Finite Group Databasebeta

← #6357931

Subgroups — #6357931

Order 512.

1930 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62546C211yesmaximal, characteristic, complemented
2#62481C211yesmaximal, characteristic, complemented
3#62427C211yesmaximal, characteristic, complemented
4#62425C211yesmaximal, characteristic, complemented
5#60722C211yesmaximal, characteristic, complemented
6#60718C211yesmaximal, characteristic, complemented
7#19750C211yesmaximal, characteristic, complemented
8#19748C211yesmaximal, characteristic, complemented
9#19747C211yesmaximal, characteristic, complemented
10#19746C211yesmaximal, characteristic, complemented
11#19730C211yesmaximal, characteristic, complemented
12#19728C211yesmaximal, characteristic, complemented
13#19722C211yesmaximal, characteristic, complemented
14#19719C211yesmaximal, characteristic, complemented
15#19712C211yesmaximal, characteristic, complemented
16#19708C211yesmaximal, characteristic, complemented
17#19695C211yesmaximal, characteristic, complemented
18#19689C211yesmaximal, characteristic, complemented
19#19683C211yesmaximal, characteristic, complemented
20#19682C211yesmaximal, characteristic, complemented
21#19646C211yesmaximal, characteristic, complemented
22#19645C211yesmaximal, characteristic, complemented
23#19644C211yesmaximal, characteristic, complemented
24#19643C211yesmaximal, characteristic, complemented
25#19641C211yesmaximal, characteristic, complemented
26#19641C211yesmaximal, characteristic, complemented
27#19631C211yesmaximal, characteristic, complemented
28#19630C211yesmaximal, characteristic, complemented
29#19620C211yesmaximal, characteristic, complemented
30#19616C211yesmaximal, characteristic, complemented
31#17337C211yesmaximal, characteristic, complemented
32#3511C2211yescharacteristic
33#3511C2211yescharacteristic
34#3511C2211yescharacteristic
35#3508C2211yescharacteristic
36#3402—22no—
37#3401—22no—
38#3389—22no—
39#3370—22no—
40#3355—22no—
41#3347—22no—
42#3347—22no—
43#3322—22no—
44#3319—22no—
45#3309—22no—
46#3277—22no—
47#3275—22no—
48#3271—22no—
49#3269—22no—
50#3269—22no—
51#3267—22no—
52#3231C2211yescharacteristic
53#3228C2211yescharacteristic
54#3228C2211yescharacteristic
55#3228C2211yescharacteristic, complemented
56#3228C2211yescharacteristic, complemented
57#3228C2211yescharacteristic, complemented
58#3226C2211yescharacteristic
59#3226C2211yescharacteristic
60#3226C2211yescharacteristic, complemented
61#3210C2211yescharacteristic
62#3210C2211yescharacteristic
63#3210C2211yescharacteristic, complemented
64#3210C2211yescharacteristic, complemented
65#3209C2211yescharacteristic
66#3209C2211yescharacteristic, complemented
67#3208C2211yescharacteristic
68#3207C2211yescharacteristic
69#3207C2211yescharacteristic
70#3207C2211yescharacteristic
71#3207C2211yescharacteristic
72#3207C2211yescharacteristic
73#3207C2211yescharacteristic, complemented
74#3206C2211yescharacteristic
75#3205C2211yescharacteristic
76#3185C2211yescharacteristic
77#3184C2211yescharacteristic
78#3184C2211yescharacteristic
79#3184C2211yescharacteristic
80#3184C2211yescharacteristic
81#3184C2211yescharacteristic
82#3184C2211yescharacteristic, complemented
83#3182C2211yescharacteristic
84#3182C2211yescharacteristic
85#3182C2211yescharacteristic
86#3182C2211yescharacteristic
87#3182C2211yescharacteristic
88#3182C2211yescharacteristic
