Finite Group Databasebeta

← #8121467

Subgroups — #8121467

Order 512.

4588 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#56757C214yesmaximal, complemented
2#56652C214yesmaximal, complemented
3#56367C214yesmaximal, complemented
4#56314C214yesmaximal, complemented
5#52511C212yesmaximal, complemented
6#52411C212yesmaximal, complemented
7#47430C214yesmaximal, complemented
8#47232C214yesmaximal, complemented
9#47126C214yesmaximal, complemented
10#47114C214yesmaximal, complemented
11#43175C212yesmaximal
12#43126C212yesmaximal, complemented
13#38392C214yesmaximal, complemented
14#38054C214yesmaximal, complemented
15#37957C212yesmaximal, complemented
16#37956C212yesmaximal, complemented
17#37685C212yesmaximal, complemented
18#37684C212yesmaximal, complemented
19#36970C211yesmaximal, characteristic, complemented
20#36962C211yesmaximal, characteristic, complemented
21#35120C212yesmaximal, complemented
22#35084C212yesmaximal, complemented
23C2×#2603C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C2×#543C2211yescharacteristic
26C22×#126C2211yescharacteristic
27C22×C22⋊Q8C2212yes—
28C22×C4×D4C2211yescharacteristic
29#2855C2212yes—
30#2855C2212yes—
31#2855C2214yes—
32#2848C2212yes—
33#2848C2212yes—
34#2838C2214yescomplemented
35#2837C2214yescomplemented
36#2836C2214yescomplemented
37#2834C2212yescomplemented
38#2832C2212yescomplemented
39#2831C2214yescomplemented
40#2827C2214yescomplemented
41#2823C2212yescomplemented
42#2817C2212yescomplemented
43#2814C2214yescomplemented
44#2806C2214yescomplemented
45#2806C2214yescomplemented
46#2803C2214yes—
47#2797C2214yes—
48#2792C2214yescomplemented
49#2792C2212yescomplemented
50#2788C2214yescomplemented
51#2787C2214yescomplemented
52#2786C2214yescomplemented
53#2777C2214yescomplemented
54#2775C2214yescomplemented
55#2772C2214yescomplemented
56#2771C2212yescomplemented
57#2770C2214yescomplemented
58#2770C2214yescomplemented
59#2764C2214yescomplemented
60#2763C2214yescomplemented
61#2761C2214yescomplemented
62#2761C2214yescomplemented
63#2759C2214yescomplemented
64#2757C2214yescomplemented
65#2757C2214yescomplemented
66#2754C2214yescomplemented
67#2752C2212yes—
68#2745C2214yescomplemented
69#2740C2214yescomplemented
70#2737C2214yescomplemented
71#2737C2214yescomplemented
72#2734C2212yescomplemented
73#2732C2214yescomplemented
74#2729C2214yescomplemented
75#2728C2212yescomplemented
76#2723C2214yescomplemented
77#2723C2214yescomplemented
78#2722C2212yescomplemented
79#2721C2214yescomplemented
80#2721C2214yescomplemented
81#2720C2214yescomplemented
82#2718C2214yescomplemented
83#2716C2214yescomplemented
84#2716C2214yescomplemented
85#2715C2214yescomplemented
86#2712C2212yes—
87#2710C2214yes—
88#2704C2214yescomplemented
89#2702C2214yescomplemented
90#2700C2214yescomplemented
91#2698C2214yescomplemented
92#2698C2214yescomplemented
93#2698C2214yescomplemented
94#2695C2214yescomplemented
95#2692C2214yescomplemented
96#2692C2214yescomplemented
97#2689C2214yescomplemented
98#2689C2214yescomplemented
99#2689C2214yescomplemented
100#2689C2214yescomplemented
101#2683C2214yescomplemented
102#2680C2212yescomplemented
103#2677C2214yescomplemented
104#2659C2212yes—
105#2659C2212yes—
106#2654C2214yescomplemented
107#2650C2214yescomplemented
108#2646C2214yes—
109#2644C2214yescomplemented
110#2640C2214yescomplemented
111#2638C2214yescomplemented
112#2638C2214yescomplemented
113#2627C2212yes—
114#2626C2212yes—
115#2612C2214yescomplemented
116#2612C2214yescomplemented
117#2612C2214yescomplemented
118#2612C2214yescomplemented
119#2606C2214yescomplemented
120#2606C2214yescomplemented
121#2605C2214yescomplemented
122#2605C2214yescomplemented
123#2603C2214yes—
