Finite Group Databasebeta

← #8678560

Subgroups — #8678560

Order 512.

4751 conjugacy classes of subgroups.

The subgroup lattice has 1478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59699C212yesmaximal, complemented
2#59698C212yesmaximal, complemented
3#59411C212yesmaximal, complemented
4#57048C214yesmaximal, complemented
5#55369C214yesmaximal, complemented
6#54842C214yesmaximal, complemented
7#53195C212yesmaximal, complemented
8#52306C211yesmaximal, characteristic, complemented
9#50870C214yesmaximal, complemented
10#50089C214yesmaximal, complemented
11#48213C214yesmaximal, complemented
12#46013C211yesmaximal, characteristic, complemented
13#46005C211yesmaximal, characteristic, complemented
14#45998C211yesmaximal, characteristic, complemented
15#45360C212yesmaximal, complemented
16#45051C212yesmaximal, complemented
17#44890C212yesmaximal, complemented
18#42939C212yesmaximal, complemented
19#42603C212yesmaximal, complemented
20#42441C212yesmaximal, complemented
21#40072C212yesmaximal, complemented
22#39626C212yesmaximal, complemented
23#39404C212yesmaximal, complemented
24#39384C212yesmaximal, complemented
25#38782C212yesmaximal, complemented
26#38445C212yesmaximal, complemented
27#36454C211yesmaximal, characteristic, complemented
28#36412C211yesmaximal, characteristic
29#36290C211yesmaximal, characteristic, complemented
30C2×#563C2212yes—
31C2×#559C2212yes—
32C2×#555C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#542C2212yes—
35C2×#539C2214yes—
36#2862C2211yescharacteristic
37#2859C2212yes—
38#2859C2211yescharacteristic
39#2858C2211yescharacteristic
40#2856C2212yes—
41#2855C2212yes—
42#2851C2212yes—
43#2845C2212yes—
44#2836C2214yes—
45#2829C2214yes—
46#2820C2212yes—
47#2820C2212yes—
48#2814C2214yes—
49#2809C2211yescharacteristic
50#2808C2212yes—
51#2806C2212yes—
52#2806C2214yes—
53#2806C2214yes—
54#2800C2214yes—
55#2793C2214yes—
56#2792C2214yes—
57#2792C2214yes—
58#2790C2214yes—
59#2788C2214yes—
60#2784C2214yes—
61#2780C2214yes—
62#2775C2212yes—
63#2775C2212yes—
64#2769C2212yes—
65#2768C2214yes—
66#2761C2214yes—
67#2757C2214yes—
68#2738C2214yes—
69#2734C2211yescharacteristic
70#2732C2212yes—
71#2732C2212yes—
72#2731C2212yes—
73#2727C2211yescharacteristic
74#2727C2211yescharacteristic
75#2727C2212yes—
76#2723C2214yes—
77#2723C2214yes—
78#2723C2214yes—
79#2721C2212yes—
80#2721C2212yes—
81#2718C2214yes—
82#2717C2214yes—
83#2715C2214yes—
84#2715C2214yes—
85#2712C2214yes—
86#2710C2214yes—
87#2709C2214yes—
88#2707C2214yes—
89#2706C2214yes—
90#2706C2214yes—
91#2706C2214yes—
92#2704C2214yes—
93#2701C2214yes—
94#2701C2214yes—
95#2700C2214yes—
96#2695C2214yes—
97#2695C2214yes—
98#2694C2214yes—
99#2694C2214yes—
100#2694C2214yes—
101#2692C2214yes—
102#2691C2214yes—
103#2690C2214yes—
104#2687C2214yes—
105#2686C2214yes—
106#2683C2212yes—
107#2681C2214yes—
108#2680C2214yes—
109#2674C2214yes—
110#2674C2214yes—
111#2672C2214yes—
112#2672C2214yes—
113#2667C2214yes—
114#2664C2214yes—
115#2660C2214yes—
116#2651C2214yes—
117#2649C2214yes—
118#2633C2214yes—
119#2630C2214yes—
120#2630C2214yes—
121#2620C2212yes—
122#2618C2214yes—
123#2608C2214yes—
124#2603C2214yes—
125#2600C2214yes—
126#2597C2214yes—
127#2582C2212yes—
128#2582C2212yes—
129#2579C2214yes—
130#2575C2214yes—
131#2571C2211yescharacteristic
132#2567C2212yes—
133#2567C2211yescharacteristic
134#2556C2214yes—
135#2555C2214yes—
136#2555C2214yes—
137#2552C2211yescharacteristic
138#2552C2212yes—
139#2552C2214yes—
140#2551C2212yes—
141#2550C2214yes—
142#2549C2214yes—
143#2547C2214yes—
144#2547C2211yescharacteristic
