Finite Group Databasebeta

← #7657030

Subgroups — #7657030

Order 512.

4651 conjugacy classes of subgroups.

The subgroup lattice has 1299 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42785C213yesmaximal, complemented
2#42779C213yesmaximal, complemented
3#42735C213yesmaximal, complemented
4#42731C213yesmaximal, complemented
5#42700C213yesmaximal, complemented
6#42666C213yesmaximal, complemented
7#42513C213yesmaximal, complemented
8#42457C213yesmaximal, complemented
9#40212C213yesmaximal, complemented
10#40203C213yesmaximal, complemented
11#39781C213yesmaximal, complemented
12#39660C213yesmaximal, complemented
13#37631C213yesmaximal, complemented
14#37593C213yesmaximal, complemented
15#36585C211yesmaximal, characteristic, complemented
16Q8×#124C211yesmaximal, characteristic, complemented
17#36467C211yesmaximal, characteristic, complemented
18#36448C211yesmaximal, characteristic, complemented
19#35996C211yesmaximal, characteristic, complemented
20#35948C211yesmaximal, characteristic, complemented
21#35937C211yesmaximal, characteristic, complemented
22#35845C211yesmaximal, characteristic, complemented
23#35771C211yesmaximal, characteristic
24#35748C211yesmaximal, characteristic, complemented
25#35723C211yesmaximal, characteristic, complemented
26#35711C211yesmaximal, characteristic, complemented
27#35117C213yesmaximal, complemented
28#34603C213yesmaximal, complemented
29#34312C211yesmaximal, characteristic, complemented
30#34262C211yesmaximal, characteristic, complemented
31C4×Q82C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×#519C2211yescharacteristic
41#2863C2213yes—
42#2862C2213yes—
43#2861C2213yes—
44#2860C2213yes—
45#2838C2216yes—
46#2838C2216yes—
47#2832C2216yes—
48#2831C2216yes—
49#2801C2216yes—
50#2777C2216yes—
51#2774C2216yes—
52#2766C2216yes—
53#2764C2216yes—
54#2763C2216yes—
55#2759C2216yes—
56#2759C2216yes—
57#2757C2216yes—
58#2755C2216yes—
59#2754C2216yes—
60#2729C2216yes—
61#2723C2216yes—
62#2710C2216yes—
63#2700C2216yes—
64#2674C2216yes—
65#2666C2213yes—
66#2666C2213yes—
67#2663C2216yes—
68#2662C2213yes—
69#2662C2213yes—
70#2660C2213yes—
71#2654C2213yes—
72#2654C2213yes—
73#2652C2216yes—
74#2651C2213yes—
75#2651C2213yes—
76#2651C2213yes—
77#2651C2213yes—
78#2650C2213yes—
79#2650C2213yes—
80#2650C2216yes—
81#2645C2216yes—
82#2640C2213yes—
83#2640C2216yes—
84#2637C2213yes—
85#2637C2213yes—
86#2632C2211yescharacteristic
87#2632C2213yes—
88#2628C2213yes—
89#2628C2213yes—
90#2628C2213yes—
91#2625C2213yes—
92#2625C2213yes—
93#2620C2213yes—
94#2592C2213yes—
95#2592C2213yes—
96#2584C2213yes—
97#2581C2213yes—
98#2581C2213yes—
99#2580C2213yes—
100#2568C2213yes—
101#2568C2213yes—
102#2567C2213yes—
103#2563C2213yes—
104#2562C2213yes—
105#2551C2213yes—
106#2551C2213yes—
107#2550C2213yes—
108#2550C2213yes—
109#2547C2213yes—
110#2546C2213yes—
111#2545C2213yes—
112#2542C2213yes—
113#2538C2213yes—
114#2532C2216yes—
115#2529C2216yes—
116#2515C2216yes—
117#2514C2213yes—
118#2514C2213yes—
119#2513C2213yes—
120#2513C2213yes—
121#2513C2213yes—
122#2511C2213yes—
123#2502C2213yes—
124#2499C2213yes—
125#2496C2213yes—
126#2495C2213yes—
127#2494C2213yes—
128#2494C2213yes—
129#2494C2213yes—
130#2494C2213yes—
131#2492C2213yes—
132#2492C2213yes—
133#2492C2213yes—
134#2492C2213yes—
135#2492C2213yes—
136#2492C2213yes—
137#2492C2213yes—
138#2491C2213yes—
139#2491C2213yes—
140#2491C2213yes—
141#2490C2213yes—
142#2489C2213yes—
143#2486C2213yes—
144#2485C2213yes—
145#2465C2216yes—
146#2465C2216yes—
147#2458C2216yes—
148#2453C2213yes—
149#2453C2213yes—
150#2452C2213yes—
151#2452C2213yes—
152#2451C2213yes—
153#2451C2216yes—
154#2451C2213yes—
155#2448C2216yes—