124#2603C2214yes—
125#2603C2214yes—
126#2603C2214yes—
127#2602C2214yes—
128#2601C2214yescomplemented
129#2600C2212yes—
130#2599C2214yescomplemented
131#2586C2212yescomplemented
132#2583C2214yes—
133#2583C2212yes—
134#2582C2212yescomplemented
135#2577C2214yescomplemented
136#2561C2214yes—
137#2561C2214yes—
138#2561C2212yes—
139#2560C2214yescomplemented
140#2557C2214yes—
141#2549C2214yes—
142#2532C2214yescomplemented
143#2530C2214yescomplemented
144#2529C2214yescomplemented
145#2527C2214yescomplemented
146#2521C2214yescomplemented
147#2512C2214yescomplemented
148#2507C2214yescomplemented
149#2507C2214yescomplemented
150#2503C2212yes—
151#2502C2212yes—
152#2493C2214yes—
153#2486C2212yescomplemented
154#2486C2212yescomplemented
155#2484C2212yes—
156#2483C2214yes—
157#2483C2212yes—
158#2483C2212yes—
159#2482C2212yes—
160#2480C2214yes—
161#2480C2214yes—
162#2480C2214yes—
163#2478C2214yescomplemented
164#2474C2214yescomplemented
165#2473C2214yescomplemented
166#2473C2214yescomplemented
167#2465C2214yescomplemented
168#2459C2214yes—
169#2455C2212yes—
170#2452C2214yescomplemented
171#2451C2214yescomplemented
172#2449C2214yescomplemented
173#2449C2214yescomplemented
174#2448C2214yescomplemented
175#2447C2214yescomplemented
176#2440C2214yes—
177#2440C2214yescomplemented
178#2438C2214yes—
179#2437C2214yes—
180#2437C2214yes—
181#2437C2214yes—
182#2435C2214yes—
183#2434C2214yescomplemented
184#2417C2214yescomplemented
185#2415C2212yescomplemented
186#2415C2212yescomplemented
187#2415C2212yescomplemented
188#2415C2212yescomplemented
189#2409C2212yescomplemented
190#2409C2212yescomplemented
191#2409C2214yescomplemented
192#2405C2214yes—
193C2×#398C2211yescharacteristic
194C2×#397C2211yescharacteristic
195C2×#394C2211yescharacteristic
196C2×#392C2211yescharacteristic
197#2368C2214yes—
198#2360C2214yes—
199#2342C2214yes—
200D4×C22⋊C4C2214yes—
201#2334C2214yescomplemented
202#2332C2214yescomplemented
203#2329C2212yes—
204#2329C2212yes—
205#2329C2214yes—
206#2326C2214yescomplemented
207#2322C2214yescomplemented
208#2322C2214yescomplemented
209#2319C2214yescomplemented
210#2313C2211yescharacteristic
211#2312C2211yescharacteristic
212C2×#390C2212yes—
213C2×#388C2212yes—
214C2×#386C2212yes—
215C2×#385C2212yes—
216#2283C2214yes—
217#2280C2212yes—
218C2×#376C2211yescharacteristic
219C23×Q8C2312yes—
220C23×D4C2312yes—
221C23×D4C2311yescharacteristic
222C24×C4C2312yes—
223#544—44no—
224#543—44no—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2314yes—
227C2×#126—44no—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#125C2314yes—
234C2×#124C2314yes—
235C2×#124C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×C22⋊Q8—48no—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×D4—44no—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2314yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2311yescharacteristic
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2314yes—
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2312yes—
285C22×C42C2311yescharacteristic
286C22×C42C2312yes—
287#401C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#399C2314yes—
301#399C2312yes—
302#399C2312yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2312yes—
309#398C2312yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2312yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2312yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2312yes—
339#397C2314yes—
340#397C2312yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2312yes—
352#397C2312yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2312yes—
373#395C2314yes—
374#395C2312yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#394C2314yes—
