Finite Group Databasebeta

← #6356531

Subgroups — #6356531

Order 512.

1493 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#62544C211yesmaximal, characteristic, complemented
2#60994C211yesmaximal, characteristic
3#60925C211yesmaximal, characteristic, complemented
4#60344C211yesmaximal, characteristic, complemented
5#19587C211yesmaximal, characteristic, complemented
6#19581C211yesmaximal, characteristic, complemented
7#19574C211yesmaximal, characteristic, complemented
8#19564C211yesmaximal, characteristic, complemented
9#19551C211yesmaximal, characteristic, complemented
10#19541C211yesmaximal, characteristic, complemented
11#19532C211yesmaximal, characteristic, complemented
12#19527C211yesmaximal, characteristic, complemented
13#19501C211yesmaximal, characteristic, complemented
14#19493C211yesmaximal, characteristic, complemented
15#19474C211yesmaximal, characteristic, complemented
16#19472C211yesmaximal, characteristic, complemented
17#19380C211yesmaximal, characteristic, complemented
18#19375C211yesmaximal, characteristic, complemented
19#19366C211yesmaximal, characteristic, complemented
20#19343C211yesmaximal, characteristic, complemented
21#19319C211yesmaximal, characteristic, complemented
22#19309C211yesmaximal, characteristic, complemented
23#19251C211yesmaximal, characteristic, complemented
24#19242C211yesmaximal, characteristic, complemented
25#19229C211yesmaximal, characteristic, complemented
26#19217C211yesmaximal, characteristic, complemented
27#19179C211yesmaximal, characteristic, complemented
28#19177C211yesmaximal, characteristic, complemented
29#17832C211yesmaximal, characteristic, complemented
30#17767C211yesmaximal, characteristic, complemented
31#17762C211yesmaximal, 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#3261—21no—
44#3261—21no—
45#3258—21no—
46#3258—21no—
47#3255C2211yescharacteristic
48#3255C2211yescharacteristic, complemented
49#3254C2211yescharacteristic
50#3252C2211yescharacteristic
51#3252C2211yescharacteristic, complemented
52#3251C2211yescharacteristic
53#3249C2211yescharacteristic
54#3249C2211yescharacteristic, complemented
55#3248C2211yescharacteristic
56#3248C2211yescharacteristic, complemented
57#3247C2211yescharacteristic
58#3246C2211yescharacteristic
59#3241—21no—
60#3237C2211yescharacteristic
61#3233C2211yescharacteristic
62#3231C2211yescharacteristic
63#3228C2211yescharacteristic
64#3227C2211yescharacteristic
65#3221—21no—
66#3217C2211yescharacteristic
67#3210C2211yescharacteristic
68#3210C2211yescharacteristic
69#3208C2211yescharacteristic
70#3208C2211yescharacteristic
71#3200—21no—
72#3198—21no—
73#3185C2211yescharacteristic
74#3182C2211yescharacteristic
75#3179—21no—
76#3174—21no—
77#3167C2211yescharacteristic
78#3141C2211yescharacteristic
79#3138C2211yescharacteristic
80#3131C2211yescharacteristic
81#3123—21no—
82#3118—21no—
83#3115C2211yescharacteristic
84#3112C2211yescharacteristic
85#3106C2211yescharacteristic
86#3103C2211yescharacteristic
87#3082—21no—
88#3078C2211yescharacteristic, complemented
89#3076C2211yescharacteristic, complemented
90#3063—21no—
91#3059—21no—
92#3044—21no—
93#3039C2211yescharacteristic, complemented
94C2×#462C2211yescharacteristic, complemented
95#2995—21no—
96#2995—21no—
97#2994C2211yescharacteristic
98#2993—21no—
99#2993C2211yescharacteristic, complemented
100#2991C2211yescharacteristic, complemented
101#2989C2211yescharacteristic
102#2986C2211yescharacteristic
103#2985—21no—
104#2985C2211yescharacteristic, complemented
