Finite Group Databasebeta

← #7688063

Subgroups — #7688063

Order 512.

5425 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59896C213yesmaximal, complemented
2#59486C213yesmaximal, complemented
3#59479C213yesmaximal, complemented
4#59275C213yesmaximal, complemented
5#59239C213yesmaximal, complemented
6#45215C213yesmaximal, complemented
7#45150C213yesmaximal, complemented
8#45149C213yesmaximal, complemented
9#45126C213yesmaximal, complemented
10#38207C213yesmaximal, complemented
11#38200C213yesmaximal, complemented
12#37974C213yesmaximal, complemented
13#37968C213yesmaximal, complemented
14Q8×#124C211yesmaximal, characteristic, complemented
15#36482C211yesmaximal, characteristic, complemented
16#36448C211yesmaximal, characteristic, complemented
17#36448C211yesmaximal, characteristic, complemented
18#36432C211yesmaximal, characteristic, complemented
19#36390C213yesmaximal, complemented
20#36279C213yesmaximal, complemented
21#35748C211yesmaximal, characteristic, complemented
22#35723C211yesmaximal, characteristic, complemented
23#35711C211yesmaximal, characteristic, complemented
24#35687C211yesmaximal, characteristic
25#34871C213yesmaximal, complemented
26#34312C211yesmaximal, characteristic, complemented
27#34311C211yesmaximal, characteristic, complemented
28#34259C211yesmaximal, characteristic, complemented
29#34257C211yesmaximal, characteristic, complemented
30#34125C211yesmaximal, characteristic, complemented
31Q8×#117C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2863C2213yes—
43#2863C2213yes—
44#2862C2213yes—
45#2855C2213yes—
46#2855C2213yes—
47#2797C2216yes—
48#2762C2216yes—
49#2759C2216yes—
50#2758C2216yes—
51#2751C2216yes—
52#2746C2216yes—
53#2745C2216yes—
54#2743C2216yes—
55#2739C2216yes—
56#2738C2216yes—
57#2737C2216yes—
58#2737C2216yes—
59#2723C2216yes—
60#2696C2216yes—
61#2628C2213yes—
62#2628C2213yes—
63#2625C2213yes—
64#2616C2213yes—
65#2612C2213yes—
66#2610C2211yescharacteristic
67#2610C2213yes—
68#2609C2213yes—
69#2605C2216yes—
70#2597C2216yes—
71#2586C2213yes—
72#2586C2216yes—
73#2581C2213yes—
74#2580C2213yes—
75#2576C2216yes—
76#2575C2216yes—
77#2572C2216yes—
78#2572C2213yes—
79#2568C2213yes—
80#2568C2213yes—
81#2563C2213yes—
82#2560C2216yes—
83#2554C2213yes—
84#2554C2213yes—
85#2542C2213yes—
86#2532C2213yes—
87#2532C2213yes—
88#2527C2216yes—
89#2526C2213yes—
90#2526C2213yes—
91#2520C2216yes—
92#2516C2216yes—
93#2516C2216yes—
94#2515C2216yes—
95#2514C2213yes—
96#2514C2213yes—
97#2514C2213yes—
98#2514C2213yes—
99#2511C2213yes—
100#2511C2213yes—
101#2510C2216yes—
102#2505C2216yes—
103#2503C2213yes—
104#2499C2213yes—
105#2499C2213yes—
106#2496C2213yes—
107#2496C2213yes—
108#2495C2213yes—
109#2495C2213yes—
110#2494C2213yes—
111#2494C2213yes—
112#2493C2216yes—
113#2492C2213yes—
114#2492C2213yes—
115#2492C2213yes—
116#2492C2213yes—
117#2488C2216yes—
118#2486C2213yes—
119#2485C2213yes—
120#2485C2213yes—
121#2479C2213yes—
122#2479C2213yes—
123#2477C2216yes—
124#2471C2213yes—
125#2471C2213yes—
126#2452C2213yes—
127#2452C2213yes—
128#2451C2213yes—
129#2451C2213yes—
130#2447C2213yes—
131#2447C2213yes—
132#2446C2213yes—
133#2446C2213yes—
134#2446C2213yes—
135#2446C2213yes—
136#2440C2213yes—
137#2440C2213yes—
138#2439C2213yes—
139#2439C2213yes—
140#2438C2216yes—
141#2434C2213yes—
142#2432C2213yes—
143#2432C2213yes—
144#2423C2213yes—
145#2422C2213yes—
146#2421C2213yes—
147#2421C2213yes—
148#2421C2213yes—
149#2420C2213yes—
150#2409C2213yes—
151#2407C2213yes—
152#2407C2213yes—
153#2396C2213yes—
154#2396C2213yes—
155#2395C2213yes—
156#2388C2213yes—
157#2368C2216yes—
158#2368C2216yes—
159#2367C2213yes—
160#2365C2213yes—
161#2363C2213yes—
162#2362C2213yes—
163#2362C2213yes—
164#2360C2213yes—
165#2357C2213yes—
166#2357C2213yes—
167#2355C2213yes—
168#2355C2213yes—
169#2354C2213yes—
170#2352C2213yes—
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179#2347C2213yes—
180#2347C2213yes—
181#2345C2213yes—
182#2345C2213yes—
183#2343C2216yes—
