Finite Group Databasebeta

← #6356403

Subgroups — #6356403

Order 512.

1483 conjugacy classes of subgroups.

The subgroup lattice has 1473 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62544C211yesmaximal, characteristic, complemented
2#60995C211yesmaximal, characteristic, complemented
3#60994C211yesmaximal, characteristic
4#60339C211yesmaximal, characteristic, complemented
5#19589C211yesmaximal, characteristic, complemented
6#19585C211yesmaximal, characteristic, complemented
7#19581C211yesmaximal, characteristic, complemented
8#19577C211yesmaximal, characteristic, complemented
9#19574C211yesmaximal, characteristic, complemented
10#19570C211yesmaximal, characteristic, complemented
11#19568C211yesmaximal, characteristic, complemented
12#19564C211yesmaximal, characteristic, complemented
13#19455C211yesmaximal, characteristic, complemented
14#19449C211yesmaximal, characteristic, complemented
15#19406C211yesmaximal, characteristic, complemented
16#19400C211yesmaximal, characteristic, complemented
17#19383C211yesmaximal, characteristic, complemented
18#19380C211yesmaximal, characteristic, complemented
19#19375C211yesmaximal, characteristic, complemented
20#19373C211yesmaximal, characteristic, complemented
21#19288C211yesmaximal, characteristic, complemented
22#19278C211yesmaximal, characteristic, complemented
23#19253C211yesmaximal, characteristic, complemented
24#19251C211yesmaximal, characteristic, complemented
25#19245C211yesmaximal, characteristic, complemented
26#19242C211yesmaximal, characteristic, complemented
27#19155C211yesmaximal, characteristic, complemented
28#19127C211yesmaximal, characteristic, complemented
29#17833C211yesmaximal, characteristic, complemented
30#17725C211yesmaximal, characteristic, complemented
31#17724C211yesmaximal, characteristic, complemented
32#3509C2211yescharacteristic
33#3508C2211yescharacteristic
34#3461C2211yescharacteristic
35#3371—21no—
36#3371—21no—
37#3323—21no—
38#3323—21no—
39#3317—21no—
40#3317—21no—
41#3311—21no—
42#3311—21no—
43#3255C2211yescharacteristic
44#3254C2211yescharacteristic
45#3252C2211yescharacteristic
46#3251C2211yescharacteristic
47#3249C2211yescharacteristic
48#3248C2211yescharacteristic
49#3247C2211yescharacteristic
50#3246C2211yescharacteristic
51#3242—21no—
52#3241—21no—
53#3237C2211yescharacteristic
54#3237C2211yescharacteristic, complemented
55#3233C2211yescharacteristic
56#3233C2211yescharacteristic, complemented
57#3231C2211yescharacteristic
58#3228C2211yescharacteristic
59#3227C2211yescharacteristic
60#3223—21no—
61#3221—21no—
62#3218C2211yescharacteristic, complemented
63#3217C2211yescharacteristic
64#3210C2211yescharacteristic
65#3210C2211yescharacteristic
66#3209C2211yescharacteristic, complemented
67#3208C2211yescharacteristic
68#3208C2211yescharacteristic
69#3202—21no—
70#3201—21no—
71#3200—21no—
72#3198—21no—
73#3185C2211yescharacteristic
74#3182C2211yescharacteristic
75#3179—21no—
76#3178—21no—
77#3177—21no—
78#3174—21no—
79#3167C2211yescharacteristic
80#3141C2211yescharacteristic
81#3138C2211yescharacteristic
82#3131C2211yescharacteristic
83#3127—21no—
84#3123—21no—
85#3121—21no—
86#3118—21no—
87#3116C2211yescharacteristic, complemented
88#3115C2211yescharacteristic
89#3113C2211yescharacteristic, complemented
90#3112C2211yescharacteristic
91#3107C2211yescharacteristic, complemented
92#3106C2211yescharacteristic
93#3104C2211yescharacteristic, complemented
94#3103C2211yescharacteristic
95#2994—21no—
96#2994—21no—
97#2994C2211yescharacteristic
98#2994C2211yescharacteristic, complemented
99#2993—21no—
100#2989C2211yescharacteristic, complemented
101#2988C2211yescharacteristic
102#2986C2211yescharacteristic
103#2986C2211yescharacteristic, complemented
104#2985—21no—
105#2982C2211yescharacteristic, complemented
106#2969C2211yescharacteristic
107#2969C2211yescharacteristic, complemented
108#2968—21no—
109#2968—21no—
110#2966—21no—