105#2984C2211yescharacteristic, complemented
106#2970C2211yescharacteristic, complemented
107#2969—21no—
108#2969C2211yescharacteristic
109#2968—21no—
110#2967—21no—
111#2966C2211yescharacteristic, complemented
112#2965C2211yescharacteristic
113Q8×M16C2211yescharacteristic, complemented
114#2962C2211yescharacteristic
115#2961—21no—
116#2960C2211yescharacteristic, complemented
117#2925C2211yescharacteristic
118#2906C2211yescharacteristic
119#1704C2211yescharacteristic, complemented
120#1704C2211yescharacteristic, complemented
121#1704C2211yescharacteristic, complemented
122#1703C2211yescharacteristic, 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#1700C2211yescharacteristic, complemented
135#1698C2211yescharacteristic
136#1698C2211yescharacteristic
137#1698C2211yescharacteristic
138#1697C2211yescharacteristic
139#1696C2211yescharacteristic, complemented
140#1696C2211yescharacteristic, complemented
141#1692C2211yescharacteristic, complemented
142#1692C2211yescharacteristic, complemented
143#1691C2211yescharacteristic, 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#1684C2211yescharacteristic, 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#1679C2211yescharacteristic, complemented
166#1679C2211yescharacteristic, complemented
167#1678C2211yescharacteristic
168#1678C2211yescharacteristic
169#1678C2211yescharacteristic
170#1677C2211yescharacteristic
171#1676C2211yescharacteristic, complemented
172#1675C2211yescharacteristic, complemented
173#1672C2211yescharacteristic, complemented
174#1672C2211yescharacteristic, complemented
175#1672C2211yescharacteristic, complemented
176#1672C2211yescharacteristic, 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#1571C2211yescharacteristic, complemented
188#1570C2211yescharacteristic, complemented
189#1569C2211yescharacteristic
190#1569C2211yescharacteristic, complemented
191#1566C2211yescharacteristic, complemented
192#1565C2211yescharacteristic
193#1565C2211yescharacteristic, complemented
194C2×#335C2211yescharacteristic, complemented
195#1561C2211yescharacteristic, complemented
196#1560C2211yescharacteristic
197#1560C2211yescharacteristic
198#1559C2211yescharacteristic, complemented
199#1559C2211yescharacteristic, complemented
200#1557C2211yescharacteristic
201#1557C2211yescharacteristic
202#1556C2211yescharacteristic, complemented
203#1554C2211yescharacteristic
204#1554C2211yescharacteristic, complemented
205#1552C2211yescharacteristic
206#1552C2211yescharacteristic, complemented
207#1551C2211yescharacteristic
208#1551C2211yescharacteristic
209#1550C2211yescharacteristic
210#1550C2211yescharacteristic, complemented
211#1549C2211yescharacteristic, complemented
212#1547C2211yescharacteristic
213#1547C2211yescharacteristic
214#1545C2211yescharacteristic
215#1544C2211yescharacteristic
216#1542C2211yescharacteristic
217#1542C2211yescharacteristic
218C2×#331C2211yescharacteristic
219C2×#137—21no—
220C22×Q16—21no—
221C2×#131—21no—
222#559—21no—
223#559—21no—
224#557—21no—
225#557—21no—
226#556—21no—
227#556—21no—
228#552—21no—
229#552—21no—
230#552—21no—
231#552—21no—
232#550—21no—
233#550—21no—
234#546—21no—
235#546—21no—
236#546—21no—
237#546—21no—
238#544D411yescharacteristic
239#542—21no—
240#542D411yescharacteristic
241#542D411yescharacteristic
242#541—21no—
243#541—21no—
244#541—21no—
245#541D411yescharacteristic
246#541D411yescharacteristic
247#540—21no—
248#540—21no—
249#539—21no—
250#539—21no—
251#537D411yescharacteristic
252#536—21no—
253#536D411yescharacteristic
