Finite Group Databasebeta

← #6355974

Subgroups — #6355974

Order 512.

1489 conjugacy classes of subgroups.

The subgroup lattice has 1477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62108C211yesmaximal, characteristic, complemented
2#61967C211yesmaximal, characteristic
3#60881C211yesmaximal, characteristic, complemented
4#60300C211yesmaximal, characteristic, complemented
5#19588C211yesmaximal, characteristic, complemented
6#19584C211yesmaximal, characteristic, complemented
7#19575C211yesmaximal, characteristic, complemented
8#19571C211yesmaximal, characteristic, complemented
9#19550C211yesmaximal, characteristic, complemented
10#19544C211yesmaximal, characteristic, complemented
11#19534C211yesmaximal, characteristic, complemented
12#19529C211yesmaximal, characteristic, complemented
13#19500C211yesmaximal, characteristic, complemented
14#19498C211yesmaximal, characteristic, complemented
15#19467C211yesmaximal, characteristic, complemented
16#19463C211yesmaximal, characteristic, complemented
17#19454C211yesmaximal, characteristic, complemented
18#19450C211yesmaximal, characteristic, complemented
19#19431C211yesmaximal, characteristic, complemented
20#19427C211yesmaximal, characteristic, complemented
21#19382C211yesmaximal, characteristic, complemented
22#19378C211yesmaximal, characteristic, complemented
23#19367C211yesmaximal, characteristic, complemented
24#19357C211yesmaximal, characteristic, complemented
25#19326C211yesmaximal, characteristic, complemented
26#19322C211yesmaximal, characteristic, complemented
27#19303C211yesmaximal, characteristic, complemented
28#19295C211yesmaximal, characteristic, complemented
29#17825C211yesmaximal, characteristic, complemented
30#17769C211yesmaximal, characteristic, complemented
31#17760C211yesmaximal, characteristic, complemented
32#3511C2211yescharacteristic
33#3503C2211yescharacteristic
34#3475C2211yescharacteristic
35#3402—21no—
36#3385—21no—
37#3376—21no—
38#3369—21no—
39#3357—21no—
40#3344—21no—
41#3344—21no—
42#3331—21no—
43#3327—21no—
44#3321—21no—
45#3315—21no—
46#3314—21no—
47#3314—21no—
48#3275—21no—
49#3269—21no—
50#3267—21no—
51#3255C2211yescharacteristic
52#3252C2211yescharacteristic
53#3252C2211yescharacteristic
54#3251C2211yescharacteristic
55#3249C2211yescharacteristic
56#3248C2211yescharacteristic
57#3244—21no—
58#3244—21no—
59#3244—21no—
60#3244—21no—
61#3238C2211yescharacteristic
62#3238C2211yescharacteristic
63#3231C2211yescharacteristic
64#3231C2211yescharacteristic, complemented
65#3230C2211yescharacteristic
66#3229C2211yescharacteristic
67#3229C2211yescharacteristic, complemented
68#3228C2211yescharacteristic
69#3228C2211yescharacteristic, complemented
70#3227C2211yescharacteristic
71#3227C2211yescharacteristic, complemented
72#3218C2211yescharacteristic
73#3216C2211yescharacteristic
74#3212C2211yescharacteristic
75#3165C2211yescharacteristic, complemented
76C2×#498C2211yescharacteristic, complemented
77#3141C2211yescharacteristic, complemented
78#3131C2211yescharacteristic, complemented
79#3116C2211yescharacteristic
80#3116C2211yescharacteristic
81#3115C2211yescharacteristic
82#3110C2211yescharacteristic
83#3107C2211yescharacteristic
84#3101C2211yescharacteristic
85#3099—21no—
86#3099—21no—
87#3084—21no—
88#3084—21no—
89#3079C2211yescharacteristic
90#3079C2211yescharacteristic
91C2×#476C2211yescharacteristic
92#3039C2211yescharacteristic
93#3036C2211yescharacteristic
94#3035C2211yescharacteristic
95#2995—21no—
96#2994C2211yescharacteristic
97#2993—21no—
98#2993C2211yescharacteristic
99#2991C2211yescharacteristic
100#2989C2211yescharacteristic
101#2989C2211yescharacteristic
102#2989C2211yescharacteristic
103#2986C2211yescharacteristic
104#2985C2211yescharacteristic
105#2978—21no—
106#2976—21no—
107#2975C2211yescharacteristic
108#2974C2211yescharacteristic
109#2971C2211yescharacteristic
110#2969—21no—
111#2969C2211yescharacteristic
112#2967—21no—
113#2966C2211yescharacteristic
114#2965C2211yescharacteristic
115#2925C2211yescharacteristic
116#2924—21no—
117#2922C2211yescharacteristic
118#2921—21no—
119#1704C2211yescharacteristic, complemented
120#1704C2211yescharacteristic, complemented
121#1703C2211yescharacteristic
122#1703C2211yescharacteristic
123#1703C2211yescharacteristic
