Finite Group Databasebeta

← #6355281

Subgroups — #6355281

Order 512.

1487 conjugacy classes of subgroups.

The subgroup lattice has 1480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62115C211yesmaximal, characteristic, complemented
2#62098C211yesmaximal, characteristic, complemented
3#61014C211yesmaximal, characteristic, complemented
4#60300C211yesmaximal, characteristic, complemented
5#19591C211yesmaximal, characteristic, complemented
6#19579C211yesmaximal, characteristic, complemented
7#19573C211yesmaximal, characteristic, complemented
8#19568C211yesmaximal, characteristic, complemented
9#19547C211yesmaximal, characteristic, complemented
10#19540C211yesmaximal, characteristic, complemented
11#19531C211yesmaximal, characteristic, complemented
12#19525C211yesmaximal, characteristic, complemented
13#19503C211yesmaximal, characteristic, complemented
14#19493C211yesmaximal, characteristic, complemented
15#19465C211yesmaximal, characteristic, complemented
16#19460C211yesmaximal, characteristic, complemented
17#19453C211yesmaximal, characteristic, complemented
18#19448C211yesmaximal, characteristic, complemented
19#19429C211yesmaximal, characteristic, complemented
20#19425C211yesmaximal, characteristic, complemented
21#19253C211yesmaximal, characteristic, complemented
22#19247C211yesmaximal, characteristic, complemented
23#19227C211yesmaximal, characteristic, complemented
24#19220C211yesmaximal, characteristic, complemented
25#19183C211yesmaximal, characteristic, complemented
26#19183C211yesmaximal, characteristic, complemented
27#19160C211yesmaximal, characteristic, complemented
28#19158C211yesmaximal, characteristic, complemented
29#17811C211yesmaximal, characteristic, complemented
30#17768C211yesmaximal, characteristic, complemented
31#17726C211yesmaximal, characteristic, complemented
32#3511C2211yescharacteristic
33#3511C2211yescharacteristic
34#3475C2211yescharacteristic
35#3389—21no—
36#3380—21no—
37#3376—21no—
38#3360—21no—
39#3351—21no—
40#3348—21no—
41#3347—21no—
42#3341—21no—
43#3337—21no—
44#3337—21no—
45#3322—21no—
46#3319—21no—
47#3307—21no—
48#3303—21no—
49#3297—21no—
50#3297—21no—
51#3262—21no—
52#3262—21no—
53#3254C2211yescharacteristic
54#3251C2211yescharacteristic
55#3247C2211yescharacteristic
56#3247C2211yescharacteristic
57#3247C2211yescharacteristic
58#3246C2211yescharacteristic
59#3238C2211yescharacteristic
60#3237C2211yescharacteristic
61#3233C2211yescharacteristic
62#3233C2211yescharacteristic
63#3233C2211yescharacteristic
64#3230C2211yescharacteristic
65#3230C2211yescharacteristic
66#3230C2211yescharacteristic, complemented
67#3226C2211yescharacteristic
68#3226C2211yescharacteristic, complemented
69#3210C2211yescharacteristic
70#3210C2211yescharacteristic, complemented
71#3207C2211yescharacteristic
72#3207C2211yescharacteristic, complemented
73#3203—21no—
74#3203—21no—
75#3182C2211yescharacteristic, complemented
76#3182C2211yescharacteristic, complemented
77#3170C2211yescharacteristic, complemented
78#3169C2211yescharacteristic, complemented
79#3124—21no—
80#3124—21no—
81#3124—21no—
82#3124—21no—
83#3115C2211yescharacteristic
84#3109C2211yescharacteristic
85#3106C2211yescharacteristic
86#3106C2211yescharacteristic
87#3106C2211yescharacteristic
88#3100C2211yescharacteristic
89#3079C2211yescharacteristic
90#3077C2211yescharacteristic
91#3076C2211yescharacteristic
92#3076C2211yescharacteristic
93#3076C2211yescharacteristic
94C2×#476C2211yescharacteristic
95#2995—21no—
96#2994C2211yescharacteristic
97#2993—21no—
98#2993C2211yescharacteristic
99#2991C2211yescharacteristic
100#2989C2211yescharacteristic
101#2989C2211yescharacteristic
102#2988C2211yescharacteristic
103#2986C2211yescharacteristic
104#2985C2211yescharacteristic
105#2978—21no—
106#2976—21no—
107#2975C2211yescharacteristic
108#2974C2211yescharacteristic
109#2971C2211yescharacteristic
110#2969—21no—
111#2969C2211yescharacteristic
112#2967—21no—
113#2966C2211yescharacteristic
114#2965C2211yescharacteristic