184#2341C2211yescharacteristic
185#2341C2211yescharacteristic
186#2341C2211yescharacteristic
187#2341C2213yes—
188#2341C2213yes—
189Q8×C22⋊C4C2211yescharacteristic
190Q8×C22⋊C4C2211yescharacteristic
191Q8×C22⋊C4C2211yescharacteristic
192Q8×C22⋊C4C2213yes—
193Q8×C22⋊C4C2211yescharacteristic
194Q8×C22⋊C4C2211yescharacteristic
195Q8×C22⋊C4C2213yes—
196Q8×C22⋊C4C2211yescharacteristic
197Q8×C22⋊C4C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202#2339C2213yes—
203#2339C2213yes—
204#2339C2213yes—
205#2339C2213yes—
206#2324C2213yes—
207#2323C2213yes—
208#2323C2213yes—
209#2323C2213yes—
210#2311C2213yes—
211#2311C2213yes—
212#2311C2213yes—
213#2310C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×#126C2213yes—
216C4×#126C2213yes—
217C4×#124C2213yes—
218C4×#124C2213yes—
219C4×#123C2213yes—
220C4×#123C2213yes—
221#2297C2213yes—
222#2297C2213yes—
223#2297C2213yes—
224#2295C2213yes—
225#2295C2213yes—
226C2×#391C2213yes—
227#2293C2213yes—
228#2293C2213yes—
229#2293C2213yes—
230#2293C2213yes—
231#2285C2213yes—
232#2283C2213yes—
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C4×#117C2213yes—
237C4×#117C2213yes—
238C2×2−1+4—28no—
239C2×2−1+4—28no—
240C2×2−1+4—44no—
241C22×#41C2313yes—
242C22×#41C2313yes—
243C22×#41C2313yes—
244C22×#41C2311yescharacteristic
245C23×Q8C2311yescharacteristic
246C23×Q8C2311yescharacteristic
247C23×Q8C2313yes—
248C23×Q8C2311yescharacteristic
249Q82—44no—
250D4×Q8—28no—
251D4×Q8—44no—
252#548—28no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×C4⋊Q8C2313yes—
257C2×C4⋊Q8C2313yes—
258C2×#126C2313yes—
259C2×#126C2313yes—
260C2×#124C2311yescharacteristic
261C2×#124C2313yes—
262C2×#123C2313yes—
263C2×#123C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2316yes—
270C2×C22⋊Q8C2313yes—
271C2×#121C2313yes—
272#520—44no—
273#519—44no—
274#519—44no—
275C4×#41—28no—
276C2×C4×Q8—28no—
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×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×#117C2313yes—
303C2×#117C2313yes—
304C2×#117C2311yescharacteristic
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C4⋊C4C2313yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316#401C2316yes—
317#401C2316yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2313yes—
323#400C2316yes—
324#400C2316yes—
325#400C2316yes—
326#400C2316yes—
327#400C2313yes—
328#400C2316yes—
329#400C2316yes—
330#400C2316yes—
331#399C2313yes—
332#399C2316yes—
333#399C2313yes—
334#399C2313yes—
335#398C2316yes—
336#398C2313yes—
337#398C2316yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#397C2316yes—
346#397C2313yes—
347#397C2316yes—
348#397C2313yes—
349#397C2313yes—
350#397C2316yes—
351#397C2316yes—
352#396C2313yes—
353#396C2313yes—
354#396C2313yes—
355#396C2313yes—
356#395C2313yes—
357#395C2311yescharacteristic
358#395C2316yes—
359#395C2316yes—
360#395C2313yes—
361#395C2316yes—
362#394C2313yes—
363#394C2313yes—
364#394C2316yes—
365#394C2316yes—
366#394C2311yescharacteristic
367#394C2313yes—
368#394C2313yes—
369#394C2316yes—
370#393C2316yes—
371#393C2316yes—
372#393C2311yescharacteristic
373#393C2313yes—
374#393C2316yes—
375#393C2316yes—
376#393C2313yes—
377#392C2311yescharacteristic
378#392C2313yes—
379#392C2313yes—
380#391C2316yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2316yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2316yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2316yes—
398#391C2316yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2316yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#390C2316yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2311yescharacteristic
428#390C2311yescharacteristic
429#389C2313yes—
430#389C2316yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#388C2311yescharacteristic
451#388C2311yescharacteristic
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2316yes—
457#388C2316yes—
458#388C2313yes—
459#388C2313yes—
460#388C2316yes—
461#388C2313yes—
