Finite Group Databasebeta

← #7715890

Subgroups — #7715890

Order 512.

4728 conjugacy classes of subgroups.

The subgroup lattice has 1387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50430C214yesmaximal, complemented
2#50410C214yesmaximal, complemented
3#49252C214yesmaximal, complemented
4#49224C214yesmaximal, complemented
5#44269C214yesmaximal, complemented
6#44217C214yesmaximal, complemented
7#44041C214yesmaximal, complemented
8#43970C214yesmaximal, complemented
9#39798C212yesmaximal, complemented
10#39551C212yesmaximal, complemented
11#39549C212yesmaximal, complemented
12#39499C212yesmaximal, complemented
13#37760C212yesmaximal, complemented
14#37708C212yesmaximal, complemented
15#36971C212yesmaximal, complemented
16#36765C212yesmaximal, complemented
17#36551C212yesmaximal, complemented
18#36148C212yesmaximal, complemented
19#35270C212yesmaximal, complemented
20#35173C211yesmaximal, characteristic, complemented
21#35013C211yesmaximal, characteristic, complemented
22#35012C211yesmaximal, characteristic, complemented
23#35004C211yesmaximal, characteristic, complemented
24#35004C211yesmaximal, characteristic, complemented
25#34575C211yesmaximal, characteristic
26#34425C212yesmaximal, complemented
27C2×#2373C211yesmaximal, characteristic, complemented
28C2×#539C2212yes—
29C2×#539C2212yes—
30C2×#533C2212yes—
31C22×#126C2211yescharacteristic
32C2×#525C2212yes—
33#2857C2212yes—
34#2857C2212yes—
35#2855C2212yes—
36#2854C2212yes—
37#2854C2212yes—
38#2851C2212yes—
39#2851C2212yes—
40#2850C2212yes—
41#2850C2212yes—
42#2848C2212yes—
43#2803C2214yes—
44#2803C2214yes—
45#2802C2214yescomplemented
46#2801C2214yes—
47#2800C2214yes—
48#2800C2214yes—
49#2800C2214yescomplemented
50#2798C2214yes—
51#2795C2214yes—
52#2783C2214yes—
53#2779C2214yes—
54#2777C2214yes—
55#2777C2214yescomplemented
56#2772C2214yescomplemented
57#2758C2214yescomplemented
58#2754C2214yes—
59#2745C2214yescomplemented
60#2740C2214yescomplemented
61#2731C2214yes—
62#2731C2214yes—
63#2729C2214yescomplemented
64#2727C2214yes—
65#2727C2214yes—
66#2725C2214yes—
67#2725C2214yes—
68#2725C2214yescomplemented
69#2720C2214yes—
70#2719C2214yescomplemented
71#2718C2214yes—
72#2716C2214yescomplemented
73#2712C2214yes—
74#2708C2214yes—
75#2707C2214yescomplemented
76#2705C2214yes—
77#2705C2214yes—
78#2705C2214yes—
79#2702C2214yes—
80#2702C2214yes—
81#2695C2214yes—
82#2680C2214yes—
83#2663C2214yes—
84#2661C2214yes—
85#2659C2211yescharacteristic
86#2659C2212yes—
87#2659C2211yescharacteristic
88#2659C2211yescharacteristic
89#2656C2211yescharacteristic
90#2647C2212yescomplemented
91#2645C2212yescomplemented
92#2644C2212yescomplemented
93#2640C2212yescomplemented
94#2639C2212yes—
95#2627C2212yes—
96#2626C2212yes—
97#2618C2212yes—
98#2618C2212yes—
99#2617C2212yes—
100#2617C2212yes—
101#2608C2214yescomplemented
102#2604C2214yescomplemented
103#2602C2214yes—
104#2594C2214yes—
105#2590C2214yescomplemented
106#2589C2214yescomplemented
107#2589C2214yescomplemented
108#2587C2214yescomplemented
109#2586C2214yescomplemented
110#2585C2214yescomplemented
111#2584C2214yescomplemented
112#2584C2214yescomplemented
113#2577C2214yescomplemented
114#2574C2214yes—
115#2567C2214yescomplemented
116#2563C2212yescomplemented
117#2558C2214yes—
118#2558C2214yes—
119#2556C2214yes—
120#2556C2214yescomplemented
121#2556C2214yescomplemented
