Finite Group Databasebeta

← #6357887

Subgroups — #6357887

Order 512.

1945 conjugacy classes of subgroups.

The subgroup lattice has 1413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62546C211yesmaximal, characteristic, complemented
2#62543C211yesmaximal, characteristic, complemented
3#62427C211yesmaximal, characteristic, complemented
4#62426C211yesmaximal, characteristic, complemented
5#60722C211yesmaximal, characteristic, complemented
6#60722C211yesmaximal, characteristic, complemented
7#19752C211yesmaximal, characteristic, complemented
8#19748C211yesmaximal, characteristic, complemented
9#19747C211yesmaximal, characteristic, complemented
10#19745C211yesmaximal, characteristic, complemented
11#19727C211yesmaximal, characteristic, complemented
12#19726C211yesmaximal, characteristic, complemented
13#19719C211yesmaximal, characteristic, complemented
14#19714C211yesmaximal, characteristic, complemented
15#19695C211yesmaximal, characteristic, complemented
16#19695C211yesmaximal, characteristic, complemented
17#19695C211yesmaximal, characteristic, complemented
18#19694C211yesmaximal, characteristic, complemented
19#19692C211yesmaximal, characteristic, complemented
20#19691C211yesmaximal, characteristic, complemented
21#19691C211yesmaximal, characteristic, complemented
22#19689C211yesmaximal, characteristic, complemented
23#19678C211yesmaximal, characteristic, complemented
24#19677C211yesmaximal, characteristic, complemented
25#19673C211yesmaximal, characteristic, complemented
26#19673C211yesmaximal, characteristic, complemented
27#19667C211yesmaximal, characteristic, complemented
28#19665C211yesmaximal, characteristic, complemented
29#19619C211yesmaximal, characteristic, complemented
30#19619C211yesmaximal, characteristic, complemented
31#17336C211yesmaximal, characteristic, complemented
32#3511C2211yescharacteristic
33#3511C2211yescharacteristic
34#3508C2211yescharacteristic
35#3508C2211yescharacteristic
36#3403—22no—
37#3401—22no—
38#3376—22no—
39#3370—22no—
40#3326—22no—
41#3322—22no—
42#3321—22no—
43#3319—22no—
44#3309—22no—
45#3307—22no—
46#3275—22no—
47#3273—22no—
48#3271—22no—
49#3268—22no—
50#3268—22no—
51#3267—22no—
52#3231C2211yescharacteristic, complemented
53#3231C2211yescharacteristic, complemented
54#3229C2211yescharacteristic, complemented
55#3228C2211yescharacteristic, complemented
56#3228C2211yescharacteristic, complemented
57#3226C2211yescharacteristic
58#3210C2211yescharacteristic
59#3210C2211yescharacteristic
60#3210C2211yescharacteristic, complemented
61#3210C2211yescharacteristic, complemented
62#3208C2211yescharacteristic, complemented
63#3207C2211yescharacteristic
64#3207C2211yescharacteristic
65#3207C2211yescharacteristic
66#3207C2211yescharacteristic
67#3207C2211yescharacteristic, complemented
68#3207C2211yescharacteristic, complemented
69#3207C2211yescharacteristic, complemented
70#3207C2211yescharacteristic, complemented
71#3206C2211yescharacteristic
72#3206C2211yescharacteristic, complemented
73#3205C2211yescharacteristic
74#3205C2211yescharacteristic
75#3205C2211yescharacteristic, complemented
76#3185C2211yescharacteristic, complemented
77#3184C2211yescharacteristic
78#3184C2211yescharacteristic
79#3184C2211yescharacteristic
80#3184C2211yescharacteristic
81#3184C2211yescharacteristic, complemented
82#3184C2211yescharacteristic, complemented
83#3184C2211yescharacteristic, complemented
84#3182C2211yescharacteristic
85#3182C2211yescharacteristic
86#3182C2211yescharacteristic
87#3182C2211yescharacteristic
88#3182C2211yescharacteristic, complemented
89#3182C2211yescharacteristic, complemented
90#3182C2211yescharacteristic, complemented
91#3182C2211yescharacteristic, complemented
92#3179—22no—
93#3179—22no—
94#3179—22no—
95#3179—22no—
96#3169C2211yescharacteristic
97#3169C2211yescharacteristic
98#3169C2211yescharacteristic
99#3169C2211yescharacteristic, complemented
100#3169C2211yescharacteristic, complemented
101#3169C2211yescharacteristic, complemented
102#3167C2211yescharacteristic
103#3167C2211yescharacteristic
104#3167C2211yescharacteristic, complemented
105#3167C2211yescharacteristic, complemented
106#3167C2211yescharacteristic, complemented
