Finite Group Databasebeta

← #6357925

Subgroups — #6357925

Order 512.

2004 conjugacy classes of subgroups.

The subgroup lattice has 1437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62546C211yesmaximal, characteristic, complemented
2#62427C211yesmaximal, characteristic, complemented
3#62426C211yesmaximal, characteristic, complemented
4#62426C211yesmaximal, characteristic, complemented
5#60722C211yesmaximal, characteristic, complemented
6#60714C211yesmaximal, characteristic, complemented
7#19749C211yesmaximal, characteristic, complemented
8#19748C211yesmaximal, characteristic, complemented
9#19747C211yesmaximal, characteristic, complemented
10#19745C211yesmaximal, characteristic, complemented
11#19729C211yesmaximal, characteristic, complemented
12#19727C211yesmaximal, characteristic, complemented
13#19726C211yesmaximal, characteristic, complemented
14#19715C211yesmaximal, characteristic, complemented
15#19710C211yesmaximal, characteristic, complemented
16#19708C211yesmaximal, characteristic, complemented
17#19695C211yesmaximal, characteristic, complemented
18#19688C211yesmaximal, characteristic, complemented
19#19676C211yesmaximal, characteristic, complemented
20#19673C211yesmaximal, characteristic, complemented
21#19647C211yesmaximal, characteristic, complemented
22#19647C211yesmaximal, characteristic, complemented
23#19644C211yesmaximal, characteristic, complemented
24#19644C211yesmaximal, characteristic, complemented
25#19642C211yesmaximal, characteristic, complemented
26#19641C211yesmaximal, characteristic, complemented
27#19631C211yesmaximal, characteristic, complemented
28#19629C211yesmaximal, characteristic, complemented
29#19619C211yesmaximal, characteristic, complemented
30#19616C211yesmaximal, characteristic, complemented
31#17337C211yesmaximal, characteristic, complemented
32#3511C2211yescharacteristic
33#3508C2211yescharacteristic
34#3508C2211yescharacteristic
35#3508C2211yescharacteristic
36#3403—22no—
37#3403—22no—
38#3401—22no—
39#3370—22no—
40#3322—22no—
41#3319—22no—
42#3309—22no—
43#3275—22no—
44#3273—22no—
45#3273—22no—
46#3271—22no—
47#3268—22no—
48#3268—22no—
49#3268—22no—
50#3268—22no—
51#3267—22no—
52#3231C2211yescharacteristic, complemented
53#3228C2211yescharacteristic, complemented
54#3226C2211yescharacteristic, complemented
55#3210C2211yescharacteristic
56#3210C2211yescharacteristic
57#3210C2211yescharacteristic, complemented
58#3210C2211yescharacteristic, complemented
59#3210C2211yescharacteristic, complemented
60#3210C2211yescharacteristic, complemented
61#3208C2211yescharacteristic, complemented
62#3207C2211yescharacteristic, complemented
63#3207C2211yescharacteristic, complemented
64#3207C2211yescharacteristic, complemented
65#3207C2211yescharacteristic, complemented
66#3207C2211yescharacteristic, complemented
67#3207C2211yescharacteristic, complemented
68#3207C2211yescharacteristic, complemented
69#3207C2211yescharacteristic, complemented
70#3206C2211yescharacteristic, complemented
71#3205C2211yescharacteristic
72#3205C2211yescharacteristic
73#3205C2211yescharacteristic, complemented
74#3205C2211yescharacteristic, complemented
75#3205C2211yescharacteristic, complemented
76#3185C2211yescharacteristic, complemented
77#3184C2211yescharacteristic
78#3184C2211yescharacteristic
79#3184C2211yescharacteristic
80#3184C2211yescharacteristic, complemented
81#3184C2211yescharacteristic, complemented
82#3184C2211yescharacteristic, complemented
83#3184C2211yescharacteristic, complemented
84#3184C2211yescharacteristic, complemented
85#3182C2211yescharacteristic
86#3182C2211yescharacteristic
87#3182C2211yescharacteristic
88#3182C2211yescharacteristic, complemented
89#3182C2211yescharacteristic, complemented
90#3182C2211yescharacteristic, complemented
91#3182C2211yescharacteristic, complemented
92#3179—22no—
93#3179—22no—
94#3176—22no—
95#3176—22no—
96#3169C2211yescharacteristic
97#3169C2211yescharacteristic