124#1703C2211yescharacteristic
125#1702C2211yescharacteristic, complemented
126#1701C2211yescharacteristic
127#1700C2211yescharacteristic, complemented
128#1700C2211yescharacteristic, complemented
129#1699C2211yescharacteristic
130#1699C2211yescharacteristic
131#1698C2211yescharacteristic, complemented
132#1698C2211yescharacteristic, complemented
133#1698C2211yescharacteristic, complemented
134#1697C2211yescharacteristic
135#1697C2211yescharacteristic
136#1697C2211yescharacteristic
137#1697C2211yescharacteristic
138#1697C2211yescharacteristic
139#1694C2211yescharacteristic, complemented
140#1693C2211yescharacteristic
141#1693C2211yescharacteristic
142#1693C2211yescharacteristic
143#1692C2211yescharacteristic, complemented
144#1692C2211yescharacteristic, complemented
145#1692C2211yescharacteristic, complemented
146#1692C2211yescharacteristic, complemented
147#1692C2211yescharacteristic, complemented
148#1692C2211yescharacteristic, complemented
149#1692C2211yescharacteristic, complemented
150#1691C2211yescharacteristic
151#1691C2211yescharacteristic
152#1691C2211yescharacteristic
153#1691C2211yescharacteristic
154#1691C2211yescharacteristic
155#1691C2211yescharacteristic
156#1691C2211yescharacteristic
157#1691C2211yescharacteristic
158#1691C2211yescharacteristic
159#1684C2211yescharacteristic, complemented
160#1684C2211yescharacteristic, complemented
161#1684C2211yescharacteristic, complemented
162#1684C2211yescharacteristic, complemented
163#1683C2211yescharacteristic
164#1683C2211yescharacteristic
165#1682C2211yescharacteristic, complemented
166#1681C2211yescharacteristic
167#1678C2211yescharacteristic, complemented
168#1678C2211yescharacteristic, complemented
169#1678C2211yescharacteristic, complemented
170#1677C2211yescharacteristic
171#1674C2211yescharacteristic, complemented
172#1674C2211yescharacteristic, complemented
173#1674C2211yescharacteristic, complemented
174#1673C2211yescharacteristic
175#1672C2211yescharacteristic, complemented
176#1672C2211yescharacteristic, complemented
177#1672C2211yescharacteristic, complemented
178#1672C2211yescharacteristic, complemented
179#1672C2211yescharacteristic, complemented
180#1671C2211yescharacteristic
181#1671C2211yescharacteristic
182#1671C2211yescharacteristic
183#1574C2211yescharacteristic
184#1574C2211yescharacteristic, complemented
185#1573C2211yescharacteristic
186#1573C2211yescharacteristic, complemented
187#1572C2211yescharacteristic
188#1572C2211yescharacteristic, complemented
189#1571C2211yescharacteristic
190#1571C2211yescharacteristic, complemented
191#1569C2211yescharacteristic, complemented
192#1569C2211yescharacteristic, complemented
193#1568C2211yescharacteristic, complemented
194#1567C2211yescharacteristic, complemented
195#1561C2211yescharacteristic, complemented
196#1559C2211yescharacteristic
197#1559C2211yescharacteristic, complemented
198#1558C2211yescharacteristic
199#1558C2211yescharacteristic, complemented
200#1557C2211yescharacteristic, complemented
201#1557C2211yescharacteristic, complemented
202#1556C2211yescharacteristic, complemented
203#1554C2211yescharacteristic
204#1554C2211yescharacteristic, complemented
205#1553C2211yescharacteristic
206#1553C2211yescharacteristic, complemented
207#1552C2211yescharacteristic
208#1552C2211yescharacteristic, complemented
209#1550C2211yescharacteristic, complemented
210#1548C2211yescharacteristic
211#1548C2211yescharacteristic, complemented
212#1548C2211yescharacteristic, complemented
213#1547C2211yescharacteristic, complemented
214#1546C2211yescharacteristic, complemented
215#1544C2211yescharacteristic
216#1542C2211yescharacteristic, complemented
217C2×#333C2211yescharacteristic, complemented
218#1540C2211yescharacteristic
219C2×#137—21no—
220C2×AGL(1,ℤ/8)—21no—
221C2×#135—21no—
222Q82—21no—
223#557—21no—
224#556—21no—
225#556D411yescharacteristic
226#555—21no—
227#555D411yescharacteristic
228#554—21no—
229#554—21no—
230#554—21no—
231#554—21no—
232#554D411yescharacteristic
233#553—21no—
234#553—21no—
235#553—21no—
236#552—21no—
237#552D411yescharacteristic
238#552D411yescharacteristic
239#551—21no—
240#551—21no—
241D4×Q8—21no—
242D4×Q8—21no—
243D4×Q8—21no—
244#548—21no—
245#548—21no—
246#547—21no—
247#547D411yescharacteristic
