Finite Group Databasebeta

← #6356848

Subgroups — #6356848

Order 512.

1513 conjugacy classes of subgroups.

The subgroup lattice has 1483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62544C211yesmaximal, characteristic, complemented
2#62133C211yesmaximal, characteristic, complemented
3#61986C211yesmaximal, characteristic
4#60341C211yesmaximal, characteristic, complemented
5#19575C211yesmaximal, characteristic, complemented
6#19568C211yesmaximal, characteristic, complemented
7#19533C211yesmaximal, characteristic, complemented
8#19529C211yesmaximal, characteristic, complemented
9#19524C211yesmaximal, characteristic, complemented
10#19520C211yesmaximal, characteristic, complemented
11#19486C211yesmaximal, characteristic, complemented
12#19481C211yesmaximal, characteristic, complemented
13#19418C211yesmaximal, characteristic, complemented
14#19414C211yesmaximal, characteristic, complemented
15#19413C211yesmaximal, characteristic, complemented
16#19409C211yesmaximal, characteristic, complemented
17#19375C211yesmaximal, characteristic, complemented
18#19372C211yesmaximal, characteristic, complemented
19#19340C211yesmaximal, characteristic, complemented
20#19318C211yesmaximal, characteristic, complemented
21#19316C211yesmaximal, characteristic, complemented
22#19278C211yesmaximal, characteristic, complemented
23#19244C211yesmaximal, characteristic, complemented
24#19242C211yesmaximal, characteristic, complemented
25#19216C211yesmaximal, characteristic, complemented
26#19181C211yesmaximal, characteristic, complemented
27#19178C211yesmaximal, characteristic, complemented
28#19124C211yesmaximal, characteristic, complemented
29#17838C211yesmaximal, characteristic, complemented
30#17780C211yesmaximal, characteristic, complemented
31#17771C211yesmaximal, characteristic, complemented
32#3509C2211yescharacteristic
33#3508C2211yescharacteristic
34#3482C2211yescharacteristic
35#3400—21no—
36#3386—21no—
37#3374—21no—
38#3373—21no—
39#3371—21no—
40#3371—21no—
41#3349—21no—
42#3349—21no—
43#3342—21no—
44#3323—21no—
45#3323—21no—
46#3317—21no—
47#3317—21no—
48#3315—21no—
49#3315—21no—
50#3311—21no—
51#3311—21no—
52#3311—21no—
53#3311—21no—
54#3304—21no—
55#3302—21no—
56#3284—21no—
57#3267—21no—
58#3267—21no—
59#3255C2211yescharacteristic
60#3255C2211yescharacteristic, complemented
61#3249C2211yescharacteristic
62#3249C2211yescharacteristic, complemented
63#3246C2211yescharacteristic
64#3246C2211yescharacteristic
65#3237C2211yescharacteristic
66#3237C2211yescharacteristic, complemented
67#3231C2211yescharacteristic
68#3230C2211yescharacteristic, complemented
69#3228C2211yescharacteristic
70#3227C2211yescharacteristic
71#3216C2211yescharacteristic
72#3216C2211yescharacteristic
73#3210C2211yescharacteristic
74#3210C2211yescharacteristic
75#3208C2211yescharacteristic
76#3208C2211yescharacteristic
77#3185C2211yescharacteristic
78#3182C2211yescharacteristic
79#3167C2211yescharacteristic
80#3141C2211yescharacteristic
81#3138C2211yescharacteristic
82#3131C2211yescharacteristic
83#3116C2211yescharacteristic
84#3116C2211yescharacteristic, complemented
85#3115C2211yescharacteristic
86#3115C2211yescharacteristic
87#3107C2211yescharacteristic
88#3107C2211yescharacteristic, complemented
89#3079C2211yescharacteristic, complemented
90#3076C2211yescharacteristic
91#3076C2211yescharacteristic, complemented
92#3038C2211yescharacteristic
93#3035C2211yescharacteristic
94#3035C2211yescharacteristic
95#2994—21no—
96#2992—21no—
97#2992—21no—
98#2990C2211yescharacteristic
99#2990C2211yescharacteristic
100#2990C2211yescharacteristic
101#2990C2211yescharacteristic, complemented
