Finite Group Databasebeta

← #6364045

Subgroups — #6364045

Order 512.

1490 conjugacy classes of subgroups.

The subgroup lattice has 1474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62188C211yesmaximal, characteristic, complemented
2#62097C211yesmaximal, characteristic, complemented
3#61922C211yesmaximal, characteristic, complemented
4#61725C211yesmaximal, characteristic
5#20267C211yesmaximal, characteristic, complemented
6#20257C211yesmaximal, characteristic, complemented
7#20231C211yesmaximal, characteristic, complemented
8#20229C211yesmaximal, characteristic, complemented
9#20145C211yesmaximal, characteristic, complemented
10#20133C211yesmaximal, characteristic, complemented
11#20118C211yesmaximal, characteristic, complemented
12#20100C211yesmaximal, characteristic, complemented
13#19950C211yesmaximal, characteristic, complemented
14#19950C211yesmaximal, characteristic, complemented
15#19923C211yesmaximal, characteristic, complemented
16#19913C211yesmaximal, characteristic, complemented
17#19881C211yesmaximal, characteristic, complemented
18#19878C211yesmaximal, characteristic, complemented
19#19829C211yesmaximal, characteristic, complemented
20#19823C211yesmaximal, characteristic, complemented
21#19716C211yesmaximal, characteristic, complemented
22#19545C211yesmaximal, characteristic, complemented
23#19532C211yesmaximal, characteristic, complemented
24#19423C211yesmaximal, characteristic, complemented
25#19419C211yesmaximal, characteristic, complemented
26#18745C211yesmaximal, characteristic, complemented
27#18584C211yesmaximal, characteristic, complemented
28#18571C211yesmaximal, characteristic, complemented
29#18561C211yesmaximal, characteristic, complemented
30#17952C211yesmaximal, characteristic, complemented
31#17927C211yesmaximal, characteristic, complemented
32#3555C2211yescharacteristic
33#3519C2211yescharacteristic
34#3509C2211yescharacteristic, complemented
35#3475C2211yescharacteristic
36#3402—21no—
37#3398—21no—
38#3398C2211yescharacteristic, complemented
39#3398C2211yescharacteristic, complemented
40#3395C2211yescharacteristic, complemented
41#3393C2211yescharacteristic, complemented
42#3385C2211yescharacteristic
43#3381C2211yescharacteristic
44#3381C2211yescharacteristic, complemented
45#3381C2211yescharacteristic, complemented
46#3377—21no—
47#3374—21no—
48#3372C2211yescharacteristic, complemented
49#3369C2211yescharacteristic, complemented
50#3368C2211yescharacteristic
51#3364C2211yescharacteristic
52#3364C2211yescharacteristic
53#3363C2211yescharacteristic, complemented
54#3362C2211yescharacteristic
55#3360C2211yescharacteristic, complemented
56#3357C2211yescharacteristic
57#3357C2211yescharacteristic
58#3357C2211yescharacteristic
59#3356C2211yescharacteristic
60#3355—21no—
61#3354C2211yescharacteristic
62#3351—21no—
63#3351—21no—
64#3350—21no—
65#3340C2211yescharacteristic
66#3340C2211yescharacteristic
67#3340C2211yescharacteristic
68#3336—21no—
69#3336—21no—
70#3333C2211yescharacteristic
71#3332C2211yescharacteristic
72#3325C2211yescharacteristic
73#3324—21no—
74#3324C2211yescharacteristic
75#3324C2211yescharacteristic
76#3323—21no—
77#3322—21no—
78#3310—21no—
79#3302C2211yescharacteristic, complemented
80#3302C2211yescharacteristic, complemented
81#3296—21no—
82#3296—21no—
83#3295C2211yescharacteristic
84#3260—21no—
85#3254C2211yescharacteristic
86#3249C2211yescharacteristic, complemented
87#3248—21no—
88#3241—21no—
89#3233—21no—
90#3233C2211yescharacteristic
91#3229C2211yescharacteristic, complemented
92#3228C2211yescharacteristic
93#3228C2211yescharacteristic
94#3225—21no—
95#3223—21no—
96#3218C2211yescharacteristic
97#3209C2211yescharacteristic, complemented
98#3197—21no—
99#3194—21no—
100#3185C2211yescharacteristic, complemented
101#3141C2211yescharacteristic
102#3127—21no—
103#3123—21no—
104#3121—21no—
105#3116C2211yescharacteristic, complemented
106#3107—21no—
107#3106C2211yescharacteristic
108#3102C2211yescharacteristic
109#3101C2211yescharacteristic
110#3094—21no—
111#3093—21no—
112#3081—21no—
113#3077C2211yescharacteristic
114#3076—21no—
115C2×#474C2211yescharacteristic
116#2993C2211yescharacteristic
