Finite Group Databasebeta

← #6367732

Subgroups — #6367732

Order 512.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62406C211yesmaximal, characteristic, complemented
2#62305C211yesmaximal, characteristic
3#62188C211yesmaximal, characteristic, complemented
4#61911C211yesmaximal, characteristic, complemented
5#20267C211yesmaximal, characteristic, complemented
6#20233C211yesmaximal, characteristic, complemented
7#20193C211yesmaximal, characteristic, complemented
8#20188C211yesmaximal, characteristic, complemented
9#20127C211yesmaximal, characteristic, complemented
10#20124C211yesmaximal, characteristic, complemented
11#20118C211yesmaximal, characteristic, complemented
12#20105C211yesmaximal, characteristic, complemented
13#20100C211yesmaximal, characteristic, complemented
14#20088C211yesmaximal, characteristic, complemented
15#20078C211yesmaximal, characteristic, complemented
16#20052C211yesmaximal, characteristic, complemented
17#19877C211yesmaximal, characteristic, complemented
18#19856C211yesmaximal, characteristic, complemented
19#19847C211yesmaximal, characteristic, complemented
20#19843C211yesmaximal, characteristic, complemented
21#19692C211yesmaximal, characteristic, complemented
22#19543C211yesmaximal, characteristic, complemented
23#19535C211yesmaximal, characteristic, complemented
24#19374C211yesmaximal, characteristic, complemented
25#19307C211yesmaximal, characteristic, complemented
26#18710C211yesmaximal, characteristic, complemented
27#18698C211yesmaximal, characteristic, complemented
28#18679C211yesmaximal, characteristic, complemented
29#18628C211yesmaximal, characteristic, complemented
30#18000C211yesmaximal, characteristic, complemented
31#17988C211yesmaximal, characteristic, complemented
32#3556C2211yescharacteristic, complemented
33#3555C2211yescharacteristic
34#3519C2211yescharacteristic
35#3506C2211yescharacteristic
36#3400—21no—
37#3400—21no—
38#3398—21no—
39#3398C2211yescharacteristic
40#3398C2211yescharacteristic, complemented
41#3398C2211yescharacteristic, complemented
42#3395C2211yescharacteristic, complemented
43#3392C2211yescharacteristic
44#3392C2211yescharacteristic, complemented
45#3390—21no—
46#3387C2211yescharacteristic, complemented
47#3385C2211yescharacteristic
48#3381C2211yescharacteristic
49#3381C2211yescharacteristic, complemented
50#3377—21no—
51#3374—21no—
52#3374C2211yescharacteristic, complemented
53#3372C2211yescharacteristic, complemented
54#3371—21no—
55#3371—21no—
56#3368C2211yescharacteristic
57#3368C2211yescharacteristic
58#3368C2211yescharacteristic, complemented
59#3364C2211yescharacteristic
60#3364C2211yescharacteristic, complemented
61#3364C2211yescharacteristic, complemented
62#3363C2211yescharacteristic, complemented
63#3362C2211yescharacteristic
64#3357C2211yescharacteristic
65#3356C2211yescharacteristic
66#3351—21no—
67#3350—21no—
68#3347—21no—
69#3340C2211yescharacteristic
70#3340C2211yescharacteristic
71#3333C2211yescharacteristic
72#3324—21no—
73#3324C2211yescharacteristic
74#3324C2211yescharacteristic
75#3319—21no—
76#3310—21no—
77#3307—21no—
78#3305C2211yescharacteristic
79#3304C2211yescharacteristic
80#3295C2211yescharacteristic
81#3287C2211yescharacteristic
82#3274C2211yescharacteristic
83#3267—21no—
84#3261—21no—
85#3260—21no—
86#3258—21no—
87#3254C2211yescharacteristic
88#3254C2211yescharacteristic
89#3251C2211yescharacteristic
90#3249C2211yescharacteristic, complemented
91#3248C2211yescharacteristic
92#3241—21no—
93#3228C2211yescharacteristic
94#3222—21no—
95#3222—21no—
96#3216C2211yescharacteristic, complemented
97#3210C2211yescharacteristic, complemented
98#3197—21no—
99#3194—21no—
100#3185C2211yescharacteristic, complemented
101#3184C2211yescharacteristic
102#3178—21no—
103#3177—21no—
104#3172C2211yescharacteristic
105#3167C2211yescharacteristic, complemented
106#3131C2211yescharacteristic
107#3123—21no—
108#3120—21no—
109#3120—21no—
110#3110C2211yescharacteristic
111#3101C2211yescharacteristic
112#3081—21no—
113#3077C2211yescharacteristic
114#3055—21no—
115#3054—21no—
116#2993C2211yescharacteristic
117#2985C2211yescharacteristic, complemented
118#2962C2211yescharacteristic, complemented