102#2988C2211yescharacteristic
103#2988C2211yescharacteristic, complemented
104#2986C2211yescharacteristic, complemented
105#2985C2211yescharacteristic
106#2985C2211yescharacteristic, complemented
107#2984—21no—
108#2970C2211yescharacteristic
109#2970C2211yescharacteristic, complemented
110#2968—21no—
111#2968—21no—
112#2966—21no—
113#2965C2211yescharacteristic
114C8×#41C2211yescharacteristic, complemented
115#2962C2211yescharacteristic
116#2962C2211yescharacteristic, complemented
117#2960C2211yescharacteristic, complemented
118C2×#446—21no—
119#1704C2211yescharacteristic, complemented
120#1704C2211yescharacteristic, complemented
121#1704C2211yescharacteristic, complemented
122#1704C2211yescharacteristic, complemented
123#1702C2211yescharacteristic
124#1702C2211yescharacteristic
125#1702C2211yescharacteristic
126#1702C2211yescharacteristic
127#1700C2211yescharacteristic, complemented
128#1700C2211yescharacteristic, complemented
129#1698C2211yescharacteristic
130#1698C2211yescharacteristic
131#1698C2211yescharacteristic
132#1698C2211yescharacteristic
133#1698C2211yescharacteristic
134#1698C2211yescharacteristic
135#1694C2211yescharacteristic, complemented
136#1694C2211yescharacteristic, complemented
137#1692C2211yescharacteristic, complemented
138#1692C2211yescharacteristic, complemented
139#1690C2211yescharacteristic, complemented
140#1690C2211yescharacteristic, complemented
141#1686C2211yescharacteristic
142#1686C2211yescharacteristic
143#1684C2211yescharacteristic, complemented
144#1684C2211yescharacteristic, complemented
145#1683C2211yescharacteristic, complemented
146#1683C2211yescharacteristic, complemented
147#1682C2211yescharacteristic
148#1682C2211yescharacteristic
149#1681C2211yescharacteristic
150#1681C2211yescharacteristic
151#1680C2211yescharacteristic, complemented
152#1680C2211yescharacteristic, complemented
153#1680C2211yescharacteristic, complemented
154#1680C2211yescharacteristic, complemented
155#1679C2211yescharacteristic, complemented
156#1679C2211yescharacteristic, complemented
157#1678C2211yescharacteristic
158#1678C2211yescharacteristic
159#1678C2211yescharacteristic
160#1678C2211yescharacteristic
161#1678C2211yescharacteristic
162#1678C2211yescharacteristic
163#1677C2211yescharacteristic
164#1677C2211yescharacteristic
165#1677C2211yescharacteristic
166#1677C2211yescharacteristic
167#1674C2211yescharacteristic, complemented
168#1673C2211yescharacteristic, complemented
169#1672C2211yescharacteristic, complemented
170#1672C2211yescharacteristic, complemented
171#1672C2211yescharacteristic, complemented
172#1672C2211yescharacteristic, complemented
173#1671C2211yescharacteristic, complemented
174#1671C2211yescharacteristic, complemented
175#1670C2211yescharacteristic, complemented
176#1669C2211yescharacteristic, complemented
177#1666C2211yescharacteristic
178#1666C2211yescharacteristic
179#1666C2211yescharacteristic
180#1666C2211yescharacteristic
181#1665C2211yescharacteristic
182#1665C2211yescharacteristic
183#1573C2211yescharacteristic, complemented
184#1573C2211yescharacteristic, complemented
185#1572C2211yescharacteristic
186#1572C2211yescharacteristic, complemented
187#1570C2211yescharacteristic
188#1570C2211yescharacteristic, complemented
189#1569C2211yescharacteristic
190#1569C2211yescharacteristic, complemented
191#1568C2211yescharacteristic, complemented
192#1565C2211yescharacteristic
193#1565C2211yescharacteristic, complemented
194C2×#334C2211yescharacteristic, complemented
195#1559C2211yescharacteristic
196#1559C2211yescharacteristic, complemented
197#1558C2211yescharacteristic, complemented
198#1557C2211yescharacteristic
