Finite Group Databasebeta

← #27102339

Subgroups — #27102339

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#20257021C211yesmaximal, characteristic, complemented
2#20255463C212yesmaximal, complemented
3#20255343C212yesmaximal, complemented
4#20255206C212yesmaximal, complemented
5#20255195C212yesmaximal, complemented
6#20255096C212yesmaximal, complemented
7#20255069C212yesmaximal, complemented
8#20254884C212yesmaximal, complemented
9#20254869C212yesmaximal, complemented
10#20254476C212yesmaximal, complemented
11#20254234C212yesmaximal, complemented
12#20254169C211yesmaximal, characteristic, complemented
13#20254153C211yesmaximal, characteristic, complemented
14#20253566C212yesmaximal, complemented
15#20252689C212yesmaximal, complemented
16C2×#15689273C211yesmaximal, characteristic, complemented
17C2×#15689256C211yesmaximal, characteristic, complemented
18#20252444C211yesmaximal, characteristic, complemented
19C47×#3536C211yesmaximal, characteristic, complemented
20C2×#13094070C2211yescharacteristic, complemented
21C23×D188C2211yescharacteristic
22C2×#13094049C2212yescomplemented
23C2×#13094044C2212yescomplemented
24C22×#10625336C2212yescomplemented
25C22×#10625334C2212yescomplemented
26#15689769C2212yes—
27#15689769C2212yescomplemented
28#15689764—21no—
29#15689764—21no—
30D4×D188C2212yes—
31D4×D188C2212yescomplemented
32#15689757—21no—
33#15689757—21no—
34#15689692C2211yescharacteristic, complemented
35#15689687C2211yescharacteristic, complemented
36#15689684—22no—
37#15689634C2211yescharacteristic
38#120×D47—22no—
39#15689597C2211yescharacteristic, complemented
40#15689513C2212yescomplemented
41#15689505C2212yescomplemented
42#15689485C2212yescomplemented
43#15689471C2212yescomplemented
44#15689461C2212yescomplemented
45#15689458C2211yescharacteristic, complemented
46#15689453C2211yescharacteristic, complemented
47#15689444C2212yescomplemented
48#15689441C2211yescharacteristic, complemented
49#15689441C2212yescomplemented
50#15689436C2211yescharacteristic, complemented
51#15689436C2212yescomplemented
52#15689410C2212yescomplemented
53#15689400C2212yescomplemented
54#15689374C2212yescomplemented
55#15689371C2212yescomplemented
56#15689362C2212yescomplemented
57#15689357C2212yescomplemented
58#15689357C2212yescomplemented
59#15689354C2212yescomplemented
60#15689354C2212yescomplemented
61#15689350C2212yescomplemented
62#15689345C2212yescomplemented
63#15689338C2212yescomplemented
64#15689335C2212yescomplemented
65#15689335C2212yescomplemented
66#15689323C2212yescomplemented
67#15689318C2212yescomplemented
68#15689283C2212yescomplemented
69#15689283C2212yescomplemented
70#15689279C2211yescharacteristic, complemented
71#15689274C2211yescharacteristic, complemented
72#15689273C2212yescomplemented
73#15689273C2212yescomplemented
74#15689273C2212yescomplemented
75#15689273C2212yescomplemented
76#15689273C2212yescomplemented
77#15689268C2212yescomplemented
78#15689268C2212yescomplemented
79#15689266C2212yescomplemented
80#15689266C2212yescomplemented
81#15689262C2211yescharacteristic, complemented
82#15689257C2211yescharacteristic, complemented
83#15689256C2212yes—
84#15689256C2212yescomplemented
85#15689256C2212yescomplemented
86#15689256C2212yescomplemented
87#15689256C2212yescomplemented
88#15689233C2212yescomplemented
89#15689221C2212yescomplemented
90C4×#10625336C2212yescomplemented