111#2965C2211yescharacteristic
112C8×#41C2211yescharacteristic, complemented
113#2962C2211yescharacteristic
114#2962C2211yescharacteristic, complemented
115#2960—21no—
116C2×#446C2211yescharacteristic, complemented
117#2925C2211yescharacteristic
118#2925C2211yescharacteristic
119#1704C2211yescharacteristic, complemented
120#1704C2211yescharacteristic, complemented
121#1704C2211yescharacteristic, complemented
122#1704C2211yescharacteristic, complemented
123#1702C2211yescharacteristic
124#1702C2211yescharacteristic
125#1702C2211yescharacteristic
126#1702C2211yescharacteristic
127#1702C2211yescharacteristic
128#1702C2211yescharacteristic
129#1701C2211yescharacteristic
130#1701C2211yescharacteristic
131#1700C2211yescharacteristic, complemented
132#1700C2211yescharacteristic, complemented
133#1700C2211yescharacteristic, complemented
134#1699C2211yescharacteristic, complemented
135#1698C2211yescharacteristic
136#1698C2211yescharacteristic
137#1698C2211yescharacteristic
138#1697C2211yescharacteristic
139#1696C2211yescharacteristic, complemented
140#1695C2211yescharacteristic, complemented
141#1692C2211yescharacteristic, complemented
142#1692C2211yescharacteristic, complemented
143#1692C2211yescharacteristic, complemented
144#1691C2211yescharacteristic, complemented
145#1690C2211yescharacteristic, complemented
146#1689C2211yescharacteristic, complemented
147#1686C2211yescharacteristic
148#1686C2211yescharacteristic
149#1686C2211yescharacteristic
150#1685C2211yescharacteristic
151#1684C2211yescharacteristic, complemented
152#1684C2211yescharacteristic, complemented
153#1683C2211yescharacteristic, complemented
154#1683C2211yescharacteristic, complemented
155#1682C2211yescharacteristic
156#1682C2211yescharacteristic
157#1682C2211yescharacteristic
158#1682C2211yescharacteristic
159#1682C2211yescharacteristic
160#1682C2211yescharacteristic
161#1681C2211yescharacteristic
162#1681C2211yescharacteristic
163#1680C2211yescharacteristic, complemented
164#1680C2211yescharacteristic, complemented
165#1680C2211yescharacteristic, complemented
166#1679C2211yescharacteristic, complemented
167#1678C2211yescharacteristic
168#1678C2211yescharacteristic
169#1678C2211yescharacteristic
170#1677C2211yescharacteristic
171#1676C2211yescharacteristic, complemented
172#1676C2211yescharacteristic, complemented
173#1672C2211yescharacteristic, complemented
174#1672C2211yescharacteristic, complemented
175#1672C2211yescharacteristic, complemented
176#1671C2211yescharacteristic, complemented
177#1670C2211yescharacteristic, complemented
178#1670C2211yescharacteristic, complemented
179#1666C2211yescharacteristic
180#1666C2211yescharacteristic
181#1666C2211yescharacteristic
182#1665C2211yescharacteristic
183#1574C2211yescharacteristic
184#1574C2211yescharacteristic, complemented
185#1573C2211yescharacteristic
186#1573C2211yescharacteristic, complemented
187#1572C2211yescharacteristic, complemented
188#1572C2211yescharacteristic, complemented
189#1569C2211yescharacteristic
190#1569C2211yescharacteristic, complemented
191#1568C2211yescharacteristic, complemented
192#1565C2211yescharacteristic
193#1565C2211yescharacteristic, complemented
194#1564C2211yescharacteristic, complemented
195#1554C2211yescharacteristic
196#1554C2211yescharacteristic, complemented
197#1553C2211yescharacteristic
198#1553C2211yescharacteristic
199#1552C2211yescharacteristic
200#1552C2211yescharacteristic, complemented
201#1551C2211yescharacteristic
202#1551C2211yescharacteristic
203#1550C2211yescharacteristic
204#1550C2211yescharacteristic, complemented
205#1546C2211yescharacteristic, complemented
206#1545C2211yescharacteristic
207#1544C2211yescharacteristic
208#1544C2211yescharacteristic, complemented
209#1543C2211yescharacteristic
210#1543C2211yescharacteristic
211#1542C2211yescharacteristic
212#1542C2211yescharacteristic
213#1542C2211yescharacteristic, complemented
