Finite Group Databasebeta

← #27102349

Subgroups — #27102349

Order 12032.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257615C211yesmaximal, characteristic, complemented
2#20255469C212yesmaximal, complemented
3#20255349C212yesmaximal, complemented
4#20255212C212yesmaximal, complemented
5#20255201C212yesmaximal, complemented
6#20255091C212yesmaximal, complemented
7#20255069C212yesmaximal, complemented
8#20254879C212yesmaximal, complemented
9#20254864C212yesmaximal, complemented
10#20254482C212yesmaximal, complemented
11#20254240C212yesmaximal, complemented
12#20254165C211yesmaximal, characteristic, complemented
13#20254149C211yesmaximal, characteristic, complemented
14#20253572C212yesmaximal, complemented
15#20252692C212yesmaximal, complemented
16C2×#15689274C211yesmaximal, characteristic, complemented
17C2×#15689257C211yesmaximal, characteristic, complemented
18#20252444C211yesmaximal, characteristic, complemented
19C47×#3484C211yesmaximal, characteristic, complemented
20C2×#13094050C2212yescomplemented
21C2×#13094044C2212yescomplemented
22C22×#10625335C2212yescomplemented
23C22×#10625334C2212yescomplemented
24#15689870—22no—
25#15689830C2212yescomplemented
26#15689782C2212yescomplemented
27#15689777C2212yescomplemented
28#15689769C2212yescomplemented
29#15689760—22no—
30#15689748—21no—
31#15689744C2212yescomplemented
32#15689722—21no—
33#15689710—21no—
34#15689701C2212yescomplemented
35#15689700—21no—
36C2×#13094003C2211yescharacteristic, complemented
37C2×#13093998C2211yescharacteristic, complemented
38#15689510C2212yescomplemented
39#15689505C2212yescomplemented
40#15689482C2212yescomplemented
41#15689469C2212yescomplemented
42#15689464C2212yescomplemented
43#15689456C2211yescharacteristic, complemented
44#15689451C2211yescharacteristic, complemented
45#15689447C2212yescomplemented
46#15689439C2211yescharacteristic, complemented
47#15689439C2212yescomplemented
48#15689434C2211yescharacteristic, complemented
49#15689434C2212yescomplemented
50#15689413C2212yescomplemented
51#15689403C2212yescomplemented
52#15689374C2212yescomplemented
53#15689367C2212yescomplemented
54#15689362C2212yescomplemented
55#15689357C2212yescomplemented
56#15689357C2212yescomplemented
57#15689354C2212yescomplemented
58#15689350C2212yescomplemented
59#15689350C2212yescomplemented
60#15689342C2212yescomplemented
61#15689338C2212yescomplemented
62#15689338C2212yescomplemented
63#15689335C2212yescomplemented
64#15689320C2212yescomplemented
65#15689315C2212yescomplemented
66#15689285C2212yescomplemented
67#15689285C2212yescomplemented
68#15689278C2211yescharacteristic, complemented
69#15689274C2212yescomplemented
70#15689274C2212yescomplemented
71#15689274C2212yescomplemented
72#15689274C2212yescomplemented
73#15689274C2212yescomplemented
74#15689273C2211yescharacteristic, complemented
75#15689268C2212yescomplemented
76#15689268C2212yescomplemented
77#15689266C2212yescomplemented
78#15689266C2212yescomplemented
79#15689261C2211yescharacteristic, complemented
80#15689257C2212yes—
81#15689257C2212yescomplemented
82#15689257C2212yescomplemented
83#15689257C2212yescomplemented
84#15689257C2212yescomplemented
85#15689256C2211yescharacteristic, complemented
86#15689233C2212yescomplemented
87#15689223C2212yescomplemented
88C4×#10625335C2212yescomplemented
89C4×#10625334C2212yescomplemented
90#15689195C2212yescomplemented
91#15689195C2212yescomplemented
92D4×C47⋊C8C2212yescomplemented
93D4×C47⋊C8C2212yescomplemented
94#15689184C2212yescomplemented
95#15689124C2212yescomplemented
96C2×#13093945C2212yescomplemented
97C2×#13093945C2212yescomplemented
98C2×#13093945C2212yescomplemented
99#15689090C2212yescomplemented