119D4×M16C2211yescharacteristic
120#1720C2211yescharacteristic, complemented
121#1720C2211yescharacteristic, complemented
122#1720C2211yescharacteristic, complemented
123#1718C2211yescharacteristic, complemented
124#1717C2211yescharacteristic, complemented
125#1717C2211yescharacteristic, complemented
126#1716C2211yescharacteristic, complemented
127#1714C2211yescharacteristic, complemented
128#1703C2211yescharacteristic
129#1702C2211yescharacteristic, complemented
130#1700C2211yescharacteristic, complemented
131#1699C2211yescharacteristic
132#1699C2211yescharacteristic, complemented
133#1698C2211yescharacteristic, complemented
134#1698C2211yescharacteristic, complemented
135#1698C2211yescharacteristic, complemented
136#1692C2211yescharacteristic, complemented
137#1692C2211yescharacteristic, complemented
138#1692C2211yescharacteristic, complemented
139#1691C2211yescharacteristic
140#1689C2211yescharacteristic
141#1688C2211yescharacteristic, complemented
142#1686C2211yescharacteristic, complemented
143#1685C2211yescharacteristic, complemented
144#1683C2211yescharacteristic, complemented
145#1682C2211yescharacteristic, complemented
146#1682C2211yescharacteristic, complemented
147#1682C2211yescharacteristic, complemented
148#1682C2211yescharacteristic, complemented
149#1681C2211yescharacteristic, complemented
150#1679C2211yescharacteristic, complemented
151#1678C2211yescharacteristic, complemented
152#1676C2211yescharacteristic, complemented
153#1676C2211yescharacteristic, complemented
154#1672C2211yescharacteristic, complemented
155#1671C2211yescharacteristic, complemented
156#1670C2211yescharacteristic, complemented
157#1669C2211yescharacteristic, complemented
158#1669C2211yescharacteristic, complemented
159#1668C2211yescharacteristic, complemented
160#1653C2211yescharacteristic, complemented
161#1652C2211yescharacteristic
162#1652C2211yescharacteristic, complemented
163#1652C2211yescharacteristic, complemented
164#1646C2211yescharacteristic
165#1646C2211yescharacteristic
166#1645C2211yescharacteristic, complemented
167#1644C2211yescharacteristic
168#1644C2211yescharacteristic, complemented
169#1643C2211yescharacteristic
170#1642C2211yescharacteristic
171#1641C2211yescharacteristic
172#1641C2211yescharacteristic
173#1641C2211yescharacteristic, complemented
174#1639C2211yescharacteristic
175#1639C2211yescharacteristic
176#1638C2211yescharacteristic
177#1638C2211yescharacteristic, complemented
178#1636C2211yescharacteristic, complemented
179#1636C2211yescharacteristic, complemented
180#1636C2211yescharacteristic, complemented
181#1636C2211yescharacteristic, complemented
182#1631C2211yescharacteristic
183#1631C2211yescharacteristic, complemented
184#1628C2211yescharacteristic, complemented
185#1626C2211yescharacteristic, complemented
186#1626C2211yescharacteristic, complemented
187#1626C2211yescharacteristic, complemented
188#1626C2211yescharacteristic, complemented
189#1626C2211yescharacteristic, complemented
190#1623C2211yescharacteristic, complemented
191#1622C2211yescharacteristic, complemented
192#1592C2211yescharacteristic
193#1592C2211yescharacteristic
194#1588C2211yescharacteristic
195#1588C2211yescharacteristic
196#1588C2211yescharacteristic, complemented
197#1587C2211yescharacteristic, complemented
198#1587C2211yescharacteristic, complemented
199#1585C2211yescharacteristic, complemented
200#1585C2211yescharacteristic, complemented
201#1585C2211yescharacteristic, complemented
202#1584C2211yescharacteristic, complemented
203#1584C2211yescharacteristic, complemented
204#1583C2211yescharacteristic, complemented
205#1582C2211yescharacteristic, complemented
206SD16⋊C8C2211yescharacteristic, complemented
207SD16⋊C8C2211yescharacteristic, complemented
208#1571C2211yescharacteristic, complemented
209#1569C2211yescharacteristic, complemented
210#1561C2211yescharacteristic, complemented
211#1559C2211yescharacteristic, complemented
212#1551C2211yescharacteristic
213#1547C2211yescharacteristic, complemented
214#1494C2211yescharacteristic
215#1493C2211yescharacteristic, complemented
216#1493C2211yescharacteristic, complemented