117#2988C2211yescharacteristic, complemented
118#2985C2211yescharacteristic, complemented
119#2975C2211yescharacteristic
120#1723C2211yescharacteristic, complemented
121#1720C2211yescharacteristic, complemented
122#1720C2211yescharacteristic, complemented
123#1720C2211yescharacteristic, complemented
124#1718C2211yescharacteristic, complemented
125#1716C2211yescharacteristic, complemented
126#1711C2211yescharacteristic, complemented
127#1707C2211yescharacteristic, complemented
128#1703C2211yescharacteristic
129#1703C2211yescharacteristic
130#1703C2211yescharacteristic, complemented
131#1703C2211yescharacteristic, complemented
132#1702C2211yescharacteristic, complemented
133#1702C2211yescharacteristic, complemented
134#1700C2211yescharacteristic, complemented
135#1699C2211yescharacteristic, complemented
136#1696C2211yescharacteristic, complemented
137#1696C2211yescharacteristic, complemented
138#1692C2211yescharacteristic, complemented
139#1691C2211yescharacteristic, complemented
140#1689C2211yescharacteristic
141#1689C2211yescharacteristic
142#1689C2211yescharacteristic, complemented
143#1689C2211yescharacteristic, complemented
144#1682C2211yescharacteristic, complemented
145#1681C2211yescharacteristic, complemented
146#1680C2211yescharacteristic, complemented
147#1679C2211yescharacteristic, complemented
148#1678C2211yescharacteristic, complemented
149#1678C2211yescharacteristic, complemented
150#1678C2211yescharacteristic, complemented
151#1677C2211yescharacteristic, complemented
152#1676C2211yescharacteristic, complemented
153#1675C2211yescharacteristic, complemented
154#1672C2211yescharacteristic, complemented
155#1672C2211yescharacteristic, complemented
156#1672C2211yescharacteristic, complemented
157#1672C2211yescharacteristic, complemented
158#1671C2211yescharacteristic, complemented
159#1671C2211yescharacteristic, complemented
160#1654C2211yescharacteristic, complemented
161#1653C2211yescharacteristic, complemented
162#1652C2211yescharacteristic
163#1652C2211yescharacteristic, complemented
164#1646C2211yescharacteristic
165#1646C2211yescharacteristic
166#1646C2211yescharacteristic
167#1645C2211yescharacteristic, complemented
168#1644C2211yescharacteristic
169#1644C2211yescharacteristic
170#1644C2211yescharacteristic, complemented
171#1644C2211yescharacteristic, complemented
172#1641C2211yescharacteristic
173#1641C2211yescharacteristic
174#1639C2211yescharacteristic
175#1639C2211yescharacteristic
176#1638C2211yescharacteristic
177#1638C2211yescharacteristic, complemented
178#1638C2211yescharacteristic, complemented
179#1638C2211yescharacteristic, complemented
180#1636C2211yescharacteristic, complemented
181#1636C2211yescharacteristic, complemented
182#1636C2211yescharacteristic, complemented
183#1635C2211yescharacteristic, complemented
184#1634C2211yescharacteristic
185#1633C2211yescharacteristic, complemented
186#1632C2211yescharacteristic, complemented
187#1632C2211yescharacteristic, complemented
188#1628C2211yescharacteristic, complemented
189#1628C2211yescharacteristic, complemented
190#1626C2211yescharacteristic, complemented
191#1626C2211yescharacteristic, complemented
192#1592C2211yescharacteristic
193#1592C2211yescharacteristic, complemented
194#1590C2211yescharacteristic
195#1590C2211yescharacteristic, complemented
196#1588C2211yescharacteristic
197#1588C2211yescharacteristic, complemented
198#1587C2211yescharacteristic, complemented
199#1586C2211yescharacteristic, complemented
200#1583C2211yescharacteristic
201#1583C2211yescharacteristic, complemented
202#1583C2211yescharacteristic, complemented
203#1582C2211yescharacteristic, complemented
204#1580C2211yescharacteristic, complemented
205#1579C2211yescharacteristic, complemented
206C8×SD16C2211yescharacteristic, complemented
207C8×SD16C2211yescharacteristic, complemented
208#1572C2211yescharacteristic, complemented
209#1570C2211yescharacteristic, complemented
210#1559C2211yescharacteristic, complemented
211#1551C2211yescharacteristic
212#1549C2211yescharacteristic, complemented
213#1542C2211yescharacteristic, complemented
214#1490C2211yescharacteristic
215#1489C2211yescharacteristic, complemented
216#1485C2211yescharacteristic, complemented