100C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
101C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
102C2×H(5,𝔽2)×C47C2211yescharacteristic, complemented
103C23×D4×C47C2211yescharacteristic
104C47×#546—21no—
105C47×#546—21no—
106C47×#546C2212yes—
107C47×#546C2212yescomplemented
108D42×C47—21no—
109D42×C47—21no—
110D42×C47C2212yes—
111D42×C47C2212yescomplemented
112C47×#535C2211yescharacteristic, complemented
113C47×#535C2211yescharacteristic, complemented
114C47×#534—22no—
115C47×#525C2211yescharacteristic
116C47×#525C2211yescharacteristic
117C2×#120×C47—22no—
118C47×#518C2211yescharacteristic, complemented
119C2×#10625350C2312yescomplemented
120C2×#10625352—22no—
121C22×Dic94C2311yescharacteristic
122C22×D188C2311yescharacteristic
123C22×C22⋊D47—21no—
124#13094050—44no—
125#13094044—44no—
126C2×#10625337C2312yescomplemented
127C2×#10625335—44no—
128C2×#10625335C2312yes—
129C2×#10625335C2312yes—
130C2×#10625335C2312yes—
131C2×#10625335C2312yes—
132C2×#10625335C2312yescomplemented
133C2×#10625336C2312yescomplemented
134C2×#10625334—44no—
135C2×#10625334C2312yes—
136C2×#10625334C2312yes—
137C2×#10625334C2312yes—
138C2×#10625334C2312yes—
139C2×#10625334C2312yescomplemented
140C2×#10625329C2312yescomplemented
141C22×C47⋊C8C2312yes—
142C22×C47⋊C8C2312yes—
143C22×C47⋊C8C2312yescomplemented
144#13094024C2312yescomplemented
145#13094019—22no—
146#13094015—22no—
147#13094012C2312yescomplemented
148#13094010—22no—
149#13094010—22no—
150#13094009—22no—
151#13094008—22no—
152#13094008—22no—
153#13094006—22no—
154#13094004—22no—
155#13094003—21no—
156#13094003—21no—
157#13094003C2312yes—
158#13094003C2312yes—
159#13094003C2312yescomplemented
160#13094002—22no—
161#13094002—22no—
162#13094001—22no—
163#13094001—22no—
164#13094000—22no—
165#13093998—21no—
166#13093998—21no—
167#13093998C2312yes—
168#13093998C2312yes—
169#13093998C2312yescomplemented
170#13093997—22no—
171#13093996—22no—
172#13093996—22no—
173#13093996—22no—
174#13093995—22no—
175#13093992—22no—
176C4×Dic94C2312yescomplemented
177C4×D188C2312yescomplemented
178D4×Dic47—22no—
179(C22⋊D47)⋊C4—22no—
180C2×C4⋊Dic47C2311yescharacteristic
181C2×C4⋊Dic47C2311yescharacteristic
182C2×C4⋊Dic47C2312yescomplemented
183C2×Dic47⋊C4—21no—
184C2×C22⋊Dic47—21no—
185C2×(C2×D47)⋊C4—21no—
186C22⋊C4×D47—22no—
187#13093957C2312yescomplemented
188#13093957C2312yescomplemented
189#13093955C2312yescomplemented
190#13093955C2312yescomplemented
191C4⋊(C47⋊C8)C2312yescomplemented
192C4⋊(C47⋊C8)C2312yescomplemented
193#13093948C2312yescomplemented
194#13093948C2312yescomplemented
195#13093947C2312yescomplemented
196#13093947C2312yescomplemented
197#13093945C2312yes—
198#13093945C2312yes—
199#13093945C2312yes—
200#13093945C2312yes—
201#13093945C2312yes—
202#13093945C2312yes—
203#13093945C2312yes—
204#13093945C2312yes—
205#13093945C2312yescomplemented
206#13093945C2312yescomplemented
207#13093944C2312yescomplemented
208#13093944C2312yescomplemented
209C22⋊(C47⋊C8)C2311yescharacteristic
210C22⋊(C47⋊C8)C2312yes—
211C22⋊(C47⋊C8)C2311yescharacteristic
212C22⋊(C47⋊C8)C2311yescharacteristic
213C22⋊(C47⋊C8)C2312yes—
214C22⋊(C47⋊C8)C2311yescharacteristic
215C22⋊(C47⋊C8)C2312yescomplemented
216C22⋊(C47⋊C8)C2312yescomplemented
217#13093935C2312yescomplemented
218C4×C47⋊C8C2312yescomplemented
219C25×C47—21no—
220H(5,𝔽2)×C47—44no—
221C2×#41×C47—21no—
222C2×#41×C47C2312yes—
223C2×#41×C47C2311yescharacteristic
224C2×#41×C47C2311yescharacteristic
225C22×D4×C47—22no—
226C22×D4×C47—21no—
227C22×D4×C47—22no—
228C22×D4×C47—22no—
229C22×D4×C47—21no—
230C22×D4×C47—21no—
231C22×D4×C47—21no—
232C22×D4×C47—44no—
233C22×D4×C47C2311yescharacteristic
234C22×D4×C47C2312yes—
235C22×D4×C47C2312yes—
