Finite Group Databasebeta

← #6357451

Subgroups — #6357451

Order 512.

1967 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60972C211yesmaximal, characteristic, complemented
2#60965C211yesmaximal, characteristic, complemented
3#60965C211yesmaximal, characteristic, complemented
4#60946C211yesmaximal, characteristic, complemented
5#60803C211yesmaximal, characteristic, complemented
6#60782C211yesmaximal, characteristic, complemented
7#19743C211yesmaximal, characteristic, complemented
8#19742C211yesmaximal, characteristic, complemented
9#19740C211yesmaximal, characteristic, complemented
10#19738C211yesmaximal, characteristic, complemented
11#19737C211yesmaximal, characteristic, complemented
12#19735C211yesmaximal, characteristic, complemented
13#19735C211yesmaximal, characteristic, complemented
14#19734C211yesmaximal, characteristic, complemented
15#19730C211yesmaximal, characteristic, complemented
16#19727C211yesmaximal, characteristic, complemented
17#19722C211yesmaximal, characteristic, complemented
18#19719C211yesmaximal, characteristic, complemented
19#19719C211yesmaximal, characteristic, complemented
20#19718C211yesmaximal, characteristic, complemented
21#19716C211yesmaximal, characteristic, complemented
22#19713C211yesmaximal, characteristic, complemented
23#19695C211yesmaximal, characteristic, complemented
24#19694C211yesmaximal, characteristic, complemented
25#19691C211yesmaximal, characteristic, complemented
26#19689C211yesmaximal, characteristic, complemented
27#19649C211yesmaximal, characteristic, complemented
28#19647C211yesmaximal, characteristic, complemented
29#19644C211yesmaximal, characteristic, complemented
30#19641C211yesmaximal, characteristic, complemented
31#17324C211yesmaximal, characteristic, complemented
32#3444C2211yescharacteristic
33#3444C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#532C2211yescharacteristic
36#3256—22no—
37#3251—22no—
38#3251—22no—
39#3247—22no—
40#3231C2211yescharacteristic, complemented
41#3231C2211yescharacteristic, complemented
42#3230C2211yescharacteristic, complemented
43#3229C2211yescharacteristic, complemented
44#3229C2211yescharacteristic, complemented
45#3228C2211yescharacteristic
46#3228C2211yescharacteristic
47#3228C2211yescharacteristic
48#3228C2211yescharacteristic
49#3228C2211yescharacteristic
50#3228C2211yescharacteristic
51#3228C2211yescharacteristic, complemented
52#3228C2211yescharacteristic, complemented
53#3227C2211yescharacteristic, complemented
54#3226C2211yescharacteristic, complemented
55#3226C2211yescharacteristic, complemented
56#3214—22no—
57#3213—22no—
58#3212—22no—
59#3211—22no—
60#3210C2211yescharacteristic
61#3210C2211yescharacteristic
62#3210C2211yescharacteristic, complemented
63#3210C2211yescharacteristic, complemented
64#3209C2211yescharacteristic, complemented
65#3208C2211yescharacteristic, complemented
66#3208C2211yescharacteristic, complemented
67#3208C2211yescharacteristic, complemented
68#3208C2211yescharacteristic, complemented
69#3207C2211yescharacteristic
70#3207C2211yescharacteristic
71#3207C2211yescharacteristic
72#3207C2211yescharacteristic
73#3207C2211yescharacteristic
74#3207C2211yescharacteristic
75#3207C2211yescharacteristic
76#3207C2211yescharacteristic
77#3207C2211yescharacteristic
78#3207C2211yescharacteristic
79#3207C2211yescharacteristic
80#3207C2211yescharacteristic
81#3207C2211yescharacteristic, complemented
82#3207C2211yescharacteristic, complemented
83#3206C2211yescharacteristic
84#3206C2211yescharacteristic
85#3206C2211yescharacteristic, complemented
86#3205C2211yescharacteristic
87#3205C2211yescharacteristic
88#3205C2211yescharacteristic, complemented
89#3205C2211yescharacteristic, complemented
90#3205C2211yescharacteristic, complemented
91#3205C2211yescharacteristic, complemented
92#3197—22no—
93#3194—22no—
94#3194—22no—
95#3188—22no—
96#3185C2211yescharacteristic, complemented
