Finite Group Databasebeta

← #28248080

Subgroups — #28248080

Order 13568.

2742 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
1C2×#16811390C211yesmaximal, characteristic, complemented
2C2×#16811388C211yesmaximal, characteristic, complemented
3#41×C22⋊D53C211yesmaximal, characteristic
4#20283455C213yesmaximal, complemented
5#20283447C213yesmaximal, complemented
6#20283445C213yesmaximal, complemented
7#20283436C213yesmaximal, complemented
8#20283423C213yesmaximal, complemented
9#20283421C213yesmaximal, complemented
10#20283414C213yesmaximal, complemented
11C2×#16810698C213yesmaximal, complemented
12#20283281C211yesmaximal, characteristic, complemented
13#20283162C211yesmaximal, characteristic, complemented
14#131×Dic53C211yesmaximal, characteristic, complemented
15C53×#2880C211yesmaximal, characteristic, complemented
16C2×#41×D53C2211yescharacteristic
17#16811390—28no—
18#16811388—28no—
19C2×#13133225C2213yescomplemented
20C2×#13133224C2211yescharacteristic
21C2×#13133224C2211yescharacteristic
22C2×#13133224C2213yescomplemented
23C2×#13133224C2213yescomplemented
24C2×#13133223C2213yescomplemented
25C22×#11719917C2213yescomplemented
26C22×#11719917C2213yescomplemented
27C22×#11719912C2213yescomplemented
28C2×M16×D53C2213yescomplemented
29#16811292C411yescharacteristic
30Q8×C22⋊D53C411yescharacteristic
31#16811284C411yescharacteristic
32#16811280C411yescharacteristic
33#16811272C413yes—
34#16811267C413yes—
35#16811261C413yes—
36D4×C22⋊D53C413yes—
37#16811169C2213yes—
38#16811134C2213yes—
39#16811130C2213yes—
40#41×Dic53C2211yescharacteristic
41C2×C4×C22⋊D53C2213yes—
42#16810698C2211yescharacteristic
43#16810698C2213yes—
44#16810698C2213yescomplemented
45#16810698C2213yescomplemented
46#16810698C2213yescomplemented
47#16810698C2213yescomplemented
48#16810698C2213yescomplemented
49#16810698C2213yescomplemented
50#16810698C2216yescomplemented
51#16810697C2216yescomplemented
52#16810697C2216yescomplemented
53#16810691C2216yescomplemented
54#16810691C2216yescomplemented
55#16810686C2216yescomplemented
56#16810686C2216yescomplemented
57#16810651C2213yescomplemented
58#16810649C2213yescomplemented
59#16810646C2213yescomplemented
60C2×#13133146C2213yescomplemented
61#16810591C2213yescomplemented
62#16810589C2213yescomplemented
63#16810586C2213yescomplemented
64C2×#13133129C2213yescomplemented
65#16810581C2213yescomplemented
66#16810578C2213yescomplemented
67M16×Dic53C2213yescomplemented
68C2×C8×Dic53C2213yescomplemented
69C22×#41×C53C2211yescharacteristic
70C2×#131×C53C2211yescharacteristic
71C2×#131×C53C2211yescharacteristic
72C53×#408C2213yescomplemented
73C53×#408C2213yescomplemented
74C53×#407C2213yescomplemented
75C2×C22⋊C8×C53C2213yescomplemented
76C2×#11719949C2×C411yescharacteristic
77C2×#11719945C2313yes—
78C2×#11719947C2×C413yes—
79#41×D53—24no—
80#41×D53—24no—
81C2×Q8×D53C2×C411yescharacteristic
82C22×C22⋊D53C2×C413yes—
83C2×D4×D53C2×C413yes—
84C22×C4×D53C2313yes—
85#13133225—212no—
86#13133224—212no—
87#13133224—212no—
88#13133224—24no—
89#13133224D418yescomplemented