115#2925C2211yescharacteristic
116#2924—21no—
117#2922C2211yescharacteristic
118#2921—21no—
119#1704C2211yescharacteristic, complemented
120#1704C2211yescharacteristic, complemented
121#1704C2211yescharacteristic, complemented
122#1704C2211yescharacteristic, complemented
123#1704C2211yescharacteristic, complemented
124#1703C2211yescharacteristic
125#1703C2211yescharacteristic
126#1703C2211yescharacteristic
127#1703C2211yescharacteristic
128#1703C2211yescharacteristic
129#1703C2211yescharacteristic
130#1703C2211yescharacteristic
131#1698C2211yescharacteristic, complemented
132#1698C2211yescharacteristic, complemented
133#1698C2211yescharacteristic, complemented
134#1697C2211yescharacteristic
135#1697C2211yescharacteristic
136#1697C2211yescharacteristic
137#1697C2211yescharacteristic
138#1697C2211yescharacteristic
139#1696C2211yescharacteristic, complemented
140#1696C2211yescharacteristic, complemented
141#1696C2211yescharacteristic, complemented
142#1696C2211yescharacteristic, complemented
143#1695C2211yescharacteristic
144#1695C2211yescharacteristic
145#1695C2211yescharacteristic
146#1695C2211yescharacteristic
147#1695C2211yescharacteristic
148#1695C2211yescharacteristic
149#1690C2211yescharacteristic, complemented
150#1689C2211yescharacteristic
151#1688C2211yescharacteristic, complemented
152#1688C2211yescharacteristic, complemented
153#1687C2211yescharacteristic
154#1687C2211yescharacteristic
155#1686C2211yescharacteristic, complemented
156#1685C2211yescharacteristic
157#1685C2211yescharacteristic
158#1685C2211yescharacteristic
159#1684C2211yescharacteristic, complemented
160#1684C2211yescharacteristic, complemented
161#1684C2211yescharacteristic, complemented
162#1683C2211yescharacteristic
163#1678C2211yescharacteristic, complemented
164#1678C2211yescharacteristic, complemented
165#1678C2211yescharacteristic, complemented
166#1678C2211yescharacteristic, complemented
167#1678C2211yescharacteristic, complemented
168#1677C2211yescharacteristic
169#1677C2211yescharacteristic
170#1677C2211yescharacteristic
171#1676C2211yescharacteristic, complemented
172#1676C2211yescharacteristic, complemented
173#1676C2211yescharacteristic, complemented
174#1676C2211yescharacteristic, complemented
175#1675C2211yescharacteristic
176#1675C2211yescharacteristic
177#1670C2211yescharacteristic, complemented
178#1669C2211yescharacteristic
179#1666C2211yescharacteristic, complemented
180#1666C2211yescharacteristic, complemented
181#1666C2211yescharacteristic, complemented
182#1665C2211yescharacteristic
183#1574C2211yescharacteristic
184#1574C2211yescharacteristic, complemented
185#1573C2211yescharacteristic
186#1573C2211yescharacteristic, complemented
187#1572C2211yescharacteristic
188#1572C2211yescharacteristic, complemented
189#1570C2211yescharacteristic
190#1570C2211yescharacteristic, complemented
191#1565C2211yescharacteristic, complemented
192#1565C2211yescharacteristic, complemented
193#1564C2211yescharacteristic, complemented
194C2×#334C2211yescharacteristic, complemented
195#1560C2211yescharacteristic, complemented
196#1559C2211yescharacteristic, complemented
197#1558C2211yescharacteristic
198#1557C2211yescharacteristic
199#1554C2211yescharacteristic
200#1554C2211yescharacteristic, complemented
201#1554C2211yescharacteristic, complemented
202#1553C2211yescharacteristic
203#1551C2211yescharacteristic
204#1551C2211yescharacteristic, complemented
205#1551C2211yescharacteristic, complemented
206#1551C2211yescharacteristic, complemented
207#1550C2211yescharacteristic, complemented
208#1548C2211yescharacteristic
209#1548C2211yescharacteristic, complemented
210#1547C2211yescharacteristic, complemented
211#1543C2211yescharacteristic
212#1543C2211yescharacteristic, complemented
213#1543C2211yescharacteristic, complemented
214#1542C2211yescharacteristic
215#1542C2211yescharacteristic, complemented
216#1542C2211yescharacteristic, complemented
217C2×#333C2211yescharacteristic, complemented
218#1540C2211yescharacteristic, complemented
