Finite Group Databasebeta

← #7658482

Subgroups — #7658482

Order 512.

4653 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42758C213yesmaximal, complemented
2#42751C213yesmaximal, complemented
3#42725C213yesmaximal, complemented
4#42720C213yesmaximal, complemented
5#42637C213yesmaximal, complemented
6#42635C213yesmaximal, complemented
7#42625C213yesmaximal, complemented
8#42624C213yesmaximal, complemented
9#42523C213yesmaximal, complemented
10#42515C213yesmaximal, complemented
11#42466C213yesmaximal, complemented
12#42457C213yesmaximal, complemented
13#37636C213yesmaximal, complemented
14#37593C213yesmaximal, complemented
15#37572C213yesmaximal, complemented
16#36693C213yesmaximal, complemented
17#36059C211yesmaximal, characteristic, complemented
18#36049C211yesmaximal, characteristic, complemented
19#36040C211yesmaximal, characteristic, complemented
20#36005C211yesmaximal, characteristic, complemented
21#35948C211yesmaximal, characteristic, complemented
22#35937C211yesmaximal, characteristic, complemented
23#35883C211yesmaximal, characteristic, complemented
24#35854C211yesmaximal, characteristic, complemented
25#35845C211yesmaximal, characteristic, complemented
26#35831C211yesmaximal, characteristic
27#35801C211yesmaximal, characteristic, complemented
28#35748C211yesmaximal, characteristic, complemented
29#34337C211yesmaximal, characteristic, complemented
30#34312C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×#519C2211yescharacteristic
41#2839C2213yes—
42#2839C2213yes—
43#2838C2211yescharacteristic
44#2838C2213yes—
45#2838C2213yes—
46#2838C2213yes—
47#2837C2213yes—
48#2837C2213yes—
49#2832C2213yes—
50#2832C2216yes—
51#2832C2213yes—
52#2831C2213yes—
53#2831C2213yes—
54#2830C2213yes—
55#2830C2213yes—
56#2829C2213yes—
57#2829C2213yes—
58#2801C2216yes—
59#2796C2216yes—
60#2777C2216yes—
61#2773C2216yes—
62#2762C2216yes—
63#2746C2216yes—
64#2742C2216yes—
65#2741C2216yes—
66#2738C2216yes—
67#2737C2216yes—
68#2730C2216yes—
69#2729C2216yes—
70#2717C2216yes—
71#2701C2216yes—
72#2674C2216yes—
73#2672C2216yes—
74#2663C2216yes—
75#2663C2216yes—
76#2660C2213yes—
77#2653C2216yes—
78#2653C2216yes—
79#2652C2216yes—
80#2651C2216yes—
81#2650C2216yes—
82#2649C2216yes—
83#2645C2213yes—
84#2644C2213yes—
85#2641C2213yes—
86#2640C2213yes—
87#2640C2213yes—
88#2632C2216yes—
89#2632C2216yes—
90#2628C2213yes—
91#2628C2216yes—
92#2628C2213yes—
93#2628C2213yes—
94#2624C2216yes—
95#2624C2213yes—
96#2624C2213yes—
97#2620C2213yes—
98#2592C2213yes—
99#2592C2213yes—
100#2584C2213yes—
101#2581C2213yes—
102#2580C2213yes—
103#2580C2213yes—
104#2567C2213yes—
105#2563C2213yes—
106#2563C2213yes—
107#2562C2213yes—
108#2551C2213yes—
109#2551C2213yes—
110#2550C2213yes—
111#2550C2213yes—
112#2548C2213yes—
113#2547C2213yes—
114#2546C2213yes—
115#2544C2213yes—
116#2542C2213yes—
117#2537C2213yes—
118#2514C2213yes—
119#2514C2213yes—
120#2513C2213yes—
121#2513C2213yes—
122#2513C2213yes—
123#2511C2213yes—
124#2501C2213yes—
125#2500C2213yes—
126#2497C2213yes—
127#2495C2213yes—
128#2495C2213yes—
129#2495C2216yes—
130#2495C2213yes—
131#2495C2213yes—
132#2494C2213yes—
133#2492C2213yes—
134#2492C2213yes—
135#2491C2216yes—
136#2491C2213yes—
137#2491C2213yes—
138#2491C2213yes—
139#2491C2213yes—
140#2490C2213yes—
141#2490C2213yes—
142#2490C2213yes—
143#2490C2213yes—
144#2489C2213yes—
145#2489C2213yes—
146#2487C2213yes—
147#2485C2213yes—
148#2477C2216yes—
149#2470C2216yes—
150#2465C2216yes—
151#2458C2216yes—
152#2454C2213yes—