91C4×#10625334C2212yescomplemented
92#15689195C2212yescomplemented
93#15689195C2212yescomplemented
94D4×C47⋊C8C2212yescomplemented
95D4×C47⋊C8C2212yescomplemented
96#15689184C2212yescomplemented
97#15689122C2212yescomplemented
98C2×#13093944C2212yescomplemented
99C2×#13093944C2212yescomplemented
100C2×#13093944C2212yescomplemented
101#15689090C2212yescomplemented
102C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
103C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
104C47×#562—22no—
105C47×#554C2212yescomplemented
106C47×#548C2212yescomplemented
107C47×#547C2212yescomplemented
108C47×#546—22no—
109C47×#546C2212yescomplemented
110C47×#543—21no—
111C47×#542C2212yescomplemented
112C47×#539—21no—
113C47×#538—21no—
114C47×#537—21no—
115C47×#537C2212yescomplemented
116C47×#525C2211yescharacteristic
117C2×C22⋊Q8×C47C2211yescharacteristic, complemented
118C2×#121×C47C2211yescharacteristic, complemented
119C24×D47—21no—
120#13094070—44no—
121C2×#10625354—21no—
122C2×#10625350C2312yes—
123C2×#10625350C2311yescharacteristic
124C22×D188—21no—
125C22×D188—21no—
126C22×D188—21no—
127C22×D188—44no—
128C22×D188C2311yescharacteristic
129C22×D188C2312yes—
130C22×D188C2312yes—
131C22×D188C2312yes—
132C22×D188C2311yescharacteristic
133C2×D4×D47—21no—
134C2×D4×D47—22no—
135C2×D4×D47—22no—
136C2×D4×D47—22no—
137#13094049—44no—
138#13094044—44no—
139C2×#10625337C2312yescomplemented
140C2×#10625335C2312yescomplemented
141C2×#10625336—44no—
142C2×#10625336C2312yes—
143C2×#10625336C2312yes—
144C2×#10625336C2312yes—
145C2×#10625336C2312yes—
146C2×#10625336C2312yescomplemented
147C2×#10625334—44no—
148C2×#10625334C2312yes—
149C2×#10625334C2312yes—
150C2×#10625334C2312yes—
151C2×#10625334C2312yes—
152C2×#10625334C2312yescomplemented
153C2×#10625329C2312yescomplemented
154C22×C47⋊C8C2312yes—
155C22×C47⋊C8C2312yes—
156C22×C47⋊C8C2312yescomplemented
157#13094021C2312yes—
158#13094020—21no—
159#13094013—21no—
160#13094012C2312yes—
161#13094009—22no—
162#13094009—22no—
163#13094007—21no—
164#13094003C2311yescharacteristic
165#13094003C2311yescharacteristic
166#13093999—21no—
167#13093999—21no—
168#13093999—22no—
169#13093999—22no—
170#13093998C2311yescharacteristic
171#13093998C2312yes—
172#13093998C2311yescharacteristic
173#13093998C2312yes—
174#13093997—22no—
175#13093997—22no—
176#13093994—22no—
177#13093994—22no—
178#13093994—22no—
179#13093994—22no—
180#13093994—22no—
181#13093993—21no—
182#13093992—22no—
183#13093992—22no—
184#13093992—22no—
185C4×D188C2312yes—
186C4×D188C2312yes—
187#13093986—21no—
188#13093986—21no—
189C4×C22⋊D47—21no—
190C4×C22⋊D47—21no—
191#13093983C2311yescharacteristic
192C22⋊C4×D47—22no—
193C22⋊C4×D47—22no—
194C22⋊C4×D47—22no—
195#13093957C2312yescomplemented
196#13093957C2312yescomplemented
197#13093955C2312yescomplemented
198#13093955C2312yescomplemented
199C4⋊(C47⋊C8)C2312yescomplemented
200C4⋊(C47⋊C8)C2312yescomplemented
201#13093948C2312yescomplemented
202#13093948C2312yescomplemented
203#13093947C2312yescomplemented
204#13093947C2312yescomplemented
205#13093945C2312yescomplemented
206#13093945C2312yescomplemented
207#13093944C2312yes—
208#13093944C2312yes—
209#13093944C2312yes—
210#13093944C2312yes—
211#13093944C2312yes—
212#13093944C2312yes—
213#13093944C2312yes—
214#13093944C2312yes—
215#13093944C2312yescomplemented
216#13093944C2312yescomplemented
217C22⋊(C47⋊C8)C2312yes—
218C22⋊(C47⋊C8)C2311yescharacteristic