98#3169C2211yescharacteristic
99#3169C2211yescharacteristic, complemented
100#3169C2211yescharacteristic, complemented
101#3169C2211yescharacteristic, complemented
102#3169C2211yescharacteristic, complemented
103#3169C2211yescharacteristic, complemented
104#3169C2211yescharacteristic, complemented
105#3167C2211yescharacteristic
106#3167C2211yescharacteristic, complemented
107#3167C2211yescharacteristic, complemented
108#3165C2211yescharacteristic, complemented
109#3160C2211yescharacteristic, complemented
110#3152C2211yescharacteristic, complemented
111#3151C2211yescharacteristic
112#3151C2211yescharacteristic
113#3151C2211yescharacteristic, complemented
114#3151C2211yescharacteristic, complemented
115#3151C2211yescharacteristic, complemented
116#3151C2211yescharacteristic, complemented
117#3147C2211yescharacteristic, complemented
118#3147C2211yescharacteristic, complemented
119#3147C2211yescharacteristic, complemented
120C2×#493C2211yescharacteristic, complemented
121#3141C2211yescharacteristic, complemented
122#3138C2211yescharacteristic, complemented
123#3138C2211yescharacteristic, complemented
124#3138C2211yescharacteristic, complemented
125#3131C2211yescharacteristic, complemented
126#3131C2211yescharacteristic, complemented
127C2×#486C2211yescharacteristic, complemented
128#3062—22no—
129#3058—22no—
130#2965C2211yescharacteristic
131#2965C2211yescharacteristic
132#2948—22no—
133#2946—22no—
134C4×#131C2211yescharacteristic
135#1723C2211yescharacteristic, complemented
136#1723C2211yescharacteristic, complemented
137#1723C2211yescharacteristic, complemented
138#1722C2211yescharacteristic, complemented
139#1722C2211yescharacteristic, complemented
140#1722C2211yescharacteristic, complemented
141#1722C2211yescharacteristic, complemented
142#1722C2211yescharacteristic, complemented
143#1721C2211yescharacteristic
144#1721C2211yescharacteristic
145#1721C2211yescharacteristic
146#1721C2211yescharacteristic
147#1721C2211yescharacteristic
148#1721C2211yescharacteristic
149#1721C2211yescharacteristic, complemented
150#1721C2211yescharacteristic, complemented
151#1721C2211yescharacteristic, complemented
152#1721C2211yescharacteristic, complemented
153#1721C2211yescharacteristic, complemented
154#1721C2211yescharacteristic, complemented
155#1720C2211yescharacteristic, complemented
156#1720C2211yescharacteristic, complemented
157#1720C2211yescharacteristic, complemented
158#1719C2211yescharacteristic, complemented
159#1719C2211yescharacteristic, complemented
160#1719C2211yescharacteristic, complemented
161#1719C2211yescharacteristic, complemented
162#1719C2211yescharacteristic, complemented
163#1719C2211yescharacteristic, complemented
164#1718C2211yescharacteristic, complemented
165#1717C2211yescharacteristic, complemented
166#1717C2211yescharacteristic, complemented
167#1717C2211yescharacteristic, complemented
168#1717C2211yescharacteristic, complemented
169#1717C2211yescharacteristic, complemented
170#1717C2211yescharacteristic, complemented
171#1717C2211yescharacteristic, complemented
172#1717C2211yescharacteristic, complemented
173#1717C2211yescharacteristic, complemented
174#1717C2211yescharacteristic, complemented
175#1715C2211yescharacteristic, complemented
176#1715C2211yescharacteristic, complemented
177#1715C2211yescharacteristic, complemented
178#1715C2211yescharacteristic, complemented
179#1715C2211yescharacteristic, complemented
180#1715C2211yescharacteristic, complemented
181#1714C2211yescharacteristic, complemented
182#1714C2211yescharacteristic, complemented
183#1712C2211yescharacteristic
184#1712C2211yescharacteristic
185#1711C2211yescharacteristic, complemented
186#1709C2211yescharacteristic, complemented
187#1709C2211yescharacteristic, complemented
188#1709C2211yescharacteristic, complemented
189#1708C2211yescharacteristic, complemented
190#1708C2211yescharacteristic, complemented
191#1707C2211yescharacteristic, complemented