254#536D411yescharacteristic
255#535—21no—
256#533—21no—
257#533C2311yescharacteristic
258#533C2311yescharacteristic
259#533C2311yescharacteristic
260#533C2311yescharacteristic
261#533C2311yescharacteristic
262#533C2311yescharacteristic
263#533C2311yescharacteristic
264#533C2311yescharacteristic
265#532C2311yescharacteristic
266#532C2311yescharacteristic
267#532C2311yescharacteristic
268#532C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2311yescharacteristic
271#529—21no—
272#529—21no—
273#529—21no—
274#529C2311yescharacteristic
275#529C2311yescharacteristic
276#519—21no—
277#518—21no—
278C4×#41C2311yescharacteristic
279C4×#41C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281#501—21no—
282#500C2311yescharacteristic
283#499—21no—
284#498C2311yescharacteristic
285#498C2311yescharacteristic
286#496—21no—
287#494C2311yescharacteristic
288#492—21no—
289#492C2311yescharacteristic
290#492C2311yescharacteristic
291#491—21no—
292#490—21no—
293#490—21no—
294#490—21no—
295#489—21no—
296#489—21no—
297#488—21no—
298#488—21no—
299#488—21no—
300#487C2311yescharacteristic
301#487C2311yescharacteristic
302#487C2311yescharacteristic
303#487C2311yescharacteristic
304#486—21no—
305#486C2311yescharacteristic
306#486C2311yescharacteristic
307#486C2311yescharacteristic
308#486C2311yescharacteristic
309#486C2311yescharacteristic
310#486C2311yescharacteristic
311#485—21no—
312#485—21no—
313#485—21no—
314#485—21no—
315#485—21no—
316#482—21no—
317#482—21no—
318#482—21no—
319#482—21no—
320#482—21no—
321#481—21no—
322#481—21no—
323#481—21no—
324#480—21no—
325#479—21no—
326#479—21no—
327#479—21no—
328#479—21no—
329#479—21no—
330#479—21no—
331#479—21no—
332#479—21no—
333#479—21no—
334#478—21no—
335#478—21no—
336#478—21no—
337#478—21no—
338#478—21no—
339#477—21no—
340#477—21no—
341#477C2311yescharacteristic
342#477C2311yescharacteristic
343#477C2311yescharacteristic
344#477C2311yescharacteristic
345#477C2311yescharacteristic
346#477C2311yescharacteristic
347#476—21no—
348#476—21no—
349#476—21no—
350#476C2311yescharacteristic
351#476C2311yescharacteristic
352#475—21no—
353#475—21no—
354#475C2311yescharacteristic
355#475C2311yescharacteristic
356#475C2311yescharacteristic
357#475C2311yescharacteristic
358#475C2311yescharacteristic
359#475C2311yescharacteristic
360#474—21no—
361#474C2311yescharacteristic
362#474C2311yescharacteristic
363#470—21no—
364#470—21no—
365#470—21no—
366#470—21no—
367#470—21no—
368#470—21no—
369#470—21no—
370#470—21no—
371#469—21no—
372#468—21no—
373#468—21no—
374#468—21no—
375#468—21no—
376#468—21no—
377#468—21no—
378#468—21no—
379#467—21no—
380#467—21no—
381#467—21no—
382#467—21no—
383#467—21no—
384#467—21no—
385#466—21no—
386#465—21no—
387#465—21no—
388#465—21no—
389#465—21no—
390#465—21no—
391#465—21no—
392#465—21no—
393#464—21no—
394#464—21no—
395#464—21no—
396#464—21no—
397#464—21no—
398#464—21no—
399#464—21no—
400#464—21no—
401#463—21no—
402#463—21no—
403#462—21no—
404#462—21no—
405#462—21no—
406#462—21no—
407#462—21no—
408#462—21no—
409#462—21no—
410#462C2311yescharacteristic
411#462C2311yescharacteristic
412#462C2311yescharacteristic
413#462C2311yescharacteristic
414#462C2311yescharacteristic
415#462C2311yescharacteristic
416#461—21no—
417#461—21no—
418#461—21no—
419#461C2311yescharacteristic
420#461C2311yescharacteristic
421#460—21no—
422#460—21no—
423#460C2311yescharacteristic
424#460C2311yescharacteristic
425#460C2311yescharacteristic
426#460C2311yescharacteristic
427#460C2311yescharacteristic
428#460C2311yescharacteristic