153#2454C2213yes—
154#2453C2213yes—
155#2453C2213yes—
156#2452C2213yes—
157#2452C2213yes—
158#2448C2213yes—
159#2448C2213yes—
160#2445C2213yes—
161#2445C2213yes—
162#2442C2213yes—
163#2442C2213yes—
164#2441C2213yes—
165#2441C2213yes—
166#2440C2213yes—
167#2440C2213yes—
168#2428C2213yes—
169#2427C2213yes—
170#2423C2213yes—
171#2422C2213yes—
172#2422C2213yes—
173#2421C2213yes—
174#2417C2213yes—
175#2416C2213yes—
176#2401C2213yes—
177#2401C2213yes—
178#2399C2213yes—
179#2398C2213yes—
180#2398C2213yes—
181#2398C2213yes—
182#2396C2213yes—
183#2396C2213yes—
184#2396C2213yes—
185#2395C2213yes—
186#2395C2213yes—
187#2392C2213yes—
188#2370C2213yes—
189#2370C2213yes—
190#2367C2213yes—
191#2365C2213yes—
192#2363C2213yes—
193#2360C2213yes—
194#2357C2213yes—
195#2354C2213yes—
196#2352C2213yes—
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2213yes—
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208#2345C2213yes—
209#2344C2213yes—
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222#2330C2213yes—
223#2330C2213yes—
224#2324C2213yes—
225#2323C2213yes—
226#2319C2213yes—
227#2314C2213yes—
228C4×C4⋊Q8C2213yes—
229C4×#124C2213yes—
230#2298C2213yes—
231#2295C2213yes—
232#2293C2213yes—
233#2293C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—44no—
242#557—28no—
243#557—44no—
244#550—44no—
245#548—28no—
246#548—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2316yes—
253C2×#127C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#124C2313yes—
259C2×#124C2313yes—
260C2×#124C2316yes—
261C2×#124C2316yes—
262C2×#123C2316yes—
263C2×#123C2316yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2316yes—
267C2×C22⋊Q8C2316yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2316yes—
273#520—28no—
274#520—44no—
275#519—44no—
276C2×C4×Q8C2313yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2316yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×#117C2313yes—
302C2×#117C2313yes—
303C2×#117C2313yes—
304C2×#117C2313yes—
305C2×#117C2316yes—
306C22×C4⋊C4C2313yes—
307C22×C4⋊C4C2313yes—
308#401C2311yescharacteristic
309#401C2313yes—
310#401C2316yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2316yes—
322#400C2316yes—
323#400C2313yes—
324#400C2313yes—
325#400C2311yescharacteristic
326#400C2311yescharacteristic
327#400C2313yes—
328#400C2313yes—
329#400C2313yes—
330#400C2316yes—
331#400C2316yes—
332#399C2311yescharacteristic
333#399C2313yes—
334#399C2313yes—
335#399C2316yes—
336#399C2313yes—
337#399C2313yes—
338#399C2316yes—
339#399C2316yes—
340#399C2316yes—
341#399C2316yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2311yescharacteristic
353#398C2313yes—
354#398C2313yes—
355#398C2316yes—
356#397C2311yescharacteristic
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2311yescharacteristic
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2316yes—
371#397C2316yes—
372#397C2311yescharacteristic
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#397C2316yes—
378#397C2316yes—
379#397C2316yes—
380#397C2316yes—
381#397C2316yes—
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#396C2311yescharacteristic
391#396C2313yes—
392#396C2316yes—
393#395C2313yes—
394#395C2316yes—
395#395C2313yes—
396#395C2313yes—
397#395C2313yes—
398#395C2311yescharacteristic
399#395C2313yes—
400#395C2316yes—
401#395C2311yescharacteristic
402#395C2316yes—
403#395C2316yes—
404#394C2316yes—
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2313yes—
417#394C2313yes—
418#394C2316yes—
419#394C2316yes—
420#394C2316yes—