90#13133223—212no—
91C2×#11719917—212no—
92C2×#11719917—212no—
93C2×#11719917C2313yes—
94C2×#11719917C2313yes—
95C2×#11719917C2311yescharacteristic
96C2×#11719917C2313yes—
97C2×#11719917C2313yes—
98C2×#11719917C2313yes—
99C2×#11719912—212no—
100C2×#11719912C2313yes—
101C2×#11719912C2311yescharacteristic
102C2×#11719912C2313yes—
103C2×#11719912C2313yes—
104M16×D53—212no—
105C22×#88322C2313yes—
106C22×#88322C2316yes—
107C22×#88322C2313yes—
108C2×C8×D53C2316yes—
109#13133215C2×C413yes—
110#13133213C2×C413yes—
111#13133206C2×C413yes—
112#13133204C2×C413yes—
113#13133200C2×C416yes—
114#13133198C2×C416yes—
115#13133196C2×C413yes—
116#13133196C2×C413yes—
117#13133193C2×C413yes—
118#13133193C2×C413yes—
119#13133191C2×C413yes—
120#13133191C2×C413yes—
121#13133189C2×C416yes—
122#13133189C2×C416yes—
123#13133188C2×C413yes—
124#13133188C2×C413yes—
125#13133186C2×C416yes—
126#13133185C2×C416yes—
127Q8×Dic53C2×C411yescharacteristic
128Q8×Dic53C2×C411yescharacteristic
129D4×Dic53C2×C413yes—
130D4×Dic53C2×C413yes—
131C4×C22⋊D53C2×C413yes—
132C4×C22⋊D53C2×C413yes—
133C4×C22⋊D53C2×C413yes—
134C4×C22⋊D53C2×C413yes—
135C4×C22⋊D53C2311yescharacteristic
136C4×C22⋊D53C2313yes—
137C4×C22⋊D53C2313yes—
138C4×C22⋊D53C2313yes—
139C4×C22⋊D53C2316yes—
140#13133176C2313yes—
141C2×#11719919C2×C413yes—
142C2×C22⋊Dic53C2×C413yes—
143C2×#11719921C2×C413yes—
144C2×C4×Dic53C2313yes—
145#13133146C2311yescharacteristic
146#13133146C2313yes—
147#13133146C2313yes—
148#13133146C2313yes—
149#13133146C2316yes—
150#13133129C2311yescharacteristic
151#13133129C2313yes—
152#13133129C2313yes—
153#13133129C2313yes—
154#13133129C2316yes—
155#13133127C2316yes—
156C8×Dic53C2311yescharacteristic
157C8×Dic53C2313yes—
158C8×Dic53C2313yes—
159C8×Dic53C2313yes—
160C2×#41×C53—24no—
161C2×#41×C53—24no—
162C2×#41×C53C2×C413yes—
163C2×#41×C53C2×C411yescharacteristic
164C2×#41×C53C2313yes—
165C2×#41×C53C2311yescharacteristic
166C22×Q8×C53C2×C411yescharacteristic
167C22×D4×C53C2×C413yes—
168C23×C4×C53C2313yes—
169#131×C53—24no—
170#131×C53—24no—
171C2×M16×C53C2313yes—
172C2×M16×C53C2313yes—
173C22×C8×C53C2313yes—
174C22×C8×C53C2313yes—
175C22⋊C8×C53C2311yescharacteristic
176C22⋊C8×C53C2313yes—
177C22⋊C8×C53C2313yes—
178C22⋊C8×C53C2313yes—
179C22⋊C8×C53C2316yes—
180C24×C53C22×C413yes—
181C23×D53C22×C413yes—
182#41×C53—24no—
183#41×C53—212no—
184#41×C53—26no—
185#41×C53—26no—
186#41×C53C2×D414yes—
187#41×C53#4114yes—
188C2×Q8×C53—24no—
189C2×Q8×C53C22×C413yes—
190C2×Q8×C53C22×C411yescharacteristic
191C2×D4×C53—212no—
192C2×D4×C53C22×C416yes—
193C2×D4×C53C22×C413yes—
194C2×D4×C53C22×C413yes—
195C22×C4×C53—26no—
196C22×C4×C53—26no—
197C22×C4×C53C22×C413yes—
198C22×C4×C53C22×C413yes—
199C22×C4×C53C22×C413yes—
200C22×C4×C53C2411yescharacteristic
201C22×C4×C53C2413yes—
202C22×C4×C53C2413yes—
203C2×C22⋊D53—46no—
204C2×C22⋊D53C22×C411yescharacteristic
205C2×C22⋊D53C22×C413yes—
206C2×C22⋊D53C22×C416yes—
207C2×C22⋊D53C22×C413yes—
208C2×C22⋊D53C22×C413yes—
209C2×C22⋊D53C22×C416yes—
210C22×Dic53C22×C413yes—
211C22×Dic53C22×C413yes—