122#2554C2214yescomplemented
123#2554C2214yescomplemented
124#2552C2212yescomplemented
125#2546C2214yescomplemented
126#2534C2214yes—
127#2532C2214yes—
128#2532C2214yescomplemented
129#2530C2214yescomplemented
130#2529C2214yescomplemented
131#2528C2214yescomplemented
132#2527C2214yescomplemented
133#2526C2214yes—
134#2522C2214yes—
135#2521C2214yescomplemented
136#2520C2214yescomplemented
137#2519C2214yescomplemented
138#2519C2214yescomplemented
139#2518C2214yes—
140#2518C2214yes—
141#2510C2214yes—
142#2509C2212yescomplemented
143#2509C2212yescomplemented
144#2497C2214yescomplemented
145#2491C2212yes—
146#2488C2214yes—
147#2487C2214yes—
148#2481C2214yes—
149#2475C2214yes—
150#2472C2214yes—
151#2469C2214yescomplemented
152#2468C2214yes—
153#2466C2214yescomplemented
154#2465C2214yes—
155#2462C2214yescomplemented
156#2461C2214yescomplemented
157#2461C2214yescomplemented
158#2460C2214yes—
159#2459C2214yes—
160#2458C2214yes—
161#2458C2214yescomplemented
162#2454C2212yescomplemented
163#2454C2212yescomplemented
164#2453C2214yescomplemented
165#2450C2214yes—
166#2450C2214yes—
167#2449C2214yes—
168#2439C2212yes—
169#2432C2212yes—
170#2429C2212yes—
171#2426C2212yes—
172#2421C2212yes—
173#2421C2214yescomplemented
174#2419C2214yes—
175#2418C2214yes—
176#2413C2214yes—
177#2411C2214yes—
178#2406C2214yes—
179#2395C2214yes—
180#2388C2214yes—
181#2383C2214yescomplemented
182#2378C2214yescomplemented
183#2373C2214yes—
184#2373C2214yes—
185#2373C2214yes—
186#2373C2214yes—
187#2373C2214yescomplemented
188#2369C2212yescomplemented
189#2367C2214yes—
190#2362C2212yes—
191#2360C2214yescomplemented
192#2359C2214yes—
193#2359C2214yes—
194#2353C2214yes—
195D4×C4⋊C4C2214yes—
196D4×C4⋊C4C2212yescomplemented
197#2345C2214yescomplemented
198#2341C2212yes—
199#2336C2214yescomplemented
200#2335C2214yescomplemented
201#2331C2212yescomplemented
202#2330C2214yescomplemented
203#2329C2212yes—
204#2329C2212yes—
205#2326C2212yescomplemented
206#2325C2212yes—
207#2325C2212yes—
208#2322C2214yescomplemented
209#2320C2212yescomplemented
210#2319C2212yescomplemented
211#2316C2212yes—
212#2316C2212yes—
213#2313C2212yes—
214#2312C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×C22⋊Q8C2212yes—
217C4×#121C2212yes—
218C4×#121C2212yes—
219C4×#121C2212yes—
220C4×#121C2212yes—
221C2×#389C2211yescharacteristic
222C2×#388C2211yescharacteristic
223C2×#388C2211yescharacteristic
224C2×#388C2211yescharacteristic
225C2×#387C2211yescharacteristic
226C2×#387C2211yescharacteristic
227C2×#387C2211yescharacteristic
228C2×#385C2211yescharacteristic
229C2×C4×C4⋊C4C2211yescharacteristic
230C2×C4×C4⋊C4C2211yescharacteristic
231C2×C4×C4⋊C4C2211yescharacteristic
232C2×C4×C22⋊C4C2211yescharacteristic
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×#376C2211yescharacteristic
235C22×#41C2312yes—
236C24×C4C2311yescharacteristic
237#539—216no—
238#539—48no—
239#533—48no—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244C2×#126—28no—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#125C2314yes—
251C2×#125C2314yes—
252C2×#125C2314yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#124C2312yes—
256C2×#124C2314yes—
257C2×#124C2312yes—
258#525—48no—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#120C2314yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×#117C2314yes—
293C2×#117C2312yes—
