Finite Group Databasebeta

← #6355975

Subgroups — #6355975

Order 512.

1510 conjugacy classes of subgroups.

The subgroup lattice has 1493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61967C211yesmaximal, characteristic
2#61960C211yesmaximal, characteristic, complemented
3#60880C211yesmaximal, characteristic, complemented
4#60300C211yesmaximal, characteristic, complemented
5#19590C211yesmaximal, characteristic, complemented
6#19586C211yesmaximal, characteristic, complemented
7#19575C211yesmaximal, characteristic, complemented
8#19572C211yesmaximal, characteristic, complemented
9#19548C211yesmaximal, characteristic, complemented
10#19546C211yesmaximal, characteristic, complemented
11#19533C211yesmaximal, characteristic, complemented
12#19530C211yesmaximal, characteristic, complemented
13#19502C211yesmaximal, characteristic, complemented
14#19498C211yesmaximal, characteristic, complemented
15#19467C211yesmaximal, characteristic, complemented
16#19464C211yesmaximal, characteristic, complemented
17#19454C211yesmaximal, characteristic, complemented
18#19452C211yesmaximal, characteristic, complemented
19#19431C211yesmaximal, characteristic, complemented
20#19428C211yesmaximal, characteristic, complemented
21#19383C211yesmaximal, characteristic, complemented
22#19378C211yesmaximal, characteristic, complemented
23#19366C211yesmaximal, characteristic, complemented
24#19358C211yesmaximal, characteristic, complemented
25#19327C211yesmaximal, characteristic, complemented
26#19322C211yesmaximal, characteristic, complemented
27#19303C211yesmaximal, characteristic, complemented
28#19296C211yesmaximal, characteristic, complemented
29#17824C211yesmaximal, characteristic, complemented
30#17769C211yesmaximal, characteristic, complemented
31#17761C211yesmaximal, characteristic, complemented
32#3511C2211yescharacteristic
33#3503C2211yescharacteristic
34#3475C2211yescharacteristic
35#3402—21no—
36#3398—21no—
37#3376—21no—
38#3372—21no—
39#3329—21no—
40#3327—21no—
41#3321—21no—
42#3315—21no—
43#3312—21no—
44#3312—21no—
45#3276—21no—
46#3275—21no—
47#3269—21no—
48#3267—21no—
49#3266—21no—
50#3266—21no—
51#3255C2211yescharacteristic
52#3252C2211yescharacteristic
53#3252C2211yescharacteristic
54#3251C2211yescharacteristic
55#3249C2211yescharacteristic
56#3248C2211yescharacteristic
57#3243—21no—
58#3243—21no—
59#3243—21no—
60#3243—21no—
61#3231C2211yescharacteristic
62#3231C2211yescharacteristic, complemented
63#3230C2211yescharacteristic
64#3230C2211yescharacteristic, complemented
65#3228C2211yescharacteristic
66#3228C2211yescharacteristic, complemented
67#3226C2211yescharacteristic
68#3226C2211yescharacteristic, complemented
69#3218C2211yescharacteristic
70#3218C2211yescharacteristic
71#3218C2211yescharacteristic
72#3216C2211yescharacteristic
73#3212C2211yescharacteristic
74#3209C2211yescharacteristic
75#3165C2211yescharacteristic, complemented
76C2×#500C2211yescharacteristic, complemented
77#3141C2211yescharacteristic, complemented
78#3131C2211yescharacteristic, complemented
79#3116C2211yescharacteristic
80#3116C2211yescharacteristic
81#3115C2211yescharacteristic
82#3110C2211yescharacteristic
83#3107C2211yescharacteristic
84#3101C2211yescharacteristic
85#3098—21no—
86#3098—21no—
87#3083—21no—
88#3083—21no—
