Finite Group Databasebeta

← #8096606

Subgroups — #8096606

Order 512.

4301 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53109C212yesmaximal, complemented
2#53056C212yesmaximal, complemented
3#52979C212yesmaximal, complemented
4#52517C214yesmaximal, complemented
5#52507C214yesmaximal, complemented
6#52439C214yesmaximal, complemented
7#52306C211yesmaximal, characteristic, complemented
8#52152C212yesmaximal, complemented
9#46343C212yesmaximal, complemented
10#46284C212yesmaximal, complemented
11C4⋊#564C211yesmaximal, characteristic, complemented
12#46135C214yesmaximal, complemented
13#46117C212yesmaximal, complemented
14#46078C212yesmaximal, complemented
15#46015C211yesmaximal, characteristic
16#46014C211yesmaximal, characteristic, complemented
17#45963C212yesmaximal, complemented
18#45957C212yesmaximal, complemented
19#45867C214yesmaximal, complemented
20#45843C214yesmaximal, complemented
21#36497C211yesmaximal, characteristic, complemented
22#36452C212yesmaximal, complemented
23#36416C212yesmaximal, complemented
24#36300C211yesmaximal, characteristic, complemented
25#36299C211yesmaximal, characteristic, complemented
26#36113C212yesmaximal, complemented
27#35838C212yesmaximal, complemented
28#35783C212yesmaximal, complemented
29#35725C212yesmaximal, complemented
30C2×#564C2212yes—
31C2×#529C2214yes—
32#2864C2212yes—
33#2863C2212yes—
34#2863C2212yes—
35#2860C2212yes—
36#2860C2212yes—
37#2859C2212yes—
38#2859C2211yescharacteristic
39#2859C2211yescharacteristic
40#2858C2211yescharacteristic
41#2852C2214yes—
42#2851C2214yes—
43#2851C2214yes—
44#2838C2214yes—
45#2838C2214yes—
46#2837C2214yes—
47#2835C2214yes—
48#2832C2214yes—
49#2830C2214yes—
50#2830C2214yes—
51#2829C2214yes—
52#2829C2214yes—
53#2827C2214yes—
54#2827C2214yes—
55#2824C2214yes—
56#2822C2212yes—
57#2821C2214yes—
58#2820C2214yes—
59#2820C2212yes—
60#2820C2214yes—
61#2819C2212yes—
62#2809C2211yescharacteristic
63#2808C2212yes—
64#2788C2214yes—
65#2777C2214yes—
66#2777C2214yes—
67#2776C2214yes—
68#2775C2214yes—
69#2775C2212yes—
70#2775C2214yes—
71#2775C2212yes—
72#2774C2214yes—
73#2772C2214yes—
74#2770C2214yes—
75#2769C2212yes—
76#2764C2214yes—
77#2759C2214yes—
78#2758C2214yes—
79#2750C2214yes—
80#2734C2211yescharacteristic
81#2731C2212yes—
82#2727C2214yes—
83#2727C2211yescharacteristic
84#2727C2211yescharacteristic
85#2727C2212yes—
86#2726C2212yes—
87#2726C2212yes—
88#2725C2214yes—
89#2725C2214yes—
90#2724C2212yes—
91#2721C2214yes—
92#2721C2212yes—
93#2721C2212yes—
94#2720C2214yes—
95#2720C2214yes—
96#2719C2214yes—
97#2719C2214yes—
98#2718C2214yes—
99#2718C2214yes—
100#2716C2214yes—
101#2715C2214yes—
102#2711C2214yes—
103#2711C2214yes—
104#2710C2214yes—
105#2710C2214yes—
106#2707C2214yes—
107#2707C2214yes—
108#2701C2214yes—
109#2694C2214yes—
110#2694C2214yes—
111#2689C2214yes—
112#2682C2212yes—
113#2674C2214yes—
114#2665C2214yes—
115#2653C2214yes—
116#2649C2214yes—
117#2628C2212yes—
118#2624C2212yes—
119#2620C2212yes—
120#2607C2214yes—
121#2597C2214yes—
122#2596C2214yes—
123#2594C2214yes—
124#2592C2212yes—
125#2589C2214yes—
126#2589C2214yes—
127#2588C2214yes—
128#2587C2214yes—
129#2587C2214yes—
130#2586C2214yes—
131#2582C2211yescharacteristic
132#2580C2212yes—
133#2580C2212yes—
134#2578C2214yes—
135#2577C2214yes—
136#2574C2214yes—
137#2573C2214yes—
138#2571C2212yes—
139#2570C2212yes—
140#2567C2212yes—
141#2567C2211yescharacteristic
142#2566C2212yes—
143#2566C2212yes—
144#2553C2214yes—
145#2552C2212yes—
146#2552C2212yes—
147#2552C2211yescharacteristic
148#2551C2211yescharacteristic
149#2550C2212yes—
150#2550C2212yes—
151#2548C2211yescharacteristic
152#2538C2211yescharacteristic
153#2525C2214yes—
154#2521C2214yes—
155#2520C2214yes—