107#3167C2211yescharacteristic, complemented
108#3165C2211yescharacteristic, complemented
109#3165C2211yescharacteristic, complemented
110#3152C2211yescharacteristic
111#3151C2211yescharacteristic
112#3151C2211yescharacteristic
113#3151C2211yescharacteristic, complemented
114#3151C2211yescharacteristic, complemented
115#3151C2211yescharacteristic, complemented
116#3147C2211yescharacteristic
117#3147C2211yescharacteristic, complemented
118#3141C2211yescharacteristic
119#3141C2211yescharacteristic, complemented
120#3139C2211yescharacteristic, complemented
121#3138C2211yescharacteristic, complemented
122#3131C2211yescharacteristic, complemented
123#3131C2211yescharacteristic, complemented
124#3131C2211yescharacteristic, complemented
125#3131C2211yescharacteristic, complemented
126C2×#486C2211yescharacteristic, complemented
127C2×#486C2211yescharacteristic, complemented
128#3062—22no—
129#3062—22no—
130#2965C2211yescharacteristic
131#2965C2211yescharacteristic
132#2946—22no—
133#2946—22no—
134C4×#131C2211yescharacteristic
135#1723C2211yescharacteristic, complemented
136#1723C2211yescharacteristic, complemented
137#1722C2211yescharacteristic, complemented
138#1722C2211yescharacteristic, complemented
139#1721C2211yescharacteristic
140#1721C2211yescharacteristic
141#1721C2211yescharacteristic
142#1721C2211yescharacteristic
143#1721C2211yescharacteristic
144#1721C2211yescharacteristic
145#1721C2211yescharacteristic, complemented
146#1721C2211yescharacteristic, complemented
147#1720C2211yescharacteristic, complemented
148#1720C2211yescharacteristic, complemented
149#1720C2211yescharacteristic, complemented
150#1720C2211yescharacteristic, complemented
151#1720C2211yescharacteristic, complemented
152#1720C2211yescharacteristic, complemented
153#1719C2211yescharacteristic, complemented
154#1719C2211yescharacteristic, complemented
155#1719C2211yescharacteristic, complemented
156#1719C2211yescharacteristic, complemented
157#1719C2211yescharacteristic, complemented
158#1719C2211yescharacteristic, complemented
159#1719C2211yescharacteristic, complemented
160#1719C2211yescharacteristic, complemented
161#1718C2211yescharacteristic, complemented
162#1718C2211yescharacteristic, complemented
163#1718C2211yescharacteristic, complemented
164#1718C2211yescharacteristic, complemented
165#1717C2211yescharacteristic
166#1717C2211yescharacteristic
167#1717C2211yescharacteristic
168#1717C2211yescharacteristic
169#1717C2211yescharacteristic
170#1717C2211yescharacteristic
171#1717C2211yescharacteristic, complemented
172#1717C2211yescharacteristic, complemented
173#1717C2211yescharacteristic, complemented
174#1717C2211yescharacteristic, complemented
175#1717C2211yescharacteristic, complemented
176#1717C2211yescharacteristic, complemented
177#1717C2211yescharacteristic, complemented
178#1717C2211yescharacteristic, complemented
179#1716C2211yescharacteristic, complemented
180#1715C2211yescharacteristic
181#1715C2211yescharacteristic
182#1715C2211yescharacteristic, complemented
183#1715C2211yescharacteristic, complemented
184#1715C2211yescharacteristic, complemented
185#1714C2211yescharacteristic, complemented
186#1714C2211yescharacteristic, complemented
187#1714C2211yescharacteristic, complemented
188#1714C2211yescharacteristic, complemented
189#1714C2211yescharacteristic, complemented
190#1714C2211yescharacteristic, complemented
191#1712C2211yescharacteristic
192#1710C2211yescharacteristic, complemented
193#1708C2211yescharacteristic, complemented
194#1707C2211yescharacteristic, complemented
195#1706C2211yescharacteristic
196#1706C2211yescharacteristic, complemented
197#1706C2211yescharacteristic, complemented
198#1705C2211yescharacteristic, complemented
199#1455C2211yescharacteristic, complemented
200#1455C2211yescharacteristic, complemented
201#1453C2211yescharacteristic, complemented
202#1453C2211yescharacteristic, complemented
203#1451C2211yescharacteristic, complemented
204#1451C2211yescharacteristic, complemented
205#1451C2211yescharacteristic, complemented
206#1451C2211yescharacteristic, complemented
207#1451C2211yescharacteristic, complemented
208#1451C2211yescharacteristic, complemented
