Finite Group Databasebeta

← #6355995

Subgroups — #6355995

Order 512.

1524 conjugacy classes of subgroups.

The subgroup lattice has 1507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61970C211yesmaximal, characteristic
2#61964C211yesmaximal, characteristic, complemented
3#60877C211yesmaximal, characteristic, complemented
4#60302C211yesmaximal, characteristic, complemented
5#19589C211yesmaximal, characteristic, complemented
6#19586C211yesmaximal, characteristic, complemented
7#19563C211yesmaximal, characteristic, complemented
8#19558C211yesmaximal, characteristic, complemented
9#19549C211yesmaximal, characteristic, complemented
10#19546C211yesmaximal, characteristic, complemented
11#19516C211yesmaximal, characteristic, complemented
12#19514C211yesmaximal, characteristic, complemented
13#19489C211yesmaximal, characteristic, complemented
14#19486C211yesmaximal, characteristic, complemented
15#19479C211yesmaximal, characteristic, complemented
16#19474C211yesmaximal, characteristic, complemented
17#19455C211yesmaximal, characteristic, complemented
18#19452C211yesmaximal, characteristic, complemented
19#19442C211yesmaximal, characteristic, complemented
20#19440C211yesmaximal, characteristic, complemented
21#19380C211yesmaximal, characteristic, complemented
22#19378C211yesmaximal, characteristic, complemented
23#19364C211yesmaximal, characteristic, complemented
24#19360C211yesmaximal, characteristic, complemented
25#19316C211yesmaximal, characteristic, complemented
26#19314C211yesmaximal, characteristic, complemented
27#19301C211yesmaximal, characteristic, complemented
28#19298C211yesmaximal, characteristic, complemented
29#17824C211yesmaximal, characteristic, complemented
30#17766C211yesmaximal, characteristic, complemented
31#17761C211yesmaximal, characteristic, complemented
32#3508C2211yescharacteristic
33#3503C2211yescharacteristic
34#3480C2211yescharacteristic
35#3403—21no—
36#3400—21no—
37#3374—21no—
38#3371—21no—
39#3328—21no—
40#3322—21no—
41#3320—21no—
42#3320—21no—
43#3311—21no—
44#3309—21no—
45#3278—21no—
46#3275—21no—
47#3271—21no—
48#3270—21no—
49#3270—21no—
50#3268—21no—
51#3253C2211yescharacteristic
52#3252C2211yescharacteristic
53#3252C2211yescharacteristic
54#3252C2211yescharacteristic, complemented
55#3247C2211yescharacteristic
56#3246C2211yescharacteristic, complemented
57#3241—21no—
58#3241—21no—
59#3241—21no—
60#3241—21no—
61#3228C2211yescharacteristic
62#3228C2211yescharacteristic
63#3228C2211yescharacteristic
64#3228C2211yescharacteristic
65#3227C2211yescharacteristic
66#3227C2211yescharacteristic
67#3226C2211yescharacteristic
68#3226C2211yescharacteristic
69#3218C2211yescharacteristic
70#3218C2211yescharacteristic, complemented
71#3217C2211yescharacteristic
72#3214C2211yescharacteristic
73#3212C2211yescharacteristic
74#3206C2211yescharacteristic, complemented
75#3165C2211yescharacteristic
76#3160C2211yescharacteristic
77#3138C2211yescharacteristic
78C2×#486C2211yescharacteristic
79#3116C2211yescharacteristic
80#3116C2211yescharacteristic
81#3116C2211yescharacteristic, complemented
82#3112C2211yescharacteristic
83#3106C2211yescharacteristic
84#3104C2211yescharacteristic, complemented
85#3096—21no—
86#3096—21no—
87#3081—21no—
88#3081—21no—
89#3039C2211yescharacteristic
90#3039C2211yescharacteristic, complemented
91#3038C2211yescharacteristic
92#3037C2211yescharacteristic
93#3035C2211yescharacteristic
94C2×#462C2211yescharacteristic, complemented
95#2995—21no—
96#2994C2211yescharacteristic, complemented