219C22⋊(C47⋊C8)C2311yescharacteristic
220C22⋊(C47⋊C8)C2311yescharacteristic
221C22⋊(C47⋊C8)C2312yes—
222C22⋊(C47⋊C8)C2311yescharacteristic
223C22⋊(C47⋊C8)C2312yescomplemented
224C22⋊(C47⋊C8)C2312yescomplemented
225#13093935C2312yescomplemented
226C4×C47⋊C8C2312yescomplemented
227C2×#41×C47—22no—
228C2×#41×C47C2311yescharacteristic
229C2×#41×C47C2312yescomplemented
230C22×Q8×C47C2311yescharacteristic
231C22×D4×C47—21no—
232C22×D4×C47C2311yescharacteristic
233C23×C4×C47C2311yescharacteristic
234C4⋊Q8×C47C2312yescomplemented
235#126×C47—22no—
236#125×C47—22no—
237#124×C47—22no—
238#124×C47—22no—
239#124×C47C2312yescomplemented
240#123×C47—22no—
241#123×C47—22no—
242#123×C47—22no—
243#123×C47—22no—
244#123×C47D412yes—
245C22⋊Q8×C47—22no—
246C22⋊Q8×C47—21no—
247C22⋊Q8×C47—21no—
248C22⋊Q8×C47—22no—
249C22⋊Q8×C47—22no—
250C22⋊Q8×C47—22no—
251C22⋊Q8×C47—22no—
252C22⋊Q8×C47—22no—
253C22⋊Q8×C47D411yescharacteristic
254C22⋊Q8×C47D411yescharacteristic
255C22⋊Q8×C47C2312yes—
256C22⋊Q8×C47C2312yes—
257C22⋊Q8×C47C2312yescomplemented
258#121×C47—22no—
259#121×C47—22no—
260#121×C47—22no—
261#121×C47—22no—
262#121×C47—21no—
263#121×C47—21no—
264#121×C47—22no—
265#121×C47D411yescharacteristic
266#121×C47D411yescharacteristic
267#121×C47C2312yes—
268#121×C47C2312yes—
269#121×C47C2312yescomplemented
270#120×C47—22no—
271#120×C47D412yes—
272C4×Q8×C47C2312yescomplemented
273C4×D4×C47—22no—
274C4×D4×C47—22no—
275C4×D4×C47C2312yes—
276C4×D4×C47C2312yes—
277C4×D4×C47C2312yescomplemented
278#117×C47C2311yescharacteristic
279C2×C4⋊C4×C47—21no—
280C2×C4⋊C4×C47C2311yescharacteristic
281C2×C4⋊C4×C47C2311yescharacteristic
282C2×C4⋊C4×C47C2312yescomplemented
283C2×C22⋊C4×C47—21no—
284C2×C22⋊C4×C47—21no—
285C2×C22⋊C4×C47—22no—
286C24×C47—21no—
287C24×C47C2×D411yescharacteristic
288C23×D47—21no—
289C23×D47—22no—
290C23×D47—22no—
291C23×D47—21no—
292C23×D47—22no—
293C23×D47—44no—
294C23×D47—82no—
295C23×D47—82no—
296#41×C47—42no—
297#41×C47—42no—
298#41×C47—42no—
299#41×C47—84no—
300C2×Q8×C47—21no—
301C2×Q8×C47—22no—
302C2×Q8×C47—42no—
303C2×Q8×C47C2×D411yescharacteristic
304C2×Q8×C47C2412yes—
305C2×D4×C47—22no—
306C2×D4×C47—22no—
307C2×D4×C47—22no—
308C2×D4×C47—22no—
309C2×D4×C47—21no—
310C2×D4×C47—42no—
311C2×D4×C47—82no—
312C2×D4×C47C2×D412yes—
313C2×D4×C47C2×D412yes—
314C2×D4×C47C2×D412yes—
315C2×D4×C47C2×D411yescharacteristic
316C2×D4×C47C2412yes—
317C22×C4×C47—21no—
318C22×C4×C47—21no—
319C22×C4×C47—21no—
320C22×C4×C47—22no—
321C22×C4×C47—22no—
322C22×C4×C47—22no—
323C22×C4×C47—42no—
324C22×C4×C47C2×D411yescharacteristic
325C22×C4×C47C2×D411yescharacteristic
326C22×C4×C47C2×D411yescharacteristic
327C22×C4×C47C2411yescharacteristic
328C22×C4×C47C2411yescharacteristic
329C22×C4×C47C2412yes—
330C22×C4×C47C2411yescharacteristic
331C2×C22⋊D47—21no—
332C2×C22⋊D47—21no—
333C2×C22⋊D47—22no—
334C2×C22⋊D47—21no—
335C2×C22⋊D47—22no—
336C2×C22⋊D47—22no—
337#10625354—44no—
338D4×D47—44no—
339D4×D47—48no—
340D4×D47—84no—
341D4×D47—84no—
342#10625350—24no—
343#10625350—42no—
344#10625350—42no—
345C2×D188—21no—
346C2×D188—24no—
347C2×D188—24no—
348C2×D188—24no—
349C2×D188—24no—
350C2×D188—22no—
351C2×D188—22no—
352C2×D188—22no—
353C2×D188—21no—
354C2×D188—22no—
355C2×D188—22no—
356C2×D188—42no—
357C2×D188—42no—
358C2×D188—42no—
359C2×D188—42no—
360C2×D188—44no—
361C2×D188—44no—
362C2×D188—44no—
363C2×D188C2412yes—
364C2×D188C2411yescharacteristic