385#394C2312yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2312yes—
393#394C2314yes—
394#394C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#392C2312yes—
405#392C2314yes—
406#392C2312yes—
407#391C2314yes—
408#391C2314yes—
409#391C2312yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2312yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
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#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
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#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2312yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2312yes—
558#385C2314yes—
559#384C2312yes—
560#384C2314yes—
561#384C2312yes—
562#383C2314yes—
563#383C2314yes—
564#383C2314yes—
565#382C2314yes—
566#382C2314yes—
567#382C2314yes—
568#381C2312yes—
569#381C2314yes—
570#381C2314yes—
571#381C2314yes—
572#381C2312yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#381C2312yes—
577#381C2314yes—
578#380C2312yes—
579#380C2312yes—
580#380C2314yes—
581#380C2314yes—
582#380C2312yes—
583#380C2314yes—
584#380C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2312yes—
591#380C2312yes—
592#379C2314yes—
593#379C2314yes—
594#379C2314yes—
595#379C2314yes—
596#379C2312yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610#376C2314yes—
611#376C2314yes—
612#376C2314yes—
613#376C2314yes—
614C2×#95C2311yescharacteristic
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2311yescharacteristic
618C2×#95C2312yes—
619C25C2412yes—
620C25C2411yescharacteristic
621C22×Q8—44no—
622C22×Q8—82no—
623C22×Q8—82no—
624C22×Q8C2414yes—
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2414yes—
630C22×D4—28no—
631C22×D4—42no—
632C22×D4—44no—
633C22×D4—44no—
634C22×D4—82no—
635C22×D4C2411yescharacteristic
636C22×D4C2414yes—
637C22×D4C2412yes—
638C22×D4C2414yes—
639C22×D4C2411yescharacteristic
640C23×C4—28no—
641C23×C4—82no—
642C23×C4—82no—
643C23×C4C2411yescharacteristic
644C23×C4C2411yescharacteristic
645C23×C4C2411yescharacteristic
646C23×C4C2411yescharacteristic
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2411yescharacteristic
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2414yes—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2411yescharacteristic
659C23×C4C2412yes—
660C4⋊Q8—48no—
661C4⋊Q8—84no—
662#126—48no—
663#126—48no—
664#126—48no—
665#126—84no—
666#126—84no—
667#125—48no—
668#124—48no—
669#124—84no—
670#123—48no—
671#123—48no—
672C22⋊Q8—28no—
673C22⋊Q8—28no—
674C22⋊Q8—216no—
675C22⋊Q8—48no—
676C22⋊Q8—48no—
677C22⋊Q8—44no—
678C22⋊Q8—44no—
679C22⋊Q8—48no—
680C22⋊Q8—48no—
681C22⋊Q8—48no—
682C22⋊Q8—44no—
683C22⋊Q8—44no—
684C22⋊Q8—84no—
685C22⋊Q8—84no—
686C22⋊Q8—82no—
687C22⋊Q8—82no—
688C22⋊Q8—82no—
689C22⋊Q8—82no—
690C4×Q8—84no—
691C4×D4—44no—
692C4×D4—44no—
693C4×D4—44no—
694C4×D4—44no—
695C4×D4—48no—
696C4×D4—84no—
697#117—44no—
698#117—82no—
699#117—82no—
700C2×C4⋊C4—24no—
701C2×C4⋊C4—44no—
702C2×C4⋊C4—48no—
703C2×C4⋊C4—42no—
704C2×C4⋊C4—42no—
705C2×C4⋊C4—42no—
706C2×C4⋊C4—82no—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C22⋊C4—24no—
759C2×C22⋊C4—28no—
760C2×C22⋊C4—44no—
761C2×C22⋊C4—48no—
762C2×C22⋊C4—44no—
763C2×C22⋊C4—44no—
764C2×C22⋊C4—42no—
765C2×C22⋊C4—42no—
766C2×C22⋊C4—82no—
767C2×C22⋊C4—82no—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2412yes—
810C2×C42—24no—
811C2×C42—28no—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2412yes—
825C2×C42C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2412yes—
829#95C2412yes—
830#95C2412yes—
831#95C2412yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2412yes—
857#95C2414yes—