219#556—21no—
220#556—21no—
221#556D411yescharacteristic
222#555—21no—
223#555—21no—
224#555D411yescharacteristic
225#554—21no—
226#554—21no—
227#554D411yescharacteristic
228#553—21no—
229#553—21no—
230#553—21no—
231#553—21no—
232#553—21no—
233#552—21no—
234#552D411yescharacteristic
235#552D411yescharacteristic
236#551—21no—
237#551—21no—
238#548—21no—
239#548—21no—
240#548—21no—
241#548—21no—
242#547—21no—
243#547—21no—
244#547D411yescharacteristic
245#546D411yescharacteristic
246#546D411yescharacteristic
247#542—21no—
248#542—21no—
249#542—21no—
250#542—21no—
251#537—21no—
252#537—21no—
253#533C2311yescharacteristic
254#533C2311yescharacteristic
255#533C2311yescharacteristic
256#533C2311yescharacteristic
257#533C2311yescharacteristic
258#532C2311yescharacteristic
259#532C2311yescharacteristic
260#532C2311yescharacteristic
261#532C2311yescharacteristic
262#532C2311yescharacteristic
263#532C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266#529—21no—
267#529—21no—
268#529C2311yescharacteristic
269#529C2311yescharacteristic
270#525—21no—
271#520—21no—
272#520—21no—
273C4×#41C2311yescharacteristic
274C4×#41C2311yescharacteristic
275C4×#41C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×#117—21no—
278#501—21no—
279#501—21no—
280#500—21no—
281#500C2311yescharacteristic
282#500C2311yescharacteristic
283#500C2311yescharacteristic
284#500C2311yescharacteristic
285#499—21no—
286#499—21no—
287#499—21no—
288#494C2311yescharacteristic
289#493C2311yescharacteristic
290#492C2311yescharacteristic
291#492C2311yescharacteristic
292#491—21no—
293#489—21no—
294#488—21no—
295#488—21no—
296#488—21no—
297#487—21no—
298#487C2311yescharacteristic
299#487C2311yescharacteristic
300#487C2311yescharacteristic
301#487C2311yescharacteristic
302#486C2311yescharacteristic
303#486C2311yescharacteristic
304#486C2311yescharacteristic
305#486C2311yescharacteristic
306#485—21no—
307#485—21no—
308#485—21no—
309#485—21no—
310#485—21no—
311#484—21no—
312#484—21no—
313#484—21no—
314#484—21no—
315#484—21no—
316#484—21no—
317#483—21no—
318#482—21no—
319#482—21no—
320#482—21no—
321#482—21no—
322#482—21no—
323#482—21no—
324#482—21no—
325#481—21no—
326#480—21no—
327#480—21no—
328#480—21no—
329#480—21no—
330#480—21no—
331#480—21no—
332#479—21no—
333#479—21no—
334#479—21no—
335#478—21no—
336#478—21no—
337#478—21no—
338#478—21no—
339#478—21no—
340#478—21no—
341#478—21no—
342#478—21no—
343#478—21no—
344#477—21no—
345#477—21no—
346#477—21no—
347#477—21no—
348#477C2311yescharacteristic
349#477C2311yescharacteristic
350#477C2311yescharacteristic
351#477C2311yescharacteristic
352#477C2311yescharacteristic
353#477C2311yescharacteristic
354#477C2311yescharacteristic
355#477C2311yescharacteristic
356#476—21no—
357#476—21no—
358#476—21no—
359#476C2311yescharacteristic
360#476C2311yescharacteristic
361#476C2311yescharacteristic
362#476C2311yescharacteristic
363#476C2311yescharacteristic
364#476C2311yescharacteristic
365#476C2311yescharacteristic
366#476C2311yescharacteristic
367#475—21no—
368#475C2311yescharacteristic
369#475C2311yescharacteristic
370#475C2311yescharacteristic
371#475C2311yescharacteristic
372#474—21no—
373#474—21no—
374#474—21no—
375#474—21no—
376#474—21no—
377#474—21no—
378#474C2311yescharacteristic
379#474C2311yescharacteristic
380#474C2311yescharacteristic
381#474C2311yescharacteristic
382#469—21no—
383#468—21no—
384#468—21no—
385#468—21no—
386#468—21no—
387#468—21no—
388#468—21no—
389#468—21no—
390#467—21no—
391#467—21no—
392#466—21no—
393#466—21no—
394#466—21no—
395#466—21no—
396#466—21no—
397#465—21no—
398#465—21no—
399#465—21no—
400#465—21no—
401#465—21no—
402#464—21no—
403#464—21no—
404#464—21no—
405#464—21no—
406#463—21no—
407#463—21no—
408#463—21no—
409#463—21no—
410#463—21no—
411#463—21no—
412#463—21no—
413#463—21no—
414#461—21no—
415#461—21no—
416#460C2311yescharacteristic
417#460C2311yescharacteristic
418#460C2311yescharacteristic
419#460C2311yescharacteristic
420#459C2311yescharacteristic
421#459C2311yescharacteristic