192#1707C2211yescharacteristic, complemented
193#1706C2211yescharacteristic, complemented
194#1706C2211yescharacteristic, complemented
195#1706C2211yescharacteristic, complemented
196#1706C2211yescharacteristic, complemented
197#1706C2211yescharacteristic, complemented
198#1705C2211yescharacteristic, 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×#137—22no—
212C2×AGL(1,ℤ/8)—22no—
213C2×AGL(1,ℤ/8)—22no—
214C2×AGL(1,ℤ/8)—22no—
215C2×AGL(1,ℤ/8)—22no—
216C2×AGL(1,ℤ/8)—22no—
217C2×AGL(1,ℤ/8)—22no—
218C2×#135—22no—
219C2×#135—22no—
220C2×#135—22no—
221C22×D8—22no—
222C2×#131D412yes—
223#559—21no—
224#559—21no—
225#559—21no—
226#559—21no—
227#559—21no—
228#559—21no—
229#556—21no—
230#555—21no—
231#554—21no—
232#553—21no—
233#553—21no—
234#550—21no—
235#550—21no—
236#550—21no—
237#550—21no—
238#550—21no—
239#550—21no—
240#548—21no—
241#548—21no—
242#547—21no—
243#546—21no—
244#546—21no—
245#546—21no—
246#546—21no—
247#546—21no—
248#546—21no—
249#546—21no—
250#546—21no—
251#546—21no—
252#546—21no—
253#546—21no—
254#546—21no—
255#542—21no—
256#542—21no—
257#540—21no—
258#540—21no—
259#540—21no—
260#540—21no—
261#540—21no—
262#540—21no—
263#537—21no—
264#535—21no—
265#535—21no—
266#535—21no—
267#533C2311yescharacteristic
268#533C2311yescharacteristic
269#533C2311yescharacteristic
270#533C2311yescharacteristic
271#533C2311yescharacteristic
272#532C2311yescharacteristic
273#532C2311yescharacteristic
274#532C2311yescharacteristic
275#532C2311yescharacteristic
276#532C2311yescharacteristic
277#532C2311yescharacteristic
278#532C2311yescharacteristic
279#532C2311yescharacteristic
280#532C2311yescharacteristic
281#532C2311yescharacteristic
282#532C2311yescharacteristic
283#532C2311yescharacteristic
284#532C2311yescharacteristic
285#532C2311yescharacteristic
286#532C2311yescharacteristic
287C2×C4⋊Q8C2311yescharacteristic
288C2×#127C2311yescharacteristic
289C2×#127C2311yescharacteristic
290C2×#127C2311yescharacteristic
291#520—21no—
292#518—21no—
293#518—21no—
294#518—21no—
295C4×#41C2311yescharacteristic
296#501—22no—
297#500C2311yescharacteristic
298#500C2311yescharacteristic
299#500C2311yescharacteristic
300#500C2311yescharacteristic
301#500C2311yescharacteristic
302#500C2311yescharacteristic
303#500C2311yescharacteristic
304#500C2311yescharacteristic
305#499—22no—
306#498C2311yescharacteristic
307#498C2311yescharacteristic
308#498C2311yescharacteristic
309#498C2311yescharacteristic
310#498C2311yescharacteristic
311#498C2311yescharacteristic
312#497—22no—
313#496—22no—
314#496—22no—
315#496—22no—
316#496—22no—
317#496—22no—
318#496—22no—
319#495—22no—
320#495—22no—
321#495—22no—
322#494C2311yescharacteristic
323#494C2311yescharacteristic
324#494C2311yescharacteristic
325#494C2311yescharacteristic
326#493—22no—
327#493C2311yescharacteristic
328#493C2311yescharacteristic
329#493C2311yescharacteristic
330#493C2311yescharacteristic
331#493C2311yescharacteristic
332#493C2311yescharacteristic
333#493C2311yescharacteristic
334#493C2311yescharacteristic
335#493C2311yescharacteristic
336#493C2311yescharacteristic
337#493C2311yescharacteristic
338#493C2311yescharacteristic
339#493C2311yescharacteristic
340#493C2311yescharacteristic
341#493C2311yescharacteristic
342#493C2311yescharacteristic
343#493C2311yescharacteristic
344#493C2311yescharacteristic
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#492C2311yescharacteristic
359#492C2311yescharacteristic
360#492C2311yescharacteristic
361#490—22no—
362#490—22no—
363#490—22no—
364#489—22no—
365#488—22no—
366#488—22no—
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#486—22no—
380#486C2311yescharacteristic
381#486C2311yescharacteristic
382#486C2311yescharacteristic
383#486C2311yescharacteristic
384#486C2311yescharacteristic
385#486C2311yescharacteristic
386#486C2311yescharacteristic
387#486C2311yescharacteristic
388#486C2311yescharacteristic
389#486C2311yescharacteristic
390#486C2311yescharacteristic
391#486C2311yescharacteristic