97#3184C2211yescharacteristic, complemented
98#3184C2211yescharacteristic, complemented
99#3184C2211yescharacteristic, complemented
100#3184C2211yescharacteristic, complemented
101#3184C2211yescharacteristic, complemented
102#3182C2211yescharacteristic, complemented
103#3182C2211yescharacteristic, complemented
104#3182C2211yescharacteristic, complemented
105#3182C2211yescharacteristic, complemented
106#3182C2211yescharacteristic, complemented
107#3182C2211yescharacteristic, complemented
108#3169C2211yescharacteristic, complemented
109#3169C2211yescharacteristic, complemented
110#3167C2211yescharacteristic, complemented
111#3167C2211yescharacteristic, complemented
112#3151C2211yescharacteristic
113#3151C2211yescharacteristic
114#3147C2211yescharacteristic, complemented
115#3147C2211yescharacteristic, complemented
116#3141C2211yescharacteristic
117#3141C2211yescharacteristic
118#3131C2211yescharacteristic, complemented
119#3131C2211yescharacteristic, complemented
120#3115—22no—
121#3115—22no—
122#3114—22no—
123#3114—22no—
124#3111—22no—
125#3111—22no—
126#3106—22no—
127#3105—22no—
128#3036—22no—
129#3035—22no—
130#3006—22no—
131#3002—22no—
132#2920C2211yescharacteristic
133#2920C2211yescharacteristic
134C2×#431C2211yescharacteristic
135#1723C2211yescharacteristic, complemented
136#1723C2211yescharacteristic, complemented
137#1722C2211yescharacteristic, complemented
138#1722C2211yescharacteristic, complemented
139#1721C2211yescharacteristic, complemented
140#1721C2211yescharacteristic, complemented
141#1721C2211yescharacteristic, complemented
142#1721C2211yescharacteristic, complemented
143#1721C2211yescharacteristic, complemented
144#1721C2211yescharacteristic, complemented
145#1721C2211yescharacteristic, complemented
146#1721C2211yescharacteristic, complemented
147#1720C2211yescharacteristic, complemented
148#1720C2211yescharacteristic, complemented
149#1720C2211yescharacteristic, complemented
150#1720C2211yescharacteristic, complemented
151#1719C2211yescharacteristic, complemented
152#1719C2211yescharacteristic, complemented
153#1719C2211yescharacteristic, complemented
154#1719C2211yescharacteristic, complemented
155#1719C2211yescharacteristic, complemented
156#1719C2211yescharacteristic, complemented
157#1718C2211yescharacteristic, complemented
158#1718C2211yescharacteristic, complemented
159#1718C2211yescharacteristic, complemented
160#1718C2211yescharacteristic, complemented
161#1717C2211yescharacteristic, complemented
162#1717C2211yescharacteristic, complemented
163#1717C2211yescharacteristic, complemented
164#1717C2211yescharacteristic, complemented
165#1717C2211yescharacteristic, complemented
166#1717C2211yescharacteristic, complemented
167#1717C2211yescharacteristic, complemented
168#1717C2211yescharacteristic, complemented
169#1717C2211yescharacteristic, complemented
170#1717C2211yescharacteristic, complemented
171#1716C2211yescharacteristic, complemented
172#1715C2211yescharacteristic, complemented
173#1715C2211yescharacteristic, complemented
174#1715C2211yescharacteristic, complemented
175#1715C2211yescharacteristic, complemented
176#1715C2211yescharacteristic, complemented
177#1714C2211yescharacteristic, complemented
178#1714C2211yescharacteristic, complemented
179#1714C2211yescharacteristic, complemented
180#1714C2211yescharacteristic, complemented
181#1714C2211yescharacteristic, complemented
182#1714C2211yescharacteristic, complemented
183#1712C2211yescharacteristic, complemented
184#1711C2211yescharacteristic, complemented
185#1711C2211yescharacteristic, complemented
186#1710C2211yescharacteristic, complemented
187#1709C2211yescharacteristic, complemented
188#1709C2211yescharacteristic, complemented
189#1708C2211yescharacteristic, complemented
190#1708C2211yescharacteristic, complemented
191#1708C2211yescharacteristic, complemented
192#1707C2211yescharacteristic, complemented