422#459C2311yescharacteristic
423#459C2311yescharacteristic
424#452—21no—
425#452—21no—
426#452—21no—
427#452—21no—
428#449—21no—
429#449—21no—
430#449—21no—
431#449—21no—
432#449—21no—
433#449—21no—
434#449—21no—
435#449—21no—
436#447—21no—
437#447—21no—
438#446—21no—
439#446—21no—
440#446—21no—
441#446—21no—
442#446C2311yescharacteristic
443#446C2311yescharacteristic
444#446C2311yescharacteristic
445#446C2311yescharacteristic
446C8×Q8—21no—
447C8×Q8—21no—
448C8×Q8C2311yescharacteristic
449C8×Q8C2311yescharacteristic
450C8×Q8C2311yescharacteristic
451C8×Q8C2311yescharacteristic
452#442—21no—
453#442—21no—
454#442—21no—
455#440—21no—
456#440—21no—
457#440—21no—
458#440—21no—
459#440—21no—
460C4×Q16—21no—
461C4×Q16—21no—
462C4×SD16—21no—
463C4×SD16—21no—
464C4×SD16—21no—
465C4×D8—21no—
466C4×D8—21no—
467C4×D8—21no—
468C4×D8—21no—
469C4×D8—21no—
470C4×D8—21no—
471C4×D8—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#436—21no—
481#436C2311yescharacteristic
482#436C2311yescharacteristic
483#436C2311yescharacteristic
484#436C2311yescharacteristic
485#436C2311yescharacteristic
486#436C2311yescharacteristic
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—
499C8×D4—21no—
500C8×D4—21no—
501C8×D4—21no—
502C8×D4—21no—
503C8×D4—21no—
504C8×D4C2311yescharacteristic
505C8×D4C2311yescharacteristic
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#433—21no—
515#433—21no—
516#433D411yescharacteristic
517#433D411yescharacteristic
518#433D411yescharacteristic
519#433D411yescharacteristic
520#432—21no—
521#432—21no—
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#431C2311yescharacteristic
537#431C2311yescharacteristic
538#428—21no—
539#428—21no—
540#427—21no—
541#427—21no—
542#427—21no—
543C2×#106—21no—
544#424—21no—
545#424—21no—
546#424D411yescharacteristic
547#424D411yescharacteristic
548#423—21no—
549#423—21no—
550#423C2311yescharacteristic
551#423C2311yescharacteristic
552#423C2311yescharacteristic
553C2×C4⋊C8C2311yescharacteristic
554C2×C4⋊C8C2311yescharacteristic
555C2×C4⋊C8C2311yescharacteristic
556C2×C4⋊C8C2311yescharacteristic
557C2×C4⋊C8C2311yescharacteristic
558#418—21no—
559#417—21no—
560#416—21no—
561#416—21no—
562#416—21no—
563C2×#102—21no—
564#408—21no—
565#408D411yescharacteristic
566#408D411yescharacteristic
567#407—21no—
568#407—21no—
569#407—21no—
570C2×C22⋊C8—21no—
571#405—21no—
572#405—21no—
573#405—21no—
574C4×M16—21no—
575C4×M16—21no—
576C4×M16C2311yescharacteristic
577C2×C4×C8C2311yescharacteristic
578#335C2311yescharacteristic
579#335C2311yescharacteristic
580#335C2311yescharacteristic
581#335C2311yescharacteristic
582#335C2311yescharacteristic
583#335C2311yescharacteristic
584#334C2311yescharacteristic
585#334C2311yescharacteristic
586#334C2311yescharacteristic
587#334C2311yescharacteristic
588#334C2311yescharacteristic
589#334C2311yescharacteristic
590#334C2311yescharacteristic
591#334C2311yescharacteristic
592#334C2311yescharacteristic
593#334C2311yescharacteristic
594#333C2311yescharacteristic
595#333C2311yescharacteristic
596#333C2311yescharacteristic
597#333C2311yescharacteristic
598#333C2311yescharacteristic
599#333C2311yescharacteristic
600#333C2311yescharacteristic
601#333C2311yescharacteristic
602#333C2311yescharacteristic
603#333C2311yescharacteristic
604#333C2311yescharacteristic
605#333C2311yescharacteristic
606#333C2311yescharacteristic
607#333C2311yescharacteristic
608#333C2311yescharacteristic
609#333C2311yescharacteristic
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×#41—21no—
632C2×#41C2×D411yescharacteristic
633C2×#41C2×D411yescharacteristic
634C2×#41C2×D411yescharacteristic
635C22×Q8—21no—
636C22×Q8—21no—
637C22×D4C2×D411yescharacteristic
638C23×C4—21no—
639C2×Q16—21no—
640C2×Q16—21no—
641C2×SD16—21no—
642C2×SD16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×D8—21no—
650C2×D8—21no—
651C2×D8—21no—
652C2×D8—21no—
653C2×D8—21no—
654C2×D8—21no—
655C2×M16—21no—
656C2×M16—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16—21no—
662C2×M16—21no—