217#1483C2211yescharacteristic
218#1453C2211yescharacteristic, complemented
219#563—41no—
220Q82C2311yescharacteristic
221#557—21no—
222#557—21no—
223#557C2311yescharacteristic
224#557C2311yescharacteristic
225#557C2311yescharacteristic
226#556—21no—
227#556—21no—
228#556—21no—
229#556C2311yescharacteristic
230#556C2311yescharacteristic
231#556C2311yescharacteristic
232#556C2311yescharacteristic
233#555C2311yescharacteristic
234#555C2311yescharacteristic
235#554C2311yescharacteristic
236#554C2311yescharacteristic
237#554C2311yescharacteristic
238#553—21no—
239#553—21no—
240#553—21no—
241#552—21no—
242#552—21no—
243#552—21no—
244#552—21no—
245#552—21no—
246#552—41no—
247#551—41no—
248#550C2311yescharacteristic
249#547C2311yescharacteristic
250#546—21no—
251#546—21no—
252#546—41no—
253D42—21no—
254D42C2311yescharacteristic
255#544—21no—
256#542—21no—
257#541—21no—
258#541—21no—
259#541—41no—
260#541—41no—
261#540—21no—
262#538—41no—
263#536—21no—
264#533—21no—
265#533—21no—
266#533C2311yescharacteristic
267#533C2311yescharacteristic
268#533C2311yescharacteristic
269#532C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271#529—21no—
272#529—41no—
273#529C2311yescharacteristic
274#525—21no—
275#525—21no—
276C2×#121—21no—
277#519—21no—
278#518—21no—
279C4×#41—21no—
280C4×#41C2311yescharacteristic
281C2×C4×D4C2311yescharacteristic
282C2×#117—21no—
283#501—21no—
284#500C2311yescharacteristic
285#500C2311yescharacteristic
286#499—21no—
287#499—21no—
288#499—21no—
289#499—21no—
290#498C2311yescharacteristic
291#498C2311yescharacteristic
292#498C2311yescharacteristic
293#498C2311yescharacteristic
294#498C2311yescharacteristic
295#497—21no—
296#497—21no—
297#497—21no—
298#495—21no—
299#494—21no—
300#494C2311yescharacteristic
301#494C2311yescharacteristic
302#494C2311yescharacteristic
303#491—21no—
304#491—21no—
305#490—21no—
306#489—21no—
307#489—41no—
308#488—21no—
309#488—21no—
310#488—21no—
311#488—21no—
312#487—21no—
313#487C2311yescharacteristic
314#487C2311yescharacteristic
315#487C2311yescharacteristic
316#487C2311yescharacteristic
317#487C2311yescharacteristic
318#487C2311yescharacteristic
319#487C2311yescharacteristic
320#487C2311yescharacteristic
321#486—21no—
322#486C2311yescharacteristic
323#486C2311yescharacteristic
324#486C2311yescharacteristic
325#486C2311yescharacteristic
326#486C2311yescharacteristic
327#486C2311yescharacteristic
328#485—21no—
329#485—21no—
330#485—21no—
331#485—21no—
332#485—21no—
333#485—21no—
334#485—21no—
335#485—21no—
336#485—21no—
337#485—21no—
338#485—21no—
339#485D411yescharacteristic
340#483—21no—
341#483—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#482—21no—
354#482—21no—
355#482—21no—
356#482—21no—
357#482—21no—
358#482D411yescharacteristic
359#481—21no—
360#481—21no—
361#481—21no—
362#480—21no—
363#480—21no—
364#480—21no—
365#480—21no—
366#479—21no—
367#479—21no—
368#479—21no—
369#479—21no—
370#479—21no—
371#479—21no—
372#479—21no—
373#479—21no—
374#479D411yescharacteristic
375#478—21no—
376#478—21no—
377#478—21no—
378#478—21no—
379#478—21no—
380#478—21no—
381#478—21no—
382#478—21no—
383#478—21no—
384#478—21no—
385#478D411yescharacteristic
386#477—21no—
387#477—21no—
388#477C2311yescharacteristic
389#477C2311yescharacteristic
390#477C2311yescharacteristic
391#477C2311yescharacteristic
392#477C2311yescharacteristic
393#477C2311yescharacteristic
394#477C2311yescharacteristic
395#476—21no—
396#476D411yescharacteristic
397#476D411yescharacteristic
398#476C2311yescharacteristic
399#476C2311yescharacteristic
400#476C2311yescharacteristic
401#476C2311yescharacteristic
402#476C2311yescharacteristic
403#475—21no—
404#475—21no—
405#475—21no—
406#475C2311yescharacteristic
407#474—21no—
408#474—21no—
409#474—21no—
410#474—21no—
411#474C2311yescharacteristic
412#474C2311yescharacteristic
413#474C2311yescharacteristic
414#474C2311yescharacteristic
415#474C2311yescharacteristic
416#474C2311yescharacteristic
417#474C2311yescharacteristic
418#470—21no—
419#470—41no—
420#469—21no—
421#469—21no—
422#469—21no—
423#468—21no—
424#468—21no—
425#468—21no—
426#468—21no—
427#468—21no—
428#468—21no—
429#468—21no—
430#468—21no—