214#1542C2211yescharacteristic, complemented
215#1540C2211yescharacteristic
216#1540C2211yescharacteristic
217C2×#332C2211yescharacteristic, complemented
218C2×#331C2211yescharacteristic
219#559—21no—
220#559—21no—
221#557—21no—
222#557—21no—
223#556—21no—
224#556—21no—
225#552—21no—
226#552—21no—
227#552—21no—
228#552—21no—
229#550—21no—
230#550—21no—
231#546—21no—
232#546—21no—
233#546—21no—
234#546—21no—
235#544D411yescharacteristic
236#542—21no—
237#542D411yescharacteristic
238#542D411yescharacteristic
239#541—21no—
240#541—21no—
241#541—21no—
242#541D411yescharacteristic
243#541D411yescharacteristic
244#540—21no—
245#540—21no—
246#539—21no—
247#539—21no—
248#537D411yescharacteristic
249#536—21no—
250#536D411yescharacteristic
251#536D411yescharacteristic
252#535—21no—
253#533—21no—
254#533C2311yescharacteristic
255#533C2311yescharacteristic
256#533C2311yescharacteristic
257#533C2311yescharacteristic
258#533C2311yescharacteristic
259#533C2311yescharacteristic
260#533C2311yescharacteristic
261#533C2311yescharacteristic
262#532C2311yescharacteristic
263#532C2311yescharacteristic
264#532C2311yescharacteristic
265#532C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×#127C2311yescharacteristic
268#529—21no—
269#529—21no—
270#529—21no—
271#529C2311yescharacteristic
272#529C2311yescharacteristic
273#519—21no—
274#518—21no—
275C4×#41C2311yescharacteristic
276C4×#41C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278#501—21no—
279#501—21no—
280#500C2311yescharacteristic
281#499—21no—
282#499—21no—
283#498C2311yescharacteristic
284#498C2311yescharacteristic
285#497—21no—
286#496—21no—
287#494—21no—
288#494C2311yescharacteristic
289#492—21no—
290#492C2311yescharacteristic
291#492C2311yescharacteristic
292#491—21no—
293#491—21no—
294#491—21no—
295#490—21no—
296#490—21no—
297#490—21no—
298#489—21no—
299#489—21no—
300#488—21no—
301#488—21no—
302#488—21no—
303#488—21no—
304#487—21no—
305#487C2311yescharacteristic
306#487C2311yescharacteristic
307#487C2311yescharacteristic
308#487C2311yescharacteristic
309#486—21no—
310#486C2311yescharacteristic
311#486C2311yescharacteristic
312#486C2311yescharacteristic
313#486C2311yescharacteristic
314#486C2311yescharacteristic
315#486C2311yescharacteristic
316#485—21no—
317#485—21no—
318#485—21no—
319#485—21no—
320#485—21no—
321#485—21no—
322#485—21no—
323#485—21no—
324#485—21no—
325#485—21no—
326#484—21no—
327#483—21no—
328#482—21no—
329#482—21no—
330#482—21no—
331#482—21no—
332#482—21no—
333#482—21no—
334#481—21no—
335#481—21no—
336#481—21no—
337#480—21no—
338#479—21no—
339#479—21no—
340#479—21no—
341#479—21no—
342#478—21no—
343#478—21no—
344#478—21no—
345#478—21no—
346#477—21no—
347#477C2311yescharacteristic
348#477C2311yescharacteristic
349#477C2311yescharacteristic
350#477C2311yescharacteristic
351#477C2311yescharacteristic
352#477C2311yescharacteristic
353#476—21no—
354#476—21no—
355#476—21no—
356#476C2311yescharacteristic
357#476C2311yescharacteristic
358#475—21no—
359#475C2311yescharacteristic
360#475C2311yescharacteristic
361#475C2311yescharacteristic
362#475C2311yescharacteristic
363#475C2311yescharacteristic
364#475C2311yescharacteristic
365#474—21no—
366#474C2311yescharacteristic
367#474C2311yescharacteristic
368#470—21no—
369#470—21no—
370#470—21no—
371#470—21no—
372#470—21no—
373#469—21no—
374#468—21no—
375#468—21no—
376#468—21no—
377#468—21no—
378#468—21no—
379#468—21no—
380#467—21no—
381#467—21no—
382#467—21no—
383#466—21no—
384#465—21no—
385#465—21no—
386#465—21no—
387#465—21no—
388#465—21no—
389#465—21no—
390#464—21no—
391#464—21no—
392#464—21no—
393#464—21no—
394#464—21no—
395#464—21no—
396#463—21no—
397#463—21no—
398#462—21no—
399#462—21no—
400#462C2311yescharacteristic
401#462C2311yescharacteristic
402#462C2311yescharacteristic
403#462C2311yescharacteristic
404#462C2311yescharacteristic
405#462C2311yescharacteristic
406#461—21no—
407#461—21no—
408#461C2311yescharacteristic
