Finite Group Databasebeta

← #27085943

Subgroups — #27085943

Order 12032.

1798 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256791C211yesmaximal, characteristic
2C2×#15689750C211yesmaximal, characteristic
3#20253941C211yesmaximal, characteristic, complemented
4#20253940C211yesmaximal, characteristic, complemented
5#20253938C212yesmaximal, complemented
6#20253932C212yesmaximal, complemented
7#20253930C211yesmaximal, characteristic, complemented
8#20253923C214yesmaximal, complemented
9#20253921C214yesmaximal, complemented
10#20253915C214yesmaximal, complemented
11#20253913C214yesmaximal, complemented
12#20251975C212yesmaximal
13#428×D47C212yesmaximal
14#20251805C211yesmaximal, characteristic
15C47×#3165C211yesmaximal, characteristic, complemented
16C2×M16×D47C2212yes—
17#15689753C2212yes—
18#15689753C2212yes—
19#15689752—21no—
20#15689752—21no—
21#15689750—22no—
22#15689750—22no—
23#15689750C2214yes—
24#15689750C2214yes—
25#15689750C2212yes—
26#15689750C2212yes—
27#15689748—21no—
28#15689748—21no—
29#15689680C2211yescharacteristic
30#15689677—22no—
31#15689677—22no—
32#15689676C2212yes—
33C2×#13094023C2211yescharacteristic
34C2×#13094022—21no—
35C2×#13094016C2211yescharacteristic
36C2×#13094015C2211yescharacteristic
37C2×#13094014—21no—
38C2×#13094002—21no—
39C2×#13094000—21no—
40C2×#13093982C2211yescharacteristic
41C2×#13093981C2211yescharacteristic
42#117×D47C2212yes—
43C2×C4⋊C4×D47C2211yescharacteristic
44#15689532C2212yescomplemented
45#15689532C2212yescomplemented
46#15689531C2214yescomplemented
47#15689531C2214yescomplemented
48#15689530C2214yescomplemented
49#15689530C2214yescomplemented
50#15689529C2212yescomplemented
51#15689529C2214yescomplemented
52#15689529C2212yescomplemented
53#15689527C2214yescomplemented
54#15689526C2212yescomplemented
55#15689525C2214yescomplemented
56#15689524C2214yescomplemented
57#15689523C2214yescomplemented
58#15689522C2214yescomplemented
59#15689520C2214yescomplemented
60#15689519C2212yescomplemented
61#15689166C2212yes—
62#15689166C2212yes—
63#15689165C2212yes—
64#15689165C2212yes—
65#15689164C2214yes—
66#15689164C2214yes—
67#15689163C2212yes—
68#15689163C2212yes—
69#15689162C2214yes—
70#15689162C2214yes—
71#15689160C2214yes—
72#15689158C2214yes—
73#107×D47C2214yes—
74#106×D47C2214yes—
75#15689080C2214yes—
76#15689077C2214yes—
77C4×#10625329C2211yescharacteristic
78M16×Dic47C2212yes—
79C47×#533C2211yescharacteristic
80C2×C4⋊Q8×C47C2211yescharacteristic
81C47×#501C2214yescomplemented
82C47×#500C2212yescomplemented
83C47×#498C2212yescomplemented
84C47×#428C2212yes—
85C47×#428C2212yes—
86C4×M16×C47C2211yescharacteristic
87C22×Dic94—21no—
88C22×C4×D47—21no—
89C22×C4×D47C2311yescharacteristic
90C2×#10625329C2312yes—
91C2×#10625324C2314yes—
92M16×D47Q8116yescomplemented
93C2×C8×D47C2314yes—
94#13094024C2311yescharacteristic
95#13094024C2311yescharacteristic