89#3182C2211yescharacteristic, complemented
90#3182C2211yescharacteristic, complemented
91#3182C2211yescharacteristic, complemented
92#3179—22no—
93#3179—22no—
94#3175—22no—
95#3175—22no—
96#3170C2211yescharacteristic
97#3170C2211yescharacteristic, complemented
98#3170C2211yescharacteristic, complemented
99#3169C2211yescharacteristic
100#3169C2211yescharacteristic
101#3169C2211yescharacteristic
102#3169C2211yescharacteristic
103#3169C2211yescharacteristic, complemented
104#3169C2211yescharacteristic, complemented
105#3167C2211yescharacteristic
106#3167C2211yescharacteristic
107#3167C2211yescharacteristic
108#3165C2211yescharacteristic
109#3165C2211yescharacteristic
110#3165C2211yescharacteristic, complemented
111#3160C2211yescharacteristic, complemented
112C2×#500C2211yescharacteristic, complemented
113#3152C2211yescharacteristic
114#3152C2211yescharacteristic
115#3152C2211yescharacteristic, complemented
116#3151C2211yescharacteristic
117#3151C2211yescharacteristic
118#3147C2211yescharacteristic
119#3147C2211yescharacteristic, complemented
120#3147C2211yescharacteristic, complemented
121#3141C2211yescharacteristic
122#3141C2211yescharacteristic, complemented
123#3141C2211yescharacteristic, complemented
124#3138C2211yescharacteristic
125#3131C2211yescharacteristic
126#3131C2211yescharacteristic
127C2×#486C2211yescharacteristic
128#3062—22no—
129#3061—22no—
130#2965C2211yescharacteristic
131#2965C2211yescharacteristic
132#2951—22no—
133#2946—22no—
134C4×#131C2211yescharacteristic
135#1723C2211yescharacteristic, complemented
136#1723C2211yescharacteristic, complemented
137#1723C2211yescharacteristic, complemented
138#1723C2211yescharacteristic, complemented
139#1723C2211yescharacteristic, complemented
140#1722C2211yescharacteristic
141#1722C2211yescharacteristic
142#1722C2211yescharacteristic
143#1722C2211yescharacteristic
144#1722C2211yescharacteristic, complemented
145#1722C2211yescharacteristic, complemented
146#1722C2211yescharacteristic, complemented
147#1722C2211yescharacteristic, complemented
148#1721C2211yescharacteristic
149#1721C2211yescharacteristic
150#1721C2211yescharacteristic
151#1721C2211yescharacteristic
152#1721C2211yescharacteristic
153#1721C2211yescharacteristic
154#1721C2211yescharacteristic, complemented
155#1720C2211yescharacteristic
156#1720C2211yescharacteristic
157#1720C2211yescharacteristic
158#1720C2211yescharacteristic
159#1720C2211yescharacteristic, complemented
160#1720C2211yescharacteristic, complemented
161#1720C2211yescharacteristic, complemented
162#1719C2211yescharacteristic
163#1719C2211yescharacteristic
164#1719C2211yescharacteristic
165#1719C2211yescharacteristic, complemented
166#1718C2211yescharacteristic, complemented
167#1718C2211yescharacteristic, complemented
168#1718C2211yescharacteristic, complemented
169#1717C2211yescharacteristic
170#1717C2211yescharacteristic
171#1717C2211yescharacteristic
172#1717C2211yescharacteristic, complemented
173#1717C2211yescharacteristic, complemented
174#1717C2211yescharacteristic, complemented
175#1716C2211yescharacteristic, complemented
176#1715C2211yescharacteristic
177#1714C2211yescharacteristic
178#1714C2211yescharacteristic
179#1714C2211yescharacteristic
180#1714C2211yescharacteristic, complemented
181#1714C2211yescharacteristic, complemented
182#1714C2211yescharacteristic, complemented
