Finite Group Databasebeta

← #8757571

Subgroups — #8757571

Order 512.

5258 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58173C214yesmaximal, complemented
2#58128C214yesmaximal, complemented
3#55284C214yesmaximal, complemented
4#55134C214yesmaximal, complemented
5#53909C214yesmaximal, complemented
6#53906C214yesmaximal, complemented
7#52054C211yesmaximal, characteristic, complemented
8#51992C212yesmaximal, complemented
9#51978C211yesmaximal, characteristic, complemented
10#51326C212yesmaximal, complemented
11#51317C212yesmaximal, complemented
12#50219C212yesmaximal, complemented
13#50200C212yesmaximal, complemented
14#47795C214yesmaximal, complemented
15#47660C212yesmaximal, complemented
16#46624C214yesmaximal, complemented
17#46426C212yesmaximal, complemented
18#45472C212yesmaximal, complemented
19#45469C214yesmaximal, complemented
20#45453C212yesmaximal, complemented
21#45446C214yesmaximal, complemented
22#35305C212yesmaximal, complemented
23#35149C211yesmaximal, characteristic
24C23×#41C2211yescharacteristic
25C2×#563C2212yes—
26C2×#563C2211yescharacteristic, complemented
27C2×#559C2211yescharacteristic, complemented
28C2×#544C2212yescomplemented
29C2×#536C2211yescharacteristic
30C2×#536C2212yes—
31C2×#536C2212yes—
32C2×#535C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×C22⋊Q8C2212yes—
35#2849C2214yes—
36#2848C2214yes—
37#2848C2214yes—
38#2841C2212yes—
39#2837C2214yescomplemented
40#2833C2212yescomplemented
41#2832C2214yescomplemented
42#2829C2214yescomplemented
43#2829C2214yescomplemented
44#2826C2214yescomplemented
45#2820C2214yescomplemented
46#2817C2212yes—
47#2817C2212yescomplemented
48#2814C2214yes—
49#2808C2214yescomplemented
50#2803C2214yescomplemented
51#2803C2214yescomplemented
52#2801C2214yescomplemented
53#2800C2214yescomplemented
54#2799C2212yescomplemented
55#2795C2214yescomplemented
56#2788C2214yescomplemented
57#2787C2214yescomplemented
58#2786C2214yescomplemented
59#2781C2214yescomplemented
60#2780C2214yescomplemented
61#2779C2214yescomplemented
62#2778C2214yescomplemented
63#2774C2214yescomplemented
64#2762C2214yescomplemented
65#2753C2214yescomplemented
66#2753C2214yescomplemented
67#2748C2212yescomplemented
68#2747C2214yescomplemented
69#2746C2214yescomplemented
70#2742C2214yescomplemented
71#2739C2214yescomplemented
72#2736C2212yes—
73#2735C2214yes—
74#2735C2214yes—
75#2735C2212yes—
76#2735C2214yes—
77#2734C2212yescomplemented
78#2731C2212yescomplemented
79#2731C2214yescomplemented
80#2730C2214yescomplemented
81#2729C2214yescomplemented
82#2729C2214yescomplemented
83#2728C2214yescomplemented
84#2724C2212yescomplemented
85#2723C2214yescomplemented
86#2720C2214yescomplemented
87#2720C2214yescomplemented
88#2718C2214yescomplemented
89#2717C2212yescomplemented
90#2713C2214yescomplemented
91#2713C2214yescomplemented
92#2712C2214yescomplemented
93#2710C2214yescomplemented
94#2709C2212yescomplemented
95#2709C2212yescomplemented
96#2707C2214yescomplemented
97#2704C2214yescomplemented
98#2704C2214yescomplemented
99#2702C2214yescomplemented
100#2700C2214yescomplemented
101#2698C2214yes—
102#2697C2212yes—
103#2694C2214yescomplemented
104#2691C2214yescomplemented