199#1557C2211yescharacteristic
200#1555C2211yescharacteristic
201#1554C2211yescharacteristic
202#1554C2211yescharacteristic, complemented
203#1553C2211yescharacteristic
204#1553C2211yescharacteristic
205#1552C2211yescharacteristic
206#1552C2211yescharacteristic
207#1552C2211yescharacteristic, complemented
208#1552C2211yescharacteristic, complemented
209#1550C2211yescharacteristic
210#1550C2211yescharacteristic, complemented
211#1547C2211yescharacteristic
212#1547C2211yescharacteristic
213#1542C2211yescharacteristic
214#1542C2211yescharacteristic, complemented
215C2×#333C2211yescharacteristic, complemented
216#1540C2211yescharacteristic
217#1540C2211yescharacteristic
218C2×#331C2211yescharacteristic
219C2×AGL(1,ℤ/8)—21no—
220C2×#135—21no—
221C2×#135—21no—
222#559—21no—
223#559—21no—
224#557—21no—
225#557—21no—
226#557D411yescharacteristic
227#556—21no—
228#556—21no—
229#556D411yescharacteristic
230#556D411yescharacteristic
231#556D411yescharacteristic
232#552—21no—
233#552—21no—
234#552—21no—
235#552—21no—
236#552—21no—
237#552—21no—
238#552—21no—
239#550—21no—
240#550—21no—
241D4×Q8D411yescharacteristic
242#548—21no—
243#547D411yescharacteristic
244#547D411yescharacteristic
245#547D411yescharacteristic
246#546—21no—
247#546—21no—
248#546—21no—
249#546—21no—
250#541—21no—
251#541—21no—
252#540—21no—
253#540—21no—
254#536—21no—
255#535—21no—
256#533C2311yescharacteristic
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#519—21no—
275#518—21no—
276C4×#41C2311yescharacteristic
277C4×#41C2311yescharacteristic
278C4×#41C2311yescharacteristic
279C4×#41C2311yescharacteristic
280C2×C4×Q8—21no—
281#501—21no—
282#501—21no—
283#500—21no—
284#500C2311yescharacteristic
285#498C2311yescharacteristic
286#498C2311yescharacteristic
287#497—21no—
288#497—21no—
289#494C2311yescharacteristic
290#492—21no—
291#492C2311yescharacteristic
292#492C2311yescharacteristic
293#491—21no—
294#491—21no—
295#490—21no—
296#490—21no—
297#489—21no—
298#489—21no—
299#489—21no—
300#489—21no—
301#488—21no—
302#488—21no—
303#487—21no—
304#487C2311yescharacteristic
305#487C2311yescharacteristic
306#487C2311yescharacteristic
307#487C2311yescharacteristic
308#486—21no—
309#486C2311yescharacteristic
310#486C2311yescharacteristic
311#486C2311yescharacteristic
312#486C2311yescharacteristic
313#486C2311yescharacteristic
314#486C2311yescharacteristic
315#485—21no—
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#484—21no—
326#484—21no—
327#482—21no—
328#482—21no—
329#482—21no—
330#482—21no—
331#481—21no—
332#481—21no—
333#479—21no—
334#479—21no—
335#479—21no—
336#479—21no—
337#478—21no—
338#478—21no—
339#478—21no—
340#478—21no—
341#477—21no—
342#477—21no—
343#477C2311yescharacteristic
344#477C2311yescharacteristic
345#477C2311yescharacteristic
346#477C2311yescharacteristic
347#477C2311yescharacteristic
348#477C2311yescharacteristic
349#476—21no—
350#476—21no—
351#476—21no—
352#476—21no—
353#476C2311yescharacteristic
354#476C2311yescharacteristic
355#475—21no—
356#475—21no—
357#475—21no—
358#475C2311yescharacteristic
359#475C2311yescharacteristic
360#475C2311yescharacteristic
361#475C2311yescharacteristic
362#475C2311yescharacteristic
363#475C2311yescharacteristic
364#474—21no—
365#474C2311yescharacteristic
366#474C2311yescharacteristic
367#470—21no—
368#470—21no—
369#470—21no—
370#470—21no—
371#470—21no—
372#470—21no—
373#468—21no—
374#468—21no—
375#467—21no—
376#467—21no—
377#467—21no—
378#467—21no—
379#465—21no—
380#465—21no—
381#465—21no—
382#465—21no—
383#465—21no—
384#465—21no—
385#464—21no—
386#464—21no—
387#464—21no—
388#464—21no—
389#464—21no—
390#464—21no—
391#463—21no—
392#463—21no—
393#462—21no—