212C22×Dic53C22×C413yes—
213#11719949—24no—
214Q8×D53—24no—
215#11719947—212no—
216D4×D53—212no—
217#11719945—26no—
218#11719945—26no—
219C2×D212C22×C413yes—
220C2×C4×D53—26no—
221C2×C4×D53—26no—
222C2×C4×D53C22×C413yes—
223C2×C4×D53C22×C413yes—
224C2×C4×D53C2413yes—
225C2×C4×D53C2411yescharacteristic
226C2×Dic106C22×C413yes—
227M16×C53—26no—
228M16×C53—26no—
229C2×C8×C53—26no—
230C2×C8×C53—26no—
231C2×C8×C53C2411yescharacteristic
232C2×C8×C53C2411yescharacteristic
233C2×C8×C53C2413yes—
234C2×C8×C53C2413yes—
235C22⋊Dic53C22×C411yescharacteristic
236C22⋊Dic53C22×C413yes—
237C22⋊Dic53C22×C413yes—
238C22⋊Dic53C22×C413yes—
239C22⋊Dic53C22×C416yes—
240C22⋊Dic53C22×C416yes—
241#11719921C22×C411yescharacteristic
242#11719921C22×C413yes—
243#11719921C22×C413yes—
244#11719921C22×C413yes—
245#11719921C22×C416yes—
246C4⋊Dic53C22×C413yes—
247C4⋊Dic53C22×C413yes—
248#11719919C22×C411yescharacteristic
249#11719919C22×C413yes—
250#11719919C22×C413yes—
251#11719919C22×C413yes—
252#11719919C22×C416yes—
253C4×Dic53C22×C413yes—
254C4×Dic53C22×C413yes—
255C4×Dic53C2411yescharacteristic
256C4×Dic53C2413yes—
257#11719917—26no—
258#11719917—26no—
259#11719917—22no—
260#11719917—26no—
261#11719917—26no—
262#11719917C2×D4112yescomplemented
263C2×#88322—26no—
264C2×#88322—212no—
265C2×#88322C2×D4112yescomplemented
266C2×#88322C2411yescharacteristic
267C2×#88322C2413yes—
268C2×#88322C2411yescharacteristic
269C2×#88322C2413yes—
270#11719912—26no—
271#11719912—22no—
272#11719912—26no—
273#11719912—26no—
274C8×D53—212no—
275C23×C53—26no—
276C23×C53—43no—
277C23×C53—43no—
278C23×C53C23×C411yescharacteristic
279C23×C53C23×C413yes—
280C23×C53C23×C413yes—
281C22×D53—26no—
282C22×D53—43no—
283C22×D53—43no—
284C22×D53C23×C411yescharacteristic
285C22×D53C23×C413yes—
286Q8×C53—26no—
287Q8×C53C4×D414yes—
288D4×C53—212no—
289D4×C53—26no—
290D4×C53C4×D4112yes—
291C2×C4×C53—26no—
292C2×C4×C53—26no—
293C2×C4×C53—26no—
294C2×C4×C53—21no—
295C2×C4×C53—23no—
296C2×C4×C53—21no—
297C2×C4×C53—23no—
298C2×C4×C53C23×C411yescharacteristic
299C2×C4×C53C23×C413yes—
300C2×C4×C53C23×C413yes—
301C2×C4×C53C22×D416yes—
302C2×C4×C53C2×#4116yes—
303C2×C4×C53C2511yescharacteristic
304C22⋊D53—212no—
305C22⋊D53—22no—
306C22⋊D53—26no—
307C22⋊D53—43no—
308C22⋊D53—43no—
309C22⋊D53—46no—
310C2×Dic53—26no—
311C2×Dic53—26no—
312C2×Dic53—43no—
313C2×Dic53C23×C413yes—
314C2×Dic53C23×C411yescharacteristic
315C2×Dic53C23×C411yescharacteristic
316C2×Dic53C23×C413yes—
317C2×Dic53C23×C413yes—
318C2×Dic53C23×C411yescharacteristic
319D212—26no—
320C4×D53—26no—
321C4×D53—26no—
322C4×D53—21no—
323C4×D53—23no—
324C4×D53—21no—
325C4×D53—23no—
326Dic106—26no—
327C8×C53—23no—
328C8×C53—21no—
329C8×C53—21no—
330C8×C53—23no—
331#88322—21no—
332#88322—23no—
333#88322C22×D416yes—
334#88322C22×D412yes—
335#60147—531nomaximal, Sylow
336C22×C53—23no—
337C22×C53—23no—
338C22×C53—21no—
339C22×C53—23no—
340C22×C53—21no—
341C22×C53—23no—
342C22×C53—23no—
343C22×C53—21no—
344C22×C53—86no—
345C22×C53C2×C4×D416yes—
346C22×C53C24×C411yescharacteristic
347C2×D53—21no—
