Finite Group Databasebeta

← #7895484

Subgroups — #7895484

Order 512.

4467 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#59871C211yesmaximal, characteristic, complemented
2#59828C212yesmaximal, complemented
3#52287C211yesmaximal, characteristic, complemented
4#51654C214yesmaximal, complemented
5#50604C214yesmaximal, complemented
6#50138C214yesmaximal, complemented
7#47642C214yesmaximal, complemented
8#45965C212yesmaximal, complemented
9#45394C212yesmaximal, complemented
10#44966C212yesmaximal, complemented
11#44964C212yesmaximal
12#44264C214yesmaximal, complemented
13#42701C212yesmaximal, complemented
14#42526C212yesmaximal, complemented
15#42126C214yesmaximal, complemented
16#40021C212yesmaximal
17#39809C212yesmaximal, complemented
18#39765C211yesmaximal, characteristic
19#39740C211yesmaximal, characteristic
20#39702C212yesmaximal, complemented
21#39162C212yesmaximal, complemented
22#38811C212yesmaximal, complemented
23#37265C212yesmaximal, complemented
24#36538C211yesmaximal, characteristic
25#35938C212yesmaximal, complemented
26#35610C212yesmaximal, complemented
27#35187C211yesmaximal, characteristic, complemented
28#34481C212yesmaximal, complemented
29#34337C211yesmaximal, characteristic, complemented
30C2×#559C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#557C2212yes—
33C2×#557C2211yescharacteristic
34C2×#556C2212yes—
35C2×#556C2212yes—
36#2864C2212yes—
37#2863C2212yes—
38#2861C2212yes—
39#2861C2212yes—
40#2858C2211yescharacteristic
41#2839C2214yes—
42#2831C2214yes—
43#2811C2211yescharacteristic
44#2808C2212yes—
45#2808C2212yes—
46#2807C2214yes—
47#2806C2212yes—
48#2806C2211yescharacteristic
49#2806C2212yes—
50#2806C2211yescharacteristic
51#2806C2212yes—
52#2806C2212yes—
53#2804C2212yes—
54#2801C2214yes—
55#2798C2214yes—
56#2792C2212yes—
57#2792C2212yes—
58#2792C2212yes—
59#2790C2214yes—
60#2788C2214yes—
61#2775C2214yes—
62#2774C2214yes—
63#2773C2214yes—
64#2772C2214yes—
65#2771C2214yes—
66#2770C2214yes—
67#2768C2214yes—
68#2767C2214yes—
69#2766C2214yes—
70#2758C2214yes—
71#2757C2214yes—
72#2734C2211yescharacteristic
73#2734C2212yes—
74#2732C2212yes—
75#2732C2212yes—
76#2731C2214yes—
77#2729C2214yes—
78#2729C2214yes—
79#2727C2212yes—
80#2727C2212yes—
81#2726C2214yes—
82#2726C2214yes—
83#2725C2214yes—
84#2725C2214yes—
85#2724C2212yes—
86#2721C2214yes—
87#2721C2214yes—
88#2720C2214yes—
89#2720C2214yes—
90#2720C2214yes—
91#2718C2214yes—
92#2718C2214yes—
93#2715C2214yes—
94#2698C2214yes—
95#2695C2214yes—
96#2680C2214yes—
97#2666C2214yes—
98#2665C2214yes—
99#2664C2214yes—
100#2658C2212yes—
101#2655C2214yes—
102#2655C2214yes—
103#2653C2214yes—
104#2642C2212yes—
105#2640C2212yes—
106#2637C2214yes—
107#2611C2214yes—
108#2604C2214yes—
109#2597C2214yes—
110#2596C2214yes—
111#2596C2214yes—
112#2592C2212yes—
113#2592C2212yes—
114#2589C2214yes—
115#2589C2214yes—
116#2587C2214yes—
117#2587C2214yes—
118#2584C2214yes—
119#2583C2214yes—
120#2582C2211yescharacteristic
121#2582C2212yes—
122#2582C2212yes—
123#2582C2212yes—
124#2581C2212yes—
125#2580C2212yes—
126#2575C2214yes—
127#2574C2214yes—
128#2571C2211yescharacteristic
129#2568C2212yes—
130#2568C2211yescharacteristic
131#2568C2211yescharacteristic
132#2567C2212yes—
133#2566C2212yes—
134#2566C2212yes—
135#2565C2212yes—
136#2558C2214yes—
137#2558C2214yes—
138#2556C2214yes—
139#2556C2214yes—
140#2552C2212yes—