183#1713C2211yescharacteristic, complemented
184#1713C2211yescharacteristic, complemented
185#1711C2211yescharacteristic, complemented
186#1710C2211yescharacteristic, complemented
187#1709C2211yescharacteristic
188#1709C2211yescharacteristic
189#1708C2211yescharacteristic, complemented
190#1708C2211yescharacteristic, complemented
191#1707C2211yescharacteristic, complemented
192#1706C2211yescharacteristic
193#1706C2211yescharacteristic
194#1706C2211yescharacteristic
195#1706C2211yescharacteristic
196#1706C2211yescharacteristic
197#1706C2211yescharacteristic
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×#137—22no—
214C2×AGL(1,ℤ/8)—22no—
215C2×AGL(1,ℤ/8)—22no—
216C2×#135—22no—
217C2×#135—22no—
218C2×#135—22no—
219C2×#131D412yes—
220#559—21no—
221#559—21no—
222#556—21no—
223#556—21no—
224#556—21no—
225#555—21no—
226#555—21no—
227#555—21no—
228#554—21no—
229#554—21no—
230#554—21no—
231#553—21no—
232#553—21no—
233#553—21no—
234#553—21no—
235#553—21no—
236#553—21no—
237#550—21no—
238#550—21no—
239#548—21no—
240#548—21no—
241#548—21no—
242#548—21no—
243#548—21no—
244#548—21no—
245#547—21no—
246#547—21no—
247#547—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#542—21no—
257#542—21no—
258#540—21no—
259#540—21no—
260#537—21no—
261#537—21no—
262#537—21no—
263#535—21no—
264#533C2311yescharacteristic
265#533C2311yescharacteristic
266#533C2311yescharacteristic
267#533C2311yescharacteristic
268#533C2311yescharacteristic
269#533C2311yescharacteristic
270#533C2311yescharacteristic
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×C4⋊Q8C2311yescharacteristic
287C2×#127C2311yescharacteristic
288#520—21no—
289#520—21no—
290#520—21no—
291#518—21no—
292C4×#41C2311yescharacteristic
293#501—22no—
294#501—22no—
295#501—22no—
296#500—22no—
297#500C2311yescharacteristic
298#500C2311yescharacteristic
299#500C2311yescharacteristic
300#500C2311yescharacteristic
301#500C2311yescharacteristic
302#500C2311yescharacteristic
303#500C2311yescharacteristic
304#500C2311yescharacteristic
305#500C2311yescharacteristic
306#500C2311yescharacteristic
307#500C2311yescharacteristic
308#500C2311yescharacteristic
309#500C2311yescharacteristic
310#500C2311yescharacteristic
311#499—22no—
312#498C2311yescharacteristic
313#498C2311yescharacteristic
314#498C2311yescharacteristic
315#498C2311yescharacteristic
316#498C2311yescharacteristic
317#498C2311yescharacteristic
318#498C2311yescharacteristic
319#498C2311yescharacteristic
320#497—22no—
321#497—22no—
322#497—22no—
323#496—22no—
324#496—22no—
325#495—22no—
326#495—22no—
327#495—22no—
328#494C2311yescharacteristic
329#494C2311yescharacteristic
330#494C2311yescharacteristic
331#494C2311yescharacteristic
332#494C2311yescharacteristic
333#494C2311yescharacteristic
334#494C2311yescharacteristic
335#493C2311yescharacteristic
336#493C2311yescharacteristic
337#493C2311yescharacteristic
338#493C2311yescharacteristic
339#493C2311yescharacteristic
340#493C2311yescharacteristic
341#493C2311yescharacteristic
342#493C2311yescharacteristic
343#493C2311yescharacteristic
344#492C2311yescharacteristic
345#492C2311yescharacteristic
346#492C2311yescharacteristic
347#492C2311yescharacteristic
348#492C2311yescharacteristic
349#492C2311yescharacteristic
350#492C2311yescharacteristic
351#492C2311yescharacteristic
352#492C2311yescharacteristic
353#492C2311yescharacteristic