89#3039C2211yescharacteristic
90#3039C2211yescharacteristic
91#3039C2211yescharacteristic
92#3036C2211yescharacteristic
93#3035C2211yescharacteristic
94C2×#461C2211yescharacteristic
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#1703C2211yescharacteristic
122#1703C2211yescharacteristic
123#1702C2211yescharacteristic, complemented
124#1702C2211yescharacteristic, complemented
125#1702C2211yescharacteristic, complemented
126#1701C2211yescharacteristic
127#1701C2211yescharacteristic
128#1701C2211yescharacteristic
129#1701C2211yescharacteristic
130#1701C2211yescharacteristic
131#1700C2211yescharacteristic, complemented
132#1700C2211yescharacteristic, complemented
133#1699C2211yescharacteristic
134#1699C2211yescharacteristic
135#1699C2211yescharacteristic
136#1699C2211yescharacteristic
137#1698C2211yescharacteristic, complemented
138#1697C2211yescharacteristic
139#1694C2211yescharacteristic, complemented
140#1694C2211yescharacteristic, complemented
141#1694C2211yescharacteristic, complemented
142#1694C2211yescharacteristic, complemented
143#1694C2211yescharacteristic, complemented
144#1694C2211yescharacteristic, complemented
145#1694C2211yescharacteristic, complemented
146#1693C2211yescharacteristic
147#1693C2211yescharacteristic
148#1693C2211yescharacteristic
149#1693C2211yescharacteristic
150#1693C2211yescharacteristic
151#1693C2211yescharacteristic
152#1693C2211yescharacteristic
153#1693C2211yescharacteristic
154#1693C2211yescharacteristic
155#1692C2211yescharacteristic, complemented
156#1691C2211yescharacteristic
157#1691C2211yescharacteristic
158#1691C2211yescharacteristic
159#1682C2211yescharacteristic, complemented
160#1682C2211yescharacteristic, complemented
161#1682C2211yescharacteristic, complemented
162#1681C2211yescharacteristic
163#1680C2211yescharacteristic, complemented
164#1680C2211yescharacteristic, complemented
165#1680C2211yescharacteristic, complemented
166#1680C2211yescharacteristic, complemented
167#1679C2211yescharacteristic
168#1679C2211yescharacteristic
169#1678C2211yescharacteristic, complemented
170#1677C2211yescharacteristic
171#1674C2211yescharacteristic, complemented
172#1674C2211yescharacteristic, complemented
173#1674C2211yescharacteristic, complemented
174#1674C2211yescharacteristic, complemented
175#1674C2211yescharacteristic, complemented
176#1673C2211yescharacteristic
177#1673C2211yescharacteristic
178#1673C2211yescharacteristic
179#1672C2211yescharacteristic, complemented
180#1672C2211yescharacteristic, complemented
181#1672C2211yescharacteristic, complemented
182#1671C2211yescharacteristic
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
197#1559C2211yescharacteristic, complemented
198#1557C2211yescharacteristic, complemented
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, complemented
211#1547C2211yescharacteristic, complemented
212#1546C2211yescharacteristic
213#1546C2211yescharacteristic, complemented
214#1546C2211yescharacteristic, complemented
215#1544C2211yescharacteristic
216#1542C2211yescharacteristic, complemented
217#1540C2211yescharacteristic
218C2×#332C2211yescharacteristic, complemented
219C2×#137—21no—
220C2×#137—21no—
221C2×#137—21no—
222C2×AGL(1,ℤ/8)—21no—
223C2×#135—21no—
224C22×SD16—21no—
225Q82—21no—
226#557—21no—
227#556—21no—