409#461C2311yescharacteristic
410#460—21no—
411#460—21no—
412#460C2311yescharacteristic
413#460C2311yescharacteristic
414#460C2311yescharacteristic
415#460C2311yescharacteristic
416#460C2311yescharacteristic
417#460C2311yescharacteristic
418#459C2311yescharacteristic
419#459C2311yescharacteristic
420#452—21no—
421#452—21no—
422#452—21no—
423#452—21no—
424#452—21no—
425#452—21no—
426#451—21no—
427#451—21no—
428#451—21no—
429#451—21no—
430#451—21no—
431#450—21no—
432#450—21no—
433#450—21no—
434#450—21no—
435#450—21no—
436#449—21no—
437#449—21no—
438#448—21no—
439#448—21no—
440#448—21no—
441#447—21no—
442#446—21no—
443#446—21no—
444#446—21no—
445#446—21no—
446#446—21no—
447#446—21no—
448#446—21no—
449#446—21no—
450#446D411yescharacteristic
451#446D411yescharacteristic
452#446C2311yescharacteristic
453#446C2311yescharacteristic
454#446C2311yescharacteristic
455#446C2311yescharacteristic
456#446C2311yescharacteristic
457#446C2311yescharacteristic
458C8×Q8—21no—
459C8×Q8—21no—
460C8×Q8—21no—
461C8×Q8—21no—
462C8×Q8—21no—
463C8×Q8C2311yescharacteristic
464C8×Q8C2311yescharacteristic
465C8×Q8C2311yescharacteristic
466C8×Q8C2311yescharacteristic
467C8×Q8C2311yescharacteristic
468C8×Q8C2311yescharacteristic
469#442—21no—
470#441—21no—
471#441—21no—
472#441—21no—
473#441—21no—
474#441—21no—
475#440—21no—
476#440—21no—
477#440—21no—
478#440—21no—
479#440—21no—
480#440—21no—
481C4×Q16—21no—
482C4×Q16—21no—
483C4×Q16—21no—
484C4×SD16—21no—
485C4×SD16—21no—
486C4×SD16—21no—
487C4×SD16—21no—
488C4×SD16—21no—
489C4×SD16—21no—
490C4×D8—21no—
491#436—21no—
492#436—21no—
493#436D411yescharacteristic
494#436D411yescharacteristic
495#436C2311yescharacteristic
496#436C2311yescharacteristic
497#435—21no—
498#435—21no—
499#435—21no—
500#435—21no—
501#435—21no—
502#435—21no—
503#435D411yescharacteristic
504#435D411yescharacteristic
505#435D411yescharacteristic
506#435D411yescharacteristic
507C8×D4—21no—
508C8×D4—21no—
509C8×D4—21no—
510C8×D4—21no—
511C8×D4—21no—
512C8×D4—21no—
513C8×D4—21no—
514C8×D4C2311yescharacteristic
515C8×D4C2311yescharacteristic
516#433—21no—
517#433—21no—
518#433—21no—
519#433—21no—
520#433—21no—
521#433—21no—
522#433—21no—
523#433—21no—
524#433—21no—
525#433—21no—
526#433—21no—
527#433—21no—
528#432—21no—
529#432C2311yescharacteristic
530#432C2311yescharacteristic
531#432C2311yescharacteristic
532#432C2311yescharacteristic
533#431—21no—
534#431—21no—
535#431—21no—
536#431C2311yescharacteristic
537#431C2311yescharacteristic
538#431C2311yescharacteristic
539#431C2311yescharacteristic
540#431C2311yescharacteristic
541#431C2311yescharacteristic
542#431C2311yescharacteristic
543#431C2311yescharacteristic
544#431C2311yescharacteristic
545#431C2311yescharacteristic
546#424—21no—
547#424—21no—
548#424—21no—
549#424—21no—
550#423—21no—
551#423C2311yescharacteristic
552#423C2311yescharacteristic
553C2×C4⋊C8—21no—
554C2×C4⋊C8C2311yescharacteristic
555C2×C4⋊C8C2311yescharacteristic
556C2×C4⋊C8C2311yescharacteristic
557C2×C4⋊C8C2311yescharacteristic
558C2×C4⋊C8C2311yescharacteristic
559#418—21no—
560#418—21no—
561#417—21no—
562#417—21no—
563#416—21no—
564#416—21no—
565#408—21no—
566#408—21no—
567#405—21no—
568#405—21no—
569#405—21no—
570#405—21no—
571#405—21no—
572#405—21no—
573C4×M16C2311yescharacteristic
574C4×M16C2311yescharacteristic
575C2×#97—21no—
576C2×C4×C8—21no—
577C2×C4×C8C2311yescharacteristic
578#335C2311yescharacteristic
579#335C2311yescharacteristic
580#335C2311yescharacteristic
581#335C2311yescharacteristic
582#335C2311yescharacteristic
583#335C2311yescharacteristic
584#335C2311yescharacteristic
585#335C2311yescharacteristic
586#334C2311yescharacteristic
587#334C2311yescharacteristic
588#334C2311yescharacteristic
589#334C2311yescharacteristic
590#334C2311yescharacteristic
591#334C2311yescharacteristic
592#334C2311yescharacteristic
593#334C2311yescharacteristic
594#333C2311yescharacteristic