156#2518C2214yes—
157#2517C2214yes—
158#2515C2214yes—
159#2514C2212yes—
160#2513C2212yes—
161#2513C2212yes—
162#2512C2212yes—
163#2512C2212yes—
164#2511C2214yes—
165#2509C2212yes—
166#2509C2212yes—
167#2506C2212yes—
168#2506C2212yes—
169#2506C2212yes—
170#2506C2212yes—
171#2500C2212yes—
172#2499C2212yes—
173#2497C2212yes—
174#2495C2212yes—
175#2491C2212yes—
176#2490C2212yes—
177#2489C2212yes—
178#2478C2214yes—
179#2477C2214yes—
180#2476C2214yes—
181#2475C2214yes—
182#2475C2214yes—
183#2474C2214yes—
184#2467C2214yes—
185#2462C2214yes—
186#2462C2214yes—
187#2460C2214yes—
188#2460C2214yes—
189#2460C2214yes—
190#2460C2214yes—
191#2459C2214yes—
192#2458C2214yes—
193#2457C2214yes—
194#2454C2214yes—
195#2454C2212yes—
196#2454C2212yes—
197#2453C2212yes—
198#2452C2212yes—
199#2451C2212yes—
200#2448C2212yes—
201#2447C2212yes—
202#2447C2212yes—
203#2445C2212yes—
204#2441C2212yes—
205#2441C2214yes—
206#2441C2214yes—
207#2441C2212yes—
208#2439C2214yes—
209#2439C2212yes—
210#2428C2212yes—
211#2427C2212yes—
212#2422C2212yes—
213#2422C2212yes—
214#2421C2212yes—
215#2414C2212yes—
216#2396C2212yes—
217#2396C2212yes—
218#2396C2214yes—
219#2395C2214yes—
220#2395C2212yes—
221#2392C2214yes—
222#2383C2214yes—
223#2383C2214yes—
224#2382C2214yes—
225#2379C2212yes—
226#2379C2212yes—
227#2370C2212yes—
228#2370C2212yes—
229#2369C2211yescharacteristic
230#2367C2212yes—
231#2366C2211yescharacteristic
232#2365C2212yes—
233#2361C2212yes—
234#2361C2212yes—
235#2360C2212yes—
236#2355C2211yescharacteristic
237#2355C2212yes—
238#2355C2211yescharacteristic
239#2355C2211yescharacteristic
240#2354C2212yes—
241#2354C2212yes—
242D4×C4⋊C4C2211yescharacteristic
243#2345C2212yes—
244#2344C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2212yes—
247C4×#125C2211yescharacteristic
248C4×#125C2211yescharacteristic
249C4×#126C2212yes—
250C4×#126C2212yes—
251C4×#124C2211yescharacteristic
252C4×#123C2214yes—
253#2296C2214yes—
254#2293C2212yes—
255#2293C2212yes—
256#2274C2212yes—
257C42×Q8C2211yescharacteristic
258C42×D4C2212yes—
259#564—48no—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×#127C2311yescharacteristic
265#529—416no—
266C2×#126C2312yes—
267C2×#126C2312yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125C2311yescharacteristic
272C2×#125C2314yes—
273C2×#125C2311yescharacteristic
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#124C2311yescharacteristic
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×#117C2314yes—
311C2×#117C2314yes—
312C2×#117C2314yes—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C42C2314yes—
317#401C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#399C2312yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2312yes—
346#399C2312yes—
347#398C2312yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2312yes—
363#398C2314yes—
364#398C2312yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2312yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2312yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#396C2314yes—
387#396C2312yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2312yes—
401#396C2314yes—
402#396C2312yes—
403#396C2314yes—
404#396C2312yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2312yes—
413#395C2312yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2312yes—
431#394C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2312yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2312yes—
441#392C2314yes—
442#392C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2312yes—
455#391C2312yes—
456#391C2314yes—
457#391C2311yescharacteristic
458#391C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2314yes—
465#390C2312yes—