228#556D411yescharacteristic
229#555—21no—
230#555D411yescharacteristic
231#554—21no—
232#554—21no—
233#554—21no—
234#554—21no—
235#554D411yescharacteristic
236#553—21no—
237#553—21no—
238#553—21no—
239#552—21no—
240#552D411yescharacteristic
241#552D411yescharacteristic
242#551—21no—
243#551—21no—
244D4×Q8—21no—
245D4×Q8—21no—
246D4×Q8—21no—
247#548—21no—
248#548—21no—
249#547—21no—
250#547D411yescharacteristic
251#546D411yescharacteristic
252#546D411yescharacteristic
253#544—21no—
254#544—21no—
255#544—21no—
256#542—21no—
257#542—21no—
258#537—21no—
259#533C2311yescharacteristic
260#533C2311yescharacteristic
261#533C2311yescharacteristic
262#533C2311yescharacteristic
263#533C2311yescharacteristic
264#533C2311yescharacteristic
265#532C2311yescharacteristic
266#532C2311yescharacteristic
267#532C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272#529—21no—
273#529—21no—
274#529C2311yescharacteristic
275#529C2311yescharacteristic
276#525—21no—
277#520—21no—
278#520—21no—
279C4×#41C2311yescharacteristic
280C4×#41C2311yescharacteristic
281C4×#41C2311yescharacteristic
282C2×C4×D4C2311yescharacteristic
283C2×#117—21no—
284#501—21no—
285#501—21no—
286#500—21no—
287#500—21no—
288#500C2311yescharacteristic
289#500C2311yescharacteristic
290#500C2311yescharacteristic
291#500C2311yescharacteristic
292#500C2311yescharacteristic
293#500C2311yescharacteristic
294#498C2311yescharacteristic
295#498C2311yescharacteristic
296#497—21no—
297#497—21no—
298#497—21no—
299#497—21no—
300#495—21no—
301#494—21no—
302#491—21no—
303#491—21no—
304#491—21no—
305#489—21no—
306#489—21no—
307#489—21no—
308#488—21no—
309#488—21no—
310#488—21no—
311#487—21no—
312#487C2311yescharacteristic
313#487C2311yescharacteristic
314#487C2311yescharacteristic
315#487C2311yescharacteristic
316#486C2311yescharacteristic
317#486C2311yescharacteristic
318#486C2311yescharacteristic
319#486C2311yescharacteristic
320#485—21no—
321#485—21no—
322#485—21no—
323#485—21no—
324#485—21no—
325#485—21no—
326#485—21no—
327#484—21no—
328#484—21no—
329#484—21no—
330#484—21no—
331#484—21no—
332#483—21no—
333#482—21no—
334#482—21no—
335#482—21no—
336#482—21no—
337#482—21no—
338#480—21no—
339#480—21no—
340#480—21no—
341#480—21no—
342#479—21no—
343#479—21no—
344#479—21no—
345#479—21no—
346#479—21no—
347#479—21no—
348#479—21no—
349#478—21no—
350#478—21no—
351#478—21no—
352#478—21no—
353#478—21no—
354#477—21no—
355#477—21no—
356#477—21no—
357#477—21no—
358#477—21no—
359#477C2311yescharacteristic
360#477C2311yescharacteristic
361#476C2311yescharacteristic
362#476C2311yescharacteristic
363#475—21no—
364#475C2311yescharacteristic
365#475C2311yescharacteristic
366#474—21no—
367#474—21no—
368#474—21no—
369#474—21no—
370#474C2311yescharacteristic
371#474C2311yescharacteristic
372#470—21no—
373#470—21no—
374#470—21no—
375#470—21no—
376#469—21no—
377#468—21no—
378#468—21no—
379#468—21no—
380#467—21no—
381#467—21no—
382#467—21no—
383#465—21no—
384#464—21no—
385#464—21no—
386#464—21no—
387#464—21no—
388#463—21no—
389#463—21no—
390#463—21no—
391#463—21no—
392#462—21no—
393#462—21no—
394#462—21no—
395#462—21no—
396#462—21no—
397#462C2311yescharacteristic
398#462C2311yescharacteristic
399#462C2311yescharacteristic
400#462C2311yescharacteristic
401#462C2311yescharacteristic
402#462C2311yescharacteristic