96#13094023—22no—
97#13094023—22no—
98#13094023—22no—
99#13094023C2314yes—
100#13094023C2312yes—
101#13094023C2312yes—
102#13094022—24no—
103#13094022—24no—
104#13094022—22no—
105#13094022—22no—
106#13094016—21no—
107#13094016—21no—
108#13094016C2312yes—
109#13094016C2312yes—
110#13094016C2312yes—
111#13094015—22no—
112#13094015C2314yes—
113#13094015C2312yes—
114#13094015C2312yes—
115#13094014—24no—
116#13094014—24no—
117#13094014—22no—
118#13094014—22no—
119#13094014—22no—
120#13094014—22no—
121#13094004—22no—
122#13094004—22no—
123#13094003—21no—
124#13094003—21no—
125#13094002—22no—
126#13094002—22no—
127#13094002—22no—
128#13094002—22no—
129#13094002—24no—
130#13094002—24no—
131#13094001—22no—
132#13094001—22no—
133#13094000—22no—
134#13094000—22no—
135#13094000—24no—
136#13094000—24no—
137C4×Dic94—21no—
138C4×Dic94—21no—
139C4×Dic94—22no—
140C4×Dic94—22no—
141#13093983C2312yes—
142#13093982—22no—
143#13093982C2314yes—
144#13093982C2312yes—
145#13093982C2312yes—
146#13093981—22no—
147#13093981D412yes—
148#13093981D412yes—
149#13093981C2312yes—
150#13093981C2312yes—
151#13093980—22no—
152C2×C4⋊Dic47—21no—
153C2×C4⋊Dic47C2311yescharacteristic
154C2×C4⋊Dic47C2311yescharacteristic
155C2×Dic47⋊C4—21no—
156C2×Dic47⋊C4—21no—
157C2×Dic47⋊C4—21no—
158C2×Dic47⋊C4—21no—
159C2×Dic47⋊C4—21no—
160C2×Dic47⋊C4D411yescharacteristic
161C2×Dic47⋊C4D411yescharacteristic
162C4⋊C4×D47—22no—
163C4⋊C4×D47C2314yes—
164C4⋊C4×D47C2312yes—
165C4⋊C4×D47C2312yes—
166C2×(C2×D47)⋊C4—21no—
167C2×(C2×D47)⋊C4D411yescharacteristic
168C2×(C2×D47)⋊C4D411yescharacteristic
169C22⋊C4×D47—22no—
170C2×C4×Dic47—21no—
171C2×C4×Dic47C2311yescharacteristic
172C42×D47—22no—
173#13093958C2314yes—
174#13093958C2314yes—
175#13093957C2314yes—
176#13093957C2314yes—
177#13093957C2314yes—
178#13093957C2314yes—
179#13093956C2314yes—
180#13093956C2314yes—
181#13093955C2314yes—
182#13093955C2314yes—
183#13093955C2314yes—
184#13093955C2314yes—
185#13093935C2312yes—
186#13093934C2314yes—
187C4×C47⋊C8C2312yes—
188C8×Dic47C2314yes—
189C22×Q8×C47—21no—
190C2×M16×C47C2312yes—
191C4⋊Q8×C47—21no—
192C4⋊Q8×C47—21no—
193C4⋊Q8×C47C2312yes—
194C4⋊Q8×C47C2311yescharacteristic
195C4⋊Q8×C47C2312yes—
196C4⋊Q8×C47C2311yescharacteristic
197#125×C47C2312yes—
198C22⋊Q8×C47—21no—
199C22⋊Q8×C47—21no—
200C4×Q8×C47—21no—
201C4×Q8×C47—21no—
202#117×C47C2312yes—
203C2×C4⋊C4×C47—21no—
204C2×C4⋊C4×C47C2311yescharacteristic
205C2×C4⋊C4×C47C2311yescharacteristic
206C2×C42×C47C2311yescharacteristic
207#107×C47C2314yes—
208#107×C47C2314yes—
209#106×C47C2314yes—
210#106×C47C2314yes—
211#97×C47C2312yes—
212C4×C8×C47C2312yes—
213C23×D47C2×D411yescharacteristic
214C2×Q8×C47—21no—
215C2×Q8×C47—21no—
216C2×Q8×C47—22no—
217C2×Q8×C47—22no—
218C2×Q8×C47—82no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2411yescharacteristic
