Finite Group Databasebeta

← #6355968

Subgroups — #6355968

Order 512.

1538 conjugacy classes of subgroups.

The subgroup lattice has 1497 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62116C211yesmaximal, characteristic, complemented
2#62107C211yesmaximal, characteristic
3#60821C211yesmaximal, characteristic, complemented
4#60300C211yesmaximal, characteristic, complemented
5#19583C211yesmaximal, characteristic, complemented
6#19579C211yesmaximal, characteristic, complemented
7#19568C211yesmaximal, characteristic, complemented
8#19567C211yesmaximal, characteristic, complemented
9#19541C211yesmaximal, characteristic, complemented
10#19539C211yesmaximal, characteristic, complemented
11#19524C211yesmaximal, characteristic, complemented
12#19523C211yesmaximal, characteristic, complemented
13#19497C211yesmaximal, characteristic, complemented
14#19493C211yesmaximal, characteristic, complemented
15#19460C211yesmaximal, characteristic, complemented
16#19459C211yesmaximal, characteristic, complemented
17#19449C211yesmaximal, characteristic, complemented
18#19447C211yesmaximal, characteristic, complemented
19#19424C211yesmaximal, characteristic, complemented
20#19423C211yesmaximal, characteristic, complemented
21#19381C211yesmaximal, characteristic, complemented
22#19377C211yesmaximal, characteristic, complemented
23#19366C211yesmaximal, characteristic, complemented
24#19354C211yesmaximal, characteristic, complemented
25#19325C211yesmaximal, characteristic, complemented
26#19321C211yesmaximal, characteristic, complemented
27#19303C211yesmaximal, characteristic, complemented
28#19293C211yesmaximal, characteristic, complemented
29#17824C211yesmaximal, characteristic, complemented
30#17767C211yesmaximal, characteristic, complemented
31#17759C211yesmaximal, characteristic, complemented
32#3509C2211yescharacteristic
33#3499C2211yescharacteristic
34#3475C2211yescharacteristic
35#3388—21no—
36#3384—21no—
37#3377—21no—
38#3367—21no—
39#3354—21no—
40#3352—21no—
41#3349—21no—
42#3348—21no—
43#3343—21no—
44#3343—21no—
45#3330—21no—
46#3323—21no—
47#3315—21no—
48#3311—21no—
49#3306—21no—
50#3306—21no—
51#3255C2211yescharacteristic
52#3252C2211yescharacteristic
53#3251C2211yescharacteristic
54#3251C2211yescharacteristic
55#3248C2211yescharacteristic
56#3246C2211yescharacteristic
57#3239C2211yescharacteristic
58#3239C2211yescharacteristic
59#3239C2211yescharacteristic
60#3237C2211yescharacteristic
61#3233C2211yescharacteristic
62#3229C2211yescharacteristic
63#3223—21no—
64#3223—21no—
65#3223—21no—
66#3223—21no—
67#3210C2211yescharacteristic
68#3210C2211yescharacteristic
69#3210C2211yescharacteristic, complemented
70#3210C2211yescharacteristic, complemented
71#3209C2211yescharacteristic
72#3209C2211yescharacteristic
73#3209C2211yescharacteristic, complemented
74#3209C2211yescharacteristic, complemented
75#3152C2211yescharacteristic, complemented
76C2×#494C2211yescharacteristic, complemented
77#3139C2211yescharacteristic, complemented
78#3131C2211yescharacteristic, complemented
79#3116C2211yescharacteristic
80#3115C2211yescharacteristic
81#3115C2211yescharacteristic
82#3110C2211yescharacteristic
83#3107C2211yescharacteristic
84#3100C2211yescharacteristic
85#3079C2211yescharacteristic
86#3079C2211yescharacteristic
87#3079C2211yescharacteristic
88#3077C2211yescharacteristic
89#3076C2211yescharacteristic
90C2×#474C2211yescharacteristic
91#3044—21no—
92#3044—21no—
93#3011—21no—
94#3011—21no—
95#2995—21no—
96#2994C2211yescharacteristic
97#2993—21no—
98#2993C2211yescharacteristic
99#2991C2211yescharacteristic
100#2989C2211yescharacteristic
101#2989C2211yescharacteristic
102#2989C2211yescharacteristic
103#2986C2211yescharacteristic
104#2985C2211yescharacteristic
105#2978—21no—
106#2976—21no—
107#2975C2211yescharacteristic
108#2974C2211yescharacteristic
109#2971C2211yescharacteristic
110#2969—21no—
111#2969C2211yescharacteristic
112#2967—21no—
113#2966C2211yescharacteristic
114#2965C2211yescharacteristic
115#2925C2211yescharacteristic
116#2924—21no—
117#2922C2211yescharacteristic
118#2921—21no—
119#1704C2211yescharacteristic, complemented
120#1704C2211yescharacteristic, complemented
121#1704C2211yescharacteristic, complemented
122#1703C2211yescharacteristic
123#1703C2211yescharacteristic
124#1703C2211yescharacteristic
125#1703C2211yescharacteristic
126#1703C2211yescharacteristic