403#462C2311yescharacteristic
404#462C2311yescharacteristic
405#462C2311yescharacteristic
406#462C2311yescharacteristic
407#461—21no—
408#461—21no—
409#461—21no—
410#461—21no—
411#461—21no—
412#461C2311yescharacteristic
413#461C2311yescharacteristic
414#461C2311yescharacteristic
415#461C2311yescharacteristic
416#461C2311yescharacteristic
417#461C2311yescharacteristic
418#461C2311yescharacteristic
419#461C2311yescharacteristic
420#461C2311yescharacteristic
421#461C2311yescharacteristic
422#460C2311yescharacteristic
423#460C2311yescharacteristic
424#459C2311yescharacteristic
425#459C2311yescharacteristic
426#452—21no—
427#452—21no—
428#452—21no—
429#452—21no—
430#452—21no—
431#452—21no—
432#451—21no—
433#451—21no—
434#451—21no—
435#451—21no—
436#451—21no—
437#450—21no—
438#450—21no—
439#449—21no—
440#449—21no—
441#448—21no—
442#448—21no—
443#448—21no—
444#446—21no—
445#446—21no—
446#446—21no—
447#446—21no—
448#446—21no—
449#446C2311yescharacteristic
450#446C2311yescharacteristic
451#446C2311yescharacteristic
452#446C2311yescharacteristic
453C8×Q8—21no—
454C8×Q8C2311yescharacteristic
455C8×Q8C2311yescharacteristic
456C8×Q8C2311yescharacteristic
457C8×Q8C2311yescharacteristic
458#442—21no—
459#441—21no—
460#441—21no—
461#440—21no—
462#440—21no—
463#440—21no—
464#440—21no—
465#440—21no—
466C4×Q16—21no—
467C4×SD16—21no—
468C4×SD16—21no—
469C4×SD16—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#436—21no—
479#436—21no—
480#436C2311yescharacteristic
481#436C2311yescharacteristic
482#436C2311yescharacteristic
483#436C2311yescharacteristic
484#436C2311yescharacteristic
485#436C2311yescharacteristic
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—
498#435—21no—
499#435—21no—
500C8×D4—21no—
501C8×D4—21no—
502C8×D4C2311yescharacteristic
503C8×D4C2311yescharacteristic
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#433—21no—
513#433—21no—
514#433D411yescharacteristic
515#433D411yescharacteristic
516#433D411yescharacteristic
517#433D411yescharacteristic
518#432—21no—
519#432—21no—
520#432C2311yescharacteristic
521#432C2311yescharacteristic
522#432C2311yescharacteristic
523#432C2311yescharacteristic
524#432C2311yescharacteristic
525#432C2311yescharacteristic
526#431—21no—
527#431—21no—
528#431C2311yescharacteristic
529#431C2311yescharacteristic
530#431C2311yescharacteristic
531#431C2311yescharacteristic
532#431C2311yescharacteristic
533#431C2311yescharacteristic
534#431C2311yescharacteristic
535#431C2311yescharacteristic
536#428—21no—
537#428—21no—
538C2×#107—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#419—21no—
557#417—21no—
558#417—21no—
559#417—21no—
560#416—21no—
561#416—21no—
562#416—21no—
563C2×#103—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
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41C2×D411yescharacteristic
630C2×#41C2×D411yescharacteristic
631C2×#41C2×D411yescharacteristic
632C22×Q8—21no—
633C22×Q8—21no—
634C22×Q8—21no—
635C22×Q8—21no—
636C22×D4C2×D411yescharacteristic
637C23×C4—21no—
638#137—82no—
639#137—82no—
640#137—82no—
641AGL(1,ℤ/8)—82no—
642#135—82no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×Q16—21no—
647C2×Q16—21no—
648C2×Q16—21no—
649C2×Q16—21no—
650C2×Q16—21no—
651C2×Q16—21no—
652C2×Q16—21no—
653C2×SD16—21no—
