Finite Group Databasebeta

← #8107593

Subgroups — #8107593

Order 512.

4080 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53153C212yesmaximal, complemented
2#53114C212yesmaximal, complemented
3#52909C214yesmaximal, complemented
4#52652C214yesmaximal, complemented
5#45148C212yesmaximal, complemented
6#44945C212yesmaximal, complemented
7#44529C214yesmaximal, complemented
8#43984C214yesmaximal, complemented
9#42961C211yesmaximal, characteristic
10#42955C211yesmaximal, characteristic, complemented
11#42817C211yesmaximal, characteristic, complemented
12#42744C212yesmaximal, complemented
13#42742C212yesmaximal, complemented
14#42517C211yesmaximal, characteristic
15#42382C214yesmaximal, complemented
16#42350C214yesmaximal, complemented
17#41544C214yesmaximal, complemented
18#40853C214yesmaximal, complemented
19#36394C212yesmaximal, complemented
20#36371C212yesmaximal, complemented
21#36367C212yesmaximal, complemented
22#36306C212yesmaximal, complemented
23#35313C211yesmaximal, characteristic, complemented
24#35296C211yesmaximal, characteristic
25#35187C212yesmaximal, complemented
26#35114C212yesmaximal, complemented
27#34552C211yesmaximal, characteristic, complemented
28#2864C2212yes—
29#2864C2211yescharacteristic
30#2863C2212yes—
31#2863C2212yes—
32#2863C2212yes—
33#2861C2212yes—
34#2860C2212yes—
35#2858C2211yescharacteristic
36#2854C2212yes—
37#2843C2212yes—
38#2841C2212yes—
39#2839C2214yes—
40#2838C2214yes—
41#2838C2214yes—
42#2838C2214yes—
43#2836C2214yes—
44#2835C2214yes—
45#2834C2214yes—
46#2832C2212yes—
47#2831C2214yes—
48#2827C2214yes—
49#2824C2212yes—
50#2821C2214yes—
51#2811C2212yes—
52#2799C2212yes—
53#2799C2214yes—
54#2789C2214yes—
55#2785C2212yes—
56#2782C2212yes—
57#2782C2214yes—
58#2780C2214yes—
59#2776C2214yes—
60#2773C2214yes—
61#2770C2214yes—
62#2769C2214yes—
63#2768C2214yes—
64#2768C2214yes—
65#2765C2214yes—
66#2765C2214yes—
67#2764C2214yes—
68#2763C2212yes—
69#2762C2214yes—
70#2760C2212yes—
71#2759C2214yes—
72#2759C2214yes—
73#2752C2212yes—
74#2749C2214yes—
75#2748C2214yes—
76#2746C2214yes—
77#2743C2214yes—
78#2742C2212yes—
79#2740C2214yes—
80#2738C2214yes—
81#2729C2214yes—
82#2729C2214yes—
83#2728C2214yes—
84#2718C2214yes—
85#2698C2214yes—
86#2687C2214yes—
87#2666C2214yes—
88#2666C2214yes—
89#2665C2214yes—
90#2655C2214yes—
91#2655C2214yes—
92#2653C2214yes—
93#2653C2214yes—
94#2651C2214yes—
95#2645C2214yes—
96#2645C2212yes—
97#2645C2212yes—
98#2644C2212yes—
99#2643C2214yes—
100#2636C2214yes—
101#2632C2214yes—
102#2628C2211yescharacteristic
103#2619C2211yescharacteristic
104#2607C2212yes—
105#2601C2214yes—
106#2599C2214yes—
107#2599C2214yes—
108#2595C2214yes—
109#2592C2212yes—
110#2592C2212yes—
111#2589C2214yes—
112#2589C2214yes—
113#2589C2214yes—
114#2584C2212yes—
115#2582C2212yes—
116#2581C2212yes—
117#2580C2212yes—
118#2580C2212yes—
119#2577C2214yes—
120#2577C2214yes—
121#2575C2214yes—
122#2575C2214yes—
123#2572C2214yes—
124#2572C2212yes—
125#2571C2212yes—
126#2571C2212yes—
127#2568C2212yes—
128#2563C2214yes—
129#2557C2214yes—
130#2550C2212yes—
131#2546C2212yes—
132#2544C2212yes—
133#2533C2214yes—
134#2532C2214yes—
135#2532C2214yes—
136#2532C2214yes—
137#2532C2214yes—
138#2532C2214yes—
139#2527C2214yes—
140#2526C2214yes—
141#2525C2214yes—
142#2525C2214yes—
143#2524C2214yes—
144#2524C2214yes—
145#2521C2214yes—
146#2514C2214yes—
147#2514C2212yes—
148#2514C2214yes—
149#2514C2212yes—
150#2514C2212yes—
151#2513C2212yes—
152#2512C2212yes—
153#2511C2212yes—
154#2511C2214yes—
155#2510C2214yes—
156#2509C2212yes—
157#2508C2212yes—
158#2508C2212yes—
159#2508C2212yes—
160#2508C2212yes—