429#459C2311yescharacteristic
430#459C2311yescharacteristic
431#452—21no—
432#452—21no—
433#452—21no—
434#452—21no—
435#450—21no—
436#450—21no—
437#450—21no—
438#450—21no—
439#450—21no—
440#449—21no—
441#449—21no—
442#448—21no—
443#448—21no—
444#447—21no—
445#446—21no—
446#446—21no—
447#446—21no—
448#446—21no—
449#446—21no—
450#446—21no—
451#446—21no—
452#446—21no—
453#446—21no—
454#446—21no—
455#446—21no—
456#446D411yescharacteristic
457#446D411yescharacteristic
458#446C2311yescharacteristic
459#446C2311yescharacteristic
460#446C2311yescharacteristic
461#446C2311yescharacteristic
462#446C2311yescharacteristic
463#446C2311yescharacteristic
464C8×Q8—21no—
465C8×Q8—21no—
466C8×Q8C2311yescharacteristic
467C8×Q8C2311yescharacteristic
468C8×Q8C2311yescharacteristic
469C8×Q8C2311yescharacteristic
470C8×Q8C2311yescharacteristic
471C8×Q8C2311yescharacteristic
472#442—21no—
473#441—21no—
474#441—21no—
475#440—21no—
476#440—21no—
477#440—21no—
478#440—21no—
479#440—21no—
480C4×SD16—21no—
481C4×SD16—21no—
482C4×SD16—21no—
483C4×SD16—21no—
484C4×SD16—21no—
485C4×D8—21no—
486#436—21no—
487#436—21no—
488#436—21no—
489#436—21no—
490#436—21no—
491#436D411yescharacteristic
492#436D411yescharacteristic
493#436C2311yescharacteristic
494#436C2311yescharacteristic
495#435—21no—
496#435—21no—
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×D4C2311yescharacteristic
510C8×D4C2311yescharacteristic
511#433—21no—
512#433—21no—
513#433—21no—
514#433—21no—
515#433—21no—
516#433—21no—
517#433—21no—
518#433—21no—
519#433—21no—
520#433—21no—
521#432—21no—
522#432—21no—
523#432C2311yescharacteristic
524#432C2311yescharacteristic
525#432C2311yescharacteristic
526#432C2311yescharacteristic
527#431—21no—
528#431—21no—
529#431C2311yescharacteristic
530#431C2311yescharacteristic
531#431C2311yescharacteristic
532#431C2311yescharacteristic
533#431C2311yescharacteristic
534#431C2311yescharacteristic
535#428—21no—
536#427—21no—
537#424—21no—
538#424—21no—
539#424—21no—
540#424—21no—
541#424—21no—
542#424—21no—
543#424—21no—
544#423—21no—
545#423—21no—
546#423C2311yescharacteristic
547#423C2311yescharacteristic
548#423C2311yescharacteristic
549#423C2311yescharacteristic
550#423C2311yescharacteristic
551#423C2311yescharacteristic
552C2×C4⋊C8C2311yescharacteristic
553C2×C4⋊C8C2311yescharacteristic
554C2×C4⋊C8C2311yescharacteristic
555C2×C4⋊C8C2311yescharacteristic
556C2×C4⋊C8C2311yescharacteristic
557#419—21no—
558#419—21no—
559#418—21no—
560#418—21no—
561#417—21no—
562#417—21no—
563#416—21no—
564#416—21no—
565#416—21no—
566C2×#103—21no—
567#408—21no—
568#405—21no—
569#405—21no—
570#405—21no—
571#405—21no—
572#405—21no—
573C4×M16—21no—
574C4×M16C2311yescharacteristic
575C4×M16C2311yescharacteristic
576C2×#97—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—
637#137—82no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×Q16—82no—
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×SD16—21no—
658C2×SD16—21no—
659C2×D8—21no—
660C2×D8—21no—
661#131—82no—
662C2×M16—21no—
663C2×M16—21no—
664C2×M16—21no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16—21no—
668C2×M16—21no—
669C2×M16—21no—
670C2×M16C2×D411yescharacteristic
671C2×M16C2×D411yescharacteristic
672C2×M16C2×D411yescharacteristic
673C2×M16C2×D411yescharacteristic
674C22×C8—21no—
675C22×C8—21no—
676C22×C8—21no—
677C22×C8—21no—
678C22×C8—21no—
679C22×C8—21no—
680C22×C8—21no—
681C22×C8C2×D411yescharacteristic
682C22×C8C2×D411yescharacteristic
683C4⋊Q8—21no—
684C4⋊Q8—21no—
685C4⋊Q8—21no—