654C2×SD16—21no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×SD16—21no—
659C2×SD16—21no—
660C2×SD16—21no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×SD16—21no—
665C2×SD16—82no—
666C2×D8—21no—
667C2×D8—21no—
668C2×M16—21no—
669C2×M16—21no—
670C2×M16—21no—
671C2×M16—21no—
672C2×M16—21no—
673C2×M16—21no—
674C2×M16—21no—
675C2×M16—21no—
676C2×M16—21no—
677C2×M16—21no—
678C2×M16—21no—
679C2×M16C2×D411yescharacteristic
680C2×M16C2×D411yescharacteristic
681C22×C8—21no—
682C22×C8—21no—
683C22×C8—21no—
684C22×C8—21no—
685C22×C8—21no—
686C22×C8C2×D411yescharacteristic
687C22×C8C2×D411yescharacteristic
688C4⋊Q8—21no—
689C4⋊Q8—21no—
690C4⋊Q8—21no—
691C4⋊Q8—21no—
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—41no—
701C4⋊Q8—41no—
702C4⋊Q8—41no—
703C4⋊Q8C2×D411yescharacteristic
704C4⋊Q8C2×D411yescharacteristic
705C4⋊Q8C2411yescharacteristic
706C4⋊Q8C2411yescharacteristic
707C4⋊Q8C2411yescharacteristic
708C4⋊Q8C2411yescharacteristic
709C4⋊Q8C2411yescharacteristic
710C4⋊Q8C2411yescharacteristic
711C4⋊Q8C2411yescharacteristic
712#127C2411yescharacteristic
713#126—21no—
714#126—21no—
715#126—21no—
716#126—21no—
717#126—21no—
718#126—21no—
719#126—41no—
720#126—41no—
721#125—21no—
722#125—21no—
723#125—21no—
724#125—21no—
725#125—21no—
726#125—21no—
727#125—21no—
728#125—21no—
729#125—41no—
730#125—41no—
731#125—41no—
732#125C2×D411yescharacteristic
733#125C2×D411yescharacteristic
734#124—21no—
735#124—21no—
736#124—21no—
737#124—21no—
738#124—21no—
739#124—41no—
740#124—41no—
741#124C2×D411yescharacteristic
742#124C2×D411yescharacteristic
743#123—21no—
744#123—21no—
745#123—21no—
746#123—21no—
747#123—21no—
748#123—21no—
749#123—21no—
750#123—21no—
751#123—41no—
752#123—41no—
753C22⋊Q8—21no—
754C22⋊Q8—21no—
755C22⋊Q8—21no—
756C22⋊Q8—21no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—21no—
760C22⋊Q8—21no—
761C22⋊Q8—21no—
762C22⋊Q8—21no—
763C22⋊Q8—21no—
764C22⋊Q8—21no—
765C22⋊Q8—21no—
766C22⋊Q8—21no—
767C22⋊Q8—21no—
768C22⋊Q8—41no—
769C22⋊Q8—41no—
770C22⋊Q8—41no—
771C22⋊Q8—41no—
772C22⋊Q8—41no—
773C22⋊Q8—41no—
774C22⋊Q8—41no—
775C22⋊Q8—41no—
776C22⋊Q8—41no—
777C22⋊Q8C2×D411yescharacteristic
778C22⋊Q8C2×D411yescharacteristic
779C22⋊Q8C2×D411yescharacteristic
780C22⋊Q8C2×D411yescharacteristic
781#121—21no—
782#121—21no—
783#121—21no—
784#121—21no—
785#121—21no—
786#121—21no—
787#121—21no—
788#121—21no—
789#121—21no—
790#121—21no—
791#121—41no—
792#121—41no—
793#121—41no—
794#121C2×D411yescharacteristic
795#121C2×D411yescharacteristic
796#120—21no—
797#120—21no—
798C4×Q8—21no—
799C4×Q8—21no—
800C4×Q8—21no—
801C4×Q8—21no—
802C4×Q8—21no—
803C4×Q8—21no—
804C4×Q8—21no—
805C4×Q8—21no—
806C4×Q8—21no—
807C4×Q8—21no—
808C4×Q8—21no—
809C4×Q8—41no—
810C4×Q8C2×D411yescharacteristic
811C4×Q8C2×D411yescharacteristic
812C4×Q8C2×D411yescharacteristic
813C4×Q8#4111yescharacteristic
814C4×Q8C2411yescharacteristic
815C4×Q8C2411yescharacteristic
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—21no—
819C4×D4—21no—
820C4×D4—21no—
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—41no—
831C4×D4—41no—
832C4×D4—41no—
833C4×D4—41no—
834C4×D4—41no—
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#117C2×D411yescharacteristic
863#117C2×D411yescharacteristic
864#117C2×D411yescharacteristic
865#117C2×D411yescharacteristic