394#462—21no—
395#462—21no—
396#462—21no—
397#462C2311yescharacteristic
398#462C2311yescharacteristic
399#462C2311yescharacteristic
400#462C2311yescharacteristic
401#462C2311yescharacteristic
402#462C2311yescharacteristic
403#461—21no—
404#461—21no—
405#461C2311yescharacteristic
406#461C2311yescharacteristic
407#460—21no—
408#460—21no—
409#460—21no—
410#460C2311yescharacteristic
411#460C2311yescharacteristic
412#460C2311yescharacteristic
413#460C2311yescharacteristic
414#460C2311yescharacteristic
415#460C2311yescharacteristic
416#459—21no—
417#459C2311yescharacteristic
418#459C2311yescharacteristic
419#452—21no—
420#452—21no—
421#452—21no—
422#452—21no—
423#452—21no—
424#452—21no—
425#452—21no—
426#452—21no—
427#452—21no—
428#452—21no—
429#452—21no—
430#452—21no—
431#450—21no—
432#450—21no—
433#450—21no—
434#450—21no—
435#449—21no—
436#449—21no—
437#446—21no—
438#446—21no—
439#446—21no—
440#446—21no—
441#446—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×Q8C2311yescharacteristic
461C8×Q8C2311yescharacteristic
462C8×Q8C2311yescharacteristic
463C8×Q8C2311yescharacteristic
464C8×Q8C2311yescharacteristic
465C8×Q8C2311yescharacteristic
466#442—21no—
467#442—21no—
468#441—21no—
469#441—21no—
470#441—21no—
471#441—21no—
472#440—21no—
473#440—21no—
474#440—21no—
475#440—21no—
476#440—21no—
477#440—21no—
478C4×Q16—21no—
479C4×Q16—21no—
480C4×SD16—21no—
481C4×SD16—21no—
482C4×SD16—21no—
483C4×SD16—21no—
484#436D411yescharacteristic
485#436D411yescharacteristic
486#435—21no—
487#435—21no—
488#435—21no—
489#435—21no—
490#435—21no—
491#435—21no—
492#435—21no—
493#435—21no—
494#435—21no—
495#435—21no—
496#435—21no—
497#435—21no—
498#435D411yescharacteristic
499#435D411yescharacteristic
500#435D411yescharacteristic
501#435D411yescharacteristic
502C8×D4—21no—
503C8×D4—21no—
504C8×D4—21no—
505C8×D4—21no—
506C8×D4—21no—
507C8×D4—21no—
508C8×D4—21no—
509C8×D4—21no—
510C8×D4—21no—
511C8×D4C2311yescharacteristic
512C8×D4C2311yescharacteristic
513C8×D4C2311yescharacteristic
514C8×D4C2311yescharacteristic
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#432—21no—
524#432C2311yescharacteristic
525#432C2311yescharacteristic
526#432C2311yescharacteristic
527#432C2311yescharacteristic
528#432C2311yescharacteristic
529#432C2311yescharacteristic
530#431—21no—
531#431—21no—
532#431—21no—
533#431C2311yescharacteristic
534#431C2311yescharacteristic
535#431C2311yescharacteristic
536#431C2311yescharacteristic
537#431C2311yescharacteristic
538#431C2311yescharacteristic
539#428—21no—
540#427—21no—
541#427—21no—
542#424—21no—
543#424—21no—
544#424—21no—
545#423C2311yescharacteristic
546#423C2311yescharacteristic
547#423C2311yescharacteristic
548C2×C4⋊C8—21no—
549C2×C4⋊C8—21no—
550C2×C4⋊C8—21no—
551C2×C4⋊C8C2311yescharacteristic
552C2×C4⋊C8C2311yescharacteristic
553C2×C4⋊C8C2311yescharacteristic
554C2×C4⋊C8C2311yescharacteristic
555C2×C4⋊C8C2311yescharacteristic
556C2×C4⋊C8C2311yescharacteristic
557#418—21no—
558#418—21no—
559#418—21no—
560#417—21no—
561#417—21no—
562#417—21no—
563#416—21no—
564#416—21no—
565#416—21no—
566#416—21no—
567#416—21no—
568#416—21no—
569#405—21no—
570#405—21no—
571#405—21no—
572C4×M16C2311yescharacteristic
573C4×M16C2311yescharacteristic
574C2×#97—21no—
575C2×#97—21no—
576C2×C4×C8—21no—
577C2×C4×C8C2311yescharacteristic
578#335C2311yescharacteristic
579#335C2311yescharacteristic
580#335C2311yescharacteristic
581#335C2311yescharacteristic
582#335C2311yescharacteristic
583#335C2311yescharacteristic
584#334C2311yescharacteristic
585#334C2311yescharacteristic
586#334C2311yescharacteristic
587#334C2311yescharacteristic
588#334C2311yescharacteristic