392#486C2311yescharacteristic
393#486C2311yescharacteristic
394#486C2311yescharacteristic
395#486C2311yescharacteristic
396#486C2311yescharacteristic
397#486C2311yescharacteristic
398#486C2311yescharacteristic
399#486C2311yescharacteristic
400#486C2311yescharacteristic
401#486C2311yescharacteristic
402#486C2311yescharacteristic
403#486C2311yescharacteristic
404#486C2311yescharacteristic
405#486C2311yescharacteristic
406#486C2311yescharacteristic
407#486C2311yescharacteristic
408#486C2311yescharacteristic
409#486C2311yescharacteristic
410#486C2311yescharacteristic
411#486C2311yescharacteristic
412#485—22no—
413#482—22no—
414#480—22no—
415#479—22no—
416#478—22no—
417#474—22no—
418#470—22no—
419#469—22no—
420#469—22no—
421#469—22no—
422#469—22no—
423#469—22no—
424#469—22no—
425#469—22no—
426#469—22no—
427#468—22no—
428#468—22no—
429#468—22no—
430#468—22no—
431#468—22no—
432#468—22no—
433#468—22no—
434#466—22no—
435#466—22no—
436#466—22no—
437#466—22no—
438#466—22no—
439#466—22no—
440#466—22no—
441#466—22no—
442#466—22no—
443#465—22no—
444#465—22no—
445#465—22no—
446#464—22no—
447#464—22no—
448#464—22no—
449#464—22no—
450#464—22no—
451#464—22no—
452#463—22no—
453#463—22no—
454#463—22no—
455#463—22no—
456#463—22no—
457#463—22no—
458#463—22no—
459#463—22no—
460#461—22no—
461#460—22no—
462#459—22no—
463#459—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#450—22no—
474#449—22no—
475#449—22no—
476#449—22no—
477#449—22no—
478#449—22no—
479#449—22no—
480#449—22no—
481#449—22no—
482#448—22no—
483#447—22no—
484#447—22no—
485#447—22no—
486#447—22no—
487#447—22no—
488#446D412yes—
489#446D412yes—
490#442—22no—
491#442—22no—
492#442—22no—
493#442—22no—
494#442—22no—
495#442—22no—
496#442—22no—
497#442—22no—
498#441—22no—
499#440—22no—
500#440—22no—
501#440—22no—
502#440—22no—
503#440—22no—
504#440—22no—
505#440—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—
515C4×D8—22no—
516C4×D8—22no—
517C4×D8—22no—
518#436D412yes—
519#436D412yes—
520#435D412yes—
521#435D412yes—
522#435D412yes—
523#435D412yes—
524#431C2311yescharacteristic
525#431C2311yescharacteristic
526#431C2311yescharacteristic
527#431C2311yescharacteristic
528#431C2311yescharacteristic
529#431C2311yescharacteristic
530#428—22no—
531#427—22no—
532#418—22no—
533#418—22no—
534#418—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×#41—21no—
584C2×#41—21no—
585C2×#41C2×D411yescharacteristic
586C22×Q8—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596#137—84no—
597AGL(1,ℤ/8)—48no—
598AGL(1,ℤ/8)—84no—
599AGL(1,ℤ/8)—84no—
600AGL(1,ℤ/8)—84no—
601AGL(1,ℤ/8)—84no—
602AGL(1,ℤ/8)—84no—
603#135—84no—
604#135—84no—
605#135—84no—
606C2×Q16—22no—
607C2×Q16—22no—
608C2×Q16—22no—
609C2×Q16—22no—
610C2×SD16—22no—
611C2×SD16—22no—
612C2×SD16—22no—
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—22no—
624C2×SD16—22no—
625C2×SD16—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—22no—
630C2×D8—22no—
631C2×D8—22no—
632C2×D8—22no—
633C2×D8—22no—
634C2×D8—22no—
635C2×D8—22no—
636C2×D8—22no—
637C2×D8—22no—
638C2×D8—22no—
639C2×D8—22no—
640C2×D8—22no—
641C2×D8—22no—
642C2×D8—22no—
643C2×D8—22no—
644C2×D8—48no—
645#131—44no—
646C2×M16C2×D412yes—
647C2×M16C2×D412yes—
648C2×M16C2×D412yes—
649C2×M16C2×D412yes—
650C2×M16C2×D412yes—
651C2×M16C2×D412yes—
652C2×M16C2×D412yes—
653C22×C8C2×D412yes—
654C22×C8C2×D412yes—
655C22×C8C2×D412yes—
656C22×C8C2×D412yes—
657C22×C8C2×D412yes—
658C4⋊Q8—21no—
659C4⋊Q8—21no—
660C4⋊Q8—21no—
661C4⋊Q8C2411yescharacteristic
662C4⋊Q8C2411yescharacteristic
663C4⋊Q8C2411yescharacteristic
664C4⋊Q8C2411yescharacteristic
665C4⋊Q8C2411yescharacteristic
666C4⋊Q8C2411yescharacteristic
667C4⋊Q8C2411yescharacteristic
668C4⋊Q8C2411yescharacteristic
669C4⋊Q8C2411yescharacteristic
670#127—21no—
671#127—21no—
672#127—21no—
673#127—21no—
674#127—21no—
675#127—21no—
676#127—21no—
677#127—21no—
678#127—21no—
679#127—41no—
680#127—41no—
681#127—41no—
682#127C2411yescharacteristic