354#492C2311yescharacteristic
355#492C2311yescharacteristic
356#492C2311yescharacteristic
357#492C2311yescharacteristic
358#490—22no—
359#489—22no—
360#489—22no—
361#489—22no—
362#488—22no—
363#488—22no—
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#487C2311yescharacteristic
378#487C2311yescharacteristic
379#487C2311yescharacteristic
380#486—22no—
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#482—22no—
411#482—22no—
412#482—22no—
413#482—22no—
414#482—22no—
415#480—22no—
416#480—22no—
417#480—22no—
418#479—22no—
419#478—22no—
420#478—22no—
421#478—22no—
422#478—22no—
423#478—22no—
424#474—22no—
425#474—22no—
426#474—22no—
427#470—22no—
428#469—22no—
429#469—22no—
430#469—22no—
431#469—22no—
432#469—22no—
433#469—22no—
434#468—22no—
435#468—22no—
436#468—22no—
437#468—22no—
438#468—22no—
439#468—22no—
440#468—22no—
441#468—22no—
442#468—22no—
443#467—22no—
444#467—22no—
445#467—22no—
446#466—22no—
447#466—22no—
448#466—22no—
449#466—22no—
450#466—22no—
451#466—22no—
452#465—22no—
453#465—22no—
454#465—22no—
455#464—22no—
456#464—22no—
457#464—22no—
458#464—22no—
459#463—22no—
460#463—22no—
461#463—22no—
462#463—22no—
463#463—22no—
464#463—22no—
465#462—22no—
466#462—22no—
467#461—22no—
468#460—22no—
469#459—22no—
470#452—22no—
471#452—22no—
472#452—22no—
473#452—22no—
474#451—22no—
475#451—22no—
476#450—22no—
477#449—22no—
478#449—22no—
479#449—22no—
480#449—22no—
481#449—22no—
482#449—22no—
483#448—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#441—22no—
494#440—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×Q16—22no—
504C4×Q16—22no—
505C4×Q16—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#428—22no—
530#427—22no—
531C2×#107—22no—
532#418—22no—
533#417—22no—
534#417—22no—
535#417—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×#41—21no—
582C2×#41—21no—
583C2×#41C2×D411yescharacteristic
584C22×Q8—21no—
585C22×Q8—21no—
586C22×Q8—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590#137—84no—
591#137—84no—
592#137—84no—
593AGL(1,ℤ/8)—48no—
594AGL(1,ℤ/8)—84no—
595#135—48no—
596#135—84no—
597#135—84no—
598C2×Q16—22no—
599C2×Q16—22no—
600C2×Q16—22no—
601C2×Q16—22no—
602C2×Q16—22no—
603C2×Q16—22no—
604C2×Q16—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×D8—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—
628#131—44no—
629C2×M16C2×D412yes—
630C2×M16C2×D412yes—
631C2×M16C2×D412yes—
632C2×M16C2×D412yes—
633C2×M16C2×D412yes—
634C2×M16C2×D412yes—
635C2×M16C2×D412yes—
636C22×C8C2×D412yes—
637C22×C8C2×D412yes—
638C22×C8C2×D412yes—
639C22×C8C2×D412yes—
640C22×C8C2×D412yes—
641C4⋊Q8—21no—
642C4⋊Q8—21no—
643C4⋊Q8—21no—
644C4⋊Q8—21no—
645C4⋊Q8—21no—
646C4⋊Q8—21no—
647C4⋊Q8—21no—
648C4⋊Q8—21no—
649C4⋊Q8—21no—
650C4⋊Q8C2411yescharacteristic
651C4⋊Q8C2411yescharacteristic
652C4⋊Q8C2411yescharacteristic
653C4⋊Q8C2411yescharacteristic
654C4⋊Q8C2411yescharacteristic
655C4⋊Q8C2411yescharacteristic
656C4⋊Q8C2411yescharacteristic
657C4⋊Q8C2411yescharacteristic
658C4⋊Q8C2411yescharacteristic
659C4⋊Q8C2411yescharacteristic
660C4⋊Q8C2411yescharacteristic
661#127—21no—
662#127—21no—
663#127—21no—
664#127—41no—
665#127C2411yescharacteristic
666#127C2411yescharacteristic
667#127C2411yescharacteristic
668#127C2411yescharacteristic
669#127C2411yescharacteristic
670#126—41no—
671#126—41no—
672#126—41no—
673#126—41no—
674#126—41no—
675#126—41no—
676#125—21no—