127#1702C2211yescharacteristic, complemented
128#1702C2211yescharacteristic, complemented
129#1701C2211yescharacteristic
130#1701C2211yescharacteristic
131#1700C2211yescharacteristic, complemented
132#1700C2211yescharacteristic, complemented
133#1699C2211yescharacteristic
134#1699C2211yescharacteristic
135#1699C2211yescharacteristic
136#1699C2211yescharacteristic
137#1698C2211yescharacteristic, complemented
138#1697C2211yescharacteristic
139#1690C2211yescharacteristic, complemented
140#1690C2211yescharacteristic, complemented
141#1690C2211yescharacteristic, complemented
142#1690C2211yescharacteristic, complemented
143#1690C2211yescharacteristic, complemented
144#1690C2211yescharacteristic, complemented
145#1690C2211yescharacteristic, complemented
146#1689C2211yescharacteristic
147#1689C2211yescharacteristic
148#1689C2211yescharacteristic
149#1689C2211yescharacteristic
150#1689C2211yescharacteristic
151#1689C2211yescharacteristic
152#1689C2211yescharacteristic
153#1689C2211yescharacteristic
154#1689C2211yescharacteristic
155#1686C2211yescharacteristic, complemented
156#1685C2211yescharacteristic
157#1685C2211yescharacteristic
158#1685C2211yescharacteristic
159#1684C2211yescharacteristic, complemented
160#1684C2211yescharacteristic, complemented
161#1684C2211yescharacteristic, complemented
162#1683C2211yescharacteristic
163#1680C2211yescharacteristic, complemented
164#1680C2211yescharacteristic, complemented
165#1680C2211yescharacteristic, complemented
166#1680C2211yescharacteristic, complemented
167#1679C2211yescharacteristic
168#1679C2211yescharacteristic
169#1678C2211yescharacteristic, complemented
170#1677C2211yescharacteristic
171#1670C2211yescharacteristic, complemented
172#1670C2211yescharacteristic, complemented
173#1670C2211yescharacteristic, complemented
174#1670C2211yescharacteristic, complemented
175#1670C2211yescharacteristic, complemented
176#1669C2211yescharacteristic
177#1669C2211yescharacteristic
178#1669C2211yescharacteristic
179#1666C2211yescharacteristic, complemented
180#1666C2211yescharacteristic, complemented
181#1666C2211yescharacteristic, complemented
182#1665C2211yescharacteristic
183#1574C2211yescharacteristic
184#1574C2211yescharacteristic, complemented
185#1573C2211yescharacteristic
186#1573C2211yescharacteristic, complemented
187#1572C2211yescharacteristic
188#1572C2211yescharacteristic, complemented
189#1570C2211yescharacteristic
190#1570C2211yescharacteristic, complemented
191#1569C2211yescharacteristic, complemented
192#1569C2211yescharacteristic, complemented
193#1568C2211yescharacteristic, complemented
194#1566C2211yescharacteristic, complemented
195#1561C2211yescharacteristic, complemented
196#1559C2211yescharacteristic, complemented
197#1559C2211yescharacteristic, complemented
198#1557C2211yescharacteristic
199#1557C2211yescharacteristic, complemented
200#1556C2211yescharacteristic
201#1556C2211yescharacteristic, complemented
202#1556C2211yescharacteristic, complemented
203#1554C2211yescharacteristic
204#1554C2211yescharacteristic, complemented
205#1553C2211yescharacteristic
206#1553C2211yescharacteristic, complemented
207#1552C2211yescharacteristic
208#1552C2211yescharacteristic, complemented
209#1550C2211yescharacteristic, complemented
210#1549C2211yescharacteristic
211#1549C2211yescharacteristic, complemented
212#1549C2211yescharacteristic, complemented
213#1547C2211yescharacteristic, complemented
214#1546C2211yescharacteristic, complemented
215#1544C2211yescharacteristic
216#1542C2211yescharacteristic
217#1540C2211yescharacteristic, complemented
218C2×#332C2211yescharacteristic, complemented
219C2×2−1+4—21no—
220C2×#137—21no—
221C2×#137—21no—
222C22×Q16—21no—
223C22×Q16—21no—
224#557—21no—
225#557—21no—
226#556—21no—
227#556—21no—
228#556D411yescharacteristic
229#555D411yescharacteristic
230#554D411yescharacteristic
231#553—21no—
232#552—21no—
233#552—21no—
234#552—21no—
235#552—21no—
236#552—21no—
237#552D411yescharacteristic
238#552D411yescharacteristic
239#551—21no—
240#551—21no—
241D4×Q8—21no—
242D4×Q8—21no—
243#547—21no—
244#547—21no—
245#547—21no—
246#547—21no—
247#547—21no—
248#547—21no—
249#547D411yescharacteristic
250#546D411yescharacteristic
251#546D411yescharacteristic
252#541—21no—
253#541—21no—
254#536—21no—
255#536—21no—
256#536—21no—
257#536—21no—
258#533C2311yescharacteristic
259#533C2311yescharacteristic
260#533C2311yescharacteristic