348C2×D53—23no—
349C2×D53—21no—
350C2×D53—23no—
351C2×D53—23no—
352C2×D53—21no—
353C2×D53—86no—
354C4×C53—21no—
355C4×C53—23no—
356C4×C53C2×C4×D416yes—
357C4×C53C23×D411yescharacteristic
358C4×C53C22×#4111yescharacteristic
359Dic53—23no—
360Dic53—21no—
361Dic53—23no—
362Dic53—21no—
363Dic53—23no—
364Dic53#56812yescomplemented
365C2×#568—531no—
366C2×#568—531no—
367D4×#41—531no—
368#2935—533no—
369D4×M16—533no—
370#2933—533no—
371#2933—533no—
372#2931—533no—
373#2930—533no—
374#2930—533no—
375C2×#436—533no—
376#2906—531no—
377#2880—531no—
378#2880D5311yescharacteristic, complemented
379C4×#131—531no—
380C2×C53—26no—
381C2×C53—43no—
382C2×C53—41no—
383C2×C53C22×C4×D411yescharacteristic
384C2×C53C2×#56811yescharacteristic
385C2×C53#357311yescharacteristic
386D53—43no—
387D53—41no—
388C22×#41—531no—
389C22×#41C2×D5311yescharacteristic
390#568—1068no—
391#568—1068no—
392C2×#131—531no—
393C2×#131—531no—
394C2×#131—533no—
395C2×#131—533no—
396C2×#131—533no—
397C2×#131—533no—
398C2×#131C2×D5311yescharacteristic
399C2×#131C2×D5311yescharacteristic
400C22×M16—533no—
401C22×M16—533no—
402C22×M16—533no—
403C22×M16—533no—
404#550—531no—
405D4×Q8—531no—
406#548—531no—
407#548—531no—
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—531no—
418#436—533no—
419#436—533no—
420#436—533no—
421#436—533no—
422#436—533no—
423#436—533no—
424#436—533no—
425#436—536no—
426#435—536no—
427#435—536no—
428#435—536no—
429#435—536no—
430C8×D4—536no—
431C8×D4—536no—
432#424—533no—
433#424—533no—
434#423—533no—
435C2×C4⋊C8—533no—
436#408—533no—
437#408—533no—
438#408C2×D5313yescomplemented
439#408C2×D5313yescomplemented
440#407—533no—
441#407C2×D5313yescomplemented
442C2×C22⋊C8—533no—
443C2×C22⋊C8C2×D5313yescomplemented
444#405—533no—
445#405—533no—
446C4×M16—533no—
447C2×C4×C8—533no—
448C53#6014711yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—531no—
452C2×#41—533no—
453C2×#41—533no—
454C2×#41—1064no—
455C2×#41—1064no—
456C2×#41C4×D5313yes—
457C2×#41C4×D5311yescharacteristic
458C2×#41C22×D5313yes—
459C2×#41C22×D5311yescharacteristic
460C22×Q8—531no—
461C22×Q8C4×D5311yescharacteristic
462C22×D4—533no—
463C22×D4—533no—
464C22×D4C4×D5313yes—
465C23×C4—533no—
466C23×C4C22×D5313yes—
467#131—24no—
468#131—24no—
469#131—538no—
470#131—10612no—
471#131—10612no—
472#131—10612no—
473#131—10612no—
474#131—1064no—
475C2×M16—533no—
476C2×M16—533no—
477C2×M16—531no—
478C2×M16—533no—
479C2×M16—533no—
480C2×M16—533no—
481C2×M16—533no—
482C2×M16—531no—
483C2×M16—533no—
484C2×M16—533no—
485C2×M16—10612no—
486C2×M16—10612no—
487C2×M16—10612no—
488C2×M16—10612no—
489C2×M16C22×D5313yes—
490C2×M16C22×D5313yes—
491C22×C8—533no—
492C22×C8—533no—
493C22×C8—536no—
494C22×C8—536no—
495C22×C8C22×D5313yes—
496C22×C8C22×D5313yes—
497C4⋊Q8—533no—
498#127—533no—
499#124—533no—
500#124—533no—
501#123—536no—
502#123—536no—
503C22⋊Q8—533no—
504C22⋊Q8—533no—
505C22⋊Q8—533no—
506C22⋊Q8—533no—
507#121—533no—
508#121—533no—
509#121—536no—
510#121—536no—
511#121—533no—
512#121—533no—
513#120—536no—
514#120—536no—
515C4×Q8—531no—
