Finite Group Databasebeta

← #27091464

Subgroups — #27091464

Order 12032.

2790 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689923C212yesmaximal, complemented
2D4×#10625350C212yesmaximal, complemented
3#20255056C212yesmaximal, complemented
4#20255046C212yesmaximal, complemented
5#20255036C212yesmaximal, complemented
6#20255024C214yesmaximal, complemented
7#20255010C212yesmaximal, complemented
8#20255000C212yesmaximal, complemented
9#20254990C212yesmaximal, complemented
10#20253816C211yesmaximal, characteristic, complemented
11#20252997C212yesmaximal, complemented
12#20252845C212yesmaximal, complemented
13#20252610C214yesmaximal, complemented
14C4×#13094046C211yesmaximal, characteristic, complemented
15C2×C47×#436C211yesmaximal, characteristic, complemented
16C22×#10625350C2214yescomplemented
17#15689923—216no—
18C2×#13094057C2214yescomplemented
19C2×#13094057C2214yescomplemented
20C2×#13094052C2214yescomplemented
21C2×#13094052C2214yescomplemented
22C2×#13094046C2211yescharacteristic
23C2×#13094046C2212yescomplemented
24C2×#13094046C2214yescomplemented
25C2×#13094046C2212yescomplemented
26#15689794C2212yes—
27D4×Dic94C2212yescomplemented
28#15689782C2214yescomplemented
29#15689778C2212yes—
30#15689774—22no—
31#15689769C2214yescomplemented
32#15689763—24no—
33D4×D188C2212yescomplemented
34D4×C22⋊D47—22no—
35#15689673C2212yescomplemented
36#15689670—22no—
37#15689634C2214yescomplemented
38#15689632—24no—
39C4×#10625350C2212yescomplemented
40C4×D4×D47—22no—
41#15689507C2212yescomplemented
42#15689507C2212yescomplemented
43#15689503C2211yescharacteristic, complemented
44#15689500C2211yescharacteristic, complemented
45#15689496C2212yescomplemented
46#15689381C2214yescomplemented
47#15689376C2214yescomplemented
48#15689369C2214yescomplemented
49#15689369C2214yescomplemented
50#15689346C2214yescomplemented
51#15689339C2214yescomplemented
52#15689334C2212yescomplemented
53#15689329C2212yescomplemented
54#15689324C2212yescomplemented
55#15689319C2212yescomplemented
56#15689287C2214yescomplemented
57#15689287C2214yescomplemented
58#15689281C2214yescomplemented
59#15689276C2214yescomplemented
60#15689270C2214yescomplemented
61#15689270C2214yescomplemented
62#15689264C2214yescomplemented
63#15689259C2214yescomplemented
64C4×Dic188C2211yescharacteristic, complemented
65C4×Dic188C2211yescharacteristic, complemented
66C4×#10625325C2212yescomplemented
67C4×#10625325C2212yescomplemented
68C4×D376C2211yescharacteristic, complemented
69C4×D376C2211yescharacteristic, complemented
70#15689161C2211yescharacteristic, complemented
71#15689120C2212yescomplemented
72#15689120C2214yescomplemented
73C22×M16×C47C2212yescomplemented
74C2×C4×D4×C47C2211yescharacteristic
75C47×#436C2212yescomplemented
76C47×#436C2212yescomplemented
77C47×#436C2212yescomplemented
78C47×#436C2212yescomplemented