141#2552C2214yes—
142#2552C2212yes—
143#2548C2211yescharacteristic
144#2546C2212yes—
145#2546C2211yescharacteristic
146#2546C2212yes—
147#2545C2212yes—
148#2545C2212yes—
149#2545C2212yes—
150#2545C2212yes—
151#2545C2212yes—
152#2544C2212yes—
153#2538C2212yes—
154#2532C2214yes—
155#2529C2214yes—
156#2525C2214yes—
157#2524C2214yes—
158#2520C2214yes—
159#2519C2214yes—
160#2519C2214yes—
161#2519C2214yes—
162#2514C2212yes—
163#2514C2212yes—
164#2512C2212yes—
165#2511C2212yes—
166#2508C2212yes—
167#2507C2214yes—
168#2506C2214yes—
169#2506C2214yes—
170#2479C2214yes—
171#2479C2214yes—
172#2479C2214yes—
173#2478C2214yes—
174#2475C2214yes—
175#2475C2214yes—
176#2475C2214yes—
177#2475C2214yes—
178#2475C2214yes—
179#2474C2214yes—
180#2473C2214yes—
181#2470C2214yes—
182#2469C2214yes—
183#2469C2214yes—
184#2469C2214yes—
185#2469C2214yes—
186#2468C2214yes—
187#2465C2214yes—
188#2458C2214yes—
189#2453C2214yes—
190#2453C2214yes—
191#2449C2214yes—
192#2448C2212yes—
193#2448C2212yes—
194#2447C2212yes—
195#2446C2212yes—
196#2446C2212yes—
197#2446C2212yes—
198#2446C2212yes—
199#2446C2212yes—
200#2445C2212yes—
201#2413C2214yes—
202#2399C2212yes—
203#2399C2212yes—
204#2399C2212yes—
205#2396C2214yes—
206#2383C2214yes—
207#2383C2214yes—
208#2370C2212yes—
209#2370C2214yes—
210#2369C2212yes—
211#2367C2212yes—
212#2367C2212yes—
213#2367C2212yes—
214#2367C2212yes—
215#2365C2211yescharacteristic
216#2365C2212yes—
217#2365C2212yes—
218#2365C2212yes—
219#2365C2214yes—
220#2360C2214yes—
221Q8×C4⋊C4C2211yescharacteristic
222Q8×C4⋊C4C2212yes—
223Q8×C4⋊C4C2211yescharacteristic
224Q8×C4⋊C4C2212yes—
225Q8×C4⋊C4C2212yes—
226Q8×C4⋊C4C2212yes—
227D4×C4⋊C4C2212yes—
228#2347C2214yes—
229#2337C2214yes—
230#2334C2214yes—
231#2334C2214yes—
232#2330C2214yes—
233#2330C2212yes—
234#2327C2212yes—
235#2326C2212yes—
236#2326C2212yes—
237#2326C2212yes—
238#2326C2212yes—
239#2323C2214yes—
240#2320C2212yes—
241#2320C2212yes—
242#2317C2214yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2212yes—
248C4×C4⋊Q8C2211yescharacteristic
249C4×C4⋊Q8C2212yes—
250C4×#124C2212yes—
251#2295C2212yes—
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2295C2211yescharacteristic
255#2295C2212yes—
256#2293C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259#559—44no—
260#557—28no—
261#557—48no—
262#557—44no—
263#556—216no—
264#556—48no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×#127C2311yescharacteristic
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2314yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×#117C2314yes—
329C2×#117C2314yes—
330C2×#117C2314yes—
331C22×C4⋊C4C2314yes—
332#401C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2312yes—
416#395C2314yes—
417#395C2312yes—
418#395C2312yes—
419#395C2312yes—
420#395C2312yes—
421#395C2312yes—
422#395C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#395C2312yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#391C2311yescharacteristic
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2311yescharacteristic
447#391C2312yes—
448#391C2311yescharacteristic
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2314yes—
459#391C2314yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2311yescharacteristic
468#391C2312yes—
469#391C2311yescharacteristic
470#391C2311yescharacteristic
471#391C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2311yescharacteristic