462#388C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2313yes—
466#388C2316yes—
467#388C2313yes—
468#388C2316yes—
469#388C2316yes—
470#388C2313yes—
471#388C2313yes—
472#388C2313yes—
473#388C2313yes—
474#388C2311yescharacteristic
475#388C2311yescharacteristic
476#388C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2313yes—
480#388C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2316yes—
488#387C2313yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2313yes—
502#387C2313yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2313yes—
510#386C2316yes—
511#386C2316yes—
512#386C2313yes—
513#386C2313yes—
514#386C2316yes—
515#386C2313yes—
516#386C2313yes—
517#386C2316yes—
518#386C2313yes—
519#386C2313yes—
520#386C2313yes—
521#386C2313yes—
522#386C2311yescharacteristic
523#386C2311yescharacteristic
524#386C2316yes—
525#385C2316yes—
526#385C2316yes—
527#385C2316yes—
528#385C2316yes—
529#385C2316yes—
530#385C2313yes—
531#385C2316yes—
532#385C2313yes—
533#385C2316yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#383C2313yes—
538#383C2313yes—
539#383C2316yes—
540#383C2316yes—
541#383C2316yes—
542#382C2316yes—
543#382C2313yes—
544#382C2313yes—
545#382C2316yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#381C2316yes—
551#381C2316yes—
552#381C2316yes—
553#381C2316yes—
554#381C2313yes—
555#381C2313yes—
556#381C2316yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2316yes—
568#380C2316yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2316yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
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⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2316yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2316yes—
608C4×C22⋊C4C2316yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2316yes—
620C4×C22⋊C4C2313yes—
621#376C2313yes—
622#376C2313yes—
623#376C2311yescharacteristic
624#376C2313yes—
625C2×#95C2316yes—
626C2×#95C2316yes—
627C43C2313yes—
628C43C2313yes—
629C43C2313yes—
6302−1+4—464no—
631C2×#41—24no—
632C2×#41—212no—
633C2×#41—24no—
634C2×#41—212no—
635C2×#41—212no—
636C2×#41—212no—
637C2×#41—212no—
638C2×#41—212no—
639C2×#41—46no—
640C2×#41—46no—
641C2×#41—46no—
642C2×#41#4118yes—
643C22×Q8—24no—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—212no—
648C22×Q8—24no—
649C22×Q8—24no—
650C22×Q8—24no—
651C22×Q8—24no—
652C22×Q8—212no—
653C22×Q8—46no—
654C22×Q8#4118yes—
655C22×Q8C2413yes—
656C22×Q8C2413yes—
657C22×Q8C2413yes—
658C22×Q8C2413yes—
659C22×Q8C2411yescharacteristic
660C22×Q8C2416yes—
661C22×Q8C2411yescharacteristic
662C22×D4C2411yescharacteristic
663C22×D4C2413yes—
664C22×D4C2411yescharacteristic
665C22×D4C2413yes—
666C22×D4C2413yes—
667C22×D4C2411yescharacteristic
668C22×D4C2413yes—
669C23×C4C2411yescharacteristic
670C23×C4C2413yes—
671C23×C4C2413yes—
672C23×C4C2413yes—
673C23×C4C2416yes—
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2413yes—
677C23×C4C2413yes—
678C23×C4C2416yes—
679C4⋊Q8—212no—
680C4⋊Q8—46no—
681C4⋊Q8—46no—
682C4⋊Q8—46no—
683C4⋊Q8—46no—
684#126—46no—
685#126—46no—
686#124—212no—
687#124—24no—
688#123—46no—
689#123—46no—
690C22⋊Q8—212no—
691C22⋊Q8—212no—
692C22⋊Q8—212no—
693C22⋊Q8—412no—
694C22⋊Q8—412no—
695C22⋊Q8—46no—
696C22⋊Q8—46no—
697#121—212no—
698C4×Q8—212no—
699C4×Q8—212no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—46no—
712C4×Q8—46no—
713C4×Q8—46no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×D4—212no—
717C4×D4—212no—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—46no—
721C4×D4—46no—
722C4×D4—46no—
723#117—212no—
724#117—24no—
725#117—212no—
726#117—46no—
727#117—46no—
728#117—46no—
729#117—46no—
730#117—46no—
731#117—46no—
732#117—46no—
733C2×C4⋊C4—212no—
734C2×C4⋊C4—46no—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2413yes—
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2411yescharacteristic
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2416yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C42—212no—