431#467—21no—
432#467—21no—
433#467—21no—
434#467—21no—
435#465—21no—
436#465—21no—
437#465—21no—
438#465—21no—
439#464—21no—
440#464—21no—
441#464—21no—
442#464—21no—
443#464—21no—
444#464—21no—
445#464—21no—
446#464D411yescharacteristic
447#463—21no—
448#463D411yescharacteristic
449#462—21no—
450#462—21no—
451#462—21no—
452#462—21no—
453#462—21no—
454#462—21no—
455#462—21no—
456#462—21no—
457#462C2311yescharacteristic
458#462C2311yescharacteristic
459#462C2311yescharacteristic
460#462C2311yescharacteristic
461#462C2311yescharacteristic
462#461—21no—
463#461—21no—
464#461D411yescharacteristic
465#461D411yescharacteristic
466#461C2311yescharacteristic
467#461C2311yescharacteristic
468#461C2311yescharacteristic
469#460—21no—
470#460—21no—
471#460C2311yescharacteristic
472#460C2311yescharacteristic
473#460C2311yescharacteristic
474#459C2311yescharacteristic
475#452—21no—
476#452—21no—
477#452—21no—
478#452—21no—
479#452D411yescharacteristic
480#451—21no—
481#451—21no—
482#451—21no—
483#450—21no—
484#450—21no—
485#450—21no—
486#450D411yescharacteristic
487#450D411yescharacteristic
488#449—21no—
489#449—21no—
490#449D411yescharacteristic
491#448—21no—
492#447—21no—
493#446—21no—
494#446—21no—
495#446C2311yescharacteristic
496#446C2311yescharacteristic
497#446C2311yescharacteristic
498C8×Q8C2311yescharacteristic
499C8×Q8C2311yescharacteristic
500C8×Q8C2311yescharacteristic
501C8×Q8C2311yescharacteristic
502C8×Q8C2311yescharacteristic
503#441—21no—
504#441—21no—
505#441—21no—
506#441—21no—
507#441—41no—
508#440—21no—
509#440—21no—
510#440—21no—
511#440—21no—
512C4×Q16—21no—
513C4×Q16—21no—
514C4×Q16—21no—
515C4×Q16—21no—
516C4×Q16—21no—
517C4×Q16C2311yescharacteristic
518C4×SD16—21no—
519C4×SD16—21no—
520C4×SD16—21no—
521C4×SD16—21no—
522C4×SD16—21no—
523C4×SD16—21no—
524C4×SD16C2311yescharacteristic
525C4×SD16C2311yescharacteristic
526C4×SD16C2311yescharacteristic
527C4×SD16C2311yescharacteristic
528C4×SD16C2311yescharacteristic
529C4×SD16C2311yescharacteristic
530C4×D8—21no—
531C4×D8C2311yescharacteristic
532#436—21no—
533#436—21no—
534#436—21no—
535#436C2311yescharacteristic
536#436C2311yescharacteristic
537#436C2311yescharacteristic
538#436C2311yescharacteristic
539#436C2311yescharacteristic
540#435—21no—
541C8×D4—21no—
542C8×D4—21no—
543C8×D4C2311yescharacteristic
544C8×D4C2311yescharacteristic
545C8×D4C2311yescharacteristic
546#433—21no—
547#433—21no—
548#433—21no—
549#432C2311yescharacteristic
550#431—21no—
551#431C2311yescharacteristic
552#431C2311yescharacteristic
553#431C2311yescharacteristic
554#428—21no—
555#428—21no—
556#428—21no—
557#428—21no—
558#428—21no—
559#428—21no—
560#427—21no—
561#427—21no—
562#427—21no—
563C2×#107—21no—
564#424—21no—
565#423C2311yescharacteristic
566C2×C4⋊C8—21no—
567C2×C4⋊C8C2311yescharacteristic
568#418—21no—
569#418—21no—
570#418—21no—
571#418—21no—
572#417—21no—
573#417—21no—
574#417—41no—
575#416—21no—
576#416—21no—
577C2×#102—21no—
578C2×#102—21no—
579#407—21no—
580#407—21no—
581C4×M16C2311yescharacteristic
582#335C2311yescharacteristic
583#335C2311yescharacteristic
584#334C2311yescharacteristic
585#334C2311yescharacteristic
586#334C2311yescharacteristic
587#334C2311yescharacteristic
588#334C2311yescharacteristic
589#334C2311yescharacteristic
590#333C2311yescharacteristic
591#333C2311yescharacteristic
592#333C2311yescharacteristic
593#333C2311yescharacteristic
594#333C2311yescharacteristic
595#333C2311yescharacteristic
596#332C2311yescharacteristic
597#332C2311yescharacteristic
598#332C2311yescharacteristic
599#332C2311yescharacteristic
600#332C2311yescharacteristic
601#332C2311yescharacteristic
602#332C2311yescharacteristic
603#332C2311yescharacteristic
604#331C2311yescharacteristic
605#331C2311yescharacteristic
606Q8⋊C8C2311yescharacteristic
607Q8⋊C8C2311yescharacteristic
608Q8⋊C8C2311yescharacteristic
609Q8⋊C8C2311yescharacteristic
610Q8⋊C8C2311yescharacteristic
611Q8⋊C8C2311yescharacteristic
612Q8⋊C8C2311yescharacteristic
613Q8⋊C8C2311yescharacteristic
614D4⋊C8C2311yescharacteristic
615D4⋊C8C2311yescharacteristic
616D4⋊C8C2311yescharacteristic
617D4⋊C8C2311yescharacteristic
618D4⋊C8C2311yescharacteristic