677#125—21no—
678#125—21no—
679#125—21no—
680#125—21no—
681#125—21no—
682#125—21no—
683#124—21no—
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—21no—
696#124—41no—
697#124—41no—
698#124—41no—
699#124—41no—
700#124—41no—
701#124—41no—
702#124—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—
712#123—41no—
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—41no—
728C22⋊Q8—41no—
729C22⋊Q8—41no—
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—41no—
763#121—41no—
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#120—41no—
776#120—41no—
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—21no—
789C4×Q8—21no—
790C4×Q8—21no—
791C4×Q8C2×D411yescharacteristic
792C4×Q8C2×D411yescharacteristic
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—21no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—21no—
819C4×D4—41no—
820C4×D4—41no—
821C4×D4—41no—
822C4×D4—41no—
823C4×D4—41no—
824C4×D4—41no—
825C4×D4—41no—
826C4×D4—41no—
827C4×D4C2×D411yescharacteristic
828C4×D4C2×D411yescharacteristic
829C4×D4C2×D411yescharacteristic
830C4×D4C2×D411yescharacteristic
831C4×D4C2×D411yescharacteristic
832C4×D4C2×D411yescharacteristic
833#117—21no—
834#117—21no—
835#117—21no—
836#117—21no—
837#117—21no—
838#117—21no—
839#117—21no—
840#117—41no—
841#117—41no—
842#117—41no—
843#117C2×D411yescharacteristic
844#117C2×D411yescharacteristic
845#117C2×D411yescharacteristic
846C2×C4⋊C4—21no—
847C2×C4⋊C4—21no—
848C2×C4⋊C4—21no—
849C2×C4⋊C4—21no—
850C2×C4⋊C4—21no—
851C2×C4⋊C4—21no—
852C2×C4⋊C4—41no—
853C2×C4⋊C4—41no—
854C2×C4⋊C4—41no—
855C2×C22⋊C4—41no—
856C2×C22⋊C4—41no—
857C2×C42C2411yescharacteristic
858C2×C42C2411yescharacteristic
859C2×C42C2411yescharacteristic
860#107—22no—
861#107—22no—
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#107—22no—
871#107—22no—
872#107—22no—
873#107—22no—
874#106—22no—
875#106—22no—
876#106—22no—
877#106—22no—
878#106—22no—
879#106—22no—
880#106—22no—
881#106—22no—
882C4⋊C8C2×D412yes—
883C4⋊C8C2×D412yes—
884C4⋊C8C2×D412yes—
885C4⋊C8C2×D412yes—
886C4⋊C8C2×D412yes—
887C4⋊C8C2×D412yes—
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#103—22no—
903#103—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—
963#41—42no—
964#41—44no—
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—
977C2×Q8—21no—
978C2×Q8—21no—
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—41no—
989C2×Q8—41no—
990C2×Q8—41no—
991C2×Q8—82no—
992C2×Q8—82no—
993C2×Q8—82no—
994C2×Q8#12711yescharacteristic
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—44no—
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—41no—
1024C2×D4—41no—
1025C2×D4—41no—
1026C2×D4—41no—
1027C2×D4—82no—
1028C2×D4—82no—
1029C2×D4#12711yescharacteristic
1030C2×D4#12711yescharacteristic
1031C2×D4#12711yescharacteristic
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×C4—41no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4C22×D411yescharacteristic
1049C22×C4C22×D411yescharacteristic
1050C22×C4C22×D411yescharacteristic
1051C22×C4C22×D411yescharacteristic
1052C22×C4C22×D411yescharacteristic
1053C22×C4C22×D411yescharacteristic
1054C22×C4C22×D411yescharacteristic
1055C22×C4C22×D411yescharacteristic
1056C22×C4C22×D411yescharacteristic
1057Q16—44no—
1058Q16—44no—
1059Q16—44no—
1060Q16—82no—
1061Q16—82no—
1062Q16—82no—
1063Q16—82no—
1064SD16—44no—
1065SD16—44no—
1066SD16—44no—
1067SD16—44no—