156#2447C2213yes—
157#2447C2213yes—
158#2446C2213yes—
159#2446C2213yes—
160#2441C2213yes—
161#2441C2213yes—
162#2440C2213yes—
163#2440C2213yes—
164#2439C2213yes—
165#2439C2213yes—
166#2429C2213yes—
167#2426C2213yes—
168#2423C2213yes—
169#2422C2213yes—
170#2422C2213yes—
171#2421C2213yes—
172#2415C2213yes—
173#2414C2213yes—
174#2399C2213yes—
175#2398C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2396C2213yes—
179#2395C2213yes—
180#2395C2213yes—
181#2392C2213yes—
182#2369C2213yes—
183#2369C2213yes—
184#2369C2213yes—
185#2367C2213yes—
186#2363C2213yes—
187#2360C2213yes—
188#2356C2213yes—
189#2355C2213yes—
190#2352C2213yes—
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2213yes—
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202#2347C2213yes—
203#2346C2213yes—
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
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#2324C2213yes—
219#2323C2213yes—
220#2320C2213yes—
221#2314C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×C4⋊Q8C2213yes—
224C4×C4⋊Q8C2213yes—
225C4×#126C2213yes—
226C4×#126C2213yes—
227C4×#124C2213yes—
228C4×#124C2213yes—
229C4×#124C2213yes—
230#2298C2213yes—
231#2295C2213yes—
232#2293C2213yes—
233#2276C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2213yes—
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—28no—
242Q82—44no—
243#557—44no—
244D4×Q8—44no—
245#548—28no—
246#548—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2316yes—
256C2×#126C2313yes—
257C2×#126C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#124C2313yes—
261C2×#124C2311yescharacteristic
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2316yes—
265C2×#123C2316yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2316yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274#520—44no—
275#519—28no—
276#519—44no—
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2316yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C22×C4⋊C4C2313yes—
310#401C2316yes—
311#401C2316yes—
312#400C2316yes—
313#400C2313yes—
314#400C2316yes—
315#400C2316yes—
316#400C2316yes—
317#400C2316yes—
318#400C2316yes—
319#400C2316yes—
320#400C2316yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#399C2316yes—
328#399C2316yes—
329#399C2313yes—
330#399C2311yescharacteristic
331#399C2313yes—
332#399C2311yescharacteristic
333#399C2313yes—
334#398C2313yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#397C2316yes—
351#397C2316yes—
352#397C2316yes—
353#397C2313yes—
354#397C2316yes—
355#397C2313yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#396C2313yes—
369#396C2316yes—
370#396C2313yes—
371#396C2316yes—
372#396C2313yes—
373#396C2313yes—
374#396C2313yes—
375#396C2313yes—
376#396C2313yes—
377#396C2313yes—
378#395C2313yes—
379#395C2316yes—
380#395C2316yes—
381#395C2316yes—
382#395C2313yes—
383#395C2313yes—
384#395C2316yes—
385#395C2316yes—
386#395C2313yes—
387#395C2311yescharacteristic
388#395C2311yescharacteristic
389#395C2313yes—
390#394C2316yes—
391#394C2313yes—
392#394C2316yes—
393#394C2313yes—
394#394C2311yescharacteristic
395#394C2311yescharacteristic
396#394C2313yes—
397#394C2313yes—
398#394C2313yes—
399#394C2313yes—
400#394C2313yes—
401#393C2316yes—
402#393C2316yes—
403#393C2316yes—
404#393C2316yes—
405#393C2316yes—
406#393C2316yes—
407#393C2313yes—
408#393C2316yes—
409#393C2313yes—
410#393C2313yes—
411#393C2311yescharacteristic
412#393C2311yescharacteristic
413#392C2313yes—
414#391C2316yes—
415#391C2316yes—
416#391C2316yes—
417#391C2313yes—
418#391C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2313yes—
423#391C2313yes—
424#391C2313yes—
425#391C2316yes—
426#391C2316yes—
427#391C2313yes—
428#391C2313yes—