663C2×M16—21no—
664C2×M16C2×D411yescharacteristic
665C2×M16C2×D411yescharacteristic
666C22×C8—21no—
667C22×C8—21no—
668C22×C8—21no—
669C22×C8—21no—
670C22×C8—21no—
671C22×C8—21no—
672C22×C8—21no—
673C22×C8C2×D411yescharacteristic
674C22×C8C2×D411yescharacteristic
675C4⋊Q8—21no—
676C4⋊Q8—21no—
677C4⋊Q8—21no—
678C4⋊Q8—21no—
679C4⋊Q8—21no—
680C4⋊Q8—21no—
681C4⋊Q8C2×D411yescharacteristic
682C4⋊Q8C2×D411yescharacteristic
683C4⋊Q8C2411yescharacteristic
684C4⋊Q8C2411yescharacteristic
685C4⋊Q8C2411yescharacteristic
686C4⋊Q8C2411yescharacteristic
687C4⋊Q8C2411yescharacteristic
688C4⋊Q8C2411yescharacteristic
689#127C2411yescharacteristic
690#127C2411yescharacteristic
691#126—21no—
692#126—21no—
693#126—21no—
694#126—21no—
695#126—21no—
696#126—21no—
697#126—41no—
698#126—41no—
699#126—41no—
700#126—41no—
701#125—21no—
702#125—21no—
703#125—21no—
704#125—21no—
705#125—21no—
706#125—21no—
707#125—21no—
708#125C2×D411yescharacteristic
709#125C2×D411yescharacteristic
710#124—21no—
711#124—21no—
712#124—21no—
713#124—21no—
714#124—21no—
715#124—21no—
716#124—21no—
717#124—21no—
718#124—41no—
719#124—41no—
720#124—41no—
721#124—41no—
722#124C2×D411yescharacteristic
723#124C2×D411yescharacteristic
724#123—21no—
725#123—21no—
726#123—21no—
727#123—21no—
728#123—21no—
729#123—21no—
730#123—21no—
731#123—21no—
732#123—41no—
733#123—41no—
734#123—41no—
735#123—41no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744C22⋊Q8—21no—
745C22⋊Q8—21no—
746C22⋊Q8—21no—
747C22⋊Q8—21no—
748C22⋊Q8—21no—
749C22⋊Q8—41no—
750C22⋊Q8—41no—
751C22⋊Q8—41no—
752C22⋊Q8—41no—
753C22⋊Q8—41no—
754C22⋊Q8—41no—
755C22⋊Q8C2×D411yescharacteristic
756C22⋊Q8C2×D411yescharacteristic
757C22⋊Q8C2×D411yescharacteristic
758C22⋊Q8C2×D411yescharacteristic
759#121—21no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—21no—
767#121—21no—
768#121—21no—
769#121—21no—
770#121—21no—
771#121—21no—
772#121—21no—
773#121—21no—
774#121—21no—
775#121—41no—
776#121—41no—
777#121—41no—
778#121—41no—
779#121—41no—
780#121—41no—
781#121C2×D411yescharacteristic
782#121C2×D411yescharacteristic
783#120—21no—
784#120—21no—
785C4×Q8—21no—
786C4×Q8—21no—
787C4×Q8—21no—
788C4×Q8—21no—
789C4×Q8—21no—
790C4×Q8—21no—
791C4×Q8—21no—
792C4×Q8—21no—
793C4×Q8—21no—
794C4×Q8C2×D411yescharacteristic
795C4×Q8C2×D411yescharacteristic
796C4×Q8C2×D411yescharacteristic
797C4×Q8#4111yescharacteristic
798C4×Q8C2411yescharacteristic
799C4×Q8C2411yescharacteristic
800C4×D4—21no—
801C4×D4—21no—
802C4×D4—21no—
803C4×D4—21no—
804C4×D4—21no—
805C4×D4—21no—
806C4×D4—21no—
807C4×D4—21no—
808C4×D4—21no—
809C4×D4—21no—
810C4×D4—21no—
811C4×D4—21no—
812C4×D4—21no—
813C4×D4—21no—
814C4×D4—21no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—21no—
819C4×D4—21no—
820C4×D4—41no—
821C4×D4—41no—
822C4×D4—41no—
823C4×D4—41no—
824C4×D4C2×D411yescharacteristic
825C4×D4C2×D411yescharacteristic
826C4×D4C2×D411yescharacteristic
827C4×D4C2×D411yescharacteristic
828C4×D4C2×D411yescharacteristic
829C4×D4C2×D411yescharacteristic
830C4×D4C2×D411yescharacteristic
831C4×D4#4111yescharacteristic
832C4×D4#4111yescharacteristic
833C4×D4#4111yescharacteristic
834C4×D4C2411yescharacteristic
835C4×D4C2411yescharacteristic
836#117—21no—
837#117—21no—
838#117—21no—
839#117—21no—
840#117—21no—
841#117—21no—
842#117—21no—
843#117—21no—
844#117—21no—
845#117—21no—
846#117—21no—
847#117—21no—
848#117—21no—
849#117—41no—
850#117—41no—
851#117C2×D411yescharacteristic
852#117C2×D411yescharacteristic
853#117C2×D411yescharacteristic
854#117C2×D411yescharacteristic
855#117C2×D411yescharacteristic
856C2×C4⋊C4—21no—
857C2×C4⋊C4—21no—
858C2×C4⋊C4—21no—
859C2×C4⋊C4—21no—
860C2×C4⋊C4—21no—
861C2×C4⋊C4—21no—
862C2×C4⋊C4—41no—
863C2×C4⋊C4—41no—
864C2×C4⋊C4C2×D411yescharacteristic
865C2×C22⋊C4—21no—
866C2×C22⋊C4—21no—
867C2×C22⋊C4—21no—
868C2×C42—21no—
869C2×C42—21no—
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2411yescharacteristic
873#107—21no—
874#107—21no—
875#107—21no—
876#107—21no—
877#107—21no—
878#107—21no—
879#107—21no—