686C4⋊Q8—21no—
687C4⋊Q8—21no—
688C4⋊Q8—41no—
689C4⋊Q8C2×D411yescharacteristic
690C4⋊Q8C2×D411yescharacteristic
691C4⋊Q8C2×D411yescharacteristic
692C4⋊Q8C2×D411yescharacteristic
693C4⋊Q8C2411yescharacteristic
694C4⋊Q8C2411yescharacteristic
695C4⋊Q8C2411yescharacteristic
696C4⋊Q8C2411yescharacteristic
697C4⋊Q8C2411yescharacteristic
698C4⋊Q8C2411yescharacteristic
699#127—21no—
700#127—21no—
701#127—21no—
702#127—41no—
703#127C2411yescharacteristic
704#127C2411yescharacteristic
705#126—21no—
706#126—21no—
707#126—21no—
708#126—21no—
709#126—21no—
710#126—21no—
711#126—21no—
712#126—21no—
713#126—41no—
714#126—41no—
715#126—41no—
716#126—41no—
717#125—21no—
718#125—21no—
719#125—21no—
720#125—21no—
721#125—21no—
722#125—21no—
723#125—21no—
724#125—21no—
725#125—21no—
726#125—21no—
727#125—21no—
728#125—21no—
729#125—21no—
730#125—41no—
731#125—41no—
732#125—41no—
733#125—41no—
734#125C2×D411yescharacteristic
735#125C2×D411yescharacteristic
736#124—21no—
737#124—21no—
738#124—21no—
739#124—21no—
740#124—21no—
741#124—21no—
742#124—21no—
743#124—41no—
744#124—41no—
745#124C2×D411yescharacteristic
746#124C2×D411yescharacteristic
747#123—21no—
748#123—21no—
749#123—21no—
750#123—21no—
751#123—21no—
752#123—21no—
753#123—21no—
754#123—21no—
755#123—41no—
756#123—41no—
757#123—41no—
758#123—41no—
759#123—41no—
760#123—41no—
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⋊Q8—21no—
776C22⋊Q8—21no—
777C22⋊Q8—21no—
778C22⋊Q8—21no—
779C22⋊Q8—21no—
780C22⋊Q8—21no—
781C22⋊Q8—21no—
782C22⋊Q8C2×D411yescharacteristic
783C22⋊Q8C2×D411yescharacteristic
784C22⋊Q8C2×D411yescharacteristic
785C22⋊Q8C2×D411yescharacteristic
786C22⋊Q8C2×D411yescharacteristic
787C22⋊Q8C2×D411yescharacteristic
788#121—21no—
789#121—21no—
790#121—21no—
791#121—21no—
792#121—21no—
793#121—21no—
794#121—21no—
795#121—21no—
796#121—21no—
797#121—21no—
798#121—21no—
799#121—41no—
800#121—41no—
801#121—41no—
802#121—41no—
803#121C2×D411yescharacteristic
804#121C2×D411yescharacteristic
805#120—41no—
806#120—41no—
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—21no—
817C4×Q8—21no—
818C4×Q8—21no—
819C4×Q8—21no—
820C4×Q8—21no—
821C4×Q8—21no—
822C4×Q8—21no—
823C4×Q8—41no—
824C4×Q8—41no—
825C4×Q8C2×D411yescharacteristic
826C4×Q8C2×D411yescharacteristic
827C4×Q8C2×D411yescharacteristic
828C4×Q8C2×D411yescharacteristic
829C4×Q8#4111yescharacteristic
830C4×Q8C2411yescharacteristic
831C4×Q8C2411yescharacteristic
832C4×Q8C2411yescharacteristic
833C4×D4—21no—
834C4×D4—21no—
835C4×D4—21no—
836C4×D4—21no—
837C4×D4—21no—
838C4×D4—21no—
839C4×D4—21no—
840C4×D4—21no—
841C4×D4—21no—
842C4×D4—21no—
843C4×D4—21no—
844C4×D4—21no—
845C4×D4—41no—
846C4×D4—41no—
847C4×D4C2×D411yescharacteristic
848C4×D4C2×D411yescharacteristic
849C4×D4C2×D411yescharacteristic
850C4×D4C2×D411yescharacteristic
851C4×D4#4111yescharacteristic
852C4×D4#4111yescharacteristic
853C4×D4#4111yescharacteristic
854C4×D4C2411yescharacteristic
855#117—21no—
856#117—21no—
857#117—21no—
858#117—21no—
859#117—21no—
860#117—21no—
861#117—21no—
862#117—21no—
863#117—21no—
864#117—21no—
865#117—21no—
866#117—41no—
867#117—41no—
868#117C2×D411yescharacteristic
869#117C2×D411yescharacteristic
870#117C2×D411yescharacteristic
871#117C2×D411yescharacteristic
872C2×C4⋊C4—21no—
873C2×C4⋊C4—21no—
874C2×C4⋊C4—21no—
875C2×C4⋊C4C2×D411yescharacteristic
876C2×C22⋊C4—41no—
877C2×C22⋊C4—41no—
878C2×C42—21no—
879C2×C42—21no—
880C2×C42C2411yescharacteristic
881C2×C42C2411yescharacteristic
882C2×C42C2411yescharacteristic