209#1450C2211yescharacteristic, complemented
210C2×#322C2211yescharacteristic, complemented
211C2×#137—22no—
212C2×AGL(1,ℤ/8)—22no—
213C2×AGL(1,ℤ/8)—22no—
214C2×AGL(1,ℤ/8)—22no—
215C2×AGL(1,ℤ/8)—22no—
216C2×AGL(1,ℤ/8)—22no—
217C2×#135—22no—
218C2×#135—22no—
219C2×#131D412yes—
220#559—21no—
221#559—21no—
222#559—21no—
223#559—21no—
224#556—21no—
225#556—21no—
226#555—21no—
227#555—21no—
228#554—21no—
229#554—21no—
230#553—21no—
231#553—21no—
232#553—21no—
233#553—21no—
234#550—21no—
235#550—21no—
236#550—21no—
237#550—21no—
238#548—21no—
239#548—21no—
240#548—21no—
241#548—21no—
242#547—21no—
243#547—21no—
244#546—21no—
245#546—21no—
246#546—21no—
247#546—21no—
248#546—21no—
249#546—21no—
250#546—21no—
251#546—21no—
252#542—21no—
253#542—21no—
254#542—21no—
255#542—21no—
256#540—21no—
257#540—21no—
258#540—21no—
259#540—21no—
260#537—21no—
261#537—21no—
262#535—21no—
263#535—21no—
264#533C2311yescharacteristic
265#533C2311yescharacteristic
266#533C2311yescharacteristic
267#533C2311yescharacteristic
268#533C2311yescharacteristic
269#533C2311yescharacteristic
270#532C2311yescharacteristic
271#532C2311yescharacteristic
272#532C2311yescharacteristic
273#532C2311yescharacteristic
274#532C2311yescharacteristic
275#532C2311yescharacteristic
276#532C2311yescharacteristic
277#532C2311yescharacteristic
278#532C2311yescharacteristic
279#532C2311yescharacteristic
280#532C2311yescharacteristic
281#532C2311yescharacteristic
282#532C2311yescharacteristic
283#532C2311yescharacteristic
284C2×C4⋊Q8C2311yescharacteristic
285C2×C4⋊Q8C2311yescharacteristic
286C2×#127C2311yescharacteristic
287C2×#127C2311yescharacteristic
288#520—21no—
289#520—21no—
290#518—21no—
291#518—21no—
292C4×#41C2311yescharacteristic
293#501—22no—
294#501—22no—
295#500C2311yescharacteristic
296#500C2311yescharacteristic
297#500C2311yescharacteristic
298#500C2311yescharacteristic
299#500C2311yescharacteristic
300#500C2311yescharacteristic
301#500C2311yescharacteristic
302#500C2311yescharacteristic
303#498C2311yescharacteristic
304#498C2311yescharacteristic
305#498C2311yescharacteristic
306#498C2311yescharacteristic
307#498C2311yescharacteristic
308#498C2311yescharacteristic
309#498C2311yescharacteristic
310#498C2311yescharacteristic
311#497—22no—
312#496—22no—
313#496—22no—
314#496—22no—
315#496—22no—
316#496—22no—
317#495—22no—
318#495—22no—
319#494C2311yescharacteristic
320#494C2311yescharacteristic
321#494C2311yescharacteristic
322#493C2311yescharacteristic
323#493C2311yescharacteristic
324#493C2311yescharacteristic
325#493C2311yescharacteristic
326#493C2311yescharacteristic
327#493C2311yescharacteristic
328#493C2311yescharacteristic
329#493C2311yescharacteristic
330#493C2311yescharacteristic
331#493C2311yescharacteristic
332#493C2311yescharacteristic
333#493C2311yescharacteristic
334#493C2311yescharacteristic
335#492C2311yescharacteristic
336#492C2311yescharacteristic
337#492C2311yescharacteristic
338#492C2311yescharacteristic
339#492C2311yescharacteristic
340#492C2311yescharacteristic
341#492C2311yescharacteristic
342#492C2311yescharacteristic
343#492C2311yescharacteristic
344#492C2311yescharacteristic
345#492C2311yescharacteristic
346#492C2311yescharacteristic
347#492C2311yescharacteristic
348#492C2311yescharacteristic
349#492C2311yescharacteristic
350#492C2311yescharacteristic
351#491—22no—
352#490—22no—
353#489—22no—
354#489—22no—
355#488—22no—
356#488—22no—
357#488—22no—
358#488—22no—
359#487C2311yescharacteristic
360#487C2311yescharacteristic
361#487C2311yescharacteristic
362#487C2311yescharacteristic
363#487C2311yescharacteristic
364#487C2311yescharacteristic
365#487C2311yescharacteristic
366#487C2311yescharacteristic
367#487C2311yescharacteristic
368#487C2311yescharacteristic
369#487C2311yescharacteristic
370#487C2311yescharacteristic
371#487C2311yescharacteristic
372#487C2311yescharacteristic
373#487C2311yescharacteristic
374#487C2311yescharacteristic
375#487C2311yescharacteristic
376#487C2311yescharacteristic
377#486—22no—
378#486—22no—
379#486C2311yescharacteristic
380#486C2311yescharacteristic
381#486C2311yescharacteristic
382#486C2311yescharacteristic
383#486C2311yescharacteristic
384#486C2311yescharacteristic
385#486C2311yescharacteristic
