Finite Group Databasebeta

← #6357928

Subgroups — #6357928

Order 512.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62546C211yesmaximal, characteristic, complemented
2#62545C211yesmaximal, characteristic, complemented
3#62544C211yesmaximal, characteristic, complemented
4#62426C211yesmaximal, characteristic, complemented
5#60722C211yesmaximal, characteristic, complemented
6#60712C211yesmaximal, characteristic, complemented
7#19754C211yesmaximal, characteristic, complemented
8#19752C211yesmaximal, characteristic, complemented
9#19749C211yesmaximal, characteristic, complemented
10#19747C211yesmaximal, characteristic, complemented
11#19729C211yesmaximal, characteristic, complemented
12#19728C211yesmaximal, characteristic, complemented
13#19723C211yesmaximal, characteristic, complemented
14#19719C211yesmaximal, characteristic, complemented
15#19709C211yesmaximal, characteristic, complemented
16#19708C211yesmaximal, characteristic, complemented
17#19693C211yesmaximal, characteristic, complemented
18#19691C211yesmaximal, characteristic, complemented
19#19678C211yesmaximal, characteristic, complemented
20#19671C211yesmaximal, characteristic, complemented
21#19650C211yesmaximal, characteristic, complemented
22#19649C211yesmaximal, characteristic, complemented
23#19646C211yesmaximal, characteristic, complemented
24#19645C211yesmaximal, characteristic, complemented
25#19644C211yesmaximal, characteristic, complemented
26#19644C211yesmaximal, characteristic, complemented
27#19627C211yesmaximal, characteristic, complemented
28#19625C211yesmaximal, characteristic, complemented
29#19619C211yesmaximal, characteristic, complemented
30#19613C211yesmaximal, characteristic, complemented
31#17337C211yesmaximal, characteristic, complemented
32#3511C2211yescharacteristic
33#3509C2211yescharacteristic
34#3508C2211yescharacteristic
35#3508C2211yescharacteristic
36#3403—22no—
37#3377—22no—
38#3371—22no—
39#3370—22no—
40#3327—22no—
41#3323—22no—
42#3322—22no—
43#3319—22no—
44#3317—22no—
45#3315—22no—
46#3313—22no—
47#3311—22no—
48#3309—22no—
49#3273—22no—
50#3268—22no—
51#3268—22no—
52#3231C2211yescharacteristic, complemented
53#3231C2211yescharacteristic, complemented
54#3231C2211yescharacteristic, complemented
55#3230C2211yescharacteristic, complemented
56#3228C2211yescharacteristic, complemented
57#3228C2211yescharacteristic, complemented
58#3228C2211yescharacteristic, complemented
59#3227C2211yescharacteristic
60#3226C2211yescharacteristic
61#3210C2211yescharacteristic
62#3210C2211yescharacteristic
63#3210C2211yescharacteristic
64#3210C2211yescharacteristic, complemented
65#3210C2211yescharacteristic, complemented
66#3210C2211yescharacteristic, complemented
67#3209C2211yescharacteristic, complemented
68#3208C2211yescharacteristic, complemented
69#3207C2211yescharacteristic
70#3207C2211yescharacteristic
71#3207C2211yescharacteristic
72#3207C2211yescharacteristic, complemented
73#3205C2211yescharacteristic
74#3205C2211yescharacteristic
75#3205C2211yescharacteristic, complemented
76#3185C2211yescharacteristic, complemented
77#3185C2211yescharacteristic, complemented
78#3184C2211yescharacteristic
79#3184C2211yescharacteristic
80#3184C2211yescharacteristic, complemented
81#3182C2211yescharacteristic
82#3182C2211yescharacteristic
83#3182C2211yescharacteristic
84#3182C2211yescharacteristic
85#3182C2211yescharacteristic
86#3182C2211yescharacteristic
87#3182C2211yescharacteristic, complemented
88#3182C2211yescharacteristic, complemented
89#3182C2211yescharacteristic, complemented
90#3182C2211yescharacteristic, complemented