105#2690C2214yescomplemented
106#2690C2214yescomplemented
107#2689C2214yes—
108#2689C2214yescomplemented
109#2686C2214yescomplemented
110#2685C2214yes—
111#2685C2214yes—
112#2684C2214yes—
113#2684C2212yes—
114#2683C2214yescomplemented
115#2681C2214yescomplemented
116#2681C2214yescomplemented
117#2680C2214yes—
118#2677C2214yescomplemented
119#2677C2214yescomplemented
120#2674C2214yes—
121#2674C2214yescomplemented
122#2674C2214yescomplemented
123#2663C2214yescomplemented
124#2651C2214yescomplemented
125#2649C2214yescomplemented
126#2648C2214yescomplemented
127#2641C2212yescomplemented
128#2632C2212yescomplemented
129#2630C2214yescomplemented
130#2616C2214yes—
131#2616C2214yes—
132#2613C2214yes—
133#2612C2214yescomplemented
134#2611C2212yes—
135#2611C2214yescomplemented
136#2610C2214yescomplemented
137#2609C2214yescomplemented
138#2599C2212yes—
139#2595C2214yescomplemented
140#2593C2214yescomplemented
141#2586C2212yescomplemented
142#2583C2212yescomplemented
143#2577C2214yescomplemented
144#2575C2214yes—
145#2574C2214yescomplemented
146#2559C2214yescomplemented
147#2558C2214yes—
148#2558C2214yescomplemented
149#2556C2214yescomplemented
150#2556C2214yescomplemented
151#2551C2214yescomplemented
152#2531C2214yescomplemented
153#2531C2214yescomplemented
154#2530C2214yescomplemented
155#2527C2214yes—
156#2521C2214yescomplemented
157#2481C2214yescomplemented
158#2481C2214yescomplemented
159#2480C2214yes—
160#2480C2214yes—
161#2478C2214yes—
162#2478C2214yescomplemented
163#2477C2214yescomplemented
164#2475C2214yes—
165#2474C2214yescomplemented
166#2474C2214yescomplemented
167#2473C2214yescomplemented
168#2472C2214yes—
169#2471C2214yescomplemented
170#2470C2214yes—
171#2468C2214yescomplemented
172#2465C2214yescomplemented
173#2461C2214yescomplemented
174#2460C2214yescomplemented
175#2452C2214yescomplemented
176#2451C2214yescomplemented
177#2449C2214yescomplemented
178#2449C2214yescomplemented
179#2443C2214yescomplemented
180#2442C2214yescomplemented
181#2440C2214yescomplemented
182#2435C2214yes—
183#2434C2214yes—
184#2434C2214yescomplemented
185#2432C2212yes—
186#2432C2214yes—
187#2432C2212yes—
188#2432C2214yes—
189#2432C2212yes—
190#2431C2212yes—
191#2431C2212yes—
192#2418C2214yes—
193#2409C2214yescomplemented
194#2407C2214yes—
195#2407C2214yes—
196#2406C2212yes—
197#2406C2212yes—
198#2406C2212yes—
199#2406C2212yes—
200#2406C2212yes—
201#2405C2212yes—
202#2405C2212yes—
203#2405C2212yes—
204#2405C2212yes—
205#2380C2211yescharacteristic, complemented
206#2378C2214yes—
207#2376C2212yes—
208#2376C2212yescomplemented
209#2374C2212yescomplemented
210#2372C2211yescharacteristic, complemented
211#2332C2212yescomplemented
212#2331C2214yescomplemented
213#2311C2212yes—
214#2311C2212yes—
215#2310C2211yescharacteristic
216#2309C2211yescharacteristic
217#2280C2211yescharacteristic
218#2280C2212yes—
219C22×#41—44no—
220C22×#41—44no—
221C22×#41—44no—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C22×#41C2311yescharacteristic
227C23×Q8C2311yescharacteristic
228C23×Q8C2312yes—
229C23×D4C2311yescharacteristic
230C23×D4C2312yes—
231C24×C4C2311yescharacteristic
232C24×C4C2312yes—
233#563—48no—
234#563—44no—
235#559—44no—