826C2×C42—212no—
827C2×C42C2411yescharacteristic
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2411yescharacteristic
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2411yescharacteristic
845C2×C42C2416yes—
846C2×C42C2416yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2411yescharacteristic
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2413yes—
885#95C2416yes—
886#95C2413yes—
887#95C2416yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2416yes—
896#95C2413yes—
897#95C2413yes—
898#95C2416yes—
899#95C2416yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2416yes—
904#95C2416yes—
905#95C2411yescharacteristic
906#95C2416yes—
907#95C2411yescharacteristic
908#95C2411yescharacteristic
909#95C2416yes—
910#95C2416yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2416yes—
916#95C2416yes—
917#95C2416yes—
918#95C2416yes—
919C24C2511yescharacteristic
920C24C2511yescharacteristic
921C24C2511yescharacteristic
922C24C2513yes—
923#41—232no—
924#41—448no—
925#41—448no—
926#41—448no—
927C2×Q8—232no—
928C2×Q8—26no—
929C2×Q8—26no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—26no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—22no—
939C2×Q8—41no—
940C2×Q8—43no—
941C2×Q8—41no—
942C2×Q8—46no—
943C2×Q8—46no—
944C2×Q8—46no—
945C2×Q8—448no—
946C2×Q8—416no—
947C2×Q8—416no—
948C2×Q8C2×#41112yes—
949C2×Q8C2×#4114yes—
950C2×Q8C2×#4114yes—
951C2×Q8H(5,𝔽2)14yes—
952C2×D4—22no—
953C2×D4—26no—
954C2×D4—22no—
955C2×D4—26no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—22no—
960C2×D4—26no—
961C2×D4—26no—
962C2×D4—22no—
963C2×D4—22no—
964C2×D4—41no—
965C2×D4—41no—
966C2×D4—41no—
967C2×D4—43no—
968C2×D4—41no—
969C2×D4—43no—
970C2×D4—43no—
971C2×D4—43no—
972C2×D4C2×#41112yes—
973C22×C4—22no—
974C22×C4—26no—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—26no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—26no—
981C22×C4—212no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—212no—
987C22×C4—26no—
988C22×C4—26no—
989C22×C4—26no—
990C22×C4—26no—
991C22×C4—26no—
992C22×C4—43no—
993C22×C4—46no—
994C22×C4—43no—
995C22×C4—43no—
996C22×C4—43no—
997C22×C4—43no—
998C22×C4—46no—
999C22×C4—46no—
1000C22×C4—46no—
1001C22×C4C2×#41112yes—
1002C22×C4C2×#41112yes—
1003C22×C4C2513yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2513yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2513yes—
1008C22×C4C2513yes—
1009C22×C4C2513yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2513yes—
1013C22×C4C2513yes—
1014C22×C4C2513yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2513yes—
1017C22×C4C2513yes—
1018C22×C4C2513yes—
1019C22×C4C2513yes—
1020C22×C4C2513yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2513yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2513yes—
1030C4⋊C4—212no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—212no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—26no—
1048C4⋊C4—26no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—43no—
1056C4⋊C4—41no—
1057C4⋊C4—46no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—41no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—46no—
1070C4⋊C4—46no—
1071C4⋊C4—46no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C22⋊C4—212no—
1076C22⋊C4—26no—
1077C22⋊C4—26no—
1078C22⋊C4—212no—
1079C22⋊C4—22no—
1080C22⋊C4—26no—
1081C22⋊C4—22no—
1082C22⋊C4—26no—
1083C22⋊C4—22no—
1084C22⋊C4—26no—
1085C22⋊C4—22no—
1086C22⋊C4—22no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—26no—
1090C22⋊C4—26no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—22no—
1094C22⋊C4—41no—
1095C22⋊C4—46no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—41no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—43no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—46no—
1111C22⋊C4—46no—
1112C22⋊C4—43no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—43no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—43no—
1120C42—22no—
1121C42—26no—
1122C42—26no—