261#533C2311yescharacteristic
262#533C2311yescharacteristic
263#533C2311yescharacteristic
264#532C2311yescharacteristic
265#532C2311yescharacteristic
266#532C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271#529—21no—
272#529—21no—
273#529C2311yescharacteristic
274#529C2311yescharacteristic
275#525—21no—
276#519—21no—
277C4×#41C2311yescharacteristic
278C4×#41C2311yescharacteristic
279C4×#41C2311yescharacteristic
280C2×C4×D4C2311yescharacteristic
281C2×#117—21no—
282#501—21no—
283#501—21no—
284#501—21no—
285#501—21no—
286#499—21no—
287#498—21no—
288#497—21no—
289#497—21no—
290#494—21no—
291#494—21no—
292#494C2311yescharacteristic
293#494C2311yescharacteristic
294#494C2311yescharacteristic
295#494C2311yescharacteristic
296#494C2311yescharacteristic
297#494C2311yescharacteristic
298#492C2311yescharacteristic
299#492C2311yescharacteristic
300#491—21no—
301#491—21no—
302#491—21no—
303#489—21no—
304#489—21no—
305#489—21no—
306#488—21no—
307#488—21no—
308#488—21no—
309#487—21no—
310#487C2311yescharacteristic
311#487C2311yescharacteristic
312#487C2311yescharacteristic
313#487C2311yescharacteristic
314#487C2311yescharacteristic
315#487C2311yescharacteristic
316#486C2311yescharacteristic
317#486C2311yescharacteristic
318#485—21no—
319#485—21no—
320#485—21no—
321#485—21no—
322#485—21no—
323#484—21no—
324#484—21no—
325#484—21no—
326#484—21no—
327#483—21no—
328#483—21no—
329#482—21no—
330#482—21no—
331#482—21no—
332#481—21no—
333#481—21no—
334#481—21no—
335#480—21no—
336#479—21no—
337#479—21no—
338#479—21no—
339#478—21no—
340#478—21no—
341#478—21no—
342#478—21no—
343#478—21no—
344#477—21no—
345#477—21no—
346#477—21no—
347#477C2311yescharacteristic
348#477C2311yescharacteristic
349#476—21no—
350#476—21no—
351#476—21no—
352#476—21no—
353#476C2311yescharacteristic
354#476C2311yescharacteristic
355#475—21no—
356#475C2311yescharacteristic
357#475C2311yescharacteristic
358#475C2311yescharacteristic
359#475C2311yescharacteristic
360#475C2311yescharacteristic
361#475C2311yescharacteristic
362#475C2311yescharacteristic
363#475C2311yescharacteristic
364#475C2311yescharacteristic
365#475C2311yescharacteristic
366#474—21no—
367#474—21no—
368#474C2311yescharacteristic
369#474C2311yescharacteristic
370#474C2311yescharacteristic
371#474C2311yescharacteristic
372#474C2311yescharacteristic
373#474C2311yescharacteristic
374#474C2311yescharacteristic
375#474C2311yescharacteristic
376#474C2311yescharacteristic
377#474C2311yescharacteristic
378#470—21no—
379#470—21no—
380#470—21no—
381#469—21no—
382#469—21no—
383#468—21no—
384#468—21no—
385#468—21no—
386#467—21no—
387#465—21no—
388#465—21no—
389#465—21no—
390#464—21no—
391#464—21no—
392#464—21no—
393#464—21no—
394#464—21no—
395#464—21no—
396#464—21no—
397#464—21no—
398#464—21no—
399#464—21no—
400#463—21no—
401#463—21no—
402#462—21no—
403#462—21no—
404#462—21no—
405#462—21no—
406#462—21no—
407#462—21no—
408#462—21no—
409#462—21no—
410#462—21no—
411#462C2311yescharacteristic
412#462C2311yescharacteristic
413#461—21no—
414#461C2311yescharacteristic
415#461C2311yescharacteristic
416#460C2311yescharacteristic
417#460C2311yescharacteristic
418#459C2311yescharacteristic
419#459C2311yescharacteristic
420#452—21no—
421#452—21no—
422#452—21no—
423#452—21no—
424#452—21no—
425#452—21no—
426#452—21no—
427#452—21no—
428#452—21no—
429#452—21no—
430#451—21no—
431#451—21no—
432#451—21no—
433#451—21no—
434#451—21no—
435#451—21no—
436#451—21no—
437#451—21no—
438#450—21no—
439#449—21no—
440#449—21no—
441#447—21no—
442#446—21no—
443#446—21no—
444#446—21no—
445#446—21no—
446#446—21no—
447#446C2311yescharacteristic
448#446C2311yescharacteristic
449#446C2311yescharacteristic
450#446C2311yescharacteristic
451C8×Q8—21no—
452C8×Q8C2311yescharacteristic
453C8×Q8C2311yescharacteristic
454C8×Q8C2311yescharacteristic
455C8×Q8C2311yescharacteristic
456#442—21no—
457#442—21no—
458#441—21no—
459#440—21no—
460#440—21no—
461#440—21no—
462#440—21no—
463#440—21no—
464C4×Q16—21no—
465C4×SD16—21no—
466C4×D8—21no—
467C4×D8—21no—
468#436—21no—
469#436—21no—
470#436—21no—
471#436—21no—
472#436—21no—
473#436—21no—
474#436—21no—
475#436—21no—
476#436—21no—
477#436—21no—
478#436C2311yescharacteristic
479#436C2311yescharacteristic
480#436C2311yescharacteristic
481#436C2311yescharacteristic
482#436C2311yescharacteristic
483#436C2311yescharacteristic
484#435—21no—
485#435—21no—
486#435—21no—
