Finite Group Databasebeta

← #8934656

Subgroups — #8934656

Order 512.

5534 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60048C211yesmaximal, characteristic, complemented
2#60047C211yesmaximal, characteristic, complemented
3#60044C212yesmaximal, complemented
4#59991C214yesmaximal, complemented
5#59948C212yesmaximal, complemented
6#59923C212yesmaximal, complemented
7#52076C212yesmaximal, complemented
8#52075C212yesmaximal, complemented
9#51952C214yesmaximal, complemented
10#51926C214yesmaximal, complemented
11#51605C214yesmaximal, complemented
12#51573C214yesmaximal, complemented
13#51542C212yesmaximal, complemented
14#51541C212yesmaximal, complemented
15#50358C214yesmaximal, complemented
16#49985C214yesmaximal, complemented
17#49565C214yesmaximal, complemented
18#47567C212yesmaximal, complemented
19#47564C214yesmaximal, complemented
20#35666C211yesmaximal, characteristic, complemented
21#35660C212yesmaximal, complemented
22#35600C214yesmaximal, complemented
23#35574C212yesmaximal, complemented
24C22×2−1+4C2211yescharacteristic
25C2×#563C2212yes—
26C2×#562C2212yes—
27C2×#537C2212yes—
28C2×#536C2212yes—
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#532C2212yes—
32C22×C4⋊Q8C2211yescharacteristic
33C2×#520C2212yes—
34#2841C2212yes—
35#2811C2211yescharacteristic
36#2809C2211yescharacteristic
37#2808C2212yes—
38#2806C2214yes—
39#2806C2212yes—
40#2797C2214yes—
41#2790C2214yes—
42#2790C2214yes—
43#2781C2214yes—
44#2779C2214yes—
45#2775C2214yes—
46#2768C2214yes—
47#2768C2214yes—
48#2764C2212yes—
49#2761C2214yes—
50#2757C2214yes—
51#2752C2212yes—
52#2748C2214yes—
53#2734C2212yes—
54#2734C2211yescharacteristic
55#2733C2211yescharacteristic
56#2733C2212yes—
57#2732C2212yes—
58#2731C2212yes—
59#2730C2214yes—
60#2730C2214yes—
61#2729C2214yes—
62#2729C2214yes—
63#2727C2212yes—
64#2717C2214yes—
65#2715C2214yes—
66#2707C2214yes—
67#2706C2214yes—
68#2705C2214yes—
69#2704C2214yes—
70#2704C2214yes—
71#2702C2214yes—
72#2701C2214yes—
73#2701C2214yes—
74#2700C2214yes—
75#2698C2214yes—
76#2698C2214yes—
77#2691C2214yes—
78#2687C2214yes—
79#2686C2214yes—
80#2683C2214yes—
81#2682C2214yes—
82#2682C2212yes—
83#2681C2214yes—
84#2681C2214yes—
85#2680C2214yes—
86#2680C2214yes—
87#2672C2214yes—
88#2671C2214yes—
89#2662C2214yes—
90#2662C2214yes—
91#2661C2214yes—
92#2660C2212yes—
93#2660C2214yes—
94#2640C2212yes—
95#2620C2214yes—
96#2612C2214yes—
97#2612C2214yes—
98#2611C2212yes—
99#2611C2214yes—
100#2610C2212yes—
101#2610C2214yes—
102#2609C2214yes—
103#2601C2214yes—
104#2601C2214yes—
105#2600C2212yes—
106#2600C2214yes—
107#2593C2212yes—
108#2586C2214yes—
109#2586C2214yes—
110#2586C2214yes—
111#2583C2214yes—
112#2579C2214yes—
113#2579C2214yes—
114#2579C2214yes—
115#2574C2214yes—
116#2574C2214yes—
117#2560C2214yes—
118#2558C2214yes—
119#2556C2214yes—
120#2556C2214yes—
121#2555C2212yes—
122#2555C2214yes—
123#2554C2214yes—
124#2553C2214yes—
125#2553C2214yes—
126#2549C2214yes—
127#2549C2214yes—
128#2532C2214yes—
129#2532C2214yes—
130#2526C2214yes—
131#2518C2214yes—
132#2488C2214yes—
133#2479C2214yes—
134#2479C2214yes—
135#2476C2214yes—
136#2476C2214yes—
137#2474C2214yes—