79C2×C4⋊C8×C47C2211yescharacteristic, complemented
80C2×C22⋊C8×C47C2212yescomplemented
81C2×C4×C8×C47C2211yescharacteristic, complemented
82C2×#10625350—24no—
83C2×#10625350—24no—
84C2×#10625350—216no—
85C2×#10625350—48no—
86C2×#10625350C2314yes—
87C2×#10625350C2314yes—
88C2×#10625350C2314yes—
89C2×#10625350C2312yes—
90C22×Dic94C2314yes—
91C22×D188C2314yes—
92C22×C22⋊D47—24no—
93C2×D4×D47—22no—
94C22×C4×D47—24no—
95#13094057—216no—
96#13094057—216no—
97#13094052—216no—
98#13094052—216no—
99#13094046—216no—
100#13094046—28no—
101#13094046—44no—
102#13094046D418yescomplemented
103C2×Dic188C2312yes—
104C2×Dic188C2314yes—
105C2×Dic188C2312yes—
106C2×Dic188C2311yescharacteristic
107C2×#10625325C2314yes—
108C2×#10625325C2314yes—
109C2×#10625325C2314yes—
110C2×#10625325C2314yes—
111C2×#10625325C2312yes—
112C2×D376C2312yes—
113C2×D376C2314yes—
114C2×D376C2312yes—
115C2×D376C2311yescharacteristic
116#13094024C2312yes—
117#13094023—22no—
118#13094021C2312yes—
119#13094020—22no—
120#13094012C2314yes—
121#13094010—24no—
122#13094009—24no—
123#13094007—24no—
124#13094006—24no—
125#13094003C2314yes—
126#13094003C2314yes—
127#13094002—24no—
128#13094001—24no—
129#13093999—22no—
130#13093998—22no—
131#13093998—22no—
132#13093998C2314yes—
133#13093998C2314yes—
134#13093997—24no—
135#13093997—24no—
136#13093996—24no—
137#13093995—22no—
138#13093994—24no—
139#13093993—24no—
140#13093992—24no—
141C4×Dic94C2312yes—
142C4×Dic94C2312yes—
143C4×D188—22no—
144C4×D188—22no—
145C4×D188C2312yes—
146C4×D188C2312yes—
147D4×Dic47—22no—
148#13093986—22no—
149C4×C22⋊D47—22no—
150C4×C22⋊D47—22no—
151C4×C22⋊D47—24no—
152C4×C22⋊D47—24no—
153(C22⋊D47)⋊C4—24no—
154#13093983C2312yes—
155#13093981—22no—
156C4⋊C4×D47—22no—
157C22⋊C4×D47—24no—
158C42×D47—22no—
159#13093958C2311yescharacteristic
160#13093958C2311yescharacteristic
161#13093956C2312yes—
162#13093949C2312yes—
163#13093949C2312yes—
164#13093949C2314yes—
165#13093949C2314yes—
166#13093946C2312yes—
167#13093946C2314yes—
168#13093946C2312yes—
169#13093946C2314yes—
170C22×D4×C47D411yescharacteristic
171C23×C4×C47C2312yes—
172C2×M16×C47—28no—
173C2×M16×C47C2314yes—
174C2×M16×C47C2314yes—
175C22×C8×C47C2312yes—
176C22×C8×C47C2311yescharacteristic
177C22×C8×C47C2311yescharacteristic
178C4×D4×C47D412yes—
179C4×D4×C47D412yes—
180C4×D4×C47C2312yes—
181C4×D4×C47C2312yes—
182C2×C4⋊C4×C47D411yescharacteristic
183C2×C22⋊C4×C47D412yes—
184C2×C42×C47C2311yescharacteristic
185C4⋊C8×C47C2312yes—
186C4⋊C8×C47C2312yes—
187C22⋊C8×C47C2314yes—
188C22⋊C8×C47C2314yes—
189C4×C8×C47C2311yescharacteristic
190C4×C8×C47C2311yescharacteristic
191C4×C8×C47C2311yescharacteristic
192C4×C8×C47C2311yescharacteristic
193C24×C47C2×D412yes—
194C23×D47—24no—
195C2×D4×C47—42no—
196C2×D4×C47C2×D412yes—
197C2×D4×C47C2×D412yes—
198C22×C4×C47—24no—