365C2×D188C2412yes—
366C2×C4×D47—22no—
367C2×C4×D47—21no—
368C2×C4×D47—22no—
369C2×C4×D47—22no—
370C2×Dic94C2411yescharacteristic
371C4⋊C4×C47—22no—
372C4⋊C4×C47—22no—
373C4⋊C4×C47—21no—
374C4⋊C4×C47—21no—
375C4⋊C4×C47—22no—
376C4⋊C4×C47—22no—
377C4⋊C4×C47—22no—
378C4⋊C4×C47—22no—
379C4⋊C4×C47C2×D411yescharacteristic
380C4⋊C4×C47C2×D411yescharacteristic
381C4⋊C4×C47C2×D412yes—
382C4⋊C4×C47C2×D412yes—
383C4⋊C4×C47C2412yes—
384C4⋊C4×C47C2412yes—
385C22⋊C4×C47—22no—
386C22⋊C4×C47—22no—
387C22⋊C4×C47—22no—
388C22⋊C4×C47—22no—
389C22⋊C4×C47—22no—
390C22⋊C4×C47—22no—
391C22⋊C4×C47—22no—
392C22⋊C4×C47—22no—
393C22⋊C4×C47—22no—
394C22⋊C4×C47C2×D412yes—
395C22⋊C4×C47C2×D412yes—
396C22⋊C4×C47C2×D412yes—
397C22⋊C4×C47C2×D412yes—
398C22⋊C4×C47C2×D412yes—
399C42×C47—22no—
400C42×C47C2412yes—
401C22⋊Dic47—21no—
402C22⋊Dic47—21no—
403C22⋊Dic47—21no—
404#10625337—42no—
405#10625336—24no—
406#10625336—24no—
407#10625336—42no—
408#10625336—42no—
409#10625336—42no—
410#10625335—42no—
411#10625334—24no—
412#10625334—24no—
413#10625334—42no—
414#10625334—42no—
415#10625334—42no—
416(C2×D47)⋊C4—22no—
417(C2×D47)⋊C4—22no—
418(C2×D47)⋊C4—22no—
419(C2×D47)⋊C4—22no—
420(C2×D47)⋊C4—22no—
421(C2×D47)⋊C4—22no—
422(C2×D47)⋊C4—21no—
423(C2×D47)⋊C4—21no—
424C4⋊Dic47C2411yescharacteristic
425C4⋊Dic47C2411yescharacteristic
426Dic47⋊C4—21no—
427Dic47⋊C4—21no—
428C4×Dic47—21no—
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—22no—
438C23×C47—22no—
439C23×C47—22no—
440C23×C47—41no—
441C23×C47—42no—
442C23×C47—81no—
443C23×C47—81no—
444C23×C47C22×D411yescharacteristic
445C23×C47C22×D412yes—
446C23×C47C22×D411yescharacteristic
447C23×C47C22×D411yescharacteristic
448C22×D47—22no—
449C22×D47—24no—
450C22×D47—22no—
451C22×D47—21no—
452C22×D47—44no—
453C22×D47—44no—
454C22×D47—44no—
455C22×D47—42no—
456C22×D47—44no—
457C22×D47—44no—
458C22×D47—81no—
459C22×D47—82no—
460C22×D47—81no—
461C22×D47—82no—
462C22×D47—81no—
463C22×D47—81no—
464C22×D47—82no—
465C22×D47—82no—
466C22×D47—816no—
467Q8×C47—22no—
468Q8×C47—22no—
469Q8×C47—41no—
470Q8×C47—81no—
471Q8×C47—82no—
472D4×C47—24no—
473D4×C47—24no—
474D4×C47—22no—
475D4×C47—22no—
476D4×C47—41no—
477D4×C47—42no—
478D4×C47—44no—
479D4×C47—81no—
480D4×C47—82no—
481D4×C47—82no—
482D4×C47—82no—
483C2×C4×C47—22no—
484C2×C4×C47—22no—
485C2×C4×C47—22no—
486C2×C4×C47—22no—
487C2×C4×C47—22no—
488C2×C4×C47—22no—
489C2×C4×C47—22no—
490C2×C4×C47—22no—
491C2×C4×C47—41no—
492C2×C4×C47—41no—
493C2×C4×C47—41no—
494C2×C4×C47—42no—
495C2×C4×C47—82no—
496C2×C4×C47—82no—
497C2×C4×C47—81no—
498C2×C4×C47—81no—
499C2×C4×C47—82no—
500C2×C4×C47C22×D411yescharacteristic
501C2×C4×C47C22×D411yescharacteristic
502C2×C4×C47C22×D411yescharacteristic
503C2×C4×C47C22×D412yes—
504C2×C4×C47C22×D412yes—
505C2×C4×C47C22×D412yes—
506C2×C4×C47C2511yescharacteristic
507C22⋊D47—44no—
508C22⋊D47—42no—
509C22⋊D47—42no—
510C22⋊D47—42no—
511C22⋊D47—82no—
512C22⋊D47—82no—
513C2×Dic47—21no—
514C2×Dic47—21no—
515C2×Dic47—21no—
516D188—24no—
517D188—22no—
518D188—22no—
519D188—22no—
520D188—22no—
521D188—44no—
522D188—44no—
523D188—44no—
524D188—42no—
525D188—82no—
526D188—82no—
527D188H(5,𝔽2)14yes—
528C4×D47—44no—
529C4×D47—42no—
530C4×D47—82no—
531C4×D47—82no—
532Dic94—22no—
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—21no—
543C22×C47—22no—
544C22×C47—22no—
545C22×C47—21no—
546C22×C47—22no—
547C22×C47—21no—
548C22×C47—44no—