248#546D411yescharacteristic
249#546D411yescharacteristic
250#544—21no—
251#544—21no—
252#544—21no—
253#542—21no—
254#542—21no—
255#537—21no—
256#533C2311yescharacteristic
257#533C2311yescharacteristic
258#533C2311yescharacteristic
259#533C2311yescharacteristic
260#533C2311yescharacteristic
261#533C2311yescharacteristic
262#532C2311yescharacteristic
263#532C2311yescharacteristic
264#532C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269#529—21no—
270#529—21no—
271#529C2311yescharacteristic
272#529C2311yescharacteristic
273#525—21no—
274#520—21no—
275#520—21no—
276C4×#41C2311yescharacteristic
277C4×#41C2311yescharacteristic
278C4×#41C2311yescharacteristic
279C2×C4×D4C2311yescharacteristic
280C2×#117—21no—
281#501—21no—
282#501—21no—
283#501—21no—
284#501—21no—
285#500—21no—
286#500C2311yescharacteristic
287#500C2311yescharacteristic
288#498—21no—
289#498—21no—
290#498C2311yescharacteristic
291#498C2311yescharacteristic
292#498C2311yescharacteristic
293#498C2311yescharacteristic
294#498C2311yescharacteristic
295#498C2311yescharacteristic
296#497—21no—
297#497—21no—
298#495—21no—
299#491—21no—
300#489—21no—
301#489—21no—
302#489—21no—
303#489—21no—
304#489—21no—
305#488—21no—
306#488—21no—
307#488—21no—
308#487—21no—
309#487C2311yescharacteristic
310#487C2311yescharacteristic
311#487C2311yescharacteristic
312#487C2311yescharacteristic
313#486C2311yescharacteristic
314#486C2311yescharacteristic
315#486C2311yescharacteristic
316#486C2311yescharacteristic
317#485—21no—
318#485—21no—
319#485—21no—
320#485—21no—
321#485—21no—
322#485—21no—
323#485—21no—
324#484—21no—
325#484—21no—
326#484—21no—
327#483—21no—
328#483—21no—
329#483—21no—
330#483—21no—
331#483—21no—
332#483—21no—
333#483—21no—
334#482—21no—
335#482—21no—
336#482—21no—
337#482—21no—
338#482—21no—
339#481—21no—
340#481—21no—
341#481—21no—
342#481—21no—
343#480—21no—
344#480—21no—
345#479—21no—
346#479—21no—
347#479—21no—
348#479—21no—
349#479—21no—
350#479—21no—
351#479—21no—
352#478—21no—
353#478—21no—
354#478—21no—
355#478—21no—
356#478—21no—
357#477—21no—
358#477C2311yescharacteristic
359#477C2311yescharacteristic
360#477C2311yescharacteristic
361#477C2311yescharacteristic
362#477C2311yescharacteristic
363#477C2311yescharacteristic
364#476—21no—
365#476—21no—
366#476—21no—
367#476—21no—
368#476—21no—
369#476—21no—
370#476C2311yescharacteristic
371#476C2311yescharacteristic
372#476C2311yescharacteristic
373#476C2311yescharacteristic
374#476C2311yescharacteristic
375#476C2311yescharacteristic
376#475—21no—
377#475—21no—
378#475—21no—
379#475—21no—
380#475—21no—
381#475—21no—
382#475—21no—
383#475C2311yescharacteristic
384#475C2311yescharacteristic
385#474—21no—
386#474—21no—
387#474C2311yescharacteristic
388#474C2311yescharacteristic
389#470—21no—
390#470—21no—
391#470—21no—
392#470—21no—
393#469—21no—
394#468—21no—
395#468—21no—
396#468—21no—
397#467—21no—
398#467—21no—
399#467—21no—
400#465—21no—
401#464—21no—
402#464—21no—
403#464—21no—
404#464—21no—
405#463—21no—
406#463—21no—
407#463—21no—
408#463—21no—
409#462—21no—
410#462—21no—
411#462—21no—
412#462C2311yescharacteristic
413#462C2311yescharacteristic
414#462C2311yescharacteristic
415#462C2311yescharacteristic
416#462C2311yescharacteristic
417#462C2311yescharacteristic
418#461—21no—
419#461C2311yescharacteristic
420#461C2311yescharacteristic
421#461C2311yescharacteristic
422#461C2311yescharacteristic
423#461C2311yescharacteristic
424#461C2311yescharacteristic
425#460C2311yescharacteristic
426#460C2311yescharacteristic
427#459C2311yescharacteristic
428#459C2311yescharacteristic
429#452—21no—
430#452—21no—
431#452—21no—
432#452—21no—
433#452—21no—
434#452—21no—
435#451—21no—
436#450—21no—
437#450—21no—
438#449—21no—
439#449—21no—
440#448—21no—
441#446—21no—
442#446—21no—
443#446—21no—
444#446—21no—
445#446—21no—
446#446C2311yescharacteristic
447#446C2311yescharacteristic
448#446C2311yescharacteristic
449#446C2311yescharacteristic
450C8×Q8—21no—
451C8×Q8C2311yescharacteristic
452C8×Q8C2311yescharacteristic
453C8×Q8C2311yescharacteristic
454C8×Q8C2311yescharacteristic
455#442—21no—
456#441—21no—
457#441—21no—
458#440—21no—
459#440—21no—
460#440—21no—
461#440—21no—
462#440—21no—
463C4×Q16—21no—
464C4×SD16—21no—
465C4×SD16—21no—
466C4×SD16—21no—