199C22×C4×C47—24no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2×D414yes—
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2414yes—
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—22no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—24no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—24no—
212C2×C22⋊D47—416no—
213C22×Dic47—24no—
214D4×D47—48no—
215#10625350—24no—
216#10625350—28no—
217#10625350—28no—
218#10625350—28no—
219#10625350—28no—
220#10625350—44no—
221#10625350—44no—
222#10625350—416no—
223#10625350—416no—
224#10625350C2×D418yescomplemented
225C2×D188—28no—
226C2×D188—22no—
227C2×D188—24no—
228C2×D188—22no—
229C2×D188—44no—
230C2×D188C2414yes—
231C2×D188C2412yes—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—24no—
235C2×C4×D47—24no—
236C2×C4×D47—24no—
237C2×C4×D47—22no—
238C2×C4×D47—416no—
239C2×Dic94—28no—
240C2×Dic94—24no—
241C2×Dic94—44no—
242C2×Dic94C2414yes—
243C2×Dic94C2412yes—
244M16×C47—28no—
245M16×C47—28no—
246C2×C8×C47—24no—
247C2×C8×C47—22no—
248C2×C8×C47C2×D414yescomplemented
249C2×C8×C47C2414yes—
250C2×C8×C47C2411yescharacteristic
251C2×C8×C47C2411yescharacteristic
252C2×C8×C47C2411yescharacteristic
253C2×C8×C47C2411yescharacteristic
254C4⋊C4×C47C2×D412yes—
255C4⋊C4×C47C2×D412yes—
256C22⋊C4×C47C2×D414yes—
257C22⋊C4×C47C2×D414yes—
258C42×C47C2×D411yescharacteristic
259C42×C47C2×D411yescharacteristic
260C42×C47C2411yescharacteristic
261C42×C47C2411yescharacteristic
262C22⋊Dic47—24no—
263C22⋊Dic47—22no—
264C22⋊Dic47—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—22no—
268(C2×D47)⋊C4—22no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271C4⋊Dic47—22no—
272C4⋊Dic47—22no—
273C4⋊Dic47C2412yes—
274C4⋊Dic47C2412yes—
275Dic47⋊C4—24no—
276Dic47⋊C4—22no—
277Dic47⋊C4—22no—
278Dic47⋊C4—24no—
279C4×Dic47—22no—
280C4×Dic47—22no—
281C4×Dic47—22no—
282Dic188—28no—
283Dic188—24no—
284Dic188—42no—
285Dic188C2×D414yescomplemented
286D376—28no—
287D376—24no—
288D376—42no—
289D376C2×D414yescomplemented
290#10625325—28no—
291#10625325—28no—
292#10625325—28no—
293#10625325—44no—
294#10625325C2×D418yescomplemented
295C23×C47—24no—
296C23×C47—42no—
297C23×C47—42no—
298C23×C47C22×D414yes—
299C23×C47C22×D411yescharacteristic
300C22×D47—22no—
301C22×D47—24no—
302C22×D47—48no—
303C22×D47—48no—
304C22×D47—84no—
305D4×C47—24no—
306D4×C47—42no—
307C2×C4×C47—24no—
308C2×C4×C47—28no—
309C2×C4×C47—22no—
310C2×C4×C47—24no—
311C2×C4×C47—24no—
312C2×C4×C47—41no—
313C2×C4×C47C22×D412yes—
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C22×D411yescharacteristic
317C2×C4×C47C22×D414yes—
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47H(5,𝔽2)12yes—
321C2×C4×C47C2511yescharacteristic
322C22⋊D47—28no—
323C22⋊D47—48no—
324C22⋊D47—48no—
325C22⋊D47—48no—
326C22⋊D47—48no—
327C22⋊D47—84no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—24no—
