Finite Group Databasebeta

← #7898328

Subgroups — #7898328

Order 512.

4873 conjugacy classes of subgroups.

The subgroup lattice has 1451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59869C211yesmaximal, characteristic, complemented
2#59144C212yesmaximal, complemented
3#52267C211yesmaximal, characteristic, complemented
4#51367C214yesmaximal, complemented
5#50511C214yesmaximal, complemented
6#48097C214yesmaximal, complemented
7#46520C214yesmaximal, complemented
8#45938C212yesmaximal, complemented
9#45156C212yesmaximal, complemented
10#45146C212yesmaximal, complemented
11#45144C212yesmaximal, complemented
12#44439C214yesmaximal, complemented
13#42941C212yesmaximal, complemented
14#42702C212yesmaximal, complemented
15#41302C214yesmaximal, complemented
16#40033C212yesmaximal, complemented
17#39820C212yesmaximal, complemented
18#39740C211yesmaximal, characteristic, complemented
19#39700C212yesmaximal, complemented
20#39356C211yesmaximal, characteristic
21#38810C212yesmaximal, complemented
22#37675C212yesmaximal, complemented
23#37252C212yesmaximal, complemented
24#36538C211yesmaximal, characteristic, complemented
25#35817C212yesmaximal, complemented
26#35667C212yesmaximal, complemented
27#35187C211yesmaximal, characteristic, complemented
28#34474C212yesmaximal, complemented
29#34311C211yesmaximal, characteristic, complemented
30C2×#559C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#556C2212yes—
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2212yes—
35C2×#536C2212yes—
36C2×#536C2212yes—
37C22×C4⋊Q8C2212yes—
38C2×#519C2212yes—
39#2864C2212yes—
40#2863C2212yes—
41#2861C2212yes—
42#2858C2211yescharacteristic
43#2850C2212yes—
44#2836C2214yes—
45#2833C2214yes—
46#2809C2212yes—
47#2809C2212yes—
48#2807C2212yes—
49#2806C2211yescharacteristic
50#2805C2211yescharacteristic
51#2804C2211yescharacteristic
52#2802C2212yes—
53#2793C2214yes—
54#2790C2214yes—
55#2790C2212yes—
56#2788C2212yes—
57#2783C2214yes—
58#2782C2214yes—
59#2780C2212yes—
60#2778C2214yes—
61#2777C2214yes—
62#2773C2214yes—
63#2772C2214yes—
64#2771C2214yes—
65#2768C2214yes—
66#2765C2214yes—
67#2765C2214yes—
68#2765C2214yes—
69#2765C2214yes—
70#2764C2214yes—
71#2757C2214yes—
72#2753C2214yes—
73#2749C2214yes—
74#2738C2214yes—
75#2732C2212yes—
76#2732C2211yescharacteristic
77#2732C2212yes—
78#2730C2214yes—
79#2729C2212yes—
80#2727C2212yes—
81#2727C2212yes—
82#2713C2214yes—
83#2713C2214yes—
84#2706C2214yes—
85#2700C2214yes—
86#2698C2214yes—
87#2695C2214yes—
88#2693C2214yes—
89#2689C2214yes—
90#2687C2214yes—
91#2687C2214yes—
92#2683C2212yes—
93#2683C2212yes—
94#2682C2212yes—
95#2682C2212yes—
96#2677C2214yes—
97#2677C2214yes—
98#2674C2214yes—
99#2674C2214yes—
100#2667C2214yes—
101#2666C2214yes—
102#2666C2214yes—
103#2658C2212yes—
104#2655C2214yes—
105#2654C2214yes—
106#2649C2214yes—
107#2637C2214yes—
108#2621C2212yes—
109#2620C2212yes—
110#2609C2214yes—
111#2601C2214yes—
112#2597C2214yes—
113#2595C2214yes—
114#2594C2214yes—
115#2587C2214yes—
116#2587C2214yes—
117#2586C2214yes—
118#2582C2211yescharacteristic
119#2576C2214yes—
120#2576C2214yes—
121#2573C2214yes—
122#2571C2211yescharacteristic
123#2571C2212yes—
124#2568C2212yes—
125#2568C2211yescharacteristic
126#2568C2212yes—
127#2568C2211yescharacteristic
128#2566C2212yes—
129#2558C2214yes—
130#2558C2214yes—
131#2557C2214yes—
132#2553C2214yes—
133#2550C2214yes—
134#2549C2214yes—
135#2548C2211yescharacteristic
136#2547C2212yes—
137#2546C2212yes—