91#3182C2211yescharacteristic, complemented
92#3179—22no—
93#3179—22no—
94#3174—22no—
95#3174—22no—
96#3170C2211yescharacteristic, complemented
97#3169C2211yescharacteristic
98#3169C2211yescharacteristic
99#3169C2211yescharacteristic, complemented
100#3169C2211yescharacteristic, complemented
101#3167C2211yescharacteristic
102#3167C2211yescharacteristic
103#3167C2211yescharacteristic
104#3167C2211yescharacteristic, complemented
105#3167C2211yescharacteristic, complemented
106#3167C2211yescharacteristic, complemented
107#3167C2211yescharacteristic, complemented
108#3165C2211yescharacteristic, complemented
109#3160C2211yescharacteristic, complemented
110#3151C2211yescharacteristic
111#3151C2211yescharacteristic
112#3151C2211yescharacteristic, complemented
113#3147C2211yescharacteristic
114C2×#492C2211yescharacteristic, complemented
115#3141C2211yescharacteristic
116#3141C2211yescharacteristic
117#3141C2211yescharacteristic, complemented
118#3139C2211yescharacteristic, complemented
119#3139C2211yescharacteristic, complemented
120#3138C2211yescharacteristic, complemented
121#3138C2211yescharacteristic, complemented
122#3138C2211yescharacteristic, complemented
123#3131C2211yescharacteristic, complemented
124#3131C2211yescharacteristic, complemented
125#3131C2211yescharacteristic, complemented
126#3131C2211yescharacteristic, complemented
127C2×#486C2211yescharacteristic, complemented
128#3062—22no—
129#3057—22no—
130#2965C2211yescharacteristic
131#2965C2211yescharacteristic
132#2949—22no—
133#2946—22no—
134C4×#131C2211yescharacteristic
135#1723C2211yescharacteristic, complemented
136#1723C2211yescharacteristic, complemented
137#1723C2211yescharacteristic, complemented
138#1722C2211yescharacteristic, complemented
139#1721C2211yescharacteristic
140#1721C2211yescharacteristic
141#1721C2211yescharacteristic
142#1721C2211yescharacteristic
143#1720C2211yescharacteristic, complemented
144#1720C2211yescharacteristic, complemented
145#1720C2211yescharacteristic, complemented
146#1720C2211yescharacteristic, complemented
147#1720C2211yescharacteristic, complemented
148#1719C2211yescharacteristic, complemented
149#1719C2211yescharacteristic, complemented
150#1719C2211yescharacteristic, complemented
151#1719C2211yescharacteristic, complemented
152#1719C2211yescharacteristic, complemented
153#1719C2211yescharacteristic, complemented
154#1719C2211yescharacteristic, complemented
155#1719C2211yescharacteristic, complemented
156#1718C2211yescharacteristic, complemented
157#1718C2211yescharacteristic, complemented
158#1718C2211yescharacteristic, complemented
159#1718C2211yescharacteristic, complemented
160#1718C2211yescharacteristic, complemented
161#1717C2211yescharacteristic
162#1717C2211yescharacteristic
163#1717C2211yescharacteristic
164#1717C2211yescharacteristic
165#1717C2211yescharacteristic
166#1717C2211yescharacteristic
167#1717C2211yescharacteristic
168#1717C2211yescharacteristic, complemented
169#1717C2211yescharacteristic, complemented
170#1717C2211yescharacteristic, complemented
171#1716C2211yescharacteristic, complemented
172#1715C2211yescharacteristic
173#1715C2211yescharacteristic, complemented
174#1715C2211yescharacteristic, complemented
175#1714C2211yescharacteristic, complemented
176#1714C2211yescharacteristic, complemented
177#1714C2211yescharacteristic, complemented
178#1714C2211yescharacteristic, complemented
179#1714C2211yescharacteristic, complemented
180#1714C2211yescharacteristic, complemented
181#1714C2211yescharacteristic, complemented
182#1714C2211yescharacteristic, complemented
