Finite Group Databasebeta

← #7656640

Subgroups — #7656640

Order 512.

4541 conjugacy classes of subgroups.

The subgroup lattice has 1287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42775C213yesmaximal, complemented
2#42772C213yesmaximal, complemented
3#42747C213yesmaximal, complemented
4#42743C213yesmaximal, complemented
5#42701C213yesmaximal, complemented
6#42665C213yesmaximal, complemented
7#42512C213yesmaximal, complemented
8#42456C213yesmaximal
9#40216C213yesmaximal, complemented
10#40199C213yesmaximal, complemented
11#39784C213yesmaximal, complemented
12#39665C213yesmaximal, complemented
13#37630C213yesmaximal, complemented
14#37598C213yesmaximal, complemented
15#36577C211yesmaximal, characteristic, complemented
16Q8×#123C211yesmaximal, characteristic, complemented
17#36482C211yesmaximal, characteristic, complemented
18#36435C211yesmaximal, characteristic, complemented
19#35957C211yesmaximal, characteristic, complemented
20#35920C211yesmaximal, characteristic, complemented
21#35910C211yesmaximal, characteristic, complemented
22#35910C211yesmaximal, characteristic, complemented
23#35910C211yesmaximal, characteristic, complemented
24#35883C211yesmaximal, characteristic, complemented
25#35786C211yesmaximal, characteristic, complemented
26#35700C211yesmaximal, characteristic
27#35110C213yesmaximal, complemented
28#34596C213yesmaximal
29#34336C211yesmaximal, characteristic, complemented
30#34262C211yesmaximal, characteristic, complemented
31C4×D4×Q8C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2857C2213yes—
42#2855C2213yes—
43#2855C2213yes—
44#2851C2213yes—
45#2839C2216yes—
46#2839C2216yes—
47#2839C2216yes—
48#2838C2216yes—
49#2799C2216yes—
50#2798C2216yes—
51#2790C2216yes—
52#2779C2216yes—
53#2774C2216yes—
54#2770C2216yes—
55#2767C2216yes—
56#2767C2216yes—
57#2766C2216yes—
58#2764C2216yes—
59#2763C2216yes—
60#2758C2216yes—
61#2754C2216yes—
62#2739C2216yes—
63#2718C2216yes—
64#2698C2216yes—
65#2666C2216yes—
66#2665C2213yes—
67#2665C2213yes—
68#2663C2213yes—
69#2663C2213yes—
70#2660C2213yes—
71#2655C2213yes—
72#2655C2213yes—
73#2655C2216yes—
74#2654C2216yes—
75#2653C2213yes—
76#2653C2213yes—
77#2652C2213yes—
78#2652C2213yes—
79#2650C2213yes—
80#2650C2213yes—
81#2647C2216yes—
82#2645C2213yes—
83#2645C2213yes—
84#2645C2216yes—
85#2642C2213yes—
86#2642C2213yes—
87#2642C2213yes—
88#2638C2213yes—
89#2638C2213yes—
90#2630C2211yescharacteristic
91#2630C2213yes—
92#2629C2213yes—
93#2621C2213yes—
94#2584C2213yes—
95#2582C2213yes—
96#2582C2213yes—
97#2581C2213yes—
98#2568C2213yes—
99#2568C2213yes—
100#2568C2213yes—
101#2568C2213yes—
102#2567C2213yes—
103#2565C2213yes—
104#2565C2213yes—
105#2562C2213yes—
106#2562C2213yes—
107#2562C2213yes—
108#2552C2213yes—
109#2552C2213yes—
110#2550C2213yes—
111#2550C2213yes—
112#2546C2213yes—
113#2536C2213yes—
114#2530C2216yes—
115#2527C2216yes—
116#2525C2216yes—
117#2520C2216yes—
118#2520C2216yes—
119#2514C2213yes—
120#2514C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2511C2216yes—
124#2511C2213yes—
125#2511C2213yes—
126#2509C2216yes—
127#2503C2213yes—
128#2502C2213yes—
129#2497C2213yes—
130#2496C2213yes—
131#2496C2213yes—
132#2496C2213yes—
133#2495C2213yes—
134#2494C2213yes—
135#2492C2213yes—
136#2492C2213yes—
137#2492C2213yes—
138#2492C2213yes—
139#2492C2213yes—
140#2492C2213yes—
141#2489C2213yes—
142#2489C2213yes—
143#2489C2213yes—
144#2489C2213yes—
145#2489C2213yes—
146#2489C2213yes—
147#2487C2213yes—
148#2486C2213yes—
149#2468C2216yes—
150#2453C2213yes—
151#2453C2213yes—