589#334C2311yescharacteristic
590#334C2311yescharacteristic
591#334C2311yescharacteristic
592#334C2311yescharacteristic
593#334C2311yescharacteristic
594#333C2311yescharacteristic
595#333C2311yescharacteristic
596#333C2311yescharacteristic
597#333C2311yescharacteristic
598#333C2311yescharacteristic
599#333C2311yescharacteristic
600#333C2311yescharacteristic
601#333C2311yescharacteristic
602#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
632C2×#41C2×D411yescharacteristic
633C2×#41#4111yescharacteristic
634C22×Q8—21no—
635C22×Q8—21no—
636C22×D4—21no—
637C22×D4—21no—
638C22×D4—21no—
639AGL(1,ℤ/8)—82no—
640#135—82no—
641#135—82no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×Q16—21no—
647C2×Q16—21no—
648C2×Q16—21no—
649C2×Q16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16—21no—
654C2×SD16—21no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×SD16—21no—
659C2×SD16—21no—
660C2×SD16—21no—
661C2×SD16—21no—
662C2×D8—21no—
663C2×D8—21no—
664C2×M16—21no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C2×D411yescharacteristic
668C2×M16C2×D411yescharacteristic
669C2×M16C2×D411yescharacteristic
670C2×M16C2×D411yescharacteristic
671C22×C8—21no—
672C22×C8—21no—
673C22×C8—21no—
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—41no—
687C4⋊Q8C2×D411yescharacteristic
688C4⋊Q8C2×D411yescharacteristic
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—41no—
712#126—41no—
713#126—41no—
714#126—41no—
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—21no—
724#125—21no—
725#125—21no—
726#125—21no—
727#125—41no—
728#125—41no—
729#125—41no—
730#125—41no—
731#124—21no—
732#124—21no—
733#124—21no—
734#124—21no—
735#124—21no—
736#124—21no—
737#124—21no—
738#124—41no—
739#124—41no—
740#123—21no—
741#123—21no—
742#123—21no—
743#123—21no—
744#123—21no—
745#123—21no—
746#123—41no—
747#123—41no—
748#123—41no—
749#123—41no—
750#123—41no—
751#123—41no—
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—21no—
763C22⋊Q8—21no—
764C22⋊Q8—21no—
765C22⋊Q8—21no—
766C22⋊Q8—21no—
767C22⋊Q8—21no—
768C22⋊Q8—21no—
769C22⋊Q8—21no—
770C22⋊Q8C2×D411yescharacteristic
771C22⋊Q8C2×D411yescharacteristic
772C22⋊Q8C2×D411yescharacteristic
773C22⋊Q8C2×D411yescharacteristic
774C22⋊Q8C2×D411yescharacteristic
775C22⋊Q8C2×D411yescharacteristic
776#121—21no—
777#121—21no—
778#121—21no—
779#121—21no—
780#121—21no—
781#121—21no—
782#121—21no—
783#121—21no—
784#121—21no—
785#121—21no—
786#121—21no—
787#121—41no—
788#121—41no—
789#121—41no—
790#121—41no—
791#120—41no—
792#120—41no—
793C4×Q8—21no—
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—21no—
812C4×Q8—41no—
813C4×Q8—41no—
814C4×Q8C2×D411yescharacteristic
815C4×Q8C2×D411yescharacteristic
816C4×Q8C2×D411yescharacteristic
817C4×Q8C2×D411yescharacteristic
818C4×Q8C2×D411yescharacteristic
819C4×Q8C2411yescharacteristic
820C4×Q8C2411yescharacteristic
821C4×Q8C2411yescharacteristic
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—21no—
832C4×D4—21no—
833C4×D4—21no—
834C4×D4—21no—
835C4×D4—21no—
836C4×D4—41no—
837C4×D4—41no—
838C4×D4C2×D411yescharacteristic
839C4×D4C2×D411yescharacteristic
840C4×D4C2×D411yescharacteristic
841C4×D4C2×D411yescharacteristic
842C4×D4C2×D411yescharacteristic
843C4×D4C2×D411yescharacteristic
844C4×D4C2×D411yescharacteristic
845C4×D4C2×D411yescharacteristic
846C4×D4C2×D411yescharacteristic
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—21no—
860#117—41no—
861#117—41no—
862#117C2×D411yescharacteristic
863#117C2×D411yescharacteristic
864#117C2×D411yescharacteristic
865#117#4111yescharacteristic
866#117#4111yescharacteristic
867#117#4111yescharacteristic
868C2×C4⋊C4—21no—
869C2×C4⋊C4—21no—
