Finite Group Databasebeta

← #6357929

Subgroups — #6357929

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#62544C211yesmaximal, characteristic, complemented
3#62544C211yesmaximal, characteristic, complemented
4#62427C211yesmaximal, characteristic, complemented
5#60723C211yesmaximal, characteristic, complemented
6#60714C211yesmaximal, characteristic, complemented
7#19753C211yesmaximal, characteristic, complemented
8#19750C211yesmaximal, characteristic, complemented
9#19749C211yesmaximal, characteristic, complemented
10#19748C211yesmaximal, characteristic, complemented
11#19726C211yesmaximal, characteristic, complemented
12#19721C211yesmaximal, characteristic, complemented
13#19717C211yesmaximal, characteristic, complemented
14#19715C211yesmaximal, characteristic, complemented
15#19712C211yesmaximal, characteristic, complemented
16#19708C211yesmaximal, characteristic, complemented
17#19695C211yesmaximal, characteristic, complemented
18#19690C211yesmaximal, characteristic, complemented
19#19676C211yesmaximal, characteristic, complemented
20#19674C211yesmaximal, characteristic, complemented
21#19650C211yesmaximal, characteristic, complemented
22#19650C211yesmaximal, characteristic, complemented
23#19644C211yesmaximal, characteristic, complemented
24#19644C211yesmaximal, characteristic, complemented
25#19642C211yesmaximal, characteristic, complemented
26#19641C211yesmaximal, characteristic, complemented
27#19640C211yesmaximal, characteristic, complemented
28#19635C211yesmaximal, characteristic, complemented
29#19619C211yesmaximal, characteristic, complemented
30#19613C211yesmaximal, characteristic, complemented
31#17337C211yesmaximal, characteristic, complemented
32#3511C2211yescharacteristic
33#3509C2211yescharacteristic
34#3508C2211yescharacteristic
35#3508C2211yescharacteristic
36#3401—22no—
37#3371—22no—
38#3371—22no—
39#3370—22no—
40#3323—22no—
41#3323—22no—
42#3322—22no—
43#3319—22no—
44#3317—22no—
45#3317—22no—
46#3311—22no—
47#3311—22no—
48#3309—22no—
49#3275—22no—
50#3271—22no—
51#3267—22no—
52#3231C2211yescharacteristic
53#3231C2211yescharacteristic
54#3231C2211yescharacteristic
55#3228C2211yescharacteristic, complemented
56#3228C2211yescharacteristic, complemented
57#3228C2211yescharacteristic, complemented
58#3227C2211yescharacteristic, complemented
59#3227C2211yescharacteristic, complemented
60#3226C2211yescharacteristic, complemented
61#3210C2211yescharacteristic
62#3210C2211yescharacteristic, complemented
63#3210C2211yescharacteristic, complemented
64#3210C2211yescharacteristic, complemented
65#3210C2211yescharacteristic, complemented
66#3210C2211yescharacteristic, complemented
67#3208C2211yescharacteristic
68#3208C2211yescharacteristic
69#3208C2211yescharacteristic
70#3207C2211yescharacteristic, complemented
71#3207C2211yescharacteristic, complemented
72#3207C2211yescharacteristic, complemented
73#3207C2211yescharacteristic, complemented
74#3206C2211yescharacteristic, complemented
75#3205C2211yescharacteristic
76#3185C2211yescharacteristic
77#3185C2211yescharacteristic
78#3185C2211yescharacteristic
79#3185C2211yescharacteristic
80#3185C2211yescharacteristic, complemented
81#3184C2211yescharacteristic
82#3184C2211yescharacteristic
83#3184C2211yescharacteristic
84#3184C2211yescharacteristic
85#3184C2211yescharacteristic, complemented
86#3184C2211yescharacteristic, complemented
87#3182C2211yescharacteristic
88#3182C2211yescharacteristic
89#3182C2211yescharacteristic, complemented
90#3182C2211yescharacteristic, complemented
91#3182C2211yescharacteristic, complemented
92#3178—22no—