1123C42—26no—
1124C42—26no—
1125C42—26no—
1126C42—26no—
1127C42—26no—
1128C42—26no—
1129C42—26no—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—26no—
1134C42—26no—
1135C42—26no—
1136C42—22no—
1137C42—22no—
1138C42—43no—
1139C42—43no—
1140C42—43no—
1141C42—43no—
1142C42—43no—
1143C42—43no—
1144C42—46no—
1145C42—46no—
1146C42—43no—
1147C42—43no—
1148C422−1+414yescomplemented
1149C23—21no—
1150C23—23no—
1151C23—21no—
1152C23—23no—
1153C23—21no—
1154C23—23no—
1155C23—23no—
1156C23—23no—
1157C23—21no—
1158C23—21no—
1159C23—23no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23C22×#4116yes—
1176C23C22×#4112yes—
1177C23C2611yescharacteristic
1178Q8—224no—
1179Q8—412no—
1180Q8—44no—
1181Q8—412no—
1182Q8—412no—
1183Q8—166no—
1184Q8#551116yes—
1185D4—224no—
1186D4—44no—
1187D4—44no—
1188D4—412no—
1189D4—44no—
1190D4—412no—
1191D4—86no—
1192C2×C4—28no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—23no—
1199C2×C4—21no—
1200C2×C4—23no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—224no—
1208C2×C4—224no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—23no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—23no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—21no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—21no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—21no—
1263C2×C4—23no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—412no—
1267C2×C4—424no—
1268C2×C4—412no—
1269C2×C4—412no—
1270C2×C4—86no—
1271C2×C4—86no—
1272C2×C4—166no—
1273C2×C4C22×#4112yes—
1274C2×C4C22×#4116yes—
1275C2×C4C22×#4116yes—
1276C2×C4C22×#4116yes—
1277C2×C4C2×H(5,𝔽2)16yes—
1278C2×C4C2×2−1+412yes—
1279C2×C4C2×2−1+412yes—
1280C2×C4C2×2−1+412yes—
1281C2×C4#58512yes—
1282C2×C4#58512yes—
1283C22—22no—
1284C22—26no—
1285C22—22no—
1286C22—26no—
1287C22—22no—
1288C22—26no—
1289C22—43no—
1290C22—41no—
1291C22—43no—
1292C22—41no—
1293C22—43no—
1294C22—41no—
1295C22—41no—
1296C22—43no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22C23×#4111yescharacteristic
1312C22C23×#4111yescharacteristic
1313C22C22×H(5,𝔽2)11yescharacteristic
1314C22C22×2−1+411yescharacteristic
1315C22C2×#58511yescharacteristic
1316C22C2×#58511yescharacteristic
1317C222−1+611yescharacteristic
1318C4—22no—
1319C4—22no—
1320C4—22no—
1321C4—22no—
1322C4—22no—
1323C4—22no—
1324C4—26no—
1325C4—43no—
1326C4—43no—
1327C4—43no—
1328C4—41no—
1329C4—43no—
1330C4—41no—
1331C4—43no—
1332C4—43no—
1333C4—43no—
1334C4—43no—
1335C4—43no—
1336C4—41no—
1337C4—43no—
1338C4—41no—
1339C4—43no—
1340C4—41no—
1341C4—41no—
1342C4—43no—
1343C4—43no—
1344C4C2×#551112yes—
1345C2—42no—
1346C2—46no—
1347C2—81no—
1348C2—81no—
1349C2C22×#55111yescharacteristic
1350C2#6278811yescharacteristic
1351C2#6280511yescharacteristic
1352C2#6291311yescharacteristic
1353C2#6300511yescharacteristic
1354C2#6300911yescharacteristic
1355C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35687C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59896C2semidirect
2. #59486C2semidirect
3. #59479C2semidirect
4. #59275C2semidirect
5. #59239C2semidirect
6. #45215C2semidirect
7. #45150C2semidirect
8. #45149C2semidirect
9. #45126C2semidirect
10. #38207C2semidirect
11. #38200C2semidirect
12. #37974C2semidirect
13. #37968C2semidirect
14. Q8×#124C2semidirect
15. #36482C2semidirect
16. #36448C2semidirect
17. #36448C2semidirect
18. #36432C2semidirect
19. #36390C2semidirect
20. #36279C2semidirect
21. #35748C2semidirect
22. #35723C2semidirect
23. #35711C2semidirect
25. #34871C2semidirect
26. #34312C2semidirect
27. #34311C2semidirect
28. #34259C2semidirect
29. #34257C2semidirect
30. #34125C2semidirect
31. Q8×#117C2semidirect
1148. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
#598962
#594862
#594792
#592752
#592392
#452152
#451502
#451492
#451262
#382072
#382002
#379742
#379682
Q8×#1242
#364822
#364482
#364322
#363902
#362792
#357482
#357232
#357112
#356872
#348712
#343122
#343112
#342592
#342572
#341252
Q8×#1172