1068SD16—44no—
1069SD16—44no—
1070SD16—44no—
1071SD16—82no—
1072SD16—82no—
1073SD16—82no—
1074SD16—82no—
1075SD16—82no—
1076SD16—82no—
1077SD16—82no—
1078D8—44no—
1079D8—44no—
1080D8—44no—
1081D8—44no—
1082D8—44no—
1083D8—82no—
1084D8—82no—
1085D8—82no—
1086D8—82no—
1087M16—24no—
1088M16—24no—
1089M16—24no—
1090M16—24no—
1091M16—42no—
1092M16—42no—
1093M16—42no—
1094C2×C8—24no—
1095C2×C8—24no—
1096C2×C8—42no—
1097C2×C8—42no—
1098C2×C8—42no—
1099C2×C8C22×D412yes—
1100C2×C8C22×D412yes—
1101C2×C8C22×D412yes—
1102C2×C8C22×D412yes—
1103C2×C8C22×D412yes—
1104C2×C8C22×D412yes—
1105C2×C8C22×D412yes—
1106C2×C8C22×D412yes—
1107C2×C8C22×D412yes—
1108C2×C8C22×D412yes—
1109C2×C8C22×D412yes—
1110C2×C8C22×D412yes—
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—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—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—41no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—41no—
1150C4⋊C4—41no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4#12711yescharacteristic
1154C4⋊C4#12711yescharacteristic
1155C4⋊C4#12711yescharacteristic
1156C4⋊C4#12711yescharacteristic
1157C4⋊C4#12711yescharacteristic
1158C4⋊C4#12711yescharacteristic
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—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#12711yescharacteristic
1193C22⋊C4#12711yescharacteristic
1194C22⋊C4#12711yescharacteristic
1195C22⋊C4#12711yescharacteristic
1196C22⋊C4#12711yescharacteristic
1197C22⋊C4#12711yescharacteristic
1198C42—41no—
1199C42—41no—
1200C42—41no—
1201C42—41no—
1202C42—41no—
1203C42—41no—
1204C42—41no—
1205C42C22×D411yescharacteristic
1206C42C22×D411yescharacteristic
1207C42C22×D411yescharacteristic
1208C42C22×D411yescharacteristic
1209C42C22×D411yescharacteristic
1210C42C22×D411yescharacteristic
1211C42C22×D411yescharacteristic
1212C42C22×D411yescharacteristic
1213C42C22×D411yescharacteristic
1214C42C2511yescharacteristic
1215C23—41no—
1216C23—41no—
1217C23—41no—
1218C23—41no—
1219C23—41no—
1220C23—82no—
1221C23—161no—
1222C23—161no—
1223C23C2×#12711yescharacteristic
1224C23C2×#12711yescharacteristic
1225C23C2×#12711yescharacteristic
1226Q8—41no—
1227Q8—42no—
1228Q8—42no—
1229Q8—42no—
1230Q8—42no—
1231Q8—42no—
1232Q8—42no—
1233Q8—42no—
1234Q8—42no—
1235Q8—42no—
1236Q8—42no—
1237Q8—42no—
1238Q8—161no—
1239Q8—161no—
1240Q8—161no—
1241D4—41no—
1242D4—41no—
1243D4—41no—
1244D4—42no—
1245D4—42no—
1246D4—42no—
1247D4—42no—
1248D4—42no—
1249D4—42no—
1250D4—42no—
1251D4—42no—
1252D4—42no—
1253D4—42no—
1254D4—42no—
1255D4—42no—
1256D4—42no—
1257D4—42no—
1258D4—42no—
1259D4—82no—
1260D4—82no—
1261D4—82no—
1262D4—82no—
1263D4—161no—
1264D4—161no—
1265D4—161no—
1266D4—161no—
1267D4—161no—
1268D4—161no—
1269D4—161no—
1270D4—161no—
1271D4—161no—
1272D4—161no—
1273D4—161no—
1274D4—161no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—82no—
1296C2×C4—82no—
1297C2×C4—82no—
1298C2×C4—161no—
1299C2×C4—161no—
1300C2×C4—161no—
1301C2×C4—161no—
1302C2×C4—161no—
1303C2×C4—161no—
1304C2×C4—161no—
1305C2×C4—161no—
1306C2×C4—161no—
1307C2×C4—161no—
1308C2×C4—161no—
1309C2×C4—161no—
1310C2×C4—161no—
1311C2×C4C2×#12711yescharacteristic
1312C2×C4C2×#12711yescharacteristic
1313C2×C4C2×#12711yescharacteristic
1314C2×C4C2×#12711yescharacteristic
1315C2×C4C2×#12711yescharacteristic
1316C2×C4C2×#12711yescharacteristic