332C2×Dic47—48no—
333D188—24no—
334D188—22no—
335D188—24no—
336D188—48no—
337D188—44no—
338D188—82no—
339D188C22×D414yes—
340C4×D47—28no—
341C4×D47—48no—
342C4×D47—48no—
343C4×D47—48no—
344C4×D47—44no—
345C4×D47—82no—
346Dic94—22no—
347Dic94—24no—
348Dic94—24no—
349Dic94—48no—
350Dic94C22×D414yes—
351C8×C47—24no—
352C8×C47—21no—
353C8×C47—21no—
354C8×C47C22×D412yes—
355C8×C47C22×D412yes—
356#61038—471nomaximal, Sylow
357C22×C47—21no—
358C22×C47—21no—
359C22×C47—24no—
360C22×C47—24no—
361C22×C47—24no—
362C22×C47—84no—
363C22×C47D4212yes—
364C22×C47C23×D411yescharacteristic
365C2×D47—24no—
366C2×D47—42no—
367C2×D47—42no—
368C2×D47—44no—
369C2×D47—44no—
370C2×D47—44no—
371C2×D47—816no—
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—24no—
375C4×C47—21no—
376C4×C47D4212yes—
377C4×C47#57512yescomplemented
378C4×C47C23×D411yescharacteristic
379C4×C47C2×H(5,𝔽2)11yescharacteristic
380Dic47—24no—
381Dic47—42no—
382Dic47—44no—
383Dic47—42no—
384C2×#575—472no—
385D4×#41—472no—
386#3278—472no—
387#3277—472no—
388#3276—472no—
389#3275—474no—
390#3274—472no—
391#3273—472no—
392#3272—472no—
393#3147—471no—
394#3054—472no—
395#3035—472no—
396#3002—474no—
397C4×#135—471no—
398C2×#436D4711yescharacteristic, complemented
399C2×C47—22no—
400C2×C47—44no—
401C2×C47C2×D4211yescharacteristic
402C2×C47C2×#57511yescharacteristic
403C2×C47#358411yescharacteristic
404D47—44no—
405D47—84no—
406C22×#41—474no—
407#575—9416no—
408C2×#137—474no—
409C2×#137—474no—
410C2×AGL(1,ℤ/8)—474no—
411C2×AGL(1,ℤ/8)—474no—
412C2×#135—471no—
413C2×#135—472no—
414C2×#135—474no—
415C2×#135—472no—
416C22×M16C2×D4712yescomplemented
417#550—472no—
418D4×Q8—472no—
419#548—474no—
420#547—472no—
421#547—942no—
422#546—474no—
423#546—944no—
424D42—472no—
425D42—942no—
426#532—472no—
427#532—942no—
428#525—474no—
429#525—944no—
430C4×#41—472no—
431C2×C4×D4—942no—
432C2×C4×D4C2×D4711yescharacteristic
433#495—472no—
434#495—472no—
435#494—471no—
436#493—471no—
437#492—472no—
438#470—474no—
439#469—474no—
440#468—474no—
441#468—474no—
442#464—474no—
443#463—474no—
444#462—472no—
445#461—472no—
446#460—472no—
447#459—472no—
448#452—474no—
449#452—474no—
450#451—474no—
451#450—474no—
452#449—474no—
453#449—474no—
454#448—474no—
455#447—474no—
456C4×Q16—471no—
457C4×Q16—471no—
458C4×SD16—472no—
459C4×SD16—472no—
460C4×D8—471no—
461C4×D8—471no—
462#436C2×D4712yescomplemented
463#436C2×D4712yescomplemented
464#436C2×D4712yescomplemented
465#436C2×D4712yescomplemented
466#427—471no—
467C2×C4⋊C8C2×D4711yescharacteristic, complemented
468#416—472no—
469#416—474no—
470C2×C22⋊C8C2×D4712yescomplemented
471C2×C4×C8C2×D4711yescharacteristic, complemented
472C47#6103811yescharacteristic, complemented, Sylow
473C2×#41—472no—
474C2×#41—474no—
475C2×#41—474no—
476C2×#41—474no—
477C2×#41—9416no—
478C2×#41—944no—
479C2×#41—944no—