183#1713C2211yescharacteristic, complemented
184#1711C2211yescharacteristic, complemented
185#1711C2211yescharacteristic, complemented
186#1711C2211yescharacteristic, complemented
187#1710C2211yescharacteristic, complemented
188#1709C2211yescharacteristic
189#1709C2211yescharacteristic
190#1709C2211yescharacteristic, complemented
191#1708C2211yescharacteristic, complemented
192#1708C2211yescharacteristic, complemented
193#1708C2211yescharacteristic, complemented
194#1707C2211yescharacteristic, complemented
195#1706C2211yescharacteristic
196#1706C2211yescharacteristic
197#1706C2211yescharacteristic, complemented
198#1706C2211yescharacteristic, complemented
199#1455C2211yescharacteristic, complemented
200#1455C2211yescharacteristic, complemented
201#1453C2211yescharacteristic, complemented
202#1453C2211yescharacteristic, complemented
203#1452C2211yescharacteristic, complemented
204#1451C2211yescharacteristic, complemented
205#1451C2211yescharacteristic, complemented
206C8×M16C2211yescharacteristic, complemented
207C8×M16C2211yescharacteristic, complemented
208C8×M16C2211yescharacteristic, complemented
209C8×M16C2211yescharacteristic, complemented
210C2×#322C2211yescharacteristic, complemented
211C2×AGL(1,ℤ/8)—22no—
212C2×AGL(1,ℤ/8)—22no—
213C2×AGL(1,ℤ/8)—22no—
214C2×#135—22no—
215C22×SD16—22no—
216C2×#131D412yes—
217#559—21no—
218#559—21no—
219#559—21no—
220#559—21no—
221#557—21no—
222#557—21no—
223#556—21no—
224#556—21no—
225#556—21no—
226#555—21no—
227#554—21no—
228#553—21no—
229#553—21no—
230#552—21no—
231#552—21no—
232#552—21no—
233#552—21no—
234#550—21no—
235#550—21no—
236#550—21no—
237#550—21no—
238#548—21no—
239#548—21no—
240#547—21no—
241#546—21no—
242#546—21no—
243#546—21no—
244#546—21no—
245#546—21no—
246#546—21no—
247#546—21no—
248#546—21no—
249#542—21no—
250#542—21no—
251#541—21no—
252#541—21no—
253#540—21no—
254#540—21no—
255#540—21no—
256#540—21no—
257#537—21no—
258#536—21no—
259#535—21no—
260#535—21no—
261#533C2311yescharacteristic
262#533C2311yescharacteristic
263#533C2311yescharacteristic
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
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2311yescharacteristic
283C2×#127C2311yescharacteristic
284C2×#127C2311yescharacteristic
285#520—21no—
286#519—21no—
287#518—21no—
288#518—21no—
289C4×#41C2311yescharacteristic
290#501—22no—
291#500C2311yescharacteristic
292#500C2311yescharacteristic
293#500C2311yescharacteristic
294#500C2311yescharacteristic
295#500C2311yescharacteristic
296#500C2311yescharacteristic
297#500C2311yescharacteristic
298#500C2311yescharacteristic
299#500C2311yescharacteristic
300#500C2311yescharacteristic
301#499—22no—
302#498C2311yescharacteristic
303#498C2311yescharacteristic
304#498C2311yescharacteristic
305#498C2311yescharacteristic
306#498C2311yescharacteristic
307#498C2311yescharacteristic
308#498C2311yescharacteristic
309#498C2311yescharacteristic
310#496—22no—
311#496—22no—
312#496—22no—
313#495—22no—
314#494C2311yescharacteristic
315#494C2311yescharacteristic
316#494C2311yescharacteristic
317#494C2311yescharacteristic
318#493C2311yescharacteristic
319#493C2311yescharacteristic
320#493C2311yescharacteristic
321#493C2311yescharacteristic
322#493C2311yescharacteristic
323#493C2311yescharacteristic
324#493C2311yescharacteristic
325#493C2311yescharacteristic
326#492—22no—
327#492C2311yescharacteristic
328#492C2311yescharacteristic
329#492C2311yescharacteristic
330#492C2311yescharacteristic
331#492C2311yescharacteristic
332#492C2311yescharacteristic
333#492C2311yescharacteristic