386#486C2311yescharacteristic
387#486C2311yescharacteristic
388#486C2311yescharacteristic
389#486C2311yescharacteristic
390#486C2311yescharacteristic
391#486C2311yescharacteristic
392#486C2311yescharacteristic
393#486C2311yescharacteristic
394#486C2311yescharacteristic
395#486C2311yescharacteristic
396#486C2311yescharacteristic
397#486C2311yescharacteristic
398#486C2311yescharacteristic
399#486C2311yescharacteristic
400#486C2311yescharacteristic
401#486C2311yescharacteristic
402#486C2311yescharacteristic
403#486C2311yescharacteristic
404#486C2311yescharacteristic
405#486C2311yescharacteristic
406#486C2311yescharacteristic
407#486C2311yescharacteristic
408#486C2311yescharacteristic
409#485—22no—
410#485—22no—
411#483—22no—
412#482—22no—
413#482—22no—
414#480—22no—
415#479—22no—
416#479—22no—
417#478—22no—
418#478—22no—
419#475—22no—
420#474—22no—
421#470—22no—
422#469—22no—
423#469—22no—
424#469—22no—
425#469—22no—
426#469—22no—
427#469—22no—
428#469—22no—
429#468—22no—
430#468—22no—
431#468—22no—
432#468—22no—
433#468—22no—
434#468—22no—
435#468—22no—
436#468—22no—
437#466—22no—
438#466—22no—
439#466—22no—
440#466—22no—
441#466—22no—
442#466—22no—
443#465—22no—
444#465—22no—
445#465—22no—
446#465—22no—
447#465—22no—
448#465—22no—
449#464—22no—
450#464—22no—
451#464—22no—
452#464—22no—
453#463—22no—
454#463—22no—
455#463—22no—
456#463—22no—
457#463—22no—
458#463—22no—
459#463—22no—
460#463—22no—
461#461—22no—
462#461—22no—
463#460—22no—
464#459—22no—
465#459—22no—
466#459—22no—
467#452—22no—
468#452—22no—
469#452—22no—
470#452—22no—
471#450—22no—
472#449—22no—
473#449—22no—
474#449—22no—
475#449—22no—
476#449—22no—
477#449—22no—
478#449—22no—
479#449—22no—
480#448—22no—
481#448—22no—
482#447—22no—
483#447—22no—
484#447—22no—
485#446D412yes—
486#446D412yes—
487#442—22no—
488#442—22no—
489#442—22no—
490#442—22no—
491#442—22no—
492#442—22no—
493#442—22no—
494#441—22no—
495#440—22no—
496#440—22no—
497#440—22no—
498#440—22no—
499#440—22no—
500#440—22no—
501#440—22no—
502#440—22no—
503C4×SD16—22no—
504C4×SD16—22no—
505C4×SD16—22no—
506C4×SD16—22no—
507C4×SD16—22no—
508C4×SD16—22no—
509C4×D8—22no—
510C4×D8—22no—
511C4×D8—22no—
512C4×D8—22no—
513C4×D8—22no—
514C4×D8—22no—
515#436D412yes—
516#436D412yes—
517#435D412yes—
518#435D412yes—
519#435D412yes—
520#435D412yes—
521#431C2311yescharacteristic
522#431C2311yescharacteristic
523#431C2311yescharacteristic
524#431C2311yescharacteristic
525#431C2311yescharacteristic
526#431C2311yescharacteristic
527#428—22no—
528#428—22no—
529#419—22no—
530#418—22no—
531#417—22no—
532#417—22no—
533#416—22no—
534#416—22no—
535#416—22no—
536#416—22no—
537C2×#102—22no—
538C2×#102—22no—
539#405D412yes—
540#405D412yes—
541#405D412yes—
542C4×M16C2311yescharacteristic
543C4×M16C2311yescharacteristic
544C4×M16C2311yescharacteristic
545C4×M16C2311yescharacteristic
546C4×M16C2311yescharacteristic
547C4×M16C2311yescharacteristic
548C4×M16C2311yescharacteristic
549C2×C4×C8C2311yescharacteristic
550C2×C4×C8C2311yescharacteristic
551C2×C4×C8C2311yescharacteristic
552C2×C4×C8C2311yescharacteristic
553C2×C4×C8C2311yescharacteristic
554#322C2311yescharacteristic
555#322C2311yescharacteristic
556#322C2311yescharacteristic
557#322C2311yescharacteristic
558#322C2311yescharacteristic
559#322C2311yescharacteristic
560#322C2311yescharacteristic
561#322C2311yescharacteristic
562#322C2311yescharacteristic
563#322C2311yescharacteristic
564#322C2311yescharacteristic
565#322C2311yescharacteristic
566#322C2311yescharacteristic
567#322C2311yescharacteristic
568C82C2311yescharacteristic
569C82C2311yescharacteristic
570C2×#41—21no—
571C2×#41—21no—
572C2×#41—21no—
573C2×#41—21no—
574C2×#41—21no—
575C2×#41—21no—
576C2×#41—21no—
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41C2×D411yescharacteristic
585C22×Q8—21no—
586C22×Q8—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593#137—84no—
594AGL(1,ℤ/8)—48no—
595AGL(1,ℤ/8)—48no—
596AGL(1,ℤ/8)—84no—
597AGL(1,ℤ/8)—84no—
598AGL(1,ℤ/8)—84no—
599#135—84no—
600#135—84no—
601C2×Q16—22no—
602C2×Q16—22no—
603C2×Q16—22no—
604C2×SD16—22no—
605C2×SD16—22no—
606C2×SD16—22no—
607C2×SD16—22no—
608C2×SD16—22no—
609C2×SD16—22no—
610C2×SD16—22no—