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47C2×D411yescharacteristic
227C22×Dic47C2×D411yescharacteristic
228C22×Dic47C2×D411yescharacteristic
229C2×C4×D47—22no—
230C2×C4×D47—22no—
231C2×C4×D47—24no—
232C2×C4×D47—82no—
233C2×C4×D47C2×D412yes—
234C2×C4×D47C2×Q818yes—
235C2×C4×D47C2412yes—
236C2×Dic94—21no—
237C2×Dic94—21no—
238C2×Dic94—22no—
239C2×Dic94—22no—
240C2×Dic94—24no—
241C2×Dic94—82no—
242M16×C47C2×Q818yes—
243C2×C8×C47C2414yes—
244C4⋊C4×C47—22no—
245C4⋊C4×C47—22no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—22no—
249C4⋊C4×C47—22no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47C2412yes—
253C4⋊C4×C47C2412yes—
254C4⋊C4×C47C2412yes—
255C4⋊C4×C47C2412yes—
256C22⋊C4×C47—22no—
257C42×C47—22no—
258C42×C47C2×D411yescharacteristic
259C42×C47C2×D411yescharacteristic
260C42×C47C2411yescharacteristic
261C42×C47C2411yescharacteristic
262C22⋊Dic47—22no—
263(C2×D47)⋊C4—22no—
264(C2×D47)⋊C4—22no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4C2×D412yes—
267(C2×D47)⋊C4C2×D412yes—
268(C2×D47)⋊C4C2×D412yes—
269(C2×D47)⋊C4C2×D412yes—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47—21no—
273C4⋊Dic47—21no—
274C4⋊Dic47—24no—
275C4⋊Dic47—22no—
276C4⋊Dic47—22no—
277C4⋊Dic47C2412yes—
278C4⋊Dic47C2412yes—
279C4⋊Dic47C2412yes—
280C4⋊Dic47C2412yes—
281Dic47⋊C4—22no—
282Dic47⋊C4—22no—
283Dic47⋊C4—22no—
284Dic47⋊C4—22no—
285Dic47⋊C4—22no—
286Dic47⋊C4—22no—
287Dic47⋊C4—24no—
288Dic47⋊C4—22no—
289Dic47⋊C4—22no—
290Dic47⋊C4—24no—
291Dic47⋊C4—24no—
292Dic47⋊C4—22no—
293Dic47⋊C4—22no—
294Dic47⋊C4—22no—
295Dic47⋊C4—22no—
296Dic47⋊C4C2×D412yes—
297Dic47⋊C4C2×D412yes—
298Dic47⋊C4C2×D412yes—
299Dic47⋊C4C2×D412yes—
300C4×Dic47—22no—
301C4×Dic47—22no—
302C4×Dic47—22no—
303C4×Dic47—24no—
304C4×Dic47C2×D412yes—
305C4×Dic47C2412yes—
306#10625329C2×Q818yes—
307C2×C47⋊C8C2414yes—
308#10625324C2×Q8116yescomplemented
309C8×D47C2×Q8116yescomplemented
310C23×C47C22×D411yescharacteristic
311C22×D47—41no—
312C22×D47—41no—
313C22×D47C4⋊Q814yes—
314C22×D47C22×D412yes—
315Q8×C47—81no—
316Q8×C47—81no—
317Q8×C47—82no—
318Q8×C47—82no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47C22×D411yescharacteristic
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C22×Q814yes—
333C2×C4×C47C2511yescharacteristic
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47C4⋊Q814yes—
343C2×Dic47C22×D412yes—
344C2×Dic47C22×D412yes—
345C2×Dic47C22×D412yes—
346C4×D47—82no—
347C4×D47—82no—
348C4×D47—84no—
349C4×D47C4⋊Q818yes—
350C4×D47C22×Q814yes—
351C4×D47C22×Q814yes—
352Dic94—82no—
353Dic94—82no—
354Dic94—84no—
355Dic94—81no—
356Dic94—81no—
357C8×C47C22×Q818yes—
358C47⋊C8C22×Q818yes—
359#60664—471nomaximal, Sylow
360C22×C47—21no—
361C22×C47—21no—
362C22×C47C2×C4⋊Q812yes—
363C22×C47C23×D411yescharacteristic
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—44no—
367C2×D47C2×C4⋊Q814yes—
368C4×C47—21no—
369C4×C47—21no—
370C4×C47—21no—
371C4×C47—21no—