467#436—21no—
468#436—21no—
469#436—21no—
470#436—21no—
471#436—21no—
472#436—21no—
473#436—21no—
474#436—21no—
475#436—21no—
476#436—21no—
477#436C2311yescharacteristic
478#436C2311yescharacteristic
479#436C2311yescharacteristic
480#436C2311yescharacteristic
481#436C2311yescharacteristic
482#436C2311yescharacteristic
483#435—21no—
484#435—21no—
485#435—21no—
486#435—21no—
487#435—21no—
488#435—21no—
489#435—21no—
490#435—21no—
491#435—21no—
492#435—21no—
493#435—21no—
494#435—21no—
495#435—21no—
496#435—21no—
497C8×D4—21no—
498C8×D4—21no—
499C8×D4C2311yescharacteristic
500C8×D4C2311yescharacteristic
501#433—21no—
502#433—21no—
503#433—21no—
504#433—21no—
505#433—21no—
506#433—21no—
507#433—21no—
508#433—21no—
509#433—21no—
510#433—21no—
511#433D411yescharacteristic
512#433D411yescharacteristic
513#433D411yescharacteristic
514#433D411yescharacteristic
515#432—21no—
516#432—21no—
517#432C2311yescharacteristic
518#432C2311yescharacteristic
519#432C2311yescharacteristic
520#432C2311yescharacteristic
521#432C2311yescharacteristic
522#432C2311yescharacteristic
523#431—21no—
524#431—21no—
525#431C2311yescharacteristic
526#431C2311yescharacteristic
527#431C2311yescharacteristic
528#431C2311yescharacteristic
529#431C2311yescharacteristic
530#431C2311yescharacteristic
531#431C2311yescharacteristic
532#431C2311yescharacteristic
533#428—21no—
534#428—21no—
535#428—21no—
536#428—21no—
537C2×#106—21no—
538C2×#106—21no—
539C2×#106—21no—
540#424—21no—
541#424—21no—
542#424D411yescharacteristic
543#424D411yescharacteristic
544#423—21no—
545#423—21no—
546#423C2311yescharacteristic
547#423C2311yescharacteristic
548#423C2311yescharacteristic
549#423C2311yescharacteristic
550#423C2311yescharacteristic
551C2×C4⋊C8C2311yescharacteristic
552C2×C4⋊C8C2311yescharacteristic
553C2×C4⋊C8C2311yescharacteristic
554#419—21no—
555#417—21no—
556#417—21no—
557#417—21no—
558#417—21no—
559#417—21no—
560#416—21no—
561#416—21no—
562#416—21no—
563C2×#102—21no—
564#408—21no—
565#408D411yescharacteristic
566#408D411yescharacteristic
567#407—21no—
568#407—21no—
569#407—21no—
570C2×C22⋊C8—21no—
571#405—21no—
572#405—21no—
573#405—21no—
574C4×M16—21no—
575C4×M16—21no—
576C4×M16C2311yescharacteristic
577C2×C4×C8C2311yescharacteristic
578#335C2311yescharacteristic
579#335C2311yescharacteristic
580#335C2311yescharacteristic
581#335C2311yescharacteristic
582#335C2311yescharacteristic
583#335C2311yescharacteristic
584#335C2311yescharacteristic
585#335C2311yescharacteristic
586#335C2311yescharacteristic
587#335C2311yescharacteristic
588#334C2311yescharacteristic
589#334C2311yescharacteristic
590#334C2311yescharacteristic
591#334C2311yescharacteristic
592#334C2311yescharacteristic
593#334C2311yescharacteristic
594#333C2311yescharacteristic
595#333C2311yescharacteristic
596#333C2311yescharacteristic
597#333C2311yescharacteristic
598#333C2311yescharacteristic
599#333C2311yescharacteristic
600#333C2311yescharacteristic
601#333C2311yescharacteristic
602#333C2311yescharacteristic
603#333C2311yescharacteristic
604#333C2311yescharacteristic
605#333C2311yescharacteristic
606#332C2311yescharacteristic
607#332C2311yescharacteristic
608#332C2311yescharacteristic
609#332C2311yescharacteristic
610#332C2311yescharacteristic
611#332C2311yescharacteristic
612#332C2311yescharacteristic
613#332C2311yescharacteristic
614#332C2311yescharacteristic
615#332C2311yescharacteristic
616#332C2311yescharacteristic
617#332C2311yescharacteristic
618#332C2311yescharacteristic
619#332C2311yescharacteristic
620#332C2311yescharacteristic
621#332C2311yescharacteristic
622#331C2311yescharacteristic
623#331C2311yescharacteristic
624#331C2311yescharacteristic
625#331C2311yescharacteristic
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41C2×D411yescharacteristic
630C2×#41C2×D411yescharacteristic
631C2×#41C2×D411yescharacteristic
632C22×Q8—21no—
633C22×Q8—21no—
634C22×Q8—21no—
635C22×Q8—21no—
636C22×D4C2×D411yescharacteristic
637C23×C4—21no—
638#137—82no—
639AGL(1,ℤ/8)—82no—
640#135—82no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×Q16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16—21no—
654C2×SD16—21no—
655C2×D8—21no—
656C2×D8—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16—21no—
662C2×M16—21no—