97#2993C2211yescharacteristic, complemented
98#2992—21no—
99#2990C2211yescharacteristic, complemented
100#2989C2211yescharacteristic
101#2989C2211yescharacteristic
102#2989C2211yescharacteristic, complemented
103#2984C2211yescharacteristic, complemented
104#2983C2211yescharacteristic, complemented
105#2981—21no—
106#2981C2211yescharacteristic, complemented
107#2980—21no—
108#2979C2211yescharacteristic, complemented
109#2970C2211yescharacteristic
110#2969C2211yescharacteristic
111#2968—21no—
112#2967—21no—
113#2966C2211yescharacteristic
114#2965C2211yescharacteristic
115#2925—21no—
116#2925C2211yescharacteristic
117#2923—21no—
118#2922C2211yescharacteristic
119#1702C2211yescharacteristic
120#1702C2211yescharacteristic
121#1702C2211yescharacteristic
122#1702C2211yescharacteristic
123#1702C2211yescharacteristic
124#1702C2211yescharacteristic
125#1702C2211yescharacteristic
126#1702C2211yescharacteristic
127#1702C2211yescharacteristic
128#1701C2211yescharacteristic
129#1701C2211yescharacteristic
130#1701C2211yescharacteristic
131#1701C2211yescharacteristic
132#1701C2211yescharacteristic
133#1701C2211yescharacteristic
134#1701C2211yescharacteristic
135#1698C2211yescharacteristic
136#1698C2211yescharacteristic
137#1698C2211yescharacteristic
138#1697C2211yescharacteristic
139#1696C2211yescharacteristic, complemented
140#1696C2211yescharacteristic, complemented
141#1695C2211yescharacteristic, complemented
142#1695C2211yescharacteristic, complemented
143#1694C2211yescharacteristic, complemented
144#1694C2211yescharacteristic, complemented
145#1694C2211yescharacteristic, complemented
146#1694C2211yescharacteristic, complemented
147#1694C2211yescharacteristic, complemented
148#1693C2211yescharacteristic, complemented
149#1693C2211yescharacteristic, complemented
150#1693C2211yescharacteristic, complemented
151#1692C2211yescharacteristic, complemented
152#1692C2211yescharacteristic, complemented
153#1692C2211yescharacteristic, complemented
154#1692C2211yescharacteristic, complemented
155#1692C2211yescharacteristic, complemented
156#1691C2211yescharacteristic, complemented
157#1691C2211yescharacteristic, complemented
158#1691C2211yescharacteristic, complemented
159#1682C2211yescharacteristic
160#1682C2211yescharacteristic
161#1682C2211yescharacteristic
162#1681C2211yescharacteristic
163#1681C2211yescharacteristic
164#1681C2211yescharacteristic
165#1681C2211yescharacteristic
166#1681C2211yescharacteristic
167#1678C2211yescharacteristic
168#1677C2211yescharacteristic
169#1677C2211yescharacteristic
170#1677C2211yescharacteristic
171#1674C2211yescharacteristic, complemented
172#1673C2211yescharacteristic, complemented
173#1673C2211yescharacteristic, complemented
174#1673C2211yescharacteristic, complemented
175#1672C2211yescharacteristic, complemented
176#1672C2211yescharacteristic, complemented
177#1672C2211yescharacteristic, complemented
178#1671C2211yescharacteristic, complemented
179#1671C2211yescharacteristic, complemented
180#1671C2211yescharacteristic, complemented
181#1671C2211yescharacteristic, complemented
182#1671C2211yescharacteristic, complemented
183#1574C2211yescharacteristic, complemented
184#1574C2211yescharacteristic, complemented
185#1573C2211yescharacteristic, complemented
186#1573C2211yescharacteristic, complemented
187#1572C2211yescharacteristic, complemented
188#1572C2211yescharacteristic, complemented
189#1570C2211yescharacteristic, complemented
190#1570C2211yescharacteristic, complemented
191#1569C2211yescharacteristic
192#1569C2211yescharacteristic