611C2×SD16—22no—
612C2×SD16—22no—
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—22no—
624C2×D8—22no—
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—22no—
630C2×D8—22no—
631C2×D8—22no—
632C2×D8—22no—
633#131—44no—
634C2×M16C2×D412yes—
635C2×M16C2×D412yes—
636C2×M16C2×D412yes—
637C2×M16C2×D412yes—
638C2×M16C2×D412yes—
639C2×M16C2×D412yes—
640C2×M16C2×D412yes—
641C22×C8C2×D412yes—
642C22×C8C2×D412yes—
643C22×C8C2×D412yes—
644C22×C8C2×D412yes—
645C22×C8C2×D412yes—
646C4⋊Q8—21no—
647C4⋊Q8—21no—
648C4⋊Q8—21no—
649C4⋊Q8—21no—
650C4⋊Q8—21no—
651C4⋊Q8—21no—
652C4⋊Q8C2411yescharacteristic
653C4⋊Q8C2411yescharacteristic
654C4⋊Q8C2411yescharacteristic
655C4⋊Q8C2411yescharacteristic
656C4⋊Q8C2411yescharacteristic
657C4⋊Q8C2411yescharacteristic
658C4⋊Q8C2411yescharacteristic
659C4⋊Q8C2411yescharacteristic
660C4⋊Q8C2411yescharacteristic
661C4⋊Q8C2411yescharacteristic
662#127—21no—
663#127—21no—
664#127—21no—
665#127—21no—
666#127—21no—
667#127—21no—
668#127—41no—
669#127—41no—
670#127C2411yescharacteristic
671#127C2411yescharacteristic
672#127C2411yescharacteristic
673#127C2411yescharacteristic
674#127C2411yescharacteristic
675#127C2411yescharacteristic
676#126—41no—
677#126—41no—
678#126—41no—
679#126—41no—
680#125—21no—
681#125—21no—
682#125—21no—
683#125—21no—
684#125—21no—
685#125—21no—
686#124—21no—
687#124—21no—
688#124—21no—
689#124—21no—
690#124—21no—
691#124—21no—
692#124—21no—
693#124—21no—
694#124—21no—
695#124—21no—
696#124—21no—
697#124—21no—
698#124—21no—
699#124—21no—
700#124—41no—
701#124—41no—
702#124—41no—
703#124—41no—
704#124—41no—
705#124—41no—
706#123—41no—
707#123—41no—
708#123—41no—
709#123—41no—
710#123—41no—
711#123—41no—
712#123—41no—
713#123—41no—
714#123—41no—
715#123—41no—
716#123—41no—
717#123—41no—
718C22⋊Q8—21no—
719C22⋊Q8—21no—
720C22⋊Q8—21no—
721C22⋊Q8—21no—
722C22⋊Q8—21no—
723C22⋊Q8—21no—
724C22⋊Q8—21no—
725C22⋊Q8—21no—
726C22⋊Q8—21no—
727C22⋊Q8—21no—
728C22⋊Q8—21no—
729C22⋊Q8—21no—
730C22⋊Q8—41no—
731C22⋊Q8—41no—
732C22⋊Q8—41no—
733C22⋊Q8—41no—
734C22⋊Q8—41no—
735C22⋊Q8—41no—
736#121—21no—
737#121—21no—
738#121—21no—
739#121—21no—
740#121—21no—
741#121—21no—
742#121—21no—
743#121—21no—
744#121—21no—
745#121—21no—
746#121—21no—
747#121—21no—
748#121—21no—
749#121—21no—
750#121—21no—
751#121—21no—
752#121—21no—
753#121—21no—
754#121—21no—
755#121—21no—
756#121—21no—
757#121—21no—
758#121—21no—
759#121—21no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—41no—
765#121—41no—
766#121—41no—
767#121—41no—
768#121—41no—
769#121—41no—
770#121—41no—
771#121—41no—
772#121—41no—
773#121—41no—
774#121—41no—
775#121—41no—
776#121—41no—
777#121—41no—
778#120—41no—
779#120—41no—
780#120—41no—
781#120—41no—
782C4×Q8—21no—
783C4×Q8—21no—
784C4×Q8—21no—
785C4×Q8—21no—
786C4×Q8—21no—
787C4×Q8—21no—
788C4×Q8—21no—
789C4×Q8—21no—
790C4×Q8—21no—
791C4×Q8—21no—
792C4×Q8—21no—
793C4×Q8—21no—
794C4×Q8C2×D411yescharacteristic
795C4×Q8C2×D411yescharacteristic
796C4×D4—21no—
797C4×D4—21no—
798C4×D4—21no—
799C4×D4—21no—
800C4×D4—21no—
801C4×D4—21no—
802C4×D4—21no—
803C4×D4—21no—
804C4×D4—21no—
805C4×D4—21no—
806C4×D4—21no—
807C4×D4—21no—
808C4×D4—21no—
809C4×D4—21no—
810C4×D4—21no—
811C4×D4—21no—
812C4×D4—21no—
813C4×D4—21no—
814C4×D4—21no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—21no—
819C4×D4—21no—
820C4×D4—21no—
821C4×D4—21no—
822C4×D4—21no—
823C4×D4—21no—
824C4×D4—41no—
825C4×D4—41no—
826C4×D4—41no—
827C4×D4—41no—
828C4×D4—41no—
829C4×D4—41no—
830C4×D4—41no—
831C4×D4—41no—
832C4×D4C2×D411yescharacteristic
833C4×D4C2×D411yescharacteristic
834C4×D4C2×D411yescharacteristic
835C4×D4C2×D411yescharacteristic
836C4×D4C2×D411yescharacteristic
837C4×D4C2×D411yescharacteristic
838#117—21no—
839#117—21no—
840#117—21no—
841#117—21no—
842#117—21no—
843#117—21no—
844#117—41no—
845#117—41no—
846#117C2×D411yescharacteristic
847#117C2×D411yescharacteristic
848#117C2×D411yescharacteristic
849C2×C4⋊C4—21no—
850C2×C4⋊C4—21no—
851C2×C4⋊C4—21no—
852C2×C4⋊C4—21no—
853C2×C4⋊C4—41no—
854C2×C4⋊C4—41no—
855C2×C22⋊C4—41no—
856C2×C22⋊C4—41no—
857C2×C22⋊C4—41no—
858C2×C22⋊C4—41no—
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862#107—22no—
863#107—22no—
864#107—22no—