138#2546C2212yes—
139#2546C2212yes—
140#2546C2212yes—
141#2546C2211yescharacteristic
142#2546C2212yes—
143#2546C2212yes—
144#2545C2212yes—
145#2545C2212yes—
146#2545C2212yes—
147#2545C2212yes—
148#2545C2212yes—
149#2545C2212yes—
150#2545C2212yes—
151#2544C2212yes—
152#2525C2214yes—
153#2525C2214yes—
154#2524C2214yes—
155#2522C2214yes—
156#2514C2212yes—
157#2514C2212yes—
158#2514C2212yes—
159#2513C2212yes—
160#2508C2214yes—
161#2508C2212yes—
162#2508C2214yes—
163#2488C2214yes—
164#2479C2214yes—
165#2479C2214yes—
166#2479C2214yes—
167#2477C2214yes—
168#2473C2214yes—
169#2473C2214yes—
170#2470C2214yes—
171#2469C2214yes—
172#2465C2214yes—
173#2461C2214yes—
174#2461C2214yes—
175#2457C2214yes—
176#2451C2214yes—
177#2450C2214yes—
178#2449C2214yes—
179#2449C2214yes—
180#2448C2212yes—
181#2447C2212yes—
182#2447C2212yes—
183#2446C2212yes—
184#2446C2212yes—
185#2446C2212yes—
186#2446C2212yes—
187#2443C2214yes—
188#2443C2214yes—
189#2442C2214yes—
190#2438C2214yes—
191#2436C2212yes—
192#2434C2212yes—
193#2434C2212yes—
194#2434C2212yes—
195#2432C2212yes—
196#2431C2212yes—
197#2429C2214yes—
198#2429C2214yes—
199#2429C2214yes—
200#2429C2214yes—
201#2413C2214yes—
202#2413C2214yes—
203#2413C2214yes—
204#2413C2214yes—
205#2402C2212yes—
206#2396C2212yes—
207#2396C2212yes—
208#2396C2214yes—
209#2379C2214yes—
210#2377C2214yes—
211#2369C2212yes—
212#2368C2214yes—
213#2367C2212yes—
214#2367C2212yes—
215#2367C2212yes—
216#2365C2212yes—
217#2365C2211yescharacteristic
218#2365C2212yes—
219#2363C2212yes—
220#2362C2212yes—
221#2362C2214yes—
222#2362C2212yes—
223#2360C2214yes—
224#2357C2214yes—
225#2355C2212yes—
226#2355C2212yes—
227#2354C2212yes—
228#2354C2211yescharacteristic
229Q8×C4⋊C4C2211yescharacteristic
230Q8×C22⋊C4C2212yes—
231Q8×C22⋊C4C2212yes—
232#2339C2212yes—
233#2337C2214yes—
234#2337C2214yes—
235#2333C2214yes—
236#2332C2214yes—
237#2327C2212yes—
238#2326C2212yes—
239#2324C2212yes—
240#2323C2212yes—
241#2323C2214yes—
242#2320C2212yes—
243#2318C2214yes—
244#2310C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2211yescharacteristic
248C4×C4⋊Q8C2211yescharacteristic
249C4×#124C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252#2297C2212yes—
253#2296C2212yes—
254#2295C2211yescharacteristic
255#2293C2211yescharacteristic
256#2293C2212yes—
257#2290C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261C23×Q8C2312yes—
262#559—44no—
263#557—44no—
264#556—48no—
265D4×Q8—28no—
266#548—216no—
267#536—48no—
268#536—48no—
269C2×C4⋊Q8—48no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2312yes—
284C2×#127C2311yescharacteristic
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#125C2312yes—
288C2×#125C2314yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×#121C2312yes—
314C2×#121C2314yes—
315#519—48no—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2314yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2314yes—
330C2×C4×Q8C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2311yescharacteristic
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2314yes—
341C2×#117C2314yes—
342C2×#117C2314yes—
343C22×C4⋊C4C2314yes—
344C22×C4⋊C4C2314yes—
345C22×C42C2312yes—
346#401C2314yes—
347#401C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2312yes—
366#400C2312yes—
367#399C2314yes—
368#399C2314yes—
369#399C2312yes—
370#399C2312yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2312yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