372C4×C47—42no—
373C4×C47—42no—
374C4×C47—42no—
375C4×C47—42no—
376C4×C47C2×C4⋊Q812yes—
377C4×C47C23×Q812yes—
378Dic47—22no—
379Dic47—22no—
380Dic47—42no—
381Dic47—42no—
382Dic47—42no—
383Dic47—42no—
384Dic47C2×C4⋊Q814yes—
385#3458—471no—
386C2×#544—471no—
387#3166—472no—
388#3166—471no—
389#3166—471no—
390#3165—472no—
391#3165—471no—
392#3165D4711yescharacteristic, complemented
393#3164—474no—
394#3164—474no—
395#3163—474no—
396#3163—474no—
397#2911—472no—
398C2×#428—472no—
399#2873—471no—
400C2×C47—22no—
401C2×C47C22×C4⋊Q811yescharacteristic
402C2×C47#358511yescharacteristic
403C2×C47#358611yescharacteristic
404D47—24no—
405C22×M16—472no—
406#544—472no—
407#544—474no—
408#544—474no—
409#544—472no—
410#544—472no—
411#544—472no—
412#544—941no—
413#544—941no—
414#544—942no—
415#544—942no—
416#543—941no—
417#543—941no—
418#533—472no—
419#533—471no—
420#533—942no—
421#533—942no—
422#533C2×D4711yescharacteristic
423C2×C4⋊Q8—471no—
424C2×C4⋊Q8—941no—
425C2×C4⋊Q8C2×D4711yescharacteristic
426C2×#125—471no—
427C2×#125—471no—
428C2×#125—941no—
429C2×C22⋊Q8—941no—
430C2×C22⋊Q8—941no—
431C2×#117—471no—
432C2×#117—472no—
433C2×#117—471no—
434C22×C4⋊C4—471no—
435#501—472no—
436#501—474no—
437#501—472no—
438#501—474no—
439#501—474no—
440#501—474no—
441#501—474no—
442#501—472no—
443#501—472no—
444#501C2×D4714yescomplemented
445#500—472no—
446#500—474no—
447#500C2×D4712yescomplemented
448#499—474no—
449#499—474no—
450#499—474no—
451#499—474no—
452#498—472no—
453#498—474no—
454#498C2×D4712yescomplemented
455#428—472no—
456#428—472no—
457#428—472no—
458#428—472no—
459#428—472no—
460#428—472no—
461#428—474no—
462#428—474no—
463#428—474no—
464#428—474no—
465#428C2×D4712yes—
466#428C2×D4712yes—
467#427—474no—
468#427—474no—
469C2×#107—474no—
470C2×#106—474no—
471#405—474no—
472#405—474no—
473C4×M16—472no—
474C4×M16—471no—
475C4×M16C2×D4711yescharacteristic
476C47#6066411yescharacteristic, complemented, Sylow
477C22×Q8—21no—
478C22×Q8—941no—
479C23×C4—471no—
480C23×C4—941no—
481C2×M16—472no—
482C2×M16—4716no—
483C2×M16—474no—
484C2×M16C22×D4712yes—
485C22×C8—474no—
486C4⋊Q8—21no—
487C4⋊Q8—21no—
488C4⋊Q8—474no—
489C4⋊Q8—472no—
490C4⋊Q8—472no—
491C4⋊Q8—471no—
492C4⋊Q8—471no—
493C4⋊Q8—942no—
494C4⋊Q8—942no—
495C4⋊Q8—942no—
496C4⋊Q8—944no—
497C4⋊Q8—944no—
498C4⋊Q8—942no—
499C4⋊Q8—942no—
500C4⋊Q8C22×D4712yes—
501C4⋊Q8C22×D4712yes—
502C4⋊Q8C22×D4711yescharacteristic
503C4⋊Q8C22×D4711yescharacteristic
504#125—474no—
505#125—472no—
506#125—472no—
507#125—472no—
508#125—472no—
509#125—472no—
510#125—942no—
511#125—944no—
512#125—944no—
513#125—942no—
514#125—942no—
515#125—942no—
516#125—942no—
517#125—941no—
518#125—941no—
519#125C22×D4712yes—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—942no—
523C22⋊Q8—942no—
524C22⋊Q8—944no—
525C22⋊Q8—944no—
526C22⋊Q8—942no—
527C22⋊Q8—942no—
528C22⋊Q8—942no—
529C22⋊Q8—942no—