193#1568C2211yescharacteristic
194#1566C2211yescharacteristic
195#1560C2211yescharacteristic
196#1559C2211yescharacteristic
197#1559C2211yescharacteristic
198#1559C2211yescharacteristic, complemented
199#1557C2211yescharacteristic
200#1556C2211yescharacteristic
201#1556C2211yescharacteristic, complemented
202#1555C2211yescharacteristic
203#1554C2211yescharacteristic
204#1554C2211yescharacteristic
205#1554C2211yescharacteristic, complemented
206#1553C2211yescharacteristic
207#1551C2211yescharacteristic
208#1551C2211yescharacteristic
209#1550C2211yescharacteristic, complemented
210#1549C2211yescharacteristic, complemented
211#1547C2211yescharacteristic
212#1546C2211yescharacteristic
213#1546C2211yescharacteristic, complemented
214#1545C2211yescharacteristic
215#1543C2211yescharacteristic
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×Q16—21no—
225#559—21no—
226#559—21no—
227#559—21no—
228#559D411yescharacteristic
229Q82—21no—
230#557—21no—
231#557D411yescharacteristic
232#556—21no—
233#556D411yescharacteristic
234#554—21no—
235#554—21no—
236#554—21no—
237#553—21no—
238#553—21no—
239#553D411yescharacteristic
240#553D411yescharacteristic
241#550—21no—
242#550—21no—
243#550D411yescharacteristic
244D4×Q8—21no—
245D4×Q8—21no—
246D4×Q8—21no—
247#548D411yescharacteristic
248#548D411yescharacteristic
249#546—21no—
250#546—21no—
251#546—21no—
252#546—21no—
253#544—21no—
254#544—21no—
255#544—21no—
256#540—21no—
257#540—21no—
258#535—21no—
259#533C2311yescharacteristic
260#533C2311yescharacteristic
261#533C2311yescharacteristic
262#533C2311yescharacteristic
263#532—21no—
264#532C2311yescharacteristic
265#532C2311yescharacteristic
266#532C2311yescharacteristic
267#532C2311yescharacteristic
268#532C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×#127C2311yescharacteristic
273#529—21no—
274#529—21no—
275#529C2311yescharacteristic
276#529C2311yescharacteristic
277#520—21no—
278#518—21no—
279C4×#41—21no—
280C4×#41C2311yescharacteristic
281C4×#41C2311yescharacteristic
282C4×#41C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284#501—21no—
285#501—21no—
286#500C2311yescharacteristic
287#500C2311yescharacteristic
288#500C2311yescharacteristic
289#500C2311yescharacteristic
290#499—21no—
291#499—21no—
292#498C2311yescharacteristic
293#498C2311yescharacteristic
294#498C2311yescharacteristic
295#498C2311yescharacteristic
296#497—21no—
297#497—21no—
298#496—21no—
299#496—21no—
300#495—21no—
301#492—21no—
302#491—21no—
303#491—21no—
304#490—21no—
305#490—21no—
306#490—21no—
307#489—21no—
308#488—21no—
309#487—21no—
310#486—21no—
311#486—21no—
312#486C2311yescharacteristic
313#486C2311yescharacteristic
314#486C2311yescharacteristic
315#486C2311yescharacteristic
316#486C2311yescharacteristic
317#486C2311yescharacteristic
318#486C2311yescharacteristic
319#486C2311yescharacteristic
320#485—21no—
321#485—21no—
322#485—21no—
323#484—21no—
324#482—21no—
325#482—21no—
326#482—21no—
327#482—21no—
328#482—21no—
329#482—21no—
330#482—21no—
331#482—21no—
332#482—21no—
333#481—21no—
334#481—21no—
335#481—21no—
336#481—21no—
337#480—21no—
338#480—21no—
339#480—21no—
340#480—21no—
341#480—21no—
342#479—21no—
343#479—21no—
344#479—21no—
345#478—21no—
346#478—21no—
347#478—21no—
348#478—21no—
349#478—21no—
350#478—21no—
351#478—21no—
352#478—21no—
353#478—21no—
354#477C2311yescharacteristic
355#477C2311yescharacteristic
356#477C2311yescharacteristic
357#477C2311yescharacteristic
358#476—21no—
359#476—21no—
360#476—21no—
361#476—21no—
362#476—21no—
363#476C2311yescharacteristic