880#107—21no—
881#107—21no—
882#107—21no—
883#107—21no—
884#107—21no—
885#107—21no—
886#107—21no—
887#107—21no—
888#107—21no—
889#107—21no—
890#107—21no—
891#107—21no—
892#107—21no—
893#106—21no—
894#106—21no—
895#106—21no—
896#106—21no—
897#106—21no—
898#106—21no—
899#106—21no—
900#106—21no—
901#106—21no—
902#106—21no—
903#106—21no—
904#106—21no—
905C4⋊C8—21no—
906C4⋊C8—21no—
907C4⋊C8—21no—
908C4⋊C8—21no—
909C4⋊C8—21no—
910C4⋊C8—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⋊C8C2×D411yescharacteristic
922C4⋊C8C2×D411yescharacteristic
923C4⋊C8C2×D411yescharacteristic
924C4⋊C8C2×D411yescharacteristic
925C4⋊C8C2×D411yescharacteristic
926C4⋊C8C2×D411yescharacteristic
927C4⋊C8C2×D411yescharacteristic
928C4⋊C8C2×D411yescharacteristic
929C4⋊C8C2411yescharacteristic
930C4⋊C8C2411yescharacteristic
931C4⋊C8C2411yescharacteristic
932C4⋊C8C2411yescharacteristic
933C4⋊C8C2411yescharacteristic
934C4⋊C8C2411yescharacteristic
935C4⋊C8C2411yescharacteristic
936C4⋊C8C2411yescharacteristic
937C4⋊C8C2411yescharacteristic
938C4⋊C8C2411yescharacteristic
939C4⋊C8C2411yescharacteristic
940C4⋊C8C2411yescharacteristic
941#103—21no—
942#103—21no—
943#103—21no—
944#103—21no—
945#103—21no—
946#103—21no—
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#102—21no—
962#102—21no—
963#102—21no—
964#102—21no—
965#102—21no—
966#102—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—
989C22⋊C8—21no—
990C22⋊C8—21no—
991C22⋊C8—21no—
992C22⋊C8—21no—
993C22⋊C8—21no—
994C22⋊C8—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⋊C8C2×D411yescharacteristic
1008C22⋊C8C2×D411yescharacteristic
1009C22⋊C8C2×D411yescharacteristic
1010C22⋊C8C2×D411yescharacteristic
1011C22⋊C8C2×D411yescharacteristic
1012C22⋊C8C2×D411yescharacteristic
1013C22⋊C8C2×D411yescharacteristic
1014C22⋊C8C2×D411yescharacteristic
1015#97—21no—
1016#97—21no—
1017#97—21no—
1018#97—21no—
1019#97—21no—
1020#97—21no—
1021#97—21no—
1022#97—21no—
1023#97C2×D411yescharacteristic
1024#97C2×D411yescharacteristic
1025C4×C8—21no—
1026C4×C8—21no—
1027C4×C8—21no—
1028C4×C8—21no—
1029C4×C8—21no—
1030C4×C8—21no—
1031C4×C8—21no—
1032C4×C8—21no—
1033C4×C8—21no—
1034C4×C8—21no—
1035C4×C8C2×D411yescharacteristic
1036C4×C8C2×D411yescharacteristic
1037C4×C8C2411yescharacteristic
1038C4×C8C2411yescharacteristic
1039C4×C8C2411yescharacteristic
1040C4×C8C2411yescharacteristic
1041C24—21no—
1042#41—41no—
1043#41—41no—
1044#41—41no—
1045#41—41no—
1046#41—41no—
1047#41—41no—
1048#41—81no—
1049#41—81no—
1050#41—81no—
1051#41—81no—
1052#41—161no—
1053#41—161no—
1054#41—161no—
1055#41—161no—
1056C2×Q8—21no—
1057C2×Q8—21no—
1058C2×Q8—21no—
1059C2×Q8—21no—
1060C2×Q8—21no—
1061C2×Q8—21no—
1062C2×Q8—21no—
1063C2×Q8—41no—
1064C2×Q8—41no—
1065C2×Q8—161no—
1066C2×Q8—161no—
1067C2×Q8#12111yescharacteristic
1068C2×Q8C22×D411yescharacteristic
1069C2×Q8C22×D411yescharacteristic
1070C2×D4—21no—
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—21no—
1080C2×D4—21no—
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#12111yescharacteristic
1090C2×D4#12111yescharacteristic
1091C2×D4#12111yescharacteristic
1092C2×D4C22×D411yescharacteristic
1093C2×D4C22×D411yescharacteristic
1094C22×C4—21no—
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—21no—
1100C22×C4—21no—
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—41no—
1104C22×C4—41no—
1105C22×C4—41no—
1106C22×C4—41no—
1107C22×C4—41no—
1108C22×C4—41no—
1109C22×C4—41no—
1110C22×C4—41no—
1111C22×C4—81no—
1112C22×C4—81no—
1113C22×C4C22×D411yescharacteristic
1114C22×C4C22×D411yescharacteristic
1115C22×C4C22×D411yescharacteristic
1116C22×C4C22×D411yescharacteristic
1117C22×C4C22×D411yescharacteristic
1118C22×C4C22×D411yescharacteristic
1119C22×C4C2×#4111yescharacteristic
1120C22×C4C2×#4111yescharacteristic
1121C22×C4C2×#4111yescharacteristic
1122Q16—81no—
1123Q16—81no—
1124SD16—81no—
1125SD16—81no—
1126SD16—81no—
1127SD16—81no—
1128SD16—81no—
1129SD16—81no—
1130SD16—81no—
1131SD16—81no—
1132D8—42no—
1133D8—42no—
1134D8—81no—
1135D8—81no—