663C2×M16—21no—
664C2×M16—21no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16—21no—
668C2×M16C2×D411yescharacteristic
669C2×M16C2×D411yescharacteristic
670C22×C8—21no—
671C22×C8—21no—
672C22×C8—21no—
673C22×C8—21no—
674C22×C8—21no—
675C22×C8C2×D411yescharacteristic
676C22×C8C2×D411yescharacteristic
677C4⋊Q8—21no—
678C4⋊Q8—21no—
679C4⋊Q8—21no—
680C4⋊Q8—21no—
681C4⋊Q8—21no—
682C4⋊Q8—21no—
683C4⋊Q8—21no—
684C4⋊Q8—21no—
685C4⋊Q8—21no—
686C4⋊Q8—21no—
687C4⋊Q8—21no—
688C4⋊Q8—21no—
689C4⋊Q8—41no—
690C4⋊Q8—41no—
691C4⋊Q8—41no—
692C4⋊Q8C2×D411yescharacteristic
693C4⋊Q8C2×D411yescharacteristic
694C4⋊Q8C2411yescharacteristic
695C4⋊Q8C2411yescharacteristic
696C4⋊Q8C2411yescharacteristic
697C4⋊Q8C2411yescharacteristic
698C4⋊Q8C2411yescharacteristic
699C4⋊Q8C2411yescharacteristic
700C4⋊Q8C2411yescharacteristic
701#127C2411yescharacteristic
702#126—21no—
703#126—21no—
704#126—21no—
705#126—21no—
706#126—21no—
707#126—21no—
708#126—41no—
709#126—41no—
710#125—21no—
711#125—21no—
712#125—21no—
713#125—21no—
714#125—21no—
715#125—21no—
716#125—21no—
717#125—21no—
718#125—41no—
719#125—41no—
720#125—41no—
721#125C2×D411yescharacteristic
722#125C2×D411yescharacteristic
723#124—21no—
724#124—21no—
725#124—21no—
726#124—21no—
727#124—21no—
728#124—41no—
729#124—41no—
730#124C2×D411yescharacteristic
731#124C2×D411yescharacteristic
732#123—21no—
733#123—21no—
734#123—21no—
735#123—21no—
736#123—21no—
737#123—21no—
738#123—21no—
739#123—21no—
740#123—41no—
741#123—41no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744C22⋊Q8—21no—
745C22⋊Q8—21no—
746C22⋊Q8—21no—
747C22⋊Q8—21no—
748C22⋊Q8—21no—
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8—21no—
754C22⋊Q8—21no—
755C22⋊Q8—21no—
756C22⋊Q8—21no—
757C22⋊Q8—41no—
758C22⋊Q8—41no—
759C22⋊Q8—41no—
760C22⋊Q8—41no—
761C22⋊Q8—41no—
762C22⋊Q8—41no—
763C22⋊Q8—41no—
764C22⋊Q8—41no—
765C22⋊Q8—41no—
766C22⋊Q8C2×D411yescharacteristic
767C22⋊Q8C2×D411yescharacteristic
768C22⋊Q8C2×D411yescharacteristic
769C22⋊Q8C2×D411yescharacteristic
770#121—21no—
771#121—21no—
772#121—21no—
773#121—21no—
774#121—21no—
775#121—21no—
776#121—21no—
777#121—21no—
778#121—21no—
779#121—21no—
780#121—41no—
781#121—41no—
782#121—41no—
783#121C2×D411yescharacteristic
784#121C2×D411yescharacteristic
785#120—21no—
786#120—21no—
787C4×Q8—21no—
788C4×Q8—21no—
789C4×Q8—21no—
790C4×Q8—21no—
791C4×Q8—21no—
792C4×Q8—21no—
793C4×Q8—21no—
794C4×Q8—21no—
795C4×Q8—21no—
796C4×Q8—21no—
797C4×Q8—21no—
798C4×Q8—41no—
799C4×Q8C2×D411yescharacteristic
800C4×Q8C2×D411yescharacteristic
801C4×Q8C2×D411yescharacteristic
802C4×Q8#4111yescharacteristic
803C4×Q8C2411yescharacteristic
804C4×Q8C2411yescharacteristic
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×D4C2×D411yescharacteristic
825C4×D4C2×D411yescharacteristic
826C4×D4C2×D411yescharacteristic
827C4×D4C2×D411yescharacteristic
828C4×D4C2×D411yescharacteristic
829C4×D4C2×D411yescharacteristic
830C4×D4C2×D411yescharacteristic
831C4×D4#4111yescharacteristic
832C4×D4#4111yescharacteristic
833C4×D4#4111yescharacteristic
834C4×D4C2411yescharacteristic
835C4×D4C2411yescharacteristic
836#117—21no—
837#117—21no—
838#117—21no—
839#117—21no—
840#117—21no—
841#117—21no—
842#117—21no—
843#117—21no—
844#117—21no—
845#117—21no—
846#117—21no—
847#117—21no—
848#117—21no—
849#117—21no—
850#117—41no—
851#117C2×D411yescharacteristic
852#117C2×D411yescharacteristic
853#117C2×D411yescharacteristic
854#117C2×D411yescharacteristic
855#117C2×D411yescharacteristic
856C2×C4⋊C4—21no—
857C2×C4⋊C4—21no—
858C2×C4⋊C4—21no—
859C2×C4⋊C4—21no—
860C2×C4⋊C4—21no—
861C2×C4⋊C4—21no—
862C2×C4⋊C4—21no—
863C2×C4⋊C4—21no—
864C2×C4⋊C4—21no—
865C2×C4⋊C4—21no—
866C2×C4⋊C4—41no—
867C2×C4⋊C4C2×D411yescharacteristic
868C2×C22⋊C4—21no—
869C2×C22⋊C4—21no—
870C2×C22⋊C4—21no—
871C2×C42—21no—
872C2×C42—21no—
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876#107—21no—
877#107—21no—
878#107—21no—
879#107—21no—
880#107—21no—
881#107—21no—
882#107—21no—
883#107—21no—
884#107—21no—
885#107—21no—
886#107—21no—
887#107—21no—
888#106—21no—
889#106—21no—
890#106—21no—
891#106—21no—
892#106—21no—
893#106—21no—
894#106—21no—
895#106—21no—
896#106—21no—
897#106—21no—
898#106—21no—
899#106—21no—
900#106—21no—
901#106—21no—
902#106—21no—
903#106—21no—
904#106—21no—