858#95C2412yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2412yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884C24—24no—
885C24—24no—
886C24—24no—
887C24—24no—
888C24—22no—
889C24—24no—
890C24—42no—
891C24—42no—
892C24—42no—
893C24—41no—
894C24—42no—
895C24—41no—
896C24C2512yes—
897C24C2512yes—
898C24C2512yes—
899C24C2511yescharacteristic
900C2×Q8—24no—
901C2×Q8—24no—
902C2×Q8—28no—
903C2×Q8—44no—
904C2×Q8—44no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8—44no—
910C2×Q8—44no—
911C2×Q8—44no—
912C2×Q8—42no—
913C2×Q8—42no—
914C2×Q8—44no—
915C2×Q8—42no—
916C2×Q8—42no—
917C2×Q8—816no—
918C2×D4—28no—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—28no—
922C2×D4—28no—
923C2×D4—41no—
924C2×D4—42no—
925C2×D4—41no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—416no—
932C2×D4—816no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—28no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—41no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—41no—
964C22×C4—42no—
965C22×C4—44no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—44no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—816no—
978C22×C4H(5,𝔽2)14yes—
979C22×C42−1+418yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2514yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2514yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C4⋊C4—28no—
1000C4⋊C4—24no—
1001C4⋊C4—28no—
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—41no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—44no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C42—24no—
1093C42—24no—
1094C42—28no—
1095C42—28no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42—44no—
1100C42—44no—
1101C42—42no—
1102C42—44no—
1103C42—44no—
1104C42—44no—
1105C42—42no—
1106C23—22no—
1107C23—21no—
1108C23—21no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—24no—
1119C23—22no—
1120C23—22no—
1121C23—24no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—48no—
1128C23—48no—
1129C23—48no—
1130C23—48no—
1131C23—44no—
1132C23—84no—
1133C23—84no—
1134C23—84no—
1135C23—84no—
1136C23—82no—
1137C23—82no—
1138C23—84no—
1139C23C2×H(5,𝔽2)12yes—
1140C23C2×2−1+414yes—
1141C23#58514yes—
1142C23C2611yescharacteristic
1143Q8—88no—
1144Q8—84no—
1145Q8—84no—
1146Q8—88no—
1147Q8—162no—
1148Q8—162no—
1149D4—416no—
1150D4—44no—
1151D4—48no—
1152D4—44no—
1153D4—88no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—44no—
1206C2×C4—48no—
1207C2×C4—48no—
1208C2×C4—48no—
1209C2×C4—44no—
1210C2×C4—44no—
1211C2×C4—44no—
1212C2×C4—84no—
1213C2×C4—84no—
1214C2×C4—88no—
1215C2×C4—82no—
1216C2×C4—82no—
1217C2×C4—84no—
1218C2×C4—84no—
1219C2×C4—88no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4C2×H(5,𝔽2)14yes—
1223C2×C4C2×2−1+418yes—
1224C22—22no—
1225C22—22no—
1226C22—24no—
1227C22—24no—
1228C22—24no—
1229C22—24no—
1230C22—24no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—44no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—44no—
1247C22—816no—
1248C22—164no—
1249C22#355014yes—
1250C22C22×H(5,𝔽2)11yescharacteristic
1251C22C22×2−1+412yes—
1252C22C2×#58512yes—
1253C22H(7,𝔽2)11yescharacteristic
1254C22H(7,𝔽2)11yescharacteristic
1255C4—24no—
1256C4—28no—
1257C4—42no—
1258C4—42no—
1259C4—41no—
1260C4—41no—
1261C4—44no—
1262C4—44no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—44no—
1267C4—44no—
1268C4—42no—
1269C4—44no—
1270C4—44no—
1271C4—44no—
1272C4—44no—
1273C4—44no—
1274C2—24no—
1275C2—44no—
1276C2—82no—
1277C2—82no—
1278C2C2×#355011yescharacteristic
1279C2#6282111yescharacteristic
1280C2#6286211yescharacteristic
1281C2#6290312yes—
1282C2#6295812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#392C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #56757C2semidirect