236C22×D4×C47C2312yes—
237C22×D4×C47C2311yescharacteristic
238C23×C4×C47C2311yescharacteristic
239#127×C47—21no—
240#127×C47C2312yes—
241#124×C47—21no—
242#124×C47C2312yes—
243#123×C47—21no—
244#123×C47—22no—
245#123×C47—22no—
246#123×C47D412yes—
247C22⋊Q8×C47D411yescharacteristic
248C22⋊Q8×C47D411yescharacteristic
249C22⋊Q8×C47C2311yescharacteristic
250C22⋊Q8×C47C2311yescharacteristic
251#121×C47—22no—
252#121×C47—22no—
253#121×C47—21no—
254#121×C47—21no—
255#121×C47—22no—
256#121×C47—22no—
257#121×C47D411yescharacteristic
258#121×C47D411yescharacteristic
259#121×C47C2311yescharacteristic
260#121×C47C2311yescharacteristic
261#121×C47C2312yes—
262#121×C47C2312yes—
263#120×C47—21no—
264#120×C47—22no—
265#120×C47—22no—
266#120×C47—22no—
267#120×C47—22no—
268#120×C47—22no—
269#120×C47—22no—
270#120×C47—22no—
271#120×C47—22no—
272#120×C47D412yes—
273C4×D4×C47—21no—
274C4×D4×C47—21no—
275C4×D4×C47—21no—
276C4×D4×C47—21no—
277C4×D4×C47C2312yes—
278C4×D4×C47C2312yes—
279C4×D4×C47C2312yes—
280C4×D4×C47C2312yes—
281#117×C47C2311yescharacteristic
282#117×C47C2311yescharacteristic
283C2×C22⋊C4×C47—22no—
284C2×C22⋊C4×C47—22no—
285C2×C22⋊C4×C47—22no—
286C24×C47—21no—
287C24×C47—22no—
288C24×C47—22no—
289C24×C47—21no—
290C24×C47—22no—
291C24×C47—44no—
292C24×C47—82no—
293C24×C47—82no—
294C24×C47C2×D411yescharacteristic
295C23×D47—21no—
296#41×C47—24no—
297#41×C47—42no—
298#41×C47—42no—
299#41×C47—42no—
300#41×C47—44no—
301C2×Q8×C47C2×D411yescharacteristic
302C2×Q8×C47C2411yescharacteristic
303C2×D4×C47—24no—
304C2×D4×C47—24no—
305C2×D4×C47—24no—
306C2×D4×C47—24no—
307C2×D4×C47—21no—
308C2×D4×C47—21no—
309C2×D4×C47—21no—
310C2×D4×C47—22no—
311C2×D4×C47—22no—
312C2×D4×C47—22no—
313C2×D4×C47—21no—
314C2×D4×C47—22no—
315C2×D4×C47—22no—
316C2×D4×C47—22no—
317C2×D4×C47—21no—
318C2×D4×C47—22no—
319C2×D4×C47—22no—
320C2×D4×C47—42no—
321C2×D4×C47—42no—
322C2×D4×C47—42no—
323C2×D4×C47—42no—
324C2×D4×C47—44no—
325C2×D4×C47—44no—
326C2×D4×C47—44no—
327C2×D4×C47—44no—
328C2×D4×C47—48no—
329C2×D4×C47—84no—
330C2×D4×C47—84no—
331C2×D4×C47C2×D412yes—
332C2×D4×C47C2×D412yes—
333C2×D4×C47C2×D412yes—
334C2×D4×C47C2×D411yescharacteristic
335C2×D4×C47C2412yes—
336C2×D4×C47C2411yescharacteristic
337C2×D4×C47C2412yes—
338C22×C4×C47—22no—
339C22×C4×C47—21no—
340C22×C4×C47—22no—
341C22×C4×C47—22no—
342C22×C4×C47—42no—
343C22×C4×C47C2×D411yescharacteristic
344C22×C4×C47C2×D411yescharacteristic
345C22×C4×C47C2×D411yescharacteristic
346C22×C4×C47C2411yescharacteristic
347C22×C4×C47C2412yes—
348C22×C4×C47C2411yescharacteristic
349C22×C4×C47C2411yescharacteristic
350C2×C22⋊D47—22no—
351C2×C22⋊D47—22no—
352C2×C22⋊D47—22no—
353C2×C22⋊D47—22no—
354C2×C22⋊D47—82no—
355C22×Dic47—21no—
356C22×Dic47—21no—
357C22×Dic47—21no—
358C22×Dic47—22no—
359#10625352—84no—
360#10625350—42no—
361#10625350—42no—
362C2×D188—21no—
363C2×D188—42no—
364C2×D188C2412yes—
365C2×C4×D47—22no—
366C2×C4×D47—22no—
367C2×Dic94—22no—
368C2×Dic94—21no—
369C2×Dic94—42no—
370C2×Dic94C2412yes—
371C4⋊C4×C47—21no—
372C4⋊C4×C47—21no—
373C4⋊C4×C47C2×D411yescharacteristic
374C4⋊C4×C47C2×D411yescharacteristic
375C4⋊C4×C47C2×D412yes—
376C4⋊C4×C47C2×D412yes—
377C4⋊C4×C47C2411yescharacteristic
378C4⋊C4×C47C2411yescharacteristic
379C22⋊C4×C47—21no—
380C22⋊C4×C47—21no—
381C22⋊C4×C47—21no—
382C22⋊C4×C47—22no—
383C22⋊C4×C47—22no—
384C22⋊C4×C47—22no—
385C22⋊C4×C47—22no—
386C22⋊C4×C47—22no—
387C22⋊C4×C47—22no—
388C22⋊C4×C47—21no—
389C22⋊C4×C47—21no—
390C22⋊C4×C47C2×D412yes—
391C22⋊C4×C47C2×D412yes—
392C22⋊C4×C47C2×D412yes—
393C22⋊C4×C47C2×D412yes—
394C22⋊C4×C47C2×D412yes—
395C42×C47—21no—
396C42×C47C2412yes—
397C22⋊Dic47—22no—
398C22⋊Dic47—22no—
399C22⋊Dic47—22no—
400#10625337—42no—