870C2×C4⋊C4—21no—
871C2×C4⋊C4—21no—
872C2×C4⋊C4—21no—
873C2×C22⋊C4—41no—
874C2×C22⋊C4—41no—
875C2×C42—21no—
876C2×C42—21no—
877C2×C42—21no—
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
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#106—21no—
892#106—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—
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⋊C8—21no—
918C4⋊C8—21no—
919C4⋊C8—21no—
920C4⋊C8—21no—
921C4⋊C8—21no—
922C4⋊C8—21no—
923C4⋊C8—21no—
924C4⋊C8C2×D411yescharacteristic
925C4⋊C8C2×D411yescharacteristic
926C4⋊C8C2×D411yescharacteristic
927C4⋊C8C2×D411yescharacteristic
928C4⋊C8C2×D411yescharacteristic
929C4⋊C8C2×D411yescharacteristic
930C4⋊C8C2411yescharacteristic
931C4⋊C8C2411yescharacteristic
932C4⋊C8C2411yescharacteristic
933C4⋊C8C2411yescharacteristic
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—21no—
967#103—21no—
968#103—21no—
969#103—21no—
970#102—21no—
971#102—21no—
972#102—21no—
973#102—21no—
974#102—21no—
975#102—21no—
976#102—21no—
977#102—21no—
978#102—21no—
979#102—21no—
980#102—21no—
981#102—21no—
982#102—21no—
983#102—21no—
984#102—21no—
985#102—21no—
986#102—21no—
987#102—21no—
988#102—21no—
989#102—21no—
990#102—21no—
991#102—21no—
992#102—21no—
993#102—21no—
994C22⋊C8—21no—
995C22⋊C8—21no—
996C22⋊C8—21no—
997C22⋊C8—21no—
998C22⋊C8—21no—
999C22⋊C8—21no—
1000C22⋊C8—21no—
1001C22⋊C8—21no—
1002C22⋊C8—21no—
1003C22⋊C8—21no—
1004C22⋊C8—21no—
1005C22⋊C8—21no—
1006C22⋊C8—21no—
1007C22⋊C8C2×D411yescharacteristic
1008C22⋊C8C2×D411yescharacteristic
1009C22⋊C8C2×D411yescharacteristic
1010C22⋊C8C2×D411yescharacteristic
1011C22⋊C8C2×D411yescharacteristic
1012C22⋊C8C2×D411yescharacteristic
1013#97—21no—
1014#97—21no—
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—22no—
1046#41—22no—
1047#41—22no—
1048#41—41no—
1049#41—41no—
1050#41—41no—
1051#41—81no—
1052#41—81no—
1053#41—81no—
1054#41—81no—
1055#41—81no—
1056#41—81no—
1057#41—81no—
1058#41—81no—
1059#41—81no—
1060C2×Q8—21no—
1061C2×Q8—21no—
1062C2×Q8—21no—
1063C2×Q8—21no—
1064C2×Q8—21no—
1065C2×Q8—21no—
1066C2×Q8—21no—
1067C2×Q8—21no—
1068C2×Q8—21no—
1069C2×Q8—41no—
1070C2×Q8—82no—
1071C2×Q8—82no—
1072C2×Q8#12111yescharacteristic
1073C2×Q8C22×D411yescharacteristic
1074C2×Q8C22×D411yescharacteristic
1075C2×Q8C22×D411yescharacteristic
1076C2×D4—21no—
1077C2×D4—21no—
1078C2×D4—21no—
1079C2×D4—21no—
1080C2×D4—21no—
1081C2×D4—21no—
1082C2×D4—21no—
1083C2×D4—21no—
1084C2×D4—21no—
1085C2×D4—41no—
1086C2×D4—41no—
1087C2×D4—41no—
1088C2×D4—41no—
1089C2×D4—41no—
1090C2×D4—41no—
1091C2×D4—41no—
1092C2×D4—81no—
1093C2×D4—81no—
1094C2×D4—81no—
1095C2×D4—81no—
1096C2×D4—82no—
1097C2×D4#12111yescharacteristic
1098C2×D4#12111yescharacteristic
1099C2×D4#12111yescharacteristic
1100C2×D4C22×D411yescharacteristic
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—21no—
1105C22×C4—21no—
1106C22×C4—21no—
1107C22×C4—21no—
1108C22×C4—41no—
1109C22×C4—41no—
1110C22×C4—41no—
1111C22×C4—41no—
1112C22×C4—41no—
1113C22×C4C22×D411yescharacteristic
1114C22×C4C22×D411yescharacteristic
1115C22×C4C22×D411yescharacteristic
1116C22×C4C22×D411yescharacteristic
1117C22×C4C22×D411yescharacteristic
1118C22×C4C22×D411yescharacteristic
1119C22×C4C2×#4111yescharacteristic
1120C22×C4C2×#4111yescharacteristic
1121C22×C4C2×#4111yescharacteristic
1122Q16—81no—
1123Q16—81no—
1124Q16—81no—
1125Q16—81no—
1126Q16—81no—
1127Q16—81no—
1128Q16—81no—
1129Q16—81no—
1130SD16—42no—
1131SD16—42no—
1132SD16—81no—
1133SD16—81no—
1134SD16—81no—
1135SD16—81no—
1136SD16—81no—
1137SD16—81no—
1138SD16—81no—
1139SD16—81no—
1140SD16—81no—
1141SD16—81no—
1142D8—42no—
1143D8—42no—
1144M16—41no—
1145M16—41no—
1146M16—41no—