217C2×D4⋊C8C2211yescharacteristic
218#1451C2211yescharacteristic, complemented
219C2×AGL(1,ℤ/8)—21no—
220C2×#135—21no—
221C22×M16—21no—
222#564—41no—
223#563—41no—
224#559—21no—
225#559—21no—
226Q82C2311yescharacteristic
227#557—21no—
228#557—21no—
229#557—21no—
230#557—21no—
231#557—21no—
232#557C2311yescharacteristic
233#557C2311yescharacteristic
234#557C2311yescharacteristic
235#557C2311yescharacteristic
236#557C2311yescharacteristic
237#556—21no—
238#556—21no—
239#556C2311yescharacteristic
240#556C2311yescharacteristic
241#556C2311yescharacteristic
242#555—21no—
243#555C2311yescharacteristic
244#554C2311yescharacteristic
245#554C2311yescharacteristic
246#553—21no—
247#553—21no—
248#553—41no—
249#552—21no—
250#550C2311yescharacteristic
251#550C2311yescharacteristic
252#550C2311yescharacteristic
253#547—21no—
254#546—21no—
255#546—41no—
256D42—21no—
257D42C2311yescharacteristic
258#544—21no—
259#542—21no—
260#541—21no—
261#541—21no—
262#541—21no—
263#541—21no—
264#541—21no—
265#541—21no—
266#541—41no—
267#541—41no—
268#540—21no—
269#538—41no—
270#538—41no—
271#535—21no—
272#533C2311yescharacteristic
273#533C2311yescharacteristic
274#533C2311yescharacteristic
275#533C2311yescharacteristic
276#532C2311yescharacteristic
277#532C2311yescharacteristic
278#529C2311yescharacteristic
279#525—21no—
280#525—21no—
281#525—21no—
282C2×#121—21no—
283#520—21no—
284#518—21no—
285C2×C4×D4C2311yescharacteristic
286#501—21no—
287#501—21no—
288#501D411yescharacteristic
289#500C2311yescharacteristic
290#499—21no—
291#499—21no—
292#498C2311yescharacteristic
293#498C2311yescharacteristic
294#498C2311yescharacteristic
295#498C2311yescharacteristic
296#497—21no—
297#497—21no—
298#497—21no—
299#497—21no—
300#497D411yescharacteristic
301#494—21no—
302#494C2311yescharacteristic
303#494C2311yescharacteristic
304#493C2311yescharacteristic
305#492—21no—
306#492—21no—
307#492C2311yescharacteristic
308#492C2311yescharacteristic
309#491—21no—
310#491—21no—
311#491D411yescharacteristic
312#490—21no—
313#490—21no—
314#490—21no—
315#489—21no—
316#489D411yescharacteristic
317#488—21no—
318#488—21no—
319#488—21no—
320#488—41no—
321#487—21no—
322#487C2311yescharacteristic
323#487C2311yescharacteristic
324#487C2311yescharacteristic
325#487C2311yescharacteristic
326#487C2311yescharacteristic
327#487C2311yescharacteristic
328#486—21no—
329#486C2311yescharacteristic
330#486C2311yescharacteristic
331#486C2311yescharacteristic
332#486C2311yescharacteristic
333#486C2311yescharacteristic
334#486C2311yescharacteristic
335#486C2311yescharacteristic
336#486C2311yescharacteristic
337#485—21no—
338#485—21no—
339#485—21no—
340#485—21no—
341#484—21no—
342#483—21no—
343#483D411yescharacteristic
344#483D411yescharacteristic
345#482—21no—
346#482—21no—
347#482—21no—
348#482—21no—
349#482—21no—
350#482—21no—
351#482—21no—
352#482—21no—
353#481—21no—
354#480—21no—
355#480—21no—
356#479—21no—
357#479—21no—
358#479—21no—
359#479—21no—
360#479—21no—
361#479—21no—
362#479—21no—
363#479—21no—
364#479—21no—
365#479—21no—
366#478—21no—
367#478—21no—
368#478—21no—
369#478—21no—
370#478—21no—
371#478—21no—
372#478—21no—
373#478—21no—
374#478—21no—
375#478—21no—
376#477—21no—
377#477—21no—
378#477C2311yescharacteristic
379#477C2311yescharacteristic
380#477C2311yescharacteristic
381#477C2311yescharacteristic
382#477C2311yescharacteristic
383#477C2311yescharacteristic
384#476—21no—
385#476D411yescharacteristic
386#476D411yescharacteristic
387#476C2311yescharacteristic
388#476C2311yescharacteristic
389#475—21no—
390#475C2311yescharacteristic
391#475C2311yescharacteristic
392#474—21no—
393#474—21no—
394#474—21no—
395#474C2311yescharacteristic
396#474C2311yescharacteristic
397#474C2311yescharacteristic
398#474C2311yescharacteristic
399#474C2311yescharacteristic
400#474C2311yescharacteristic
401#470—21no—
402#470—21no—
403#470—21no—
404#470D411yescharacteristic
405#470D411yescharacteristic
406#469—21no—
407#469—21no—
408#469—21no—
409#469—21no—
410#468—21no—
411#468—21no—
412#468—21no—
413#468—21no—
414#468—21no—
415#468—21no—
416#468—21no—
417#468—21no—
418#468—21no—
419#468D411yescharacteristic
420#468D411yescharacteristic