334#492C2311yescharacteristic
335#492C2311yescharacteristic
336#492C2311yescharacteristic
337#492C2311yescharacteristic
338#492C2311yescharacteristic
339#492C2311yescharacteristic
340#492C2311yescharacteristic
341#491—22no—
342#491—22no—
343#490—22no—
344#490—22no—
345#490—22no—
346#489—22no—
347#489—22no—
348#489—22no—
349#488—22no—
350#488—22no—
351#488—22no—
352#488—22no—
353#487C2311yescharacteristic
354#487C2311yescharacteristic
355#487C2311yescharacteristic
356#487C2311yescharacteristic
357#487C2311yescharacteristic
358#487C2311yescharacteristic
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#486—22no—
376#486C2311yescharacteristic
377#486C2311yescharacteristic
378#486C2311yescharacteristic
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#485—22no—
407#485—22no—
408#485—22no—
409#484—22no—
410#482—22no—
411#482—22no—
412#482—22no—
413#481—22no—
414#480—22no—
415#479—22no—
416#479—22no—
417#479—22no—
418#478—22no—
419#478—22no—
420#478—22no—
421#477—22no—
422#476—22no—
423#474—22no—
424#470—22no—
425#470—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#468—22no—
438#468—22no—
439#468—22no—
440#467—22no—
441#466—22no—
442#466—22no—
443#466—22no—
444#466—22no—
445#465—22no—
446#465—22no—
447#465—22no—
448#465—22no—
449#465—22no—
450#465—22no—
451#465—22no—
452#464—22no—
453#464—22no—
454#464—22no—
455#464—22no—
456#464—22no—
457#464—22no—
458#463—22no—
459#463—22no—
460#463—22no—
461#463—22no—
462#462—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#452—22no—
472#452—22no—
473#451—22no—
474#450—22no—
475#449—22no—
476#449—22no—
477#449—22no—
478#449—22no—
479#447—22no—
480#447—22no—
481#447—22no—
482#446D412yes—
483#446D412yes—
484#442—22no—
485#442—22no—
486#442—22no—
487#441—22no—
488#441—22no—
489#440—22no—
490#440—22no—
491#440—22no—
492#440—22no—
493#440—22no—
494#440—22no—
495#440—22no—
496#440—22no—
497#440—22no—
498#440—22no—
499#440—22no—
500C4×Q16—22no—
501C4×SD16—22no—
502C4×SD16—22no—
503C4×SD16—22no—
504C4×SD16—22no—
505C4×SD16—22no—
506C4×SD16—22no—
507C4×SD16—22no—
508C4×D8—22no—
509C4×D8—22no—
510C4×D8—22no—
511C4×D8—22no—
512#436D412yes—
513#436D412yes—
514#435D412yes—
515#435D412yes—
516#435D412yes—
517#435D412yes—
518#431C2311yescharacteristic
519#431C2311yescharacteristic
520#431C2311yescharacteristic
521#431C2311yescharacteristic
522#431C2311yescharacteristic
523#431C2311yescharacteristic
524#428—22no—
525#427—22no—
526#419—22no—
527#419—22no—
528#418—22no—
529#418—22no—
530#418—22no—
531#417—22no—
532#417—22no—
533#417—22no—
534#416—22no—
535#416—22no—
536#416—22no—
537#416—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
566C82C2311yescharacteristic
567C82C2311yescharacteristic
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×#41C2×D411yescharacteristic
582C22×Q8—21no—
583C22×Q8—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590AGL(1,ℤ/8)—48no—
591AGL(1,ℤ/8)—84no—
592AGL(1,ℤ/8)—84no—
593#135—84no—
594C2×Q16—22no—
595C2×Q16—22no—
596C2×Q16—22no—
597C2×Q16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—22no—
602C2×SD16—22no—
603C2×SD16—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—48no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—22no—
621#131—44no—
622C2×M16C2×D412yes—
623C2×M16C2×D412yes—
624C2×M16C2×D412yes—
625C2×M16C2×D412yes—
626C2×M16C2×D412yes—
627C2×M16C2×D412yes—
628C2×M16C2×D412yes—
629C22×C8C2×D412yes—
630C22×C8C2×D412yes—
631C22×C8C2×D412yes—
632C22×C8C2×D412yes—
633C22×C8C2×D412yes—
634C4⋊Q8—21no—
635C4⋊Q8—21no—
636C4⋊Q8—21no—
637C4⋊Q8—21no—
638C4⋊Q8—21no—
639C4⋊Q8—21no—
640C4⋊Q8—41no—