1147M16—41no—
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—81no—
1167C2×C8—81no—
1168C2×C8—81no—
1169C2×C8—81no—
1170C2×C8—81no—
1171C2×C8—81no—
1172C2×C8—81no—
1173C2×C8—81no—
1174C2×C8—81no—
1175C2×C8C22×D411yescharacteristic
1176C2×C8C22×D411yescharacteristic
1177C2×C8C22×D411yescharacteristic
1178C2×C8C22×D411yescharacteristic
1179C2×C8C22×D411yescharacteristic
1180C2×C8C22×D411yescharacteristic
1181C2×C8C22×D411yescharacteristic
1182C2×C8C22×D411yescharacteristic
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—21no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C4⋊C4—41no—
1228C4⋊C4—41no—
1229C4⋊C4—41no—
1230C4⋊C4#12111yescharacteristic
1231C4⋊C4#12111yescharacteristic
1232C4⋊C4#12111yescharacteristic
1233C4⋊C4#12111yescharacteristic
1234C4⋊C4#12111yescharacteristic
1235C4⋊C4#12111yescharacteristic
1236C4⋊C4C22×D411yescharacteristic
1237C4⋊C4C22×D411yescharacteristic
1238C4⋊C4C22×D411yescharacteristic
1239C4⋊C4C22×D411yescharacteristic
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—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#12111yescharacteristic
1268C22⋊C4#12111yescharacteristic
1269C22⋊C4#12111yescharacteristic
1270C22⋊C4#12111yescharacteristic
1271C22⋊C4#12111yescharacteristic
1272C22⋊C4#12111yescharacteristic
1273C42—21no—
1274C42—21no—
1275C42—21no—
1276C42—21no—
1277C42—21no—
1278C42—21no—
1279C42—21no—
1280C42—21no—
1281C42—21no—
1282C42—41no—
1283C42—41no—
1284C42—41no—
1285C42—41no—
1286C42—41no—
1287C42—41no—
1288C42C22×D411yescharacteristic
1289C42C22×D411yescharacteristic
1290C42C22×D411yescharacteristic
1291C42C22×D411yescharacteristic
1292C42C22×D411yescharacteristic
1293C42C22×D411yescharacteristic
1294C42C2×#4111yescharacteristic
1295C42C2×#4111yescharacteristic
1296C42C2×#4111yescharacteristic
1297C42C2511yescharacteristic
1298C23—21no—
1299C23—41no—
1300C23—41no—
1301C23—82no—
1302C23—161no—
1303C23—161no—
1304C23C2×#12111yescharacteristic
1305C23C2×#12111yescharacteristic
1306C23C2×#12111yescharacteristic
1307Q8—21no—
1308Q8—21no—
1309Q8—21no—
1310Q8—21no—
1311Q8—21no—
1312Q8—21no—
1313Q8—41no—
1314Q8—42no—
1315Q8—41no—
1316Q8—41no—
1317Q8—41no—
1318Q8—41no—
1319Q8—41no—
1320Q8—41no—
1321Q8—41no—
1322Q8—41no—
1323Q8—81no—
1324Q8—81no—
1325Q8—81no—
1326Q8—81no—
1327Q8—82no—
1328D4—21no—
1329D4—41no—
1330D4—41no—
1331D4—41no—
1332D4—42no—
1333D4—42no—
1334D4—42no—
1335D4—41no—
1336D4—41no—
1337D4—41no—
1338D4—41no—
1339D4—41no—
1340D4—41no—
1341D4—41no—
1342D4—41no—
1343D4—81no—
1344D4—81no—
1345D4—82no—
1346D4—161no—
1347D4—161no—
1348D4—161no—
1349D4—161no—
1350D4—161no—
1351D4—161no—
1352D4#57712yes—
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—21no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—42no—
1376C2×C4—42no—
1377C2×C4—42no—
1378C2×C4—42no—
1379C2×C4—41no—
1380C2×C4—41no—
1381C2×C4—41no—
1382C2×C4—41no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—41no—
1387C2×C4—81no—
1388C2×C4—81no—
1389C2×C4—82no—
1390C2×C4—161no—
1391C2×C4—161no—
1392C2×C4—161no—
1393C2×C4—161no—
1394C2×C4C2×#12111yescharacteristic
1395C2×C4C2×#12111yescharacteristic
1396C2×C4C2×#12111yescharacteristic
1397C2×C4C2×#12111yescharacteristic
1398C2×C4C2×#12111yescharacteristic
1399C2×C4C2×#12111yescharacteristic
1400C2×C4C2×#12111yescharacteristic
1401C2×C4C2×#12111yescharacteristic
1402C2×C4C2×#12111yescharacteristic
1403C2×C4C23×D411yescharacteristic
1404C2×C4C23×D411yescharacteristic
1405C2×C4C22×#4111yescharacteristic
1406C8—21no—
1407C8—21no—
1408C8—21no—
1409C8—21no—
1410C8—21no—
1411C8—21no—
1412C8—21no—
1413C8—21no—
1414C8—41no—
1415C8—41no—
1416C8—41no—
1417C8—41no—
1418C8—41no—
1419C8—41no—