480C2×#41—1888no—
481C22×Q8—474no—
482C22×D4—474no—
483C22×D4—944no—
484C22×D4—942no—
485C22×D4D18811yescharacteristic
486C23×C4—944no—
487C23×C4C22×D4712yes—
488#137—9416no—
489#137—9416no—
490AGL(1,ℤ/8)—9416no—
491AGL(1,ℤ/8)—9416no—
492#135—478no—
493#135—9416no—
494#135—948no—
495#135—1884no—
496C2×Q16—471no—
497C2×Q16—474no—
498C2×Q16—472no—
499C2×Q16—472no—
500C2×SD16—472no—
501C2×SD16—474no—
502C2×SD16—474no—
503C2×SD16—474no—
504C2×SD16—474no—
505C2×D8—471no—
506C2×D8—474no—
507C2×D8—472no—
508C2×D8—472no—
509C2×M16—28no—
510C2×M16C22×D4714yes—
511C2×M16C22×D4714yes—
512C22×C8C22×D4712yes—
513C22×C8C22×D4711yescharacteristic
514C22×C8C22×D4711yescharacteristic
515C4⋊Q8—472no—
516C4⋊Q8—942no—
517#127—472no—
518#127—942no—
519#124—474no—
520#124—944no—
521#123—944no—
522#123—944no—
523#123—944no—
524C22⋊Q8—474no—
525C22⋊Q8—474no—
526C22⋊Q8—944no—
527C22⋊Q8—944no—
528#121—474no—
529#121—474no—
530#121—944no—
531#121—942no—
532#121—942no—
533#121—942no—
534#121—942no—
535#121—944no—
536#121—944no—
537#120—944no—
538#120—944no—
539#120—944no—
540C4×Q8—472no—
541C4×Q8—472no—
542C4×D4—472no—
543C4×D4—472no—
544C4×D4—942no—
545C4×D4—944no—
546C4×D4—942no—
547C4×D4—942no—
548C4×D4—944no—
549C4×D4—942no—
550C4×D4—944no—
551C4×D4—942no—
552C4×D4—942no—
553C4×D4D18812yes—
554C4×D4D18812yes—
555C4×D4C22×D4712yes—
556C4×D4C22×D4712yes—
557#117—472no—
558#117—942no—
559C2×C4⋊C4—942no—
560C2×C4⋊C4D18811yescharacteristic
561C2×C22⋊C4—944no—
562C2×C22⋊C4D18812yes—
563C2×C42—942no—
564C2×C42C22×D4711yescharacteristic
565#107—471no—
566#107—471no—
567#106—472no—
568C4⋊C8C22×D4712yes—
569C4⋊C8C22×D4712yes—
570#103—472no—
571#103—472no—
572#103—474no—
573#103—474no—
574#102—472no—
575#102—472no—
576#102—474no—
577#102—474no—
578C22⋊C8C22×D4714yes—
579C22⋊C8C22×D4714yes—
580C4×C8C22×D4711yescharacteristic
581C4×C8C22×D4711yescharacteristic
582C4×C8C22×D4711yescharacteristic
583C4×C8C22×D4711yescharacteristic
584C24—944no—
585C24C2×D18812yes—
586#41—478no—
587#41—948no—
588#41—948no—
589#41—944no—
590#41—948no—
591#41—948no—
592#41—18816no—
593#41—1884no—
594#41—1884no—
595#41—18816no—
596C2×Q8—472no—
597C2×Q8—474no—
598C2×Q8—948no—
599C2×Q8—944no—
600C2×Q8—1884no—
601C2×D4—42no—
602C2×D4—472no—
603C2×D4—474no—
604C2×D4—948no—
605C2×D4—942no—
606C2×D4—944no—
607C2×D4—944no—
608C2×D4—944no—
609C2×D4—944no—
610C2×D4—944no—
611C2×D4—942no—
612C2×D4—942no—
613C2×D4—944no—
614C2×D4—1884no—
615C2×D4—1888no—
616C2×D4—18816no—
617C2×D4C2×D18812yes—
618C2×D4C2×D18812yes—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—942no—
622C22×C4—944no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—944no—
626C22×C4—944no—
627C22×C4—944no—
628C22×C4—18816no—
629C22×C4C2×D18811yescharacteristic
630C22×C4C2×D18812yes—
631C22×C4C2×D18814yes—
632C22×C4C2×D18811yescharacteristic