138#2474C2214yes—
139#2471C2214yes—
140#2467C2214yes—
141#2464C2214yes—
142#2464C2214yes—
143#2461C2214yes—
144#2461C2214yes—
145#2452C2214yes—
146#2452C2214yes—
147#2451C2214yes—
148#2451C2214yes—
149#2451C2214yes—
150#2445C2214yes—
151#2440C2214yes—
152#2440C2214yes—
153#2440C2214yes—
154#2439C2214yes—
155#2439C2214yes—
156#2436C2212yes—
157#2436C2212yes—
158#2434C2212yes—
159#2434C2212yes—
160#2434C2212yes—
161#2434C2212yes—
162#2434C2214yes—
163#2432C2212yes—
164#2432C2212yes—
165#2432C2212yes—
166#2432C2214yes—
167#2432C2212yes—
168#2431C2214yes—
169#2431C2212yes—
170#2431C2212yes—
171#2430C2214yes—
172#2430C2214yes—
173#2430C2214yes—
174#2430C2214yes—
175#2426C2214yes—
176#2425C2214yes—
177#2422C2214yes—
178#2416C2214yes—
179#2413C2214yes—
180#2409C2214yes—
181#2409C2214yes—
182#2409C2214yes—
183#2407C2214yes—
184#2407C2214yes—
185#2407C2214yes—
186#2407C2214yes—
187#2406C2214yes—
188#2406C2214yes—
189#2406C2214yes—
190#2379C2214yes—
191#2379C2214yes—
192#2373C2214yes—
193#2372C2212yes—
194#2372C2212yes—
195#2372C2214yes—
196#2369C2212yes—
197#2369C2212yes—
198#2368C2214yes—
199#2368C2214yes—
200#2363C2214yes—
201#2359C2214yes—
202#2343C2214yes—
203#2326C2214yes—
204#2324C2214yes—
205#2319C2214yes—
206#2317C2212yes—
207#2316C2212yes—
208#2311C2212yes—
209#2311C2212yes—
210#2310C2211yescharacteristic
211C4×C22⋊Q8C2214yes—
212#2297C2212yes—
213#2297C2211yescharacteristic
214#2297C2211yescharacteristic
215#2297C2212yes—
216#2296C2212yes—
217C2×#391C2212yes—
218#2290C2214yes—
219C2×2−1+4—44no—
220C2×2−1+4—44no—
221C2×2−1+4—44no—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2311yescharacteristic
225C22×#41C2311yescharacteristic
226C22×#41C2312yes—
227C22×#41C2312yes—
228C22×#41C2312yes—
229C22×#41C2312yes—
230C23×Q8C2311yescharacteristic
231C23×Q8C2312yes—
232C23×Q8C2312yes—
233C23×Q8C2311yescharacteristic
234#563—48no—
235#562—48no—
236#537—48no—
237#536—44no—
238#536—48no—
239#536—44no—
240#532—48no—
241C2×C4⋊Q8—44no—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2314yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×#127C2312yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#125C2312yes—
255C2×#125C2314yes—
256C2×#124C2314yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295#520—48no—
296C2×C4×Q8C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×#117C2311yescharacteristic
303C2×#117C2311yescharacteristic
304C2×#117C2312yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2314yes—
309C2×#117C2314yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2314yes—
314C22×C42C2311yescharacteristic
315C22×C42C2312yes—
316#400C2314yes—
317#400C2312yes—
318#400C2314yes—
319#400C2314yes—
320#399C2312yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#397C2314yes—
343#397C2312yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2312yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2312yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2312yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#392C2312yes—
409#392C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#391C2314yes—