530C22⋊Q8—942no—
531C22⋊Q8—942no—
532C22⋊Q8—944no—
533C22⋊Q8—944no—
534C22⋊Q8—942no—
535C22⋊Q8—942no—
536C22⋊Q8—941no—
537C22⋊Q8—941no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—942no—
541C4×Q8—942no—
542C4×Q8—941no—
543C4×Q8—941no—
544#117—472no—
545#117—472no—
546#117—472no—
547#117—472no—
548#117—472no—
549#117—472no—
550#117—474no—
551#117—472no—
552#117—942no—
553#117—942no—
554#117—942no—
555#117C22×D4712yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—471no—
558C2×C4⋊C4—471no—
559C2×C4⋊C4—471no—
560C2×C4⋊C4—471no—
561C2×C4⋊C4—474no—
562C2×C4⋊C4—472no—
563C2×C4⋊C4—472no—
564C2×C4⋊C4—942no—
565C2×C4⋊C4—941no—
566C2×C4⋊C4—941no—
567C2×C4⋊C4—941no—
568C2×C4⋊C4—941no—
569C2×C4⋊C4—941no—
570C2×C4⋊C4—941no—
571C2×C4⋊C4C22×D4711yescharacteristic
572C2×C4⋊C4C22×D4711yescharacteristic
573C2×C22⋊C4—471no—
574C2×C22⋊C4—471no—
575C2×C22⋊C4—942no—
576C2×C22⋊C4—941no—
577C2×C42—471no—
578C2×C42—942no—
579C2×C42—941no—
580C2×C42C22×D4711yescharacteristic
581#107—474no—
582#107—474no—
583#107—474no—
584#107—474no—
585#107—474no—
586#107—474no—
587#107C22×D4714yes—
588#107C22×D4714yes—
589#106—474no—
590#106—474no—
591#106—474no—
592#106—474no—
593#106—474no—
594#106—474no—
595#106C22×D4714yes—
596#106C22×D4714yes—
597#97—474no—
598#97—472no—
599#97C22×D4712yes—
600C4×C8—474no—
601C4×C8—472no—
602C4×C8C22×D4712yes—
603C24—471no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—82no—
609C2×Q8—942no—
610C2×Q8—942no—
611C2×Q8—944no—
612C2×Q8—941no—
613C2×Q8—941no—
614C2×Q8—3762no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—471no—
618C22×C4—472no—
619C22×C4—478no—
620C22×C4—472no—
621C22×C4—471no—
622C22×C4—471no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—944no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—3762no—
629C22×C4D4×D4711yescharacteristic
630C22×C4D4×D4711yescharacteristic
631C22×C4C23×D4711yescharacteristic
632M16—478no—
633M16—4716no—
634M16Q8×D4718yes—
635C2×C8—474no—
636C2×C8—4716no—
637C2×C8C23×D4714yes—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—472no—
647C4⋊C4—472no—
648C4⋊C4—472no—
649C4⋊C4—472no—
650C4⋊C4—472no—
651C4⋊C4—472no—
652C4⋊C4—472no—
653C4⋊C4—472no—
654C4⋊C4—944no—
655C4⋊C4—942no—
656C4⋊C4—942no—
657C4⋊C4—944no—
658C4⋊C4—944no—
659C4⋊C4—942no—
660C4⋊C4—942no—
661C4⋊C4—942no—
662C4⋊C4—942no—
663C4⋊C4—944no—
664C4⋊C4—942no—
665C4⋊C4—942no—
666C4⋊C4—942no—
667C4⋊C4—942no—
668C4⋊C4—942no—
669C4⋊C4—942no—
670C4⋊C4—942no—
671C4⋊C4—942no—
672C4⋊C4—941no—
673C4⋊C4—941no—
674C4⋊C4—941no—
675C4⋊C4—941no—
676C4⋊C4C23×D4712yes—
677C4⋊C4C23×D4712yes—
678C4⋊C4C23×D4712yes—
679C4⋊C4C23×D4712yes—
680C22⋊C4—22no—
681C22⋊C4—472no—
682C22⋊C4—472no—
683C22⋊C4—472no—
684C22⋊C4—472no—
685C22⋊C4—942no—
686C22⋊C4—942no—
687C22⋊C4—944no—
688C22⋊C4—942no—
689C42—22no—
690C42—472no—
691C42—472no—
692C42—942no—
693C42—942no—
694C42—944no—