549C22×C47—42no—
550C22×C47—42no—
551C22×C47—42no—
552C22×C47—162no—
553C22×C47#57612yes—
554C22×C47#57712yes—
555C22×C47C23×D411yescharacteristic
556C2×D47—24no—
557C2×D47—42no—
558C2×D47—42no—
559C2×D47—41no—
560C2×D47—42no—
561C2×D47—41no—
562C2×D47—42no—
563C2×D47—41no—
564C2×D47—42no—
565C2×D47—84no—
566C2×D47—88no—
567C2×D47—88no—
568C2×D47—84no—
569C2×D47—164no—
570C4×C47—21no—
571C4×C47—22no—
572C4×C47—21no—
573C4×C47—21no—
574C4×C47—22no—
575C4×C47—22no—
576C4×C47—42no—
577C4×C47—42no—
578C4×C47—42no—
579C4×C47C2×H(5,𝔽2)12yes—
580Dic47—41no—
581Dic47—41no—
582Dic47—41no—
583#3536D4711yescharacteristic, complemented
584#3484—471no—
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—82no—
607C2×C47#348411yescharacteristic
608C2×C47C2×#57611yescharacteristic
609C2×C47C2×#57711yescharacteristic
610D47—44no—
611D47—82no—
612D47—81no—
613C2×H(5,𝔽2)—471no—
614C23×D4—471no—
615C2×AGL(1,ℤ/8)—472no—
616C2×#135—472no—
617C22×SD16—472no—
618C22×D8—472no—
619#562—22no—
620#554C2×D4712yescomplemented
621#548C2×D4712yescomplemented
622#547C2×D4712yescomplemented
623#546—22no—
624#546—472no—
625#546—472no—
626#546—941no—
627#546—941no—
628#546C2×D4712yescomplemented
629D42—472no—
630D42—472no—
631D42—941no—
632D42—941no—
633#543—21no—
634#542C2×D4712yescomplemented
635#539—21no—
636#538—21no—
637#537—21no—
638#537C2×D4712yescomplemented
639#535—471no—
640#535—471no—
641#534—942no—
642#525—471no—
643#525C2×D4711yescharacteristic
644C2×C22⋊Q8C2×D4711yescharacteristic, complemented
645C2×#121C2×D4711yescharacteristic, complemented
646C2×#120—942no—
647#518—471no—
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—471no—
680#450—472no—
681#450—472no—
682#450—472no—
683#450—472no—
684#450—472no—
685#449—472no—
686#449—472no—
687#449—472no—
688#449—472no—
689#448—471no—
690#447—471no—
691#447—472no—
692#447—472no—
693#447—472no—
694#447—472no—
695#447—472no—
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—941no—
714H(5,𝔽2)—1884no—
715C2×#41—22no—
716C2×#41—472no—
717C2×#41—471no—
718C2×#41—941no—
719C2×#41C22×D4711yescharacteristic
720C2×#41C22×D4712yescomplemented
721C22×Q8C22×D4711yescharacteristic
722C22×D4—21no—
723C22×D4—471no—
724C22×D4—472no—
725C22×D4—472no—
726C22×D4—472no—
727C22×D4—471no—
728C22×D4—942no—
729C22×D4—942no—
730C22×D4—942no—
731C22×D4—941no—
732C22×D4—941no—
733C22×D4—941no—
734C22×D4—941no—
735C22×D4—1884no—
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⋊Q8C22×D4712yescomplemented
759#127—472no—
760#127—941no—
761#126—22no—
762#125—22no—
763#124—22no—
764#124—22no—
765#124—472no—
766#124—941no—
767#124C22×D4712yescomplemented
768#123—22no—
769#123—22no—
770#123—22no—
771#123—22no—
772#123—941no—
773#123—942no—
774#123—942no—
775#123C22⋊D4712yes—
776C22⋊Q8—22no—
777C22⋊Q8—21no—
778C22⋊Q8—21no—
779C22⋊Q8—22no—
780C22⋊Q8—22no—
781C22⋊Q8—22no—
782C22⋊Q8—22no—
783C22⋊Q8—22no—
784C22⋊Q8—471no—
785C22⋊Q8—471no—
786C22⋊Q8C22⋊D4711yescharacteristic
787C22⋊Q8C22⋊D4711yescharacteristic
788C22⋊Q8C22×D4712yes—
789C22⋊Q8C22×D4712yes—
790C22⋊Q8C22×D4712yescomplemented
791#121—22no—
792#121—22no—
793#121—22no—
794#121—22no—
795#121—21no—
796#121—21no—
797#121—22no—
798#121—471no—
799#121—471no—
800#121—472no—
801#121—472no—
802#121—942no—
803#121—942no—
804#121—941no—
805#121—941no—
806#121—942no—
807#121—942no—
808#121C22⋊D4711yescharacteristic
809#121C22⋊D4711yescharacteristic