866#117C2×D411yescharacteristic
867C2×C4⋊C4—21no—
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—41no—
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#107—21no—
900#107—21no—
901#107—21no—
902#107—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#103—21no—
976#103—21no—
977#103—21no—
978#103—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—
1060C2×Q8—21no—
1061C2×Q8—21no—
1062C2×Q8—21no—
1063C2×Q8—21no—
1064C2×Q8—21no—
1065C2×Q8—21no—
1066C2×Q8—21no—
1067C2×Q8—21no—
1068C2×Q8—41no—
1069C2×Q8—41no—
1070C2×Q8—41no—
1071C2×Q8—41no—
1072C2×Q8—81no—
1073C2×Q8—81no—
1074C2×Q8—81no—
1075C2×Q8—81no—
1076C2×Q8—81no—
1077C2×Q8—81no—
1078C2×Q8—81no—
1079C2×Q8—81no—
1080C2×Q8#12111yescharacteristic
1081C2×Q8C22×D411yescharacteristic
1082C2×Q8C22×D411yescharacteristic
1083C2×D4—21no—
1084C2×D4—21no—
1085C2×D4—21no—
1086C2×D4—21no—
1087C2×D4—21no—
1088C2×D4—21no—
1089C2×D4—21no—
1090C2×D4—21no—
1091C2×D4—41no—
1092C2×D4—41no—
1093C2×D4—41no—
1094C2×D4—41no—
1095C2×D4—41no—
1096C2×D4#12111yescharacteristic
1097C2×D4#12111yescharacteristic
1098C2×D4#12111yescharacteristic
1099C2×D4C22×D411yescharacteristic
1100C2×D4C22×D411yescharacteristic
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—21no—
1105C22×C4—21no—
1106C22×C4—21no—
1107C22×C4—21no—
1108C22×C4—21no—
1109C22×C4—21no—
1110C22×C4—41no—
1111C22×C4—41no—
1112C22×C4—41no—
1113C22×C4—41no—
1114C22×C4—41no—
1115C22×C4—41no—
1116C22×C4—41no—
1117C22×C4—81no—
1118C22×C4—81no—
1119C22×C4C22×D411yescharacteristic
1120C22×C4C22×D411yescharacteristic
1121C22×C4C22×D411yescharacteristic
1122C22×C4C22×D411yescharacteristic
1123C22×C4C22×D411yescharacteristic
1124C22×C4C22×D411yescharacteristic
1125C22×C4C2×#4111yescharacteristic
1126C22×C4C2×#4111yescharacteristic
1127C22×C4C2×#4111yescharacteristic
1128Q16—81no—
1129Q16—81no—
1130Q16—81no—
1131Q16—81no—
1132Q16—81no—
1133Q16—81no—
1134Q16—81no—
1135Q16—81no—
1136Q16—81no—
1137Q16—81no—
1138SD16—42no—
1139SD16—42no—
1140SD16—42no—
1141SD16—42no—
1142SD16—42no—
1143SD16—81no—
1144SD16—81no—
1145SD16—81no—
1146SD16—81no—
1147SD16—81no—
1148SD16—81no—
1149SD16—81no—
1150D8—42no—
1151D8—81no—
1152M16—41no—
1153M16—41no—
1154M16—81no—
1155M16—81no—
1156M16—81no—
1157M16—81no—
1158M16—81no—
1159M16—81no—
1160M16—81no—
1161M16—81no—
1162M16—81no—
1163M16—81no—
1164M16—81no—
1165C2×C8—21no—
1166C2×C8—21no—
1167C2×C8—21no—
1168C2×C8—21no—
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—41no—
1178C2×C8—41no—
1179C2×C8—81no—
1180C2×C8—81no—
1181C2×C8—81no—
1182C2×C8—81no—
1183C2×C8—81no—
1184C2×C8C22×D411yescharacteristic
1185C2×C8C22×D411yescharacteristic
1186C2×C8C22×D411yescharacteristic
1187C2×C8C22×D411yescharacteristic
1188C2×C8C22×D411yescharacteristic
1189C2×C8C22×D411yescharacteristic
1190C2×C8C22×D411yescharacteristic
1191C2×C8C22×D411yescharacteristic
1192C4⋊C4—21no—
1193C4⋊C4—21no—
1194C4⋊C4—21no—
1195C4⋊C4—21no—
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—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
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#12111yescharacteristic
1241C4⋊C4#12111yescharacteristic
1242C4⋊C4#12111yescharacteristic
1243C4⋊C4#12111yescharacteristic
1244C4⋊C4#12111yescharacteristic
1245C4⋊C4#12111yescharacteristic
1246C4⋊C4C22×D411yescharacteristic