152#2453C2213yes—
153#2453C2213yes—
154#2451C2213yes—
155#2451C2213yes—
156#2446C2213yes—
157#2446C2213yes—
158#2446C2213yes—
159#2446C2213yes—
160#2442C2213yes—
161#2442C2213yes—
162#2442C2213yes—
163#2441C2213yes—
164#2440C2213yes—
165#2439C2213yes—
166#2429C2213yes—
167#2429C2213yes—
168#2423C2213yes—
169#2423C2213yes—
170#2421C2213yes—
171#2421C2213yes—
172#2415C2213yes—
173#2415C2213yes—
174#2401C2213yes—
175#2401C2213yes—
176#2399C2213yes—
177#2398C2213yes—
178#2398C2213yes—
179#2398C2213yes—
180#2396C2213yes—
181#2392C2213yes—
182#2370C2213yes—
183#2370C2213yes—
184#2369C2213yes—
185#2365C2213yes—
186#2360C2213yes—
187#2360C2213yes—
188#2356C2213yes—
189#2355C2213yes—
190#2355C2213yes—
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201D4×C4⋊C4C2213yes—
202#2347C2213yes—
203#2346C2213yes—
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2334C2216yes—
217#2332C2216yes—
218#2331C2213yes—
219#2330C2213yes—
220#2320C2213yes—
221#2314C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×#125C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×#123C2213yes—
229C4×#123C2213yes—
230#2298C2213yes—
231#2295C2213yes—
232#2295C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C23×Q8C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—28no—
242#557—44no—
243#557—44no—
244D4×Q8—28no—
245D4×Q8—44no—
246D4×Q8—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×#126C2316yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#123C2311yescharacteristic
261C2×#123C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270#519—28no—
271C2×C4×Q8—44no—
272C2×C4×Q8—44no—
273C2×C4×Q8C2313yes—
274C2×C4×Q8C2313yes—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×D4C2313yes—
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×#117C2313yes—
300C2×#117C2313yes—
301C22×C4⋊C4C2313yes—
302C22×C4⋊C4C2313yes—
303C22×C42C2313yes—
304C22×C42C2313yes—
305#401C2316yes—
306#401C2313yes—
307#401C2313yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2316yes—
315#400C2316yes—
316#400C2316yes—
317#400C2316yes—
318#400C2316yes—
319#400C2313yes—
320#400C2313yes—
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#400C2316yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2316yes—
329#400C2316yes—
330#400C2316yes—
331#400C2316yes—
332#400C2316yes—
333#400C2313yes—
334#400C2313yes—
335#400C2313yes—
336#400C2313yes—
337#400C2313yes—
338#400C2313yes—
339#400C2313yes—
340#400C2313yes—
341#399C2316yes—
342#399C2313yes—
343#398C2313yes—
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2313yes—
348#398C2316yes—
349#398C2316yes—
350#398C2313yes—
351#398C2313yes—
352#398C2316yes—
353#398C2316yes—
354#398C2316yes—
355#398C2316yes—
356#398C2316yes—
357#398C2316yes—
358#398C2316yes—
359#398C2316yes—
360#398C2313yes—
361#398C2311yescharacteristic
362#398C2313yes—
363#397C2313yes—
364#397C2316yes—
365#397C2316yes—
366#397C2313yes—
367#397C2311yescharacteristic
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#396C2316yes—
379#396C2313yes—
380#396C2311yescharacteristic
381#396C2311yescharacteristic
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#395C2313yes—
386#395C2316yes—
387#395C2316yes—
388#395C2313yes—
389#395C2313yes—
390#395C2313yes—
391#395C2313yes—
392#394C2313yes—
393#394C2313yes—
394#394C2313yes—
395#394C2311yescharacteristic
396#394C2311yescharacteristic
397#394C2311yescharacteristic
398#394C2313yes—
399#394C2313yes—
400#394C2313yes—
401#393C2313yes—
402#393C2313yes—
403#393C2313yes—
404#393C2313yes—
405#393C2313yes—
406#393C2313yes—