421#394C2316yes—
422#394C2316yes—
423#394C2316yes—
424#394C2316yes—
425#393C2313yes—
426#393C2313yes—
427#393C2316yes—
428#393C2316yes—
429#393C2311yescharacteristic
430#393C2313yes—
431#393C2313yes—
432#393C2313yes—
433#393C2313yes—
434#393C2313yes—
435#393C2313yes—
436#393C2316yes—
437#393C2316yes—
438#393C2316yes—
439#392C2313yes—
440#391C2313yes—
441#391C2313yes—
442#391C2313yes—
443#391C2313yes—
444#391C2313yes—
445#391C2313yes—
446#391C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2316yes—
451#391C2316yes—
452#390C2313yes—
453#390C2313yes—
454#390C2316yes—
455#390C2313yes—
456#390C2313yes—
457#390C2313yes—
458#390C2313yes—
459#390C2313yes—
460#390C2313yes—
461#390C2313yes—
462#390C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2316yes—
472#389C2316yes—
473#389C2313yes—
474#389C2313yes—
475#389C2316yes—
476#389C2316yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2311yescharacteristic
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2316yes—
493#389C2316yes—
494#389C2316yes—
495#389C2313yes—
496#389C2316yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#388C2316yes—
504#388C2316yes—
505#388C2316yes—
506#388C2316yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2313yes—
513#388C2311yescharacteristic
514#388C2313yes—
515#388C2316yes—
516#388C2316yes—
517#388C2316yes—
518#388C2316yes—
519#388C2316yes—
520#388C2316yes—
521#388C2316yes—
522#388C2316yes—
523#388C2316yes—
524#388C2316yes—
525#388C2316yes—
526#388C2316yes—
527#388C2316yes—
528#387C2313yes—
529#387C2316yes—
530#387C2313yes—
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2311yescharacteristic
537#387C2316yes—
538#387C2316yes—
539#387C2316yes—
540#387C2316yes—
541#387C2316yes—
542#387C2316yes—
543#387C2316yes—
544#387C2316yes—
545#386C2316yes—
546#386C2316yes—
547#386C2316yes—
548#386C2316yes—
549#385C2316yes—
550#385C2316yes—
551#385C2316yes—
552#385C2316yes—
553#385C2316yes—
554#385C2316yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#383C2316yes—
561#383C2316yes—
562#382C2313yes—
563#382C2313yes—
564#382C2316yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#381C2316yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2316yes—
577#380C2316yes—
578#380C2313yes—
579#380C2316yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2316yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2316yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2316yes—
622C4×C22⋊C4C2316yes—
623#376C2313yes—
624#376C2313yes—
625#376C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2411yescharacteristic
639C22×Q8C2413yes—
640C22×Q8C2416yes—
641C22×Q8C2411yescharacteristic
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2416yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2416yes—
652C23×C4C2416yes—
653C4⋊Q8—212no—
654C4⋊Q8—46no—
655C4⋊Q8—46no—
656C4⋊Q8—46no—
657C4⋊Q8—46no—
658C4⋊Q8—86no—
659#127—46no—
660#125—212no—
661#125—212no—
662#125—46no—
663#125—46no—
664#124—212no—
665#124—46no—
666#124—86no—
667#124—86no—
668#123—86no—
669#123—86no—
670C22⋊Q8—212no—
671C22⋊Q8—46no—
672C22⋊Q8—86no—
673C22⋊Q8—86no—
674#121—212no—
675#121—46no—
676#121—46no—
677#121—46no—
678#121—86no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—212no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×Q8—46no—
694C4×Q8—46no—
695C4×Q8—86no—
696C4×Q8#4118yes—
697C4×D4—212no—
698C4×D4—212no—
699C4×D4—212no—
700C4×D4—46no—
701C4×D4—46no—
702C4×D4—46no—
703C4×D4—46no—
704#117—212no—
705#117—46no—
706#117—46no—