905#106—21no—
906#106—21no—
907#106—21no—
908C4⋊C8—21no—
909C4⋊C8—21no—
910C4⋊C8—21no—
911C4⋊C8—21no—
912C4⋊C8—21no—
913C4⋊C8—21no—
914C4⋊C8—21no—
915C4⋊C8—21no—
916C4⋊C8—21no—
917C4⋊C8—21no—
918C4⋊C8—21no—
919C4⋊C8—21no—
920C4⋊C8—21no—
921C4⋊C8—21no—
922C4⋊C8—21no—
923C4⋊C8—21no—
924C4⋊C8C2×D411yescharacteristic
925C4⋊C8C2×D411yescharacteristic
926C4⋊C8C2×D411yescharacteristic
927C4⋊C8C2×D411yescharacteristic
928C4⋊C8C2×D411yescharacteristic
929C4⋊C8C2×D411yescharacteristic
930C4⋊C8C2×D411yescharacteristic
931C4⋊C8C2×D411yescharacteristic
932C4⋊C8C2411yescharacteristic
933C4⋊C8C2411yescharacteristic
934C4⋊C8C2411yescharacteristic
935C4⋊C8C2411yescharacteristic
936C4⋊C8C2411yescharacteristic
937C4⋊C8C2411yescharacteristic
938C4⋊C8C2411yescharacteristic
939C4⋊C8C2411yescharacteristic
940C4⋊C8C2411yescharacteristic
941C4⋊C8C2411yescharacteristic
942C4⋊C8C2411yescharacteristic
943C4⋊C8C2411yescharacteristic
944#103—21no—
945#103—21no—
946#103—21no—
947#103—21no—
948#103—21no—
949#103—21no—
950#103—21no—
951#103—21no—
952#103—21no—
953#103—21no—
954#103—21no—
955#103—21no—
956#103—21no—
957#103—21no—
958#103—21no—
959#103—21no—
960#103—21no—
961#103—21no—
962#103—21no—
963#103—21no—
964#103—21no—
965#103—21no—
966#103—21no—
967#103—21no—
968#103—21no—
969#103—21no—
970#103—21no—
971#103—21no—
972#102—21no—
973#102—21no—
974#102—21no—
975#102—21no—
976#102—21no—
977#102—21no—
978#102—21no—
979#102—21no—
980#102—21no—
981#102—21no—
982#102—21no—
983#102—21no—
984#102—21no—
985#102—21no—
986#102—21no—
987#102—21no—
988#102—21no—
989#102—21no—
990#102—21no—
991#102—21no—
992C22⋊C8—21no—
993C22⋊C8—21no—
994C22⋊C8—21no—
995C22⋊C8—21no—
996C22⋊C8—21no—
997C22⋊C8—21no—
998C22⋊C8—21no—
999C22⋊C8—21no—
1000C22⋊C8—21no—
1001C22⋊C8—21no—
1002C22⋊C8—21no—
1003C22⋊C8—21no—
1004C22⋊C8—21no—
1005C22⋊C8—21no—
1006C22⋊C8—21no—
1007C22⋊C8—21no—
1008C22⋊C8—21no—
1009C22⋊C8—21no—
1010C22⋊C8C2×D411yescharacteristic
1011C22⋊C8C2×D411yescharacteristic
1012C22⋊C8C2×D411yescharacteristic
1013C22⋊C8C2×D411yescharacteristic
1014C22⋊C8C2×D411yescharacteristic
1015C22⋊C8C2×D411yescharacteristic
1016C22⋊C8C2×D411yescharacteristic
1017C22⋊C8C2×D411yescharacteristic
1018#97—21no—
1019#97—21no—
1020#97—21no—
1021#97—21no—
1022#97—21no—
1023#97—21no—
1024#97—21no—
1025#97—21no—
1026#97—21no—
1027#97—21no—
1028#97C2×D411yescharacteristic
1029#97C2×D411yescharacteristic
1030C4×C8—21no—
1031C4×C8—21no—
1032C4×C8—21no—
1033C4×C8—21no—
1034C4×C8—21no—
1035C4×C8—21no—
1036C4×C8—21no—
1037C4×C8—21no—
1038C4×C8C2×D411yescharacteristic
1039C4×C8C2×D411yescharacteristic
1040C4×C8C2411yescharacteristic
1041C4×C8C2411yescharacteristic
1042C4×C8C2411yescharacteristic
1043C4×C8C2411yescharacteristic
1044C24—21no—
1045#41—41no—
1046#41—41no—
1047#41—41no—
1048#41—41no—
1049#41—41no—
1050#41—41no—
1051#41—42no—
1052#41—42no—
1053#41—81no—
1054#41—81no—
1055#41—81no—
1056#41—81no—
1057C2×Q8—21no—
1058C2×Q8—21no—
1059C2×Q8—21no—
1060C2×Q8—21no—
1061C2×Q8—21no—
1062C2×Q8—21no—
1063C2×Q8—21no—
1064C2×Q8—21no—
1065C2×Q8—41no—
1066C2×Q8—41no—
1067C2×Q8—41no—
1068C2×Q8—41no—
1069C2×Q8—81no—
1070C2×Q8—81no—
1071C2×Q8—161no—
1072C2×Q8—161no—
1073C2×Q8—161no—
1074C2×Q8#12111yescharacteristic
1075C2×Q8C22×D411yescharacteristic
1076C2×Q8C22×D411yescharacteristic
1077C2×D4—21no—
1078C2×D4—21no—
1079C2×D4—21no—
1080C2×D4—21no—
1081C2×D4—21no—
1082C2×D4—21no—
1083C2×D4—21no—
1084C2×D4—21no—
1085C2×D4—41no—
1086C2×D4—41no—
1087C2×D4—41no—
1088C2×D4—41no—
1089C2×D4—41no—
1090C2×D4#12111yescharacteristic
1091C2×D4#12111yescharacteristic
1092C2×D4#12111yescharacteristic
1093C2×D4C22×D411yescharacteristic
1094C2×D4C22×D411yescharacteristic
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—21no—
1100C22×C4—21no—
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—41no—
1105C22×C4—41no—
1106C22×C4—41no—
1107C22×C4—41no—
1108C22×C4—41no—
1109C22×C4—41no—
1110C22×C4—41no—
1111C22×C4—81no—
1112C22×C4—81no—
1113C22×C4C22×D411yescharacteristic
1114C22×C4C22×D411yescharacteristic
1115C22×C4C22×D411yescharacteristic
1116C22×C4C22×D411yescharacteristic
1117C22×C4C22×D411yescharacteristic
1118C22×C4C22×D411yescharacteristic
1119C22×C4C2×#4111yescharacteristic
1120C22×C4C2×#4111yescharacteristic
1121C22×C4C2×#4111yescharacteristic