145#2545C2212yes—
146#2544C2212yes—
147#2544C2212yes—
148#2542C2211yescharacteristic
149#2542C2212yes—
150#2541C2211yescharacteristic
151#2538C2212yes—
152#2538C2214yes—
153#2531C2214yes—
154#2526C2214yes—
155#2525C2214yes—
156#2521C2214yes—
157#2517C2214yes—
158#2517C2214yes—
159#2512C2212yes—
160#2512C2212yes—
161#2512C2214yes—
162#2511C2212yes—
163#2509C2212yes—
164#2507C2212yes—
165#2507C2212yes—
166#2505C2214yes—
167#2502C2212yes—
168#2501C2214yes—
169#2501C2212yes—
170#2500C2212yes—
171#2499C2212yes—
172#2489C2212yes—
173#2488C2214yes—
174#2478C2214yes—
175#2473C2214yes—
176#2468C2214yes—
177#2465C2214yes—
178#2461C2214yes—
179#2455C2214yes—
180#2452C2212yes—
181#2452C2212yes—
182#2451C2212yes—
183#2451C2212yes—
184#2450C2214yes—
185#2449C2214yes—
186#2449C2214yes—
187#2448C2212yes—
188#2447C2212yes—
189#2447C2212yes—
190#2447C2212yes—
191#2445C2212yes—
192#2445C2212yes—
193#2445C2214yes—
194#2442C2212yes—
195#2442C2212yes—
196#2440C2212yes—
197#2439C2212yes—
198#2438C2214yes—
199#2432C2214yes—
200#2431C2212yes—
201#2429C2212yes—
202#2428C2212yes—
203#2428C2212yes—
204#2427C2214yes—
205#2427C2212yes—
206#2427C2212yes—
207#2426C2212yes—
208#2426C2212yes—
209#2425C2214yes—
210#2425C2214yes—
211#2425C2214yes—
212#2423C2212yes—
213#2422C2214yes—
214#2422C2212yes—
215#2422C2212yes—
216#2421C2212yes—
217#2417C2214yes—
218#2417C2212yes—
219#2396C2212yes—
220#2396C2212yes—
221#2395C2212yes—
222#2379C2212yes—
223#2379C2212yes—
224#2373C2214yes—
225#2367C2212yes—
226#2365C2211yescharacteristic
227#2365C2211yescharacteristic
228#2363C2212yes—
229#2363C2212yes—
230#2362C2212yes—
231#2361C2212yes—
232#2361C2214yes—
233#2361C2212yes—
234#2355C2212yes—
235Q8×C4⋊C4C2212yes—
236#2349C2212yes—
237#2349C2212yes—
238D4×C4⋊C4C2211yescharacteristic
239D4×C4⋊C4C2212yes—
240D4×C4⋊C4C2211yescharacteristic
241#2339C2214yes—
242#2331C2214yes—
243#2329C2214yes—
244#2324C2212yes—
245#2316C2212yes—
246C4×C4⋊Q8C2212yes—
247C4×#127C2212yes—
248C4×#125C2211yescharacteristic
249C4×#125C2211yescharacteristic
250C4×#126C2212yes—
251C4×#126C2212yes—
252C4×#124C2212yes—
253C4×#124C2211yescharacteristic
254C4×C22⋊Q8C2212yes—
255#2297C2212yes—
256#2295C2212yes—
257C2×#389C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260#563—48no—
261#559—48no—
262#555—44no—
263#550—44no—
264#542—48no—
265#539—416no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2314yes—
272C2×#127C2312yes—
273C2×#127C2311yescharacteristic
274C2×#127C2312yes—
275C2×#126C2312yes—
276C2×#126C2314yes—
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2311yescharacteristic
281C2×#125C2311yescharacteristic
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2312yes—
286C2×#124C2312yes—
287C2×#124C2311yescharacteristic
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2314yes—
293C2×#124C2312yes—
294C2×#124C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2314yes—
315C2×#121C2312yes—
316C2×#121C2312yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2314yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2312yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2314yes—
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2312yes—
350C22×C42C2312yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#400C2312yes—
357#400C2312yes—
358#400C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2312yes—
365#399C2312yes—
366#399C2312yes—
367#399C2314yes—
368#399C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2312yes—
404#397C2314yes—
405#397C2314yes—
406#397C2312yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2312yes—