417#391C2312yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#391C2311yescharacteristic
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2311yescharacteristic
440#391C2312yes—
441#390C2314yes—
442#390C2312yes—
443#390C2314yes—
444#390C2312yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2311yescharacteristic
451#390C2314yes—
452#390C2312yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#390C2311yescharacteristic
457#390C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
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#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
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#384C2314yes—
580#384C2314yes—
581#383C2314yes—
582#382C2314yes—
583#382C2314yes—
584#382C2314yes—
585#382C2314yes—
586#381C2312yes—
587#381C2312yes—
588#381C2314yes—
589#381C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2314yes—
620#376C2314yes—
621#376C2314yes—
622#376C2312yes—
623#376C2312yes—
624C2×#95C2314yes—
625C2×#95C2314yes—
6262−1+4—464no—
627C2×#41—24no—
628C2×#41—28no—
629C2×#41—24no—
630C2×#41—28no—
631C2×#41—28no—
632C2×#41—44no—
633C2×#41—44no—
634C2×#41—42no—
635C2×#41—42no—
636C2×#41—44no—
637C2×#41—44no—
638C2×#41—42no—
639C2×#41—42no—
640C2×#41—44no—
641C2×#41—44no—
642C2×#41—44no—
643C2×#41—44no—
644C2×#41—44no—
645C2×#41—44no—
646C2×#41—44no—
647C2×#41—44no—
648C2×#41—44no—
649C2×#41—44no—
650C2×#41—44no—
651C22×Q8—28no—
652C22×Q8—24no—
653C22×Q8—44no—
654C22×Q8—42no—
655C22×Q8—44no—
656C22×Q8—42no—
657C22×Q8—42no—
658C22×Q8—44no—
659C22×Q8—44no—
660C22×Q8—44no—
661C22×Q8—42no—
662C22×Q8—42no—
663C22×Q8C2412yes—
664C22×Q8C2412yes—
665C22×Q8C2412yes—
666C22×Q8C2412yes—
667C22×Q8C2412yes—
668C22×Q8C2412yes—
669C22×Q8C2412yes—
670C22×Q8C2411yescharacteristic
671C22×Q8C2412yes—
672C22×Q8C2411yescharacteristic
673C22×Q8C2412yes—
674C22×D4C2414yes—
675C22×D4C2412yes—
676C22×D4C2412yes—
677C22×D4C2412yes—
678C22×D4C2412yes—
679C22×D4C2414yes—
680C22×D4C2414yes—
681C22×D4C2414yes—
682C22×D4C2412yes—
683C22×D4C2412yes—
684C22×D4C2411yescharacteristic
685C22×D4C2414yes—
686C22×D4C2412yes—
687C22×D4C2411yescharacteristic
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C23×C4C2414yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2411yescharacteristic
697C23×C4C2414yes—
698C23×C4C2414yes—
699C23×C4C2412yes—
700C23×C4C2414yes—
701C23×C4C2414yes—
702C23×C4C2412yes—
703C23×C4C2411yescharacteristic
704C4⋊Q8—28no—
705C4⋊Q8—28no—
706C4⋊Q8—44no—
707C4⋊Q8—44no—
708C4⋊Q8—44no—
709C4⋊Q8—48no—
710C4⋊Q8—44no—
711C4⋊Q8—44no—
712#127—44no—
713#126—48no—
714#126—48no—
715#126—48no—
716#125—44no—
717#125—48no—
718#124—28no—
719#124—216no—
720#124—28no—
721#124—48no—
722#124—44no—
723#124—44no—
724#124—44no—
725#124—44no—
726#124—44no—
727#123—48no—
728#123—48no—
729#123—48no—
730#123—48no—
731#123—48no—
732#123—48no—
733#123—48no—
734#123—48no—
735C22⋊Q8—216no—
736C22⋊Q8—44no—
737C22⋊Q8—44no—
738C22⋊Q8—44no—
739C22⋊Q8—48no—
740C22⋊Q8—48no—
741C22⋊Q8—48no—
742C22⋊Q8—48no—
743C22⋊Q8—48no—
744C22⋊Q8—48no—
745C22⋊Q8—48no—
746C22⋊Q8—48no—
747C22⋊Q8—44no—
748#121—216no—
749#121—48no—
750#121—44no—
751#121—48no—
752#121—48no—