429#391C2313yes—
430#391C2313yes—
431#391C2316yes—
432#391C2316yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2313yes—
438#391C2316yes—
439#391C2316yes—
440#391C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2313yes—
444#390C2313yes—
445#390C2313yes—
446#390C2313yes—
447#390C2313yes—
448#390C2313yes—
449#390C2313yes—
450#390C2313yes—
451#390C2313yes—
452#390C2316yes—
453#390C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2316yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2316yes—
462#389C2316yes—
463#389C2316yes—
464#389C2316yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2316yes—
473#389C2313yes—
474#389C2313yes—
475#389C2316yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2316yes—
484#388C2311yescharacteristic
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2316yes—
492#388C2313yes—
493#388C2316yes—
494#388C2316yes—
495#388C2313yes—
496#388C2316yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#388C2316yes—
501#388C2316yes—
502#388C2316yes—
503#388C2316yes—
504#388C2316yes—
505#388C2316yes—
506#388C2313yes—
507#388C2313yes—
508#388C2316yes—
509#388C2316yes—
510#388C2316yes—
511#388C2311yescharacteristic
512#388C2311yescharacteristic
513#388C2311yescharacteristic
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2316yes—
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2316yes—
527#387C2316yes—
528#387C2313yes—
529#387C2313yes—
530#387C2316yes—
531#387C2316yes—
532#387C2316yes—
533#387C2316yes—
534#387C2316yes—
535#387C2316yes—
536#387C2316yes—
537#387C2316yes—
538#387C2316yes—
539#387C2313yes—
540#387C2313yes—
541#387C2316yes—
542#386C2316yes—
543#385C2316yes—
544#385C2316yes—
545#385C2316yes—
546#385C2316yes—
547#385C2316yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2313yes—
553#383C2311yescharacteristic
554#383C2313yes—
555#383C2316yes—
556#383C2316yes—
557#382C2316yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2316yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#381C2316yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
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⋊C4C2316yes—
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⋊C4C2316yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2316yes—
622#376C2313yes—
623#376C2316yes—
624C43C2313yes—
625C43C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2411yescharacteristic
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×Q8C2416yes—
641C22×Q8C2413yes—
642C22×Q8C2416yes—
643C22×Q8C2411yescharacteristic
644C22×D4C2413yes—
645C22×D4C2411yescharacteristic
646C22×D4C2413yes—
647C22×D4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2416yes—
652C4⋊Q8—212no—
653C4⋊Q8—212no—
654C4⋊Q8—212no—
655C4⋊Q8—46no—
656C4⋊Q8—46no—
657C4⋊Q8—46no—
658C4⋊Q8—46no—
659C4⋊Q8—46no—
660C4⋊Q8—86no—
661#126—212no—
662#126—46no—
663#125—46no—
664#125—46no—
665#124—212no—
666#124—24no—
667#124—46no—
668#124—46no—
669#124—86no—
670#123—86no—
671C22⋊Q8—212no—
672C22⋊Q8—412no—
673C22⋊Q8—46no—
674C22⋊Q8—46no—
675C22⋊Q8—46no—
676C22⋊Q8—86no—
677#121—212no—
678#121—46no—
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—212no—
692C4×Q8—212no—
693C4×Q8—24no—
694C4×Q8—46no—
695C4×Q8—46no—
696C4×Q8—46no—
697C4×Q8—46no—
698C4×Q8—46no—
699C4×Q8—86no—
700C4×Q8#4118yes—
701C4×D4—212no—
702C4×D4—46no—
703C4×D4—46no—
704C4×D4—46no—
705C4×D4—46no—
706#117—212no—
707#117—212no—
708#117—46no—
709#117—46no—
710#117—46no—
711C2×C4⋊C4—46no—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2416yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2411yescharacteristic
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2411yescharacteristic