683#127C2411yescharacteristic
684#127C2411yescharacteristic
685#127C2411yescharacteristic
686#127C2411yescharacteristic
687#127C2411yescharacteristic
688#127C2411yescharacteristic
689#126—41no—
690#126—41no—
691#125—21no—
692#125—21no—
693#125—21no—
694#125—21no—
695#125—21no—
696#124—21no—
697#124—21no—
698#124—21no—
699#124—21no—
700#124—21no—
701#124—21no—
702#124—21no—
703#124—21no—
704#124—21no—
705#124—21no—
706#124—21no—
707#124—21no—
708#124—21no—
709#124—21no—
710#124—21no—
711#124—41no—
712#124—41no—
713#124—41no—
714#124—41no—
715#124—41no—
716#123—41no—
717#123—41no—
718#123—41no—
719#123—41no—
720#123—41no—
721#123—41no—
722#123—41no—
723#123—41no—
724#123—41no—
725#123—41no—
726#123—41no—
727#123—41no—
728#123—41no—
729#123—41no—
730C22⋊Q8—21no—
731C22⋊Q8—21no—
732C22⋊Q8—21no—
733C22⋊Q8—21no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—41no—
741C22⋊Q8—41no—
742C22⋊Q8—41no—
743#121—21no—
744#121—21no—
745#121—21no—
746#121—21no—
747#121—21no—
748#121—21no—
749#121—21no—
750#121—21no—
751#121—21no—
752#121—21no—
753#121—21no—
754#121—21no—
755#121—21no—
756#121—21no—
757#121—21no—
758#121—21no—
759#121—21no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—21no—
767#121—21no—
768#121—21no—
769#121—21no—
770#121—21no—
771#121—21no—
772#121—21no—
773#121—41no—
774#121—41no—
775#121—41no—
776#121—41no—
777#121—41no—
778#121—41no—
779#121—41no—
780#121—41no—
781#121—41no—
782#121—41no—
783#121—41no—
784#121—41no—
785#121—41no—
786#121—41no—
787#121—41no—
788#120—41no—
789#120—41no—
790#120—41no—
791#120—41no—
792#120—41no—
793#120—41no—
794C4×Q8—21no—
795C4×Q8—21no—
796C4×Q8—21no—
797C4×Q8—21no—
798C4×Q8—21no—
799C4×Q8—21no—
800C4×Q8—21no—
801C4×Q8—21no—
802C4×Q8—21no—
803C4×Q8—21no—
804C4×Q8C2×D411yescharacteristic
805C4×Q8C2×D411yescharacteristic
806C4×D4—21no—
807C4×D4—21no—
808C4×D4—21no—
809C4×D4—21no—
810C4×D4—21no—
811C4×D4—21no—
812C4×D4—21no—
813C4×D4—21no—
814C4×D4—21no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—21no—
819C4×D4—21no—
820C4×D4—21no—
821C4×D4—21no—
822C4×D4—21no—
823C4×D4—21no—
824C4×D4—21no—
825C4×D4—21no—
826C4×D4—21no—
827C4×D4—21no—
828C4×D4—21no—
829C4×D4—21no—
830C4×D4—21no—
831C4×D4—21no—
832C4×D4—21no—
833C4×D4—21no—
834C4×D4—21no—
835C4×D4—21no—
836C4×D4—41no—
837C4×D4—41no—
838C4×D4—41no—
839C4×D4—41no—
840C4×D4—41no—
841C4×D4—41no—
842C4×D4—41no—
843C4×D4—41no—
844C4×D4C2×D411yescharacteristic
845C4×D4C2×D411yescharacteristic
846C4×D4C2×D411yescharacteristic
847C4×D4C2×D411yescharacteristic
848C4×D4C2×D411yescharacteristic
849C4×D4C2×D411yescharacteristic
850#117—21no—
851#117—21no—
852#117—21no—
853#117—21no—
854#117—21no—
855#117—41no—
856#117C2×D411yescharacteristic
857#117C2×D411yescharacteristic
858#117C2×D411yescharacteristic
859C2×C4⋊C4—21no—
860C2×C4⋊C4—21no—
861C2×C4⋊C4—41no—
862C2×C22⋊C4—41no—
863C2×C22⋊C4—41no—
864C2×C22⋊C4—41no—
865C2×C22⋊C4—41no—
866C2×C22⋊C4—41no—
867C2×C22⋊C4—41no—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871#107—22no—
872#107—22no—
873#107—22no—
874#107—22no—
875#107—22no—
876#107—22no—
877#107—22no—
878#107—22no—
879#106—22no—
880#106—22no—
881#106—22no—
882#106—22no—
883#106—22no—
884#106—22no—
885C4⋊C8C2×D412yes—
886C4⋊C8C2×D412yes—
887C4⋊C8C2×D412yes—
888C4⋊C8C2×D412yes—
889C4⋊C8C2×D412yes—
890C4⋊C8C2×D412yes—
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#102—22no—
904#102—22no—
905#102—22no—
906#102—22no—
907#102—22no—
908#102—22no—
909#102—22no—
910#102—22no—
911#102—22no—
912#102—22no—
913#102—22no—
914#102—22no—
915#102—22no—
916#102—22no—
917#102—22no—
918#102—22no—
919#102—22no—
920#102—22no—
921#102—22no—
922#102—22no—
923#102—22no—
924#102—22no—
925#102—22no—
926#102—22no—
927#102—22no—
928#102—22no—
929#102—22no—
930#102—22no—
931#102—22no—
932#102—22no—
933#102—22no—
934#102—22no—
935C22⋊C8C2×D412yes—
936C22⋊C8C2×D412yes—
937C22⋊C8C2×D412yes—
938C22⋊C8C2×D412yes—
939C22⋊C8C2×D412yes—
940C22⋊C8C2×D412yes—
941#97C2×D412yes—