161#2507C2212yes—
162#2505C2214yes—
163#2500C2212yes—
164#2498C2214yes—
165#2493C2214yes—
166#2493C2214yes—
167#2488C2214yes—
168#2479C2214yes—
169#2478C2214yes—
170#2477C2214yes—
171#2474C2214yes—
172#2474C2214yes—
173#2471C2214yes—
174#2470C2214yes—
175#2469C2214yes—
176#2469C2214yes—
177#2465C2214yes—
178#2458C2214yes—
179#2458C2214yes—
180#2455C2212yes—
181#2454C2212yes—
182#2453C2212yes—
183#2452C2212yes—
184#2452C2212yes—
185#2451C2212yes—
186#2451C2212yes—
187#2450C2214yes—
188#2448C2212yes—
189#2448C2212yes—
190#2447C2212yes—
191#2447C2212yes—
192#2447C2212yes—
193#2446C2214yes—
194#2445C2212yes—
195#2442C2212yes—
196#2439C2212yes—
197#2436C2212yes—
198#2402C2212yes—
199#2402C2212yes—
200#2402C2212yes—
201#2399C2211yescharacteristic
202#2399C2212yes—
203#2399C2211yescharacteristic
204#2399C2212yes—
205#2396C2211yescharacteristic
206#2396C2212yes—
207#2396C2212yes—
208#2396C2212yes—
209#2396C2212yes—
210#2396C2211yescharacteristic
211#2396C2212yes—
212#2373C2214yes—
213#2373C2214yes—
214#2370C2212yes—
215#2367C2212yes—
216#2363C2212yes—
217#2362C2214yes—
218#2362C2214yes—
219#2361C2212yes—
220#2359C2214yes—
221#2356C2212yes—
222#2353C2214yes—
223#2349C2212yes—
224#2347C2212yes—
225#2343C2214yes—
226#2343C2214yes—
227Q8×C22⋊C4C2212yes—
228#2337C2214yes—
229#2335C2214yes—
230#2331C2211yescharacteristic
231#2328C2211yescharacteristic
232#2327C2214yes—
233#2324C2212yes—
234#2320C2214yes—
235#2317C2211yescharacteristic
236#2316C2211yescharacteristic
237#2310C2211yescharacteristic
238#2310C2211yescharacteristic
239C4×C4⋊Q8C2212yes—
240C4×#124C2212yes—
241#2296C2211yescharacteristic
242#2295C2212yes—
243C2×#391C2211yescharacteristic
244#2293C2212yes—
245#2293C2212yes—
246C42×Q8C2211yescharacteristic
247C42×Q8C2212yes—
248C42×Q8C2211yescharacteristic
249C4×#117C2212yes—
250C4×#117C2211yescharacteristic
251C23×Q8C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2314yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×#127C2311yescharacteristic
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#125C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×#121C2312yes—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C2×#117C2311yescharacteristic
285C2×#117C2314yes—
286C2×#117C2314yes—
287C2×#117C2312yes—
288C2×#117C2312yes—
289C22×C4⋊C4C2311yescharacteristic
290C22×C42C2311yescharacteristic
291#401C2314yes—
292#401C2314yes—
293#401C2314yes—
294#401C2314yes—
295#401C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2311yescharacteristic
302#400C2312yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2314yes—
323#400C2312yes—
324#400C2312yes—
325#400C2312yes—
326#400C2312yes—
327#400C2311yescharacteristic
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2312yes—
334#399C2311yescharacteristic
335#399C2311yescharacteristic
336#399C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2312yes—
356#398C2312yes—
357#398C2312yes—
358#398C2312yes—
359#398C2312yes—
360#398C2312yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2312yes—
388#396C2312yes—
389#396C2312yes—
390#396C2312yes—
391#395C2312yes—
392#395C2314yes—
393#395C2311yescharacteristic
394#395C2312yes—
395#395C2314yes—
396#395C2314yes—
397#395C2312yes—
398#395C2312yes—
399#395C2314yes—
400#395C2314yes—
401#395C2312yes—
402#395C2312yes—
403#395C2311yescharacteristic
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2312yes—
408#394C2314yes—
409#394C2312yes—
410#394C2314yes—
411#394C2314yes—
412#393C2312yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2311yescharacteristic
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2312yes—