466#390C2314yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2311yescharacteristic
476#389C2311yescharacteristic
477#389C2311yescharacteristic
478#389C2311yescharacteristic
479#389C2311yescharacteristic
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
528#388C2312yes—
529#388C2312yes—
530#388C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2312yes—
560#388C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#384C2312yes—
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2312yes—
633#384C2312yes—
634#384C2314yes—
635#384C2311yescharacteristic
636#384C2312yes—
637#384C2311yescharacteristic
638#384C2311yescharacteristic
639#383C2312yes—
640#383C2312yes—
641#383C2314yes—
642#383C2314yes—
643#383C2314yes—
644#382C2311yescharacteristic
645#382C2311yescharacteristic
646#382C2312yes—
647#382C2314yes—
648#382C2314yes—
649#382C2312yes—
650#382C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2312yes—
654#382C2312yes—
655#382C2311yescharacteristic
656#381C2314yes—
657#381C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2312yes—
663#380C2312yes—
664#380C2314yes—
665#380C2312yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C43C2312yes—
712C43C2311yescharacteristic
713C43C2312yes—
714C22×Q8C2411yescharacteristic
715C22×Q8C2411yescharacteristic
716C22×Q8C2414yes—
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×D4C2412yes—
720C22×D4C2411yescharacteristic
721C22×D4C2412yes—
722C22×D4C2414yes—
723C22×D4C2414yes—
724C22×D4C2412yes—
725C23×C4C2412yes—
726C23×C4C2414yes—
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2414yes—
730C4⋊Q8—44no—
731C4⋊Q8—42no—
732C4⋊Q8—44no—
733C4⋊Q8—44no—
734#127—42no—
735#126—28no—
736#126—48no—
737#126—48no—
738#126—48no—
739#126—44no—
740#125—216no—
741#125—24no—
742#125—44no—
743#125—44no—
744#125—42no—
745#125—48no—
746#125—48no—
747#125—44no—
748#125—44no—
749#125—48no—
750#125—48no—
751#125—48no—
752#124—44no—
753#124—44no—
754#124—48no—
755#124—44no—
756#124—42no—
757#123—48no—
758#123—48no—
759#123—48no—
760C22⋊Q8—48no—
761C22⋊Q8—44no—
762#121—48no—
763#121—44no—
764#121—44no—
765C4×Q8—24no—
766C4×Q8—44no—
767C4×Q8—42no—
768C4×Q8—48no—
769C4×Q8—42no—
770C4×Q8—42no—
771C4×D4—28no—
772C4×D4—28no—
773C4×D4—44no—
774C4×D4—44no—
775C4×D4—44no—
776C4×D4—42no—
777C4×D4—48no—
778C4×D4—48no—
779#117—44no—
780#117—48no—
781#117—48no—
782#117—44no—
783#117—48no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2411yescharacteristic
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C42—48no—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2414yes—
916C2×C42C2411yescharacteristic
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999C24C2512yes—
1000C24C2514yes—
1001C2×Q8—22no—
1002C2×Q8—22no—
1003C2×Q8—22no—
1004C2×Q8—22no—
1005C2×Q8—44no—
1006C2×Q8—41no—
1007C2×Q8—42no—
1008C2×Q8—44no—
1009C2×Q8—44no—
1010C2×Q8—42no—
1011C2×Q8—41no—
1012C2×Q8—42no—
1013C2×Q8—42no—
1014C2×Q8—42no—
1015C2×Q8—42no—
1016C2×D4—24no—
1017C2×D4—24no—
1018C2×D4—22no—
1019C2×D4—24no—
1020C2×D4—24no—
1021C2×D4—41no—
1022C2×D4—41no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—42no—
1029C2×D4—42no—
1030C2×D4—44no—
1031C2×D4—42no—
1032C2×D4—42no—
1033C2×D4—42no—
1034C22×C4—28no—
1035C22×C4—24no—
1036C22×C4—28no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—28no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4C2511yescharacteristic
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2514yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2514yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—24no—
1098C4⋊C4—22no—
1099C4⋊C4—22no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—41no—
1103C4⋊C4—41no—
1104C4⋊C4—42no—
1105C4⋊C4—41no—
1106C4⋊C4—41no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—41no—