1420C8—41no—
1421C8—41no—
1422C8—41no—
1423C8—41no—
1424C8—41no—
1425C8—41no—
1426C22—21no—
1427C22—21no—
1428C22—21no—
1429C22—21no—
1430C22—21no—
1431C22—21no—
1432C22—22no—
1433C22—21no—
1434C22—21no—
1435C22—21no—
1436C22—41no—
1437C22—41no—
1438C22—81no—
1439C22—81no—
1440C22—81no—
1441C22—81no—
1442C22—81no—
1443C22—81no—
1444C22—322no—
1445C22C22×#12111yescharacteristic
1446C4—21no—
1447C4—21no—
1448C4—21no—
1449C4—21no—
1450C4—21no—
1451C4—21no—
1452C4—21no—
1453C4—21no—
1454C4—21no—
1455C4—21no—
1456C4—41no—
1457C4—41no—
1458C4—41no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4—81no—
1464C4—81no—
1465C4—81no—
1466C4—81no—
1467C4—81no—
1468C4—81no—
1469C4C2×#57711yescharacteristic
1470C4#358411yescharacteristic
1471C4#358411yescharacteristic
1472C4#358611yescharacteristic
1473C2—41no—
1474C2—41no—
1475C2—41no—
1476C2—42no—
1477C2—161no—
1478C2—161no—
1479C2#6043311yescharacteristic
1480C2#6045711yescharacteristic
1481C2#6046911yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
prime radical#61986C2
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. #62133C2semidirect
4. #60341C2semidirect
5. #19575C2semidirect
6. #19568C2semidirect
7. #19533C2semidirect
8. #19529C2semidirect
9. #19524C2semidirect
10. #19520C2semidirect
11. #19486C2semidirect
12. #19481C2semidirect
13. #19418C2semidirect
14. #19414C2semidirect
15. #19413C2semidirect
16. #19409C2semidirect
17. #19375C2semidirect
18. #19372C2semidirect
19. #19340C2semidirect
20. #19318C2semidirect
21. #19316C2semidirect
22. #19278C2semidirect
23. #19244C2semidirect
24. #19242C2semidirect
25. #19216C2semidirect
26. #19181C2semidirect
27. #19178C2semidirect
28. #19124C2semidirect
29. #17838C2semidirect
30. #17780C2semidirect
31. #17771C2semidirect
60. #3255C22semidirect
62. #3249C22semidirect
66. #3237C22semidirect
68. #3230C22semidirect
84. #3116C22semidirect
88. #3107C22semidirect
89. #3079C22semidirect
91. #3076C22semidirect
101. #2990C22semidirect
103. #2988C22semidirect
104. #2986C22semidirect
106. #2985C22semidirect
109. #2970C22semidirect
114. C8×#41C22semidirect
116. #2962C22semidirect
117. #2960C22semidirect
119. #1704C22semidirect
120. #1704C22semidirect
121. #1704C22semidirect
122. #1704C22semidirect
127. #1700C22semidirect
128. #1700C22semidirect
135. #1694C22semidirect
136. #1694C22semidirect
137. #1692C22semidirect
138. #1692C22semidirect
139. #1690C22semidirect
140. #1690C22semidirect
143. #1684C22semidirect
144. #1684C22semidirect
145. #1683C22semidirect
146. #1683C22semidirect
151. #1680C22semidirect
152. #1680C22semidirect
153. #1680C22semidirect
154. #1680C22semidirect
155. #1679C22semidirect
156. #1679C22semidirect
167. #1674C22semidirect
168. #1673C22semidirect
169. #1672C22semidirect
170. #1672C22semidirect
171. #1672C22semidirect
172. #1672C22semidirect
173. #1671C22semidirect
174. #1671C22semidirect
175. #1670C22semidirect
176. #1669C22semidirect
183. #1573C22semidirect
184. #1573C22semidirect
186. #1572C22semidirect
188. #1570C22semidirect
190. #1569C22semidirect
191. #1568C22semidirect
193. #1565C22semidirect
194. C2×#334C22semidirect
196. #1559C22semidirect
197. #1558C22semidirect
202. #1554C22semidirect
207. #1552C22semidirect
208. #1552C22semidirect
210. #1550C22semidirect
214. #1542C22semidirect
215. C2×#333C22semidirect

Maximal subgroups

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

subgroupindex
#625442
#621332
#619862
#603412
#195752
#195682
#195332
#195292
#195242
#195202
#194862
#194812
#194182
#194142
#194132
#194092
#193752
#193722
#193402
#193182
#193162
#192782
#192442
#192422
#192162
#191812
#191782
#191242
#178382
#177802
#177712