707#117—46no—
708#117—86no—
709C2×C4⋊C4—212no—
710C2×C4⋊C4—46no—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2416yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2411yescharacteristic
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2416yes—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2416yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2416yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2416yes—
827C2×C42C2416yes—
828C2×C42C2413yes—
829C2×C42C2416yes—
830C2×C42C2416yes—
831C2×C42C2411yescharacteristic
832C2×C42C2413yes—
833C2×C42C2413yes—
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2411yescharacteristic
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2413yes—
850#95C2411yescharacteristic
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2416yes—
876#95C2411yescharacteristic
877#95C2413yes—
878#95C2413yes—
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2416yes—
895#95C2416yes—
896#95C2416yes—
897#95C2416yes—
898#95C2416yes—
899#95C2416yes—
900C24C2513yes—
901C24C2513yes—
902C24C2511yescharacteristic
903#41—416no—
904#41—416no—
905C2×Q8—26no—
906C2×Q8—26no—
907C2×Q8—26no—
908C2×Q8—26no—
909C2×Q8—41no—
910C2×Q8—43no—
911C2×Q8—43no—
912C2×Q8—41no—
913C2×Q8—41no—
914C2×Q8—43no—
915C2×Q8—43no—
916C2×Q8—43no—
917C2×Q8—46no—
918C2×Q8—46no—
919C2×Q8—46no—
920C2×Q8—416no—
921C2×Q8C2×#4114yes—
922C2×Q8H(5,𝔽2)14yes—
923C2×Q82−1+414yes—
924C2×D4—26no—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—26no—
931C2×D4—43no—
932C2×D4—43no—
933C2×D4—43no—
934C2×D4—43no—
935C2×D4—43no—
936C2×D4—43no—
937C2×D4—43no—
938C2×D4—43no—
939C2×D4—46no—
940C2×D4—46no—
941C2×D4—46no—
942C22×C4—26no—
943C22×C4—26no—
944C22×C4—26no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—212no—
952C22×C4—46no—
953C22×C4—46no—
954C22×C4—46no—
955C22×C4—46no—
956C22×C4—46no—
957C22×C4C2511yescharacteristic
958C22×C4C2513yes—
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2513yes—
963C22×C4C2511yescharacteristic
964C22×C4C2513yes—
965C22×C4C2513yes—
966C22×C4C2513yes—
967C22×C4C2513yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2511yescharacteristic
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2513yes—
982C22×C4C2511yescharacteristic
983C22×C4C2513yes—
984C22×C4C2513yes—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—22no—
988C4⋊C4—26no—
989C4⋊C4—22no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—212no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—46no—
1019C4⋊C4—41no—
1020C4⋊C4—43no—
1021C4⋊C4—41no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4—46no—
1029C4⋊C4—46no—
1030C4⋊C4—46no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—46no—
1038C4⋊C4—46no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4C2×#41112yes—
1042C22⋊C4—26no—
1043C22⋊C4—26no—
1044C22⋊C4—22no—
1045C22⋊C4—26no—
1046C22⋊C4—212no—
1047C22⋊C4—41no—
1048C22⋊C4—43no—
1049C22⋊C4—43no—
1050C22⋊C4—43no—
1051C22⋊C4—46no—
1052C22⋊C4—43no—
1053C22⋊C4—43no—
1054C22⋊C4—46no—
1055C22⋊C4—41no—
1056C22⋊C4—46no—
1057C22⋊C4—43no—
1058C22⋊C4—43no—
1059C22⋊C4—41no—
1060C22⋊C4—43no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—43no—
1064C22⋊C4—43no—
1065C22⋊C4—43no—
1066C22⋊C4—43no—
1067C22⋊C4—46no—
1068C22⋊C4—41no—
1069C22⋊C4—43no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—46no—
1073C22⋊C4—43no—
1074C22⋊C4—46no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—46no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—46no—
1083C22⋊C4—43no—
1084C22⋊C4—46no—