407#393C2313yes—
408#392C2311yescharacteristic
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#391C2316yes—
416#391C2313yes—
417#391C2313yes—
418#391C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2316yes—
422#391C2316yes—
423#391C2313yes—
424#391C2313yes—
425#391C2313yes—
426#391C2313yes—
427#391C2313yes—
428#391C2316yes—
429#391C2316yes—
430#391C2313yes—
431#391C2313yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2316yes—
436#391C2313yes—
437#391C2316yes—
438#391C2313yes—
439#391C2313yes—
440#391C2313yes—
441#391C2313yes—
442#391C2313yes—
443#391C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2316yes—
447#389C2316yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2316yes—
460#389C2313yes—
461#389C2316yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2313yes—
467#389C2316yes—
468#389C2316yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2316yes—
475#389C2316yes—
476#389C2313yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2316yes—
483#388C2313yes—
484#388C2316yes—
485#388C2313yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2313yes—
490#388C2311yescharacteristic
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#387C2313yes—
496#387C2316yes—
497#387C2313yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2316yes—
517#387C2313yes—
518#387C2316yes—
519#387C2316yes—
520#387C2311yescharacteristic
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2316yes—
527#387C2316yes—
528#387C2313yes—
529#387C2313yes—
530#387C2316yes—
531#386C2311yescharacteristic
532#386C2313yes—
533#385C2313yes—
534#385C2313yes—
535#385C2316yes—
536#385C2316yes—
537#385C2316yes—
538#385C2316yes—
539#385C2311yescharacteristic
540#385C2313yes—
541#385C2313yes—
542#385C2313yes—
543#384C2313yes—
544#384C2313yes—
545#384C2313yes—
546#384C2316yes—
547#384C2313yes—
548#384C2313yes—
549#383C2316yes—
550#383C2316yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#382C2316yes—
556#382C2316yes—
557#382C2316yes—
558#382C2316yes—
559#382C2313yes—
560#381C2313yes—
561#381C2316yes—
562#381C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2316yes—
576#380C2311yescharacteristic
577#380C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2316yes—
581C4×C4⋊C4C2316yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2316yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
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×C22⋊C4C2313yes—
607C4×C22⋊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⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622#376C2313yes—
623#376C2313yes—
624#376C2313yes—
625#376C2316yes—
626C43C2313yes—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2413yes—
640C22×Q8C2413yes—
641C22×Q8C2413yes—
642C22×Q8C2411yescharacteristic
643C22×D4C2411yescharacteristic
644C22×D4C2411yescharacteristic
645C22×D4C2411yescharacteristic
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2411yescharacteristic
651C23×C4C2413yes—
652C23×C4C2411yescharacteristic
653C4⋊Q8—212no—
654C4⋊Q8—212no—
655C4⋊Q8—46no—
656C4⋊Q8—46no—
657C4⋊Q8—46no—
658C4⋊Q8—46no—
659#126—412no—
660#125—212no—
661#125—212no—
662#125—46no—
663#125—46no—
664#125—46no—
665#125—46no—
666#123—24no—
667#123—46no—
668C22⋊Q8—212no—
669C22⋊Q8—212no—
670C22⋊Q8—212no—
671C22⋊Q8—46no—
672C22⋊Q8—46no—
673C22⋊Q8—46no—
674C22⋊Q8—46no—
675C22⋊Q8—46no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
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—212no—
688C4×Q8—212no—
689C4×Q8—212no—
690C4×Q8—46no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×Q8—46no—