424#393C2311yescharacteristic
425#392C2312yes—
426#392C2312yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2312yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2314yes—
452#391C2312yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
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#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
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#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#385C2312yes—
579#385C2314yes—
580#385C2314yes—
581#385C2312yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#384C2312yes—
598#384C2312yes—
599#383C2314yes—
600#383C2314yes—
601#383C2314yes—
602#383C2314yes—
603#383C2314yes—
604#383C2314yes—
605#383C2314yes—
606#383C2314yes—
607#382C2314yes—
608#382C2314yes—
609#382C2311yescharacteristic
610#382C2312yes—
611#382C2311yescharacteristic
612#382C2314yes—
613#382C2314yes—
614#382C2312yes—
615#382C2314yes—
616#382C2312yes—
617#382C2312yes—
618#381C2314yes—
619#381C2312yes—
620#381C2312yes—
621#381C2314yes—
622#381C2314yes—
623#381C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2314yes—
627#380C2314yes—
628#380C2312yes—
629#380C2314yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678#376C2314yes—
679#376C2311yescharacteristic
680#376C2314yes—
681#376C2312yes—
682#376C2311yescharacteristic
683#376C2312yes—
684C2×#95C2314yes—
685C2×#95C2314yes—
686C43C2312yes—
687C43C2311yescharacteristic
688C43C2311yescharacteristic
689C43C2312yes—
690C22×Q8—24no—
691C22×Q8—42no—
692C22×Q8—42no—
693C22×Q8C2412yes—
694C22×Q8C2412yes—
695C22×Q8C2414yes—
696C22×Q8C2412yes—
697C22×Q8C2411yescharacteristic
698C22×Q8C2411yescharacteristic
699C22×Q8C2412yes—
700C22×D4C2412yes—
701C22×D4C2414yes—
702C22×D4C2412yes—
703C22×D4C2412yes—
704C23×C4C2412yes—
705C23×C4C2411yescharacteristic
706C23×C4C2412yes—
707C23×C4C2412yes—
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2414yes—
711C4⋊Q8—42no—
712C4⋊Q8—44no—
713C4⋊Q8—48no—
714#127—42no—
715#126—48no—
716#126—48no—
717#125—44no—
718#124—48no—
719#124—44no—
720#124—44no—
721#123—48no—
722#123—48no—
723C22⋊Q8—48no—
724C22⋊Q8—48no—
725#121—28no—
726C4×Q8—44no—
727C4×Q8—42no—
728C4×Q8—44no—
729C4×Q8—44no—
730C4×Q8—42no—
731C4×Q8—44no—
732C4×Q8—48no—
733C4×Q8—44no—
734C4×Q8—44no—
735C4×Q8—44no—
736C4×D4—48no—
737C4×D4—44no—
738C4×D4—44no—
739C4×D4—44no—
740#117—24no—
741#117—42no—
742#117—44no—
743#117—42no—
744#117—48no—
745#117—48no—
746#117—44no—
747#117—42no—
748C2×C4⋊C4—42no—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C42—24no—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2411yescharacteristic
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2411yescharacteristic
849C2×C42C2411yescharacteristic
850C2×C42C2412yes—
851C2×C42C2411yescharacteristic
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2411yescharacteristic
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875#95C2412yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2414yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2412yes—
912#95C2412yes—
913#95C2411yescharacteristic
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2411yescharacteristic
919#95C2412yes—
920#95C2411yescharacteristic
921#95C2412yes—
922#95C2411yescharacteristic
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#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955C24C2514yes—
956C24C2511yescharacteristic
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—28no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—41no—
966C2×Q8—42no—
967C2×Q8—41no—