236#544—48no—
237#536—44no—
238#536—48no—
239#536—48no—
240#535—44no—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2314yes—
246C2×C4⋊Q8C2312yes—
247C2×#127C2311yescharacteristic
248C2×#127C2311yescharacteristic
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#125C2314yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#124C2311yescharacteristic
257C2×#124C2314yes—
258C2×#124C2311yescharacteristic
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2314yes—
263#525—44no—
264C2×#123C2312yes—
265C2×#123C2312yes—
266C2×#123C2312yes—
267C2×#123C2314yes—
268C2×#123C2312yes—
269C2×#123C2312yes—
270C2×#123C2312yes—
271C2×#123C2312yes—
272C2×#123C2312yes—
273C2×#123C2312yes—
274C2×#123C2312yes—
275C2×#123C2312yes—
276C2×C22⋊Q8—48no—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#120C2314yes—
295C2×#120C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2311yescharacteristic
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2314yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C22⋊C4C2312yes—
310C22×C22⋊C4C2312yes—
311#401C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2312yes—
330#399C2314yes—
331#399C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2312yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#397C2312yes—
348#397C2312yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2312yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2312yes—
429#393C2314yes—
430#393C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#390C2314yes—
449#390C2312yes—
450#390C2312yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
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#388C2314yes—
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#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#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#386C2312yes—
539#386C2312yes—
540#386C2312yes—
541#386C2312yes—
542#386C2312yes—
543#386C2312yes—
544#386C2312yes—
545#386C2312yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2312yes—
555#386C2314yes—
556#386C2312yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
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#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#384C2314yes—
587#383C2312yes—
588#382C2314yes—
589#382C2314yes—
590#381C2312yes—
591#381C2312yes—
592#381C2314yes—
593#381C2312yes—
594#381C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#379C2314yes—
606#379C2314yes—
607#379C2314yes—
608#379C2314yes—
609#379C2314yes—
610#379C2312yes—
611#379C2312yes—
612#379C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2312yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2314yes—
623C4×C22⋊C4C2314yes—
624C4×C22⋊C4C2312yes—
625#376C2314yes—
626#376C2312yes—
627C25C2412yes—
628C25C2411yescharacteristic
629C2×#41—28no—
630C2×#41—28no—
631C2×#41—44no—
632C2×#41—44no—
633C2×#41—44no—
634C2×#41—44no—
635C2×#41—42no—
636C2×#41—44no—
637C2×#41—44no—
638C2×#41—42no—
639C2×#41—44no—
640C2×#41—44no—
641C2×#41—44no—
642C2×#41—44no—
643C2×#41—42no—
644C2×#41—464no—
645C22×Q8—24no—
646C22×Q8—42no—
647C22×Q8—44no—
648C22×Q8—42no—
649C22×Q8—44no—
650C22×Q8—44no—
651C22×Q8C2412yes—
652C22×Q8C2414yes—