942#97C2×D412yes—
943#97C2×D412yes—
944#97C2×D412yes—
945#97C2×D412yes—
946#97C2×D412yes—
947#97C2×D412yes—
948C4×C8C2×D412yes—
949C4×C8C2×D412yes—
950C4×C8C2×D412yes—
951C4×C8C2×D412yes—
952C4×C8C2×D412yes—
953C4×C8C2411yescharacteristic
954C4×C8C2411yescharacteristic
955C4×C8C2411yescharacteristic
956C4×C8C2411yescharacteristic
957C4×C8C2411yescharacteristic
958C4×C8C2411yescharacteristic
959C4×C8C2411yescharacteristic
960C4×C8C2411yescharacteristic
961C4×C8C2411yescharacteristic
962C4×C8C2411yescharacteristic
963C4×C8C2411yescharacteristic
964C4×C8C2411yescharacteristic
965C24—41no—
966C24—41no—
967C24—41no—
968#41—42no—
969#41—44no—
970#41—82no—
971#41—82no—
972#41—82no—
973#41—82no—
974#41—82no—
975#41—82no—
976#41—82no—
977#41—82no—
978#41—82no—
979#41—82no—
980#41—82no—
981#41—82no—
982#41—82no—
983#41—82no—
984C2×Q8—21no—
985C2×Q8—21no—
986C2×Q8—21no—
987C2×Q8—21no—
988C2×Q8—21no—
989C2×Q8—21no—
990C2×Q8—21no—
991C2×Q8—21no—
992C2×Q8—21no—
993C2×Q8—41no—
994C2×Q8—82no—
995C2×Q8#12711yescharacteristic
996C2×D4—21no—
997C2×D4—21no—
998C2×D4—21no—
999C2×D4—21no—
1000C2×D4—21no—
1001C2×D4—21no—
1002C2×D4—21no—
1003C2×D4—21no—
1004C2×D4—21no—
1005C2×D4—21no—
1006C2×D4—21no—
1007C2×D4—21no—
1008C2×D4—21no—
1009C2×D4—21no—
1010C2×D4—21no—
1011C2×D4—21no—
1012C2×D4—21no—
1013C2×D4—21no—
1014C2×D4—21no—
1015C2×D4—21no—
1016C2×D4—21no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—41no—
1021C2×D4—41no—
1022C2×D4—41no—
1023C2×D4—41no—
1024C2×D4—41no—
1025C2×D4—41no—
1026C2×D4—41no—
1027C2×D4—41no—
1028C2×D4—41no—
1029C2×D4—41no—
1030C2×D4—41no—
1031C2×D4—41no—
1032C2×D4—41no—
1033C2×D4—41no—
1034C2×D4—41no—
1035C2×D4—41no—
1036C2×D4—41no—
1037C2×D4—41no—
1038C2×D4—41no—
1039C2×D4—41no—
1040C2×D4—41no—
1041C2×D4—41no—
1042C2×D4—41no—
1043C2×D4—41no—
1044C2×D4—82no—
1045C2×D4—82no—
1046C2×D4—82no—
1047C2×D4—82no—
1048C2×D4—82no—
1049C2×D4—82no—
1050C2×D4#12711yescharacteristic
1051C2×D4#12711yescharacteristic
1052C2×D4#12711yescharacteristic
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—41no—
1068C22×C4—41no—
1069C22×C4C22×D411yescharacteristic
1070C22×C4C22×D411yescharacteristic
1071C22×C4C22×D411yescharacteristic
1072C22×C4C22×D411yescharacteristic
1073C22×C4C22×D411yescharacteristic
1074C22×C4C22×D411yescharacteristic
1075C22×C4C22×D411yescharacteristic
1076C22×C4C22×D411yescharacteristic
1077C22×C4C22×D411yescharacteristic
1078Q16—44no—
1079Q16—82no—
1080Q16—82no—
1081Q16—82no—
1082SD16—44no—
1083SD16—44no—
1084SD16—44no—
1085SD16—44no—
1086SD16—44no—
1087SD16—44no—
1088SD16—44no—
1089SD16—82no—
1090SD16—82no—
1091SD16—82no—
1092SD16—82no—
1093SD16—82no—
1094SD16—82no—
1095SD16—82no—
1096SD16—82no—
1097SD16—82no—
1098D8—44no—
1099D8—44no—
1100D8—44no—
1101D8—44no—
1102D8—44no—
1103D8—44no—
1104D8—44no—
1105D8—44no—
1106D8—44no—
1107D8—82no—
1108D8—82no—
1109D8—82no—
1110D8—82no—
1111D8—82no—
1112D8—82no—
1113D8—82no—
1114D8—82no—
1115D8—82no—
1116M16—24no—
1117M16—24no—
1118M16—24no—
1119M16—24no—
1120M16—42no—
1121M16—42no—
1122M16—42no—
1123C2×C8—24no—
1124C2×C8—24no—
1125C2×C8—42no—
1126C2×C8—42no—
1127C2×C8—42no—
1128C2×C8C22×D412yes—
1129C2×C8C22×D412yes—
1130C2×C8C22×D412yes—
1131C2×C8C22×D412yes—
1132C2×C8C22×D412yes—
1133C2×C8C22×D412yes—
1134C2×C8C22×D412yes—
1135C2×C8C22×D412yes—
1136C2×C8C22×D412yes—
1137C2×C8C22×D412yes—
1138C2×C8C22×D412yes—
1139C2×C8C22×D412yes—
1140C4⋊C4—21no—
1141C4⋊C4—21no—
1142C4⋊C4—21no—
1143C4⋊C4—21no—
1144C4⋊C4—21no—
1145C4⋊C4—21no—
1146C4⋊C4—21no—
1147C4⋊C4—21no—
1148C4⋊C4—21no—
1149C4⋊C4—21no—
1150C4⋊C4—21no—
1151C4⋊C4—21no—
1152C4⋊C4—21no—
1153C4⋊C4—21no—
1154C4⋊C4—21no—
1155C4⋊C4—21no—
1156C4⋊C4—21no—
1157C4⋊C4—21no—
1158C4⋊C4—41no—
1159C4⋊C4—41no—
1160C4⋊C4—41no—
1161C4⋊C4—41no—
1162C4⋊C4—41no—
1163C4⋊C4—41no—
1164C4⋊C4—41no—
1165C4⋊C4—41no—
1166C4⋊C4—41no—
1167C4⋊C4—41no—
1168C4⋊C4—41no—
1169C4⋊C4—41no—
1170C4⋊C4#12711yescharacteristic
1171C4⋊C4#12711yescharacteristic
1172C4⋊C4#12711yescharacteristic