2. #56652C2semidirect
3. #56367C2semidirect
4. #56314C2semidirect
5. #52511C2semidirect
6. #52411C2semidirect
7. #47430C2semidirect
8. #47232C2semidirect
9. #47126C2semidirect
10. #47114C2semidirect
12. #43126C2semidirect
13. #38392C2semidirect
14. #38054C2semidirect
15. #37957C2semidirect
16. #37956C2semidirect
17. #37685C2semidirect
18. #37684C2semidirect
19. #36970C2semidirect
20. #36962C2semidirect
21. #35120C2semidirect
22. #35084C2semidirect
34. #2838C22semidirect
35. #2837C22semidirect
36. #2836C22semidirect
37. #2834C22semidirect
38. #2832C22semidirect
39. #2831C22semidirect
40. #2827C22semidirect
41. #2823C22semidirect
42. #2817C22semidirect
43. #2814C22semidirect
44. #2806C22semidirect
45. #2806C22semidirect
48. #2792C22semidirect
49. #2792C22semidirect
50. #2788C22semidirect
51. #2787C22semidirect
52. #2786C22semidirect
53. #2777C22semidirect
54. #2775C22semidirect
55. #2772C22semidirect
56. #2771C22semidirect
57. #2770C22semidirect
58. #2770C22semidirect
59. #2764C22semidirect
60. #2763C22semidirect
61. #2761C22semidirect
62. #2761C22semidirect
63. #2759C22semidirect
64. #2757C22semidirect
65. #2757C22semidirect
66. #2754C22semidirect
68. #2745C22semidirect
69. #2740C22semidirect
70. #2737C22semidirect
71. #2737C22semidirect
72. #2734C22semidirect
73. #2732C22semidirect
74. #2729C22semidirect
75. #2728C22semidirect
76. #2723C22semidirect
77. #2723C22semidirect
78. #2722C22semidirect
79. #2721C22semidirect
80. #2721C22semidirect
81. #2720C22semidirect
82. #2718C22semidirect
83. #2716C22semidirect
84. #2716C22semidirect
85. #2715C22semidirect
88. #2704C22semidirect
89. #2702C22semidirect
90. #2700C22semidirect
91. #2698C22semidirect
92. #2698C22semidirect
93. #2698C22semidirect
94. #2695C22semidirect
95. #2692C22semidirect
96. #2692C22semidirect
97. #2689C22semidirect
98. #2689C22semidirect
99. #2689C22semidirect
100. #2689C22semidirect
101. #2683C22semidirect
102. #2680C22semidirect
103. #2677C22semidirect
106. #2654C22semidirect
107. #2650C22semidirect
109. #2644C22semidirect
110. #2640C22semidirect
111. #2638C22semidirect
112. #2638C22semidirect
115. #2612C22semidirect
116. #2612C22semidirect
117. #2612C22semidirect
118. #2612C22semidirect
119. #2606C22semidirect
120. #2606C22semidirect
121. #2605C22semidirect
122. #2605C22semidirect
128. #2601C22semidirect
130. #2599C22semidirect
131. #2586C22semidirect
134. #2582C22semidirect
135. #2577C22semidirect
139. #2560C22semidirect
142. #2532C22semidirect
143. #2530C22semidirect
144. #2529C22semidirect
145. #2527C22semidirect
146. #2521C22semidirect
147. #2512C22semidirect
148. #2507C22semidirect
149. #2507C22semidirect
153. #2486C22semidirect
154. #2486C22semidirect
163. #2478C22semidirect
164. #2474C22semidirect
165. #2473C22semidirect
166. #2473C22semidirect
167. #2465C22semidirect
170. #2452C22semidirect
171. #2451C22semidirect
172. #2449C22semidirect
173. #2449C22semidirect
174. #2448C22semidirect
175. #2447C22semidirect
177. #2440C22semidirect
183. #2434C22semidirect
184. #2417C22semidirect
185. #2415C22semidirect
186. #2415C22semidirect
187. #2415C22semidirect
188. #2415C22semidirect
189. #2409C22semidirect
190. #2409C22semidirect
191. #2409C22semidirect
201. #2334C22semidirect
202. #2332C22semidirect
206. #2326C22semidirect
207. #2322C22semidirect
208. #2322C22semidirect
209. #2319C22semidirect

Maximal subgroups

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

subgroupindex
#567572
#566522
#563672
#563142
#525112
#524112
#474302
#472322
#471262
#471142
#431752
#431262
#383922
#380542
#379572
#379562
#376852
#376842
#369702
#369622
#351202
#350842
C2×#26032