424#396C2314yes—
425#396C2314yes—
426#396C2312yes—
427#396C2314yes—
428#396C2312yes—
429#396C2312yes—
430#396C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2312yes—
437#395C2312yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2312yes—
454#394C2312yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#393C2312yes—
462#393C2312yes—
463#393C2314yes—
464#393C2314yes—
465#393C2314yes—
466#392C2314yes—
467#392C2314yes—
468#392C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2314yes—
473#391C2312yes—
474#391C2314yes—
475#391C2314yes—
476#391C2312yes—
477#391C2312yes—
478#391C2314yes—
479#391C2314yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2314yes—
486#391C2312yes—
487#391C2311yescharacteristic
488#390C2314yes—
489#390C2312yes—
490#390C2314yes—
491#390C2312yes—
492#390C2314yes—
493#390C2312yes—
494#390C2314yes—
495#390C2311yescharacteristic
496#390C2312yes—
497#390C2314yes—
498#390C2314yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2314yes—
506#389C2311yescharacteristic
507#389C2311yescharacteristic
508#389C2311yescharacteristic
509#389C2311yescharacteristic
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2314yes—
546#388C2312yes—
547#388C2312yes—
548#388C2312yes—
549#388C2312yes—
550#388C2312yes—
551#388C2312yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2312yes—
574#388C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
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#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#384C2312yes—
642#384C2312yes—
643#384C2312yes—
644#384C2314yes—
645#384C2311yescharacteristic
646#384C2312yes—
647#384C2311yescharacteristic
648#384C2312yes—
649#384C2312yes—
650#384C2314yes—
651#383C2312yes—
652#383C2312yes—
653#382C2311yescharacteristic
654#382C2311yescharacteristic
655#382C2312yes—
656#382C2312yes—
657#382C2312yes—
658#382C2312yes—
659#382C2314yes—
660#382C2311yescharacteristic
661#382C2312yes—
662#382C2314yes—
663#381C2314yes—
664#381C2314yes—
665#381C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2312yes—
670#380C2314yes—
671#380C2314yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2312yes—
679#380C2314yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C43C2312yes—
717C43C2311yescharacteristic
718C2×#41—28no—
719C2×#41—44no—
720C2×#41—82no—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2414yes—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2414yes—
729C22×D4C2411yescharacteristic
730C22×D4C2414yes—
731C22×D4C2414yes—
732C22×D4C2411yescharacteristic
733C22×D4C2414yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C4⋊Q8—28no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750C4⋊Q8—42no—
751C4⋊Q8—48no—
752C4⋊Q8—42no—
753#127—28no—
754#127—42no—
755#127—82no—
756#126—28no—
757#126—216no—
758#126—48no—
759#126—48no—
760#126—44no—
761#125—24no—
762#125—42no—
763#125—48no—
764#125—48no—
765#125—44no—
766#125—82no—
767#124—24no—
768#124—28no—
769#124—44no—
770#124—44no—
771#124—44no—
772#124—44no—
773#124—48no—
774#124—48no—
775#124—48no—
776#123—48no—
777#123—48no—
778#123—48no—
779#123—48no—
780#123—48no—
781#123—48no—
782#123—48no—
783#123—48no—
784#123—84no—
785C22⋊Q8—28no—
786C22⋊Q8—48no—
787C22⋊Q8—48no—
788C22⋊Q8—48no—
789C22⋊Q8—48no—
790C22⋊Q8—48no—
791C22⋊Q8—48no—
792C22⋊Q8—44no—
793C22⋊Q8—44no—
794C22⋊Q8—82no—
795C22⋊Q8—84no—
796#121—28no—
797#121—28no—
798#121—48no—
799#121—48no—
800#121—48no—
801#121—44no—
802#121—44no—
803#121—44no—
804C4×Q8—28no—
805C4×Q8—42no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—82no—