193#1706C2211yescharacteristic, complemented
194#1706C2211yescharacteristic, complemented
195#1706C2211yescharacteristic, complemented
196#1706C2211yescharacteristic, complemented
197#1706C2211yescharacteristic, complemented
198#1705C2211yescharacteristic, complemented
199#1454C2211yescharacteristic, complemented
200#1454C2211yescharacteristic, complemented
201#1454C2211yescharacteristic, complemented
202#1454C2211yescharacteristic, complemented
203#1453C2211yescharacteristic, complemented
204#1453C2211yescharacteristic, complemented
205#1453C2211yescharacteristic, complemented
206#1453C2211yescharacteristic, complemented
207#1451C2211yescharacteristic, complemented
208#1451C2211yescharacteristic, complemented
209C8×M16C2211yescharacteristic, complemented
210C8×M16C2211yescharacteristic, complemented
211C22×#41—21no—
212C22×#41—21no—
213C2×AGL(1,ℤ/8)—22no—
214C2×AGL(1,ℤ/8)—22no—
215C2×#135—22no—
216C2×#135—22no—
217#533C2311yescharacteristic
218#533C2311yescharacteristic
219#533C2311yescharacteristic
220#533C2311yescharacteristic
221#533C2311yescharacteristic
222#533C2311yescharacteristic
223#532—21no—
224#532—21no—
225#532—21no—
226#532—21no—
227#532—21no—
228#532—21no—
229#532—21no—
230#532—21no—
231#532—21no—
232#532—21no—
233#532—21no—
234#532—21no—
235#532C2311yescharacteristic
236#532C2311yescharacteristic
237#532C2311yescharacteristic
238#532C2311yescharacteristic
239#532C2311yescharacteristic
240#532C2311yescharacteristic
241#532C2311yescharacteristic
242#532C2311yescharacteristic
243#532C2311yescharacteristic
244#532C2311yescharacteristic
245#532C2311yescharacteristic
246#532C2311yescharacteristic
247#532C2311yescharacteristic
248#532C2311yescharacteristic
249C2×C4⋊Q8C2311yescharacteristic
250C2×C4⋊Q8C2311yescharacteristic
251C2×#127C2311yescharacteristic
252C2×#127C2311yescharacteristic
253#529—21no—
254#529—21no—
255#529—21no—
256#529—21no—
257#529—21no—
258#529—21no—
259#529—21no—
260#529—21no—
261#529—21no—
262#529—21no—
263#529—21no—
264#529—21no—
265C2×#124—21no—
266C2×#124—21no—
267#525—21no—
268#525—21no—
269#525—21no—
270#525—21no—
271#525—21no—
272#525—21no—
273C2×#121—21no—
274C2×#121—21no—
275C2×#121—21no—
276C2×#121—21no—
277C4×#41—21no—
278C4×#41—21no—
279C4×#41—21no—
280C4×#41—21no—
281C4×#41—21no—
282C4×#41—21no—
283C2×C4×D4—21no—
284C2×C4×D4—21no—
285C2×C4×D4—21no—
286C2×C4×D4—21no—
287C22×C42C2311yescharacteristic
288#500C2311yescharacteristic
289#500C2311yescharacteristic
290#500C2311yescharacteristic
291#500C2311yescharacteristic
292#500C2311yescharacteristic
293#500C2311yescharacteristic
294#500C2311yescharacteristic
295#500C2311yescharacteristic
296#498C2311yescharacteristic
297#498C2311yescharacteristic
298#498C2311yescharacteristic
299#498C2311yescharacteristic
300#498C2311yescharacteristic
301#498C2311yescharacteristic
302#498C2311yescharacteristic
303#498C2311yescharacteristic
304#496—22no—
305#496—22no—
306#495—22no—
307#495—22no—
308#494C2311yescharacteristic
309#494C2311yescharacteristic
310#494C2311yescharacteristic
311#493C2311yescharacteristic
312#493C2311yescharacteristic
313#493C2311yescharacteristic
314#493C2311yescharacteristic
315#493C2311yescharacteristic
316#493C2311yescharacteristic
317#493C2311yescharacteristic
318#493C2311yescharacteristic
319#493C2311yescharacteristic
320#493C2311yescharacteristic
321#493C2311yescharacteristic
322#493C2311yescharacteristic
323#493C2311yescharacteristic
324#492C2311yescharacteristic
325#492C2311yescharacteristic
326#492C2311yescharacteristic
327#492C2311yescharacteristic
328#492C2311yescharacteristic
329#492C2311yescharacteristic
330#492C2311yescharacteristic
331#492C2311yescharacteristic
332#492C2311yescharacteristic
333#492C2311yescharacteristic
334#492C2311yescharacteristic
335#492C2311yescharacteristic
336#492C2311yescharacteristic
337#492C2311yescharacteristic
338#492C2311yescharacteristic