810#121C22×D4712yes—
811#121C22×D4712yes—
812#121C22×D4712yescomplemented
813#120—22no—
814#120—941no—
815#120—942no—
816#120—942no—
817#120—942no—
818#120—942no—
819#120—942no—
820#120—942no—
821#120—942no—
822#120—942no—
823#120C22⋊D4712yes—
824C4×Q8C22×D4712yescomplemented
825C4×D4—22no—
826C4×D4—22no—
827C4×D4—472no—
828C4×D4—472no—
829C4×D4—941no—
830C4×D4—941no—
831C4×D4—941no—
832C4×D4—941no—
833C4×D4C22×D4712yes—
834C4×D4C22×D4712yes—
835C4×D4C22×D4712yescomplemented
836#117—471no—
837#117C22×D4711yescharacteristic
838C2×C4⋊C4—21no—
839C2×C4⋊C4C22×D4711yescharacteristic
840C2×C4⋊C4C22×D4711yescharacteristic
841C2×C4⋊C4C22×D4712yescomplemented
842C2×C22⋊C4—21no—
843C2×C22⋊C4—21no—
844C2×C22⋊C4—22no—
845C2×C22⋊C4—942no—
846C2×C22⋊C4—942no—
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—941no—
882C24—941no—
883C24—942no—
884C24—942no—
885C24—942no—
886C24—3762no—
887C24—3762no—
888C24—1884no—
889C24C2×C22⋊D4711yescharacteristic
890#41—42no—
891#41—42no—
892#41—42no—
893#41—84no—
894#41—944no—
895#41—1882no—
896#41—1882no—
897#41—1884no—
898C2×Q8—21no—
899C2×Q8—22no—
900C2×Q8—42no—
901C2×Q8—471no—
902C2×Q8C2×C22⋊D4711yescharacteristic
903C2×Q8C23×D4712yes—
904C2×D4—22no—
905C2×D4—22no—
906C2×D4—22no—
907C2×D4—22no—
908C2×D4—21no—
909C2×D4—42no—
910C2×D4—82no—
911C2×D4—472no—
912C2×D4—472no—
913C2×D4—471no—
914C2×D4—944no—
915C2×D4—944no—
916C2×D4—944no—
917C2×D4—944no—
918C2×D4—942no—
919C2×D4—942no—
920C2×D4—941no—
921C2×D4—941no—
922C2×D4—941no—
923C2×D4—942no—
924C2×D4—941no—
925C2×D4—942no—
926C2×D4—942no—
927C2×D4—942no—
928C2×D4—942no—
929C2×D4—942no—
930C2×D4—941no—
931C2×D4—3764no—
932C2×D4—3764no—
933C2×D4—1882no—
934C2×D4—1882no—
935C2×D4—1882no—
936C2×D4—1882no—
937C2×D4—1884no—
938C2×D4—1884no—
939C2×D4—1884no—
940C2×D4—1884no—
941C2×D4—1888no—
942C2×D4C2×C22⋊D4712yes—
943C2×D4C2×C22⋊D4712yes—
944C2×D4C2×C22⋊D4712yes—
945C2×D4C2×C22⋊D4711yescharacteristic
946C2×D4C23×D4712yes—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—42no—
954C22×C4—942no—
955C22×C4—942no—
956C22×C4—942no—
957C22×C4—941no—
958C22×C4C2×C22⋊D4711yescharacteristic
959C22×C4C2×C22⋊D4711yescharacteristic
960C22×C4C2×C22⋊D4711yescharacteristic
961C22×C4C23×D4711yescharacteristic
962C22×C4C23×D4711yescharacteristic
963C22×C4C23×D4711yescharacteristic
964C22×C4C23×D4712yes—
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—22no—
986C4⋊C4—22no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—471no—
994C4⋊C4—471no—
995C4⋊C4—941no—
996C4⋊C4—941no—
997C4⋊C4C2×C22⋊D4711yescharacteristic
998C4⋊C4C2×C22⋊D4711yescharacteristic
999C4⋊C4C2×C22⋊D4712yes—
1000C4⋊C4C2×C22⋊D4712yes—
1001C4⋊C4C23×D4712yes—
1002C4⋊C4C23×D4712yes—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—941no—
1013C22⋊C4—941no—
1014C22⋊C4—941no—
1015C22⋊C4—942no—
1016C22⋊C4—942no—
1017C22⋊C4—942no—
1018C22⋊C4—942no—
1019C22⋊C4—942no—
1020C22⋊C4—942no—
1021C22⋊C4—941no—
1022C22⋊C4—941no—
1023C22⋊C4C2×C22⋊D4712yes—
1024C22⋊C4C2×C22⋊D4712yes—
1025C22⋊C4C2×C22⋊D4712yes—
1026C22⋊C4C2×C22⋊D4712yes—
1027C22⋊C4C2×C22⋊D4712yes—
1028C42—22no—
1029C42—941no—
1030C42C23×D4712yes—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—41no—
1035C23—42no—
1036C23—81no—
1037C23—81no—
1038C23—944no—
1039C23—942no—
1040C23—942no—
1041C23—941no—
1042C23—3762no—
1043C23—3762no—
1044C23—3761no—
1045C23—3761no—
1046C23—3761no—
1047C23—3761no—
1048C23—3762no—