487#435—21no—
488#435—21no—
489#435—21no—
490#435—21no—
491#435—21no—
492#435—21no—
493#435—21no—
494#435—21no—
495#435—21no—
496#435—21no—
497#435—21no—
498C8×D4—21no—
499C8×D4—21no—
500C8×D4C2311yescharacteristic
501C8×D4C2311yescharacteristic
502#433—21no—
503#433—21no—
504#433—21no—
505#433—21no—
506#433—21no—
507#433—21no—
508#433—21no—
509#433—21no—
510#433—21no—
511#433—21no—
512#433D411yescharacteristic
513#433D411yescharacteristic
514#433D411yescharacteristic
515#433D411yescharacteristic
516#432—21no—
517#432—21no—
518#432C2311yescharacteristic
519#432C2311yescharacteristic
520#432C2311yescharacteristic
521#432C2311yescharacteristic
522#432C2311yescharacteristic
523#432C2311yescharacteristic
524#431—21no—
525#431—21no—
526#431C2311yescharacteristic
527#431C2311yescharacteristic
528#431C2311yescharacteristic
529#431C2311yescharacteristic
530#431C2311yescharacteristic
531#431C2311yescharacteristic
532#431C2311yescharacteristic
533#431C2311yescharacteristic
534#428—21no—
535#428—21no—
536#428—21no—
537#428—21no—
538#427—21no—
539C2×#107—21no—
540#424—21no—
541#424—21no—
542#424D411yescharacteristic
543#424D411yescharacteristic
544#423—21no—
545#423—21no—
546#423C2311yescharacteristic
547#423C2311yescharacteristic
548#423C2311yescharacteristic
549#423C2311yescharacteristic
550#423C2311yescharacteristic
551C2×C4⋊C8C2311yescharacteristic
552C2×C4⋊C8C2311yescharacteristic
553C2×C4⋊C8C2311yescharacteristic
554#419—21no—
555#419—21no—
556#418—21no—
557#417—21no—
558#417—21no—
559#417—21no—
560#416—21no—
561#416—21no—
562#416—21no—
563C2×#102—21no—
564#408—21no—
565#408D411yescharacteristic
566#408D411yescharacteristic
567#407—21no—
568#407—21no—
569#407—21no—
570C2×C22⋊C8—21no—
571#405—21no—
572#405—21no—
573#405—21no—
574C4×M16—21no—
575C4×M16—21no—
576C4×M16C2311yescharacteristic
577C2×C4×C8C2311yescharacteristic
578#335C2311yescharacteristic
579#335C2311yescharacteristic
580#335C2311yescharacteristic
581#335C2311yescharacteristic
582#335C2311yescharacteristic
583#335C2311yescharacteristic
584#334C2311yescharacteristic
585#334C2311yescharacteristic
586#334C2311yescharacteristic
587#334C2311yescharacteristic
588#334C2311yescharacteristic
589#334C2311yescharacteristic
590#334C2311yescharacteristic
591#334C2311yescharacteristic
592#334C2311yescharacteristic
593#334C2311yescharacteristic
594#333C2311yescharacteristic
595#333C2311yescharacteristic
596#333C2311yescharacteristic
597#333C2311yescharacteristic
598#332C2311yescharacteristic
599#332C2311yescharacteristic
600#332C2311yescharacteristic
601#332C2311yescharacteristic
602#332C2311yescharacteristic
603#332C2311yescharacteristic
604#332C2311yescharacteristic
605#332C2311yescharacteristic
606#332C2311yescharacteristic
607#332C2311yescharacteristic
608#332C2311yescharacteristic
609#332C2311yescharacteristic
610#332C2311yescharacteristic
611#332C2311yescharacteristic
612#332C2311yescharacteristic
613#332C2311yescharacteristic
614#332C2311yescharacteristic
615#332C2311yescharacteristic
616#332C2311yescharacteristic
617#332C2311yescharacteristic
618#332C2311yescharacteristic
619#332C2311yescharacteristic
620#332C2311yescharacteristic
621#332C2311yescharacteristic
622#331C2311yescharacteristic
623#331C2311yescharacteristic
624#331C2311yescharacteristic
625#331C2311yescharacteristic
6262−1+4—82no—
6272−1+4—82no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—41no—
632C2×#41—41no—
633C2×#41—41no—
634C2×#41C2×D411yescharacteristic
635C2×#41C2×D411yescharacteristic
636C2×#41C2×D411yescharacteristic
637C22×Q8—21no—
638C22×Q8—21no—
639C22×Q8—21no—
640C22×Q8—21no—
641C22×Q8—41no—
642C22×D4C2×D411yescharacteristic
643C23×C4—21no—
644#137—82no—
645#137—82no—
646C2×Q16—21no—
647C2×Q16—21no—
648C2×Q16—21no—
649C2×Q16—21no—
650C2×Q16—21no—
651C2×Q16—21no—
652C2×Q16—21no—
653C2×Q16—21no—
654C2×Q16—21no—
655C2×Q16—21no—
656C2×Q16—21no—
657C2×Q16—21no—
658C2×Q16—21no—
659C2×Q16—21no—
660C2×Q16—82no—
661C2×Q16—82no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×SD16—21no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—21no—
668C2×SD16—21no—
669C2×SD16—21no—
670C2×D8—21no—
671C2×D8—21no—
672C2×M16—21no—
673C2×M16—21no—
674C2×M16—21no—
675C2×M16—21no—
676C2×M16—21no—
677C2×M16—21no—
678C2×M16—21no—
679C2×M16—21no—
680C2×M16—21no—
681C2×M16—21no—
682C2×M16—21no—
683C2×M16C2×D411yescharacteristic
684C2×M16C2×D411yescharacteristic