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⋊C8—21no—
922C4⋊C8—21no—
923C4⋊C8—21no—
924C4⋊C8—21no—
925C4⋊C8—21no—
926C4⋊C8—21no—
927C4⋊C8—21no—
928C4⋊C8C2×D411yescharacteristic
929C4⋊C8C2×D411yescharacteristic
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
942C4⋊C8C2411yescharacteristic
943C4⋊C8C2411yescharacteristic
944C4⋊C8C2411yescharacteristic
945C4⋊C8C2411yescharacteristic
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—21no—
967#103—21no—
968#103—21no—
969#103—21no—
970#103—21no—
971#103—21no—
972#103—21no—
973#103—21no—
974#102—21no—
975#102—21no—
976#102—21no—
977#102—21no—
978#102—21no—
979#102—21no—
980#102—21no—
981#102—21no—
982#102—21no—
983#102—21no—
984#102—21no—
985#102—21no—
986#102—21no—
987#102—21no—
988#102—21no—
989#102—21no—
990#102—21no—
991#102—21no—
992#102—21no—
993#102—21no—
994#102—21no—
995#102—21no—
996#102—21no—
997#102—21no—
998C22⋊C8—21no—
999C22⋊C8—21no—
1000C22⋊C8—21no—
1001C22⋊C8—21no—
1002C22⋊C8—21no—
1003C22⋊C8—21no—
1004C22⋊C8—21no—
1005C22⋊C8—21no—
1006C22⋊C8—21no—
1007C22⋊C8—21no—
1008C22⋊C8—21no—
1009C22⋊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#97—21no—
1024#97—21no—
1025#97C2×D411yescharacteristic
1026#97C2×D411yescharacteristic
1027#97C2×D411yescharacteristic
1028#97C2×D411yescharacteristic
1029C4×C8—21no—
1030C4×C8—21no—
1031C4×C8—21no—
1032C4×C8—21no—
1033C4×C8—21no—
1034C4×C8—21no—
1035C4×C8—21no—
1036C4×C8—21no—
1037C4×C8—21no—
1038C4×C8C2×D411yescharacteristic
1039C4×C8C2×D411yescharacteristic
1040C4×C8C2411yescharacteristic
1041C4×C8C2411yescharacteristic
1042C4×C8C2411yescharacteristic
1043C4×C8C2411yescharacteristic
1044C24—41no—
1045#41—41no—
1046#41—41no—
1047#41—41no—
1048#41—41no—
1049#41—81no—
1050#41—81no—
1051#41—81no—
1052#41—81no—
1053#41—161no—
1054#41—161no—
1055C2×Q8—21no—
1056C2×Q8—21no—
1057C2×Q8—21no—
1058C2×Q8—21no—
1059C2×Q8—21no—
1060C2×Q8—21no—
1061C2×Q8—21no—
1062C2×Q8—21no—
1063C2×Q8—21no—
1064C2×Q8—41no—
1065C2×Q8—41no—
1066C2×Q8—42no—
1067C2×Q8—42no—
1068C2×Q8—41no—
1069C2×Q8#12111yescharacteristic
1070C2×Q8C22×D411yescharacteristic
1071C2×Q8C22×D411yescharacteristic
1072C2×Q8C22×D411yescharacteristic
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—21no—
1082C2×D4—41no—
1083C2×D4—41no—
1084C2×D4—41no—
1085C2×D4—41no—
1086C2×D4—41no—
1087C2×D4—41no—
1088C2×D4—41no—
1089C2×D4—81no—
1090C2×D4—81no—
1091C2×D4—81no—
1092C2×D4—81no—
1093C2×D4—161no—
1094C2×D4#12111yescharacteristic
1095C2×D4#12111yescharacteristic
1096C2×D4#12111yescharacteristic
1097C2×D4C22×D411yescharacteristic
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×C4C22×D411yescharacteristic
1109C22×C4C22×D411yescharacteristic
1110C22×C4C22×D411yescharacteristic
1111C22×C4C22×D411yescharacteristic
1112C22×C4C22×D411yescharacteristic
1113C22×C4C22×D411yescharacteristic
1114C22×C4C2×#4111yescharacteristic
1115C22×C4C2×#4111yescharacteristic
1116C22×C4C2×#4111yescharacteristic
1117Q16—81no—
1118Q16—81no—
1119Q16—81no—
1120Q16—81no—
1121Q16—81no—
1122Q16—81no—
1123Q16—81no—
1124Q16—81no—
1125SD16—81no—
1126SD16—81no—
1127SD16—81no—
1128SD16—81no—
1129SD16—81no—
1130SD16—81no—
1131SD16—81no—
1132SD16—81no—
1133SD16—81no—
1134SD16—81no—
1135SD16—81no—
1136SD16—81no—
1137D8—81no—
1138D8—81no—
1139M16—41no—
1140M16—41no—
1141M16—41no—
1142M16—41no—
1143M16—42no—
1144M16—81no—
1145M16—81no—
1146M16—81no—
1147M16—81no—
1148M16—81no—
1149M16—81no—
1150M16—81no—
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—21no—
1162C2×C8—21no—
1163C2×C8—41no—
1164C2×C8—41no—