421#467—21no—
422#467—21no—
423#467—21no—
424#466—21no—
425#466—21no—
426#465—21no—
427#465—21no—
428#465—21no—
429#465—21no—
430#465—21no—
431#465—41no—
432#464—21no—
433#464—21no—
434#464—21no—
435#464—21no—
436#464—21no—
437#464—21no—
438#464—21no—
439#464—21no—
440#464—21no—
441#463—21no—
442#462—21no—
443#462—21no—
444#462—21no—
445#462—21no—
446#462—21no—
447#462—21no—
448#462—21no—
449#462—21no—
450#462C2311yescharacteristic
451#462C2311yescharacteristic
452#462C2311yescharacteristic
453#462C2311yescharacteristic
454#462C2311yescharacteristic
455#461—21no—
456#461—21no—
457#461—21no—
458#461—21no—
459#461—21no—
460#461D411yescharacteristic
461#461D411yescharacteristic
462#461C2311yescharacteristic
463#461C2311yescharacteristic
464#461C2311yescharacteristic
465#460—21no—
466#460—21no—
467#460—21no—
468#460—21no—
469#460—21no—
470#460—21no—
471#460C2311yescharacteristic
472#460C2311yescharacteristic
473#460C2311yescharacteristic
474#460C2311yescharacteristic
475#460C2311yescharacteristic
476#460C2311yescharacteristic
477#460C2311yescharacteristic
478#459C2311yescharacteristic
479#452—21no—
480#452—21no—
481#452—21no—
482#452—21no—
483#452—21no—
484#452—21no—
485#450—21no—
486#450—21no—
487#450—21no—
488#450—21no—
489#450D411yescharacteristic
490#450D411yescharacteristic
491#449—21no—
492#449—21no—
493#449—21no—
494#449—21no—
495#447—21no—
496#446—21no—
497#446—21no—
498#446—21no—
499#446—21no—
500#446C2311yescharacteristic
501#446C2311yescharacteristic
502#446C2311yescharacteristic
503#446C2311yescharacteristic
504#446C2311yescharacteristic
505C8×Q8C2311yescharacteristic
506C8×Q8C2311yescharacteristic
507C8×Q8C2311yescharacteristic
508C8×Q8C2311yescharacteristic
509C8×Q8C2311yescharacteristic
510#442—21no—
511#442—21no—
512#441—21no—
513#441—21no—
514#441—21no—
515#441—21no—
516#441—21no—
517#441—21no—
518#441—21no—
519#440—21no—
520#440—21no—
521#440—21no—
522#440—21no—
523#440—21no—
524#440—21no—
525#440—21no—
526C4×Q16—21no—
527C4×Q16—21no—
528C4×Q16—21no—
529C4×Q16—21no—
530C4×Q16—21no—
531C4×Q16C2311yescharacteristic
532C4×Q16C2311yescharacteristic
533C4×SD16—21no—
534C4×SD16—21no—
535C4×SD16—21no—
536C4×SD16—21no—
537C4×SD16—21no—
538C4×SD16—41no—
539C4×SD16C2311yescharacteristic
540C4×SD16C2311yescharacteristic
541C4×SD16C2311yescharacteristic
542C4×SD16C2311yescharacteristic
543C4×SD16C2311yescharacteristic
544C4×SD16C2311yescharacteristic
545#436—21no—
546#436C2311yescharacteristic
547#436C2311yescharacteristic
548#436C2311yescharacteristic
549#435—21no—
550#435—21no—
551#435—21no—
552C8×D4C2311yescharacteristic
553C8×D4C2311yescharacteristic
554C8×D4C2311yescharacteristic
555#433—21no—
556#433—21no—
557#433—21no—
558#432C2311yescharacteristic
559#431C2311yescharacteristic
560#428—21no—
561#428—21no—
562#428—21no—
563#427—21no—
564#427—21no—
565#424—21no—
566#424—21no—
567#423C2311yescharacteristic
568#423C2311yescharacteristic
569C2×C4⋊C8C2311yescharacteristic
570#418—21no—
571#418—21no—
572#418—21no—
573#417—21no—
574#416—21no—
575#416—21no—
576#416—41no—
577C2×#102—21no—
578#407—21no—
579#405—21no—
580C4×M16C2311yescharacteristic
581C2×C4×C8C2311yescharacteristic
582#335C2311yescharacteristic
583#335C2311yescharacteristic
584#335C2311yescharacteristic
585#335C2311yescharacteristic
586#335C2311yescharacteristic
587#335C2311yescharacteristic
588#334C2311yescharacteristic
589#334C2311yescharacteristic
590#333C2311yescharacteristic
591#333C2311yescharacteristic
592#333C2311yescharacteristic
593#333C2311yescharacteristic
594#332C2311yescharacteristic
595#332C2311yescharacteristic
596#332C2311yescharacteristic
597#332C2311yescharacteristic
598#332C2311yescharacteristic
599#332C2311yescharacteristic
600#332C2311yescharacteristic
601#332C2311yescharacteristic
602#331C2311yescharacteristic
603#331C2311yescharacteristic
604#331C2311yescharacteristic
605#331C2311yescharacteristic
606Q8⋊C8C2311yescharacteristic
607Q8⋊C8C2311yescharacteristic
608Q8⋊C8C2311yescharacteristic
609Q8⋊C8C2311yescharacteristic
610Q8⋊C8C2311yescharacteristic
611Q8⋊C8C2311yescharacteristic
612Q8⋊C8C2311yescharacteristic
613Q8⋊C8C2311yescharacteristic