653C22×Q8C2414yes—
654C22×Q8C2411yescharacteristic
655C22×Q8C2411yescharacteristic
656C22×Q8C2412yes—
657C22×Q8C2412yes—
658C22×Q8C2411yescharacteristic
659C22×D4—24no—
660C22×D4—42no—
661C22×D4—44no—
662C22×D4—42no—
663C22×D4—44no—
664C22×D4—44no—
665C22×D4C2412yes—
666C22×D4C2412yes—
667C22×D4C2414yes—
668C22×D4C2412yes—
669C22×D4C2411yescharacteristic
670C22×D4C2412yes—
671C22×D4C2412yes—
672C22×D4C2411yescharacteristic
673C22×D4C2414yes—
674C22×D4C2414yes—
675C22×D4C2412yes—
676C22×D4C2411yescharacteristic
677C23×C4—28no—
678C23×C4—24no—
679C23×C4—42no—
680C23×C4—42no—
681C23×C4—44no—
682C23×C4—44no—
683C23×C4C2412yes—
684C23×C4C2411yescharacteristic
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2412yes—
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2411yescharacteristic
699C4⋊Q8—216no—
700C4⋊Q8—48no—
701C4⋊Q8—44no—
702C4⋊Q8—48no—
703C4⋊Q8—48no—
704C4⋊Q8—44no—
705#127—24no—
706#127—42no—
707#126—48no—
708#126—48no—
709#126—48no—
710#125—48no—
711#125—44no—
712#125—48no—
713#125—48no—
714#124—24no—
715#124—42no—
716#124—48no—
717#124—48no—
718#124—48no—
719#124—44no—
720#124—44no—
721#123—28no—
722#123—28no—
723#123—28no—
724#123—44no—
725#123—48no—
726#123—44no—
727#123—44no—
728#123—44no—
729#123—44no—
730#123—44no—
731#123—44no—
732#123—44no—
733C22⋊Q8—28no—
734C22⋊Q8—216no—
735C22⋊Q8—48no—
736C22⋊Q8—48no—
737C22⋊Q8—48no—
738C22⋊Q8—48no—
739C22⋊Q8—48no—
740C22⋊Q8—48no—
741C22⋊Q8—44no—
742C22⋊Q8—48no—
743C22⋊Q8—48no—
744C22⋊Q8—48no—
745C22⋊Q8—44no—
746C22⋊Q8—48no—
747C22⋊Q8—44no—
748#121—44no—
749#121—48no—
750#120—44no—
751#120—48no—
752C4×Q8—44no—
753C4×D4—48no—
754C4×D4—48no—
755#117—42no—
756#117—44no—
757#117—48no—
758#117—42no—
759#117—44no—
760#117—42no—
761C2×C4⋊C4—44no—
762C2×C4⋊C4—44no—
763C2×C4⋊C4—44no—
764C2×C4⋊C4—44no—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C22⋊C4—44no—
810C2×C22⋊C4—44no—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C42C2414yes—
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2412yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924C24—24no—
925C24—22no—
926C24—24no—
927C24—42no—
928C24—41no—
929C24—41no—
930C24—44no—
931C24—44no—
932C24—44no—
933C24C2512yes—
934C24C2512yes—
935C24C2512yes—
936C24C2511yescharacteristic
937C24C2512yes—
938#41—432no—
939#41—432no—
940#41—432no—
941#41—432no—
942#41—88no—
943C2×Q8—22no—
944C2×Q8—24no—
945C2×Q8—24no—
946C2×Q8—28no—
947C2×Q8—28no—
948C2×Q8—22no—
949C2×Q8—41no—
950C2×Q8—41no—
951C2×Q8—41no—
952C2×Q8—42no—
953C2×Q8—41no—
954C2×Q8—42no—
955C2×Q8—44no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×Q8—41no—
959C2×Q8—44no—
960C2×Q8—41no—
961C2×Q8—44no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—416no—
966C2×Q8—816no—
967C2×Q8H(5,𝔽2)14yes—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—24no—
971C2×D4—28no—
972C2×D4—24no—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—24no—
976C2×D4—22no—
977C2×D4—22no—
978C2×D4—42no—
979C2×D4—42no—
980C2×D4—41no—
981C2×D4—41no—
982C2×D4—41no—
983C2×D4—41no—
984C2×D4—42no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—42no—
988C2×D4—42no—
989C2×D4—42no—
990C2×D4—42no—
991C2×D4—416no—
992C2×D4—44no—
993C2×D4—42no—