865#107—22no—
866#107—22no—
867#107—22no—
868#107—22no—
869#107—22no—
870#106—22no—
871#106—22no—
872#106—22no—
873#106—22no—
874#106—22no—
875#106—22no—
876#106—22no—
877#106—22no—
878C4⋊C8C2×D412yes—
879C4⋊C8C2×D412yes—
880C4⋊C8C2×D412yes—
881C4⋊C8C2×D412yes—
882C4⋊C8C2×D412yes—
883C4⋊C8C2×D412yes—
884#103—22no—
885#103—22no—
886#103—22no—
887#103—22no—
888#103—22no—
889#103—22no—
890#103—22no—
891#103—22no—
892#103—22no—
893#103—22no—
894#103—22no—
895#103—22no—
896#103—22no—
897#103—22no—
898#103—22no—
899#103—22no—
900#103—22no—
901#103—22no—
902#102—22no—
903#102—22no—
904#102—22no—
905#102—22no—
906#102—22no—
907#102—22no—
908#102—22no—
909#102—22no—
910#102—22no—
911#102—22no—
912#102—22no—
913#102—22no—
914#102—22no—
915#102—22no—
916#102—22no—
917#102—22no—
918#102—22no—
919#102—22no—
920#102—22no—
921#102—22no—
922#102—22no—
923#102—22no—
924#102—22no—
925#102—22no—
926#102—22no—
927#102—22no—
928#102—22no—
929#102—22no—
930#102—22no—
931#102—22no—
932C22⋊C8C2×D412yes—
933C22⋊C8C2×D412yes—
934C22⋊C8C2×D412yes—
935C22⋊C8C2×D412yes—
936C22⋊C8C2×D412yes—
937C22⋊C8C2×D412yes—
938#97C2×D412yes—
939#97C2×D412yes—
940#97C2×D412yes—
941#97C2×D412yes—
942#97C2×D412yes—
943#97C2×D412yes—
944#97C2×D412yes—
945C4×C8C2×D412yes—
946C4×C8C2×D412yes—
947C4×C8C2×D412yes—
948C4×C8C2×D412yes—
949C4×C8C2×D412yes—
950C4×C8C2411yescharacteristic
951C4×C8C2411yescharacteristic
952C4×C8C2411yescharacteristic
953C4×C8C2411yescharacteristic
954C4×C8C2411yescharacteristic
955C4×C8C2411yescharacteristic
956C4×C8C2411yescharacteristic
957C4×C8C2411yescharacteristic
958C4×C8C2411yescharacteristic
959C4×C8C2411yescharacteristic
960C4×C8C2411yescharacteristic
961C4×C8C2411yescharacteristic
962C24—41no—
963C24—41no—
964#41—42no—
965#41—44no—
966#41—44no—
967#41—82no—
968#41—82no—
969#41—82no—
970#41—82no—
971#41—82no—
972#41—82no—
973#41—82no—
974#41—82no—
975#41—82no—
976#41—82no—
977#41—82no—
978#41—82no—
979C2×Q8—21no—
980C2×Q8—21no—
981C2×Q8—21no—
982C2×Q8—21no—
983C2×Q8—21no—
984C2×Q8—21no—
985C2×Q8—21no—
986C2×Q8—21no—
987C2×Q8—21no—
988C2×Q8—21no—
989C2×Q8—41no—
990C2×Q8—41no—
991C2×Q8—82no—
992C2×Q8—82no—
993C2×Q8#12711yescharacteristic
994C2×D4—21no—
995C2×D4—21no—
996C2×D4—21no—
997C2×D4—21no—
998C2×D4—21no—
999C2×D4—21no—
1000C2×D4—21no—
1001C2×D4—21no—
1002C2×D4—21no—
1003C2×D4—21no—
1004C2×D4—21no—
1005C2×D4—21no—
1006C2×D4—21no—
1007C2×D4—21no—
1008C2×D4—21no—
1009C2×D4—21no—
1010C2×D4—21no—
1011C2×D4—21no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—41no—
1015C2×D4—41no—
1016C2×D4—41no—
1017C2×D4—41no—
1018C2×D4—41no—
1019C2×D4—41no—
1020C2×D4—41no—
1021C2×D4—41no—
1022C2×D4—41no—
1023C2×D4—41no—
1024C2×D4—41no—
1025C2×D4—41no—
1026C2×D4—41no—
1027C2×D4—41no—
1028C2×D4—41no—
1029C2×D4—41no—
1030C2×D4—41no—
1031C2×D4—41no—
1032C2×D4—41no—
1033C2×D4—41no—
1034C2×D4—82no—
1035C2×D4—82no—
1036C2×D4—82no—
1037C2×D4—82no—
1038C2×D4#12711yescharacteristic
1039C2×D4#12711yescharacteristic
1040C2×D4#12711yescharacteristic
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—41no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—41no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4C22×D411yescharacteristic
1058C22×C4C22×D411yescharacteristic
1059C22×C4C22×D411yescharacteristic
1060C22×C4C22×D411yescharacteristic
1061C22×C4C22×D411yescharacteristic
1062C22×C4C22×D411yescharacteristic
1063C22×C4C22×D411yescharacteristic
1064C22×C4C22×D411yescharacteristic
1065C22×C4C22×D411yescharacteristic
1066Q16—44no—
1067Q16—82no—
1068Q16—82no—
1069SD16—44no—
1070SD16—44no—
1071SD16—44no—
1072SD16—44no—
1073SD16—44no—
1074SD16—44no—
1075SD16—44no—
1076SD16—82no—
1077SD16—82no—
1078SD16—82no—
1079SD16—82no—
1080SD16—82no—
1081SD16—82no—
1082SD16—82no—
1083SD16—82no—
1084SD16—82no—
1085D8—44no—
1086D8—44no—
1087D8—44no—
1088D8—44no—
1089D8—44no—
1090D8—44no—
1091D8—82no—
1092D8—82no—
1093D8—82no—
1094D8—82no—
1095D8—82no—
1096D8—82no—
1097D8—82no—
1098M16—24no—
1099M16—24no—
1100M16—42no—
1101M16—42no—
1102M16—42no—
1103M16—42no—
1104M16—42no—
1105C2×C8—24no—
1106C2×C8—42no—
1107C2×C8—42no—
1108C2×C8—42no—
1109C2×C8—42no—
1110C2×C8C22×D412yes—
1111C2×C8C22×D412yes—
1112C2×C8C22×D412yes—
1113C2×C8C22×D412yes—