685C22×C8—21no—
686C22×C8—21no—
687C22×C8—21no—
688C22×C8—21no—
689C22×C8—21no—
690C22×C8C2×D411yescharacteristic
691C22×C8C2×D411yescharacteristic
692C4⋊Q8—21no—
693C4⋊Q8—21no—
694C4⋊Q8—21no—
695C4⋊Q8—21no—
696C4⋊Q8—21no—
697C4⋊Q8—21no—
698C4⋊Q8—21no—
699C4⋊Q8—21no—
700C4⋊Q8—21no—
701C4⋊Q8—21no—
702C4⋊Q8—21no—
703C4⋊Q8—21no—
704C4⋊Q8—41no—
705C4⋊Q8C2×D411yescharacteristic
706C4⋊Q8C2×D411yescharacteristic
707C4⋊Q8C2411yescharacteristic
708C4⋊Q8C2411yescharacteristic
709C4⋊Q8C2411yescharacteristic
710C4⋊Q8C2411yescharacteristic
711C4⋊Q8C2411yescharacteristic
712C4⋊Q8C2411yescharacteristic
713C4⋊Q8C2411yescharacteristic
714#127C2411yescharacteristic
715#126—21no—
716#126—21no—
717#126—21no—
718#126—21no—
719#126—21no—
720#126—21no—
721#126—41no—
722#126—41no—
723#126—41no—
724#126—41no—
725#125—21no—
726#125—21no—
727#125—21no—
728#125—21no—
729#125—21no—
730#125—21no—
731#125—21no—
732#125—21no—
733#125—41no—
734#125—41no—
735#125—41no—
736#125—41no—
737#125C2×D411yescharacteristic
738#125C2×D411yescharacteristic
739#124—21no—
740#124—21no—
741#124—21no—
742#124—21no—
743#124—21no—
744#124—41no—
745#124C2×D411yescharacteristic
746#124C2×D411yescharacteristic
747#123—21no—
748#123—21no—
749#123—21no—
750#123—21no—
751#123—21no—
752#123—21no—
753#123—21no—
754#123—21no—
755#123—41no—
756#123—41no—
757#123—41no—
758#123—41no—
759#123—41no—
760#123—41no—
761#123—41no—
762#123—41no—
763C22⋊Q8—21no—
764C22⋊Q8—21no—
765C22⋊Q8—21no—
766C22⋊Q8—21no—
767C22⋊Q8—21no—
768C22⋊Q8—21no—
769C22⋊Q8—21no—
770C22⋊Q8—21no—
771C22⋊Q8—21no—
772C22⋊Q8—21no—
773C22⋊Q8—21no—
774C22⋊Q8—21no—
775C22⋊Q8—21no—
776C22⋊Q8—21no—
777C22⋊Q8—21no—
778C22⋊Q8—41no—
779C22⋊Q8—41no—
780C22⋊Q8—41no—
781C22⋊Q8—41no—
782C22⋊Q8—41no—
783C22⋊Q8—41no—
784C22⋊Q8C2×D411yescharacteristic
785C22⋊Q8C2×D411yescharacteristic
786C22⋊Q8C2×D411yescharacteristic
787C22⋊Q8C2×D411yescharacteristic
788#121—21no—
789#121—21no—
790#121—21no—
791#121—21no—
792#121—21no—
793#121—21no—
794#121—21no—
795#121—21no—
796#121—21no—
797#121—21no—
798#121C2×D411yescharacteristic
799#121C2×D411yescharacteristic
800#120—21no—
801#120—21no—
802C4×Q8—21no—
803C4×Q8—21no—
804C4×Q8—21no—
805C4×Q8—21no—
806C4×Q8—21no—
807C4×Q8—21no—
808C4×Q8—21no—
809C4×Q8—21no—
810C4×Q8—21no—
811C4×Q8—21no—
812C4×Q8—21no—
813C4×Q8—41no—
814C4×Q8—41no—
815C4×Q8C2×D411yescharacteristic
816C4×Q8C2×D411yescharacteristic
817C4×Q8C2×D411yescharacteristic
818C4×Q8#4111yescharacteristic
819C4×Q8C2411yescharacteristic
820C4×Q8C2411yescharacteristic
821C4×D4—21no—
822C4×D4—21no—
823C4×D4—21no—
824C4×D4—21no—
825C4×D4—21no—
826C4×D4—21no—
827C4×D4—21no—
828C4×D4—21no—
829C4×D4—21no—
830C4×D4—21no—
831C4×D4—21no—
832C4×D4—21no—
833C4×D4—21no—
834C4×D4—21no—
835C4×D4C2×D411yescharacteristic
836C4×D4C2×D411yescharacteristic
837C4×D4C2×D411yescharacteristic
838C4×D4C2×D411yescharacteristic
839C4×D4C2×D411yescharacteristic
840C4×D4C2×D411yescharacteristic
841C4×D4C2×D411yescharacteristic
842C4×D4#4111yescharacteristic
843C4×D4#4111yescharacteristic
844C4×D4#4111yescharacteristic
845C4×D4C2411yescharacteristic
846C4×D4C2411yescharacteristic
847#117—21no—
848#117—21no—
849#117—21no—
850#117—21no—
851#117—21no—
852#117—21no—
853#117—21no—
854#117—21no—
855#117—21no—
856#117—21no—
857#117—21no—
858#117—21no—
859#117—21no—
860#117—21no—
861#117—41no—
862#117—41no—
863#117C2×D411yescharacteristic
864#117C2×D411yescharacteristic
865#117C2×D411yescharacteristic
866#117C2×D411yescharacteristic
867#117C2×D411yescharacteristic
868C2×C4⋊C4—21no—
869C2×C4⋊C4—21no—
870C2×C4⋊C4—21no—
871C2×C4⋊C4—21no—
872C2×C4⋊C4—21no—
873C2×C4⋊C4—21no—
874C2×C4⋊C4—21no—
875C2×C4⋊C4—21no—
876C2×C4⋊C4—21no—
877C2×C4⋊C4—21no—
878C2×C4⋊C4C2×D411yescharacteristic
879C2×C22⋊C4—21no—
880C2×C22⋊C4—21no—
881C2×C22⋊C4—21no—
882C2×C42—21no—
883C2×C42—21no—
884C2×C42C2411yescharacteristic
885C2×C42C2411yescharacteristic
886C2×C42C2411yescharacteristic
887#107—21no—
888#107—21no—
889#107—21no—
890#107—21no—
891#107—21no—
892#107—21no—
893#107—21no—
894#107—21no—
895#107—21no—
896#107—21no—
897#107—21no—
898#107—21no—
899#106—21no—
900#106—21no—
901#106—21no—
902#106—21no—
903#106—21no—
904#106—21no—
905#106—21no—
906#106—21no—
907#106—21no—
908#106—21no—
909#106—21no—
910#106—21no—
911C4⋊C8—21no—
912C4⋊C8—21no—
913C4⋊C8—21no—
914C4⋊C8—21no—
915C4⋊C8—21no—
916C4⋊C8—21no—
917C4⋊C8—21no—
918C4⋊C8—21no—
919C4⋊C8—21no—
920C4⋊C8—21no—