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2311yescharacteristic
302C22×C4⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317#401C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2314yes—
413#391C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#390C2312yes—
425#390C2312yes—
426#390C2314yes—
427#390C2314yes—
428#390C2312yes—
429#390C2314yes—
430#390C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#384C2312yes—
584#384C2312yes—
585#384C2314yes—
586#383C2314yes—
587#383C2314yes—
588#382C2312yes—
589#382C2312yes—
590#382C2314yes—
591#382C2312yes—
592#382C2312yes—
593#381C2314yes—
594#381C2314yes—
595#381C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2312yes—
599#380C2312yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2314yes—
604#380C2314yes—
605#380C2312yes—
606#380C2314yes—
607#380C2312yes—
608#380C2312yes—
609#380C2314yes—
610#380C2314yes—
611#379C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2312yes—
646#376C2312yes—
647#376C2312yes—
648#376C2314yes—
649#376C2312yes—
650#376C2312yes—
651C2×#95C2311yescharacteristic
652C2×#95C2311yescharacteristic
653C2×#95C2311yescharacteristic
654C2×#95C2311yescharacteristic
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2311yescharacteristic
660C2×#95C2311yescharacteristic
661C2×#95C2311yescharacteristic
662C2×#95C2311yescharacteristic
663C25C2411yescharacteristic
664C2×#41—44no—
665C2×#41—44no—
666C2×#41—82no—
667C22×Q8C2412yes—
668C22×Q8C2412yes—
669C22×Q8C2412yes—
670C22×Q8C2414yes—
671C22×D4C2414yes—
672C22×D4C2412yes—
673C22×D4C2412yes—
674C22×D4C2412yes—
675C22×D4C2414yes—
676C22×D4C2414yes—
677C23×C4—24no—
678C23×C4—42no—
679C23×C4—81no—
680C23×C4C2411yescharacteristic
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2414yes—
692C23×C4C2414yes—
693C23×C4C2412yes—
694C23×C4C2414yes—
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C4⋊Q8—44no—
700C4⋊Q8—44no—
701C4⋊Q8—44no—
702C4⋊Q8—44no—
703#126—216no—
704#126—216no—
705#126—216no—
706#126—48no—
707#126—84no—
708#125—216no—
709#125—48no—
710#125—48no—
711#125—82no—
712#125—82no—
713#124—44no—
714#124—48no—
715#124—82no—
716#123—216no—
717#123—216no—
718#123—48no—
719#123—48no—
720#123—48no—
721#123—84no—
722C22⋊Q8—28no—
723C22⋊Q8—28no—
724C22⋊Q8—28no—
725C22⋊Q8—216no—
726C22⋊Q8—48no—
727C22⋊Q8—48no—
728C22⋊Q8—44no—
729C22⋊Q8—44no—
730C22⋊Q8—82no—
731#121—28no—
732#121—28no—
733#121—28no—
734#121—44no—
735#120—48no—
736C4×Q8—44no—
737C4×Q8—48no—
738C4×Q8—44no—
739C4×Q8—44no—
740C4×Q8—82no—
741C4×D4—216no—
742C4×D4—44no—
743C4×D4—44no—
744C4×D4—48no—
745C4×D4—48no—
746C4×D4—48no—
747C4×D4—82no—
748C4×D4—82no—
749#117—48no—
750#117—44no—
751C2×C4⋊C4—24no—
752C2×C4⋊C4—24no—
753C2×C4⋊C4—24no—
754C2×C4⋊C4—24no—
755C2×C4⋊C4—24no—
756C2×C4⋊C4—42no—
757C2×C4⋊C4—48no—
758C2×C4⋊C4—81no—
759C2×C4⋊C4#4118yescomplemented
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C22⋊C4—24no—
816C2×C22⋊C4—24no—
817C2×C22⋊C4—24no—
818C2×C22⋊C4—24no—
819C2×C22⋊C4—42no—
820C2×C22⋊C4—81no—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C42—24no—
861C2×C42—24no—
862C2×C42—42no—
863C2×C42—42no—
864C2×C42—42no—
865C2×C42—81no—
866C2×C42—81no—
867C2×C42—81no—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2412yes—
908#95C2414yes—
909#95C2412yes—
910#95C2414yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951C24—22no—
952C24—22no—
953C24—22no—