614Q8⋊C8C2311yescharacteristic
615Q8⋊C8C2311yescharacteristic
616D4⋊C8C2311yescharacteristic
617D4⋊C8C2311yescharacteristic
618D4⋊C8C2311yescharacteristic
619D4⋊C8C2311yescharacteristic
620D4⋊C8C2311yescharacteristic
621D4⋊C8C2311yescharacteristic
622#322C2311yescharacteristic
623#322C2311yescharacteristic
624#322C2311yescharacteristic
625#322C2311yescharacteristic
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—41no—
634C22×D4C2×D411yescharacteristic
635C23×C4—21no—
636AGL(1,ℤ/8)—82no—
637#135—82no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×Q16—21no—
647C2×Q16C2×D411yescharacteristic
648C2×Q16C2×D411yescharacteristic
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—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—41no—
662C2×SD16C2×D411yescharacteristic
663C2×SD16C2×D411yescharacteristic
664C2×SD16C2×D411yescharacteristic
665C2×SD16C2×D411yescharacteristic
666C2×SD16C2×D411yescharacteristic
667C2×SD16C2×D411yescharacteristic
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—82no—
677C2×M16C2×D411yescharacteristic
678C2×M16C2×D411yescharacteristic
679C22×C8—21no—
680C22×C8—21no—
681C22×C8—21no—
682C22×C8—21no—
683C22×C8—21no—
684C4⋊Q8—21no—
685C4⋊Q8—21no—
686C4⋊Q8—21no—
687C4⋊Q8—21no—
688C4⋊Q8—21no—
689C4⋊Q8—21no—
690C4⋊Q8—21no—
691C4⋊Q8—41no—
692C4⋊Q8—41no—
693C4⋊Q8—41no—
694C4⋊Q8C2×D411yescharacteristic
695C4⋊Q8C2×D411yescharacteristic
696C4⋊Q8C2×D411yescharacteristic
697C4⋊Q8C2×D411yescharacteristic
698C4⋊Q8C2411yescharacteristic
699C4⋊Q8C2411yescharacteristic
700C4⋊Q8C2411yescharacteristic
701C4⋊Q8C2411yescharacteristic
702C4⋊Q8C2411yescharacteristic
703C4⋊Q8C2411yescharacteristic
704#127—21no—
705#127—21no—
706#127—21no—
707#127C2411yescharacteristic
708#127C2411yescharacteristic
709#126—21no—
710#126—41no—
711#126—41no—
712#126—41no—
713#126—41no—
714#126—41no—
715#126—41no—
716#126—41no—
717#126—41no—
718#126—41no—
719#126—41no—
720#126—41no—
721#126—41no—
722#126—41no—
723#125—21no—
724#125—21no—
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—21no—
734#125—41no—
735#125—41no—
736#125—41no—
737#125—41no—
738#125—41no—
739#125—41no—
740#125—41no—
741#125—41no—
742#125—41no—
743#125—41no—
744#125—41no—
745#125—41no—
746#125—41no—
747#125—41no—
748#125—41no—
749#125—41no—
750#125—41no—
751#125—41no—
752#125C2×D411yescharacteristic
753#124—21no—
754#124—21no—
755#124—21no—
756#124—21no—
757#124—21no—
758#124—41no—
759#124—41no—
760#124—41no—
761#124—41no—
762#124C2×D411yescharacteristic
763#123—21no—
764#123—41no—
765#123—41no—
766#123—41no—
767#123—41no—
768#123—41no—
769#123—41no—
770#123—41no—
771#123—41no—
772C22⋊Q8—21no—
773C22⋊Q8—21no—
774C22⋊Q8—21no—
775C22⋊Q8—21no—
776C22⋊Q8—21no—
777C22⋊Q8—21no—
778C22⋊Q8—21no—
779C22⋊Q8—21no—
780C22⋊Q8—21no—
781C22⋊Q8—21no—
782C22⋊Q8—21no—
783C22⋊Q8—41no—
784C22⋊Q8—41no—
785C22⋊Q8—41no—
786C22⋊Q8—41no—
787C22⋊Q8C2×D411yescharacteristic
788C22⋊Q8C2×D411yescharacteristic
789C22⋊Q8C2×D411yescharacteristic
790C22⋊Q8C2×D411yescharacteristic
791C22⋊Q8C2×D411yescharacteristic
792#121—21no—
793#121—21no—
794#121—21no—
795#121—21no—
796#121—21no—
797#121—21no—
798#121—21no—
799#121—21no—
800#121—21no—
801#121—21no—
802#121—21no—
803#121—41no—
804#121—41no—
805#121—41no—
806#121—41no—
807#121—41no—
808#121—41no—
809#121—41no—
810#121—41no—
811#121—41no—
812#121C2×D411yescharacteristic
813#120—41no—
814#120—41no—
815#120—41no—
816#120—41no—
817#120—41no—
818C4×Q8—21no—
819C4×Q8—21no—
820C4×Q8—21no—
821C4×Q8—21no—
822C4×Q8—21no—
823C4×Q8—21no—
824C4×Q8—21no—
825C4×Q8—21no—
826C4×Q8—21no—
827C4×Q8—21no—
828C4×Q8—21no—
829C4×Q8—21no—
830C4×Q8—21no—
831C4×Q8—21no—
832C4×Q8—21no—
833C4×Q8—21no—
834C4×Q8—21no—
835C4×Q8—21no—
836C4×Q8—21no—
837C4×Q8—21no—
838C4×Q8—21no—
839C4×Q8—41no—
840C4×Q8—41no—
841C4×Q8—41no—
842C4×Q8C2411yescharacteristic
843C4×Q8C2411yescharacteristic
844C4×Q8C2411yescharacteristic
845C4×Q8C2411yescharacteristic
846C4×Q8C2411yescharacteristic
847C4×D4—21no—
848C4×D4—21no—
849C4×D4—21no—
850C4×D4—21no—
851C4×D4—21no—
852C4×D4—21no—
853C4×D4—21no—
854C4×D4—21no—
855C4×D4—21no—
856C4×D4—21no—
857C4×D4—21no—
858C4×D4—21no—
859C4×D4—41no—
860C4×D4—41no—