753#121—48no—
754#121—48no—
755#121—44no—
756#121—48no—
757C4×Q8—48no—
758C4×D4—216no—
759C4×D4—48no—
760C4×D4—48no—
761C4×D4—48no—
762C4×D4—48no—
763#117—44no—
764#117—42no—
765#117—44no—
766#117—42no—
767#117—48no—
768#117—48no—
769#117—44no—
770#117—44no—
771C2×C4⋊C4—28no—
772C2×C4⋊C4—48no—
773C2×C4⋊C4—44no—
774C2×C4⋊C4—44no—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C42—44no—
866C2×C42—42no—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2412yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2411yescharacteristic
883C2×C42C2412yes—
884C2×C42C2411yescharacteristic
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2412yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2412yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2412yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
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—
931C24C2514yes—
932C24C2512yes—
933C24C2512yes—
934C24C2511yescharacteristic
935#41—432no—
936#41—416no—
937#41—416no—
938#41—432no—
939#41—432no—
940#41—432no—
941#41—432no—
942#41—816no—
943C2×Q8—24no—
944C2×Q8—24no—
945C2×Q8—24no—
946C2×Q8—24no—
947C2×Q8—24no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—22no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—42no—
955C2×Q8—41no—
956C2×Q8—42no—
957C2×Q8—41no—
958C2×Q8—41no—
959C2×Q8—42no—
960C2×Q8—42no—
961C2×Q8—42no—
962C2×Q8—42no—
963C2×Q8—41no—
964C2×Q8—42no—
965C2×Q8—42no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—44no—
973C2×Q8—416no—
974C2×Q8—432no—
975C2×Q8—432no—
976C2×Q8—88no—
977C2×Q8H(5,𝔽2)14yes—
978C2×Q82−1+418yescomplemented
979C2×D4—28no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—28no—
986C2×D4—28no—
987C2×D4—24no—
988C2×D4—24no—
989C2×D4—22no—
990C2×D4—24no—
991C2×D4—28no—
992C2×D4—24no—
993C2×D4—28no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—44no—
997C2×D4—41no—
998C2×D4—41no—
999C2×D4—42no—
1000C2×D4—41no—
1001C2×D4—41no—
1002C2×D4—42no—
1003C2×D4—42no—
1004C2×D4—42no—
1005C2×D4—42no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—42no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—42no—
1014C2×D4—44no—
1015C2×D4—42no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4H(5,𝔽2)14yes—
1020C22×C4—24no—
1021C22×C4—22no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—22no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—28no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—28no—
1040C22×C4—28no—
1041C22×C4—28no—
1042C22×C4—28no—
1043C22×C4—44no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—41no—
1048C22×C4—42no—
1049C22×C4—41no—
1050C22×C4—42no—
1051C22×C4—41no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—41no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4H(5,𝔽2)14yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2514yes—
1079C22×C4C2514yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—41no—
1113C4⋊C4—41no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C22⋊C4—28no—
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—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
1156C22⋊C4—44no—
1157C22⋊C4—42no—