1115C4⋊C4—41no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4H(5,𝔽2)14yes—
1150C4⋊C42−1+414yes—
1151C22⋊C4—24no—
1152C22⋊C4—28no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—24no—
1158C22⋊C4—28no—
1159C22⋊C4—44no—
1160C22⋊C4—42no—
1161C22⋊C4—42no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—42no—
1165C22⋊C4—42no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C42—24no—
1193C42—28no—
1194C42—24no—
1195C42—22no—
1196C42—24no—
1197C42—22no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—24no—
1202C42—22no—
1203C42—24no—
1204C42—24no—
1205C42—22no—
1206C42—22no—
1207C42—22no—
1208C42—24no—
1209C42—44no—
1210C42—44no—
1211C42—41no—
1212C42—42no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—42no—
1217C42—42no—
1218C42—44no—
1219C42—44no—
1220C42—42no—
1221C42—42no—
1222C23—22no—
1223C23—24no—
1224C23—24no—
1225C23—22no—
1226C23—24no—
1227C23—22no—
1228C23—24no—
1229C23—22no—
1230C23—22no—
1231C23—24no—
1232C23—22no—
1233C23—24no—
1234C23—24no—
1235C23—22no—
1236C23C2611yescharacteristic
1237Q8—44no—
1238Q8—82no—
1239Q8—88no—
1240Q8—84no—
1241Q8—162no—
1242D4—44no—
1243D4—48no—
1244D4—84no—
1245D4—88no—
1246D4—88no—
1247D4—162no—
1248C2×C4—22no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—21no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—416no—
1322C2×C4—48no—
1323C2×C4—88no—
1324C2×C4—88no—
1325C2×C4—88no—
1326C2×C4C2×H(5,𝔽2)14yes—
1327C2×C4C2×H(5,𝔽2)12yes—
1328C2×C4C2×2−1+414yes—
1329C2×C4C2×2−1+412yes—
1330C2×C4#58512yes—
1331C2×C4#58512yes—
1332C2×C4#58512yes—
1333C2×C4#58512yes—
1334C22—44no—
1335C22—42no—
1336C22—44no—
1337C22—42no—
1338C22—44no—
1339C22—42no—
1340C22—42no—
1341C22—44no—
1342C22—42no—
1343C22—44no—
1344C22—44no—
1345C22—42no—
1346C22—44no—
1347C22—42no—
1348C22C22×H(5,𝔽2)11yescharacteristic
1349C22C22×2−1+411yescharacteristic
1350C22C2×#58511yescharacteristic
1351C22C2×#58511yescharacteristic
1352C22C2×#58511yescharacteristic
1353C22C2×#58511yescharacteristic
1354C222−1+611yescharacteristic
1355C4—24no—
1356C4—24no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—41no—
1361C4—44no—
1362C4—41no—
1363C4—42no—
1364C4—42no—
1365C4—44no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—41no—
1371C4—44no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—42no—
1378C4—44no—
1379C4—42no—
1380C4—44no—
1381C4#353114yes—
1382C2—84no—
1383C2—82no—
1384C2C2×#353111yescharacteristic
1385C2#6290711yescharacteristic
1386C2#6294911yescharacteristic
1387C2#6296011yescharacteristic
1388C2#6301311yescharacteristic
1389C2#6302211yescharacteristic
1390C2#6303611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#46015C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53109C2semidirect
2. #53056C2semidirect
3. #52979C2semidirect
4. #52517C2semidirect
5. #52507C2semidirect
6. #52439C2semidirect
7. #52306C2semidirect
8. #52152C2semidirect
9. #46343C2semidirect
10. #46284C2semidirect
11. C4⋊#564C2semidirect
12. #46135C2semidirect
13. #46117C2semidirect
14. #46078C2semidirect
16. #46014C2semidirect
17. #45963C2semidirect
18. #45957C2semidirect
19. #45867C2semidirect
20. #45843C2semidirect
21. #36497C2semidirect
22. #36452C2semidirect
23. #36416C2semidirect
24. #36300C2semidirect
25. #36299C2semidirect
26. #36113C2semidirect
27. #35838C2semidirect
28. #35783C2semidirect
29. #35725C2semidirect

Maximal subgroups

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

subgroupindex
#531092
#530562
#529792
#525172
#525072
#524392
#523062
#521522
#463432
#462842
C4⋊#5642
#461352
#461172
#460782
#460152
#460142
#459632
#459572
#458672
#458432
#364972
#364522
#364162
#363002
#362992
#361132
#358382
#357832
#357252