1165C2×C8—42no—
1166C2×C8—42no—
1167C2×C8—81no—
1168C2×C8—81no—
1169C2×C8—81no—
1170C2×C8—81no—
1171C2×C8—81no—
1172C2×C8C22×D411yescharacteristic
1173C2×C8C22×D411yescharacteristic
1174C2×C8C22×D411yescharacteristic
1175C2×C8C22×D411yescharacteristic
1176C2×C8C22×D411yescharacteristic
1177C2×C8C22×D411yescharacteristic
1178C2×C8C22×D411yescharacteristic
1179C2×C8C22×D411yescharacteristic
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—21no—
1209C4⋊C4—21no—
1210C4⋊C4—21no—
1211C4⋊C4—21no—
1212C4⋊C4—21no—
1213C4⋊C4—21no—
1214C4⋊C4—21no—
1215C4⋊C4—41no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C4⋊C4—41no—
1228C4⋊C4—41no—
1229C4⋊C4#12111yescharacteristic
1230C4⋊C4#12111yescharacteristic
1231C4⋊C4#12111yescharacteristic
1232C4⋊C4#12111yescharacteristic
1233C4⋊C4#12111yescharacteristic
1234C4⋊C4#12111yescharacteristic
1235C4⋊C4C22×D411yescharacteristic
1236C4⋊C4C22×D411yescharacteristic
1237C4⋊C4C22×D411yescharacteristic
1238C4⋊C4C22×D411yescharacteristic
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—21no—
1248C22⋊C4—21no—
1249C22⋊C4—21no—
1250C22⋊C4—21no—
1251C22⋊C4—21no—
1252C22⋊C4—21no—
1253C22⋊C4—21no—
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—
1268C22⋊C4#12111yescharacteristic
1269C22⋊C4#12111yescharacteristic
1270C22⋊C4#12111yescharacteristic
1271C22⋊C4#12111yescharacteristic
1272C22⋊C4#12111yescharacteristic
1273C22⋊C4#12111yescharacteristic
1274C42—21no—
1275C42—21no—
1276C42—21no—
1277C42—21no—
1278C42—21no—
1279C42—21no—
1280C42—21no—
1281C42—41no—
1282C42—41no—
1283C42—41no—
1284C42—41no—
1285C42—41no—
1286C42—41no—
1287C42C22×D411yescharacteristic
1288C42C22×D411yescharacteristic
1289C42C22×D411yescharacteristic
1290C42C22×D411yescharacteristic
1291C42C22×D411yescharacteristic
1292C42C22×D411yescharacteristic
1293C42C2×#4111yescharacteristic
1294C42C2×#4111yescharacteristic
1295C42C2×#4111yescharacteristic
1296C42C2511yescharacteristic
1297C23—21no—
1298C23—41no—
1299C23—41no—
1300C23—82no—
1301C23—161no—
1302C23—161no—
1303C23C2×#12111yescharacteristic
1304C23C2×#12111yescharacteristic
1305C23C2×#12111yescharacteristic
1306Q8—21no—
1307Q8—21no—
1308Q8—21no—
1309Q8—21no—
1310Q8—21no—
1311Q8—21no—
1312Q8—41no—
1313Q8—41no—
1314Q8—41no—
1315Q8—41no—
1316Q8—41no—
1317Q8—41no—
1318Q8—41no—
1319Q8—41no—
1320Q8—41no—
1321Q8—81no—
1322Q8—81no—
1323Q8—81no—
1324Q8—81no—
1325Q8—81no—
1326Q8—82no—
1327D4—21no—
1328D4—21no—
1329D4—41no—
1330D4—41no—
1331D4—41no—
1332D4—41no—
1333D4—41no—
1334D4—41no—
1335D4—41no—
1336D4—41no—
1337D4—41no—
1338D4—41no—
1339D4—41no—
1340D4—81no—
1341D4—81no—
1342D4—82no—
1343D4—81no—
1344D4—81no—
1345D4—81no—
1346D4—161no—
1347D4—161no—
1348D4—161no—
1349D4—161no—
1350D4—161no—
1351D4—161no—
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—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
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—41no—
1382C2×C4—81no—
1383C2×C4—81no—
1384C2×C4—81no—
1385C2×C4—81no—
1386C2×C4—82no—
1387C2×C4—161no—
1388C2×C4—161no—
1389C2×C4—161no—
1390C2×C4—161no—
1391C2×C4C2×#12111yescharacteristic
1392C2×C4C2×#12111yescharacteristic
1393C2×C4C2×#12111yescharacteristic
1394C2×C4C2×#12111yescharacteristic
1395C2×C4C2×#12111yescharacteristic
1396C2×C4C2×#12111yescharacteristic
1397C2×C4C2×#12111yescharacteristic
1398C2×C4C2×#12111yescharacteristic
1399C2×C4C2×#12111yescharacteristic
1400C2×C4C23×D411yescharacteristic
1401C2×C4C23×D411yescharacteristic
1402C2×C4C22×#4111yescharacteristic
1403C8—21no—
1404C8—21no—
1405C8—21no—