1247C4⋊C4C22×D411yescharacteristic
1248C4⋊C4C22×D411yescharacteristic
1249C4⋊C4C22×D411yescharacteristic
1250C22⋊C4—21no—
1251C22⋊C4—21no—
1252C22⋊C4—21no—
1253C22⋊C4—21no—
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—41no—
1269C22⋊C4—41no—
1270C22⋊C4—41no—
1271C22⋊C4—41no—
1272C22⋊C4—41no—
1273C22⋊C4—41no—
1274C22⋊C4—41no—
1275C22⋊C4—41no—
1276C22⋊C4—41no—
1277C22⋊C4—41no—
1278C22⋊C4—41no—
1279C22⋊C4#12111yescharacteristic
1280C22⋊C4#12111yescharacteristic
1281C22⋊C4#12111yescharacteristic
1282C22⋊C4#12111yescharacteristic
1283C22⋊C4#12111yescharacteristic
1284C22⋊C4#12111yescharacteristic
1285C42—21no—
1286C42—21no—
1287C42—21no—
1288C42—21no—
1289C42—21no—
1290C42—21no—
1291C42—41no—
1292C42—41no—
1293C42—41no—
1294C42—41no—
1295C42—41no—
1296C42C22×D411yescharacteristic
1297C42C22×D411yescharacteristic
1298C42C22×D411yescharacteristic
1299C42C22×D411yescharacteristic
1300C42C22×D411yescharacteristic
1301C42C22×D411yescharacteristic
1302C42C2×#4111yescharacteristic
1303C42C2×#4111yescharacteristic
1304C42C2×#4111yescharacteristic
1305C42C2511yescharacteristic
1306C23—21no—
1307C23—21no—
1308C23—41no—
1309C23—81no—
1310C23—81no—
1311C23—81no—
1312C23C2×#12111yescharacteristic
1313C23C2×#12111yescharacteristic
1314C23C2×#12111yescharacteristic
1315Q8—21no—
1316Q8—21no—
1317Q8—21no—
1318Q8—21no—
1319Q8—41no—
1320Q8—41no—
1321Q8—41no—
1322Q8—41no—
1323Q8—41no—
1324Q8—41no—
1325Q8—41no—
1326Q8—41no—
1327Q8—41no—
1328Q8—41no—
1329Q8—41no—
1330Q8—41no—
1331Q8—41no—
1332Q8—81no—
1333Q8—81no—
1334Q8—161no—
1335Q8—161no—
1336Q8—161no—
1337Q8—161no—
1338D4—21no—
1339D4—21no—
1340D4—21no—
1341D4—21no—
1342D4—41no—
1343D4—41no—
1344D4—41no—
1345D4—41no—
1346D4—41no—
1347D4—41no—
1348D4—41no—
1349D4—81no—
1350D4—81no—
1351D4—81no—
1352D4—81no—
1353D4—81no—
1354D4—81no—
1355D4—82no—
1356D4—161no—
1357D4—161no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
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—41no—
1377C2×C4—41no—
1378C2×C4—41no—
1379C2×C4—41no—
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—81no—
1391C2×C4—81no—
1392C2×C4—81no—
1393C2×C4—81no—
1394C2×C4—81no—
1395C2×C4—81no—
1396C2×C4—82no—
1397C2×C4—81no—
1398C2×C4—161no—
1399C2×C4—161no—
1400C2×C4—161no—
1401C2×C4—161no—
1402C2×C4—161no—
1403C2×C4—161no—
1404C2×C4C2×#12111yescharacteristic
1405C2×C4C2×#12111yescharacteristic
1406C2×C4C2×#12111yescharacteristic
1407C2×C4C2×#12111yescharacteristic
1408C2×C4C2×#12111yescharacteristic
1409C2×C4C2×#12111yescharacteristic
1410C2×C4C2×#12111yescharacteristic
1411C2×C4C2×#12111yescharacteristic
1412C2×C4C2×#12111yescharacteristic
1413C2×C4C23×D411yescharacteristic
1414C2×C4C23×D411yescharacteristic
1415C2×C4C22×#4111yescharacteristic
1416C8—21no—
1417C8—21no—
1418C8—21no—
1419C8—21no—
1420C8—21no—
1421C8—21no—
1422C8—21no—
1423C8—21no—
1424C8—41no—
1425C8—41no—
1426C8—41no—
1427C8—41no—
1428C8—41no—
1429C8—41no—
1430C8—41no—
1431C8—41no—
1432C8—41no—
1433C8—41no—
1434C8—41no—
1435C8—41no—
1436C22—21no—
1437C22—21no—
1438C22—21no—
1439C22—21no—
1440C22—21no—
1441C22—21no—
1442C22—21no—
1443C22—21no—
1444C22—21no—
1445C22—41no—
1446C22—41no—
1447C22—41no—
1448C22—41no—
1449C22—41no—
1450C22—41no—
1451C22—81no—
1452C22—81no—
1453C22—81no—
1454C22—162no—
1455C22C22×#12111yescharacteristic