339#492C2311yescharacteristic
340#489—22no—
341#489—22no—
342#488—22no—
343#488—22no—
344#487C2311yescharacteristic
345#487C2311yescharacteristic
346#487C2311yescharacteristic
347#487C2311yescharacteristic
348#487C2311yescharacteristic
349#487C2311yescharacteristic
350#487C2311yescharacteristic
351#487C2311yescharacteristic
352#487C2311yescharacteristic
353#487C2311yescharacteristic
354#487C2311yescharacteristic
355#487C2311yescharacteristic
356#487C2311yescharacteristic
357#487C2311yescharacteristic
358#487C2311yescharacteristic
359#487C2311yescharacteristic
360#487C2311yescharacteristic
361#487C2311yescharacteristic
362#486C2311yescharacteristic
363#486C2311yescharacteristic
364#486C2311yescharacteristic
365#486C2311yescharacteristic
366#486C2311yescharacteristic
367#486C2311yescharacteristic
368#486C2311yescharacteristic
369#486C2311yescharacteristic
370#486C2311yescharacteristic
371#486C2311yescharacteristic
372#486C2311yescharacteristic
373#486C2311yescharacteristic
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#485—22no—
393#485—22no—
394#484—22no—
395#483—22no—
396#483—22no—
397#482—22no—
398#482—22no—
399#482—22no—
400#482—22no—
401#482—22no—
402#482—22no—
403#482—22no—
404#482—22no—
405#481—22no—
406#480—22no—
407#480—22no—
408#479—22no—
409#479—22no—
410#478—22no—
411#478—22no—
412#478—22no—
413#478—22no—
414#478—22no—
415#478—22no—
416#478—22no—
417#478—22no—
418#477—22no—
419#476—22no—
420#475—22no—
421#475—22no—
422#474—22no—
423#474—22no—
424#470—22no—
425#469—22no—
426#469—22no—
427#469—22no—
428#469—22no—
429#469—22no—
430#468—22no—
431#468—22no—
432#468—22no—
433#468—22no—
434#468—22no—
435#468—22no—
436#466—22no—
437#466—22no—
438#465—22no—
439#465—22no—
440#464—22no—
441#464—22no—
442#464—22no—
443#464—22no—
444#463—22no—
445#463—22no—
446#463—22no—
447#463—22no—
448#463—22no—
449#463—22no—
450#463—22no—
451#463—22no—
452#463—22no—
453#463—22no—
454#463—22no—
455#463—22no—
456#463—22no—
457#463—22no—
458#462—22no—
459#461—22no—
460#461—22no—
461#461—22no—
462#460—22no—
463#460—22no—
464#460—22no—
465#460—22no—
466#459—22no—
467#459—22no—
468#459—22no—
469#459—22no—
470#459—22no—
471#459—22no—
472#452—22no—
473#452—22no—
474#452—22no—
475#452—22no—
476#451—22no—
477#450—22no—
478#450—22no—
479#450—22no—
480#450—22no—
481#449—22no—
482#449—22no—
483#449—22no—
484#449—22no—
485#449—22no—
486#449—22no—
487#449—22no—
488#449—22no—
489#449—22no—
490#449—22no—
491#449—22no—
492#449—22no—
493#449—22no—
494#449—22no—
495#448—22no—
496#448—22no—
497#448—22no—
498#447—22no—
499#447—22no—
500#447—22no—
501#447—22no—
502#447—22no—
503#447—22no—
504#442—22no—
505#442—22no—
506#442—22no—
507#442—22no—
508#442—22no—
509#441—22no—
510#440—22no—
511#440—22no—
512#440—22no—
513#440—22no—
514#440—22no—
515#440—22no—
516C4×SD16—22no—
517C4×SD16—22no—
518C4×D8—22no—
519C4×D8—22no—
520#432D412yes—
521#432D412yes—
522#432D412yes—
523#432D412yes—
524#431D412yes—
525#431D412yes—
526#431C2311yescharacteristic
527#431C2311yescharacteristic
528#431C2311yescharacteristic
529#431C2311yescharacteristic
530#431C2311yescharacteristic
531#431C2311yescharacteristic
532#431C2311yescharacteristic
533#431C2311yescharacteristic
534#431C2311yescharacteristic
535#431C2311yescharacteristic
536#431C2311yescharacteristic
537#431C2311yescharacteristic
538#423D412yes—
539#423D412yes—
540C2×C4⋊C8D412yes—
541#417—22no—
542#417—22no—
543#416—22no—
544#416—22no—
545#407D412yes—
546#407D412yes—
547C2×C22⋊C8D412yes—
548C4×M16C2311yescharacteristic
549C4×M16C2311yescharacteristic
550C4×M16C2311yescharacteristic
551C4×M16C2311yescharacteristic
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—41no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—84no—
589C2×#41—84no—
590C22×Q8—21no—
591C22×Q8—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—41no—
599C22×D4—41no—
600C23×C4—41no—
601C23×C4—41no—
602C23×C4C2×D411yescharacteristic