93#3178—22no—
94#3176—22no—
95#3176—22no—
96#3170C2211yescharacteristic
97#3170C2211yescharacteristic, complemented
98#3169C2211yescharacteristic
99#3169C2211yescharacteristic
100#3169C2211yescharacteristic
101#3169C2211yescharacteristic
102#3169C2211yescharacteristic, complemented
103#3167C2211yescharacteristic
104#3167C2211yescharacteristic, complemented
105#3167C2211yescharacteristic, complemented
106#3167C2211yescharacteristic, complemented
107#3167C2211yescharacteristic, complemented
108#3165C2211yescharacteristic, complemented
109#3160C2211yescharacteristic
110#3152C2211yescharacteristic, complemented
111#3152C2211yescharacteristic, complemented
112#3151C2211yescharacteristic
113#3147C2211yescharacteristic, complemented
114C2×#493C2211yescharacteristic
115#3141C2211yescharacteristic, complemented
116#3141C2211yescharacteristic, complemented
117#3141C2211yescharacteristic, complemented
118#3138C2211yescharacteristic
119#3138C2211yescharacteristic
120#3138C2211yescharacteristic
121#3138C2211yescharacteristic
122#3138C2211yescharacteristic
123#3131C2211yescharacteristic, complemented
124#3131C2211yescharacteristic, complemented
125#3131C2211yescharacteristic, complemented
126#3131C2211yescharacteristic, complemented
127C2×#487C2211yescharacteristic, complemented
128#3063—22no—
129#3058—22no—
130#2965C2211yescharacteristic
131#2965C2211yescharacteristic
132#2948—22no—
133#2947—22no—
134C4×#131C2211yescharacteristic
135#1723C2211yescharacteristic, complemented
136#1723C2211yescharacteristic, complemented
137#1723C2211yescharacteristic, complemented
138#1723C2211yescharacteristic, complemented
139#1723C2211yescharacteristic, complemented
140#1722C2211yescharacteristic, complemented
141#1722C2211yescharacteristic, complemented
142#1722C2211yescharacteristic, complemented
143#1721C2211yescharacteristic
144#1721C2211yescharacteristic
145#1721C2211yescharacteristic
146#1721C2211yescharacteristic
147#1720C2211yescharacteristic, complemented
148#1720C2211yescharacteristic, complemented
149#1720C2211yescharacteristic, complemented
150#1720C2211yescharacteristic, complemented
151#1720C2211yescharacteristic, complemented
152#1720C2211yescharacteristic, complemented
153#1720C2211yescharacteristic, complemented
154#1720C2211yescharacteristic, complemented
155#1720C2211yescharacteristic, complemented
156#1719C2211yescharacteristic, complemented
157#1719C2211yescharacteristic, complemented
158#1719C2211yescharacteristic, complemented
159#1719C2211yescharacteristic, complemented
160#1719C2211yescharacteristic, complemented
161#1719C2211yescharacteristic, 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#1716C2211yescharacteristic, complemented
176#1716C2211yescharacteristic, complemented
177#1715C2211yescharacteristic
178#1715C2211yescharacteristic
179#1715C2211yescharacteristic, complemented
180#1715C2211yescharacteristic, complemented
181#1714C2211yescharacteristic, complemented
182#1714C2211yescharacteristic, complemented
183#1711C2211yescharacteristic, complemented
184#1711C2211yescharacteristic, complemented
185#1711C2211yescharacteristic, complemented
186#1709C2211yescharacteristic
187#1709C2211yescharacteristic
188#1709C2211yescharacteristic, complemented
189#1708C2211yescharacteristic, complemented
190#1708C2211yescharacteristic, complemented
191#1708C2211yescharacteristic, complemented
192#1708C2211yescharacteristic, complemented
193#1707C2211yescharacteristic, complemented
194#1707C2211yescharacteristic, complemented
195#1706C2211yescharacteristic
196#1706C2211yescharacteristic