1114C2×C8C22×D412yes—
1115C2×C8C22×D412yes—
1116C2×C8C22×D412yes—
1117C2×C8C22×D412yes—
1118C2×C8C22×D412yes—
1119C2×C8C22×D412yes—
1120C2×C8C22×D412yes—
1121C2×C8C22×D412yes—
1122C4⋊C4—21no—
1123C4⋊C4—21no—
1124C4⋊C4—21no—
1125C4⋊C4—21no—
1126C4⋊C4—21no—
1127C4⋊C4—21no—
1128C4⋊C4—21no—
1129C4⋊C4—21no—
1130C4⋊C4—21no—
1131C4⋊C4—21no—
1132C4⋊C4—21no—
1133C4⋊C4—21no—
1134C4⋊C4—21no—
1135C4⋊C4—21no—
1136C4⋊C4—21no—
1137C4⋊C4—21no—
1138C4⋊C4—21no—
1139C4⋊C4—21no—
1140C4⋊C4—21no—
1141C4⋊C4—21no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—41no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—41no—
1150C4⋊C4—41no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4—41no—
1154C4⋊C4—41no—
1155C4⋊C4—41no—
1156C4⋊C4—41no—
1157C4⋊C4—41no—
1158C4⋊C4#12711yescharacteristic
1159C4⋊C4#12711yescharacteristic
1160C4⋊C4#12711yescharacteristic
1161C4⋊C4#12711yescharacteristic
1162C4⋊C4#12711yescharacteristic
1163C4⋊C4#12711yescharacteristic
1164C22⋊C4—41no—
1165C22⋊C4—41no—
1166C22⋊C4—41no—
1167C22⋊C4—41no—
1168C22⋊C4—41no—
1169C22⋊C4—41no—
1170C22⋊C4—41no—
1171C22⋊C4—41no—
1172C22⋊C4—41no—
1173C22⋊C4—41no—
1174C22⋊C4—41no—
1175C22⋊C4—41no—
1176C22⋊C4—41no—
1177C22⋊C4—41no—
1178C22⋊C4—41no—
1179C22⋊C4—41no—
1180C22⋊C4—41no—
1181C22⋊C4—41no—
1182C22⋊C4—41no—
1183C22⋊C4—41no—
1184C22⋊C4—41no—
1185C22⋊C4—41no—
1186C22⋊C4—41no—
1187C22⋊C4—41no—
1188C22⋊C4—41no—
1189C22⋊C4—41no—
1190C22⋊C4—41no—
1191C22⋊C4—41no—
1192C22⋊C4—41no—
1193C22⋊C4—41no—
1194C22⋊C4—41no—
1195C22⋊C4—41no—
1196C22⋊C4—41no—
1197C22⋊C4—41no—
1198C22⋊C4#12711yescharacteristic
1199C22⋊C4#12711yescharacteristic
1200C22⋊C4#12711yescharacteristic
1201C22⋊C4#12711yescharacteristic
1202C22⋊C4#12711yescharacteristic
1203C22⋊C4#12711yescharacteristic
1204C42—41no—
1205C42—41no—
1206C42—41no—
1207C42—41no—
1208C42—41no—
1209C42—41no—
1210C42C22×D411yescharacteristic
1211C42C22×D411yescharacteristic
1212C42C22×D411yescharacteristic
1213C42C22×D411yescharacteristic
1214C42C22×D411yescharacteristic
1215C42C22×D411yescharacteristic
1216C42C22×D411yescharacteristic
1217C42C22×D411yescharacteristic
1218C42C22×D411yescharacteristic
1219C42C2511yescharacteristic
1220C23—41no—
1221C23—41no—
1222C23—41no—
1223C23—41no—
1224C23—41no—
1225C23—41no—
1226C23—82no—
1227C23—82no—
1228C23—161no—
1229C23—161no—
1230C23—161no—
1231C23—161no—
1232C23C2×#12711yescharacteristic
1233C23C2×#12711yescharacteristic
1234C23C2×#12711yescharacteristic
1235Q8—41no—
1236Q8—42no—
1237Q8—42no—
1238Q8—42no—
1239Q8—42no—
1240Q8—42no—
1241Q8—42no—
1242Q8—42no—
1243Q8—42no—
1244Q8—42no—
1245Q8—42no—
1246Q8—161no—
1247Q8—161no—
1248D4—41no—
1249D4—41no—
1250D4—41no—
1251D4—42no—
1252D4—42no—
1253D4—42no—
1254D4—42no—
1255D4—42no—
1256D4—42no—
1257D4—42no—
1258D4—42no—
1259D4—42no—
1260D4—42no—
1261D4—42no—
1262D4—42no—
1263D4—42no—
1264D4—42no—
1265D4—42no—
1266D4—42no—
1267D4—42no—
1268D4—42no—
1269D4—82no—
1270D4—82no—
1271D4—82no—
1272D4—82no—
1273D4—161no—
1274D4—161no—
1275D4—161no—
1276D4—161no—
1277D4—161no—
1278D4—161no—
1279D4—161no—
1280D4—161no—
1281D4—161no—
1282D4—161no—
1283D4—161no—
1284D4—161no—
1285D4—161no—
1286D4—161no—
1287D4—161no—
1288D4—161no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—82no—
1309C2×C4—82no—
1310C2×C4—161no—
1311C2×C4—161no—
1312C2×C4—161no—
1313C2×C4—161no—
1314C2×C4—161no—
1315C2×C4—161no—
1316C2×C4—161no—
1317C2×C4—161no—
1318C2×C4—161no—
1319C2×C4—161no—
1320C2×C4—161no—
1321C2×C4—161no—
1322C2×C4—161no—
1323C2×C4—161no—
1324C2×C4C2×#12711yescharacteristic
1325C2×C4C2×#12711yescharacteristic
1326C2×C4C2×#12711yescharacteristic
1327C2×C4C2×#12711yescharacteristic
1328C2×C4C2×#12711yescharacteristic
1329C2×C4C2×#12711yescharacteristic
1330C2×C4C2×#12711yescharacteristic
1331C2×C4C2×#12711yescharacteristic
1332C2×C4C2×#12711yescharacteristic
1333C2×C4C23×D411yescharacteristic
1334C2×C4C23×D411yescharacteristic
1335C2×C4C23×D411yescharacteristic
1336C8—22no—
1337C8—22no—
1338C8—22no—
1339C8—22no—
1340C8—22no—
1341C8—22no—
1342C8—22no—
1343C8—22no—
1344C8—22no—
1345C8—22no—
1346C8—22no—
1347C8#57514yes—
1348C22—21no—
1349C22—21no—
1350C22—21no—
1351C22—21no—
1352C22—21no—
1353C22—21no—
1354C22—21no—
1355C22—21no—