861C4×D4—41no—
862C4×D4—41no—
863C4×D4—41no—
864C4×D4—41no—
865C4×D4—41no—
866C4×D4C2×D411yescharacteristic
867C4×D4C2×D411yescharacteristic
868C4×D4C2411yescharacteristic
869C4×D4C2411yescharacteristic
870C4×D4C2411yescharacteristic
871#117—21no—
872#117—21no—
873#117—21no—
874#117—21no—
875#117—21no—
876#117—21no—
877#117—21no—
878#117—21no—
879#117—21no—
880#117—21no—
881#117—41no—
882#117—41no—
883C2×C4⋊C4—21no—
884C2×C4⋊C4—21no—
885C2×C4⋊C4—41no—
886C2×C4⋊C4C2×D411yescharacteristic
887C2×C22⋊C4—21no—
888C2×C22⋊C4—41no—
889C2×C22⋊C4—41no—
890C2×C42C2411yescharacteristic
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#107—21no—
904#107—21no—
905#107C2×D411yescharacteristic
906#107C2×D411yescharacteristic
907#106—21no—
908#106—21no—
909#106—21no—
910#106—21no—
911#106—21no—
912#106—21no—
913#106—21no—
914#106—21no—
915#106—21no—
916#106—21no—
917#106—41no—
918#106C2×D411yescharacteristic
919#106C2×D411yescharacteristic
920#106C2×D411yescharacteristic
921#106C2×D411yescharacteristic
922#106C2×D411yescharacteristic
923#106C2×D411yescharacteristic
924C4⋊C8—21no—
925C4⋊C8—21no—
926C4⋊C8—21no—
927C4⋊C8—21no—
928C4⋊C8—21no—
929C4⋊C8—21no—
930C4⋊C8—21no—
931C4⋊C8—21no—
932C4⋊C8—21no—
933C4⋊C8—21no—
934C4⋊C8—21no—
935C4⋊C8—21no—
936C4⋊C8—21no—
937C4⋊C8C2×D411yescharacteristic
938C4⋊C8C2×D411yescharacteristic
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—41no—
970#103—41no—
971#103—41no—
972#103C2×D411yescharacteristic
973#103C2×D411yescharacteristic
974#103C2×D411yescharacteristic
975#103C2×D411yescharacteristic
976#103C2×D411yescharacteristic
977#103C2×D411yescharacteristic
978#103C2×D411yescharacteristic
979#103C2×D411yescharacteristic
980#103C2×D411yescharacteristic
981#103C2×D411yescharacteristic
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—
995#102—21no—
996#102—21no—
997#102—21no—
998#102—21no—
999#102—21no—
1000#102—21no—
1001#102—21no—
1002#102—21no—
1003#102—21no—
1004#102—21no—
1005#102—21no—
1006#102—21no—
1007#102—21no—
1008#102—41no—
1009#102—41no—
1010#102—41no—
1011#102C2×D411yescharacteristic
1012#102C2×D411yescharacteristic
1013#102C2×D411yescharacteristic
1014#102C2×D411yescharacteristic
1015#102C2×D411yescharacteristic
1016#102C2×D411yescharacteristic
1017C22⋊C8—21no—
1018C22⋊C8—21no—
1019C22⋊C8—21no—
1020C22⋊C8—21no—
1021C22⋊C8—21no—
1022C22⋊C8—21no—
1023C22⋊C8—21no—
1024C22⋊C8C2×D411yescharacteristic
1025C22⋊C8C2×D411yescharacteristic
1026#97—21no—
1027#97—21no—
1028#97—21no—
1029#97—21no—
1030#97—21no—
1031#97—21no—
1032#97C2×D411yescharacteristic
1033#97C2×D411yescharacteristic
1034C4×C8—21no—
1035C4×C8—21no—
1036C4×C8—21no—
1037C4×C8—21no—
1038C4×C8—21no—
1039C4×C8—21no—
1040C4×C8C2411yescharacteristic
1041C4×C8C2411yescharacteristic
1042C4×C8C2411yescharacteristic
1043C4×C8C2411yescharacteristic
1044C4×C8C2411yescharacteristic
1045C4×C8C2411yescharacteristic
1046C24—21no—
1047C24—41no—
1048#41—81no—
1049#41—81no—
1050#41—81no—
1051#41—81no—
1052#41—81no—
1053#41—81no—
1054#41—81no—
1055#41—81no—
1056#41—82no—
1057C2×Q8—21no—
1058C2×Q8—21no—
1059C2×Q8—21no—
1060C2×Q8—21no—
1061C2×Q8—21no—
1062C2×Q8—21no—
1063C2×Q8—21no—
1064C2×Q8—21no—
1065C2×Q8—41no—
1066C2×Q8C22×D411yescharacteristic
1067C2×Q8C22×D411yescharacteristic
1068C2×Q8C22×D411yescharacteristic
1069C2×Q8C22×D411yescharacteristic
1070C2×Q8C22×D411yescharacteristic
1071C2×D4—21no—
1072C2×D4—21no—
1073C2×D4—21no—
1074C2×D4—21no—
1075C2×D4—21no—
1076C2×D4—21no—
1077C2×D4—21no—
1078C2×D4—21no—
1079C2×D4—41no—
1080C2×D4—41no—
1081C2×D4—41no—
1082C2×D4—41no—
1083C2×D4—41no—
1084C2×D4—41no—
1085C2×D4—41no—
1086C2×D4—41no—
1087C2×D4—41no—
1088C2×D4—41no—
1089C2×D4—42no—
1090C2×D4—41no—
1091C2×D4—41no—
1092C2×D4—41no—
1093C2×D4—81no—
1094C2×D4—81no—
1095C2×D4—81no—
1096C2×D4—162no—
1097C2×D4C22×D411yescharacteristic
1098C2×D4C22×D411yescharacteristic
1099C2×D4C22×D411yescharacteristic
1100C22×C4—21no—
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—21no—
1105C22×C4—21no—
1106C22×C4—41no—
1107C22×C4—41no—
1108C22×C4—41no—
1109C22×C4—41no—
1110C22×C4—41no—
1111C22×C4—41no—
1112C22×C4—41no—
1113C22×C4—81no—
1114C22×C4—81no—
1115C22×C4C22×D411yescharacteristic