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2411yescharacteristic
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2411yescharacteristic
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2416yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2416yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825C2×C42C2413yes—
826C2×C42C2416yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2416yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2416yes—
845#95C2416yes—
846#95C2411yescharacteristic
847#95C2413yes—
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2411yescharacteristic
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2416yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2416yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2416yes—
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2413yes—
879#95C2411yescharacteristic
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2416yes—
884#95C2413yes—
885#95C2416yes—
886#95C2416yes—
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—
900#95C2416yes—
901#95C2416yes—
902C24C2511yescharacteristic
903C24C2513yes—
904C24C2511yescharacteristic
905#41—416no—
906C2×Q8—22no—
907C2×Q8—26no—
908C2×Q8—26no—
909C2×Q8—212no—
910C2×Q8—26no—
911C2×Q8—26no—
912C2×Q8—22no—
913C2×Q8—22no—
914C2×Q8—26no—
915C2×Q8—26no—
916C2×Q8—22no—
917C2×Q8—41no—
918C2×Q8—41no—
919C2×Q8—43no—
920C2×Q8—46no—
921C2×Q8—43no—
922C2×Q8—43no—
923C2×Q8—46no—
924C2×Q8—46no—
925C2×Q8—46no—
926C2×Q8—46no—
927C2×Q8—416no—
928C2×Q8—416no—
929C2×Q8C2×#4114yes—
930C2×Q8H(5,𝔽2)14yes—
931C2×Q82−1+414yes—
932C2×D4—26no—
933C2×D4—26no—
934C2×D4—26no—
935C2×D4—22no—
936C2×D4—26no—
937C2×D4—41no—
938C2×D4—41no—
939C2×D4—43no—
940C2×D4—43no—
941C2×D4—43no—
942C2×D4—43no—
943C2×D4—43no—
944C22×C4—26no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—26no—
953C22×C4—46no—
954C22×C4—46no—
955C22×C4—46no—
956C22×C4C2513yes—
957C22×C4C2511yescharacteristic
958C22×C4C2513yes—
959C22×C4C2513yes—
960C22×C4C2513yes—
961C22×C4C2511yescharacteristic
962C22×C4C2513yes—
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2513yes—
966C22×C4C2513yes—
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2513yes—
970C22×C4C2513yes—
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
974C22×C4C2513yes—
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2511yescharacteristic
978C22×C4C2513yes—
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2511yescharacteristic
983C22×C4C2513yes—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—43no—
1014C4⋊C4—41no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—41no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—46no—
1028C4⋊C4—46no—
1029C4⋊C4—46no—
1030C4⋊C4—46no—
1031C4⋊C4—46no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—46no—
1035C4⋊C4—46no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4C2×#41112yes—
1041C22⋊C4—26no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—26no—
1045C22⋊C4—212no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—26no—
1051C22⋊C4—26no—
1052C22⋊C4—26no—
1053C22⋊C4—26no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—46no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—43no—
1060C22⋊C4—43no—
1061C22⋊C4—43no—
1062C22⋊C4—41no—
1063C22⋊C4—43no—
1064C22⋊C4—43no—
1065C22⋊C4—43no—
1066C22⋊C4—41no—
1067C22⋊C4—43no—
1068C22⋊C4—43no—
1069C22⋊C4—43no—
1070C22⋊C4—46no—
1071C22⋊C4—46no—
1072C22⋊C4—43no—
1073C22⋊C4—46no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—46no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—43no—
1083C42—26no—
1084C42—212no—
1085C42—26no—
1086C42—26no—
1087C42—26no—
1088C42—26no—
1089C42—26no—