994C2×D4—41no—
995C2×D4—42no—
996C2×D4—41no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—432no—
1005C2×D4H(5,𝔽2)14yes—
1006C22×C4—22no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—42no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—416no—
1051C22×C4—432no—
1052C22×C4H(5,𝔽2)14yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2514yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
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—42no—
1165C22⋊C4—42no—
1166C42—28no—
1167C42—22no—
1168C42—22no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—42no—
1173C42—44no—
1174C42—42no—
1175C42—44no—
1176C42—44no—
1177C42—42no—
1178C42—42no—
1179C42—44no—
1180C23—21no—
1181C23—22no—
1182C23—21no—
1183C23—22no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—24no—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—48no—
1203C23—44no—
1204C23—48no—
1205C23—88no—
1206C23—84no—
1207C23—84no—
1208C23—88no—
1209C23—84no—
1210C23—84no—
1211C23C2×H(5,𝔽2)12yes—
1212C23C2×H(5,𝔽2)14yes—
1213C23C2611yescharacteristic
1214Q8—44no—
1215Q8—48no—
1216Q8—44no—
1217Q8—88no—
1218Q8—88no—
1219Q8—82no—
1220Q8—84no—
1221Q8—162no—
1222D4—44no—
1223D4—48no—
1224D4—48no—
1225D4—44no—
1226D4—48no—
1227D4—48no—
1228D4—48no—
1229D4—82no—
1230D4—88no—
1231D4—84no—
1232D4—88no—
1233D4—164no—
1234C2×C4—28no—
1235C2×C4—216no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—44no—
1285C2×C4—48no—
1286C2×C4—48no—
1287C2×C4—48no—
1288C2×C4—48no—
1289C2×C4—48no—
1290C2×C4—48no—
1291C2×C4—48no—
1292C2×C4—84no—
1293C2×C4—84no—
1294C2×C4—84no—
1295C2×C4—84no—
1296C2×C4—84no—
1297C2×C4—162no—
1298C2×C4C2×H(5,𝔽2)14yes—
1299C2×C4C2×H(5,𝔽2)12yes—
1300C2×C4C2×H(5,𝔽2)14yes—
1301C2×C4C2×H(5,𝔽2)12yes—
1302C22—28no—
1303C22—22no—
1304C22—24no—
1305C22—24no—
1306C22—44no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—44no—
1314C22—44no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—44no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—816no—
1327C22—88no—
1328C22C22×H(5,𝔽2)11yescharacteristic
1329C22C22×H(5,𝔽2)11yescharacteristic
1330C22C22×H(5,𝔽2)11yescharacteristic
1331C222−1+614yes—
1332C4—24no—
1333C4—22no—
1334C4—22no—
1335C4—24no—
1336C4—44no—
1337C4—44no—
1338C4—44no—
1339C4—44no—
1340C4—42no—
1341C4—42no—
1342C4—44no—
1343C4—42no—
1344C4—44no—
1345C4—42no—
1346C4—44no—
1347C4—44no—
1348C4—44no—
1349C4—44no—
1350C2—44no—
1351C2—42no—
1352C2—82no—
1353C2—82no—
1354C2—82no—
1355C2#6281711yescharacteristic
1356C2#6288612yes—
1357C2#6304412yes—
1358C2#6306312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35149C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58173C2semidirect
2. #58128C2semidirect
3. #55284C2semidirect
4. #55134C2semidirect
5. #53909C2semidirect
6. #53906C2semidirect
7. #52054C2semidirect
8. #51992C2semidirect
9. #51978C2semidirect
10. #51326C2semidirect
11. #51317C2semidirect
12. #50219C2semidirect
13. #50200C2semidirect
14. #47795C2semidirect
15. #47660C2semidirect
16. #46624C2semidirect
17. #46426C2semidirect
18. #45472C2semidirect
19. #45469C2semidirect
20. #45453C2semidirect
21. #45446C2semidirect
22. #35305C2semidirect
26. C2×#563C22semidirect
27. C2×#559C22semidirect