1136D8—81no—
1137D8—81no—
1138M16—41no—
1139M16—41no—
1140M16—81no—
1141M16—81no—
1142M16—81no—
1143M16—81no—
1144M16—81no—
1145M16—81no—
1146M16—81no—
1147M16—81no—
1148M16—81no—
1149C2×C8—21no—
1150C2×C8—21no—
1151C2×C8—21no—
1152C2×C8—21no—
1153C2×C8—21no—
1154C2×C8—21no—
1155C2×C8—21no—
1156C2×C8—21no—
1157C2×C8—21no—
1158C2×C8—21no—
1159C2×C8—21no—
1160C2×C8—21no—
1161C2×C8—41no—
1162C2×C8—41no—
1163C2×C8—81no—
1164C2×C8—81no—
1165C2×C8—81no—
1166C2×C8—81no—
1167C2×C8—81no—
1168C2×C8—81no—
1169C2×C8—81no—
1170C2×C8C22×D411yescharacteristic
1171C2×C8C22×D411yescharacteristic
1172C2×C8C22×D411yescharacteristic
1173C2×C8C22×D411yescharacteristic
1174C2×C8C22×D411yescharacteristic
1175C2×C8C22×D411yescharacteristic
1176C2×C8C22×D411yescharacteristic
1177C2×C8C22×D411yescharacteristic
1178C4⋊C4—21no—
1179C4⋊C4—21no—
1180C4⋊C4—21no—
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—41no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—41no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4#12111yescharacteristic
1219C4⋊C4#12111yescharacteristic
1220C4⋊C4#12111yescharacteristic
1221C4⋊C4#12111yescharacteristic
1222C4⋊C4#12111yescharacteristic
1223C4⋊C4#12111yescharacteristic
1224C4⋊C4C22×D411yescharacteristic
1225C4⋊C4C22×D411yescharacteristic
1226C4⋊C4C22×D411yescharacteristic
1227C4⋊C4C22×D411yescharacteristic
1228C22⋊C4—21no—
1229C22⋊C4—21no—
1230C22⋊C4—21no—
1231C22⋊C4—21no—
1232C22⋊C4—21no—
1233C22⋊C4—21no—
1234C22⋊C4—21no—
1235C22⋊C4—21no—
1236C22⋊C4—21no—
1237C22⋊C4—21no—
1238C22⋊C4—21no—
1239C22⋊C4—21no—
1240C22⋊C4—21no—
1241C22⋊C4—21no—
1242C22⋊C4—21no—
1243C22⋊C4—21no—
1244C22⋊C4—21no—
1245C22⋊C4—21no—
1246C22⋊C4—41no—
1247C22⋊C4—41no—
1248C22⋊C4—41no—
1249C22⋊C4—41no—
1250C22⋊C4—41no—
1251C22⋊C4—41no—
1252C22⋊C4—41no—
1253C22⋊C4—41no—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—41no—
1257C22⋊C4—41no—
1258C22⋊C4—41no—
1259C22⋊C4—41no—
1260C22⋊C4—41no—
1261C22⋊C4—41no—
1262C22⋊C4#12111yescharacteristic
1263C22⋊C4#12111yescharacteristic
1264C22⋊C4#12111yescharacteristic
1265C22⋊C4#12111yescharacteristic
1266C22⋊C4#12111yescharacteristic
1267C22⋊C4#12111yescharacteristic
1268C42—21no—
1269C42—21no—
1270C42—21no—
1271C42—21no—
1272C42—21no—
1273C42—21no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42C22×D411yescharacteristic
1279C42C22×D411yescharacteristic
1280C42C22×D411yescharacteristic
1281C42C22×D411yescharacteristic
1282C42C22×D411yescharacteristic
1283C42C22×D411yescharacteristic
1284C42C2×#4111yescharacteristic
1285C42C2×#4111yescharacteristic
1286C42C2×#4111yescharacteristic
1287C42C2511yescharacteristic
1288C23—21no—
1289C23—21no—
1290C23—41no—
1291C23—41no—
1292C23—81no—
1293C23—81no—
1294C23—81no—
1295C23C2×#12111yescharacteristic
1296C23C2×#12111yescharacteristic
1297C23C2×#12111yescharacteristic
1298Q8—21no—
1299Q8—21no—
1300Q8—21no—
1301Q8—21no—
1302Q8—41no—
1303Q8—41no—
1304Q8—41no—
1305Q8—41no—
1306Q8—41no—
1307Q8—81no—
1308Q8—81no—
1309Q8—81no—
1310Q8—81no—
1311Q8—81no—
1312Q8—161no—
1313Q8—161no—
1314D4—21no—
1315D4—21no—
1316D4—21no—
1317D4—21no—
1318D4—41no—
1319D4—41no—
1320D4—41no—
1321D4—41no—
1322D4—41no—
1323D4—41no—
1324D4—41no—
1325D4—41no—
1326D4—41no—
1327D4—41no—
1328D4—41no—
1329D4—81no—
1330D4—81no—
1331D4—81no—
1332D4—81no—
1333D4—81no—
1334D4—81no—
1335D4—81no—
1336D4—82no—
1337D4—82no—
1338D4—161no—
1339D4—161no—
1340D4—161no—
1341D4—161no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—41no—
1361C2×C4—41no—
1362C2×C4—41no—
1363C2×C4—41no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—81no—
1374C2×C4—81no—
1375C2×C4—81no—
1376C2×C4—81no—
1377C2×C4—81no—
1378C2×C4—81no—
1379C2×C4—82no—
1380C2×C4—82no—
1381C2×C4—81no—
1382C2×C4—161no—
1383C2×C4—161no—
1384C2×C4—161no—
1385C2×C4—161no—
1386C2×C4—161no—
1387C2×C4—161no—
1388C2×C4C2×#12111yescharacteristic
1389C2×C4C2×#12111yescharacteristic
1390C2×C4C2×#12111yescharacteristic
1391C2×C4C2×#12111yescharacteristic
1392C2×C4C2×#12111yescharacteristic
1393C2×C4C2×#12111yescharacteristic