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#396C2312yes—
426#396C2314yes—
427#396C2312yes—
428#396C2312yes—
429#396C2314yes—
430#396C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2312yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2312yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2312yes—
449#393C2312yes—
450#392C2314yes—
451#392C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2314yes—
455#391C2311yescharacteristic
456#391C2311yescharacteristic
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2312yes—
462#391C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2314yes—
467#391C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2314yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2314yes—
480#391C2311yescharacteristic
481#391C2312yes—
482#391C2311yescharacteristic
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2314yes—
487#390C2312yes—
488#390C2314yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2311yescharacteristic
494#390C2312yes—
495#390C2312yes—
496#390C2311yescharacteristic
497#389C2311yescharacteristic
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2311yescharacteristic
522#389C2312yes—
523#389C2314yes—
524#389C2311yescharacteristic
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2314yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2311yescharacteristic
535#388C2314yes—
536#388C2314yes—
537#388C2312yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
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#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2312yes—
569#388C2312yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
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#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2312yes—
622#386C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2312yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2312yes—
641#385C2312yes—
642#385C2312yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2312yes—
647#385C2312yes—
648#384C2311yescharacteristic
649#384C2311yescharacteristic
650#384C2311yescharacteristic
651#384C2312yes—
652#383C2314yes—
653#383C2314yes—
654#383C2314yes—
655#382C2312yes—
656#382C2314yes—
657#382C2312yes—
658#382C2314yes—
659#382C2314yes—
660#382C2312yes—
661#382C2312yes—
662#382C2314yes—
663#382C2314yes—
664#381C2314yes—
665#381C2314yes—
666#381C2314yes—
667#381C2314yes—
668#381C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717#376C2312yes—
718C2×#95C2314yes—
719C43C2311yescharacteristic
720C43C2312yes—
721C2×#41—28no—
722C2×#41—44no—
723C2×#41—44no—
724C22×Q8—28no—
725C22×Q8—28no—
726C22×Q8—28no—
727C22×Q8—44no—
728C22×Q8—44no—
729C22×Q8—44no—
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×Q8C2412yes—
733C22×Q8C2414yes—
734C22×Q8C2411yescharacteristic
735C22×Q8C2411yescharacteristic
736C22×Q8C2411yescharacteristic
737C22×Q8C2414yes—
738C22×Q8C2411yescharacteristic
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2412yes—
742C22×D4C2414yes—
743C22×D4C2412yes—
744C22×D4C2411yescharacteristic
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2414yes—
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2412yes—
751C23×C4C2414yes—
752C23×C4C2414yes—
753C4⋊Q8—28no—
754C4⋊Q8—28no—
755C4⋊Q8—24no—
756C4⋊Q8—28no—
757C4⋊Q8—24no—
758C4⋊Q8—24no—
759C4⋊Q8—44no—
760C4⋊Q8—44no—
761C4⋊Q8—44no—
762C4⋊Q8—44no—
763C4⋊Q8—44no—
764C4⋊Q8—42no—
765C4⋊Q8—48no—
766C4⋊Q8—48no—
767#127—42no—
768#126—48no—
769#126—48no—
770#125—44no—
771#125—48no—