401#10625336—42no—
402#10625335—24no—
403#10625335—24no—
404#10625335—42no—
405#10625335—42no—
406#10625335—42no—
407#10625334—24no—
408#10625334—24no—
409#10625334—42no—
410#10625334—42no—
411#10625334—42no—
412(C2×D47)⋊C4—22no—
413(C2×D47)⋊C4—22no—
414(C2×D47)⋊C4—22no—
415(C2×D47)⋊C4—22no—
416(C2×D47)⋊C4—22no—
417(C2×D47)⋊C4—22no—
418C4⋊Dic47—21no—
419C4⋊Dic47—21no—
420C4⋊Dic47—22no—
421C4⋊Dic47—22no—
422C4⋊Dic47C2412yes—
423C4⋊Dic47C2412yes—
424Dic47⋊C4—22no—
425Dic47⋊C4—22no—
426Dic47⋊C4—22no—
427Dic47⋊C4—22no—
428C4×Dic47—22no—
429#10625329—42no—
430C2×C47⋊C8—42no—
431C2×C47⋊C8—42no—
432C2×C47⋊C8—42no—
433C2×C47⋊C8C2412yes—
434C2×C47⋊C8C2412yes—
435C2×C47⋊C8C2412yes—
436C2×C47⋊C8C2412yes—
437C23×C47—24no—
438C23×C47—22no—
439C23×C47—22no—
440C23×C47—22no—
441C23×C47—22no—
442C23×C47—21no—
443C23×C47—41no—
444C23×C47—44no—
445C23×C47—44no—
446C23×C47—44no—
447C23×C47—42no—
448C23×C47—44no—
449C23×C47—44no—
450C23×C47—82no—
451C23×C47—82no—
452C23×C47—81no—
453C23×C47—81no—
454C23×C47—81no—
455C23×C47—81no—
456C23×C47—82no—
457C23×C47—82no—
458C23×C47—816no—
459C23×C47C22×D411yescharacteristic
460C23×C47C22×D412yes—
461C23×C47C22×D411yescharacteristic
462C23×C47C22×D411yescharacteristic
463C22×D47—22no—
464C22×D47—42no—
465C22×D47—81no—
466C22×D47—81no—
467Q8×C47—22no—
468Q8×C47—41no—
469D4×C47—24no—
470D4×C47—24no—
471D4×C47—24no—
472D4×C47—22no—
473D4×C47—22no—
474D4×C47—22no—
475D4×C47—22no—
476D4×C47—42no—
477D4×C47—41no—
478D4×C47—44no—
479D4×C47—44no—
480D4×C47—44no—
481D4×C47—42no—
482D4×C47—44no—
483D4×C47—42no—
484D4×C47—42no—
485D4×C47—42no—
486D4×C47—82no—
487D4×C47—82no—
488D4×C47—82no—
489D4×C47—82no—
490D4×C47H(5,𝔽2)14yes—
491C2×C4×C47—22no—
492C2×C4×C47—22no—
493C2×C4×C47—22no—
494C2×C4×C47—22no—
495C2×C4×C47—22no—
496C2×C4×C47—21no—
497C2×C4×C47—21no—
498C2×C4×C47—21no—
499C2×C4×C47—41no—
500C2×C4×C47—41no—
501C2×C4×C47—41no—
502C2×C4×C47—44no—
503C2×C4×C47—42no—
504C2×C4×C47—82no—
505C2×C4×C47—82no—
506C2×C4×C47C22×D412yes—
507C2×C4×C47C22×D411yescharacteristic
508C2×C4×C47C22×D411yescharacteristic
509C2×C4×C47C22×D412yes—
510C2×C4×C47C22×D412yes—
511C2×C4×C47C22×D411yescharacteristic
512C2×C4×C47C2511yescharacteristic
513C22⋊D47—44no—
514C22⋊D47—82no—
515C22⋊D47—82no—
516C22⋊D47—82no—
517C2×Dic47—22no—
518C2×Dic47—22no—
519C2×Dic47—22no—
520C2×Dic47—42no—
521C2×Dic47—81no—
522C2×Dic47—82no—
523C2×Dic47—81no—
524D188—22no—
525D188—22no—
526D188—81no—
527C4×D47—82no—
528C4×D47—82no—
529Dic94—22no—
530Dic94—22no—
531Dic94—81no—
532Dic94—82no—
533C47⋊C8—22no—
534C47⋊C8—22no—
535C47⋊C8—22no—
536C47⋊C8—22no—
537#61629—471nomaximal, Sylow
538C22×C47—21no—
539C22×C47—21no—
540C22×C47—21no—
541C22×C47—21no—
542C22×C47—22no—
543C22×C47—21no—
544C22×C47—24no—
545C22×C47—22no—
546C22×C47—21no—
547C22×C47—22no—
548C22×C47—21no—
549C22×C47—44no—
550C22×C47—42no—
551C22×C47—42no—
552C22×C47—41no—
553C22×C47—42no—
554C22×C47—41no—
555C22×C47—42no—
556C22×C47—41no—
557C22×C47—42no—
558C22×C47—88no—
559C22×C47—88no—
560C22×C47—84no—
561C22×C47—84no—
562C22×C47—164no—
563C22×C47#57612yes—
564C22×C47#57712yes—
565C22×C47C23×D411yescharacteristic
566C2×D47—42no—
567C2×D47—42no—
568C2×D47—42no—
569C2×D47—162no—
570C4×C47—21no—
571C4×C47—22no—
572C4×C47—21no—
573C4×C47—21no—
574C4×C47—22no—
575C4×C47—22no—
576C4×C47—41no—
577C4×C47—41no—
578C4×C47—41no—
579C4×C47C2×H(5,𝔽2)12yes—
580Dic47—42no—
581Dic47—42no—
582Dic47—42no—
583#3536—471no—
584#3484D4711yescharacteristic, complemented
585#3314—472no—
586#3306—472no—
587#3295—472no—
588#3294—472no—
589#3282—472no—
590#3280—472no—
591#3265—472no—
592#3264—472no—
593#3224—472no—
594#3198—472no—
595#3190—471no—
596#3188—471no—
597#3118—472no—