641C4⋊Q8C2411yescharacteristic
642C4⋊Q8C2411yescharacteristic
643C4⋊Q8C2411yescharacteristic
644C4⋊Q8C2411yescharacteristic
645C4⋊Q8C2411yescharacteristic
646C4⋊Q8C2411yescharacteristic
647C4⋊Q8C2411yescharacteristic
648C4⋊Q8C2411yescharacteristic
649C4⋊Q8C2411yescharacteristic
650C4⋊Q8C2411yescharacteristic
651C4⋊Q8C2411yescharacteristic
652#127—21no—
653#127—21no—
654#127—21no—
655#127—21no—
656#127—21no—
657#127—21no—
658#127—41no—
659#127—41no—
660#127C2411yescharacteristic
661#127C2411yescharacteristic
662#127C2411yescharacteristic
663#127C2411yescharacteristic
664#127C2411yescharacteristic
665#126—41no—
666#126—41no—
667#126—41no—
668#126—41no—
669#126—41no—
670#126—41no—
671#125—21no—
672#125—21no—
673#125—21no—
674#125—21no—
675#125—21no—
676#125—21no—
677#125—21no—
678#125—21no—
679#125—21no—
680#125—41no—
681#125—41no—
682#125—41no—
683#125—41no—
684#124—21no—
685#124—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—41no—
696#124—41no—
697#124—41no—
698#124—41no—
699#124—41no—
700#123—41no—
701#123—41no—
702#123—41no—
703#123—41no—
704#123—41no—
705#123—41no—
706#123—41no—
707#123—41no—
708#123—41no—
709#123—41no—
710#123—41no—
711#123—41no—
712C22⋊Q8—21no—
713C22⋊Q8—21no—
714C22⋊Q8—21no—
715C22⋊Q8—21no—
716C22⋊Q8—21no—
717C22⋊Q8—21no—
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—
733#121—21no—
734#121—21no—
735#121—21no—
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—41no—
756#121—41no—
757#121—41no—
758#121—41no—
759#121—41no—
760#121—41no—
761#121—41no—
762#121—41no—
763#121—41no—
764#121—41no—
765#121—41no—
766#120—41no—
767#120—41no—
768#120—41no—
769#120—41no—
770C4×Q8—21no—
771C4×Q8—21no—
772C4×Q8—21no—
773C4×Q8—21no—
774C4×Q8—21no—
775C4×Q8—21no—
776C4×Q8—21no—
777C4×Q8—21no—
778C4×Q8—21no—
779C4×Q8—21no—
780C4×Q8—21no—
781C4×Q8—21no—
782C4×Q8—21no—
783C4×Q8—21no—
784C4×Q8—21no—
785C4×Q8—21no—
786C4×Q8—21no—
787C4×Q8—21no—
788C4×Q8—41no—
789C4×Q8—41no—
790C4×Q8C2×D411yescharacteristic
791C4×Q8C2×D411yescharacteristic
792C4×D4—21no—
793C4×D4—21no—
794C4×D4—21no—
795C4×D4—21no—
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—41no—
815C4×D4—41no—
816C4×D4—41no—
817C4×D4—41no—
818C4×D4—41no—
819C4×D4—41no—
820C4×D4C2×D411yescharacteristic
821C4×D4C2×D411yescharacteristic
822C4×D4C2×D411yescharacteristic
823C4×D4C2×D411yescharacteristic
824C4×D4C2×D411yescharacteristic
825C4×D4C2×D411yescharacteristic
826#117—21no—
827#117—21no—
828#117—21no—
829#117—21no—
830#117—21no—
831#117—21no—
832#117—21no—
833#117—21no—
834#117—21no—
835#117—41no—
836#117—41no—
837#117—41no—
838#117C2×D411yescharacteristic
839#117C2×D411yescharacteristic
840#117C2×D411yescharacteristic
841C2×C4⋊C4—21no—
842C2×C4⋊C4—21no—
843C2×C4⋊C4—21no—
844C2×C4⋊C4—21no—
845C2×C4⋊C4—41no—
846C2×C22⋊C4—41no—
847C2×C22⋊C4—41no—
848C2×C22⋊C4—41no—
849C2×C22⋊C4—41no—
850C2×C42C2411yescharacteristic
851C2×C42C2411yescharacteristic
852C2×C42C2411yescharacteristic
853#107—22no—
854#107—22no—
855#107—22no—
856#107—22no—
857#107—22no—
858#107—22no—
859#107—22no—
860#107—22no—
861#107—22no—
862#107—22no—
863#106—22no—
864#106—22no—
865#106—22no—
866#106—22no—
867#106—22no—
868#106—22no—
869#106—22no—
870#106—22no—
871C4⋊C8C2×D412yes—
872C4⋊C8C2×D412yes—
873C4⋊C8C2×D412yes—
874C4⋊C8C2×D412yes—
875C4⋊C8C2×D412yes—
876C4⋊C8C2×D412yes—
877#103—22no—
878#103—22no—
879#103—22no—
880#103—22no—
881#103—22no—
882#103—22no—
883#103—22no—
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#102—22no—
900#102—22no—
901#102—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—
929C22⋊C8C2×D412yes—