772#124—28no—
773#124—28no—
774#124—216no—
775#124—28no—
776#124—28no—
777#124—44no—
778#124—44no—
779#124—44no—
780#124—44no—
781#123—48no—
782#123—48no—
783#123—48no—
784#123—48no—
785#123—48no—
786C22⋊Q8—28no—
787C22⋊Q8—28no—
788C22⋊Q8—28no—
789C22⋊Q8—216no—
790C22⋊Q8—216no—
791C22⋊Q8—48no—
792C22⋊Q8—48no—
793C22⋊Q8—48no—
794C22⋊Q8—48no—
795C22⋊Q8—48no—
796#121—216no—
797#121—28no—
798C4×Q8—24no—
799C4×Q8—28no—
800C4×Q8—24no—
801C4×Q8—24no—
802C4×Q8—28no—
803C4×Q8—24no—
804C4×Q8—42no—
805C4×Q8—42no—
806C4×Q8—48no—
807C4×Q8—48no—
808C4×Q8—44no—
809C4×Q8—44no—
810C4×Q8—44no—
811C4×Q8—44no—
812C4×Q8—44no—
813C4×D4—28no—
814C4×D4—216no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—44no—
818C4×D4#4118yes—
819#117—28no—
820#117—44no—
821#117—48no—
822#117—48no—
823#117—48no—
824#117—44no—
825C2×C4⋊C4—48no—
826C2×C4⋊C4—48no—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C42—44no—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2411yescharacteristic
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2411yescharacteristic
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2411yescharacteristic
962C2×C42C2411yescharacteristic
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034C24C2514yes—
1035C24C2512yes—
1036#41—816no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—28no—
1041C2×Q8—24no—
1042C2×Q8—28no—
1043C2×Q8—22no—
1044C2×Q8—24no—
1045C2×Q8—24no—
1046C2×Q8—24no—
1047C2×Q8—28no—
1048C2×Q8—24no—
1049C2×Q8—24no—
1050C2×Q8—24no—
1051C2×Q8—22no—
1052C2×Q8—22no—
1053C2×Q8—41no—
1054C2×Q8—44no—
1055C2×Q8—41no—
1056C2×Q8—41no—
1057C2×Q8—44no—
1058C2×Q8—44no—
1059C2×Q8—41no—
1060C2×Q8—41no—
1061C2×Q8—41no—
1062C2×Q8—432no—
1063C2×Q8—816no—
1064C2×Q8H(5,𝔽2)14yes—
1065C2×Q82−1+414yes—
1066C2×D4—28no—
1067C2×D4—28no—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—41no—
1073C2×D4—41no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—42no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—42no—
1081C2×D4—42no—
1082C2×D4—42no—
1083C2×D4C2×#4114yes—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—28no—
1087C22×C4—28no—
1088C22×C4—28no—
1089C22×C4—24no—
1090C22×C4—28no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4C2×#4118yes—
1108C22×C4C2512yes—
1109C22×C4C2514yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2514yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2514yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2512yes—
1132C22×C4C2511yescharacteristic
1133C22×C4C2512yes—
1134C22×C4C2511yescharacteristic
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—22no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—28no—
1144C4⋊C4—28no—
1145C4⋊C4—28no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—22no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—28no—
1154C4⋊C4—22no—
1155C4⋊C4—24no—
1156C4⋊C4—22no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—41no—
1169C4⋊C4—41no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—41no—
1177C4⋊C4—42no—
1178C4⋊C4—41no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—41no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C4⋊C4—41no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4C2×#4114yes—
1207C22⋊C4—28no—
1208C22⋊C4—28no—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—28no—
1212C22⋊C4—24no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4C2×#4118yes—
1245C42—28no—
1246C42—24no—
1247C42—24no—
1248C42—24no—
1249C42—24no—
1250C42—24no—