598#3012—472no—
599C2×#450—471no—
600C2×#447—471no—
601#2977—471no—
602C2×C47—22no—
603C2×C47—22no—
604C2×C47—41no—
605C2×C47—42no—
606C2×C47—44no—
607C2×C47—82no—
608C2×C47—81no—
609C2×C47#348411yescharacteristic
610C2×C47C2×#57611yescharacteristic
611C2×C47C2×#57711yescharacteristic
612D47—82no—
613C2×H(5,𝔽2)C2×D4711yescharacteristic, complemented
614C23×D4C2×D4711yescharacteristic
615C2×AGL(1,ℤ/8)—472no—
616C2×#135—472no—
617C22×SD16—472no—
618C22×D8—472no—
619#562—942no—
620#554—472no—
621#548—472no—
622#547—472no—
623#546—21no—
624#546—21no—
625#546—472no—
626#546—942no—
627#546C2×D4712yes—
628#546C2×D4712yescomplemented
629D42—21no—
630D42—21no—
631D42C2×D4712yes—
632D42C2×D4712yescomplemented
633#543—941no—
634#542—472no—
635#539—941no—
636#538—941no—
637#537—472no—
638#537—941no—
639#535C2×D4711yescharacteristic, complemented
640#535C2×D4711yescharacteristic, complemented
641#534—22no—
642#525C2×D4711yescharacteristic
643#525C2×D4711yescharacteristic
644C2×C22⋊Q8—471no—
645C2×#121—471no—
646C2×#120—22no—
647#518C2×D4711yescharacteristic, complemented
648#496—472no—
649#495—472no—
650#489—472no—
651#486—472no—
652#485—472no—
653#484—471no—
654#483—471no—
655#482—472no—
656#481—471no—
657#481—472no—
658#480—471no—
659#480—472no—
660#476—472no—
661#474—472no—
662#469—472no—
663#468—472no—
664#467—472no—
665#466—472no—
666#466—472no—
667#465—472no—
668#465—472no—
669#465—472no—
670#464—472no—
671#463—472no—
672#463—472no—
673#463—472no—
674#460—472no—
675#459—472no—
676#452—472no—
677#452—472no—
678#451—471no—
679#450—472no—
680#450—472no—
681#450—472no—
682#450—472no—
683#450—472no—
684#450—471no—
685#449—472no—
686#449—472no—
687#449—472no—
688#449—472no—
689#448—471no—
690#447—472no—
691#447—472no—
692#447—472no—
693#447—472no—
694#447—472no—
695#447—471no—
696#442—472no—
697#440—472no—
698C4×SD16—472no—
699C4×D8—472no—
700#435—472no—
701#435—472no—
702C8×D4—472no—
703C8×D4—472no—
704#433—472no—
705#417—472no—
706C2×#102—472no—
707C2×#102—472no—
708C2×#102—472no—
709#408—472no—
710C2×C22⋊C8—471no—
711C2×C22⋊C8—471no—
712C47#6162911yescharacteristic, complemented, Sylow
713C25—21no—
714H(5,𝔽2)—44no—
715C2×#41—21no—
716C2×#41—472no—
717C2×#41—942no—
718C2×#41C22×D4712yes—
719C2×#41C22×D4711yescharacteristic
720C2×#41C22×D4711yescharacteristic
721C22×Q8—471no—
722C22×D4—22no—
723C22×D4—21no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—21no—
727C22×D4—21no—
728C22×D4—21no—
729C22×D4—44no—
730C22×D4—471no—
731C22×D4—941no—
732C22×D4C22×D4711yescharacteristic
733C22×D4C22×D4712yes—
734C22×D4C22×D4712yes—
735C22×D4C22×D4712yes—
736C22×D4C22×D4711yescharacteristic
737C23×C4C22×D4711yescharacteristic
738AGL(1,ℤ/8)—1884no—
739#135—1884no—
740C2×Q16—472no—
741C2×SD16—472no—
742C2×SD16—472no—
743C2×SD16—472no—
744C2×SD16—472no—
745C2×SD16—472no—
746C2×SD16—472no—
747C2×SD16—1884no—
748C2×D8—472no—
749C2×D8—472no—
750C2×D8—472no—
751C2×D8—472no—
752C2×D8—472no—
753C2×D8—1884no—
754C2×M16—472no—
755C22×C8—472no—
756C22×C8—472no—
757C22×C8—472no—
758C4⋊Q8—472no—
759#127—21no—
760#127C22×D4712yes—
761#126—942no—
762#125—942no—
763#124—21no—
764#124—472no—
765#124—942no—
766#124—942no—
767#124C22×D4712yes—
768#123—21no—
769#123—22no—
770#123—22no—
771#123—942no—
772#123—942no—
773#123—942no—
774#123—942no—
775#123C22⋊D4712yes—
776C22⋊Q8—472no—
777C22⋊Q8—472no—
778C22⋊Q8—472no—
779C22⋊Q8—942no—
780C22⋊Q8—941no—
781C22⋊Q8—941no—
782C22⋊Q8—942no—
783C22⋊Q8—942no—
784C22⋊Q8—942no—
785C22⋊Q8—942no—
786C22⋊Q8—942no—
787C22⋊Q8C22⋊D4711yescharacteristic
788C22⋊Q8C22⋊D4711yescharacteristic
789C22⋊Q8C22×D4711yescharacteristic
790C22⋊Q8C22×D4711yescharacteristic
791#121—22no—
792#121—22no—
793#121—21no—