1173C4⋊C4#12711yescharacteristic
1174C4⋊C4#12711yescharacteristic
1175C4⋊C4#12711yescharacteristic
1176C22⋊C4—41no—
1177C22⋊C4—41no—
1178C22⋊C4—41no—
1179C22⋊C4—41no—
1180C22⋊C4—41no—
1181C22⋊C4—41no—
1182C22⋊C4—41no—
1183C22⋊C4—41no—
1184C22⋊C4—41no—
1185C22⋊C4—41no—
1186C22⋊C4—41no—
1187C22⋊C4—41no—
1188C22⋊C4—41no—
1189C22⋊C4—41no—
1190C22⋊C4—41no—
1191C22⋊C4—41no—
1192C22⋊C4—41no—
1193C22⋊C4—41no—
1194C22⋊C4—41no—
1195C22⋊C4—41no—
1196C22⋊C4—41no—
1197C22⋊C4—41no—
1198C22⋊C4—41no—
1199C22⋊C4—41no—
1200C22⋊C4—41no—
1201C22⋊C4—41no—
1202C22⋊C4—41no—
1203C22⋊C4—41no—
1204C22⋊C4—41no—
1205C22⋊C4—41no—
1206C22⋊C4—41no—
1207C22⋊C4—41no—
1208C22⋊C4—41no—
1209C22⋊C4—41no—
1210C22⋊C4—41no—
1211C22⋊C4#12711yescharacteristic
1212C22⋊C4#12711yescharacteristic
1213C22⋊C4#12711yescharacteristic
1214C22⋊C4#12711yescharacteristic
1215C22⋊C4#12711yescharacteristic
1216C22⋊C4#12711yescharacteristic
1217C42—41no—
1218C42—41no—
1219C42—41no—
1220C42—41no—
1221C42—41no—
1222C42C22×D411yescharacteristic
1223C42C22×D411yescharacteristic
1224C42C22×D411yescharacteristic
1225C42C22×D411yescharacteristic
1226C42C22×D411yescharacteristic
1227C42C22×D411yescharacteristic
1228C42C22×D411yescharacteristic
1229C42C22×D411yescharacteristic
1230C42C22×D411yescharacteristic
1231C42C2511yescharacteristic
1232C23—41no—
1233C23—41no—
1234C23—41no—
1235C23—41no—
1236C23—41no—
1237C23—41no—
1238C23—41no—
1239C23—82no—
1240C23—82no—
1241C23—82no—
1242C23—161no—
1243C23—161no—
1244C23—161no—
1245C23—161no—
1246C23—161no—
1247C23—161no—
1248C23C2×#12711yescharacteristic
1249C23C2×#12711yescharacteristic
1250C23C2×#12711yescharacteristic
1251Q8—41no—
1252Q8—42no—
1253Q8—42no—
1254Q8—42no—
1255Q8—42no—
1256Q8—42no—
1257Q8—42no—
1258Q8—42no—
1259Q8—42no—
1260Q8—42no—
1261Q8—161no—
1262D4—41no—
1263D4—41no—
1264D4—41no—
1265D4—42no—
1266D4—42no—
1267D4—42no—
1268D4—42no—
1269D4—42no—
1270D4—42no—
1271D4—42no—
1272D4—42no—
1273D4—42no—
1274D4—42no—
1275D4—42no—
1276D4—42no—
1277D4—42no—
1278D4—42no—
1279D4—42no—
1280D4—42no—
1281D4—42no—
1282D4—42no—
1283D4—42no—
1284D4—42no—
1285D4—42no—
1286D4—82no—
1287D4—82no—
1288D4—82no—
1289D4—82no—
1290D4—161no—
1291D4—161no—
1292D4—161no—
1293D4—161no—
1294D4—161no—
1295D4—161no—
1296D4—161no—
1297D4—161no—
1298D4—161no—
1299D4—161no—
1300D4—161no—
1301D4—161no—
1302D4—161no—
1303D4—161no—
1304D4—161no—
1305D4—161no—
1306D4—161no—
1307D4—161no—
1308D4—161no—
1309D4—161no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—82no—
1329C2×C4—161no—
1330C2×C4—161no—
1331C2×C4—161no—
1332C2×C4—161no—
1333C2×C4—161no—
1334C2×C4—161no—
1335C2×C4—161no—
1336C2×C4—161no—
1337C2×C4—161no—
1338C2×C4—161no—
1339C2×C4—161no—
1340C2×C4—161no—
1341C2×C4—161no—
1342C2×C4—161no—
1343C2×C4—161no—
1344C2×C4C2×#12711yescharacteristic
1345C2×C4C2×#12711yescharacteristic
1346C2×C4C2×#12711yescharacteristic
1347C2×C4C2×#12711yescharacteristic
1348C2×C4C2×#12711yescharacteristic
1349C2×C4C2×#12711yescharacteristic
1350C2×C4C2×#12711yescharacteristic
1351C2×C4C2×#12711yescharacteristic
1352C2×C4C2×#12711yescharacteristic
1353C2×C4C23×D411yescharacteristic
1354C2×C4C23×D411yescharacteristic
1355C2×C4C23×D411yescharacteristic
1356C8—22no—
1357C8—22no—
1358C8—22no—
1359C8—22no—
1360C8—22no—
1361C8—22no—
1362C8—22no—
1363C8—22no—
1364C8—22no—
1365C8—22no—
1366C8#57514yes—
1367C8#57614yes—
1368C22—21no—
1369C22—21no—
1370C22—21no—
1371C22—21no—
1372C22—21no—
1373C22—21no—
1374C22—21no—
1375C22—21no—
1376C22—21no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—81no—
1392C22—81no—
1393C22—81no—
1394C22—81no—
1395C22—81no—
1396C22—81no—
1397C22—81no—
1398C22—322no—
1399C22—322no—
1400C22—322no—
1401C22C22×#12711yescharacteristic
1402C4—21no—
1403C4—21no—
1404C4—21no—
1405C4—21no—
1406C4—21no—
1407C4—21no—
1408C4—21no—
1409C4—21no—
1410C4—21no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4—81no—
1416C4—81no—
1417C4—81no—
1418C4—81no—
1419C4—81no—
1420C4C2×#57512yes—