921C4⋊C8—21no—
922C4⋊C8—21no—
923C4⋊C8—21no—
924C4⋊C8—21no—
925C4⋊C8—21no—
926C4⋊C8—21no—
927C4⋊C8C2×D411yescharacteristic
928C4⋊C8C2×D411yescharacteristic
929C4⋊C8C2×D411yescharacteristic
930C4⋊C8C2×D411yescharacteristic
931C4⋊C8C2×D411yescharacteristic
932C4⋊C8C2×D411yescharacteristic
933C4⋊C8C2×D411yescharacteristic
934C4⋊C8C2×D411yescharacteristic
935C4⋊C8C2411yescharacteristic
936C4⋊C8C2411yescharacteristic
937C4⋊C8C2411yescharacteristic
938C4⋊C8C2411yescharacteristic
939C4⋊C8C2411yescharacteristic
940C4⋊C8C2411yescharacteristic
941C4⋊C8C2411yescharacteristic
942C4⋊C8C2411yescharacteristic
943C4⋊C8C2411yescharacteristic
944C4⋊C8C2411yescharacteristic
945C4⋊C8C2411yescharacteristic
946C4⋊C8C2411yescharacteristic
947#103—21no—
948#103—21no—
949#103—21no—
950#103—21no—
951#103—21no—
952#103—21no—
953#103—21no—
954#103—21no—
955#103—21no—
956#103—21no—
957#103—21no—
958#103—21no—
959#103—21no—
960#103—21no—
961#103—21no—
962#103—21no—
963#103—21no—
964#103—21no—
965#103—21no—
966#103—21no—
967#103—21no—
968#103—21no—
969#103—21no—
970#103—21no—
971#103—21no—
972#103—21no—
973#103—21no—
974#103—21no—
975#102—21no—
976#102—21no—
977#102—21no—
978#102—21no—
979#102—21no—
980#102—21no—
981#102—21no—
982#102—21no—
983#102—21no—
984#102—21no—
985#102—21no—
986#102—21no—
987#102—21no—
988#102—21no—
989#102—21no—
990#102—21no—
991#102—21no—
992#102—21no—
993#102—21no—
994#102—21no—
995C22⋊C8—21no—
996C22⋊C8—21no—
997C22⋊C8—21no—
998C22⋊C8—21no—
999C22⋊C8—21no—
1000C22⋊C8—21no—
1001C22⋊C8—21no—
1002C22⋊C8—21no—
1003C22⋊C8—21no—
1004C22⋊C8—21no—
1005C22⋊C8—21no—
1006C22⋊C8—21no—
1007C22⋊C8—21no—
1008C22⋊C8—21no—
1009C22⋊C8—21no—
1010C22⋊C8—21no—
1011C22⋊C8—21no—
1012C22⋊C8—21no—
1013C22⋊C8C2×D411yescharacteristic
1014C22⋊C8C2×D411yescharacteristic
1015C22⋊C8C2×D411yescharacteristic
1016C22⋊C8C2×D411yescharacteristic
1017C22⋊C8C2×D411yescharacteristic
1018C22⋊C8C2×D411yescharacteristic
1019C22⋊C8C2×D411yescharacteristic
1020C22⋊C8C2×D411yescharacteristic
1021#97—21no—
1022#97—21no—
1023#97—21no—
1024#97—21no—
1025#97—21no—
1026#97—21no—
1027#97—21no—
1028#97—21no—
1029#97—21no—
1030#97—21no—
1031#97C2×D411yescharacteristic
1032#97C2×D411yescharacteristic
1033C4×C8—21no—
1034C4×C8—21no—
1035C4×C8—21no—
1036C4×C8—21no—
1037C4×C8—21no—
1038C4×C8—21no—
1039C4×C8—21no—
1040C4×C8—21no—
1041C4×C8C2×D411yescharacteristic
1042C4×C8C2×D411yescharacteristic
1043C4×C8C2411yescharacteristic
1044C4×C8C2411yescharacteristic
1045C4×C8C2411yescharacteristic
1046C4×C8C2411yescharacteristic
1047C24—21no—
1048#41—41no—
1049#41—41no—
1050#41—41no—
1051#41—41no—
1052#41—41no—
1053#41—41no—
1054#41—42no—
1055#41—42no—
1056#41—81no—
1057#41—81no—
1058#41—81no—
1059#41—81no—
1060#41—84no—
1061#41—84no—
1062#41—84no—
1063C2×Q8—21no—
1064C2×Q8—21no—
1065C2×Q8—21no—
1066C2×Q8—21no—
1067C2×Q8—21no—
1068C2×Q8—21no—
1069C2×Q8—21no—
1070C2×Q8—21no—
1071C2×Q8—42no—
1072C2×Q8—42no—
1073C2×Q8—42no—
1074C2×Q8—42no—
1075C2×Q8—41no—
1076C2×Q8—41no—
1077C2×Q8—41no—
1078C2×Q8—41no—
1079C2×Q8—81no—
1080C2×Q8—81no—
1081C2×Q8—81no—
1082C2×Q8—81no—
1083C2×Q8—84no—
1084C2×Q8#12111yescharacteristic
1085C2×Q8C22×D411yescharacteristic
1086C2×Q8C22×D411yescharacteristic
1087C2×D4—21no—
1088C2×D4—21no—
1089C2×D4—21no—
1090C2×D4—21no—
1091C2×D4—21no—
1092C2×D4—21no—
1093C2×D4—21no—
1094C2×D4—21no—
1095C2×D4—41no—
1096C2×D4—41no—
1097C2×D4—41no—
1098C2×D4—41no—
1099C2×D4—41no—
1100C2×D4#12111yescharacteristic
1101C2×D4#12111yescharacteristic
1102C2×D4#12111yescharacteristic
1103C2×D4C22×D411yescharacteristic
1104C2×D4C22×D411yescharacteristic
1105C22×C4—21no—
1106C22×C4—21no—
1107C22×C4—21no—
1108C22×C4—21no—
1109C22×C4—21no—
1110C22×C4—21no—
1111C22×C4—21no—
1112C22×C4—21no—
1113C22×C4—21no—
1114C22×C4—41no—
1115C22×C4—41no—
1116C22×C4—41no—
1117C22×C4—41no—
1118C22×C4—41no—
1119C22×C4—41no—
1120C22×C4—41no—
1121C22×C4—81no—
1122C22×C4—81no—
1123C22×C4C22×D411yescharacteristic
1124C22×C4C22×D411yescharacteristic
1125C22×C4C22×D411yescharacteristic
1126C22×C4C22×D411yescharacteristic
1127C22×C4C22×D411yescharacteristic
1128C22×C4C22×D411yescharacteristic
1129C22×C4C2×#4111yescharacteristic
1130C22×C4C2×#4111yescharacteristic
1131C22×C4C2×#4111yescharacteristic
1132Q16—81no—
1133Q16—81no—
1134Q16—81no—
1135Q16—81no—
1136Q16—81no—
1137Q16—81no—
1138Q16—81no—
1139Q16—81no—
1140Q16—81no—
1141Q16—81no—
1142Q16—81no—
1143Q16—81no—