930C22⋊C8C2×D412yes—
931C22⋊C8C2×D412yes—
932C22⋊C8C2×D412yes—
933C22⋊C8C2×D412yes—
934C22⋊C8C2×D412yes—
935#97C2×D412yes—
936#97C2×D412yes—
937#97C2×D412yes—
938#97C2×D412yes—
939#97C2×D412yes—
940#97C2×D412yes—
941#97C2×D412yes—
942C4×C8C2×D412yes—
943C4×C8C2×D412yes—
944C4×C8C2×D412yes—
945C4×C8C2×D412yes—
946C4×C8C2×D412yes—
947C4×C8C2411yescharacteristic
948C4×C8C2411yescharacteristic
949C4×C8C2411yescharacteristic
950C4×C8C2411yescharacteristic
951C4×C8C2411yescharacteristic
952C4×C8C2411yescharacteristic
953C4×C8C2411yescharacteristic
954C4×C8C2411yescharacteristic
955C4×C8C2411yescharacteristic
956C4×C8C2411yescharacteristic
957C4×C8C2411yescharacteristic
958C4×C8C2411yescharacteristic
959C24—41no—
960C24—41no—
961#41—42no—
962#41—44no—
963#41—82no—
964#41—82no—
965#41—82no—
966#41—82no—
967#41—82no—
968#41—82no—
969#41—82no—
970#41—82no—
971#41—82no—
972#41—82no—
973C2×Q8—21no—
974C2×Q8—21no—
975C2×Q8—21no—
976C2×Q8—21no—
977C2×Q8—21no—
978C2×Q8—21no—
979C2×Q8—21no—
980C2×Q8—21no—
981C2×Q8—21no—
982C2×Q8—21no—
983C2×Q8—21no—
984C2×Q8—44no—
985C2×Q8—41no—
986C2×Q8—41no—
987C2×Q8—82no—
988C2×Q8#12711yescharacteristic
989C2×D4—21no—
990C2×D4—21no—
991C2×D4—21no—
992C2×D4—21no—
993C2×D4—21no—
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—44no—
1005C2×D4—44no—
1006C2×D4—41no—
1007C2×D4—41no—
1008C2×D4—41no—
1009C2×D4—41no—
1010C2×D4—41no—
1011C2×D4—41no—
1012C2×D4—41no—
1013C2×D4—41no—
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—82no—
1024C2×D4—82no—
1025C2×D4—82no—
1026C2×D4—82no—
1027C2×D4#12711yescharacteristic
1028C2×D4#12711yescharacteristic
1029C2×D4#12711yescharacteristic
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—41no—
1038C22×C4—41no—
1039C22×C4—41no—
1040C22×C4—41no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4C22×D411yescharacteristic
1044C22×C4C22×D411yescharacteristic
1045C22×C4C22×D411yescharacteristic
1046C22×C4C22×D411yescharacteristic
1047C22×C4C22×D411yescharacteristic
1048C22×C4C22×D411yescharacteristic
1049C22×C4C22×D411yescharacteristic
1050C22×C4C22×D411yescharacteristic
1051C22×C4C22×D411yescharacteristic
1052Q16—82no—
1053Q16—82no—
1054Q16—82no—
1055Q16—82no—
1056SD16—44no—
1057SD16—44no—
1058SD16—44no—
1059SD16—44no—
1060SD16—44no—
1061SD16—44no—
1062SD16—44no—
1063SD16—44no—
1064SD16—82no—
1065SD16—82no—
1066SD16—82no—
1067SD16—82no—
1068SD16—82no—
1069SD16—82no—
1070D8—44no—
1071D8—44no—
1072D8—44no—
1073D8—82no—
1074D8—82no—
1075D8—82no—
1076D8—82no—
1077D8—82no—
1078M16—24no—
1079M16—24no—
1080M16—42no—
1081M16—42no—
1082M16—42no—
1083M16—42no—
1084M16—42no—
1085C2×C8—24no—
1086C2×C8—42no—
1087C2×C8—42no—
1088C2×C8—42no—
1089C2×C8—42no—
1090C2×C8C22×D412yes—
1091C2×C8C22×D412yes—
1092C2×C8C22×D412yes—
1093C2×C8C22×D412yes—
1094C2×C8C22×D412yes—
1095C2×C8C22×D412yes—
1096C2×C8C22×D412yes—
1097C2×C8C22×D412yes—
1098C2×C8C22×D412yes—
1099C2×C8C22×D412yes—
1100C2×C8C22×D412yes—
1101C2×C8C22×D412yes—
1102C4⋊C4—21no—
1103C4⋊C4—21no—
1104C4⋊C4—21no—
1105C4⋊C4—21no—
1106C4⋊C4—21no—
1107C4⋊C4—21no—
1108C4⋊C4—21no—
1109C4⋊C4—21no—
1110C4⋊C4—21no—
1111C4⋊C4—21no—
1112C4⋊C4—21no—
1113C4⋊C4—21no—
1114C4⋊C4—21no—
1115C4⋊C4—21no—
1116C4⋊C4—21no—
1117C4⋊C4—21no—
1118C4⋊C4—21no—
1119C4⋊C4—21no—
1120C4⋊C4—21no—
1121C4⋊C4—21no—
1122C4⋊C4—21no—
1123C4⋊C4—21no—
1124C4⋊C4—41no—
1125C4⋊C4—41no—
1126C4⋊C4—41no—
1127C4⋊C4—41no—
1128C4⋊C4—41no—
1129C4⋊C4—41no—
1130C4⋊C4—41no—
1131C4⋊C4—41no—
1132C4⋊C4—41no—
1133C4⋊C4—41no—
1134C4⋊C4—41no—
1135C4⋊C4—41no—
1136C4⋊C4—41no—
1137C4⋊C4—41no—
1138C4⋊C4—41no—
1139C4⋊C4—41no—
1140C4⋊C4—41no—