1317C2×C4C2×#12711yescharacteristic
1318C2×C4C2×#12711yescharacteristic
1319C2×C4C2×#12711yescharacteristic
1320C2×C4C23×D411yescharacteristic
1321C2×C4C23×D411yescharacteristic
1322C2×C4C23×D411yescharacteristic
1323C8—22no—
1324C8—22no—
1325C8—22no—
1326C8—22no—
1327C8—22no—
1328C8—22no—
1329C8—22no—
1330C8—22no—
1331C8—22no—
1332C8—22no—
1333C8#57514yes—
1334C8#57614yes—
1335C22—21no—
1336C22—21no—
1337C22—21no—
1338C22—21no—
1339C22—21no—
1340C22—21no—
1341C22—21no—
1342C22—21no—
1343C22—21no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—322no—
1360C22C22×#12711yescharacteristic
1361C4—21no—
1362C4—21no—
1363C4—21no—
1364C4—21no—
1365C4—21no—
1366C4—21no—
1367C4—21no—
1368C4—21no—
1369C4—21no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4C2×#57512yes—
1382C4C2×#57612yes—
1383C4#358612yes—
1384C2—41no—
1385C2—41no—
1386C2—41no—
1387C2—161no—
1388C2—161no—
1389C2—161no—
1390C2—161no—
1391C2—161no—
1392C2#6063911yescharacteristic
1393C2#6064711yescharacteristic
1394C2#6065111yescharacteristic
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. #62481C2semidirect
3. #62427C2semidirect
4. #62425C2semidirect
5. #60722C2semidirect
6. #60718C2semidirect
7. #19750C2semidirect
8. #19748C2semidirect
9. #19747C2semidirect
10. #19746C2semidirect
11. #19730C2semidirect
12. #19728C2semidirect
13. #19722C2semidirect
14. #19719C2semidirect
15. #19712C2semidirect
16. #19708C2semidirect
17. #19695C2semidirect
18. #19689C2semidirect
19. #19683C2semidirect
20. #19682C2semidirect
21. #19646C2semidirect
22. #19645C2semidirect
23. #19644C2semidirect
24. #19643C2semidirect
25. #19641C2semidirect
26. #19641C2semidirect
27. #19631C2semidirect
28. #19630C2semidirect
29. #19620C2semidirect
30. #19616C2semidirect
31. #17337C2semidirect
55. #3228C22semidirect
56. #3228C22semidirect
57. #3228C22semidirect
60. #3226C22semidirect
63. #3210C22semidirect
64. #3210C22semidirect
66. #3209C22semidirect
73. #3207C22semidirect
82. #3184C22semidirect
89. #3182C22semidirect
90. #3182C22semidirect
91. #3182C22semidirect
97. #3170C22semidirect
98. #3170C22semidirect
103. #3169C22semidirect
104. #3169C22semidirect
110. #3165C22semidirect
111. #3160C22semidirect
112. C2×#500C22semidirect
115. #3152C22semidirect
119. #3147C22semidirect
120. #3147C22semidirect
122. #3141C22semidirect
123. #3141C22semidirect
135. #1723C22semidirect
136. #1723C22semidirect
137. #1723C22semidirect
138. #1723C22semidirect
139. #1723C22semidirect
144. #1722C22semidirect
145. #1722C22semidirect
146. #1722C22semidirect
147. #1722C22semidirect
154. #1721C22semidirect
159. #1720C22semidirect
160. #1720C22semidirect
161. #1720C22semidirect
165. #1719C22semidirect
166. #1718C22semidirect
167. #1718C22semidirect
168. #1718C22semidirect
172. #1717C22semidirect
173. #1717C22semidirect
174. #1717C22semidirect
175. #1716C22semidirect
180. #1714C22semidirect
181. #1714C22semidirect
182. #1714C22semidirect
183. #1713C22semidirect
184. #1713C22semidirect
185. #1711C22semidirect
186. #1710C22semidirect
189. #1708C22semidirect
190. #1708C22semidirect
191. #1707C22semidirect
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
#624812
#624272
#624252
#607222
#607182
#197502
#197482
#197472
#197462
#197302
#197282
#197222
#197192
#197122
#197082
#196952
#196892
#196832
#196822
#196462
#196452
#196442
#196432
#196412
#196312
#196302
#196202
#196162
#173372