1356C22—21no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—322no—
1376C22—322no—
1377C22C22×#12711yescharacteristic
1378C4—21no—
1379C4—21no—
1380C4—21no—
1381C4—21no—
1382C4—21no—
1383C4—21no—
1384C4—21no—
1385C4—21no—
1386C4—21no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4C2×#57512yes—
1398C4#358512yes—
1399C4#358512yes—
1400C2—41no—
1401C2—41no—
1402C2—41no—
1403C2—161no—
1404C2—161no—
1405C2—161no—
1406C2—161no—
1407C2—161no—
1408C2—161no—
1409C2#6063911yescharacteristic
1410C2#6065011yescharacteristic
1411C2#6065011yescharacteristic
subgroupG/H
center, socleC22C22×#127
commutator, Frattini, cosocleC42C25
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62546C2semidirect
2. #62543C2semidirect
3. #62427C2semidirect
4. #62426C2semidirect
5. #60722C2semidirect
6. #60722C2semidirect
7. #19752C2semidirect
8. #19748C2semidirect
9. #19747C2semidirect
10. #19745C2semidirect
11. #19727C2semidirect
12. #19726C2semidirect
13. #19719C2semidirect
14. #19714C2semidirect
15. #19695C2semidirect
16. #19695C2semidirect
17. #19695C2semidirect
18. #19694C2semidirect
19. #19692C2semidirect
20. #19691C2semidirect
21. #19691C2semidirect
22. #19689C2semidirect
23. #19678C2semidirect
24. #19677C2semidirect
25. #19673C2semidirect
26. #19673C2semidirect
27. #19667C2semidirect
28. #19665C2semidirect
29. #19619C2semidirect
30. #19619C2semidirect
31. #17336C2semidirect
52. #3231C22semidirect
53. #3231C22semidirect
54. #3229C22semidirect
55. #3228C22semidirect
56. #3228C22semidirect
60. #3210C22semidirect
61. #3210C22semidirect
62. #3208C22semidirect
67. #3207C22semidirect
68. #3207C22semidirect
69. #3207C22semidirect
70. #3207C22semidirect
72. #3206C22semidirect
75. #3205C22semidirect
76. #3185C22semidirect
81. #3184C22semidirect
82. #3184C22semidirect
83. #3184C22semidirect
88. #3182C22semidirect
89. #3182C22semidirect
90. #3182C22semidirect
91. #3182C22semidirect
99. #3169C22semidirect
100. #3169C22semidirect
101. #3169C22semidirect
104. #3167C22semidirect
105. #3167C22semidirect
106. #3167C22semidirect
107. #3167C22semidirect
108. #3165C22semidirect
109. #3165C22semidirect
113. #3151C22semidirect
114. #3151C22semidirect
115. #3151C22semidirect
117. #3147C22semidirect
119. #3141C22semidirect
120. #3139C22semidirect
121. #3138C22semidirect
122. #3131C22semidirect
123. #3131C22semidirect
124. #3131C22semidirect
125. #3131C22semidirect
126. C2×#486C22semidirect
127. C2×#486C22semidirect
135. #1723C22semidirect
136. #1723C22semidirect
137. #1722C22semidirect
138. #1722C22semidirect
145. #1721C22semidirect
146. #1721C22semidirect
147. #1720C22semidirect
148. #1720C22semidirect
149. #1720C22semidirect
150. #1720C22semidirect
151. #1720C22semidirect
152. #1720C22semidirect
153. #1719C22semidirect
154. #1719C22semidirect
155. #1719C22semidirect
156. #1719C22semidirect
157. #1719C22semidirect
158. #1719C22semidirect
159. #1719C22semidirect
160. #1719C22semidirect
161. #1718C22semidirect
162. #1718C22semidirect
163. #1718C22semidirect
164. #1718C22semidirect
171. #1717C22semidirect
172. #1717C22semidirect
173. #1717C22semidirect
174. #1717C22semidirect
175. #1717C22semidirect
176. #1717C22semidirect
177. #1717C22semidirect
178. #1717C22semidirect
179. #1716C22semidirect
182. #1715C22semidirect
183. #1715C22semidirect
184. #1715C22semidirect
185. #1714C22semidirect
186. #1714C22semidirect
187. #1714C22semidirect
188. #1714C22semidirect
189. #1714C22semidirect
190. #1714C22semidirect
192. #1710C22semidirect
193. #1708C22semidirect
194. #1707C22semidirect
196. #1706C22semidirect
197. #1706C22semidirect
198. #1705C22semidirect
199. #1455C22semidirect
200. #1455C22semidirect
201. #1453C22semidirect
202. #1453C22semidirect
203. #1451C22semidirect
204. #1451C22semidirect
205. #1451C22semidirect
206. #1451C22semidirect
207. #1451C22semidirect
208. #1451C22semidirect
209. #1450C22semidirect
210. C2×#322C22semidirect

Maximal subgroups

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

subgroupindex
#625462
#625432
#624272
#624262
#607222
#197522
#197482
#197472
#197452
#197272
#197262
#197192
#197142
#196952
#196942
#196922
#196912
#196892
#196782
#196772
#196732
#196672
#196652
#196192
#173362