619D4⋊C8C2311yescharacteristic
620D4⋊C8C2311yescharacteristic
621D4⋊C8C2311yescharacteristic
622#322C2311yescharacteristic
623#322C2311yescharacteristic
624#322C2311yescharacteristic
625C82C2311yescharacteristic
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41C2×D411yescharacteristic
630C22×Q8—21no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—41no—
634C22×D4C2×D411yescharacteristic
635C23×C4—21no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—41no—
646C2×Q16C2×D411yescharacteristic
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16C2×D411yescharacteristic
654C2×SD16C2×D411yescharacteristic
655C2×SD16C2×D411yescharacteristic
656C2×SD16C2×D411yescharacteristic
657C2×SD16C2×D411yescharacteristic
658C2×SD16C2×D411yescharacteristic
659C2×D8—21no—
660C2×D8C2×D411yescharacteristic
661C2×M16—21no—
662C2×M16—21no—
663C2×M16—21no—
664C2×M16—21no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16—21no—
668C22×C8—21no—
669C22×C8—21no—
670C22×C8—21no—
671C22×C8—21no—
672C4⋊Q8—21no—
673C4⋊Q8—21no—
674C4⋊Q8—21no—
675C4⋊Q8—21no—
676C4⋊Q8—21no—
677C4⋊Q8—21no—
678C4⋊Q8—21no—
679C4⋊Q8—21no—
680C4⋊Q8—41no—
681C4⋊Q8—41no—
682C4⋊Q8C2×D411yescharacteristic
683C4⋊Q8C2×D411yescharacteristic
684C4⋊Q8C2411yescharacteristic
685C4⋊Q8C2411yescharacteristic
686C4⋊Q8C2411yescharacteristic
687C4⋊Q8C2411yescharacteristic
688C4⋊Q8C2411yescharacteristic
689C4⋊Q8C2411yescharacteristic
690C4⋊Q8C2411yescharacteristic
691#127—21no—
692#127C2411yescharacteristic
693#126—21no—
694#126—41no—
695#126—41no—
696#126—41no—
697#126—41no—
698#126—41no—
699#126—41no—
700#126—41no—
701#126—41no—
702#126—41no—
703#126—41no—
704#126—41no—
705#126—41no—
706#126—41no—
707#126—41no—
708#125—21no—
709#125—21no—
710#125—21no—
711#125—21no—
712#125—21no—
713#125—21no—
714#125—21no—
715#125—21no—
716#125—21no—
717#125—41no—
718#125—41no—
719#125—41no—
720#125—41no—
721#125—41no—
722#125—41no—
723#125—41no—
724#125—41no—
725#125—41no—
726#125—41no—
727#125—41no—
728#125C2×D411yescharacteristic
729#124—21no—
730#124—21no—
731#124—21no—
732#124—21no—
733#124—21no—
734#124—41no—
735#124—41no—
736#124—41no—
737#124C2×D411yescharacteristic
738#123—21no—
739#123—41no—
740#123—41no—
741#123—41no—
742#123—41no—
743#123—41no—
744#123—41no—
745#123—41no—
746#123—41no—
747#123—41no—
748#123—41no—
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8—21no—
754C22⋊Q8—21no—
755C22⋊Q8—21no—
756C22⋊Q8—21no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—21no—
760C22⋊Q8—21no—
761C22⋊Q8—21no—
762C22⋊Q8—41no—
763C22⋊Q8—41no—
764C22⋊Q8—41no—
765C22⋊Q8—41no—
766C22⋊Q8—41no—
767C22⋊Q8—41no—
768C22⋊Q8—41no—
769C22⋊Q8—41no—
770C22⋊Q8C2×D411yescharacteristic
771C22⋊Q8C2×D411yescharacteristic
772C22⋊Q8C2×D411yescharacteristic
773#121—21no—
774#121—21no—
775#121—21no—
776#121—21no—
777#121—21no—
778#121—21no—
779#121—21no—
780#121—21no—
781#121—21no—
782#121—21no—
783#121—41no—
784#121—41no—
785#121—41no—
786#121—41no—
787#121—41no—
788#121—41no—
789#121C2×D411yescharacteristic
790#120—41no—
791#120—41no—
792#120—41no—
793#120—41no—
794C4×Q8—21no—
795C4×Q8—21no—
796C4×Q8—21no—
797C4×Q8—21no—
798C4×Q8—21no—
799C4×Q8—21no—
800C4×Q8—21no—
801C4×Q8—21no—
802C4×Q8—21no—
803C4×Q8—21no—
804C4×Q8—21no—
805C4×Q8—21no—
806C4×Q8—21no—
807C4×Q8—21no—
808C4×Q8—21no—
809C4×Q8—21no—
810C4×Q8—21no—
811C4×Q8—41no—
812C4×Q8—41no—
813C4×Q8—41no—
814C4×Q8—41no—
815C4×Q8C2×D411yescharacteristic
816C4×Q8C2411yescharacteristic
817C4×Q8C2411yescharacteristic
818C4×Q8C2411yescharacteristic
819C4×Q8C2411yescharacteristic
820C4×D4—21no—
821C4×D4—21no—
822C4×D4—21no—
823C4×D4—21no—
824C4×D4—21no—
825C4×D4—21no—
826C4×D4—21no—
827C4×D4—21no—
828C4×D4—21no—
829C4×D4—21no—
830C4×D4—21no—
831C4×D4—41no—
832C4×D4—41no—
833C4×D4—41no—
834C4×D4—41no—
835C4×D4—41no—
836C4×D4—41no—
837C4×D4C2×D411yescharacteristic
838C4×D4C2×D411yescharacteristic
839C4×D4C2×D411yescharacteristic
840C4×D4C2411yescharacteristic
841C4×D4C2411yescharacteristic
842C4×D4C2411yescharacteristic
843C4×D4C2411yescharacteristic
844#117—21no—
845#117—21no—
846#117—21no—
847#117—21no—
848#117—21no—
849#117—21no—
850#117—21no—
851#117—21no—
852#117—21no—
853#117—21no—
854#117—21no—
855#117—21no—