1116C22×C4C22×D411yescharacteristic
1117C22×C4H(5,𝔽2)11yescharacteristic
1118Q16—41no—
1119Q16—41no—
1120Q16—42no—
1121Q16—81no—
1122Q16—81no—
1123Q16—81no—
1124Q16—81no—
1125Q16—81no—
1126Q16—81no—
1127Q16—81no—
1128Q16—81no—
1129SD16—41no—
1130SD16—41no—
1131SD16—41no—
1132SD16—41no—
1133SD16—41no—
1134SD16—41no—
1135SD16—81no—
1136SD16—81no—
1137SD16—81no—
1138SD16—81no—
1139SD16—81no—
1140SD16—81no—
1141SD16—81no—
1142SD16—81no—
1143SD16—81no—
1144SD16—81no—
1145SD16—81no—
1146SD16—81no—
1147SD16—82no—
1148D8—42no—
1149D8—81no—
1150D8—81no—
1151M16—41no—
1152M16—41no—
1153M16—42no—
1154M16—81no—
1155M16—81no—
1156M16—81no—
1157M16—81no—
1158C2×C8—21no—
1159C2×C8—21no—
1160C2×C8—21no—
1161C2×C8—21no—
1162C2×C8—21no—
1163C2×C8—21no—
1164C2×C8—21no—
1165C2×C8—21no—
1166C2×C8—21no—
1167C2×C8—21no—
1168C2×C8—42no—
1169C2×C8—81no—
1170C2×C8—81no—
1171C2×C8—81no—
1172C2×C8—81no—
1173C2×C8C22×D411yescharacteristic
1174C2×C8C22×D411yescharacteristic
1175C2×C8C22×D411yescharacteristic
1176C2×C8C22×D411yescharacteristic
1177C2×C8C22×D411yescharacteristic
1178C2×C8C22×D411yescharacteristic
1179C2×C8C22×D411yescharacteristic
1180C2×C8C22×D411yescharacteristic
1181C4⋊C4—21no—
1182C4⋊C4—21no—
1183C4⋊C4—21no—
1184C4⋊C4—21no—
1185C4⋊C4—21no—
1186C4⋊C4—21no—
1187C4⋊C4—21no—
1188C4⋊C4—21no—
1189C4⋊C4—21no—
1190C4⋊C4—21no—
1191C4⋊C4—21no—
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—41no—
1213C4⋊C4—41no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
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⋊C4C22×D411yescharacteristic
1241C4⋊C4C22×D411yescharacteristic
1242C4⋊C4C22×D411yescharacteristic
1243C4⋊C4C22×D411yescharacteristic
1244C4⋊C4C22×D411yescharacteristic
1245C4⋊C4C22×D411yescharacteristic
1246C4⋊C4C22×D411yescharacteristic
1247C4⋊C4C22×D411yescharacteristic
1248C22⋊C4—21no—
1249C22⋊C4—21no—
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—41no—
1262C22⋊C4—41no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4—41no—
1266C22⋊C4—41no—
1267C22⋊C4—41no—
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—41no—
1280C22⋊C4—41no—
1281C42—21no—
1282C42—21no—
1283C42—21no—
1284C42—21no—
1285C42—21no—
1286C42—41no—
1287C42—41no—
1288C42—41no—
1289C42—41no—
1290C42—41no—
1291C42—41no—
1292C42—41no—
1293C42—41no—
1294C42—41no—
1295C42—41no—
1296C42—41no—
1297C42—41no—
1298C42C22×D411yescharacteristic
1299C42C22×D411yescharacteristic
1300C42H(5,𝔽2)11yescharacteristic
1301C42C2511yescharacteristic
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—41no—
1306C23—41no—
1307C23—81no—
1308C23—81no—
1309C23—81no—
1310C23—82no—
1311C23—161no—
1312C23—161no—
1313C23D4211yescharacteristic
1314Q8—21no—
1315Q8—21no—
1316Q8—21no—
1317Q8—21no—
1318Q8—21no—
1319Q8—21no—
1320Q8—21no—
1321Q8—21no—
1322Q8—21no—
1323Q8—21no—
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—
1337D4—21no—
1338D4—21no—
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—81no—
1352D4—81no—
1353D4—81no—
1354D4—81no—
1355D4—82no—
1356D4—82no—
1357D4—82no—
1358D4—161no—
1359D4—161no—
1360D4—161no—
1361D4—161no—
1362D4—161no—
1363D4—161no—
1364D4—161no—
1365D4—161no—
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—21no—
1381C2×C4—21no—
1382C2×C4—21no—
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—41no—
1395C2×C4—41no—
1396C2×C4—81no—
1397C2×C4—81no—
1398C2×C4—82no—
1399C2×C4—81no—
1400C2×C4—161no—
1401C2×C4—161no—
1402C2×C4—161no—
1403C2×C4—161no—
1404C2×C4—161no—
1405C2×C4—161no—
1406C2×C4D4211yescharacteristic
1407C2×C4D4211yescharacteristic
1408C2×C4D4211yescharacteristic
1409C2×C4C23×D411yescharacteristic
1410C2×C4C23×D411yescharacteristic
1411C2×C4C2×H(5,𝔽2)11yescharacteristic
1412C8—21no—
1413C8—21no—
1414C8—21no—
1415C8—21no—
1416C8—21no—
1417C8—21no—
1418C8—21no—
1419C8—21no—
1420C8—41no—
1421C8—41no—
1422C8—41no—
1423C8—41no—
1424C8—41no—
1425C8—41no—
1426C8—41no—
1427C8—41no—
1428C8—41no—
1429C8—41no—
1430C22—21no—
1431C22—21no—
1432C22—21no—
1433C22—41no—
1434C22—41no—
1435C22—41no—
1436C22—41no—
1437C22—41no—
1438C22—41no—
1439C22—41no—
1440C22—41no—
1441C22—41no—
1442C22—81no—
1443C22—81no—
1444C22—81no—
1445C22—81no—
1446C22—81no—