694C4×Q8—46no—
695C4×Q8—46no—
696C4×Q8#4118yes—
697C4×D4—24no—
698C4×D4—212no—
699C4×D4—46no—
700C4×D4—46no—
701C4×D4—46no—
702#117—212no—
703#117—212no—
704C2×C4⋊C4—46no—
705C2×C4⋊C4—46no—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C22⋊C4C2411yescharacteristic
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2411yescharacteristic
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2411yescharacteristic
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C42—46no—
798C2×C42—46no—
799C2×C42C2416yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2411yescharacteristic
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2416yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2416yes—
821C2×C42C2416yes—
822C2×C42C2413yes—
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2416yes—
838#95C2416yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2413yes—
867#95C2413yes—
868#95C2416yes—
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2411yescharacteristic
872#95C2416yes—
873#95C2413yes—
874#95C2416yes—
875#95C2416yes—
876#95C2416yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2416yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2416yes—
888#95C2416yes—
889#95C2416yes—
890#95C2416yes—
891#95C2416yes—
892#95C2416yes—
893#95C2416yes—
894#95C2416yes—
895#95C2416yes—
896#95C2416yes—
897C24C2511yescharacteristic
898C24C2511yescharacteristic
899C24C2511yescharacteristic
900C2×Q8—26no—
901C2×Q8—26no—
902C2×Q8—26no—
903C2×Q8—26no—
904C2×Q8—26no—
905C2×Q8—26no—
906C2×Q8—26no—
907C2×Q8—26no—
908C2×Q8—26no—
909C2×Q8—26no—
910C2×Q8—26no—
911C2×Q8—43no—
912C2×Q8—43no—
913C2×Q8—43no—
914C2×Q8—43no—
915C2×Q8—43no—
916C2×Q8—43no—
917C2×Q8—43no—
918C2×Q8—416no—
919C2×Q8—416no—
920C2×Q8—416no—
921C2×Q8C2×#4114yes—
922C2×Q8H(5,𝔽2)14yes—
923C2×Q82−1+414yes—
924C2×D4—22no—
925C2×D4—22no—
926C2×D4—22no—
927C2×D4—22no—
928C2×D4—22no—
929C2×D4—41no—
930C2×D4—41no—
931C2×D4—41no—
932C2×D4—41no—
933C22×C4—26no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—26no—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—22no—
941C22×C4—26no—
942C22×C4—26no—
943C22×C4—26no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—43no—
949C22×C4—43no—
950C22×C4—43no—
951C22×C4—43no—
952C22×C4—43no—
953C22×C42−1+414yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2513yes—
960C22×C4C2513yes—
961C22×C4C2513yes—
962C22×C4C2513yes—
963C22×C4C2511yescharacteristic
964C22×C4C2513yes—
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2513yes—
968C22×C4C2513yes—
969C22×C4C2513yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2513yes—
973C22×C4C2513yes—
974C22×C4C2513yes—
975C22×C4C2511yescharacteristic
976C22×C4C2513yes—
977C22×C4C2513yes—
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2513yes—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—22no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—212no—
992C4⋊C4—212no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—22no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—46no—
1008C4⋊C4—46no—
1009C4⋊C4—43no—
1010C4⋊C4—46no—
1011C4⋊C4—43no—
1012C4⋊C4—41no—
1013C4⋊C4—43no—
1014C4⋊C4—41no—
1015C4⋊C4—43no—
1016C4⋊C4—46no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—46no—
1032C4⋊C4—46no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—46no—
1036C4⋊C4—46no—
1037C4⋊C4—46no—
1038C4⋊C4—46no—
1039C4⋊C4—46no—
1040C4⋊C4C2×#41112yes—
1041C22⋊C4—22no—
1042C22⋊C4—26no—
1043C22⋊C4—26no—
1044C22⋊C4—22no—
1045C22⋊C4—26no—
1046C22⋊C4—22no—
1047C22⋊C4—26no—