603C23×C4C2×D411yescharacteristic
604C23×C4C2×D411yescharacteristic
605AGL(1,ℤ/8)—84no—
606AGL(1,ℤ/8)—84no—
607#135—84no—
608#135—84no—
609C2×Q16—22no—
610C2×Q16—22no—
611C2×Q16—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×SD16—22no—
627C2×SD16—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×M16C2×D412yes—
642C2×M16C2×D412yes—
643C2×M16C2×D412yes—
644C2×M16C2×D412yes—
645C22×C8C2×D412yes—
646C22×C8C2×D412yes—
647C4⋊Q8—21no—
648C4⋊Q8—21no—
649C4⋊Q8—21no—
650C4⋊Q8—21no—
651C4⋊Q8—21no—
652C4⋊Q8—21no—
653C4⋊Q8C2411yescharacteristic
654C4⋊Q8C2411yescharacteristic
655C4⋊Q8C2411yescharacteristic
656C4⋊Q8C2411yescharacteristic
657C4⋊Q8C2411yescharacteristic
658C4⋊Q8C2411yescharacteristic
659C4⋊Q8C2411yescharacteristic
660C4⋊Q8C2411yescharacteristic
661C4⋊Q8C2411yescharacteristic
662C4⋊Q8C2411yescharacteristic
663#127—21no—
664#127—21no—
665#127—21no—
666#127—21no—
667#127—21no—
668#127—21no—
669#127C2411yescharacteristic
670#127C2411yescharacteristic
671#127C2411yescharacteristic
672#127C2411yescharacteristic
673#127C2411yescharacteristic
674#127C2411yescharacteristic
675#126—41no—
676#126—41no—
677#126—41no—
678#126—41no—
679#125—21no—
680#125—21no—
681#125—21no—
682#125—21no—
683#125—21no—
684#125—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—21no—
697#124—21no—
698#124—21no—
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—
709C22⋊Q8—21no—
710C22⋊Q8—21no—
711C22⋊Q8—21no—
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—
721#121—21no—
722#121—21no—
723#121—21no—
724#121—21no—
725#121—21no—
726#121—21no—
727#121—21no—
728#121—21no—
729#121—21no—
730#121—21no—
731#121—21no—
732#121—21no—
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—41no—
750#121—41no—
751#121—41no—
752#121—41no—
753#121—41no—
754#121—41no—
755#121—41no—
756#121—41no—
757#120—41no—
758#120—41no—
759C4×Q8—21no—
760C4×Q8—21no—
761C4×Q8—21no—
762C4×Q8—21no—
763C4×Q8—21no—
764C4×Q8—21no—
765C4×Q8—21no—
766C4×Q8—21no—
767C4×Q8—21no—
768C4×Q8—21no—
769C4×Q8—21no—
770C4×Q8—21no—
771C4×D4—21no—
772C4×D4—21no—
773C4×D4—21no—
774C4×D4—21no—
775C4×D4—21no—
776C4×D4—21no—
777C4×D4—21no—
778C4×D4—21no—
779C4×D4—21no—
780C4×D4—21no—
781C4×D4—21no—
782C4×D4—21no—
783C4×D4—21no—
784C4×D4—21no—
785C4×D4—21no—
786C4×D4—21no—
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—21no—
790C4×D4—21no—
791C4×D4—21no—
792C4×D4—21no—
793C4×D4—21no—
794C4×D4—21no—
795C4×D4—21no—
796C4×D4—21no—
797C4×D4—21no—
798C4×D4—21no—
799C4×D4—41no—
800C4×D4—41no—
801C4×D4—41no—
802C4×D4—41no—
803C4×D4—41no—
804C4×D4—41no—
805C4×D4—41no—
806C4×D4—41no—
807C4×D4—41no—
808C4×D4—41no—
809C4×D4—41no—
810C4×D4—41no—
811C4×D4—41no—
812C4×D4—41no—
813C4×D4—41no—
814C4×D4—41no—
815C4×D4—41no—
816C4×D4—41no—
817C4×D4—41no—
818C4×D4—41no—
819#117—21no—
820#117—21no—
821#117—21no—
822#117—21no—
823#117—21no—
824#117—21no—
825#117—41no—
826#117—41no—
827#117—41no—
828#117—41no—
829#117—41no—
830#117—41no—
831C2×C4⋊C4—21no—
832C2×C4⋊C4—21no—
833C2×C4⋊C4—21no—
834C2×C4⋊C4—21no—
835C2×C22⋊C4—41no—
836C2×C22⋊C4—41no—
837C2×C22⋊C4—41no—
838C2×C22⋊C4—41no—
839C2×C42—41no—
840C2×C42—41no—
841C2×C42C2×D411yescharacteristic
842C2×C42C2×D411yescharacteristic
843C2×C42C2×D411yescharacteristic
844C2×C42C2×D411yescharacteristic
845C2×C42C2×D411yescharacteristic
846C2×C42C2×D411yescharacteristic
847C2×C42C2×D411yescharacteristic
848C2×C42C2×D411yescharacteristic
849C2×C42C2×D411yescharacteristic
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—
869C4⋊C8C2×D412yes—
870C4⋊C8C2×D412yes—
871C4⋊C8C2×D412yes—
872C4⋊C8C2×D412yes—
873C4⋊C8C2×D412yes—
874C4⋊C8C2×D412yes—
875C4⋊C8C2×D412yes—
876C4⋊C8C2×D412yes—
877C4⋊C8C2×D412yes—
878C4⋊C8C2×D412yes—
879C4⋊C8C2×D412yes—
880C4⋊C8C2×D412yes—
881#103—22no—
882#103—22no—
883#103—22no—
884#103—22no—
885#103—22no—
886#103—22no—
887#103—22no—
888#103—22no—
889#103—22no—
890#103—22no—
891#103—22no—