1085C22⋊C4—43no—
1086C22⋊C4—43no—
1087C22⋊C4—43no—
1088C42—26no—
1089C42—26no—
1090C42—26no—
1091C42—26no—
1092C42—26no—
1093C42—26no—
1094C42—26no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—43no—
1100C42—41no—
1101C42—46no—
1102C42—43no—
1103C42—46no—
1104C42—43no—
1105C42—46no—
1106C42—46no—
1107C42C2×#41112yes—
1108C23—23no—
1109C23—23no—
1110C23—21no—
1111C23—21no—
1112C23—23no—
1113C23—23no—
1114C23—21no—
1115C23—23no—
1116C23—23no—
1117C23—21no—
1118C23—23no—
1119C23—23no—
1120C23—23no—
1121C23—23no—
1122C23—21no—
1123C23—21no—
1124C23—23no—
1125C23—23no—
1126C23—23no—
1127C23—23no—
1128C23—21no—
1129C23C2611yescharacteristic
1130Q8—412no—
1131Q8—44no—
1132Q8—412no—
1133Q8—86no—
1134Q8—166no—
1135Q8#542116yes—
1136D4—412no—
1137D4—412no—
1138D4—86no—
1139D4—86no—
1140D4—86no—
1141D4—166no—
1142C2×C4—23no—
1143C2×C4—21no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—21no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—23no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—412no—
1222C2×C4—412no—
1223C2×C4—412no—
1224C2×C4—812no—
1225C2×C4—166no—
1226C2×C4C22×#4112yes—
1227C2×C4C22×#4116yes—
1228C2×C4C22×#4116yes—
1229C2×C4C2×H(5,𝔽2)16yes—
1230C2×C4C2×2−1+416yes—
1231C22—43no—
1232C22—43no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—43no—
1237C22—43no—
1238C22—43no—
1239C22—43no—
1240C22—43no—
1241C22—41no—
1242C22—43no—
1243C22—43no—
1244C22—43no—
1245C22—41no—
1246C22—43no—
1247C22—41no—
1248C22—43no—
1249C22—41no—
1250C22—43no—
1251C22—43no—
1252C22C23×#4111yescharacteristic
1253C22C22×H(5,𝔽2)11yescharacteristic
1254C22C22×2−1+411yescharacteristic
1255C22H(7,𝔽2)11yescharacteristic
1256C22H(7,𝔽2)11yescharacteristic
1257C222−1+611yescharacteristic
1258C222−1+611yescharacteristic
1259C4—22no—
1260C4—26no—
1261C4—41no—
1262C4—43no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—43no—
1270C4—43no—
1271C4—43no—
1272C4—43no—
1273C4—43no—
1274C4—43no—
1275C4—41no—
1276C4—43no—
1277C4—41no—
1278C4—43no—
1279C4—43no—
1280C4—41no—
1281C4—41no—
1282C4—43no—
1283C4—41no—
1284C4—41no—
1285C4—43no—
1286C4C2×#542112yes—
1287C2—83no—
1288C2—83no—
1289C2—81no—
1290C2C22×#54211yescharacteristic
1291C2#6285111yescharacteristic
1292C2#6285711yescharacteristic
1293C2#6304411yescharacteristic
1294C2#6306111yescharacteristic
1295C2#6306111yescharacteristic
1296C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35831C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42758C2semidirect
2. #42751C2semidirect
3. #42725C2semidirect
4. #42720C2semidirect
5. #42637C2semidirect
6. #42635C2semidirect
7. #42625C2semidirect
8. #42624C2semidirect
9. #42523C2semidirect
10. #42515C2semidirect
11. #42466C2semidirect
12. #42457C2semidirect
13. #37636C2semidirect
14. #37593C2semidirect
15. #37572C2semidirect
16. #36693C2semidirect
17. #36059C2semidirect
18. #36049C2semidirect
19. #36040C2semidirect
20. #36005C2semidirect
21. #35948C2semidirect
22. #35937C2semidirect
23. #35883C2semidirect
24. #35854C2semidirect
25. #35845C2semidirect
27. #35801C2semidirect
28. #35748C2semidirect
29. #34337C2semidirect
30. #34312C2semidirect
31. #34263C2semidirect

Maximal subgroups

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

subgroupindex
#427582
#427512
#427252
#427202
#426372
#426352
#426252
#426242
#425232
#425152
#424662
#424572
#376362
#375932
#375722
#366932
#360592
#360492
#360402
#360052
#359482
#359372
#358832
#358542
#358452
#358312
#358012
#357482
#343372
#343122
#342632