1048C22⋊C4—26no—
1049C22⋊C4—26no—
1050C22⋊C4—22no—
1051C22⋊C4—26no—
1052C22⋊C4—26no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—43no—
1057C22⋊C4—41no—
1058C22⋊C4—43no—
1059C22⋊C4—43no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—43no—
1065C22⋊C4—41no—
1066C22⋊C4—43no—
1067C22⋊C4—43no—
1068C22⋊C4—43no—
1069C22⋊C4—43no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—43no—
1073C42—26no—
1074C42—212no—
1075C42—26no—
1076C42—26no—
1077C42—26no—
1078C42—26no—
1079C42—26no—
1080C42—26no—
1081C42—26no—
1082C42—26no—
1083C42—22no—
1084C42—26no—
1085C42—26no—
1086C42—43no—
1087C42—43no—
1088C42—43no—
1089C42—43no—
1090C42—43no—
1091C42—46no—
1092C42—43no—
1093C42—46no—
1094C42—43no—
1095C42—46no—
1096C42C2×#41112yes—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23C2×2−1+412yes—
1117C23#58512yes—
1118C23C2611yescharacteristic
1119Q8—412no—
1120Q8—412no—
1121Q8—412no—
1122Q8—86no—
1123Q8—86no—
1124Q8—86no—
1125Q8#542116yes—
1126D4—28no—
1127D4—44no—
1128D4—44no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—23no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—21no—
1137C2×C4—23no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—21no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—21no—
1184C2×C4—23no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—44no—
1207C2×C4—44no—
1208C2×C4—412no—
1209C2×C4—412no—
1210C2×C4—412no—
1211C2×C4—86no—
1212C2×C4—86no—
1213C2×C4C22×#4116yes—
1214C2×C4C22×#4112yes—
1215C2×C4C22×#4116yes—
1216C2×C4C2×H(5,𝔽2)16yes—
1217C2×C4C2×2−1+412yes—
1218C2×C4C2×2−1+412yes—
1219C2×C4C2×2−1+416yes—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22C23×#4111yescharacteristic
1242C22C22×H(5,𝔽2)11yescharacteristic
1243C22C22×2−1+411yescharacteristic
1244C22C22×2−1+411yescharacteristic
1245C22C2×#58511yescharacteristic
1246C222−1+611yescharacteristic
1247C222−1+611yescharacteristic
1248C4—22no—
1249C4—26no—
1250C4—22no—
1251C4—22no—
1252C4—43no—
1253C4—41no—
1254C4—43no—
1255C4—41no—
1256C4—43no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—43no—
1261C4—43no—
1262C4—43no—
1263C4—43no—
1264C4—43no—
1265C4—41no—
1266C4—43no—
1267C4—41no—
1268C4—43no—
1269C4—43no—
1270C4—43no—
1271C4—41no—
1272C4—41no—
1273C4—43no—
1274C4—43no—
1275C4C2×#542112yes—
1276C2—42no—
1277C2—42no—
1278C2—81no—
1279C2C22×#54211yescharacteristic
1280C2#6278811yescharacteristic
1281C2#6286111yescharacteristic
1282C2#6289311yescharacteristic
1283C2#6289711yescharacteristic
1284C2#6294711yescharacteristic
1285C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42775C2semidirect
2. #42772C2semidirect
3. #42747C2semidirect
4. #42743C2semidirect
5. #42701C2semidirect
6. #42665C2semidirect
7. #42512C2semidirect
9. #40216C2semidirect
10. #40199C2semidirect
11. #39784C2semidirect
12. #39665C2semidirect
13. #37630C2semidirect
14. #37598C2semidirect
15. #36577C2semidirect
16. Q8×#123C2semidirect
17. #36482C2semidirect
18. #36435C2semidirect
19. #35957C2semidirect
20. #35920C2semidirect
21. #35910C2semidirect
22. #35910C2semidirect
23. #35910C2semidirect
24. #35883C2semidirect
25. #35786C2semidirect
27. #35110C2semidirect
29. #34336C2semidirect
30. #34262C2semidirect
31. C4×D4×Q8C2semidirect

Maximal subgroups

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

subgroupindex
#427752
#427722
#427472
#427432
#427012
#426652
#425122
#424562
#402162
#401992
#397842
#396652
#376302
#375982
#365772
Q8×#1232
#364822
#364352
#359572
#359202
#359102
#358832
#357862
#357002
#351102
#345962
#343362
#342622
C4×D4×Q82