954C24—41no—
955C24—41no—
956C24—41no—
957C24—41no—
958C24C2512yes—
959C24C2514yes—
960C24C2511yescharacteristic
961#41—816no—
962C2×Q8—24no—
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—28no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—44no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—42no—
973C2×Q8—44no—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—28no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—42no—
981C2×D4—42no—
982C2×D4—44no—
983C2×D4—42no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—42no—
987C2×D4—44no—
988C2×D4—42no—
989C2×D4—44no—
990C2×D4—42no—
991C2×D4—44no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—24no—
1006C22×C4—22no—
1007C22×C4—22no—
1008C22×C4—24no—
1009C22×C4—28no—
1010C22×C4—24no—
1011C22×C4—28no—
1012C22×C4—41no—
1013C22×C4—41no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—42no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—44no—
1034C22×C4—41no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—41no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—88no—
1045C22×C4C2×#4114yes—
1046C22×C4C2×#4114yes—
1047C22×C4C2×#4114yes—
1048C22×C4H(5,𝔽2)14yes—
1049C22×C42−1+414yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2512yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—28no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4C2×#41116yes—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—24no—
1144C22⋊C4—28no—
1145C22⋊C4—42no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C42—24no—
1169C42—24no—
1170C42—28no—
1171C42—24no—
1172C42—24no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—42no—
1177C42—42no—
1178C42—42no—
1179C42—42no—
1180C42—42no—
1181C42—42no—
1182C42—42no—
1183C42—42no—
1184C42—42no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—22no—
1198C23—24no—
1199C23—24no—
1200C23—22no—
1201C23—22no—
1202C23—24no—
1203C23—22no—
1204C23—24no—
1205C23—22no—
1206C23—24no—
1207C23—24no—
1208C23—22no—
1209C23—24no—
1210C23—22no—
1211C23—44no—
1212C23—44no—
1213C23—44no—
1214C23—82no—
1215C23—82no—
1216C23—82no—
1217C23—82no—
1218C23C22×#4112yes—
1219C23C2×H(5,𝔽2)12yes—
1220C23C2×2−1+412yes—
1221C23C2611yescharacteristic
1222Q8—48no—
1223Q8—84no—
1224Q8—84no—
1225Q8—88no—
1226D4—48no—
1227D4—416no—
1228D4—84no—
1229D4—84no—
1230D4—88no—
1231D4—88no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—28no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—21no—
1298C2×C4—44no—
1299C2×C4—44no—
1300C2×C4—44no—
1301C2×C4—44no—
1302C2×C4—48no—
1303C2×C4—44no—
1304C2×C4—44no—
1305C2×C4—44no—
1306C2×C4—44no—
1307C2×C4—44no—
1308C2×C4—88no—
1309C2×C4—84no—
1310C2×C4—88no—
1311C2×C4—82no—
1312C2×C4—82no—
1313C2×C4—82no—
1314C2×C4—82no—
1315C2×C4—164no—
1316C2×C4C22×#4114yes—
1317C2×C4C22×#4114yes—
1318C2×C4C22×#4114yes—
1319C2×C4C2×H(5,𝔽2)14yes—
1320C2×C4C2×2−1+414yes—
1321C2×C4#58512yes—
1322C2×C4#58512yes—
1323C22—22no—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—44no—
1330C22—42no—
1331C22—44no—
1332C22—42no—
1333C22—44no—
1334C22—42no—
1335C22—42no—
1336C22—44no—
1337C22—44no—
1338C22—42no—
1339C22—42no—
1340C22—44no—
1341C22—44no—
1342C22—42no—
1343C22—88no—
1344C22#351114yes—
1345C22C23×#4111yescharacteristic
1346C22C22×H(5,𝔽2)11yescharacteristic
1347C22C22×2−1+411yescharacteristic
1348C22C2×#58511yescharacteristic
1349C22C2×#58511yescharacteristic
