2×D53⋊#1312
#202914602
#202914542
#202914502
#202914452
#202914392
#202914312
#202914292
D4×D53⋊C82
#202913632
#202913062
#202913042
C4×#131333052
#202882042
D4×#13153