856#117—21no—
857#117—41no—
858#117—41no—
859#117—41no—
860#117—41no—
861#117—41no—
862#117—41no—
863#117—41no—
864#117C2×D411yescharacteristic
865C2×C4⋊C4—21no—
866C2×C4⋊C4—21no—
867C2×C4⋊C4—21no—
868C2×C4⋊C4—21no—
869C2×C4⋊C4—21no—
870C2×C4⋊C4—21no—
871C2×C4⋊C4C2×D411yescharacteristic
872C2×C22⋊C4—21no—
873C2×C22⋊C4—41no—
874C2×C22⋊C4—41no—
875C2×C22⋊C4—41no—
876C2×C42—21no—
877C2×C42—41no—
878C2×C42C2411yescharacteristic
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#107—21no—
894#107—21no—
895#107—21no—
896#107—21no—
897#107C2×D411yescharacteristic
898#107C2×D411yescharacteristic
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—
911#106—21no—
912#106—21no—
913#106—41no—
914#106C2×D411yescharacteristic
915#106C2×D411yescharacteristic
916#106C2×D411yescharacteristic
917#106C2×D411yescharacteristic
918#106C2×D411yescharacteristic
919#106C2×D411yescharacteristic
920C4⋊C8—21no—
921C4⋊C8—21no—
922C4⋊C8—21no—
923C4⋊C8—21no—
924C4⋊C8—21no—
925C4⋊C8—21no—
926C4⋊C8—21no—
927C4⋊C8—21no—
928C4⋊C8—21no—
929C4⋊C8—21no—
930C4⋊C8C2×D411yescharacteristic
931C4⋊C8C2×D411yescharacteristic
932C4⋊C8C2×D411yescharacteristic
933C4⋊C8C2×D411yescharacteristic
934C4⋊C8C2411yescharacteristic
935C4⋊C8C2411yescharacteristic
936C4⋊C8C2411yescharacteristic
937C4⋊C8C2411yescharacteristic
938C4⋊C8C2411yescharacteristic
939C4⋊C8C2411yescharacteristic
940C4⋊C8C2411yescharacteristic
941C4⋊C8C2411yescharacteristic
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#103—21no—
962#103—21no—
963#103—21no—
964#103—21no—
965#103—21no—
966#103—41no—
967#103—41no—
968#103—41no—
969#103—41no—
970#103C2×D411yescharacteristic
971#103C2×D411yescharacteristic
972#103C2×D411yescharacteristic
973#103C2×D411yescharacteristic
974#103C2×D411yescharacteristic
975#103C2×D411yescharacteristic
976#103C2×D411yescharacteristic
977#103C2×D411yescharacteristic
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—
995#102—21no—
996#102—21no—
997#102—21no—
998#102—21no—
999#102—21no—
1000#102—21no—
1001#102—21no—
1002#102—41no—
1003#102—41no—
1004#102C2×D411yescharacteristic
1005#102C2×D411yescharacteristic
1006#102C2×D411yescharacteristic
1007#102C2×D411yescharacteristic
1008#102C2×D411yescharacteristic
1009#102C2×D411yescharacteristic
1010#102C2×D411yescharacteristic
1011#102C2×D411yescharacteristic
1012C22⋊C8—21no—
1013C22⋊C8—21no—
1014C22⋊C8—21no—
1015C22⋊C8—21no—
1016C22⋊C8—21no—
1017C22⋊C8—21no—
1018C22⋊C8—21no—
1019C22⋊C8—21no—
1020C22⋊C8—21no—
1021C22⋊C8—21no—
1022C22⋊C8C2×D411yescharacteristic
1023C22⋊C8C2×D411yescharacteristic
1024C22⋊C8C2×D411yescharacteristic
1025C22⋊C8C2×D411yescharacteristic
1026#97—21no—
1027#97—21no—
1028#97—21no—
1029#97—21no—
1030#97—21no—
1031C4×C8—21no—
1032C4×C8—21no—
1033C4×C8—21no—
1034C4×C8—21no—
1035C4×C8—21no—
1036C4×C8—21no—
1037C4×C8C2411yescharacteristic
1038C4×C8C2411yescharacteristic
1039C4×C8C2411yescharacteristic
1040C4×C8C2411yescharacteristic
1041C4×C8C2411yescharacteristic
1042C4×C8C2411yescharacteristic
1043C24—21no—
1044C24—41no—
1045#41—41no—
1046#41—41no—
1047#41—42no—
1048#41—81no—
1049#41—81no—
1050#41—81no—
1051#41—82no—
1052C2×Q8—21no—
1053C2×Q8—21no—
1054C2×Q8—21no—
1055C2×Q8—21no—
1056C2×Q8—21no—
1057C2×Q8—21no—
1058C2×Q8—21no—
1059C2×Q8—21no—
1060C2×Q8—41no—
1061C2×Q8—41no—
1062C2×Q8—81no—
1063C2×Q8—81no—
1064C2×Q8C22×D411yescharacteristic
1065C2×Q8C22×D411yescharacteristic
1066C2×Q8C22×D411yescharacteristic
1067C2×Q8C22×D411yescharacteristic
1068C2×D4—21no—
1069C2×D4—21no—
1070C2×D4—21no—
1071C2×D4—21no—
1072C2×D4—21no—
1073C2×D4—21no—
1074C2×D4—41no—
1075C2×D4—41no—
1076C2×D4—41no—
1077C2×D4—41no—
1078C2×D4—41no—
1079C2×D4—41no—
1080C2×D4—42no—
1081C2×D4—41no—
1082C2×D4—41no—
1083C2×D4—41no—
1084C2×D4—41no—
1085C2×D4—81no—
1086C2×D4—81no—
1087C2×D4—81no—
1088C2×D4—162no—
1089C2×D4C22×D411yescharacteristic
1090C2×D4C22×D411yescharacteristic
1091C2×D4C22×D411yescharacteristic
1092C2×D4C22×D411yescharacteristic
1093C22×C4—21no—
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—41no—
1103C22×C4—41no—
1104C22×C4—41no—
1105C22×C4—41no—
1106C22×C4—41no—
1107C22×C4—41no—
1108C22×C4—41no—
1109C22×C4—81no—
1110C22×C4—81no—
1111C22×C4C22×D411yescharacteristic