1406C8—21no—
1407C8—21no—
1408C8—21no—
1409C8—21no—
1410C8—21no—
1411C8—41no—
1412C8—41no—
1413C8—41no—
1414C8—41no—
1415C8—41no—
1416C8—41no—
1417C8—41no—
1418C8—41no—
1419C8—41no—
1420C8—41no—
1421C8—41no—
1422C8—41no—
1423C22—21no—
1424C22—21no—
1425C22—21no—
1426C22—21no—
1427C22—21no—
1428C22—21no—
1429C22—21no—
1430C22—21no—
1431C22—21no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—81no—
1436C22—81no—
1437C22—81no—
1438C22—81no—
1439C22—81no—
1440C22—81no—
1441C22—322no—
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—41no—
1460C4—81no—
1461C4—81no—
1462C4—81no—
1463C4—81no—
1464C4—81no—
1465C4—81no—
1466C4#358411yescharacteristic
1467C4#358511yescharacteristic
1468C4#358611yescharacteristic
1469C4#358611yescharacteristic
1470C2—41no—
1471C2—41no—
1472C2—41no—
1473C2—81no—
1474C2—161no—
1475C2—161no—
1476C2#6043311yescharacteristic
1477C2#6045611yescharacteristic
1478C2#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
3. #60925C2semidirect
4. #60344C2semidirect
5. #19587C2semidirect
6. #19581C2semidirect
7. #19574C2semidirect
8. #19564C2semidirect
9. #19551C2semidirect
10. #19541C2semidirect
11. #19532C2semidirect
12. #19527C2semidirect
13. #19501C2semidirect
14. #19493C2semidirect
15. #19474C2semidirect
16. #19472C2semidirect
17. #19380C2semidirect
18. #19375C2semidirect
19. #19366C2semidirect
20. #19343C2semidirect
21. #19319C2semidirect
22. #19309C2semidirect
23. #19251C2semidirect
24. #19242C2semidirect
25. #19229C2semidirect
26. #19217C2semidirect
27. #19179C2semidirect
28. #19177C2semidirect
29. #17832C2semidirect
30. #17767C2semidirect
31. #17762C2semidirect
48. #3255C22semidirect
51. #3252C22semidirect
54. #3249C22semidirect
56. #3248C22semidirect
88. #3078C22semidirect
89. #3076C22semidirect
93. #3039C22semidirect
94. C2×#462C22semidirect
99. #2993C22semidirect
100. #2991C22semidirect
104. #2985C22semidirect
105. #2984C22semidirect
106. #2970C22semidirect
111. #2966C22semidirect
113. Q8×M16C22semidirect
116. #2960C22semidirect
119. #1704C22semidirect
120. #1704C22semidirect
121. #1704C22semidirect
122. #1703C22semidirect
131. #1700C22semidirect
132. #1700C22semidirect
133. #1700C22semidirect
134. #1700C22semidirect
139. #1696C22semidirect
140. #1696C22semidirect
141. #1692C22semidirect
142. #1692C22semidirect
143. #1691C22semidirect
144. #1691C22semidirect
145. #1690C22semidirect
146. #1689C22semidirect
151. #1684C22semidirect
152. #1684C22semidirect
153. #1684C22semidirect
154. #1683C22semidirect
163. #1680C22semidirect
164. #1680C22semidirect
165. #1679C22semidirect
166. #1679C22semidirect
171. #1676C22semidirect
172. #1675C22semidirect
173. #1672C22semidirect
174. #1672C22semidirect
175. #1672C22semidirect
176. #1672C22semidirect
177. #1670C22semidirect
178. #1670C22semidirect
184. #1574C22semidirect
186. #1573C22semidirect
187. #1571C22semidirect
188. #1570C22semidirect
190. #1569C22semidirect
191. #1566C22semidirect
193. #1565C22semidirect
194. C2×#335C22semidirect
195. #1561C22semidirect
198. #1559C22semidirect
199. #1559C22semidirect
202. #1556C22semidirect
204. #1554C22semidirect
206. #1552C22semidirect
210. #1550C22semidirect
211. #1549C22semidirect

Maximal subgroups

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

subgroupindex
#625442
#609942
#609252
#603442
#195872
#195812
#195742
#195642
#195512
#195412
#195322
#195272
#195012
#194932
#194742
#194722
#193802
#193752
#193662
#193432
#193192
#193092
#192512
#192422
#192292
#192172
#191792
#191772
#178322
#177672
#177622