197#1706C2211yescharacteristic, complemented
198#1705C2211yescharacteristic, complemented
199#1455C2211yescharacteristic
200#1455C2211yescharacteristic, complemented
201#1453C2211yescharacteristic
202#1453C2211yescharacteristic, complemented
203#1452C2211yescharacteristic, complemented
204#1451C2211yescharacteristic
205#1451C2211yescharacteristic, complemented
206C8×M16C2211yescharacteristic
207C8×M16C2211yescharacteristic, complemented
208C8×M16C2211yescharacteristic, complemented
209C8×M16C2211yescharacteristic, complemented
210C2×#322C2211yescharacteristic, complemented
211C2×#137—22no—
212C2×#137—22no—
213C2×AGL(1,ℤ/8)—22no—
214C2×#135—22no—
215C22×D8—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#499—22no—
300#498C2311yescharacteristic
301#498C2311yescharacteristic
302#498C2311yescharacteristic
303#498C2311yescharacteristic
304#498C2311yescharacteristic
305#498C2311yescharacteristic
306#498C2311yescharacteristic
307#498C2311yescharacteristic
308#498C2311yescharacteristic
309#498C2311yescharacteristic
310#497—22no—
311#497—22no—
312#496—22no—
313#495—22no—
314#494C2311yescharacteristic
315#494C2311yescharacteristic
316#494C2311yescharacteristic
317#494C2311yescharacteristic
318#494C2311yescharacteristic
319#494C2311yescharacteristic
320#493—22no—
321#493C2311yescharacteristic
322#493C2311yescharacteristic
323#493C2311yescharacteristic
324#493C2311yescharacteristic
325#493C2311yescharacteristic
326#493C2311yescharacteristic
327#493C2311yescharacteristic
328#493C2311yescharacteristic
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#490—22no—
342#490—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#487—22no—
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#486C2311yescharacteristic
375#486C2311yescharacteristic
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#482—22no—
410#482—22no—
411#482—22no—
412#481—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#476—22no—
422#476—22no—
423#474—22no—
424#470—22no—
425#470—22no—
426#470—22no—
427#470—22no—
428#470—22no—
429#469—22no—
430#469—22no—
431#469—22no—
432#469—22no—
433#469—22no—
434#469—22no—
435#468—22no—
436#468—22no—
437#468—22no—
438#468—22no—
439#468—22no—
440#467—22no—
441#467—22no—
442#466—22no—
443#466—22no—
444#466—22no—
445#466—22no—
446#466—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#461—22no—
463#460—22no—
464#460—22no—
465#460—22no—
466#459—22no—
467#452—22no—
468#452—22no—
469#452—22no—
470#452—22no—
471#452—22no—
472#452—22no—
473#450—22no—
474#450—22no—
475#450—22no—
476#449—22no—
477#449—22no—
478#449—22no—
479#449—22no—
480#448—22no—
481#447—22no—
482#446D412yes—
483#446D412yes—
484#442—22no—
485#442—22no—
486#442—22no—
487#442—22no—
488#442—22no—
489#442—22no—
490#441—22no—
491#441—22no—
492#441—22no—
493#441—22no—
494#441—22no—
495#440—22no—
496#440—22no—
497#440—22no—
498#440—22no—
499#440—22no—
500C4×Q16—22no—
501C4×Q16—22no—
502C4×SD16—22no—
503C4×SD16—22no—
504C4×SD16—22no—
505C4×SD16—22no—
506C4×SD16—22no—
507C4×D8—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#418—22no—
527#418—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×#103—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—
590#137—48no—
591#137—84no—
592AGL(1,ℤ/8)—84no—
593#135—84no—
594C2×Q16—22no—
595C2×Q16—22no—
596C2×Q16—22no—
597C2×Q16—22no—
598C2×Q16—22no—
599C2×Q16—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×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—48no—
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#106—22no—
862#106—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#102—22no—