595#333C2311yescharacteristic
596#333C2311yescharacteristic
597#333C2311yescharacteristic
598#333C2311yescharacteristic
599#333C2311yescharacteristic
600#333C2311yescharacteristic
601#333C2311yescharacteristic
602#332C2311yescharacteristic
603#332C2311yescharacteristic
604#332C2311yescharacteristic
605#332C2311yescharacteristic
606#332C2311yescharacteristic
607#332C2311yescharacteristic
608#332C2311yescharacteristic
609#332C2311yescharacteristic
610#332C2311yescharacteristic
611#332C2311yescharacteristic
612#332C2311yescharacteristic
613#332C2311yescharacteristic
614#332C2311yescharacteristic
615#332C2311yescharacteristic
616#332C2311yescharacteristic
617#332C2311yescharacteristic
618#331C2311yescharacteristic
619#331C2311yescharacteristic
620#331C2311yescharacteristic
621#331C2311yescharacteristic
622#331C2311yescharacteristic
623#331C2311yescharacteristic
624#331C2311yescharacteristic
625#331C2311yescharacteristic
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41C2×D411yescharacteristic
631C2×#41C2×D411yescharacteristic
632C22×Q8—21no—
633C22×Q8C2×D411yescharacteristic
634C22×D4—21no—
635C22×D4—21no—
636C22×D4—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×SD16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
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×D8—21no—
658C2×D8—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16—21no—
662C2×M16—21no—
663C2×M16C2×D411yescharacteristic
664C2×M16C2×D411yescharacteristic
665C2×M16C2×D411yescharacteristic
666C2×M16C2×D411yescharacteristic
667C22×C8—21no—
668C22×C8—21no—
669C22×C8—21no—
670C22×C8—21no—
671C22×C8—21no—
672C22×C8—21no—
673C22×C8—21no—
674C22×C8C2×D411yescharacteristic
675C22×C8C2×D411yescharacteristic
676C4⋊Q8—21no—
677C4⋊Q8—21no—
678C4⋊Q8—21no—
679C4⋊Q8—21no—
680C4⋊Q8—21no—
681C4⋊Q8—41no—
682C4⋊Q8C2×D411yescharacteristic
683C4⋊Q8C2×D411yescharacteristic
684C4⋊Q8C2×D411yescharacteristic
685C4⋊Q8C2×D411yescharacteristic
686C4⋊Q8C2411yescharacteristic
687C4⋊Q8C2411yescharacteristic
688C4⋊Q8C2411yescharacteristic
689C4⋊Q8C2411yescharacteristic
690C4⋊Q8C2411yescharacteristic
691C4⋊Q8C2411yescharacteristic
692#127—21no—
693#127—21no—
694#127—21no—
695#127—41no—
696#127C2411yescharacteristic
697#127C2411yescharacteristic
698#126—21no—
699#126—21no—
700#126—21no—
701#126—21no—
702#126—21no—
703#126—21no—
704#126—21no—
705#126—21no—
706#126—41no—
707#126—41no—
708#126—41no—
709#126—41no—
710#125—21no—
711#125—21no—
712#125—21no—
713#125—21no—
714#125—21no—
715#125—21no—
716#125—21no—
717#125—21no—
718#125—21no—
719#125—21no—
720#125—21no—
721#125—21no—
722#125—21no—
723#125—41no—
724#125—41no—
725#125—41no—
726#125—41no—
727#125C2×D411yescharacteristic
728#125C2×D411yescharacteristic
729#124—21no—
730#124—21no—
731#124—21no—
732#124—21no—
733#124—21no—
734#124—21no—
735#124—21no—
736#124—41no—
737#124—41no—
738#124C2×D411yescharacteristic
739#124C2×D411yescharacteristic
740#123—21no—
741#123—21no—
742#123—21no—
743#123—21no—
744#123—21no—
745#123—21no—
746#123—21no—
747#123—21no—
748#123—41no—
749#123—41no—
750#123—41no—
751#123—41no—
752#123—41no—
753#123—41no—
754C22⋊Q8—21no—
755C22⋊Q8—21no—
756C22⋊Q8—21no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—21no—
760C22⋊Q8—21no—
761C22⋊Q8—21no—
762C22⋊Q8—21no—
763C22⋊Q8—21no—
764C22⋊Q8—21no—
765C22⋊Q8—21no—
766C22⋊Q8—21no—
767C22⋊Q8—21no—
768C22⋊Q8—21no—
769C22⋊Q8—21no—
770C22⋊Q8—21no—
771C22⋊Q8—21no—
772C22⋊Q8—21no—
773C22⋊Q8—21no—
774C22⋊Q8—21no—
775C22⋊Q8C2×D411yescharacteristic
776C22⋊Q8C2×D411yescharacteristic
777C22⋊Q8C2×D411yescharacteristic
778C22⋊Q8C2×D411yescharacteristic
779C22⋊Q8C2×D411yescharacteristic
780C22⋊Q8C2×D411yescharacteristic
781#121—21no—
782#121—21no—
783#121—21no—
784#121—21no—
785#121—21no—
786#121—21no—
787#121—21no—
788#121—21no—
789#121—21no—
790#121—21no—
791#121—21no—
792#121—41no—
793#121—41no—
794#121—41no—
795#121—41no—
796#121C2×D411yescharacteristic