1112C22×C4C22×D411yescharacteristic
1113C22×C4H(5,𝔽2)11yescharacteristic
1114Q16—41no—
1115Q16—81no—
1116Q16—81no—
1117Q16—81no—
1118Q16—81no—
1119Q16—81no—
1120Q16—81no—
1121Q16—81no—
1122Q16—81no—
1123Q16—81no—
1124Q16—82no—
1125SD16—41no—
1126SD16—41no—
1127SD16—41no—
1128SD16—41no—
1129SD16—41no—
1130SD16—41no—
1131SD16—81no—
1132SD16—81no—
1133SD16—81no—
1134SD16—81no—
1135SD16—81no—
1136SD16—81no—
1137D8—41no—
1138D8—81no—
1139M16—81no—
1140M16—81no—
1141M16—81no—
1142M16—81no—
1143M16—81no—
1144M16—81no—
1145M16—81no—
1146C2×C8—21no—
1147C2×C8—21no—
1148C2×C8—21no—
1149C2×C8—21no—
1150C2×C8—21no—
1151C2×C8—21no—
1152C2×C8—21no—
1153C2×C8—21no—
1154C2×C8—21no—
1155C2×C8—21no—
1156C2×C8—81no—
1157C2×C8—81no—
1158C2×C8—81no—
1159C2×C8—81no—
1160C2×C8C22×D411yescharacteristic
1161C2×C8C22×D411yescharacteristic
1162C2×C8C22×D411yescharacteristic
1163C2×C8C22×D411yescharacteristic
1164C2×C8C22×D411yescharacteristic
1165C2×C8C22×D411yescharacteristic
1166C2×C8C22×D411yescharacteristic
1167C2×C8C22×D411yescharacteristic
1168C4⋊C4—21no—
1169C4⋊C4—21no—
1170C4⋊C4—21no—
1171C4⋊C4—21no—
1172C4⋊C4—21no—
1173C4⋊C4—21no—
1174C4⋊C4—21no—
1175C4⋊C4—21no—
1176C4⋊C4—21no—
1177C4⋊C4—21no—
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—41no—
1197C4⋊C4—41no—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
1201C4⋊C4—41no—
1202C4⋊C4—41no—
1203C4⋊C4—41no—
1204C4⋊C4—41no—
1205C4⋊C4—41no—
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—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4C22×D411yescharacteristic
1225C4⋊C4C22×D411yescharacteristic
1226C4⋊C4C22×D411yescharacteristic
1227C4⋊C4C22×D411yescharacteristic
1228C4⋊C4C22×D411yescharacteristic
1229C4⋊C4C22×D411yescharacteristic
1230C4⋊C4C22×D411yescharacteristic
1231C4⋊C4C22×D411yescharacteristic
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—41no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4—41no—
1266C22⋊C4—41no—
1267C22⋊C4—41no—
1268C42—21no—
1269C42—21no—
1270C42—21no—
1271C42—21no—
1272C42—21no—
1273C42—21no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42—41no—
1279C42—41no—
1280C42—41no—
1281C42—41no—
1282C42—41no—
1283C42—41no—
1284C42—41no—
1285C42—41no—
1286C42C22×D411yescharacteristic
1287C42C22×D411yescharacteristic
1288C42H(5,𝔽2)11yescharacteristic
1289C42C2511yescharacteristic
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—41no—
1295C23—81no—
1296C23—81no—
1297C23—81no—
1298C23—82no—
1299C23—161no—
1300C23—161no—
1301C23D4211yescharacteristic
1302Q8—21no—
1303Q8—21no—
1304Q8—21no—
1305Q8—21no—
1306Q8—21no—
1307Q8—21no—
1308Q8—21no—
1309Q8—21no—
1310Q8—41no—
1311Q8—41no—
1312Q8—41no—
1313Q8—41no—
1314Q8—41no—
1315Q8—41no—
1316Q8—41no—
1317Q8—41no—
1318Q8—81no—
1319Q8—81no—
1320Q8—81no—
1321Q8—81no—
1322Q8—82no—
1323Q8—161no—
1324D4—21no—
1325D4—21no—
1326D4—21no—
1327D4—21no—
1328D4—21no—
1329D4—21no—
1330D4—21no—
1331D4—21no—
1332D4—42no—
1333D4—41no—
1334D4—41no—
1335D4—41no—
1336D4—41no—
1337D4—81no—
1338D4—81no—
1339D4—81no—
1340D4—82no—
1341D4—82no—
1342D4—82no—
1343D4—161no—
1344D4—161no—
1345D4—161no—
1346D4—161no—
1347D4—161no—
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—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—41no—
1365C2×C4—42no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—41no—
1376C2×C4—41no—
1377C2×C4—41no—
1378C2×C4—41no—
1379C2×C4—41no—
1380C2×C4—41no—
1381C2×C4—81no—
1382C2×C4—81no—
1383C2×C4—81no—
1384C2×C4—81no—
1385C2×C4—82no—
1386C2×C4—82no—
1387C2×C4—161no—
1388C2×C4—161no—
1389C2×C4—161no—
1390C2×C4—161no—
1391C2×C4—161no—
1392C2×C4D4211yescharacteristic
1393C2×C4D4211yescharacteristic
1394C2×C4D4211yescharacteristic
1395C2×C4C23×D411yescharacteristic
1396C2×C4C23×D411yescharacteristic
1397C2×C4C2×H(5,𝔽2)11yescharacteristic
1398C8—21no—
1399C8—21no—
1400C8—21no—
1401C8—21no—
1402C8—21no—
1403C8—21no—
1404C8—21no—
1405C8—21no—
1406C8—41no—
1407C8—41no—
1408C8—41no—
1409C8—41no—
1410C8—41no—
1411C8—41no—
1412C8—41no—
1413C8—41no—
1414C8—41no—
1415C8—41no—
1416C22—21no—
1417C22—21no—
1418C22—21no—
1419C22—41no—
1420C22—41no—
1421C22—41no—
1422C22—41no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—81no—