1049C23—3762no—
1050C23—37616no—
1051C23—1884no—
1052C23—1884no—
1053C23—1884no—
1054C23—1882no—
1055C23—1884no—
1056C23—1884no—
1057C23C22×C22⋊D4711yescharacteristic
1058C23C22×C22⋊D4712yes—
1059C23C22×C22⋊D4711yescharacteristic
1060C23C22×C22⋊D4711yescharacteristic
1061Q8—22no—
1062Q8—22no—
1063Q8—41no—
1064Q8—81no—
1065Q8—82no—
1066Q8—942no—
1067D4—24no—
1068D4—24no—
1069D4—22no—
1070D4—22no—
1071D4—41no—
1072D4—42no—
1073D4—44no—
1074D4—81no—
1075D4—82no—
1076D4—82no—
1077D4—82no—
1078D4—474no—
1079D4—944no—
1080D4—942no—
1081D4—942no—
1082D4—942no—
1083D4—942no—
1084D4—3762no—
1085D4—3762no—
1086D4—3762no—
1087D4—3762no—
1088D4—1884no—
1089D4—1884no—
1090D4—1884no—
1091D4—1882no—
1092D4—1884no—
1093D4—1882no—
1094D4—1882no—
1095D4—1882no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—42no—
1108C2×C4—82no—
1109C2×C4—82no—
1110C2×C4—81no—
1111C2×C4—81no—
1112C2×C4—82no—
1113C2×C4—941no—
1114C2×C4—941no—
1115C2×C4—941no—
1116C2×C4—3762no—
1117C2×C4—3762no—
1118C2×C4—1884no—
1119C2×C4—1882no—
1120C2×C4C22×C22⋊D4712yes—
1121C2×C4C22×C22⋊D4711yescharacteristic
1122C2×C4C22×C22⋊D4712yes—
1123C2×C4C22×C22⋊D4711yescharacteristic
1124C2×C4C22×C22⋊D4712yes—
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—44no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—162no—
1146C22—944no—
1147C22—3768no—
1148C22—3768no—
1149C22—3764no—
1150C22—3764no—
1151C22—1881no—
1152C22—1882no—
1153C22—1881no—
1154C22—1882no—
1155C22—1881no—
1156C22—1882no—
1157C22—1882no—
1158C22—1882no—
1159C22—7524no—
1160C22#1568992612yes—
1161C22#1568993112yes—
1162C22C23×C22⋊D4711yescharacteristic
1163C4—22no—
1164C4—22no—
1165C4—21no—
1166C4—21no—
1167C4—21no—
1168C4—22no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—1881no—
1173C4—1881no—
1174C4—1881no—
1175C4H(5,𝔽2)×D4712yes—
1176C2—22no—
1177C2—22no—
1178C2—41no—
1179C2—42no—
1180C2—82no—
1181C2—3762no—
1182C2—3761no—
1183C2—1884no—
1184C2#2025701911yescharacteristic
1185C2C2×#1568992611yescharacteristic
1186C2C2×#1568993111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3536C2
socleC22×C47C23×D4
hypercenter#3536D47
hypocenterC47#61629
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #525 ◁ #3536

Complements

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

NH ≅ G/Ntype
1. #20257021C2semidirect
2. #20255463C2semidirect
3. #20255343C2semidirect
4. #20255206C2semidirect
5. #20255195C2semidirect
6. #20255096C2semidirect
7. #20255069C2semidirect
8. #20254884C2semidirect
9. #20254869C2semidirect
10. #20254476C2semidirect
11. #20254234C2semidirect
12. #20254169C2semidirect
13. #20254153C2semidirect
14. #20253566C2semidirect
15. #20252689C2semidirect
16. C2×#15689273C2semidirect
17. C2×#15689256C2semidirect
18. #20252444C2semidirect
19. C47×#3536C2semidirect
20. C2×#13094070C22semidirect
22. C2×#13094049C22semidirect
23. C2×#13094044C22semidirect
24. C22×#10625336C22semidirect
25. C22×#10625334C22semidirect
27. #15689769C22semidirect
31. D4×D188C22semidirect
34. #15689692C22semidirect
35. #15689687C22semidirect
39. #15689597C22semidirect
40. #15689513C22semidirect
41. #15689505C22semidirect
42. #15689485C22semidirect
43. #15689471C22semidirect
44. #15689461C22semidirect
45. #15689458C22semidirect
46. #15689453C22semidirect
47. #15689444C22semidirect
48. #15689441C22semidirect
49. #15689441C22semidirect
50. #15689436C22semidirect
51. #15689436C22semidirect