1090C42—26no—
1091C42—26no—
1092C42—26no—
1093C42—26no—
1094C42—22no—
1095C42—22no—
1096C42—26no—
1097C42—26no—
1098C42—43no—
1099C42—43no—
1100C42—43no—
1101C42—46no—
1102C42—43no—
1103C42—43no—
1104C42—43no—
1105C42—43no—
1106C42—43no—
1107C42—46no—
1108C42C2×#41112yes—
1109C422−1+414yes—
1110C23—21no—
1111C23—23no—
1112C23—21no—
1113C23—21no—
1114C23—23no—
1115C23—21no—
1116C23—23no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—23no—
1122C23—21no—
1123C23—23no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—23no—
1128C23—23no—
1129C23—21no—
1130C23—21no—
1131C23C2611yescharacteristic
1132Q8—28no—
1133Q8—44no—
1134Q8—412no—
1135Q8—412no—
1136Q8—812no—
1137Q8—86no—
1138Q8—166no—
1139Q8#542116yes—
1140D4—44no—
1141D4—412no—
1142D4—86no—
1143D4—86no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—23no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—21no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—21no—
1195C2×C4—23no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—21no—
1215C2×C4—23no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—412no—
1220C2×C4—412no—
1221C2×C4—412no—
1222C2×C4—166no—
1223C2×C4C22×#4116yes—
1224C2×C4C22×#4112yes—
1225C2×C4C22×#4116yes—
1226C2×C4C2×H(5,𝔽2)16yes—
1227C2×C4C2×2−1+412yes—
1228C2×C4C2×2−1+412yes—
1229C2×C4C2×2−1+412yes—
1230C2×C4C2×2−1+416yes—
1231C2×C4#58512yes—
1232C22—41no—
1233C22—43no—
1234C22—41no—
1235C22—41no—
1236C22—43no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—43no—
1241C22—43no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—43no—
1247C22—43no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—43no—
1253C22C23×#4111yescharacteristic
1254C22C22×H(5,𝔽2)11yescharacteristic
1255C22C22×2−1+411yescharacteristic
1256C22C22×2−1+411yescharacteristic
1257C22C2×#58511yescharacteristic
1258C22H(7,𝔽2)11yescharacteristic
1259C222−1+611yescharacteristic
1260C4—22no—
1261C4—22no—
1262C4—22no—
1263C4—26no—
1264C4—22no—
1265C4—22no—
1266C4—43no—
1267C4—41no—
1268C4—43no—
1269C4—43no—
1270C4—41no—
1271C4—41no—
1272C4—43no—
1273C4—41no—
1274C4—41no—
1275C4—43no—
1276C4—43no—
1277C4—43no—
1278C4—41no—
1279C4—43no—
1280C4—43no—
1281C4—41no—
1282C4—43no—
1283C4—43no—
1284C4—43no—
1285C4—41no—
1286C4—43no—
1287C4C2×#542112yes—
1288C2—81no—
1289C2—83no—
1290C2—81no—
1291C2C22×#54211yescharacteristic
1292C2#6278811yescharacteristic
1293C2#6285711yescharacteristic
1294C2#6291311yescharacteristic
1295C2#6292311yescharacteristic
1296C2#6294311yescharacteristic
1297C2#6295311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35771C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42785C2semidirect
2. #42779C2semidirect
3. #42735C2semidirect
4. #42731C2semidirect
5. #42700C2semidirect
6. #42666C2semidirect
7. #42513C2semidirect
8. #42457C2semidirect
9. #40212C2semidirect
10. #40203C2semidirect
11. #39781C2semidirect
12. #39660C2semidirect
13. #37631C2semidirect
14. #37593C2semidirect
15. #36585C2semidirect
16. Q8×#124C2semidirect
17. #36467C2semidirect
18. #36448C2semidirect
19. #35996C2semidirect
20. #35948C2semidirect
21. #35937C2semidirect
22. #35845C2semidirect
24. #35748C2semidirect
25. #35723C2semidirect
26. #35711C2semidirect
27. #35117C2semidirect
28. #34603C2semidirect
29. #34312C2semidirect
30. #34262C2semidirect
31. C4×Q82C2semidirect

Maximal subgroups

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

subgroupindex
#427852
#427792
#427352
#427312
#427002
#426662
#425132
#424572
#402122
#402032
#397812
#396602
#376312
#375932
#365852
Q8×#1242
#364672
#364482
#359962
#359482
#359372
#358452
#357712
#357482
#357232
#357112
#351172
#346032
#343122
#342622
C4×Q822