1122Q16—81no—
1123Q16—81no—
1124Q16—81no—
1125Q16—81no—
1126Q16—81no—
1127Q16—81no—
1128SD16—42no—
1129SD16—42no—
1130SD16—42no—
1131SD16—81no—
1132SD16—81no—
1133SD16—81no—
1134SD16—81no—
1135SD16—81no—
1136D8—42no—
1137D8—81no—
1138M16—41no—
1139M16—41no—
1140M16—81no—
1141M16—81no—
1142M16—81no—
1143M16—81no—
1144M16—81no—
1145M16—81no—
1146M16—81no—
1147M16—81no—
1148M16—81no—
1149M16—81no—
1150M16—81no—
1151C2×C8—21no—
1152C2×C8—21no—
1153C2×C8—21no—
1154C2×C8—21no—
1155C2×C8—21no—
1156C2×C8—21no—
1157C2×C8—21no—
1158C2×C8—21no—
1159C2×C8—21no—
1160C2×C8—21no—
1161C2×C8—21no—
1162C2×C8—21no—
1163C2×C8—41no—
1164C2×C8—41no—
1165C2×C8—81no—
1166C2×C8—81no—
1167C2×C8—81no—
1168C2×C8—81no—
1169C2×C8—81no—
1170C2×C8C22×D411yescharacteristic
1171C2×C8C22×D411yescharacteristic
1172C2×C8C22×D411yescharacteristic
1173C2×C8C22×D411yescharacteristic
1174C2×C8C22×D411yescharacteristic
1175C2×C8C22×D411yescharacteristic
1176C2×C8C22×D411yescharacteristic
1177C2×C8C22×D411yescharacteristic
1178C4⋊C4—21no—
1179C4⋊C4—21no—
1180C4⋊C4—21no—
1181C4⋊C4—21no—
1182C4⋊C4—21no—
1183C4⋊C4—21no—
1184C4⋊C4—21no—
1185C4⋊C4—21no—
1186C4⋊C4—21no—
1187C4⋊C4—21no—
1188C4⋊C4—21no—
1189C4⋊C4—21no—
1190C4⋊C4—21no—
1191C4⋊C4—21no—
1192C4⋊C4—21no—
1193C4⋊C4—21no—
1194C4⋊C4—21no—
1195C4⋊C4—21no—
1196C4⋊C4—21no—
1197C4⋊C4—21no—
1198C4⋊C4—21no—
1199C4⋊C4—21no—
1200C4⋊C4—21no—
1201C4⋊C4—21no—
1202C4⋊C4—21no—
1203C4⋊C4—21no—
1204C4⋊C4—21no—
1205C4⋊C4—21no—
1206C4⋊C4—21no—
1207C4⋊C4—21no—
1208C4⋊C4—41no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—41no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4#12111yescharacteristic
1227C4⋊C4#12111yescharacteristic
1228C4⋊C4#12111yescharacteristic
1229C4⋊C4#12111yescharacteristic
1230C4⋊C4#12111yescharacteristic
1231C4⋊C4#12111yescharacteristic
1232C4⋊C4C22×D411yescharacteristic
1233C4⋊C4C22×D411yescharacteristic
1234C4⋊C4C22×D411yescharacteristic
1235C4⋊C4C22×D411yescharacteristic
1236C22⋊C4—21no—
1237C22⋊C4—21no—
1238C22⋊C4—21no—
1239C22⋊C4—21no—
1240C22⋊C4—21no—
1241C22⋊C4—21no—
1242C22⋊C4—21no—
1243C22⋊C4—21no—
1244C22⋊C4—21no—
1245C22⋊C4—21no—
1246C22⋊C4—21no—
1247C22⋊C4—21no—
1248C22⋊C4—21no—
1249C22⋊C4—21no—
1250C22⋊C4—21no—
1251C22⋊C4—21no—
1252C22⋊C4—21no—
1253C22⋊C4—21no—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—41no—
1257C22⋊C4—41no—
1258C22⋊C4—41no—
1259C22⋊C4—41no—
1260C22⋊C4—41no—
1261C22⋊C4—41no—
1262C22⋊C4—41no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4#12111yescharacteristic
1266C22⋊C4#12111yescharacteristic
1267C22⋊C4#12111yescharacteristic
1268C22⋊C4#12111yescharacteristic
1269C22⋊C4#12111yescharacteristic
1270C22⋊C4#12111yescharacteristic
1271C42—21no—
1272C42—21no—
1273C42—21no—
1274C42—21no—
1275C42—21no—
1276C42—21no—
1277C42—41no—
1278C42—41no—
1279C42—41no—
1280C42—41no—
1281C42—41no—
1282C42C22×D411yescharacteristic
1283C42C22×D411yescharacteristic
1284C42C22×D411yescharacteristic
1285C42C22×D411yescharacteristic
1286C42C22×D411yescharacteristic
1287C42C22×D411yescharacteristic
1288C42C2×#4111yescharacteristic
1289C42C2×#4111yescharacteristic
1290C42C2×#4111yescharacteristic
1291C42C2511yescharacteristic
1292C23—21no—
1293C23—21no—
1294C23—41no—
1295C23—81no—
1296C23—81no—
1297C23—81no—
1298C23C2×#12111yescharacteristic
1299C23C2×#12111yescharacteristic
1300C23C2×#12111yescharacteristic
1301Q8—21no—
1302Q8—21no—
1303Q8—21no—
1304Q8—21no—
1305Q8—41no—
1306Q8—41no—
1307Q8—41no—
1308Q8—41no—
1309Q8—41no—
1310Q8—41no—
1311Q8—41no—
1312Q8—41no—
1313Q8—41no—
1314Q8—81no—
1315Q8—81no—
1316Q8—81no—
1317Q8—81no—
1318Q8—161no—
1319Q8—161no—
1320Q8—161no—
1321Q8—161no—
1322D4—21no—
1323D4—21no—
1324D4—21no—
1325D4—21no—
1326D4—41no—
1327D4—41no—
1328D4—41no—
1329D4—41no—
1330D4—41no—
1331D4—41no—
1332D4—41no—
1333D4—81no—
1334D4—81no—
1335D4—81no—
1336D4—81no—
1337D4—81no—
1338D4—81no—
1339D4—82no—
1340D4—161no—
1341D4—161no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—41no—
1361C2×C4—41no—
1362C2×C4—41no—
1363C2×C4—41no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—81no—
1375C2×C4—81no—
1376C2×C4—81no—
1377C2×C4—81no—
1378C2×C4—81no—
1379C2×C4—81no—
1380C2×C4—82no—
1381C2×C4—81no—
1382C2×C4—161no—
1383C2×C4—161no—
1384C2×C4—161no—
1385C2×C4—161no—
1386C2×C4—161no—