1144Q16—81no—
1145Q16—81no—
1146SD16—42no—
1147SD16—81no—
1148SD16—81no—
1149SD16—81no—
1150SD16—81no—
1151SD16—81no—
1152SD16—81no—
1153SD16—81no—
1154D8—42no—
1155D8—81no—
1156M16—41no—
1157M16—41no—
1158M16—81no—
1159M16—81no—
1160M16—81no—
1161M16—81no—
1162M16—81no—
1163M16—81no—
1164M16—81no—
1165M16—81no—
1166M16—81no—
1167M16—81no—
1168M16—81no—
1169C2×C8—21no—
1170C2×C8—21no—
1171C2×C8—21no—
1172C2×C8—21no—
1173C2×C8—21no—
1174C2×C8—21no—
1175C2×C8—21no—
1176C2×C8—21no—
1177C2×C8—21no—
1178C2×C8—21no—
1179C2×C8—21no—
1180C2×C8—21no—
1181C2×C8—41no—
1182C2×C8—41no—
1183C2×C8—81no—
1184C2×C8—81no—
1185C2×C8—81no—
1186C2×C8—81no—
1187C2×C8—81no—
1188C2×C8C22×D411yescharacteristic
1189C2×C8C22×D411yescharacteristic
1190C2×C8C22×D411yescharacteristic
1191C2×C8C22×D411yescharacteristic
1192C2×C8C22×D411yescharacteristic
1193C2×C8C22×D411yescharacteristic
1194C2×C8C22×D411yescharacteristic
1195C2×C8C22×D411yescharacteristic
1196C4⋊C4—21no—
1197C4⋊C4—21no—
1198C4⋊C4—21no—
1199C4⋊C4—21no—
1200C4⋊C4—21no—
1201C4⋊C4—21no—
1202C4⋊C4—21no—
1203C4⋊C4—21no—
1204C4⋊C4—21no—
1205C4⋊C4—21no—
1206C4⋊C4—21no—
1207C4⋊C4—21no—
1208C4⋊C4—21no—
1209C4⋊C4—21no—
1210C4⋊C4—21no—
1211C4⋊C4—21no—
1212C4⋊C4—21no—
1213C4⋊C4—21no—
1214C4⋊C4—21no—
1215C4⋊C4—21no—
1216C4⋊C4—21no—
1217C4⋊C4—21no—
1218C4⋊C4—21no—
1219C4⋊C4—21no—
1220C4⋊C4—21no—
1221C4⋊C4—21no—
1222C4⋊C4—21no—
1223C4⋊C4—21no—
1224C4⋊C4—21no—
1225C4⋊C4—21no—
1226C4⋊C4—41no—
1227C4⋊C4—41no—
1228C4⋊C4—41no—
1229C4⋊C4—41no—
1230C4⋊C4—41no—
1231C4⋊C4—41no—
1232C4⋊C4—41no—
1233C4⋊C4—41no—
1234C4⋊C4—41no—
1235C4⋊C4—41no—
1236C4⋊C4—41no—
1237C4⋊C4—41no—
1238C4⋊C4—41no—
1239C4⋊C4—41no—
1240C4⋊C4—41no—
1241C4⋊C4—41no—
1242C4⋊C4—41no—
1243C4⋊C4—41no—
1244C4⋊C4#12111yescharacteristic
1245C4⋊C4#12111yescharacteristic
1246C4⋊C4#12111yescharacteristic
1247C4⋊C4#12111yescharacteristic
1248C4⋊C4#12111yescharacteristic
1249C4⋊C4#12111yescharacteristic
1250C4⋊C4C22×D411yescharacteristic
1251C4⋊C4C22×D411yescharacteristic
1252C4⋊C4C22×D411yescharacteristic
1253C4⋊C4C22×D411yescharacteristic
1254C22⋊C4—21no—
1255C22⋊C4—21no—
1256C22⋊C4—21no—
1257C22⋊C4—21no—
1258C22⋊C4—21no—
1259C22⋊C4—21no—
1260C22⋊C4—21no—
1261C22⋊C4—21no—
1262C22⋊C4—21no—
1263C22⋊C4—21no—
1264C22⋊C4—21no—
1265C22⋊C4—21no—
1266C22⋊C4—21no—
1267C22⋊C4—21no—
1268C22⋊C4—21no—
1269C22⋊C4—21no—
1270C22⋊C4—21no—
1271C22⋊C4—21no—
1272C22⋊C4—41no—
1273C22⋊C4—41no—
1274C22⋊C4—41no—
1275C22⋊C4—41no—
1276C22⋊C4—41no—
1277C22⋊C4—41no—
1278C22⋊C4—41no—
1279C22⋊C4—41no—
1280C22⋊C4—41no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4#12111yescharacteristic
1284C22⋊C4#12111yescharacteristic
1285C22⋊C4#12111yescharacteristic
1286C22⋊C4#12111yescharacteristic
1287C22⋊C4#12111yescharacteristic
1288C22⋊C4#12111yescharacteristic
1289C42—21no—
1290C42—21no—
1291C42—21no—
1292C42—21no—
1293C42—21no—
1294C42—21no—
1295C42—41no—
1296C42—41no—
1297C42—41no—
1298C42—41no—
1299C42—41no—
1300C42C22×D411yescharacteristic
1301C42C22×D411yescharacteristic
1302C42C22×D411yescharacteristic
1303C42C22×D411yescharacteristic
1304C42C22×D411yescharacteristic
1305C42C22×D411yescharacteristic
1306C42C2×#4111yescharacteristic
1307C42C2×#4111yescharacteristic
1308C42C2×#4111yescharacteristic
1309C42C2511yescharacteristic
1310C23—21no—
1311C23—21no—
1312C23—41no—
1313C23—81no—
1314C23—81no—
1315C23—81no—
1316C23C2×#12111yescharacteristic
1317C23C2×#12111yescharacteristic
1318C23C2×#12111yescharacteristic
1319Q8—21no—
1320Q8—21no—
1321Q8—21no—
1322Q8—21no—
1323Q8—41no—
1324Q8—41no—
1325Q8—41no—
1326Q8—41no—
1327Q8—41no—
1328Q8—41no—
1329Q8—41no—
1330Q8—41no—
1331Q8—41no—
1332Q8—41no—
1333Q8—41no—
1334Q8—41no—
1335Q8—41no—
1336Q8—81no—
1337Q8—81no—
1338Q8—82no—
1339Q8—82no—
1340Q8—82no—
1341Q8—82no—
1342D4—21no—
1343D4—21no—
1344D4—21no—
1345D4—21no—
1346D4—41no—
1347D4—41no—
1348D4—41no—
1349D4—41no—
1350D4—41no—
1351D4—41no—
1352D4—41no—
1353D4—81no—
1354D4—81no—
1355D4—81no—
1356D4—81no—
1357D4—81no—
1358D4—81no—
1359D4—82no—
1360D4—82no—
1361D4—82no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—41no—
1381C2×C4—41no—
1382C2×C4—41no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—41no—
1387C2×C4—41no—
1388C2×C4—41no—
1389C2×C4—41no—
1390C2×C4—41no—
1391C2×C4—41no—
1392C2×C4—41no—
1393C2×C4—41no—
1394C2×C4—81no—
1395C2×C4—81no—
1396C2×C4—81no—
1397C2×C4—81no—
1398C2×C4—81no—
1399C2×C4—81no—
1400C2×C4—82no—