968C2×Q8—42no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—42no—
972C2×Q8—42no—
973C2×Q8—44no—
974C2×Q8—42no—
975C2×Q8—88no—
976C2×D4—28no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—42no—
985C2×D4—42no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—42no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C42−1+414yes—
1006C22×C4C2514yes—
1007C22×C4C2511yescharacteristic
1008C22×C4C2514yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2514yes—
1014C22×C4C2511yescharacteristic
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2512yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2514yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2511yescharacteristic
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—41no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—41no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C22⋊C4—24no—
1091C22⋊C4—28no—
1092C22⋊C4—24no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C42—22no—
1125C42—24no—
1126C42—22no—
1127C42—24no—
1128C42—24no—
1129C42—24no—
1130C42—22no—
1131C42—24no—
1132C42—24no—
1133C42—22no—
1134C42—22no—
1135C42—24no—
1136C42—22no—
1137C42—24no—
1138C42—24no—
1139C42—28no—
1140C42—24no—
1141C42—24no—
1142C42—24no—
1143C42—24no—
1144C42—42no—
1145C42—42no—
1146C42—44no—
1147C42—44no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—42no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C23—22no—
1157C23—21no—
1158C23—22no—
1159C23—21no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23C2×2−1+412yes—
1168C23C2611yescharacteristic
1169Q8—48no—
1170Q8—44no—
1171Q8—44no—
1172Q8—48no—
1173Q8—88no—
1174Q8—84no—
1175Q8—162no—
1176D4—48no—
1177D4—88no—
1178D4—162no—
1179D4—162no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—28no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—48no—
1247C2×C4—84no—
1248C2×C4—88no—
1249C2×C4—88no—
1250C2×C4—162no—
1251C2×C4—164no—
1252C2×C4C2×2−1+412yes—
1253C2×C4C2×2−1+412yes—
1254C2×C4#58514yes—
1255C2×C4#58514yes—
1256C2×C4#58512yes—
1257C2×C4#58512yes—
1258C22—22no—
1259C22—24no—
1260C22—42no—
1261C22—41no—
1262C22—41no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22C22×2−1+411yescharacteristic
1271C22C2×#58511yescharacteristic
1272C22C2×#58511yescharacteristic
1273C22C2×#58512yes—
1274C22C2×#58512yes—
1275C4—22no—
1276C4—24no—
1277C4—24no—
1278C4—44no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—44no—
1283C4—44no—
1284C4—42no—
1285C4—42no—
1286C4—44no—
1287C4—42no—
1288C4—44no—
1289C4—42no—
1290C4—41no—
1291C4—42no—
1292C4—41no—
1293C4—44no—
1294C4—42no—
1295C4—44no—
1296C4—41no—
1297C4—42no—
1298C4—41no—
1299C4#356414yes—
1300C2—42no—
1301C2—84no—
1302C2C2×#356411yescharacteristic
1303C2#6274312yes—
1304C2#6283112yes—
1305C2#6283911yescharacteristic
1306C2#6284111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2619C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53153C2semidirect
2. #53114C2semidirect
3. #52909C2semidirect
4. #52652C2semidirect
5. #45148C2semidirect
6. #44945C2semidirect
7. #44529C2semidirect
8. #43984C2semidirect
10. #42955C2semidirect
11. #42817C2semidirect
12. #42744C2semidirect
13. #42742C2semidirect
15. #42382C2semidirect
16. #42350C2semidirect
17. #41544C2semidirect
18. #40853C2semidirect
19. #36394C2semidirect
20. #36371C2semidirect
21. #36367C2semidirect
22. #36306C2semidirect
23. #35313C2semidirect
25. #35187C2semidirect
26. #35114C2semidirect
27. #34552C2semidirect

Maximal subgroups

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

subgroupindex
#531532
#531142
#529092
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