1421C4C2×#57612yes—
1422C4#358512yes—
1423C2—41no—
1424C2—41no—
1425C2—41no—
1426C2—161no—
1427C2—161no—
1428C2—161no—
1429C2—161no—
1430C2—161no—
1431C2—161no—
1432C2—161no—
1433C2#6063911yescharacteristic
1434C2#6064711yescharacteristic
1435C2#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. #62427C2semidirect
3. #62426C2semidirect
4. #62426C2semidirect
5. #60722C2semidirect
6. #60714C2semidirect
7. #19749C2semidirect
8. #19748C2semidirect
9. #19747C2semidirect
10. #19745C2semidirect
11. #19729C2semidirect
12. #19727C2semidirect
13. #19726C2semidirect
14. #19715C2semidirect
15. #19710C2semidirect
16. #19708C2semidirect
17. #19695C2semidirect
18. #19688C2semidirect
19. #19676C2semidirect
20. #19673C2semidirect
21. #19647C2semidirect
22. #19647C2semidirect
23. #19644C2semidirect
24. #19644C2semidirect
25. #19642C2semidirect
26. #19641C2semidirect
27. #19631C2semidirect
28. #19629C2semidirect
29. #19619C2semidirect
30. #19616C2semidirect
31. #17337C2semidirect
52. #3231C22semidirect
53. #3228C22semidirect
54. #3226C22semidirect
57. #3210C22semidirect
58. #3210C22semidirect
59. #3210C22semidirect
60. #3210C22semidirect
61. #3208C22semidirect
62. #3207C22semidirect
63. #3207C22semidirect
64. #3207C22semidirect
65. #3207C22semidirect
66. #3207C22semidirect
67. #3207C22semidirect
68. #3207C22semidirect
69. #3207C22semidirect
70. #3206C22semidirect
73. #3205C22semidirect
74. #3205C22semidirect
75. #3205C22semidirect
76. #3185C22semidirect
80. #3184C22semidirect
81. #3184C22semidirect
82. #3184C22semidirect
83. #3184C22semidirect
84. #3184C22semidirect
88. #3182C22semidirect
89. #3182C22semidirect
90. #3182C22semidirect
91. #3182C22semidirect
99. #3169C22semidirect
100. #3169C22semidirect
101. #3169C22semidirect
102. #3169C22semidirect
103. #3169C22semidirect
104. #3169C22semidirect
106. #3167C22semidirect
107. #3167C22semidirect
108. #3165C22semidirect
109. #3160C22semidirect
110. #3152C22semidirect
113. #3151C22semidirect
114. #3151C22semidirect
115. #3151C22semidirect
116. #3151C22semidirect
117. #3147C22semidirect
118. #3147C22semidirect
119. #3147C22semidirect
120. C2×#493C22semidirect
121. #3141C22semidirect
122. #3138C22semidirect
123. #3138C22semidirect
124. #3138C22semidirect
125. #3131C22semidirect
126. #3131C22semidirect
127. C2×#486C22semidirect
135. #1723C22semidirect
136. #1723C22semidirect
137. #1723C22semidirect
138. #1722C22semidirect
139. #1722C22semidirect
140. #1722C22semidirect
141. #1722C22semidirect
142. #1722C22semidirect
149. #1721C22semidirect
150. #1721C22semidirect
151. #1721C22semidirect
152. #1721C22semidirect
153. #1721C22semidirect
154. #1721C22semidirect
155. #1720C22semidirect
156. #1720C22semidirect
157. #1720C22semidirect
158. #1719C22semidirect
159. #1719C22semidirect
160. #1719C22semidirect
161. #1719C22semidirect
162. #1719C22semidirect
163. #1719C22semidirect
164. #1718C22semidirect
165. #1717C22semidirect
166. #1717C22semidirect
167. #1717C22semidirect
168. #1717C22semidirect
169. #1717C22semidirect
170. #1717C22semidirect
171. #1717C22semidirect
172. #1717C22semidirect
173. #1717C22semidirect
174. #1717C22semidirect
175. #1715C22semidirect
176. #1715C22semidirect
177. #1715C22semidirect
178. #1715C22semidirect
179. #1715C22semidirect
180. #1715C22semidirect
181. #1714C22semidirect
182. #1714C22semidirect
185. #1711C22semidirect
186. #1709C22semidirect
187. #1709C22semidirect
188. #1709C22semidirect
189. #1708C22semidirect
190. #1708C22semidirect
191. #1707C22semidirect
192. #1707C22semidirect
193. #1706C22semidirect
194. #1706C22semidirect
195. #1706C22semidirect
196. #1706C22semidirect
197. #1706C22semidirect
198. #1705C22semidirect
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
#624272
#624262
#607222
#607142
#197492
#197482
#197472
#197452
#197292
#197272
#197262
#197152
#197102
#197082
#196952
#196882
#196762
#196732
#196472
#196442
#196422
#196412
#196312
#196292
#196192
#196162
#173372