1394C2×C4C2×#12111yescharacteristic
1395C2×C4C2×#12111yescharacteristic
1396C2×C4C2×#12111yescharacteristic
1397C2×C4C23×D411yescharacteristic
1398C2×C4C23×D411yescharacteristic
1399C2×C4C22×#4111yescharacteristic
1400C8—21no—
1401C8—21no—
1402C8—21no—
1403C8—21no—
1404C8—21no—
1405C8—21no—
1406C8—21no—
1407C8—21no—
1408C8—41no—
1409C8—41no—
1410C8—41no—
1411C8—41no—
1412C8—41no—
1413C8—41no—
1414C8—41no—
1415C8—41no—
1416C8—41no—
1417C8—41no—
1418C8—41no—
1419C8—41no—
1420C22—21no—
1421C22—21no—
1422C22—21no—
1423C22—21no—
1424C22—21no—
1425C22—21no—
1426C22—21no—
1427C22—21no—
1428C22—21no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—81no—
1436C22—81no—
1437C22—81no—
1438C22—81no—
1439C22—81no—
1440C22—81no—
1441C22—162no—
1442C22C22×#12111yescharacteristic
1443C4—21no—
1444C4—21no—
1445C4—21no—
1446C4—21no—
1447C4—21no—
1448C4—21no—
1449C4—21no—
1450C4—21no—
1451C4—21no—
1452C4—21no—
1453C4—41no—
1454C4—41no—
1455C4—41no—
1456C4—41no—
1457C4—41no—
1458C4—41no—
1459C4—81no—
1460C4—81no—
1461C4—81no—
1462C4—81no—
1463C4—81no—
1464C4—81no—
1465C4#358411yescharacteristic
1466C4#358411yescharacteristic
1467C4#358611yescharacteristic
1468C4#358611yescharacteristic
1469C2—41no—
1470C2—41no—
1471C2—41no—
1472C2—81no—
1473C2—81no—
1474C2—161no—
1475C2—161no—
1476C2#6042211yescharacteristic
1477C2#6046211yescharacteristic
1478C2#6047111yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62115C2semidirect
2. #62098C2semidirect
3. #61014C2semidirect
4. #60300C2semidirect
5. #19591C2semidirect
6. #19579C2semidirect
7. #19573C2semidirect
8. #19568C2semidirect
9. #19547C2semidirect
10. #19540C2semidirect
11. #19531C2semidirect
12. #19525C2semidirect
13. #19503C2semidirect
14. #19493C2semidirect
15. #19465C2semidirect
16. #19460C2semidirect
17. #19453C2semidirect
18. #19448C2semidirect
19. #19429C2semidirect
20. #19425C2semidirect
21. #19253C2semidirect
22. #19247C2semidirect
23. #19227C2semidirect
24. #19220C2semidirect
25. #19183C2semidirect
26. #19183C2semidirect
27. #19160C2semidirect
28. #19158C2semidirect
29. #17811C2semidirect
30. #17768C2semidirect
31. #17726C2semidirect
66. #3230C22semidirect
68. #3226C22semidirect
70. #3210C22semidirect
72. #3207C22semidirect
75. #3182C22semidirect
76. #3182C22semidirect
77. #3170C22semidirect
78. #3169C22semidirect
119. #1704C22semidirect
120. #1704C22semidirect
121. #1704C22semidirect
122. #1704C22semidirect
123. #1704C22semidirect
131. #1698C22semidirect
132. #1698C22semidirect
133. #1698C22semidirect
139. #1696C22semidirect
140. #1696C22semidirect
141. #1696C22semidirect
142. #1696C22semidirect
149. #1690C22semidirect
151. #1688C22semidirect
152. #1688C22semidirect
155. #1686C22semidirect
159. #1684C22semidirect
160. #1684C22semidirect
161. #1684C22semidirect
163. #1678C22semidirect
164. #1678C22semidirect
165. #1678C22semidirect
166. #1678C22semidirect
167. #1678C22semidirect
171. #1676C22semidirect
172. #1676C22semidirect
173. #1676C22semidirect
174. #1676C22semidirect
177. #1670C22semidirect
179. #1666C22semidirect
180. #1666C22semidirect
181. #1666C22semidirect
184. #1574C22semidirect
186. #1573C22semidirect
188. #1572C22semidirect
190. #1570C22semidirect
191. #1565C22semidirect
192. #1565C22semidirect
193. #1564C22semidirect
194. C2×#334C22semidirect
195. #1560C22semidirect
196. #1559C22semidirect
200. #1554C22semidirect
201. #1554C22semidirect
204. #1551C22semidirect
205. #1551C22semidirect
206. #1551C22semidirect
207. #1550C22semidirect
209. #1548C22semidirect
210. #1547C22semidirect
212. #1543C22semidirect
213. #1543C22semidirect
215. #1542C22semidirect
216. #1542C22semidirect
217. C2×#333C22semidirect
218. #1540C22semidirect

Maximal subgroups

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

subgroupindex
#621152
#620982
#610142
#603002
#195912
#195792
#195732
#195682
#195472
#195402
#195312
#195252
#195032
#194932
#194652
#194602
#194532
#194482
#194292
#194252
#192532
#192472
#192272
#192202
#191832
#191602
#191582
#178112
#177682
#177262