633C22×C4C23×D4714yes—
634C22×C4C23×D4711yescharacteristic
635Q16—474no—
636Q16—948no—
637Q16—944no—
638Q16—1882no—
639SD16—478no—
640SD16—948no—
641SD16—948no—
642SD16—948no—
643SD16—1884no—
644D8—474no—
645D8—948no—
646D8—944no—
647D8—1882no—
648M16—28no—
649M16—28no—
650C2×C8—24no—
651C2×C8—22no—
652C2×C8D4×D4714yescomplemented
653C2×C8C23×D4711yescharacteristic
654C2×C8C23×D4711yescharacteristic
655C2×C8C23×D4714yes—
656C2×C8C23×D4711yescharacteristic
657C2×C8C23×D4711yescharacteristic
658C4⋊C4—472no—
659C4⋊C4—472no—
660C4⋊C4—944no—
661C4⋊C4—942no—
662C4⋊C4—942no—
663C4⋊C4—944no—
664C4⋊C4—942no—
665C4⋊C4—942no—
666C4⋊C4C2×D18812yes—
667C4⋊C4C2×D18812yes—
668C22⋊C4—944no—
669C22⋊C4—942no—
670C22⋊C4—944no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C22⋊C4—942no—
674C22⋊C4—942no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C22⋊C4C2×D18814yes—
678C22⋊C4C2×D18814yes—
679C42—942no—
680C42—942no—
681C42—942no—
682C42C2×D18811yescharacteristic
683C42C2×D18811yescharacteristic
684C42C23×D4711yescharacteristic
685C42C23×D4711yescharacteristic
686C23—24no—
687C23—42no—
688C23—42no—
689C23—942no—
690C23—944no—
691C23—3764no—
692C23—1888no—
693C23—1888no—
694C23C22×D18814yes—
695C23C22×D18811yescharacteristic
696Q8—474no—
697Q8—942no—
698Q8—944no—
699Q8—944no—
700Q8—1888no—
701D4—24no—
702D4—42no—
703D4—474no—
704D4—948no—
705D4—944no—
706D4—942no—
707D4—944no—
708D4—3762no—
709D4—3764no—
710D4—1888no—
711D4—1888no—
712D4—1888no—
713D4—1888no—
714D4—1888no—
715D4—1884no—
716C2×C4—24no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—41no—
722C2×C4—942no—
723C2×C4—948no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—944no—
727C2×C4—3762no—
728C2×C4—1888no—
729C2×C4—1888no—
730C2×C4—1888no—
731C2×C4—1888no—
732C2×C4—1884no—
733C2×C4C2×D4×D4712yes—
734C2×C4C22×D18811yescharacteristic
735C2×C4C22×D18811yescharacteristic
736C2×C4C22×D18811yescharacteristic
737C2×C4C22×D18814yes—
738C2×C4C22×D18811yescharacteristic
739C2×C4C22×D18811yescharacteristic
740C2×C4#1309407012yes—
741C2×C4C24×D4711yescharacteristic
742C8—24no—
743C8—21no—
744C8—21no—
745C8C2×D4×D4712yes—
746C8C2×D4×D4712yes—
747C22—21no—
748C22—21no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—84no—
753C22—944no—
754C22—37616no—
755C22—1884no—
756C22—1884no—
757C22—1884no—
758C22—1882no—
759C22—1882no—
760C22D4×D18812yes—
761C22C23×D18811yescharacteristic
762C4—24no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—944no—
767C4—1884no—
768C4—1882no—
769C4—1882no—
770C4D4×D18812yes—
771C4#1568992312yescomplemented
772C4C22×D4×D4711yescharacteristic
773C4C2×#1309407011yescharacteristic
774C2—22no—
775C2—44no—
776C2—3764no—
777C2—1884no—
778C2C2×D4×D18811yescharacteristic
779C2C2×#1568992311yescharacteristic
780C2#2025816211yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#436C2