898#102—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—44no—
1053Q16—44no—
1054Q16—44no—
1055Q16—82no—
1056Q16—82no—
1057Q16—82no—
1058SD16—44no—
1059SD16—44no—
1060SD16—44no—
1061SD16—82no—
1062SD16—82no—
1063SD16—82no—
1064SD16—82no—
1065SD16—82no—
1066SD16—82no—
1067SD16—82no—
1068SD16—82no—
1069SD16—82no—
1070D8—44no—
1071D8—44no—
1072D8—44no—
1073D8—44no—
1074D8—44no—
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. #62544C2semidirect
3. #62544C2semidirect
4. #62427C2semidirect
5. #60723C2semidirect
6. #60714C2semidirect
7. #19753C2semidirect
8. #19750C2semidirect
9. #19749C2semidirect
10. #19748C2semidirect
11. #19726C2semidirect
12. #19721C2semidirect
13. #19717C2semidirect
14. #19715C2semidirect
15. #19712C2semidirect
16. #19708C2semidirect
17. #19695C2semidirect
18. #19690C2semidirect
19. #19676C2semidirect
20. #19674C2semidirect
21. #19650C2semidirect
22. #19650C2semidirect
23. #19644C2semidirect
24. #19644C2semidirect
25. #19642C2semidirect
26. #19641C2semidirect
27. #19640C2semidirect
28. #19635C2semidirect
29. #19619C2semidirect
30. #19613C2semidirect
31. #17337C2semidirect
55. #3228C22semidirect
56. #3228C22semidirect
57. #3228C22semidirect
58. #3227C22semidirect
59. #3227C22semidirect
60. #3226C22semidirect
62. #3210C22semidirect
63. #3210C22semidirect
64. #3210C22semidirect
65. #3210C22semidirect
66. #3210C22semidirect
70. #3207C22semidirect
71. #3207C22semidirect
72. #3207C22semidirect
73. #3207C22semidirect
74. #3206C22semidirect
80. #3185C22semidirect
85. #3184C22semidirect
86. #3184C22semidirect
89. #3182C22semidirect
90. #3182C22semidirect
91. #3182C22semidirect
97. #3170C22semidirect
102. #3169C22semidirect
104. #3167C22semidirect
105. #3167C22semidirect
106. #3167C22semidirect
107. #3167C22semidirect
108. #3165C22semidirect
110. #3152C22semidirect
111. #3152C22semidirect
113. #3147C22semidirect
115. #3141C22semidirect
116. #3141C22semidirect
117. #3141C22semidirect
123. #3131C22semidirect
124. #3131C22semidirect
125. #3131C22semidirect
126. #3131C22semidirect
127. C2×#487C22semidirect
135. #1723C22semidirect
136. #1723C22semidirect
137. #1723C22semidirect
138. #1723C22semidirect
139. #1723C22semidirect
140. #1722C22semidirect
141. #1722C22semidirect
142. #1722C22semidirect
147. #1720C22semidirect
148. #1720C22semidirect
149. #1720C22semidirect
150. #1720C22semidirect
151. #1720C22semidirect
152. #1720C22semidirect
153. #1720C22semidirect
154. #1720C22semidirect
155. #1720C22semidirect
156. #1719C22semidirect
157. #1719C22semidirect
158. #1719C22semidirect
159. #1719C22semidirect
160. #1719C22semidirect
161. #1719C22semidirect
162. #1718C22semidirect
163. #1718C22semidirect
164. #1718C22semidirect
171. #1717C22semidirect
172. #1717C22semidirect
173. #1717C22semidirect
174. #1717C22semidirect
175. #1716C22semidirect
176. #1716C22semidirect
179. #1715C22semidirect
180. #1715C22semidirect
181. #1714C22semidirect
182. #1714C22semidirect
183. #1711C22semidirect
184. #1711C22semidirect
185. #1711C22semidirect
188. #1709C22semidirect
189. #1708C22semidirect
190. #1708C22semidirect
191. #1708C22semidirect
192. #1708C22semidirect
193. #1707C22semidirect
194. #1707C22semidirect
197. #1706C22semidirect
198. #1705C22semidirect
200. #1455C22semidirect
202. #1453C22semidirect
203. #1452C22semidirect
205. #1451C22semidirect
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
#625442
#624272
#607232
#607142
#197532
#197502
#197492
#197482
#197262
#197212
#197172
#197152
#197122
#197082
#196952
#196902
#196762
#196742
#196502
#196442
#196422
#196412
#196402
#196352
#196192
#196132
#173372