892#103—22no—
893#103—22no—
894#103—22no—
895#103—22no—
896#103—22no—
897#103—22no—
898#103—22no—
899#102—22no—
900#102—22no—
901#102—22no—
902#102—22no—
903#102—22no—
904#102—22no—
905#102—22no—
906#102—22no—
907#102—22no—
908#102—22no—
909#102—22no—
910#102—22no—
911#102—22no—
912#102—22no—
913#102—22no—
914#102—22no—
915#102—22no—
916#102—22no—
917#102—22no—
918#102—22no—
919#102—22no—
920#102—22no—
921#102—22no—
922#102—22no—
923#102—22no—
924#102—22no—
925#102—22no—
926#102—22no—
927#102—22no—
928#102—22no—
929C22⋊C8C2×D412yes—
930C22⋊C8C2×D412yes—
931C22⋊C8C2×D412yes—
932C22⋊C8C2×D412yes—
933C22⋊C8C2×D412yes—
934C22⋊C8C2×D412yes—
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—
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—
961C24#12711yescharacteristic
962#41—44no—
963#41—44no—
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—84no—
977#41—84no—
978#41—84no—
979#41—84no—
980C2×Q8—21no—
981C2×Q8—21no—
982C2×Q8—21no—
983C2×Q8—21no—
984C2×Q8—21no—
985C2×Q8—21no—
986C2×Q8—21no—
987C2×Q8—21no—
988C2×Q8—21no—
989C2×Q8—21no—
990C2×Q8—41no—
991C2×Q8—41no—
992C2×Q8—82no—
993C2×Q8—82no—
994C2×D4—21no—
995C2×D4—21no—
996C2×D4—21no—
997C2×D4—21no—
998C2×D4—21no—
999C2×D4—21no—
1000C2×D4—21no—
1001C2×D4—21no—
1002C2×D4—21no—
1003C2×D4—21no—
1004C2×D4—21no—
1005C2×D4—21no—
1006C2×D4—21no—
1007C2×D4—21no—
1008C2×D4—21no—
1009C2×D4—21no—
1010C2×D4—21no—
1011C2×D4—21no—
1012C2×D4—44no—
1013C2×D4—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—41no—
1028C2×D4—41no—
1029C2×D4—41no—
1030C2×D4—41no—
1031C2×D4—41no—
1032C2×D4—41no—
1033C2×D4—82no—
1034C2×D4—82no—
1035C2×D4—82no—
1036C2×D4—82no—
1037C2×D4—82no—
1038C2×D4—84no—
1039C2×D4—84no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—41no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—41no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—84no—
1060C22×C4—84no—
1061C22×C4#12711yescharacteristic
1062C22×C4#12711yescharacteristic
1063C22×C4#12711yescharacteristic
1064C22×C4#12711yescharacteristic
1065C22×C4#12711yescharacteristic
1066C22×C4#12711yescharacteristic
1067C22×C4#12711yescharacteristic
1068C22×C4#12711yescharacteristic
1069C22×C4#12711yescharacteristic
1070C22×C4C22×D411yescharacteristic
1071C22×C4C22×D411yescharacteristic
1072C22×C4C22×D411yescharacteristic
1073C22×C4C22×D411yescharacteristic
1074C22×C4C22×D411yescharacteristic
1075C22×C4C22×D411yescharacteristic
1076C22×C4C22×D411yescharacteristic
1077C22×C4C22×D411yescharacteristic
1078C22×C4C22×D411yescharacteristic
1079Q16—82no—
1080Q16—82no—
1081Q16—82no—
1082SD16—82no—
1083SD16—82no—
1084SD16—82no—
1085SD16—82no—
1086SD16—82no—
1087SD16—82no—
1088SD16—82no—
1089SD16—82no—
1090SD16—82no—
1091SD16—82no—
1092SD16—82no—
1093SD16—82no—
1094SD16—82no—
1095SD16—82no—
1096SD16—82no—
1097SD16—82no—
1098D8—82no—
1099D8—82no—
1100D8—82no—
1101D8—82no—
1102D8—82no—
1103D8—82no—
1104D8—82no—
1105D8—82no—
1106D8—82no—
1107D8—82no—
1108D8—82no—
1109D8—82no—
1110D8—82no—
1111M16—42no—
1112M16—42no—
1113M16—42no—
1114M16—42no—
1115C2×C8—42no—
1116C2×C8—42no—
1117C2×C8C22×D412yes—
1118C2×C8C22×D412yes—
1119C2×C8C22×D412yes—
1120C2×C8C22×D412yes—
1121C2×C8C22×D412yes—
1122C2×C8C22×D412yes—
1123C2×C8C22×D412yes—
1124C2×C8C22×D412yes—
1125C2×C8C22×D412yes—
1126C2×C8C22×D412yes—
1127C2×C8C22×D412yes—
1128C2×C8C22×D412yes—
1129C4⋊C4—21no—
1130C4⋊C4—21no—
1131C4⋊C4—21no—
1132C4⋊C4—21no—
1133C4⋊C4—21no—
1134C4⋊C4—21no—
1135C4⋊C4—21no—
1136C4⋊C4—21no—
1137C4⋊C4—21no—
1138C4⋊C4—21no—
1139C4⋊C4—21no—
1140C4⋊C4—21no—
1141C4⋊C4—21no—
1142C4⋊C4—21no—
1143C4⋊C4—21no—
1144C4⋊C4—21no—
1145C4⋊C4—21no—
1146C4⋊C4—21no—
1147C4⋊C4—21no—
1148C4⋊C4—21no—
1149C4⋊C4—41no—
1150C4⋊C4—41no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4—41no—
1154C4⋊C4—41no—
1155C4⋊C4—41no—
1156C4⋊C4—41no—
1157C4⋊C4—41no—
1158C4⋊C4—41no—
1159C4⋊C4—41no—
1160C4⋊C4—41no—
1161C4⋊C4—41no—
1162C4⋊C4—41no—