794#121—21no—
795#121—22no—
796#121—22no—
797#121—472no—
798#121—472no—
799#121—472no—
800#121—942no—
801#121—942no—
802#121—942no—
803#121—942no—
804#121—941no—
805#121—941no—
806#121—942no—
807#121C22⋊D4711yescharacteristic
808#121C22⋊D4711yescharacteristic
809#121C22×D4711yescharacteristic
810#121C22×D4711yescharacteristic
811#121C22×D4712yes—
812#121C22×D4712yes—
813#120—21no—
814#120—22no—
815#120—22no—
816#120—22no—
817#120—22no—
818#120—22no—
819#120—22no—
820#120—22no—
821#120—22no—
822#120—942no—
823#120C22⋊D4712yes—
824C4×Q8—472no—
825C4×D4—21no—
826C4×D4—21no—
827C4×D4—21no—
828C4×D4—21no—
829C4×D4—472no—
830C4×D4—942no—
831C4×D4—942no—
832C4×D4C22×D4712yes—
833C4×D4C22×D4712yes—
834C4×D4C22×D4712yes—
835C4×D4C22×D4712yes—
836#117C22×D4711yescharacteristic
837#117C22×D4711yescharacteristic
838C2×C4⋊C4—471no—
839C2×C4⋊C4—471no—
840C2×C4⋊C4—472no—
841C2×C4⋊C4—941no—
842C2×C22⋊C4—22no—
843C2×C22⋊C4—22no—
844C2×C22⋊C4—22no—
845C2×C22⋊C4—941no—
846C2×C22⋊C4—941no—
847C2×C22⋊C4—942no—
848#107—472no—
849#107—472no—
850#106—472no—
851#106—472no—
852C4⋊C8—472no—
853C4⋊C8—472no—
854#103—472no—
855#103—472no—
856#103—472no—
857#103—472no—
858#102—472no—
859#102—472no—
860#102—472no—
861#102—472no—
862#102—472no—
863#102—472no—
864#102—472no—
865#102—472no—
866#102—472no—
867#102—472no—
868#102—472no—
869#102—472no—
870C22⋊C8—472no—
871C22⋊C8—472no—
872C22⋊C8—471no—
873C22⋊C8—471no—
874C22⋊C8—471no—
875C22⋊C8—471no—
876C22⋊C8—472no—
877C22⋊C8—472no—
878#97—472no—
879C4×C8—472no—
880C24—21no—
881C24—22no—
882C24—22no—
883C24—21no—
884C24—22no—
885C24—44no—
886C24—82no—
887C24—82no—
888C24—941no—
889C24C2×C22⋊D4711yescharacteristic
890#41—24no—
891#41—42no—
892#41—42no—
893#41—42no—
894#41—44no—
895#41—3764no—
896#41—1882no—
897#41—1882no—
898C2×Q8—472no—
899C2×Q8—941no—
900C2×Q8—942no—
901C2×Q8—1882no—
902C2×Q8C2×C22⋊D4711yescharacteristic
903C2×Q8C23×D4711yescharacteristic
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—22no—
912C2×D4—22no—
913C2×D4—22no—
914C2×D4—21no—
915C2×D4—22no—
916C2×D4—22no—
917C2×D4—22no—
918C2×D4—21no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—48no—
930C2×D4—84no—
931C2×D4—84no—
932C2×D4—472no—
933C2×D4—942no—
934C2×D4—942no—
935C2×D4—942no—
936C2×D4—942no—
937C2×D4—941no—
938C2×D4—3762no—
939C2×D4—1882no—
940C2×D4C2×C22⋊D4712yes—
941C2×D4C2×C22⋊D4712yes—
942C2×D4C2×C22⋊D4712yes—
943C2×D4C2×C22⋊D4711yescharacteristic
944C2×D4C23×D4712yes—
945C2×D4C23×D4711yescharacteristic
946C2×D4C23×D4712yes—
947C22×C4—22no—
948C22×C4—21no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—42no—
952C22×C4—941no—
953C22×C4—941no—
954C22×C4—942no—
955C22×C4—941no—
956C22×C4—942no—
957C22×C4—942no—
958C22×C4C2×C22⋊D4711yescharacteristic
959C22×C4C2×C22⋊D4711yescharacteristic
960C22×C4C2×C22⋊D4711yescharacteristic
961C22×C4C23×D4711yescharacteristic
962C22×C4C23×D4711yescharacteristic
963C22×C4C23×D4712yes—
964C22×C4C23×D4711yescharacteristic
965Q16—1882no—
966SD16—944no—
967SD16—944no—
968SD16—1882no—
969SD16—1882no—
970SD16—1882no—
971SD16—1882no—
972D8—944no—
973D8—944no—
974D8—1882no—
975D8—1882no—
976D8—1882no—
977M16—1882no—
978C2×C8—472no—
979C2×C8—472no—
980C2×C8—472no—
981C2×C8—472no—
982C2×C8—1882no—
983C2×C8—1882no—
984C2×C8—1882no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—472no—
988C4⋊C4—472no—
989C4⋊C4—942no—
990C4⋊C4—942no—
991C4⋊C4—942no—
992C4⋊C4—942no—
993C4⋊C4—941no—
994C4⋊C4—942no—
995C4⋊C4—941no—
996C4⋊C4—942no—
997C4⋊C4C2×C22⋊D4711yescharacteristic
998C4⋊C4C2×C22⋊D4711yescharacteristic
999C4⋊C4C2×C22⋊D4712yes—
1000C4⋊C4C2×C22⋊D4712yes—
1001C4⋊C4C23×D4711yescharacteristic
1002C4⋊C4C23×D4711yescharacteristic
1003C22⋊C4—21no—
1004C22⋊C4—21no—