28. C2×#544C22semidirect
39. #2837C22semidirect
40. #2833C22semidirect
41. #2832C22semidirect
42. #2829C22semidirect
43. #2829C22semidirect
44. #2826C22semidirect
45. #2820C22semidirect
47. #2817C22semidirect
49. #2808C22semidirect
50. #2803C22semidirect
51. #2803C22semidirect
52. #2801C22semidirect
53. #2800C22semidirect
54. #2799C22semidirect
55. #2795C22semidirect
56. #2788C22semidirect
57. #2787C22semidirect
58. #2786C22semidirect
59. #2781C22semidirect
60. #2780C22semidirect
61. #2779C22semidirect
62. #2778C22semidirect
63. #2774C22semidirect
64. #2762C22semidirect
65. #2753C22semidirect
66. #2753C22semidirect
67. #2748C22semidirect
68. #2747C22semidirect
69. #2746C22semidirect
70. #2742C22semidirect
71. #2739C22semidirect
77. #2734C22semidirect
78. #2731C22semidirect
79. #2731C22semidirect
80. #2730C22semidirect
81. #2729C22semidirect
82. #2729C22semidirect
83. #2728C22semidirect
84. #2724C22semidirect
85. #2723C22semidirect
86. #2720C22semidirect
87. #2720C22semidirect
88. #2718C22semidirect
89. #2717C22semidirect
90. #2713C22semidirect
91. #2713C22semidirect
92. #2712C22semidirect
93. #2710C22semidirect
94. #2709C22semidirect
95. #2709C22semidirect
96. #2707C22semidirect
97. #2704C22semidirect
98. #2704C22semidirect
99. #2702C22semidirect
100. #2700C22semidirect
103. #2694C22semidirect
104. #2691C22semidirect
105. #2690C22semidirect
106. #2690C22semidirect
108. #2689C22semidirect
109. #2686C22semidirect
114. #2683C22semidirect
115. #2681C22semidirect
116. #2681C22semidirect
118. #2677C22semidirect
119. #2677C22semidirect
121. #2674C22semidirect
122. #2674C22semidirect
123. #2663C22semidirect
124. #2651C22semidirect
125. #2649C22semidirect
126. #2648C22semidirect
127. #2641C22semidirect
128. #2632C22semidirect
129. #2630C22semidirect
133. #2612C22semidirect
135. #2611C22semidirect
136. #2610C22semidirect
137. #2609C22semidirect
139. #2595C22semidirect
140. #2593C22semidirect
141. #2586C22semidirect
142. #2583C22semidirect
143. #2577C22semidirect
145. #2574C22semidirect
146. #2559C22semidirect
148. #2558C22semidirect
149. #2556C22semidirect
150. #2556C22semidirect
151. #2551C22semidirect
152. #2531C22semidirect
153. #2531C22semidirect
154. #2530C22semidirect
156. #2521C22semidirect
157. #2481C22semidirect
158. #2481C22semidirect
162. #2478C22semidirect
163. #2477C22semidirect
165. #2474C22semidirect
166. #2474C22semidirect
167. #2473C22semidirect
169. #2471C22semidirect
171. #2468C22semidirect
172. #2465C22semidirect
173. #2461C22semidirect
174. #2460C22semidirect
175. #2452C22semidirect
176. #2451C22semidirect
177. #2449C22semidirect
178. #2449C22semidirect
179. #2443C22semidirect
180. #2442C22semidirect
181. #2440C22semidirect
184. #2434C22semidirect
193. #2409C22semidirect
205. #2380C22semidirect
208. #2376C22semidirect
209. #2374C22semidirect
210. #2372C22semidirect
211. #2332C22semidirect
212. #2331C22semidirect

Maximal subgroups

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

subgroupindex
#581732
#581282
#552842
#551342
#539092
#539062
#520542
#519922
#519782
#513262
#513172
#502192
#502002
#477952
#476602
#466242
#464262
#454722
#454692
#454532
#454462
#353052
#351492