1163C4⋊C4—41no—
1164C4⋊C4—41no—
1165C22⋊C4—41no—
1166C22⋊C4—41no—
1167C22⋊C4—41no—
1168C22⋊C4—41no—
1169C22⋊C4—41no—
1170C22⋊C4—41no—
1171C22⋊C4—41no—
1172C22⋊C4—41no—
1173C22⋊C4—41no—
1174C22⋊C4—41no—
1175C22⋊C4—41no—
1176C22⋊C4—41no—
1177C22⋊C4—41no—
1178C22⋊C4—41no—
1179C22⋊C4—41no—
1180C22⋊C4—41no—
1181C22⋊C4—41no—
1182C22⋊C4—41no—
1183C22⋊C4—41no—
1184C22⋊C4—41no—
1185C22⋊C4—41no—
1186C22⋊C4—41no—
1187C22⋊C4—41no—
1188C22⋊C4—41no—
1189C22⋊C4—41no—
1190C22⋊C4—41no—
1191C22⋊C4—41no—
1192C22⋊C4—41no—
1193C22⋊C4—41no—
1194C22⋊C4—41no—
1195C22⋊C4—41no—
1196C22⋊C4—41no—
1197C22⋊C4—41no—
1198C22⋊C4—41no—
1199C42—41no—
1200C42—41no—
1201C42—41no—
1202C42—41no—
1203C42—41no—
1204C42—41no—
1205C42#12711yescharacteristic
1206C42#12711yescharacteristic
1207C42#12711yescharacteristic
1208C42#12711yescharacteristic
1209C42#12711yescharacteristic
1210C42#12711yescharacteristic
1211C42C22×D411yescharacteristic
1212C42C22×D411yescharacteristic
1213C42C22×D411yescharacteristic
1214C42C22×D411yescharacteristic
1215C42C22×D411yescharacteristic
1216C42C22×D411yescharacteristic
1217C42C22×D411yescharacteristic
1218C42C22×D411yescharacteristic
1219C42C22×D411yescharacteristic
1220C42C2511yescharacteristic
1221C23—41no—
1222C23—41no—
1223C23—41no—
1224C23—41no—
1225C23—41no—
1226C23—41no—
1227C23—41no—
1228C23—41no—
1229C23—41no—
1230C23—82no—
1231C23—82no—
1232C23—82no—
1233C23—82no—
1234C23—82no—
1235C23—82no—
1236C23C2×#12711yescharacteristic
1237C23C2×#12711yescharacteristic
1238C23C2×#12711yescharacteristic
1239Q8—42no—
1240Q8—42no—
1241Q8—42no—
1242Q8—42no—
1243Q8—42no—
1244Q8—42no—
1245Q8—42no—
1246Q8—42no—
1247Q8—42no—
1248Q8—42no—
1249Q8—82no—
1250Q8—82no—
1251D4—42no—
1252D4—42no—
1253D4—42no—
1254D4—42no—
1255D4—42no—
1256D4—42no—
1257D4—42no—
1258D4—42no—
1259D4—42no—
1260D4—42no—
1261D4—42no—
1262D4—42no—
1263D4—42no—
1264D4—42no—
1265D4—42no—
1266D4—42no—
1267D4—42no—
1268D4—42no—
1269D4—82no—
1270D4—82no—
1271D4—82no—
1272D4—82no—
1273D4—82no—
1274D4—82no—
1275D4—82no—
1276D4—82no—
1277D4—82no—
1278D4—82no—
1279D4—82no—
1280D4—82no—
1281D4—82no—
1282D4—82no—
1283D4—82no—
1284D4—82no—
1285D4—82no—
1286D4—82no—
1287D4—82no—
1288D4—82no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—82no—
1318C2×C4—82no—
1319C2×C4—82no—
1320C2×C4—82no—
1321C2×C4—82no—
1322C2×C4—82no—
1323C2×C4—82no—
1324C2×C4—82no—
1325C2×C4—82no—
1326C2×C4—82no—
1327C2×C4—82no—
1328C2×C4—82no—
1329C2×C4—82no—
1330C2×C4—82no—
1331C2×C4—82no—
1332C2×C4—82no—
1333C2×C4C2×#12711yescharacteristic
1334C2×C4C2×#12711yescharacteristic
1335C2×C4C2×#12711yescharacteristic
1336C2×C4C2×#12711yescharacteristic
1337C2×C4C2×#12711yescharacteristic
1338C2×C4C2×#12711yescharacteristic
1339C2×C4C2×#12711yescharacteristic
1340C2×C4C2×#12711yescharacteristic
1341C2×C4C2×#12711yescharacteristic
1342C2×C4C23×D411yescharacteristic
1343C2×C4C23×D411yescharacteristic
1344C2×C4C23×D411yescharacteristic
1345C8—22no—
1346C8—22no—
1347C8—22no—
1348C8—22no—
1349C8—22no—
1350C8—22no—
1351C8—22no—
1352C8—22no—
1353C8—22no—
1354C8—22no—
1355C8—22no—
1356C8—22no—
1357C22—21no—
1358C22—21no—
1359C22—21no—
1360C22—21no—
1361C22—21no—
1362C22—21no—
1363C22—21no—
1364C22—21no—
1365C22—21no—
1366C22—82no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—164no—
1386C22—164no—
1387C22C22×#12711yescharacteristic
1388C4—21no—
1389C4—21no—
1390C4—21no—
1391C4—21no—
1392C4—21no—
1393C4—21no—
1394C4—21no—
1395C4—21no—
1396C4—21no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4#358412yes—
1408C4#358512yes—
1409C4#358512yes—
1410C2—41no—
1411C2—41no—
1412C2—41no—
1413C2—161no—
1414C2—161no—
1415C2—161no—
1416C2—161no—
1417C2—161no—
1418C2—161no—
1419C2#6064311yescharacteristic
1420C2#6064411yescharacteristic
1421C2#6064411yescharacteristic
subgroupG/H
center, socleC22C22×#127
commutator, Frattini, cosocleC42C25
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60972C2semidirect