socleC22×C47C23×D4
hypercenterC2×#436D47
hypocenterC47#61038
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#15689923C2semidirect
2. D4×#10625350C2semidirect
3. #20255056C2semidirect
4. #20255046C2semidirect
5. #20255036C2semidirect
6. #20255024C2semidirect
7. #20255010C2semidirect
8. #20255000C2semidirect
9. #20254990C2semidirect
10. #20253816C2semidirect
11. #20252997C2semidirect
12. #20252845C2semidirect
13. #20252610C2semidirect
14. C4×#13094046C2semidirect
15. C2×C47×#436C2semidirect
16. C22×#10625350C22semidirect
18. C2×#13094057C22semidirect
19. C2×#13094057C22semidirect
20. C2×#13094052C22semidirect
21. C2×#13094052C22semidirect
23. C2×#13094046C22semidirect
24. C2×#13094046C22semidirect
25. C2×#13094046C22semidirect
27. D4×Dic94C22semidirect
28. #15689782C22semidirect
31. #15689769C22semidirect
33. D4×D188C22semidirect
35. #15689673C22semidirect
37. #15689634C22semidirect
39. C4×#10625350C22semidirect
41. #15689507C22semidirect
42. #15689507C22semidirect
43. #15689503C22semidirect
44. #15689500C22semidirect
45. #15689496C22semidirect
46. #15689381C22semidirect
47. #15689376C22semidirect
48. #15689369C22semidirect
49. #15689369C22semidirect
50. #15689346C22semidirect
51. #15689339C22semidirect
52. #15689334C22semidirect
53. #15689329C22semidirect
54. #15689324C22semidirect
55. #15689319C22semidirect
56. #15689287C22semidirect
57. #15689287C22semidirect
58. #15689281C22semidirect
59. #15689276C22semidirect
60. #15689270C22semidirect
61. #15689270C22semidirect
62. #15689264C22semidirect
63. #15689259C22semidirect
64. C4×Dic188C22semidirect
65. C4×Dic188C22semidirect
66. C4×#10625325C22semidirect
67. C4×#10625325C22semidirect
68. C4×D376C22semidirect
69. C4×D376C22semidirect
70. #15689161C22semidirect
71. #15689120C22semidirect
72. #15689120C22semidirect
73. C22×M16×C47C22semidirect
75. C47×#436C22semidirect
76. C47×#436C22semidirect
77. C47×#436C22semidirect
78. C47×#436C22semidirect
79. C2×C4⋊C8×C47C22semidirect
80. C2×C22⋊C8×C47C22semidirect
81. C2×C4×C8×C47C22semidirect
102. #13094046D4semidirect
224. #10625350C2×D4semidirect
248. C2×C8×C47C2×D4semidirect
285. Dic188C2×D4semidirect
289. D376C2×D4semidirect
294. #10625325C2×D4semidirect
377. C4×C47#575semidirect
398. C2×#436D47semidirect
416. C22×M16C2×D47semidirect
462. #436C2×D47semidirect
463. #436C2×D47semidirect
464. #436C2×D47semidirect
465. #436C2×D47semidirect
467. C2×C4⋊C8C2×D47semidirect
470. C2×C22⋊C8C2×D47semidirect
471. C2×C4×C8C2×D47semidirect
472. C47#61038semidirect
652. C2×C8D4×D47semidirect
771. C4#15689923semidirect

Maximal subgroups

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

subgroupindex
C2×#156899232
D4×#106253502
#202550562
#202550462
#202550362
#202550242
#202550102
#202550002
#202549902
#202538162
#202529972
#202528452
#202526102
C4×#130940462
C2×C47×#4362
#6103847