1005C22⋊C4—21no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—21no—
1013C22⋊C4—21no—
1014C22⋊C4—942no—
1015C22⋊C4—942no—
1016C22⋊C4—942no—
1017C22⋊C4—942no—
1018C22⋊C4—942no—
1019C22⋊C4—942no—
1020C22⋊C4—942no—
1021C22⋊C4—942no—
1022C22⋊C4—942no—
1023C22⋊C4C2×C22⋊D4712yes—
1024C22⋊C4C2×C22⋊D4712yes—
1025C22⋊C4C2×C22⋊D4712yes—
1026C22⋊C4C2×C22⋊D4712yes—
1027C22⋊C4C2×C22⋊D4712yes—
1028C42—21no—
1029C42—942no—
1030C42C23×D4712yes—
1031C23—24no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—21no—
1037C23—41no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—42no—
1042C23—44no—
1043C23—44no—
1044C23—82no—
1045C23—82no—
1046C23—81no—
1047C23—81no—
1048C23—81no—
1049C23—81no—
1050C23—82no—
1051C23—82no—
1052C23—816no—
1053C23—942no—
1054C23—3761no—
1055C23—3761no—
1056C23—1882no—
1057C23C22×C22⋊D4711yescharacteristic
1058C23C22×C22⋊D4712yes—
1059C23C22×C22⋊D4711yescharacteristic
1060C23C22×C22⋊D4711yescharacteristic
1061Q8—22no—
1062Q8—41no—
1063Q8—942no—
1064Q8—942no—
1065Q8—3761no—
1066Q8—3762no—
1067D4—24no—
1068D4—24no—
1069D4—24no—
1070D4—22no—
1071D4—22no—
1072D4—22no—
1073D4—22no—
1074D4—41no—
1075D4—42no—
1076D4—44no—
1077D4—44no—
1078D4—44no—
1079D4—42no—
1080D4—44no—
1081D4—42no—
1082D4—42no—
1083D4—42no—
1084D4—82no—
1085D4—82no—
1086D4—82no—
1087D4—82no—
1088D4—942no—
1089D4—942no—
1090D4—3761no—
1091D4—3762no—
1092D4—3762no—
1093D4—3762no—
1094D4—1884no—
1095D4#1309406914yes—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—44no—
1108C2×C4—42no—
1109C2×C4—82no—
1110C2×C4—82no—
1111C2×C4—942no—
1112C2×C4—942no—
1113C2×C4—942no—
1114C2×C4—3762no—
1115C2×C4—3762no—
1116C2×C4—3761no—
1117C2×C4—3761no—
1118C2×C4—3762no—
1119C2×C4—1882no—
1120C2×C4C22×C22⋊D4711yescharacteristic
1121C2×C4C22×C22⋊D4712yes—
1122C2×C4C22×C22⋊D4712yes—
1123C2×C4C22×C22⋊D4712yes—
1124C2×C4C22×C22⋊D4711yescharacteristic
1125C2×C4C22×C22⋊D4711yescharacteristic
1126C2×C4C24×D4711yescharacteristic
1127C8—942no—
1128C8—942no—
1129C8—942no—
1130C8—942no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—22no—
1136C22—21no—
1137C22—22no—
1138C22—21no—
1139C22—21no—
1140C22—22no—
1141C22—24no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—41no—
1146C22—42no—
1147C22—41no—
1148C22—42no—
1149C22—41no—
1150C22—42no—
1151C22—88no—
1152C22—88no—
1153C22—84no—
1154C22—84no—
1155C22—164no—
1156C22—1882no—
1157C22—1882no—
1158C22—1882no—
1159C22—7522no—
1160C22#1568992612yes—
1161C22#1568993412yes—
1162C22C23×C22⋊D4711yescharacteristic
1163C4—22no—
1164C4—22no—
1165C4—21no—
1166C4—22no—
1167C4—21no—
1168C4—21no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—1882no—
1173C4—1882no—
1174C4—1882no—
1175C4C2×#1309406912yes—
1176C2—22no—
1177C2—22no—
1178C2—41no—
1179C2—42no—
1180C2—44no—
1181C2—82no—
1182C2—81no—
1183C2—3762no—
1184C2#2025702311yescharacteristic
1185C2C2×#1568992611yescharacteristic
1186C2C2×#1568993411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3484C2
socleC22×C47C23×D4
hypercenter#3484D47
hypocenterC47#61629
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #525 ◁ #3484

Complements

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

NH ≅ G/Ntype
1. #20257615C2semidirect
2. #20255469C2semidirect
3. #20255349C2semidirect
4. #20255212C2semidirect
5. #20255201C2semidirect
6. #20255091C2semidirect
7. #20255069C2semidirect
8. #20254879C2semidirect
9. #20254864C2semidirect
10. #20254482C2semidirect
11. #20254240C2semidirect
12. #20254165C2semidirect
13. #20254149C2semidirect
14. #20253572C2semidirect
15. #20252692C2semidirect
16. C2×#15689274C2semidirect
17. C2×#15689257C2semidirect
18. #20252444C2semidirect
19. C47×#3484C2semidirect
20. C2×#13094050C22semidirect