1432C22—81no—
1433C22—81no—
1434C22—162no—
1435C22—322no—
1436C22C2×D4211yescharacteristic
1437C4—21no—
1438C4—21no—
1439C4—21no—
1440C4—21no—
1441C4—41no—
1442C4—41no—
1443C4—41no—
1444C4—41no—
1445C4—41no—
1446C4—41no—
1447C4—41no—
1448C4—41no—
1449C4—41no—
1450C4—41no—
1451C4—41no—
1452C4—41no—
1453C4—81no—
1454C4—81no—
1455C4—81no—
1456C4—81no—
1457C4—81no—
1458C4—81no—
1459C4—81no—
1460C4#358411yescharacteristic
1461C4#358411yescharacteristic
1462C4#358611yescharacteristic
1463C4#358611yescharacteristic
1464C2—41no—
1465C2—81no—
1466C2—81no—
1467C2—81no—
1468C2—81no—
1469C2—161no—
1470C2#6105211yescharacteristic
1471C2#6106411yescharacteristic
1472C2#6110911yescharacteristic
subgroupG/H
center, socleC22C2×D42
commutator, Frattini, cosocleC42C25
prime radical#61725C2
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. #62188C2semidirect
2. #62097C2semidirect
3. #61922C2semidirect
5. #20267C2semidirect
6. #20257C2semidirect
7. #20231C2semidirect
8. #20229C2semidirect
9. #20145C2semidirect
10. #20133C2semidirect
11. #20118C2semidirect
12. #20100C2semidirect
13. #19950C2semidirect
14. #19950C2semidirect
15. #19923C2semidirect
16. #19913C2semidirect
17. #19881C2semidirect
18. #19878C2semidirect
19. #19829C2semidirect
20. #19823C2semidirect
21. #19716C2semidirect
22. #19545C2semidirect
23. #19532C2semidirect
24. #19423C2semidirect
25. #19419C2semidirect
26. #18745C2semidirect
27. #18584C2semidirect
28. #18571C2semidirect
29. #18561C2semidirect
30. #17952C2semidirect
31. #17927C2semidirect
34. #3509C22semidirect
38. #3398C22semidirect
39. #3398C22semidirect
40. #3395C22semidirect
41. #3393C22semidirect
44. #3381C22semidirect
45. #3381C22semidirect
48. #3372C22semidirect
49. #3369C22semidirect
53. #3363C22semidirect
55. #3360C22semidirect
79. #3302C22semidirect
80. #3302C22semidirect
86. #3249C22semidirect
91. #3229C22semidirect
97. #3209C22semidirect
100. #3185C22semidirect
105. #3116C22semidirect
117. #2988C22semidirect
118. #2985C22semidirect
120. #1723C22semidirect
121. #1720C22semidirect
122. #1720C22semidirect
123. #1720C22semidirect
124. #1718C22semidirect
125. #1716C22semidirect
126. #1711C22semidirect
127. #1707C22semidirect
130. #1703C22semidirect
131. #1703C22semidirect
132. #1702C22semidirect
133. #1702C22semidirect
134. #1700C22semidirect
135. #1699C22semidirect
136. #1696C22semidirect
137. #1696C22semidirect
138. #1692C22semidirect
139. #1691C22semidirect
142. #1689C22semidirect
143. #1689C22semidirect
144. #1682C22semidirect
145. #1681C22semidirect
146. #1680C22semidirect
147. #1679C22semidirect
148. #1678C22semidirect
149. #1678C22semidirect
150. #1678C22semidirect
151. #1677C22semidirect
152. #1676C22semidirect
153. #1675C22semidirect
154. #1672C22semidirect
155. #1672C22semidirect
156. #1672C22semidirect
157. #1672C22semidirect
158. #1671C22semidirect
159. #1671C22semidirect
160. #1654C22semidirect
161. #1653C22semidirect
163. #1652C22semidirect
167. #1645C22semidirect
170. #1644C22semidirect
171. #1644C22semidirect
177. #1638C22semidirect
178. #1638C22semidirect
179. #1638C22semidirect
180. #1636C22semidirect
181. #1636C22semidirect
182. #1636C22semidirect
183. #1635C22semidirect
185. #1633C22semidirect
186. #1632C22semidirect
187. #1632C22semidirect
188. #1628C22semidirect
189. #1628C22semidirect
190. #1626C22semidirect
191. #1626C22semidirect
193. #1592C22semidirect
195. #1590C22semidirect
197. #1588C22semidirect
198. #1587C22semidirect
199. #1586C22semidirect
201. #1583C22semidirect
202. #1583C22semidirect
203. #1582C22semidirect
204. #1580C22semidirect
205. #1579C22semidirect
206. C8×SD16C22semidirect
207. C8×SD16C22semidirect
208. #1572C22semidirect
209. #1570C22semidirect
210. #1559C22semidirect
212. #1549C22semidirect
213. #1542C22semidirect
215. #1489C22semidirect
216. #1485C22semidirect
218. #1453C22semidirect

Maximal subgroups

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

subgroupindex
#621882
#620972
#619222
#617252
#202672
#202572
#202312
#202292
#201452
#201332
#201182
#201002
#199502
#199232
#199132
#198812
#198782
#198292
#198232
#197162
#195452
#195322
#194232
#194192
#187452
#185842
#185712
#185612
#179522
#179272