797#121C2×D411yescharacteristic
798#120—41no—
799#120—41no—
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—21no—
812C4×Q8—21no—
813C4×Q8—21no—
814C4×Q8—21no—
815C4×Q8—21no—
816C4×Q8—41no—
817C4×Q8—41no—
818C4×Q8C2×D411yescharacteristic
819C4×Q8C2×D411yescharacteristic
820C4×Q8C2×D411yescharacteristic
821C4×Q8C2×D411yescharacteristic
822C4×Q8#4111yescharacteristic
823C4×Q8C2411yescharacteristic
824C4×Q8C2411yescharacteristic
825C4×Q8C2411yescharacteristic
826C4×D4—21no—
827C4×D4—21no—
828C4×D4—21no—
829C4×D4—21no—
830C4×D4—21no—
831C4×D4—21no—
832C4×D4—21no—
833C4×D4—21no—
834C4×D4—21no—
835C4×D4—21no—
836C4×D4—21no—
837C4×D4—21no—
838C4×D4—41no—
839C4×D4—41no—
840C4×D4C2×D411yescharacteristic
841C4×D4C2×D411yescharacteristic
842C4×D4C2×D411yescharacteristic
843C4×D4C2×D411yescharacteristic
844C4×D4#4111yescharacteristic
845C4×D4#4111yescharacteristic
846C4×D4#4111yescharacteristic
847C4×D4C2411yescharacteristic
848#117—21no—
849#117—21no—
850#117—21no—
851#117—21no—
852#117—21no—
853#117—21no—
854#117—21no—
855#117—21no—
856#117—21no—
857#117—21no—
858#117—21no—
859#117—41no—
860#117—41no—
861#117C2×D411yescharacteristic
862#117C2×D411yescharacteristic
863#117C2×D411yescharacteristic
864#117C2×D411yescharacteristic
865C2×C4⋊C4—21no—
866C2×C4⋊C4—21no—
867C2×C4⋊C4—21no—
868C2×C4⋊C4C2×D411yescharacteristic
869C2×C22⋊C4—41no—
870C2×C22⋊C4—41no—
871C2×C42—21no—
872C2×C42—21no—
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
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#106—21no—
887#106—21no—
888#106—21no—
889#106—21no—
890#106—21no—
891#106—21no—
892#106—21no—
893#106—21no—
894#106—21no—
895#106—21no—
896#106—21no—
897#106—21no—
898C4⋊C8—21no—
899C4⋊C8—21no—
900C4⋊C8—21no—
901C4⋊C8—21no—
902C4⋊C8—21no—
903C4⋊C8—21no—
904C4⋊C8—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⋊C8C2×D411yescharacteristic
918C4⋊C8C2×D411yescharacteristic
919C4⋊C8C2×D411yescharacteristic
920C4⋊C8C2×D411yescharacteristic
921C4⋊C8C2×D411yescharacteristic
922C4⋊C8C2×D411yescharacteristic
923C4⋊C8C2411yescharacteristic
924C4⋊C8C2411yescharacteristic
925C4⋊C8C2411yescharacteristic
926C4⋊C8C2411yescharacteristic
927C4⋊C8C2411yescharacteristic
928C4⋊C8C2411yescharacteristic
929C4⋊C8C2411yescharacteristic
930C4⋊C8C2411yescharacteristic
931C4⋊C8C2411yescharacteristic
932C4⋊C8C2411yescharacteristic
933C4⋊C8C2411yescharacteristic
934C4⋊C8C2411yescharacteristic
935#103—21no—
936#103—21no—
937#103—21no—
938#103—21no—
939#103—21no—
940#103—21no—
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#103—21no—
962#103—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—
987C22⋊C8—21no—
988C22⋊C8—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⋊C8C2×D411yescharacteristic
1003C22⋊C8C2×D411yescharacteristic
1004C22⋊C8C2×D411yescharacteristic
1005C22⋊C8C2×D411yescharacteristic
1006C22⋊C8C2×D411yescharacteristic
1007C22⋊C8C2×D411yescharacteristic
1008#97—21no—
1009#97—21no—
1010#97—21no—
1011#97—21no—
1012#97—21no—
1013#97—21no—
1014#97—21no—
1015#97—21no—
1016#97—21no—
1017#97—21no—
1018#97C2×D411yescharacteristic
1019#97C2×D411yescharacteristic
1020#97C2×D411yescharacteristic
1021#97C2×D411yescharacteristic
1022C4×C8—21no—
1023C4×C8—21no—
1024C4×C8—21no—
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—41no—
1042#41—41no—
1043#41—41no—
1044#41—41no—
1045#41—41no—
1046#41—81no—
1047#41—81no—
1048#41—81no—
1049#41—81no—
1050#41—161no—
1051#41—161no—
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—21no—
1061C2×Q8—41no—
1062C2×Q8—41no—
1063C2×Q8—41no—
1064C2×Q8—81no—
1065C2×Q8—81no—
1066C2×Q8#12111yescharacteristic
1067C2×Q8C22×D411yescharacteristic
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—41no—
1080C2×D4—41no—
1081C2×D4—41no—
1082C2×D4—41no—
1083C2×D4—41no—
1084C2×D4—41no—
1085C2×D4—41no—
1086C2×D4—81no—
1087C2×D4—81no—
1088C2×D4—81no—
1089C2×D4—81no—
1090C2×D4—161no—
1091C2×D4#12111yescharacteristic