695C42—942no—
696C42D4×D4711yescharacteristic
697C42D4×D4711yescharacteristic
698C42C23×D4711yescharacteristic
699C42C23×D4711yescharacteristic
700C23—472no—
701C23—474no—
702C23—1881no—
703C23—1881no—
704C23C2×D4×D4711yescharacteristic
705Q8—81no—
706Q8—81no—
707Q8—82no—
708Q8—82no—
709Q8—3761no—
710Q8—3761no—
711Q8—3762no—
712Q8—3762no—
713Q8—3764no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—474no—
723C2×C4—472no—
724C2×C4—478no—
725C2×C4—474no—
726C2×C4—474no—
727C2×C4—472no—
728C2×C4—472no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—3762no—
734C2×C4—3762no—
735C2×C4—3764no—
736C2×C4—1881no—
737C2×C4—1881no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4C2×D4×D4711yescharacteristic
741C2×C4C2×D4×D4711yescharacteristic
742C2×C4C2×D4×D4711yescharacteristic
743C2×C4C2×D4×D4711yescharacteristic
744C2×C4C2×D4×D4711yescharacteristic
745C2×C4C2×Q8×D4714yes—
746C2×C4C24×D4711yescharacteristic
747C8—478no—
748C8C2×Q8×D4718yes—
749C22—21no—
750C22—21no—
751C22—474no—
752C22—942no—
753C22—942no—
754C22—1884no—
755C22C4⋊Q8×D4712yes—
756C22C22×D4×D4711yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—474no—
766C4—942no—
767C4—942no—
768C4—1882no—
769C4—1882no—
770C4—1882no—
771C4—1882no—
772C4C4⋊Q8×D4712yes—
773C4C22×Q8×D4712yes—
774C2—22no—
775C2—944no—
776C2C2×C4⋊Q8×D4711yescharacteristic
777C2#2025816411yescharacteristic
778C2#2025817111yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3165C2
socleC22×C47C23×D4
prime radicalC23×D47C2×D4
hypercenter#3165D47
hypocenterC47#60664
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. #20253941C2semidirect
4. #20253940C2semidirect
5. #20253938C2semidirect
6. #20253932C2semidirect
7. #20253930C2semidirect
8. #20253923C2semidirect
9. #20253921C2semidirect
10. #20253915C2semidirect
11. #20253913C2semidirect
15. C47×#3165C2semidirect
44. #15689532C22semidirect
45. #15689532C22semidirect
46. #15689531C22semidirect
47. #15689531C22semidirect
48. #15689530C22semidirect
49. #15689530C22semidirect
50. #15689529C22semidirect
51. #15689529C22semidirect
52. #15689529C22semidirect
53. #15689527C22semidirect
54. #15689526C22semidirect
55. #15689525C22semidirect
56. #15689524C22semidirect
57. #15689523C22semidirect
58. #15689522C22semidirect
59. #15689520C22semidirect
60. #15689519C22semidirect
81. C47×#501C22semidirect
82. C47×#500C22semidirect
83. C47×#498C22semidirect
92. M16×D47Q8semidirect
308. #10625324C2×Q8semidirect
309. C8×D47C2×Q8semidirect
392. #3165D47semidirect
444. #501C2×D47semidirect
447. #500C2×D47semidirect
454. #498C2×D47semidirect
476. C47#60664semidirect

Maximal subgroups

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

subgroupindex
#202567912
C2×#156897502
#202539412
#202539402
#202539382
#202539322
#202539302
#202539232
#202539212
#202539152
#202539132
#202519752
#428×D472
#202518052
C47×#31652
#6066447