1387C2×C4—161no—
1388C2×C4C2×#12111yescharacteristic
1389C2×C4C2×#12111yescharacteristic
1390C2×C4C2×#12111yescharacteristic
1391C2×C4C2×#12111yescharacteristic
1392C2×C4C2×#12111yescharacteristic
1393C2×C4C2×#12111yescharacteristic
1394C2×C4C2×#12111yescharacteristic
1395C2×C4C2×#12111yescharacteristic
1396C2×C4C2×#12111yescharacteristic
1397C2×C4C23×D411yescharacteristic
1398C2×C4C23×D411yescharacteristic
1399C2×C4C22×#4111yescharacteristic
1400C8—21no—
1401C8—21no—
1402C8—21no—
1403C8—21no—
1404C8—21no—
1405C8—21no—
1406C8—21no—
1407C8—21no—
1408C8—41no—
1409C8—41no—
1410C8—41no—
1411C8—41no—
1412C8—41no—
1413C8—41no—
1414C8—41no—
1415C8—41no—
1416C8—41no—
1417C8—41no—
1418C8—41no—
1419C8—41no—
1420C22—21no—
1421C22—21no—
1422C22—21no—
1423C22—21no—
1424C22—21no—
1425C22—21no—
1426C22—21no—
1427C22—21no—
1428C22—21no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—81no—
1436C22—81no—
1437C22—81no—
1438C22—162no—
1439C22C22×#12111yescharacteristic
1440C4—21no—
1441C4—21no—
1442C4—21no—
1443C4—21no—
1444C4—21no—
1445C4—21no—
1446C4—21no—
1447C4—21no—
1448C4—21no—
1449C4—21no—
1450C4—41no—
1451C4—41no—
1452C4—41no—
1453C4—41no—
1454C4—41no—
1455C4—41no—
1456C4—81no—
1457C4—81no—
1458C4—81no—
1459C4—81no—
1460C4—81no—
1461C4—81no—
1462C4—81no—
1463C4#358511yescharacteristic
1464C4#358611yescharacteristic
1465C4#358611yescharacteristic
1466C4#358611yescharacteristic
1467C2—41no—
1468C2—41no—
1469C2—41no—
1470C2—81no—
1471C2—81no—
1472C2—161no—
1473C2#6042711yescharacteristic
1474C2#6046011yescharacteristic
1475C2#6047011yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
prime radical#61967C2
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. #62108C2semidirect
3. #60881C2semidirect
4. #60300C2semidirect
5. #19588C2semidirect
6. #19584C2semidirect
7. #19575C2semidirect
8. #19571C2semidirect
9. #19550C2semidirect
10. #19544C2semidirect
11. #19534C2semidirect
12. #19529C2semidirect
13. #19500C2semidirect
14. #19498C2semidirect
15. #19467C2semidirect
16. #19463C2semidirect
17. #19454C2semidirect
18. #19450C2semidirect
19. #19431C2semidirect
20. #19427C2semidirect
21. #19382C2semidirect
22. #19378C2semidirect
23. #19367C2semidirect
24. #19357C2semidirect
25. #19326C2semidirect
26. #19322C2semidirect
27. #19303C2semidirect
28. #19295C2semidirect
29. #17825C2semidirect
30. #17769C2semidirect
31. #17760C2semidirect
64. #3231C22semidirect
67. #3229C22semidirect
69. #3228C22semidirect
71. #3227C22semidirect
75. #3165C22semidirect
76. C2×#498C22semidirect
77. #3141C22semidirect
78. #3131C22semidirect
119. #1704C22semidirect
120. #1704C22semidirect
125. #1702C22semidirect
127. #1700C22semidirect
128. #1700C22semidirect
131. #1698C22semidirect
132. #1698C22semidirect
133. #1698C22semidirect
139. #1694C22semidirect
143. #1692C22semidirect
144. #1692C22semidirect
145. #1692C22semidirect
146. #1692C22semidirect
147. #1692C22semidirect
148. #1692C22semidirect
149. #1692C22semidirect
159. #1684C22semidirect
160. #1684C22semidirect
161. #1684C22semidirect
162. #1684C22semidirect
165. #1682C22semidirect
167. #1678C22semidirect
168. #1678C22semidirect
169. #1678C22semidirect
171. #1674C22semidirect
172. #1674C22semidirect
173. #1674C22semidirect
175. #1672C22semidirect
176. #1672C22semidirect
177. #1672C22semidirect
178. #1672C22semidirect
179. #1672C22semidirect
184. #1574C22semidirect
186. #1573C22semidirect
188. #1572C22semidirect
190. #1571C22semidirect
191. #1569C22semidirect
192. #1569C22semidirect
193. #1568C22semidirect
194. #1567C22semidirect
195. #1561C22semidirect
197. #1559C22semidirect
199. #1558C22semidirect
200. #1557C22semidirect
201. #1557C22semidirect
202. #1556C22semidirect
204. #1554C22semidirect
206. #1553C22semidirect
208. #1552C22semidirect
209. #1550C22semidirect
211. #1548C22semidirect
212. #1548C22semidirect
213. #1547C22semidirect
214. #1546C22semidirect
216. #1542C22semidirect
217. C2×#333C22semidirect

Maximal subgroups

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

subgroupindex
#621082
#619672
#608812
#603002
#195882
#195842
#195752
#195712
#195502
#195442
#195342
#195292
#195002
#194982
#194672
#194632
#194542
#194502
#194312
#194272
#193822
#193782
#193672
#193572
#193262
#193222
#193032
#192952
#178252
#177692
#177602