1401C2×C4—82no—
1402C2×C4—82no—
1403C2×C4—81no—
1404C2×C4—82no—
1405C2×C4—82no—
1406C2×C4—82no—
1407C2×C4—82no—
1408C2×C4C2×#12111yescharacteristic
1409C2×C4C2×#12111yescharacteristic
1410C2×C4C2×#12111yescharacteristic
1411C2×C4C2×#12111yescharacteristic
1412C2×C4C2×#12111yescharacteristic
1413C2×C4C2×#12111yescharacteristic
1414C2×C4C2×#12111yescharacteristic
1415C2×C4C2×#12111yescharacteristic
1416C2×C4C2×#12111yescharacteristic
1417C2×C4C23×D411yescharacteristic
1418C2×C4C23×D411yescharacteristic
1419C2×C4C22×#4111yescharacteristic
1420C8—21no—
1421C8—21no—
1422C8—21no—
1423C8—21no—
1424C8—21no—
1425C8—21no—
1426C8—21no—
1427C8—21no—
1428C8—41no—
1429C8—41no—
1430C8—41no—
1431C8—41no—
1432C8—41no—
1433C8—41no—
1434C8—41no—
1435C8—41no—
1436C8—41no—
1437C8—41no—
1438C8—41no—
1439C8—41no—
1440C22—21no—
1441C22—21no—
1442C22—21no—
1443C22—21no—
1444C22—21no—
1445C22—21no—
1446C22—21no—
1447C22—21no—
1448C22—21no—
1449C22—41no—
1450C22—41no—
1451C22—41no—
1452C22—41no—
1453C22—41no—
1454C22—41no—
1455C22—81no—
1456C22—81no—
1457C22—81no—
1458C22—162no—
1459C22C22×#12111yescharacteristic
1460C4—21no—
1461C4—21no—
1462C4—21no—
1463C4—21no—
1464C4—21no—
1465C4—21no—
1466C4—21no—
1467C4—21no—
1468C4—21no—
1469C4—21no—
1470C4—41no—
1471C4—41no—
1472C4—41no—
1473C4—41no—
1474C4—41no—
1475C4—41no—
1476C4—81no—
1477C4—81no—
1478C4—81no—
1479C4—81no—
1480C4—81no—
1481C4—81no—
1482C4—81no—
1483C4#358511yescharacteristic
1484C4#358511yescharacteristic
1485C4#358611yescharacteristic
1486C4#358611yescharacteristic
1487C2—41no—
1488C2—41no—
1489C2—41no—
1490C2—81no—
1491C2—81no—
1492C2—161no—
1493C2#6042611yescharacteristic
1494C2#6046211yescharacteristic
1495C2#6047211yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
prime radical#62107C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62116C2semidirect
3. #60821C2semidirect
4. #60300C2semidirect
5. #19583C2semidirect
6. #19579C2semidirect
7. #19568C2semidirect
8. #19567C2semidirect
9. #19541C2semidirect
10. #19539C2semidirect
11. #19524C2semidirect
12. #19523C2semidirect
13. #19497C2semidirect
14. #19493C2semidirect
15. #19460C2semidirect
16. #19459C2semidirect
17. #19449C2semidirect
18. #19447C2semidirect
19. #19424C2semidirect
20. #19423C2semidirect
21. #19381C2semidirect
22. #19377C2semidirect
23. #19366C2semidirect
24. #19354C2semidirect
25. #19325C2semidirect
26. #19321C2semidirect
27. #19303C2semidirect
28. #19293C2semidirect
29. #17824C2semidirect
30. #17767C2semidirect
31. #17759C2semidirect
69. #3210C22semidirect
70. #3210C22semidirect
73. #3209C22semidirect
74. #3209C22semidirect
75. #3152C22semidirect
76. C2×#494C22semidirect
77. #3139C22semidirect
78. #3131C22semidirect
119. #1704C22semidirect
120. #1704C22semidirect
121. #1704C22semidirect
127. #1702C22semidirect
128. #1702C22semidirect
131. #1700C22semidirect
132. #1700C22semidirect
137. #1698C22semidirect
139. #1690C22semidirect
140. #1690C22semidirect
141. #1690C22semidirect
142. #1690C22semidirect
143. #1690C22semidirect
144. #1690C22semidirect
145. #1690C22semidirect
155. #1686C22semidirect
159. #1684C22semidirect
160. #1684C22semidirect
161. #1684C22semidirect
163. #1680C22semidirect
164. #1680C22semidirect
165. #1680C22semidirect
166. #1680C22semidirect
169. #1678C22semidirect
171. #1670C22semidirect
172. #1670C22semidirect
173. #1670C22semidirect
174. #1670C22semidirect
175. #1670C22semidirect
179. #1666C22semidirect
180. #1666C22semidirect
181. #1666C22semidirect
184. #1574C22semidirect
186. #1573C22semidirect
188. #1572C22semidirect
190. #1570C22semidirect
191. #1569C22semidirect
192. #1569C22semidirect
193. #1568C22semidirect
194. #1566C22semidirect
195. #1561C22semidirect
196. #1559C22semidirect
197. #1559C22semidirect
199. #1557C22semidirect
201. #1556C22semidirect
202. #1556C22semidirect
204. #1554C22semidirect
206. #1553C22semidirect
208. #1552C22semidirect
209. #1550C22semidirect
211. #1549C22semidirect
212. #1549C22semidirect
213. #1547C22semidirect
214. #1546C22semidirect
217. #1540C22semidirect
218. C2×#332C22semidirect

Maximal subgroups

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

subgroupindex
#621162
#621072
#608212
#603002
#195832
#195792
#195682
#195672
#195412
#195392
#195242
#195232
#194972
#194932
#194602
#194592
#194492
#194472
#194242
#194232
#193812
#193772
#193662
#193542
#193252
#193212
#193032
#192932
#178242
#177672
#177592