364#476C2311yescharacteristic
365#476C2311yescharacteristic
366#476C2311yescharacteristic
367#475—21no—
368#474—21no—
369#474—21no—
370#474—21no—
371#474—21no—
372#470—21no—
373#470—21no—
374#470—21no—
375#469—21no—
376#469—21no—
377#468—21no—
378#468—21no—
379#468—21no—
380#466—21no—
381#465—21no—
382#465—21no—
383#465—21no—
384#464—21no—
385#464—21no—
386#464—21no—
387#464—21no—
388#464—21no—
389#464—21no—
390#463—21no—
391#463—21no—
392#462—21no—
393#462—21no—
394#462—21no—
395#462—21no—
396#462C2311yescharacteristic
397#462C2311yescharacteristic
398#462C2311yescharacteristic
399#462C2311yescharacteristic
400#462C2311yescharacteristic
401#462C2311yescharacteristic
402#462C2311yescharacteristic
403#462C2311yescharacteristic
404#461—21no—
405#461—21no—
406#461C2311yescharacteristic
407#461C2311yescharacteristic
408#461C2311yescharacteristic
409#461C2311yescharacteristic
410#461C2311yescharacteristic
411#461C2311yescharacteristic
412#461C2311yescharacteristic
413#461C2311yescharacteristic
414#460—21no—
415#460—21no—
416#460C2311yescharacteristic
417#460C2311yescharacteristic
418#460C2311yescharacteristic
419#460C2311yescharacteristic
420#459—21no—
421#459—21no—
422#459C2311yescharacteristic
423#459C2311yescharacteristic
424#459C2311yescharacteristic
425#459C2311yescharacteristic
426#452—21no—
427#452—21no—
428#452—21no—
429#452—21no—
430#451—21no—
431#451—21no—
432#451—21no—
433#450—21no—
434#449—21no—
435#449—21no—
436#449—21no—
437#449—21no—
438#448—21no—
439#448—21no—
440#448—21no—
441#448—21no—
442#448—21no—
443#447—21no—
444#446—21no—
445#446—21no—
446#446—21no—
447#446—21no—
448#446—21no—
449#446—21no—
450#446C2311yescharacteristic
451#446C2311yescharacteristic
452#446C2311yescharacteristic
453#446C2311yescharacteristic
454#446C2311yescharacteristic
455#446C2311yescharacteristic
456C8×Q8C2311yescharacteristic
457C8×Q8C2311yescharacteristic
458#441—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×Q16—21no—
468C4×SD16—21no—
469C4×D8—21no—
470#436—21no—
471#436—21no—
472#436—21no—
473#436—21no—
474#436—21no—
475#436C2311yescharacteristic
476#436C2311yescharacteristic
477#436C2311yescharacteristic
478#436C2311yescharacteristic
479#435—21no—
480#435—21no—
481#435—21no—
482#435—21no—
483#435—21no—
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—
497C8×D4—21no—
498C8×D4—21no—
499C8×D4—21no—
500C8×D4C2311yescharacteristic
501C8×D4C2311yescharacteristic
502C8×D4C2311yescharacteristic
503C8×D4C2311yescharacteristic
504#433—21no—
505#433—21no—
506#433—21no—
507#433—21no—
508#433—21no—
509#433—21no—
510#433D411yescharacteristic
511#433D411yescharacteristic
512#433D411yescharacteristic
513#433D411yescharacteristic
514#432—21no—
515#432—21no—
516#432—21no—
517#432—21no—
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—
538#427—21no—
539#427—21no—
540#424—21no—
541#424—21no—
542#424D411yescharacteristic
543#424D411yescharacteristic
544#423—21no—
545#423C2311yescharacteristic
546#423C2311yescharacteristic
547#423C2311yescharacteristic
548#423C2311yescharacteristic
549#423C2311yescharacteristic
550C2×C4⋊C8—21no—
551C2×C4⋊C8C2311yescharacteristic
552C2×C4⋊C8C2311yescharacteristic
553C2×C4⋊C8C2311yescharacteristic
554#419—21no—
555#419—21no—
556#418—21no—
557#418—21no—
558#418—21no—
559#417—21no—
560#416—21no—
561C2×#103—21no—
562C2×#102—21no—
563C2×#102—21no—
564#408—21no—
565#408—21no—
566#408—21no—
567#408—21no—
568#408—21no—
569#408D411yescharacteristic
570#408D411yescharacteristic
571#405—21no—
572#405—21no—
573#405—21no—