516C4×Q8—531no—
517C4×D4—533no—
518C4×D4—533no—
519C4×D4—533no—
520C4×D4—533no—
521C4×D4—533no—
522C4×D4—533no—
523C4×D4—531no—
524C4×D4—533no—
525C4×D4—533no—
526C4×D4—533no—
527C4×D4—536no—
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—533no—
540C22⋊C8—533no—
541C22⋊C8—533no—
542C22⋊C8—536no—
543C22⋊C8C22×D5311yescharacteristic
544C22⋊C8C22×D5313yes—
545C22⋊C8C22×D5313yes—
546C22⋊C8C22×D5313yes—
547C22⋊C8C22×D5316yes—
548#97—536no—
549C4×C8—531no—
550C4×C8—533no—
551C4×C8—533no—
552C4×C8—533no—
553C24—533no—
554C24C2×C4×D5313yes—
555#41—24no—
556#41—212no—
557#41—26no—
558#41—26no—
559#41—1064no—
560#41—10612no—
561#41—1066no—
562#41—1066no—
563#41D4×D5314yes—
564#41#1171994714yes—
565C2×Q8—24no—
566C2×Q8—533no—
567C2×Q8—1064no—
568C2×Q8C2×C4×D5313yes—
569C2×Q8C2×C4×D5311yescharacteristic
570C2×D4—212no—
571C2×D4—531no—
572C2×D4—533no—
573C2×D4—536no—
574C2×D4—533no—
575C2×D4—533no—
576C2×D4—536no—
577C2×D4—533no—
578C2×D4—10612no—
579C2×D4—2126no—
580C2×D4C2×C4×D5316yes—
581C2×D4C2×C4×D5313yes—
582C2×D4C2×C4×D5313yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—533no—
586C22×C4—533no—
587C22×C4—533no—
588C22×C4—533no—
589C22×C4—533no—
590C22×C4—533no—
591C22×C4—531no—
592C22×C4—1066no—
593C22×C4—1066no—
594C22×C4C2×C4×D5313yes—
595C22×C4C2×C4×D5313yes—
596C22×C4C2×C4×D5313yes—
597C22×C4C23×D5313yes—
598C22×C4C23×D5311yescharacteristic
599C22×C4C23×D5313yes—
600M16—26no—
601M16—26no—
602M16—5312no—
603M16—1062no—
604M16—1066no—
605M16—1066no—
606M16—1066no—
607M16—1062no—
608M16—1066no—
609M16—1066no—
610M16—1066no—
611M16—1066no—
612C2×C8—26no—
613C2×C8—26no—
614C2×C8—5312no—
615C2×C8—531no—
616C2×C8—533no—
617C2×C8—531no—
618C2×C8—533no—
619C2×C8—10612no—
620C2×C8—10612no—
621C2×C8—1066no—
622C2×C8C23×D5311yescharacteristic
623C2×C8C23×D5313yes—
624C2×C8C23×D5313yes—
625C2×C8C23×D5311yescharacteristic
626C4⋊C4—531no—
627C4⋊C4—533no—
628C4⋊C4—533no—
629C4⋊C4—533no—
630C4⋊C4—533no—
631C4⋊C4—533no—
632C4⋊C4—536no—
633C22⋊C4—531no—
634C22⋊C4—533no—
635C22⋊C4—533no—
636C22⋊C4—533no—
637C22⋊C4—536no—
638C22⋊C4—536no—
639C22⋊C4—531no—
640C22⋊C4—533no—
641C22⋊C4—533no—
642C22⋊C4—533no—
643C22⋊C4—536no—
644C42—533no—
645C42—533no—
646C42—531no—
647C42—533no—
648C23—26no—
649C23—43no—
650C23—43no—
651C23—531no—
652C23—533no—
653C23—1066no—
654C23—2123no—
655C23—2123no—
656C23C22×C4×D5311yescharacteristic
657C23C22×C4×D5313yes—
658C23C22×C4×D5313yes—
659Q8—26no—
660Q8—1066no—
661Q8#1313317714yes—
662D4—212no—
663D4—26no—
664D4—1066no—
665D4—1062no—
666D4—10612no—
667D4—1066no—
668D4—2126no—
669D4—2123no—
670D4—2123no—
671D4#13133177112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—23no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—23no—
679C2×C4—531no—
680C2×C4—531no—
681C2×C4—533no—
682C2×C4—533no—
683C2×C4—531no—
684C2×C4—533no—
685C2×C4—1066no—
686C2×C4—1066no—
687C2×C4—1066no—
688C2×C4—1066no—
689C2×C4—1063no—
690C2×C4—1061no—
691C2×C4—1061no—
692C2×C4—1063no—
693C2×C4—2123no—
694C2×C4C22×C4×D5311yescharacteristic
695C2×C4C22×C4×D5313yes—