2. #60965C2semidirect
3. #60965C2semidirect
4. #60946C2semidirect
5. #60803C2semidirect
6. #60782C2semidirect
7. #19743C2semidirect
8. #19742C2semidirect
9. #19740C2semidirect
10. #19738C2semidirect
11. #19737C2semidirect
12. #19735C2semidirect
13. #19735C2semidirect
14. #19734C2semidirect
15. #19730C2semidirect
16. #19727C2semidirect
17. #19722C2semidirect
18. #19719C2semidirect
19. #19719C2semidirect
20. #19718C2semidirect
21. #19716C2semidirect
22. #19713C2semidirect
23. #19695C2semidirect
24. #19694C2semidirect
25. #19691C2semidirect
26. #19689C2semidirect
27. #19649C2semidirect
28. #19647C2semidirect
29. #19644C2semidirect
30. #19641C2semidirect
31. #17324C2semidirect
40. #3231C22semidirect
41. #3231C22semidirect
42. #3230C22semidirect
43. #3229C22semidirect
44. #3229C22semidirect
51. #3228C22semidirect
52. #3228C22semidirect
53. #3227C22semidirect
54. #3226C22semidirect
55. #3226C22semidirect
62. #3210C22semidirect
63. #3210C22semidirect
64. #3209C22semidirect
65. #3208C22semidirect
66. #3208C22semidirect
67. #3208C22semidirect
68. #3208C22semidirect
81. #3207C22semidirect
82. #3207C22semidirect
85. #3206C22semidirect
88. #3205C22semidirect
89. #3205C22semidirect
90. #3205C22semidirect
91. #3205C22semidirect
96. #3185C22semidirect
97. #3184C22semidirect
98. #3184C22semidirect
99. #3184C22semidirect
100. #3184C22semidirect
101. #3184C22semidirect
102. #3182C22semidirect
103. #3182C22semidirect
104. #3182C22semidirect
105. #3182C22semidirect
106. #3182C22semidirect
107. #3182C22semidirect
108. #3169C22semidirect
109. #3169C22semidirect
110. #3167C22semidirect
111. #3167C22semidirect
114. #3147C22semidirect
115. #3147C22semidirect
118. #3131C22semidirect
119. #3131C22semidirect
135. #1723C22semidirect
136. #1723C22semidirect
137. #1722C22semidirect
138. #1722C22semidirect
139. #1721C22semidirect
140. #1721C22semidirect
141. #1721C22semidirect
142. #1721C22semidirect
143. #1721C22semidirect
144. #1721C22semidirect
145. #1721C22semidirect
146. #1721C22semidirect
147. #1720C22semidirect
148. #1720C22semidirect
149. #1720C22semidirect
150. #1720C22semidirect
151. #1719C22semidirect
152. #1719C22semidirect
153. #1719C22semidirect
154. #1719C22semidirect
155. #1719C22semidirect
156. #1719C22semidirect
157. #1718C22semidirect
158. #1718C22semidirect
159. #1718C22semidirect
160. #1718C22semidirect
161. #1717C22semidirect
162. #1717C22semidirect
163. #1717C22semidirect
164. #1717C22semidirect
165. #1717C22semidirect
166. #1717C22semidirect
167. #1717C22semidirect
168. #1717C22semidirect
169. #1717C22semidirect
170. #1717C22semidirect
171. #1716C22semidirect
172. #1715C22semidirect
173. #1715C22semidirect
174. #1715C22semidirect
175. #1715C22semidirect
176. #1715C22semidirect
177. #1714C22semidirect
178. #1714C22semidirect
179. #1714C22semidirect
180. #1714C22semidirect
181. #1714C22semidirect
182. #1714C22semidirect
183. #1712C22semidirect
184. #1711C22semidirect
185. #1711C22semidirect
186. #1710C22semidirect
187. #1709C22semidirect
188. #1709C22semidirect
189. #1708C22semidirect
190. #1708C22semidirect
191. #1708C22semidirect
192. #1707C22semidirect
193. #1706C22semidirect
194. #1706C22semidirect
195. #1706C22semidirect
196. #1706C22semidirect
197. #1706C22semidirect
198. #1705C22semidirect
199. #1454C22semidirect
200. #1454C22semidirect
201. #1454C22semidirect
202. #1454C22semidirect
203. #1453C22semidirect
204. #1453C22semidirect
205. #1453C22semidirect
206. #1453C22semidirect
207. #1451C22semidirect
208. #1451C22semidirect
209. C8×M16C22semidirect
210. C8×M16C22semidirect

Maximal subgroups

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

subgroupindex
#609722
#609652
#609462
#608032
#607822
#197432
#197422
#197402
#197382
#197372
#197352
#197342
#197302
#197272
#197222
#197192
#197182
#197162
#197132
#196952
#196942
#196912
#196892
#196492
#196472
#196442
#196412
#173242