574C4×M16—21no—
575C4×M16C2311yescharacteristic
576C2×#97—21no—
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#333C2311yescharacteristic
599#333C2311yescharacteristic
600#333C2311yescharacteristic
601#333C2311yescharacteristic
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#331C2311yescharacteristic
619#331C2311yescharacteristic
620#331C2311yescharacteristic
621#331C2311yescharacteristic
622#331C2311yescharacteristic
623#331C2311yescharacteristic
624#331C2311yescharacteristic
625#331C2311yescharacteristic
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41C2×D411yescharacteristic
632C2×#41C2×D411yescharacteristic
633C2×#41C2×D411yescharacteristic
634C22×Q8—21no—
635C22×Q8—21no—
636C22×Q8—21no—
637C22×Q8C2×D411yescharacteristic
638C22×D4—21no—
639C22×D4—21no—
640C22×D4—21no—
641#137—82no—
642#137—82no—
643#137—82no—
644AGL(1,ℤ/8)—82no—
645#135—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—82no—
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—21no—
666C2×SD16—21no—
667C2×D8—21no—
668C2×D8—21no—
669C2×D8—21no—
670C2×D8—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×M16—21no—
680C2×M16C2×D411yescharacteristic
681C2×M16C2×D411yescharacteristic
682C22×C8—21no—
683C22×C8—21no—
684C22×C8—21no—
685C22×C8—21no—
686C22×C8—21no—
687C22×C8—21no—
688C22×C8—21no—
689C22×C8C2×D411yescharacteristic
690C22×C8C2×D411yescharacteristic
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—21no—
701C4⋊Q8—41no—
702C4⋊Q8—41no—
703C4⋊Q8—41no—
704C4⋊Q8C2×D411yescharacteristic
705C4⋊Q8C2411yescharacteristic
706C4⋊Q8C2411yescharacteristic
707C4⋊Q8C2411yescharacteristic
708C4⋊Q8C2411yescharacteristic
709C4⋊Q8C2411yescharacteristic
710C4⋊Q8C2411yescharacteristic
711#127—21no—
712#127—21no—
713#127—21no—
714#127—21no—
715#127—41no—
716#127C2×D411yescharacteristic
717#127C2411yescharacteristic
718#127C2411yescharacteristic
719#126—21no—
720#126—21no—
721#126—21no—
722#126—21no—
723#126—21no—
724#126—21no—
725#125—21no—
726#125—21no—
727#125—21no—
728#125—21no—
729#125—21no—
730#125—21no—
731#125—41no—
732#125—41no—
733#125—41no—
734#125C2×D411yescharacteristic
735#125C2×D411yescharacteristic
736#124—21no—
737#124—21no—
738#124—21no—
739#124—21no—
740#124—21no—
741#124—21no—
742#124—21no—
743#124—21no—
744#124—21no—
745#124—41no—
746#124C2×D411yescharacteristic
747#124C2×D411yescharacteristic
748#123—21no—
749#123—21no—
750#123—21no—
751#123—21no—
752#123—21no—
753#123—21no—
754#123—41no—
755#123—41no—
756#123—41no—
757#123—41no—
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⋊Q8C2×D411yescharacteristic
775C22⋊Q8C2×D411yescharacteristic
776#121—21no—
777#121—21no—
778#121—21no—
779#121—21no—
780#121—21no—
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#121—41no—
795#121C2×D411yescharacteristic
796#121C2×D411yescharacteristic
797#121C2×D411yescharacteristic
798#121C2×D411yescharacteristic
799#120—41no—
800#120—41no—
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—21no—
810C4×Q8—21no—
811C4×Q8—21no—
812C4×Q8—21no—
813C4×Q8—41no—
814C4×Q8C2×D411yescharacteristic
815C4×Q8C2×D411yescharacteristic
816C4×Q8C2×D411yescharacteristic
817C4×Q8C2×D411yescharacteristic
818C4×Q8C2×D411yescharacteristic
819C4×Q8#4111yescharacteristic
820C4×Q8C2411yescharacteristic
821C4×Q8C2411yescharacteristic
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×D4—21no—
836C4×D4—21no—
837C4×D4—21no—
838C4×D4—21no—
839C4×D4—21no—
840C4×D4—21no—
841C4×D4—21no—
842C4×D4—21no—
843C4×D4—41no—
844C4×D4—41no—
845C4×D4—41no—
846C4×D4—41no—
847C4×D4—41no—