696C2×C4C22×C4×D5313yes—
697C2×C4C2×D4×D5316yes—
698C2×C4C2×#1171994716yes—
699C2×C4C24×D5311yescharacteristic
700C8—21no—
701C8—23no—
702C8—21no—
703C8—23no—
704C8—532no—
705C8—536no—
706C8—1063no—
707C8—1061no—
708C22—23no—
709C22—23no—
710C22—21no—
711C22—23no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—86no—
717C22—1061no—
718C22—1063no—
719C22—1061no—
720C22—1063no—
721C22—1063no—
722C22—1061no—
723C22—4246no—
724C22C2×#1313317716yes—
725C22C23×C4×D5311yescharacteristic
726C4—21no—
727C4—23no—
728C4—532no—
729C4—1061no—
730C4—1063no—
731C4—1063no—
732C4—1061no—
733C4—1063no—
734C4C2×#1313317716yes—
735C4C22×D4×D5311yescharacteristic
736C4C22×#1171994711yescharacteristic
737C2—26no—
738C2—41no—
739C2—43no—
740C2—2121no—
741C2—2123no—
742C2C22×#1313317711yescharacteristic
743C2#568×D5311yescharacteristic
744C2#2028942611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D53
commutator, socleC22×C53C24×C4
FittingC53×#2880C2
prime radical#41×C22⋊D53C2
cosocleC2×C4×C53C25
hypercenter#2880D53
hypocenterC53#60147
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. C2×#16811390C2semidirect
2. C2×#16811388C2semidirect
4. #20283455C2semidirect
5. #20283447C2semidirect
6. #20283445C2semidirect
7. #20283436C2semidirect
8. #20283423C2semidirect
9. #20283421C2semidirect
10. #20283414C2semidirect
11. C2×#16810698C2semidirect
12. #20283281C2semidirect
13. #20283162C2semidirect
14. #131×Dic53C2semidirect
15. C53×#2880C2semidirect
19. C2×#13133225C22semidirect
22. C2×#13133224C22semidirect
23. C2×#13133224C22semidirect
24. C2×#13133223C22semidirect
25. C22×#11719917C22semidirect
26. C22×#11719917C22semidirect
27. C22×#11719912C22semidirect
28. C2×M16×D53C22semidirect
44. #16810698C22semidirect
45. #16810698C22semidirect
46. #16810698C22semidirect
47. #16810698C22semidirect
48. #16810698C22semidirect
49. #16810698C22semidirect
50. #16810698C22semidirect
51. #16810697C22semidirect
52. #16810697C22semidirect
53. #16810691C22semidirect
54. #16810691C22semidirect
55. #16810686C22semidirect
56. #16810686C22semidirect
57. #16810651C22semidirect
58. #16810649C22semidirect
59. #16810646C22semidirect
60. C2×#13133146C22semidirect
61. #16810591C22semidirect
62. #16810589C22semidirect
63. #16810586C22semidirect
64. C2×#13133129C22semidirect
65. #16810581C22semidirect
66. #16810578C22semidirect
67. M16×Dic53C22semidirect
68. C2×C8×Dic53C22semidirect
72. C53×#408C22semidirect
73. C53×#408C22semidirect
74. C53×#407C22semidirect
75. C2×C22⋊C8×C53C22semidirect
89. #13133224D4semidirect
262. #11719917C2×D4semidirect
265. C2×#88322C2×D4semidirect
364. Dic53#568semidirect
378. #2880D53semidirect
438. #408C2×D53semidirect
439. #408C2×D53semidirect
441. #407C2×D53semidirect
443. C2×C22⋊C8C2×D53semidirect
448. C53#60147semidirect

Maximal subgroups

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

subgroupindex
C2×#168113902
C2×#168113882
#41×C22⋊D532
#202834552
#202834472
#202834452
#202834362
#202834232
#202834212
#202834142
C2×#168106982
#202832812
#202831622
#131×Dic532
C53×#28802
#6014753