1447C22—81no—
1448C22—162no—
1449C22—322no—
1450C22C2×D4211yescharacteristic
1451C4—21no—
1452C4—21no—
1453C4—21no—
1454C4—21no—
1455C4—41no—
1456C4—41no—
1457C4—41no—
1458C4—41no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4—41no—
1464C4—41no—
1465C4—41no—
1466C4—41no—
1467C4—41no—
1468C4—81no—
1469C4—81no—
1470C4—81no—
1471C4—81no—
1472C4—81no—
1473C4—81no—
1474C4#358411yescharacteristic
1475C4#358511yescharacteristic
1476C4#358611yescharacteristic
1477C4#358611yescharacteristic
1478C2—41no—
1479C2—81no—
1480C2—81no—
1481C2—81no—
1482C2—161no—
1483C2—161no—
1484C2#6107811yescharacteristic
1485C2#6108011yescharacteristic
1486C2#6110911yescharacteristic
subgroupG/H
center, socleC22C2×D42
commutator, Frattini, cosocleC42C25
prime radical#62305C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62406C2semidirect
3. #62188C2semidirect
4. #61911C2semidirect
5. #20267C2semidirect
6. #20233C2semidirect
7. #20193C2semidirect
8. #20188C2semidirect
9. #20127C2semidirect
10. #20124C2semidirect
11. #20118C2semidirect
12. #20105C2semidirect
13. #20100C2semidirect
14. #20088C2semidirect
15. #20078C2semidirect
16. #20052C2semidirect
17. #19877C2semidirect
18. #19856C2semidirect
19. #19847C2semidirect
20. #19843C2semidirect
21. #19692C2semidirect
22. #19543C2semidirect
23. #19535C2semidirect
24. #19374C2semidirect
25. #19307C2semidirect
26. #18710C2semidirect
27. #18698C2semidirect
28. #18679C2semidirect
29. #18628C2semidirect
30. #18000C2semidirect
31. #17988C2semidirect
32. #3556C22semidirect
40. #3398C22semidirect
41. #3398C22semidirect
42. #3395C22semidirect
44. #3392C22semidirect
46. #3387C22semidirect
49. #3381C22semidirect
52. #3374C22semidirect
53. #3372C22semidirect
58. #3368C22semidirect
60. #3364C22semidirect
61. #3364C22semidirect
62. #3363C22semidirect
90. #3249C22semidirect
96. #3216C22semidirect
97. #3210C22semidirect
100. #3185C22semidirect
105. #3167C22semidirect
117. #2985C22semidirect
118. #2962C22semidirect
120. #1720C22semidirect
121. #1720C22semidirect
122. #1720C22semidirect
123. #1718C22semidirect
124. #1717C22semidirect
125. #1717C22semidirect
126. #1716C22semidirect
127. #1714C22semidirect
129. #1702C22semidirect
130. #1700C22semidirect
132. #1699C22semidirect
133. #1698C22semidirect
134. #1698C22semidirect
135. #1698C22semidirect
136. #1692C22semidirect
137. #1692C22semidirect
138. #1692C22semidirect
141. #1688C22semidirect
142. #1686C22semidirect
143. #1685C22semidirect
144. #1683C22semidirect
145. #1682C22semidirect
146. #1682C22semidirect
147. #1682C22semidirect
148. #1682C22semidirect
149. #1681C22semidirect
150. #1679C22semidirect
151. #1678C22semidirect
152. #1676C22semidirect
153. #1676C22semidirect
154. #1672C22semidirect
155. #1671C22semidirect
156. #1670C22semidirect
157. #1669C22semidirect
158. #1669C22semidirect
159. #1668C22semidirect
160. #1653C22semidirect
162. #1652C22semidirect
163. #1652C22semidirect
166. #1645C22semidirect
168. #1644C22semidirect
173. #1641C22semidirect
177. #1638C22semidirect
178. #1636C22semidirect
179. #1636C22semidirect
180. #1636C22semidirect
181. #1636C22semidirect
183. #1631C22semidirect
184. #1628C22semidirect
185. #1626C22semidirect
186. #1626C22semidirect
187. #1626C22semidirect
188. #1626C22semidirect
189. #1626C22semidirect
190. #1623C22semidirect
191. #1622C22semidirect
196. #1588C22semidirect
197. #1587C22semidirect
198. #1587C22semidirect
199. #1585C22semidirect
200. #1585C22semidirect
201. #1585C22semidirect
202. #1584C22semidirect
203. #1584C22semidirect
204. #1583C22semidirect
205. #1582C22semidirect
206. SD16⋊C8C22semidirect
207. SD16⋊C8C22semidirect
208. #1571C22semidirect
209. #1569C22semidirect
210. #1561C22semidirect
211. #1559C22semidirect
213. #1547C22semidirect
215. #1493C22semidirect
216. #1493C22semidirect
218. #1451C22semidirect

Maximal subgroups

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

subgroupindex
#624062
#623052
#621882
#619112
#202672
#202332
#201932
#201882
#201272
#201242
#201182
#201052
#201002
#200882
#200782
#200522
#198772
#198562
#198472
#198432
#196922
#195432
#195352
#193742
#193072
#187102
#186982
#186792
#186282
#180002
#179882