848C4×D4C2×D411yescharacteristic
849C4×D4C2×D411yescharacteristic
850C4×D4C2×D411yescharacteristic
851C4×D4C2×D411yescharacteristic
852C4×D4C2×D411yescharacteristic
853C4×D4#4111yescharacteristic
854C4×D4#4111yescharacteristic
855C4×D4#4111yescharacteristic
856C4×D4C2411yescharacteristic
857C4×D4C2411yescharacteristic
858#117—21no—
859#117—21no—
860#117—21no—
861#117—21no—
862#117—21no—
863#117—21no—
864#117—21no—
865#117—21no—
866#117C2×D411yescharacteristic
867#117C2×D411yescharacteristic
868#117C2×D411yescharacteristic
869#117C2×D411yescharacteristic
870#117C2×D411yescharacteristic
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—41no—
880C2×C22⋊C4—41no—
881C2×C42—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#102—21no—
968#102—21no—
969#102—21no—
970#102—21no—
971#102—21no—
972#102—21no—
973#102—21no—
974#102—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#97—21no—
1032#97—21no—
1033#97C2×D411yescharacteristic
1034#97C2×D411yescharacteristic
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—41no—
1048#41—41no—
1049#41—41no—
1050#41—41no—
1051#41—41no—
1052#41—41no—
1053#41—41no—
1054#41—81no—
1055#41—81no—
1056#41—81no—
1057#41—81no—
1058#41—81no—
1059#41—81no—
1060#41—161no—
1061#41—161no—
1062C2×Q8—21no—
1063C2×Q8—21no—
1064C2×Q8—21no—
1065C2×Q8—21no—
1066C2×Q8—21no—
1067C2×Q8—21no—
1068C2×Q8—21no—
1069C2×Q8—21no—
1070C2×Q8—41no—
1071C2×Q8—41no—
1072C2×Q8—41no—
1073C2×Q8—41no—
1074C2×Q8—41no—
1075C2×Q8—81no—
1076C2×Q8—81no—
1077C2×Q8—81no—
1078C2×Q8—81no—
1079C2×Q8—81no—
1080C2×Q8—81no—
1081C2×Q8#12111yescharacteristic
1082C2×Q8C22×D411yescharacteristic
1083C2×Q8C22×D411yescharacteristic
1084C2×D4—21no—
1085C2×D4—21no—
1086C2×D4—21no—
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—21no—
1096C2×D4—21no—
1097C2×D4—21no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—41no—
1101C2×D4—41no—
1102C2×D4—41no—
1103C2×D4—41no—
1104C2×D4—41no—
1105C2×D4—41no—
1106C2×D4—41no—
1107C2×D4—81no—
1108C2×D4—81no—
1109C2×D4—161no—
1110C2×D4#12111yescharacteristic
1111C2×D4#12111yescharacteristic
1112C2×D4#12111yescharacteristic
1113C2×D4C22×D411yescharacteristic
1114C2×D4C22×D411yescharacteristic
1115C22×C4—21no—
1116C22×C4—21no—
1117C22×C4—21no—
1118C22×C4—21no—
1119C22×C4—21no—
1120C22×C4—21no—
1121C22×C4—21no—
1122C22×C4—21no—
1123C22×C4—41no—
1124C22×C4—41no—
1125C22×C4—41no—
1126C22×C4—41no—
1127C22×C4—41no—
1128C22×C4—41no—
1129C22×C4—41no—
1130C22×C4C22×D411yescharacteristic
1131C22×C4C22×D411yescharacteristic
1132C22×C4C22×D411yescharacteristic
1133C22×C4C22×D411yescharacteristic
1134C22×C4C22×D411yescharacteristic
1135C22×C4C22×D411yescharacteristic
1136C22×C4C2×#4111yescharacteristic
1137C22×C4C2×#4111yescharacteristic
1138C22×C4C2×#4111yescharacteristic
1139Q16—42no—
1140Q16—42no—
1141Q16—42no—
1142Q16—42no—
1143Q16—81no—
1144Q16—81no—
1145Q16—81no—
1146Q16—81no—
1147SD16—42no—
1148SD16—42no—
1149SD16—81no—
1150SD16—81no—
1151SD16—81no—
1152SD16—81no—
1153SD16—81no—
1154SD16—81no—
1155SD16—81no—
1156SD16—81no—
1157SD16—81no—
1158SD16—81no—
1159D8—81no—
1160D8—81no—
1161D8—81no—
1162D8—81no—
1163M16—41no—
1164M16—41no—
1165M16—81no—
1166M16—81no—
1167M16—81no—
1168M16—81no—
1169M16—81no—
1170M16—81no—
1171M16—81no—
1172M16—81no—
1173M16—81no—
1174C2×C8—21no—
1175C2×C8—21no—
1176C2×C8—21no—
1177C2×C8—21no—
1178C2×C8—21no—
1179C2×C8—21no—
1180C2×C8—21no—
1181C2×C8—21no—
1182C2×C8—21no—
1183C2×C8—21no—
1184C2×C8—21no—
1185C2×C8—21no—
1186C2×C8—41no—
1187C2×C8—41no—
1188C2×C8—81no—
1189C2×C8—81no—
1190C2×C8—81no—
1191C2×C8—81no—