1092C2×D4#12111yescharacteristic
1093C2×D4#12111yescharacteristic
1094C2×D4C22×D411yescharacteristic
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—21no—
1100C22×C4—41no—
1101C22×C4—41no—
1102C22×C4—41no—
1103C22×C4—41no—
1104C22×C4—41no—
1105C22×C4C22×D411yescharacteristic
1106C22×C4C22×D411yescharacteristic
1107C22×C4C22×D411yescharacteristic
1108C22×C4C22×D411yescharacteristic
1109C22×C4C22×D411yescharacteristic
1110C22×C4C22×D411yescharacteristic
1111C22×C4C2×#4111yescharacteristic
1112C22×C4C2×#4111yescharacteristic
1113C22×C4C2×#4111yescharacteristic
1114Q16—81no—
1115Q16—81no—
1116Q16—81no—
1117Q16—81no—
1118Q16—81no—
1119Q16—81no—
1120Q16—81no—
1121Q16—81no—
1122SD16—81no—
1123SD16—81no—
1124SD16—81no—
1125SD16—81no—
1126SD16—81no—
1127SD16—81no—
1128SD16—81no—
1129SD16—81no—
1130SD16—81no—
1131SD16—81no—
1132SD16—81no—
1133SD16—81no—
1134D8—81no—
1135D8—81no—
1136M16—41no—
1137M16—41no—
1138M16—41no—
1139M16—41no—
1140M16—81no—
1141M16—81no—
1142M16—81no—
1143M16—81no—
1144C2×C8—21no—
1145C2×C8—21no—
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—41no—
1157C2×C8—41no—
1158C2×C8—42no—
1159C2×C8—81no—
1160C2×C8—81no—
1161C2×C8—81no—
1162C2×C8—81no—
1163C2×C8—81no—
1164C2×C8—81no—
1165C2×C8C22×D411yescharacteristic
1166C2×C8C22×D411yescharacteristic
1167C2×C8C22×D411yescharacteristic
1168C2×C8C22×D411yescharacteristic
1169C2×C8C22×D411yescharacteristic
1170C2×C8C22×D411yescharacteristic
1171C2×C8C22×D411yescharacteristic
1172C2×C8C22×D411yescharacteristic
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—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—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#12111yescharacteristic
1223C4⋊C4#12111yescharacteristic
1224C4⋊C4#12111yescharacteristic
1225C4⋊C4#12111yescharacteristic
1226C4⋊C4#12111yescharacteristic
1227C4⋊C4#12111yescharacteristic
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—21no—
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#12111yescharacteristic
1262C22⋊C4#12111yescharacteristic
1263C22⋊C4#12111yescharacteristic
1264C22⋊C4#12111yescharacteristic
1265C22⋊C4#12111yescharacteristic
1266C22⋊C4#12111yescharacteristic
1267C42—21no—
1268C42—21no—
1269C42—21no—
1270C42—21no—
1271C42—21no—
1272C42—21no—
1273C42—21no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42—41no—
1279C42—41no—
1280C42C22×D411yescharacteristic
1281C42C22×D411yescharacteristic
1282C42C22×D411yescharacteristic
1283C42C22×D411yescharacteristic
1284C42C22×D411yescharacteristic
1285C42C22×D411yescharacteristic
1286C42C2×#4111yescharacteristic
1287C42C2×#4111yescharacteristic
1288C42C2×#4111yescharacteristic
1289C42C2511yescharacteristic
1290C23—21no—
1291C23—41no—
1292C23—41no—
1293C23—82no—
1294C23—161no—
1295C23—161no—
1296C23C2×#12111yescharacteristic
1297C23C2×#12111yescharacteristic
1298C23C2×#12111yescharacteristic
1299Q8—21no—
1300Q8—21no—
1301Q8—21no—
1302Q8—21no—
1303Q8—21no—
1304Q8—21no—
1305Q8—41no—
1306Q8—42no—
1307Q8—41no—
1308Q8—41no—
1309Q8—41no—
1310Q8—41no—
1311Q8—41no—
1312Q8—41no—
1313Q8—41no—
1314Q8—41no—
1315Q8—81no—
1316Q8—81no—
1317Q8—81no—
1318Q8—81no—
1319Q8—82no—
1320D4—21no—
1321D4—21no—
1322D4—41no—
1323D4—41no—
1324D4—41no—
1325D4—42no—
1326D4—41no—
1327D4—41no—
1328D4—41no—
1329D4—41no—
1330D4—41no—
1331D4—41no—
1332D4—41no—
1333D4—41no—
1334D4—81no—
1335D4—81no—
1336D4—82no—
1337D4—81no—
1338D4—81no—
1339D4—161no—
1340D4—161no—
1341D4—161no—
1342D4—161no—
1343D4—161no—
1344D4—161no—
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—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—42no—
1368C2×C4—42no—
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—81no—
1378C2×C4—81no—
1379C2×C4—82no—
1380C2×C4—161no—
1381C2×C4—161no—
1382C2×C4—161no—
1383C2×C4—161no—
1384C2×C4C2×#12111yescharacteristic
1385C2×C4C2×#12111yescharacteristic
1386C2×C4C2×#12111yescharacteristic
1387C2×C4C2×#12111yescharacteristic