52. #15689410C22semidirect
53. #15689400C22semidirect
54. #15689374C22semidirect
55. #15689371C22semidirect
56. #15689362C22semidirect
57. #15689357C22semidirect
58. #15689357C22semidirect
59. #15689354C22semidirect
60. #15689354C22semidirect
61. #15689350C22semidirect
62. #15689345C22semidirect
63. #15689338C22semidirect
64. #15689335C22semidirect
65. #15689335C22semidirect
66. #15689323C22semidirect
67. #15689318C22semidirect
68. #15689283C22semidirect
69. #15689283C22semidirect
70. #15689279C22semidirect
71. #15689274C22semidirect
72. #15689273C22semidirect
73. #15689273C22semidirect
74. #15689273C22semidirect
75. #15689273C22semidirect
76. #15689273C22semidirect
77. #15689268C22semidirect
78. #15689268C22semidirect
79. #15689266C22semidirect
80. #15689266C22semidirect
81. #15689262C22semidirect
82. #15689257C22semidirect
84. #15689256C22semidirect
85. #15689256C22semidirect
86. #15689256C22semidirect
87. #15689256C22semidirect
88. #15689233C22semidirect
89. #15689221C22semidirect
90. C4×#10625336C22semidirect
91. C4×#10625334C22semidirect
92. #15689195C22semidirect
93. #15689195C22semidirect
94. D4×C47⋊C8C22semidirect
95. D4×C47⋊C8C22semidirect
96. #15689184C22semidirect
97. #15689122C22semidirect
98. C2×#13093944C22semidirect
99. C2×#13093944C22semidirect
100. C2×#13093944C22semidirect
101. #15689090C22semidirect
102. C2×C22⋊(C47⋊C8)C22semidirect
103. C2×C22⋊(C47⋊C8)C22semidirect
105. C47×#554C22semidirect
106. C47×#548C22semidirect
107. C47×#547C22semidirect
109. C47×#546C22semidirect
111. C47×#542C22semidirect
115. C47×#537C22semidirect
117. C2×C22⋊Q8×C47C22semidirect
118. C2×#121×C47C22semidirect
139. C2×#10625337C23semidirect
140. C2×#10625335C23semidirect
146. C2×#10625336C23semidirect
152. C2×#10625334C23semidirect
153. C2×#10625329C23semidirect
156. C22×C47⋊C8C23semidirect
195. #13093957C23semidirect
196. #13093957C23semidirect
197. #13093955C23semidirect
198. #13093955C23semidirect
199. C4⋊(C47⋊C8)C23semidirect
200. C4⋊(C47⋊C8)C23semidirect
201. #13093948C23semidirect
202. #13093948C23semidirect
203. #13093947C23semidirect
204. #13093947C23semidirect
205. #13093945C23semidirect
206. #13093945C23semidirect
215. #13093944C23semidirect
216. #13093944C23semidirect
223. C22⋊(C47⋊C8)C23semidirect
224. C22⋊(C47⋊C8)C23semidirect
225. #13093935C23semidirect
226. C4×C47⋊C8C23semidirect
229. C2×#41×C47C23semidirect
234. C4⋊Q8×C47C23semidirect
239. #124×C47C23semidirect
257. C22⋊Q8×C47C23semidirect
269. #121×C47C23semidirect
272. C4×Q8×C47C23semidirect
277. C4×D4×C47C23semidirect
282. C2×C4⋊C4×C47C23semidirect
583. #3536D47semidirect
620. #554C2×D47semidirect
621. #548C2×D47semidirect
622. #547C2×D47semidirect
628. #546C2×D47semidirect
634. #542C2×D47semidirect
638. #537C2×D47semidirect
644. C2×C22⋊Q8C2×D47semidirect
645. C2×#121C2×D47semidirect
712. C47#61629semidirect
720. C2×#41C22×D47semidirect
758. C4⋊Q8C22×D47semidirect
767. #124C22×D47semidirect
790. C22⋊Q8C22×D47semidirect
812. #121C22×D47semidirect
824. C4×Q8C22×D47semidirect
835. C4×D4C22×D47semidirect
841. C2×C4⋊C4C22×D47semidirect

Maximal subgroups

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

subgroupindex
#202570212
#202554632
#202553432
#202552062
#202551952
#202550962
#202550692
#202548842
#202548692
#202544762
#202542342
#202541692
#202541532
#202535662
#202526892
C2×#156892732
C2×#156892562
#202524442
C47×#35362
#6162947