1192C2×C8—81no—
1193C2×C8—81no—
1194C2×C8—81no—
1195C2×C8C22×D411yescharacteristic
1196C2×C8C22×D411yescharacteristic
1197C2×C8C22×D411yescharacteristic
1198C2×C8C22×D411yescharacteristic
1199C2×C8C22×D411yescharacteristic
1200C2×C8C22×D411yescharacteristic
1201C2×C8C22×D411yescharacteristic
1202C2×C8C22×D411yescharacteristic
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—21no—
1227C4⋊C4—21no—
1228C4⋊C4—21no—
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#12111yescharacteristic
1244C4⋊C4#12111yescharacteristic
1245C4⋊C4#12111yescharacteristic
1246C4⋊C4#12111yescharacteristic
1247C4⋊C4#12111yescharacteristic
1248C4⋊C4#12111yescharacteristic
1249C4⋊C4C22×D411yescharacteristic
1250C4⋊C4C22×D411yescharacteristic
1251C4⋊C4C22×D411yescharacteristic
1252C4⋊C4C22×D411yescharacteristic
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—21no—
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—41no—
1280C22⋊C4—41no—
1281C22⋊C4#12111yescharacteristic
1282C22⋊C4#12111yescharacteristic
1283C22⋊C4#12111yescharacteristic
1284C22⋊C4#12111yescharacteristic
1285C22⋊C4#12111yescharacteristic
1286C22⋊C4#12111yescharacteristic
1287C42—21no—
1288C42—21no—
1289C42—21no—
1290C42—21no—
1291C42—21no—
1292C42—21no—
1293C42—21no—
1294C42—21no—
1295C42—41no—
1296C42—41no—
1297C42—41no—
1298C42—41no—
1299C42C22×D411yescharacteristic
1300C42C22×D411yescharacteristic
1301C42C22×D411yescharacteristic
1302C42C22×D411yescharacteristic
1303C42C22×D411yescharacteristic
1304C42C22×D411yescharacteristic
1305C42C2×#4111yescharacteristic
1306C42C2×#4111yescharacteristic
1307C42C2×#4111yescharacteristic
1308C42C2511yescharacteristic
1309C23—21no—
1310C23—21no—
1311C23—41no—
1312C23—41no—
1313C23—82no—
1314C23—161no—
1315C23—161no—
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—81no—
1333Q8—81no—
1334Q8—81no—
1335Q8—81no—
1336Q8—161no—
1337Q8—161no—
1338Q8—161no—
1339D4—21no—
1340D4—21no—
1341D4—21no—
1342D4—21no—
1343D4—41no—
1344D4—41no—
1345D4—41no—
1346D4—41no—
1347D4—41no—
1348D4—41no—
1349D4—41no—
1350D4—41no—
1351D4—41no—
1352D4—41no—
1353D4—41no—
1354D4—81no—
1355D4—81no—
1356D4—81no—
1357D4—81no—
1358D4—82no—
1359D4—81no—
1360D4—81no—
1361D4—81no—
1362D4—81no—
1363D4—81no—
1364D4—81no—
1365D4—161no—
1366D4—161no—
1367D4—161no—
1368D4—161no—
1369D4—161no—
1370D4—161no—
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—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—41no—
1390C2×C4—41no—
1391C2×C4—41no—
1392C2×C4—41no—
1393C2×C4—41no—
1394C2×C4—41no—
1395C2×C4—41no—
1396C2×C4—41no—
1397C2×C4—41no—
1398C2×C4—41no—
1399C2×C4—41no—
1400C2×C4—41no—
1401C2×C4—41no—
1402C2×C4—81no—
1403C2×C4—81no—
1404C2×C4—81no—
1405C2×C4—81no—
1406C2×C4—81no—
1407C2×C4—81no—
1408C2×C4—161no—
1409C2×C4—161no—
1410C2×C4—161no—
1411C2×C4—161no—
1412C2×C4—161no—
1413C2×C4—161no—
1414C2×C4—161no—
1415C2×C4C2×#12111yescharacteristic
1416C2×C4C2×#12111yescharacteristic
1417C2×C4C2×#12111yescharacteristic
1418C2×C4C2×#12111yescharacteristic
1419C2×C4C2×#12111yescharacteristic
1420C2×C4C2×#12111yescharacteristic
1421C2×C4C2×#12111yescharacteristic
1422C2×C4C2×#12111yescharacteristic
1423C2×C4C2×#12111yescharacteristic
1424C2×C4C23×D411yescharacteristic
1425C2×C4C23×D411yescharacteristic
1426C2×C4C22×#4111yescharacteristic
1427C8—21no—
1428C8—21no—
1429C8—21no—
1430C8—21no—
1431C8—21no—
1432C8—21no—
1433C8—21no—
1434C8—21no—
1435C8—41no—
1436C8—41no—
1437C8—41no—
1438C8—41no—
1439C8—41no—
1440C8—41no—
1441C8—41no—
1442C8—41no—
1443C8—41no—
1444C8—41no—
1445C8—41no—