1388C2×C4C2×#12111yescharacteristic
1389C2×C4C2×#12111yescharacteristic
1390C2×C4C2×#12111yescharacteristic
1391C2×C4C2×#12111yescharacteristic
1392C2×C4C2×#12111yescharacteristic
1393C2×C4C23×D411yescharacteristic
1394C2×C4C23×D411yescharacteristic
1395C2×C4C22×#4111yescharacteristic
1396C8—21no—
1397C8—21no—
1398C8—21no—
1399C8—21no—
1400C8—21no—
1401C8—21no—
1402C8—21no—
1403C8—21no—
1404C8—41no—
1405C8—41no—
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—21no—
1420C22—21no—
1421C22—21no—
1422C22—21no—
1423C22—21no—
1424C22—21no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—81no—
1429C22—81no—
1430C22—81no—
1431C22—81no—
1432C22—81no—
1433C22—81no—
1434C22—322no—
1435C22C22×#12111yescharacteristic
1436C4—21no—
1437C4—21no—
1438C4—21no—
1439C4—21no—
1440C4—21no—
1441C4—21no—
1442C4—21no—
1443C4—21no—
1444C4—21no—
1445C4—21no—
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#358411yescharacteristic
1460C4#358411yescharacteristic
1461C4#358411yescharacteristic
1462C4#358611yescharacteristic
1463C2—41no—
1464C2—41no—
1465C2—41no—
1466C2—81no—
1467C2—161no—
1468C2—161no—
1469C2#6043311yescharacteristic
1470C2#6045311yescharacteristic
1471C2#6047011yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
prime radical#60994C2
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. #62544C2semidirect
2. #60995C2semidirect
4. #60339C2semidirect
5. #19589C2semidirect
6. #19585C2semidirect
7. #19581C2semidirect
8. #19577C2semidirect
9. #19574C2semidirect
10. #19570C2semidirect
11. #19568C2semidirect
12. #19564C2semidirect
13. #19455C2semidirect
14. #19449C2semidirect
15. #19406C2semidirect
16. #19400C2semidirect
17. #19383C2semidirect
18. #19380C2semidirect
19. #19375C2semidirect
20. #19373C2semidirect
21. #19288C2semidirect
22. #19278C2semidirect
23. #19253C2semidirect
24. #19251C2semidirect
25. #19245C2semidirect
26. #19242C2semidirect
27. #19155C2semidirect
28. #19127C2semidirect
29. #17833C2semidirect
30. #17725C2semidirect
31. #17724C2semidirect
54. #3237C22semidirect
56. #3233C22semidirect
62. #3218C22semidirect
66. #3209C22semidirect
87. #3116C22semidirect
89. #3113C22semidirect
91. #3107C22semidirect
93. #3104C22semidirect
98. #2994C22semidirect
100. #2989C22semidirect
103. #2986C22semidirect
105. #2982C22semidirect
107. #2969C22semidirect
112. C8×#41C22semidirect
114. #2962C22semidirect
116. C2×#446C22semidirect
119. #1704C22semidirect
120. #1704C22semidirect
121. #1704C22semidirect
122. #1704C22semidirect
131. #1700C22semidirect
132. #1700C22semidirect
133. #1700C22semidirect
134. #1699C22semidirect
139. #1696C22semidirect
140. #1695C22semidirect
141. #1692C22semidirect
142. #1692C22semidirect
143. #1692C22semidirect
144. #1691C22semidirect
145. #1690C22semidirect
146. #1689C22semidirect
151. #1684C22semidirect
152. #1684C22semidirect
153. #1683C22semidirect
154. #1683C22semidirect
163. #1680C22semidirect
164. #1680C22semidirect
165. #1680C22semidirect
166. #1679C22semidirect
171. #1676C22semidirect
172. #1676C22semidirect
173. #1672C22semidirect
174. #1672C22semidirect
175. #1672C22semidirect
176. #1671C22semidirect
177. #1670C22semidirect
178. #1670C22semidirect
184. #1574C22semidirect
186. #1573C22semidirect
187. #1572C22semidirect
188. #1572C22semidirect
190. #1569C22semidirect
191. #1568C22semidirect
193. #1565C22semidirect
194. #1564C22semidirect
196. #1554C22semidirect
200. #1552C22semidirect
204. #1550C22semidirect
205. #1546C22semidirect
208. #1544C22semidirect
213. #1542C22semidirect
214. #1542C22semidirect
217. C2×#332C22semidirect

Maximal subgroups

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

subgroupindex
#625442
#609952
#609942
#603392
#195892
#195852
#195812
#195772
#195742
#195702
#195682
#195642
#194552
#194492
#194062
#194002
#193832
#193802
#193752
#193732
#192882
#192782
#192532
#192512
#192452
#192422
#191552
#191272
#178332
#177252
#177242