1141C4⋊C4—41no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4#12711yescharacteristic
1147C4⋊C4#12711yescharacteristic
1148C4⋊C4#12711yescharacteristic
1149C4⋊C4#12711yescharacteristic
1150C4⋊C4#12711yescharacteristic
1151C4⋊C4#12711yescharacteristic
1152C22⋊C4—41no—
1153C22⋊C4—41no—
1154C22⋊C4—41no—
1155C22⋊C4—41no—
1156C22⋊C4—41no—
1157C22⋊C4—41no—
1158C22⋊C4—41no—
1159C22⋊C4—41no—
1160C22⋊C4—41no—
1161C22⋊C4—41no—
1162C22⋊C4—41no—
1163C22⋊C4—41no—
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#12711yescharacteristic
1184C22⋊C4#12711yescharacteristic
1185C22⋊C4#12711yescharacteristic
1186C22⋊C4#12711yescharacteristic
1187C22⋊C4#12711yescharacteristic
1188C22⋊C4#12711yescharacteristic
1189C42—41no—
1190C42—41no—
1191C42—41no—
1192C42—41no—
1193C42—41no—
1194C42—41no—
1195C42—41no—
1196C42—41no—
1197C42—41no—
1198C42C22×D411yescharacteristic
1199C42C22×D411yescharacteristic
1200C42C22×D411yescharacteristic
1201C42C22×D411yescharacteristic
1202C42C22×D411yescharacteristic
1203C42C22×D411yescharacteristic
1204C42C22×D411yescharacteristic
1205C42C22×D411yescharacteristic
1206C42C22×D411yescharacteristic
1207C42C2511yescharacteristic
1208C23—41no—
1209C23—41no—
1210C23—41no—
1211C23—41no—
1212C23—41no—
1213C23—82no—
1214C23—82no—
1215C23—161no—
1216C23—161no—
1217C23—161no—
1218C23—161no—
1219C23C2×#12711yescharacteristic
1220C23C2×#12711yescharacteristic
1221C23C2×#12711yescharacteristic
1222Q8—41no—
1223Q8—42no—
1224Q8—42no—
1225Q8—42no—
1226Q8—42no—
1227Q8—42no—
1228Q8—42no—
1229Q8—42no—
1230Q8—42no—
1231Q8—42no—
1232Q8—42no—
1233Q8—42no—
1234Q8—82no—
1235Q8—161no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—42no—
1240D4—42no—
1241D4—42no—
1242D4—42no—
1243D4—42no—
1244D4—42no—
1245D4—42no—
1246D4—42no—
1247D4—42no—
1248D4—42no—
1249D4—42no—
1250D4—42no—
1251D4—42no—
1252D4—42no—
1253D4—42no—
1254D4—82no—
1255D4—82no—
1256D4—82no—
1257D4—161no—
1258D4—161no—
1259D4—161no—
1260D4—161no—
1261D4—161no—
1262D4—161no—
1263D4—161no—
1264D4—161no—
1265D4—161no—
1266D4—161no—
1267D4—161no—
1268D4—161no—
1269D4—161no—
1270D4—161no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—82no—
1292C2×C4—82no—
1293C2×C4—161no—
1294C2×C4—161no—
1295C2×C4—161no—
1296C2×C4—161no—
1297C2×C4—161no—
1298C2×C4—161no—
1299C2×C4—161no—
1300C2×C4—161no—
1301C2×C4—161no—
1302C2×C4—161no—
1303C2×C4—161no—
1304C2×C4C2×#12711yescharacteristic
1305C2×C4C2×#12711yescharacteristic
1306C2×C4C2×#12711yescharacteristic
1307C2×C4C2×#12711yescharacteristic
1308C2×C4C2×#12711yescharacteristic
1309C2×C4C2×#12711yescharacteristic
1310C2×C4C2×#12711yescharacteristic
1311C2×C4C2×#12711yescharacteristic
1312C2×C4C2×#12711yescharacteristic
1313C2×C4C23×D411yescharacteristic
1314C2×C4C23×D411yescharacteristic
1315C2×C4C23×D411yescharacteristic
1316C8—22no—
1317C8—22no—
1318C8—22no—
1319C8—22no—
1320C8—22no—
1321C8—22no—
1322C8—22no—
1323C8—22no—
1324C8—22no—
1325C8—22no—
1326C8—22no—
1327C8#57514yes—
1328C22—21no—
1329C22—21no—
1330C22—21no—
1331C22—21no—
1332C22—21no—
1333C22—21no—
1334C22—21no—
1335C22—21no—
1336C22—21no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—322no—
1353C22—322no—
1354C22C22×#12711yescharacteristic
1355C4—21no—
1356C4—21no—
1357C4—21no—
1358C4—21no—
1359C4—21no—
1360C4—21no—
1361C4—21no—
1362C4—21no—
1363C4—21no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4C2×#57512yes—
1376C4#358412yes—
1377C4#358512yes—
1378C2—41no—
1379C2—41no—
1380C2—41no—
1381C2—161no—
1382C2—161no—
1383C2—161no—
1384C2—161no—
1385C2—161no—
1386C2#6063911yescharacteristic
1387C2#6064911yescharacteristic