1350C22H(7,𝔽2)11yescharacteristic
1351C222−1+611yescharacteristic
1352C4—24no—
1353C4—24no—
1354C4—24no—
1355C4—22no—
1356C4—24no—
1357C4—24no—
1358C4—22no—
1359C4—44no—
1360C4—42no—
1361C4—44no—
1362C4—44no—
1363C4—41no—
1364C4—41no—
1365C4—42no—
1366C4—41no—
1367C4—42no—
1368C4—44no—
1369C4—44no—
1370C4—42no—
1371C4—42no—
1372C4—41no—
1373C4—44no—
1374C4—44no—
1375C4—42no—
1376C2—24no—
1377C2—84no—
1378C2—82no—
1379C2#6278111yescharacteristic
1380C2C2×#351111yescharacteristic
1381C2#6285111yescharacteristic
1382C2#6290011yescharacteristic
1383C2#6290211yescharacteristic
1384C2#6292711yescharacteristic
1385C2#6293211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34575C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50430C2semidirect
2. #50410C2semidirect
3. #49252C2semidirect
4. #49224C2semidirect
5. #44269C2semidirect
6. #44217C2semidirect
7. #44041C2semidirect
8. #43970C2semidirect
9. #39798C2semidirect
10. #39551C2semidirect
11. #39549C2semidirect
12. #39499C2semidirect
13. #37760C2semidirect
14. #37708C2semidirect
15. #36971C2semidirect
16. #36765C2semidirect
17. #36551C2semidirect
18. #36148C2semidirect
19. #35270C2semidirect
20. #35173C2semidirect
21. #35013C2semidirect
22. #35012C2semidirect
23. #35004C2semidirect
24. #35004C2semidirect
26. #34425C2semidirect
27. C2×#2373C2semidirect
45. #2802C22semidirect
49. #2800C22semidirect
55. #2777C22semidirect
56. #2772C22semidirect
57. #2758C22semidirect
59. #2745C22semidirect
60. #2740C22semidirect
63. #2729C22semidirect
68. #2725C22semidirect
70. #2719C22semidirect
72. #2716C22semidirect
75. #2707C22semidirect
90. #2647C22semidirect
91. #2645C22semidirect
92. #2644C22semidirect
93. #2640C22semidirect
101. #2608C22semidirect
102. #2604C22semidirect
105. #2590C22semidirect
106. #2589C22semidirect
107. #2589C22semidirect
108. #2587C22semidirect
109. #2586C22semidirect
110. #2585C22semidirect
111. #2584C22semidirect
112. #2584C22semidirect
113. #2577C22semidirect
115. #2567C22semidirect
116. #2563C22semidirect
120. #2556C22semidirect
121. #2556C22semidirect
122. #2554C22semidirect
123. #2554C22semidirect
124. #2552C22semidirect
125. #2546C22semidirect
128. #2532C22semidirect
129. #2530C22semidirect
130. #2529C22semidirect
131. #2528C22semidirect
132. #2527C22semidirect
135. #2521C22semidirect
136. #2520C22semidirect
137. #2519C22semidirect
138. #2519C22semidirect
142. #2509C22semidirect
143. #2509C22semidirect
144. #2497C22semidirect
151. #2469C22semidirect
153. #2466C22semidirect
155. #2462C22semidirect
156. #2461C22semidirect
157. #2461C22semidirect
161. #2458C22semidirect
162. #2454C22semidirect
163. #2454C22semidirect
164. #2453C22semidirect
173. #2421C22semidirect
181. #2383C22semidirect
182. #2378C22semidirect
187. #2373C22semidirect
188. #2369C22semidirect
191. #2360C22semidirect
196. D4×C4⋊C4C22semidirect
197. #2345C22semidirect
199. #2336C22semidirect
200. #2335C22semidirect
201. #2331C22semidirect
202. #2330C22semidirect
205. #2326C22semidirect
208. #2322C22semidirect
209. #2320C22semidirect
210. #2319C22semidirect
759. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
#504302
#504102
#492522
#492242
#442692
#442172
#440412
#439702
#397982
#395512
#395492
#394992
#377602
#377082
#369712
#367652
#365512
#361482
#352702
#351732
#350132
#350122
#350042
#345752
#344252
C2×#23732