810C4×D4—28no—
811C4×D4—24no—
812C4×D4—24no—
813C4×D4—48no—
814C4×D4—48no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—42no—
818C4×D4—44no—
819C4×D4—44no—
820C4×D4—42no—
821C4×D4—48no—
822C4×D4—84no—
823C4×D4—84no—
824#117—44no—
825#117—44no—
826#117—44no—
827C2×C4⋊C4—44no—
828C2×C4⋊C4—44no—
829C2×C4⋊C4—48no—
830C2×C4⋊C4—82no—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2411yescharacteristic
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C42—82no—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2411yescharacteristic
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2414yes—
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2412yes—
966C2×C42C2414yes—
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2411yescharacteristic
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035C24C2514yes—
1036C24C2512yes—
1037C24C2512yes—
1038#41—816no—
1039C2×Q8—24no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—24no—
1043C2×Q8—24no—
1044C2×Q8—41no—
1045C2×Q8—41no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—42no—
1050C2×Q8—44no—
1051C2×Q8—44no—
1052C2×Q8—44no—
1053C2×Q8—42no—
1054C2×Q8—42no—
1055C2×Q8—42no—
1056C2×Q82−1+414yes—
1057C2×D4—28no—
1058C2×D4—28no—
1059C2×D4—28no—
1060C2×D4—24no—
1061C2×D4—22no—
1062C2×D4—24no—
1063C2×D4—28no—
1064C2×D4—28no—
1065C2×D4—22no—
1066C2×D4—24no—
1067C2×D4—22no—
1068C2×D4—24no—
1069C2×D4—44no—
1070C2×D4—41no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—41no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C2×D4—42no—
1086C2×D4H(5,𝔽2)14yes—
1087C22×C4—24no—
1088C22×C4—28no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—28no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—44no—
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×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2511yescharacteristic
1128C22×C4C2512yes—
1129C22×C4C2514yes—
1130C22×C4C2512yes—
1131C22×C4C2514yes—
1132C22×C4C2514yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2512yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2512yes—
1141C22×C4C2511yescharacteristic
1142C22×C4C2511yescharacteristic
1143C4⋊C4—24no—
1144C4⋊C4—28no—
1145C4⋊C4—22no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—22no—
1150C4⋊C4—24no—
1151C4⋊C4—28no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—28no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—22no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—22no—
1164C4⋊C4—24no—
1165C4⋊C4—22no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—41no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—41no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—41no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—41no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—41no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4—41no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4H(5,𝔽2)14yes—
1213C4⋊C42−1+414yes—
1214C22⋊C4—28no—
1215C22⋊C4—24no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—24no—
1221C22⋊C4—28no—
1222C22⋊C4—24no—
1223C22⋊C4—28no—
1224C22⋊C4—28no—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—28no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—28no—
1232C22⋊C4—44no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—42no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C42—24no—
1263C42—24no—
1264C42—22no—
1265C42—24no—
1266C42—24no—
1267C42—28no—
1268C42—22no—
1269C42—22no—
1270C42—24no—
1271C42—28no—
1272C42—22no—
1273C42—24no—
1274C42—24no—
1275C42—22no—