1388C2#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. #62545C2semidirect
3. #62544C2semidirect
4. #62426C2semidirect
5. #60722C2semidirect
6. #60712C2semidirect
7. #19754C2semidirect
8. #19752C2semidirect
9. #19749C2semidirect
10. #19747C2semidirect
11. #19729C2semidirect
12. #19728C2semidirect
13. #19723C2semidirect
14. #19719C2semidirect
15. #19709C2semidirect
16. #19708C2semidirect
17. #19693C2semidirect
18. #19691C2semidirect
19. #19678C2semidirect
20. #19671C2semidirect
21. #19650C2semidirect
22. #19649C2semidirect
23. #19646C2semidirect
24. #19645C2semidirect
25. #19644C2semidirect
26. #19644C2semidirect
27. #19627C2semidirect
28. #19625C2semidirect
29. #19619C2semidirect
30. #19613C2semidirect
31. #17337C2semidirect
52. #3231C22semidirect
53. #3231C22semidirect
54. #3231C22semidirect
55. #3230C22semidirect
56. #3228C22semidirect
57. #3228C22semidirect
58. #3228C22semidirect
64. #3210C22semidirect
65. #3210C22semidirect
66. #3210C22semidirect
67. #3209C22semidirect
68. #3208C22semidirect
72. #3207C22semidirect
75. #3205C22semidirect
76. #3185C22semidirect
77. #3185C22semidirect
80. #3184C22semidirect
87. #3182C22semidirect
88. #3182C22semidirect
89. #3182C22semidirect
90. #3182C22semidirect
91. #3182C22semidirect
96. #3170C22semidirect
99. #3169C22semidirect
100. #3169C22semidirect
104. #3167C22semidirect
105. #3167C22semidirect
106. #3167C22semidirect
107. #3167C22semidirect
108. #3165C22semidirect
109. #3160C22semidirect
112. #3151C22semidirect
114. C2×#492C22semidirect
117. #3141C22semidirect
118. #3139C22semidirect
119. #3139C22semidirect
120. #3138C22semidirect
121. #3138C22semidirect
122. #3138C22semidirect
123. #3131C22semidirect
124. #3131C22semidirect
125. #3131C22semidirect
126. #3131C22semidirect
127. C2×#486C22semidirect
135. #1723C22semidirect
136. #1723C22semidirect
137. #1723C22semidirect
138. #1722C22semidirect
143. #1720C22semidirect
144. #1720C22semidirect
145. #1720C22semidirect
146. #1720C22semidirect
147. #1720C22semidirect
148. #1719C22semidirect
149. #1719C22semidirect
150. #1719C22semidirect
151. #1719C22semidirect
152. #1719C22semidirect
153. #1719C22semidirect
154. #1719C22semidirect
155. #1719C22semidirect
156. #1718C22semidirect
157. #1718C22semidirect
158. #1718C22semidirect
159. #1718C22semidirect
160. #1718C22semidirect
168. #1717C22semidirect
169. #1717C22semidirect
170. #1717C22semidirect
171. #1716C22semidirect
173. #1715C22semidirect
174. #1715C22semidirect
175. #1714C22semidirect
176. #1714C22semidirect
177. #1714C22semidirect
178. #1714C22semidirect
179. #1714C22semidirect
180. #1714C22semidirect
181. #1714C22semidirect
182. #1714C22semidirect
183. #1713C22semidirect
184. #1711C22semidirect
185. #1711C22semidirect
186. #1711C22semidirect
187. #1710C22semidirect
190. #1709C22semidirect
191. #1708C22semidirect
192. #1708C22semidirect
193. #1708C22semidirect
194. #1707C22semidirect
197. #1706C22semidirect
198. #1706C22semidirect
199. #1455C22semidirect
200. #1455C22semidirect
201. #1453C22semidirect
202. #1453C22semidirect
203. #1452C22semidirect
204. #1451C22semidirect
205. #1451C22semidirect
206. C8×M16C22semidirect
207. C8×M16C22semidirect
208. C8×M16C22semidirect
209. C8×M16C22semidirect
210. C2×#322C22semidirect

Maximal subgroups

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

subgroupindex
#625462
#625452
#625442
#624262
#607222
#607122
#197542
#197522
#197492
#197472
#197292
#197282
#197232
#197192
#197092
#197082
#196932
#196912
#196782
#196712
#196502
#196492
#196462
#196452
#196442
#196272
#196252
#196192
#196132
#173372