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—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C42—28no—
1178C42—24no—
1179C42—24no—
1180C42—24no—
1181C42—24no—
1182C42—28no—
1183C42—28no—
1184C42—42no—
1185C42—42no—
1186C42—41no—
1187C42—42no—
1188C42—41no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C23—22no—
1196C23—21no—
1197C23—21no—
1198C23—22no—
1199C23—24no—
1200C23—22no—
1201C23—24no—
1202C23—22no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23C2×H(5,𝔽2)14yes—
1216C23C2×H(5,𝔽2)12yes—
1217C23C2611yescharacteristic
1218Q8—44no—
1219Q8—48no—
1220Q8—48no—
1221Q8—48no—
1222Q8—48no—
1223Q8—48no—
1224Q8—44no—
1225Q8—84no—
1226Q8—84no—
1227Q8—84no—
1228Q8—162no—
1229D4—44no—
1230D4—416no—
1231D4—48no—
1232D4—48no—
1233D4—48no—
1234D4—44no—
1235D4—48no—
1236D4—48no—
1237D4—88no—
1238D4—84no—
1239D4—88no—
1240D4—88no—
1241D4—164no—
1242D4—162no—
1243C2×C4—28no—
1244C2×C4—216no—
1245C2×C4—216no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—44no—
1295C2×C4—48no—
1296C2×C4—416no—
1297C2×C4—48no—
1298C2×C4—48no—
1299C2×C4—48no—
1300C2×C4—44no—
1301C2×C4—48no—
1302C2×C4—88no—
1303C2×C4—88no—
1304C2×C4—88no—
1305C2×C4—84no—
1306C2×C4—164no—
1307C2×C4C2×H(5,𝔽2)12yes—
1308C2×C4C2×H(5,𝔽2)12yes—
1309C2×C4C2×H(5,𝔽2)14yes—
1310C2×C4C2×H(5,𝔽2)14yes—
1311C2×C4C2×2−1+418yes—
1312C2×C4C2×2−1+414yes—
1313C2×C4#58514yes—
1314C22—24no—
1315C22—24no—
1316C22—22no—
1317C22—24no—
1318C22—24no—
1319C22—41no—
1320C22—41no—
1321C22—44no—
1322C22—42no—
1323C22—44no—
1324C22—44no—
1325C22—42no—
1326C22—44no—
1327C22—42no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—42no—
1332C22—44no—
1333C22—44no—
1334C22—44no—
1335C22—44no—
1336C22C22×H(5,𝔽2)11yescharacteristic
1337C22C22×H(5,𝔽2)11yescharacteristic
1338C22C22×H(5,𝔽2)11yescharacteristic
1339C22C22×2−1+412yes—
1340C22C2×#58512yes—
1341C4—24no—
1342C4—24no—
1343C4—22no—
1344C4—22no—
1345C4—24no—
1346C4—24no—
1347C4—28no—
1348C4—44no—
1349C4—44no—
1350C4—42no—
1351C4—42no—
1352C4—44no—
1353C4—44no—
1354C4—44no—
1355C4—42no—
1356C4—42no—
1357C4—44no—
1358C4—44no—
1359C4—44no—
1360C2—44no—
1361C2—42no—
1362C2—84no—
1363C2—82no—
1364C2#6281711yescharacteristic
1365C2#6281912yes—
1366C2#6302411yescharacteristic
1367C2#6303711yescharacteristic
1368C2#6303912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60048C2semidirect
2. #60047C2semidirect
3. #60044C2semidirect
4. #59991C2semidirect
5. #59948C2semidirect
6. #59923C2semidirect
7. #52076C2semidirect
8. #52075C2semidirect
9. #51952C2semidirect
10. #51926C2semidirect
11. #51605C2semidirect
12. #51573C2semidirect
13. #51542C2semidirect
14. #51541C2semidirect
15. #50358C2semidirect
16. #49985C2semidirect
17. #49565C2semidirect
18. #47567C2semidirect
19. #47564C2semidirect
20. #35666C2semidirect
21. #35660C2semidirect
22. #35600C2semidirect
23. #35574C2semidirect
978. C2×Q82−1+4semidirect

Maximal subgroups

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

subgroupindex
#600482
#600472
#600442
#599912
#599482
#599232
#520762
#520752
#519522
#519262
#516052
#515732
#515422
#515412
#503582
#499852
#495652
#475672
#475642
#356662
#356602
#356002
#355742