1251C42—28no—
1252C42—24no—
1253C42—24no—
1254C42—24no—
1255C42—22no—
1256C42—24no—
1257C42—22no—
1258C42—42no—
1259C42—42no—
1260C42—41no—
1261C42—42no—
1262C42—41no—
1263C42—42no—
1264C42—44no—
1265C42—41no—
1266C42—44no—
1267C42—44no—
1268C42—44no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42C2×#4114yes—
1273C42H(5,𝔽2)14yes—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—24no—
1281C23—24no—
1282C23—24no—
1283C23—24no—
1284C23—24no—
1285C23—24no—
1286C23—24no—
1287C23C22×#4114yes—
1288C23C2611yescharacteristic
1289Q8—28no—
1290Q8—44no—
1291Q8—416no—
1292Q8—48no—
1293Q8—48no—
1294Q8—48no—
1295Q8—82no—
1296Q8—82no—
1297Q8—88no—
1298D4—44no—
1299D4—48no—
1300D4—84no—
1301D4—88no—
1302D4—88no—
1303D4—162no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—216no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—21no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—21no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—416no—
1376C2×C4—48no—
1377C2×C4—48no—
1378C2×C4—88no—
1379C2×C4—88no—
1380C2×C4—88no—
1381C2×C4—164no—
1382C2×C4C22×#4112yes—
1383C2×C4C22×#4112yes—
1384C2×C4C22×#4114yes—
1385C2×C4C22×#4112yes—
1386C2×C4C2×H(5,𝔽2)12yes—
1387C2×C4C2×H(5,𝔽2)12yes—
1388C2×C4C2×H(5,𝔽2)14yes—
1389C2×C4C2×H(5,𝔽2)12yes—
1390C2×C4C2×H(5,𝔽2)12yes—
1391C2×C4C2×2−1+412yes—
1392C2×C4C2×2−1+414yes—
1393C22—24no—
1394C22—24no—
1395C22—24no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—44no—
1401C22—44no—
1402C22—44no—
1403C22—44no—
1404C22—44no—
1405C22—44no—
1406C22—44no—
1407C22C23×#4111yescharacteristic
1408C22C22×H(5,𝔽2)11yescharacteristic
1409C22C22×H(5,𝔽2)11yescharacteristic
1410C22C22×2−1+411yescharacteristic
1411C222−1+611yescharacteristic
1412C222−1+611yescharacteristic
1413C222−1+611yescharacteristic
1414C4—22no—
1415C4—24no—
1416C4—24no—
1417C4—22no—
1418C4—22no—
1419C4—24no—
1420C4—22no—
1421C4—22no—
1422C4—42no—
1423C4—44no—
1424C4—44no—
1425C4—44no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—42no—
1430C4—41no—
1431C4—44no—
1432C4—42no—
1433C4—44no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—42no—
1438C4—42no—
1439C4—42no—
1440C4#351914yes—
1441C2—44no—
1442C2—84no—
1443C2C2×#351911yescharacteristic
1444C2#6286011yescharacteristic
1445C2#6288811yescharacteristic
1446C2#6289311yescharacteristic
1447C2#6294611yescharacteristic
1448C2#6300111yescharacteristic
1449C2#6304811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39356C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59869C2semidirect
2. #59144C2semidirect
3. #52267C2semidirect
4. #51367C2semidirect
5. #50511C2semidirect
6. #48097C2semidirect
7. #46520C2semidirect
8. #45938C2semidirect
9. #45156C2semidirect
10. #45146C2semidirect
11. #45144C2semidirect
12. #44439C2semidirect
13. #42941C2semidirect
14. #42702C2semidirect
15. #41302C2semidirect
16. #40033C2semidirect
17. #39820C2semidirect
18. #39740C2semidirect
19. #39700C2semidirect
21. #38810C2semidirect
22. #37675C2semidirect
23. #37252C2semidirect
24. #36538C2semidirect
25. #35817C2semidirect
26. #35667C2semidirect
27. #35187C2semidirect
28. #34474C2semidirect
29. #34311C2semidirect

Maximal subgroups

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

subgroupindex
#598692
#591442
#522672
#513672
#505112
#480972
#465202
#459382
#451562
#451462
#451442
#444392
#429412
#427022
#413022
#400332
#398202
#397402
#397002
#393562
#388102
#376752
#372522
#365382
#358172
#356672
#351872
#344742
#343112