21. C2×#13094044C22semidirect
22. C22×#10625335C22semidirect
23. C22×#10625334C22semidirect
25. #15689830C22semidirect
26. #15689782C22semidirect
27. #15689777C22semidirect
28. #15689769C22semidirect
31. #15689744C22semidirect
34. #15689701C22semidirect
36. C2×#13094003C22semidirect
37. C2×#13093998C22semidirect
38. #15689510C22semidirect
39. #15689505C22semidirect
40. #15689482C22semidirect
41. #15689469C22semidirect
42. #15689464C22semidirect
43. #15689456C22semidirect
44. #15689451C22semidirect
45. #15689447C22semidirect
46. #15689439C22semidirect
47. #15689439C22semidirect
48. #15689434C22semidirect
49. #15689434C22semidirect
50. #15689413C22semidirect
51. #15689403C22semidirect
52. #15689374C22semidirect
53. #15689367C22semidirect
54. #15689362C22semidirect
55. #15689357C22semidirect
56. #15689357C22semidirect
57. #15689354C22semidirect
58. #15689350C22semidirect
59. #15689350C22semidirect
60. #15689342C22semidirect
61. #15689338C22semidirect
62. #15689338C22semidirect
63. #15689335C22semidirect
64. #15689320C22semidirect
65. #15689315C22semidirect
66. #15689285C22semidirect
67. #15689285C22semidirect
68. #15689278C22semidirect
69. #15689274C22semidirect
70. #15689274C22semidirect
71. #15689274C22semidirect
72. #15689274C22semidirect
73. #15689274C22semidirect
74. #15689273C22semidirect
75. #15689268C22semidirect
76. #15689268C22semidirect
77. #15689266C22semidirect
78. #15689266C22semidirect
79. #15689261C22semidirect
81. #15689257C22semidirect
82. #15689257C22semidirect
83. #15689257C22semidirect
84. #15689257C22semidirect
85. #15689256C22semidirect
86. #15689233C22semidirect
87. #15689223C22semidirect
88. C4×#10625335C22semidirect
89. C4×#10625334C22semidirect
90. #15689195C22semidirect
91. #15689195C22semidirect
92. D4×C47⋊C8C22semidirect
93. D4×C47⋊C8C22semidirect
94. #15689184C22semidirect
95. #15689124C22semidirect
96. C2×#13093945C22semidirect
97. C2×#13093945C22semidirect
98. C2×#13093945C22semidirect
99. #15689090C22semidirect
100. C2×C22⋊(C47⋊C8)C22semidirect
101. C2×C22⋊(C47⋊C8)C22semidirect
102. C2×H(5,𝔽2)×C47C22semidirect
107. C47×#546C22semidirect
111. D42×C47C22semidirect
112. C47×#535C22semidirect
113. C47×#535C22semidirect
118. C47×#518C22semidirect
119. C2×#10625350C23semidirect
126. C2×#10625337C23semidirect
132. C2×#10625335C23semidirect
133. C2×#10625336C23semidirect
139. C2×#10625334C23semidirect
140. C2×#10625329C23semidirect
143. C22×C47⋊C8C23semidirect
144. #13094024C23semidirect
147. #13094012C23semidirect
159. #13094003C23semidirect
169. #13093998C23semidirect
176. C4×Dic94C23semidirect
177. C4×D188C23semidirect
182. C2×C4⋊Dic47C23semidirect
187. #13093957C23semidirect
188. #13093957C23semidirect
189. #13093955C23semidirect
190. #13093955C23semidirect
191. C4⋊(C47⋊C8)C23semidirect
192. C4⋊(C47⋊C8)C23semidirect
193. #13093948C23semidirect
194. #13093948C23semidirect
195. #13093947C23semidirect
196. #13093947C23semidirect
205. #13093945C23semidirect
206. #13093945C23semidirect
207. #13093944C23semidirect
208. #13093944C23semidirect
215. C22⋊(C47⋊C8)C23semidirect
216. C22⋊(C47⋊C8)C23semidirect
217. #13093935C23semidirect
218. C4×C47⋊C8C23semidirect
584. #3484D47semidirect
613. C2×H(5,𝔽2)C2×D47semidirect
628. #546C2×D47semidirect
632. D42C2×D47semidirect
639. #535C2×D47semidirect
640. #535C2×D47semidirect
647. #518C2×D47semidirect
712. C47#61629semidirect

Maximal subgroups

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

subgroupindex
#202576152
#202554692
#202553492
#202552122
#202552012
#202550912
#202550692
#202548792
#202548642
#202544822
#202542402
#202541652
#202541492
#202535722
#202526922
C2×#156892742
C2×#156892572
#202524442
C47×#34842
#6162947