1446C8—41no—
1447C22—21no—
1448C22—21no—
1449C22—21no—
1450C22—21no—
1451C22—21no—
1452C22—21no—
1453C22—21no—
1454C22—21no—
1455C22—21no—
1456C22—41no—
1457C22—41no—
1458C22—41no—
1459C22—41no—
1460C22—41no—
1461C22—41no—
1462C22—81no—
1463C22—81no—
1464C22—81no—
1465C22—81no—
1466C22—81no—
1467C22—81no—
1468C22—322no—
1469C22C22×#12111yescharacteristic
1470C4—21no—
1471C4—21no—
1472C4—21no—
1473C4—21no—
1474C4—21no—
1475C4—21no—
1476C4—21no—
1477C4—21no—
1478C4—21no—
1479C4—21no—
1480C4—41no—
1481C4—41no—
1482C4—41no—
1483C4—41no—
1484C4—41no—
1485C4—41no—
1486C4—81no—
1487C4—81no—
1488C4—81no—
1489C4—81no—
1490C4—81no—
1491C4—81no—
1492C4#358511yescharacteristic
1493C4#358511yescharacteristic
1494C4#358611yescharacteristic
1495C4#358611yescharacteristic
1496C2—41no—
1497C2—41no—
1498C2—41no—
1499C2—81no—
1500C2—81no—
1501C2—161no—
1502C2—161no—
1503C2#6042711yescharacteristic
1504C2#6046111yescharacteristic
1505C2#6047011yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
prime radical#61970C2
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. #61964C2semidirect
3. #60877C2semidirect
4. #60302C2semidirect
5. #19589C2semidirect
6. #19586C2semidirect
7. #19563C2semidirect
8. #19558C2semidirect
9. #19549C2semidirect
10. #19546C2semidirect
11. #19516C2semidirect
12. #19514C2semidirect
13. #19489C2semidirect
14. #19486C2semidirect
15. #19479C2semidirect
16. #19474C2semidirect
17. #19455C2semidirect
18. #19452C2semidirect
19. #19442C2semidirect
20. #19440C2semidirect
21. #19380C2semidirect
22. #19378C2semidirect
23. #19364C2semidirect
24. #19360C2semidirect
25. #19316C2semidirect
26. #19314C2semidirect
27. #19301C2semidirect
28. #19298C2semidirect
29. #17824C2semidirect
30. #17766C2semidirect
31. #17761C2semidirect
54. #3252C22semidirect
56. #3246C22semidirect
70. #3218C22semidirect
74. #3206C22semidirect
81. #3116C22semidirect
84. #3104C22semidirect
90. #3039C22semidirect
94. C2×#462C22semidirect
96. #2994C22semidirect
97. #2993C22semidirect
99. #2990C22semidirect
102. #2989C22semidirect
103. #2984C22semidirect
104. #2983C22semidirect
106. #2981C22semidirect
108. #2979C22semidirect
139. #1696C22semidirect
140. #1696C22semidirect
141. #1695C22semidirect
142. #1695C22semidirect
143. #1694C22semidirect
144. #1694C22semidirect
145. #1694C22semidirect
146. #1694C22semidirect
147. #1694C22semidirect
148. #1693C22semidirect
149. #1693C22semidirect
150. #1693C22semidirect
151. #1692C22semidirect
152. #1692C22semidirect
153. #1692C22semidirect
154. #1692C22semidirect
155. #1692C22semidirect
156. #1691C22semidirect
157. #1691C22semidirect
158. #1691C22semidirect
171. #1674C22semidirect
172. #1673C22semidirect
173. #1673C22semidirect
174. #1673C22semidirect
175. #1672C22semidirect
176. #1672C22semidirect
177. #1672C22semidirect
178. #1671C22semidirect
179. #1671C22semidirect
180. #1671C22semidirect
181. #1671C22semidirect
182. #1671C22semidirect
183. #1574C22semidirect
184. #1574C22semidirect
185. #1573C22semidirect
186. #1573C22semidirect
187. #1572C22semidirect
188. #1572C22semidirect
189. #1570C22semidirect
190. #1570C22semidirect
198. #1559C22semidirect
201. #1556C22semidirect
205. #1554C22semidirect
209. #1550C22semidirect
210. #1549C22semidirect
213. #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
#619702
#619642
#608772
#603022
#195892
#195862
#195632
#195582
#195492
#195462
#195162
#195142
#194892
#194862
#194792
#194742
#194552
#194522
#194422
#194402
#193802
#193782
#193642
#193602
#193162
#193142
#193012
#192982
#178242
#177662
#177612