1276C42—22no—
1277C42—41no—
1278C42—42no—
1279C42—42no—
1280C42—42no—
1281C42—44no—
1282C42—44no—
1283C42—42no—
1284C42—44no—
1285C42—44no—
1286C42—42no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—24no—
1294C23—22no—
1295C23—22no—
1296C23—24no—
1297C23—22no—
1298C23—24no—
1299C23—22no—
1300C23—24no—
1301C23—24no—
1302C23—22no—
1303C23—24no—
1304C23—22no—
1305C23—24no—
1306C23—22no—
1307C23C2×H(5,𝔽2)14yes—
1308C23C2611yescharacteristic
1309Q8—44no—
1310Q8—48no—
1311Q8—84no—
1312Q8—84no—
1313Q8—164no—
1314Q8—162no—
1315D4—28no—
1316D4—416no—
1317D4—48no—
1318D4—82no—
1319D4—88no—
1320D4—84no—
1321D4—88no—
1322D4—88no—
1323D4—162no—
1324D4—164no—
1325C2×C4—22no—
1326C2×C4—21no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—21no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—21no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—21no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—22no—
1373C2×C4—21no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—48no—
1395C2×C4—48no—
1396C2×C4—48no—
1397C2×C4—84no—
1398C2×C4—88no—
1399C2×C4—88no—
1400C2×C4—164no—
1401C2×C4—164no—
1402C2×C4—164no—
1403C2×C4—164no—
1404C2×C4C2×H(5,𝔽2)14yes—
1405C2×C4C2×H(5,𝔽2)12yes—
1406C2×C4C2×H(5,𝔽2)12yes—
1407C2×C4C2×2−1+414yes—
1408C2×C4C2×2−1+414yes—
1409C2×C4C2×2−1+412yes—
1410C2×C4C2×2−1+412yes—
1411C2×C4#58512yes—
1412C2×C4#58512yes—
1413C22—24no—
1414C22—24no—
1415C22—24no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—44no—
1422C22—44no—
1423C22—42no—
1424C22—42no—
1425C22—44no—
1426C22—44no—
1427C22—42no—
1428C22—44no—
1429C22—42no—
1430C22—42no—
1431C22—44no—
1432C22—42no—
1433C22—44no—
1434C22C22×H(5,𝔽2)11yescharacteristic
1435C22C22×H(5,𝔽2)11yescharacteristic
1436C22C22×2−1+411yescharacteristic
1437C22C22×2−1+411yescharacteristic
1438C22C2×#58511yescharacteristic
1439C22C2×#58511yescharacteristic
1440C22H(7,𝔽2)11yescharacteristic
1441C4—24no—
1442C4—22no—
1443C4—24no—
1444C4—22no—
1445C4—24no—
1446C4—22no—
1447C4—42no—
1448C4—44no—
1449C4—42no—
1450C4—44no—
1451C4—42no—
1452C4—42no—
1453C4—44no—
1454C4—41no—
1455C4—41no—
1456C4—42no—
1457C4—41no—
1458C4—42no—
1459C4—42no—
1460C4—42no—
1461C4—42no—
1462C4—42no—
1463C4—44no—
1464C4—42no—
1465C4—44no—
1466C4#355914yes—
1467C2—44no—
1468C2—82no—
1469C2—84no—
1470C2C2×#355911yescharacteristic
1471C2#6289411yescharacteristic
1472C2#6294811yescharacteristic
1473C2#6296111yescharacteristic
1474C2#6301411yescharacteristic
1475C2#6303411yescharacteristic
1476C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36412C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59699C2semidirect
2. #59698C2semidirect
3. #59411C2semidirect
4. #57048C2semidirect
5. #55369C2semidirect
6. #54842C2semidirect
7. #53195C2semidirect
8. #52306C2semidirect
9. #50870C2semidirect
10. #50089C2semidirect
11. #48213C2semidirect
12. #46013C2semidirect
13. #46005C2semidirect
14. #45998C2semidirect
15. #45360C2semidirect
16. #45051C2semidirect
17. #44890C2semidirect
18. #42939C2semidirect
19. #42603C2semidirect
20. #42441C2semidirect
21. #40072C2semidirect
22. #39626C2semidirect
23. #39404C2semidirect
24. #39384C2semidirect
25. #38782C2semidirect
26. #38445C2semidirect
27. #36454C2semidirect
29. #36290C2semidirect

Maximal subgroups

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

subgroupindex
#596992
#596982
#594112
#570482
#553692
#548422
#531952
#523062
#508702
#500892
#482132
#460132
#460052
#459982
#453602
#450512
#448902
#429392
#426032
#424412
#400722
#396262
#394042
#393842
#387822
#384452
#364542
#364122
#362902