1456C4—21no—
1457C4—21no—
1458C4—21no—
1459C4—21no—
1460C4—21no—
1461C4—21no—
1462C4—21no—
1463C4—21no—
1464C4—21no—
1465C4—21no—
1466C4—41no—
1467C4—41no—
1468C4—41no—
1469C4—41no—
1470C4—41no—
1471C4—41no—
1472C4—81no—
1473C4—81no—
1474C4—81no—
1475C4—81no—
1476C4—81no—
1477C4—81no—
1478C4—81no—
1479C4#358511yescharacteristic
1480C4#358511yescharacteristic
1481C4#358611yescharacteristic
1482C4#358611yescharacteristic
1483C2—41no—
1484C2—41no—
1485C2—41no—
1486C2—81no—
1487C2—81no—
1488C2—161no—
1489C2#6042711yescharacteristic
1490C2#6046111yescharacteristic
1491C2#6047211yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
prime radical#61967C2
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
2. #61960C2semidirect
3. #60880C2semidirect
4. #60300C2semidirect
5. #19590C2semidirect
6. #19586C2semidirect
7. #19575C2semidirect
8. #19572C2semidirect
9. #19548C2semidirect
10. #19546C2semidirect
11. #19533C2semidirect
12. #19530C2semidirect
13. #19502C2semidirect
14. #19498C2semidirect
15. #19467C2semidirect
16. #19464C2semidirect
17. #19454C2semidirect
18. #19452C2semidirect
19. #19431C2semidirect
20. #19428C2semidirect
21. #19383C2semidirect
22. #19378C2semidirect
23. #19366C2semidirect
24. #19358C2semidirect
25. #19327C2semidirect
26. #19322C2semidirect
27. #19303C2semidirect
28. #19296C2semidirect
29. #17824C2semidirect
30. #17769C2semidirect
31. #17761C2semidirect
62. #3231C22semidirect
64. #3230C22semidirect
66. #3228C22semidirect
68. #3226C22semidirect
75. #3165C22semidirect
76. C2×#500C22semidirect
77. #3141C22semidirect
78. #3131C22semidirect
119. #1704C22semidirect
120. #1704C22semidirect
123. #1702C22semidirect
124. #1702C22semidirect
125. #1702C22semidirect
131. #1700C22semidirect
132. #1700C22semidirect
137. #1698C22semidirect
139. #1694C22semidirect
140. #1694C22semidirect
141. #1694C22semidirect
142. #1694C22semidirect
143. #1694C22semidirect
144. #1694C22semidirect
145. #1694C22semidirect
155. #1692C22semidirect
159. #1682C22semidirect
160. #1682C22semidirect
161. #1682C22semidirect
163. #1680C22semidirect
164. #1680C22semidirect
165. #1680C22semidirect
166. #1680C22semidirect
169. #1678C22semidirect
171. #1674C22semidirect
172. #1674C22semidirect
173. #1674C22semidirect
174. #1674C22semidirect
175. #1674C22semidirect
179. #1672C22semidirect
180. #1672C22semidirect
181. #1672C22semidirect
184. #1574C22semidirect
186. #1573C22semidirect
188. #1572C22semidirect
190. #1570C22semidirect
191. #1569C22semidirect
192. #1569C22semidirect
193. #1568C22semidirect
194. #1566C22semidirect
195. #1561C22semidirect
197. #1559C22semidirect
198. #1557C22semidirect
199. #1557C22semidirect
201. #1556C22semidirect
202. #1556C22semidirect
204. #1554C22semidirect
206. #1553C22semidirect
208. #1552C22semidirect
209. #1550C22semidirect
210. #1549C22semidirect
211. #1547C22semidirect
213. #1546C22semidirect
214. #1546C22semidirect
216. #1542C22semidirect
218. C2×#332C22semidirect

Maximal subgroups

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

subgroupindex
#619672
#619602
#608802
#603002
#195902
#195862
#195752
#195722
#195482
#195462
#195332
#195302
#195022
#194982
#194672
#194642
#194542
#194522
#194312
#194282
#193832
#193782
#193662
#193582
#193272
#193222
#193032
#192962
#178242
#177692
#177612