531#389C2312yes—
532#389C2311yescharacteristic
533#389C2314yes—
534#389C2314yes—
535#389C2311yescharacteristic
536#389C2311yescharacteristic
537#389C2314yes—
538#389C2312yes—
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#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#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
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#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2312yes—
602#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2314yes—
607#387C2314yes—
608#387C2312yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2312yes—
616#387C2314yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2312yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
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#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#384C2311yescharacteristic
647#384C2312yes—
648#384C2311yescharacteristic
649#384C2311yescharacteristic
650#384C2312yes—
651#384C2312yes—
652#384C2312yes—
653#384C2312yes—
654#384C2314yes—
655#384C2314yes—
656#384C2314yes—
657#383C2314yes—
658#383C2314yes—
659#383C2314yes—
660#382C2312yes—
661#382C2312yes—
662#382C2312yes—
663#382C2314yes—
664#382C2312yes—
665#382C2314yes—
666#382C2314yes—
667#381C2314yes—
668#380C2314yes—
669#380C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711#376C2312yes—
712#376C2312yes—
713#376C2312yes—
714#376C2314yes—
715C43C2311yescharacteristic
716C43C2312yes—
717C43C2312yes—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2414yes—
734C4⋊Q8—28no—
735C4⋊Q8—28no—
736C4⋊Q8—28no—
737C4⋊Q8—28no—
738C4⋊Q8—24no—
739C4⋊Q8—28no—
740C4⋊Q8—24no—
741C4⋊Q8—24no—
742C4⋊Q8—44no—
743C4⋊Q8—42no—
744#127—42no—
745#126—216no—
746#126—216no—
747#126—48no—
748#126—48no—
749#126—84no—
750#125—216no—
751#125—28no—
752#125—48no—
753#125—44no—
754#125—48no—
755#125—48no—
756#125—48no—
757#125—84no—
758#124—28no—
759#124—28no—
760#124—28no—
761#124—28no—
762#124—28no—
763#124—44no—
764#124—44no—
765#123—48no—
766#123—84no—
767C22⋊Q8—216no—
768C22⋊Q8—48no—
769C22⋊Q8—84no—
770C4×Q8—28no—
771C4×Q8—24no—
772C4×Q8—28no—
773C4×Q8—28no—
774C4×Q8—28no—
775C4×Q8—28no—
776C4×Q8—24no—
777C4×Q8—24no—
778C4×Q8—24no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—42no—
782C4×Q8—42no—
783C4×Q8—48no—
784C4×Q8—44no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—82no—
790C4×Q8—82no—
791C4×Q8—82no—
792C4×Q8#4118yes—
793C4×D4—28no—
794C4×D4—44no—
795C4×D4—44no—
796C4×D4—44no—
797#117—216no—
798#117—48no—
799#117—84no—
800C2×C4⋊C4—84no—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
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×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2411yescharacteristic
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943#95C2412yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
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#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014C24C2514yes—
1015C2×Q8—22no—
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—22no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—22no—
1026C2×Q8—22no—
1027C2×Q8—41no—
1028C2×Q8—42no—
1029C2×Q8—41no—
1030C2×Q8—42no—
1031C2×Q8—41no—
1032C2×Q8—42no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—41no—
1037C2×Q8—42no—
1038C2×Q8—41no—
1039C2×Q8—41no—
1040C2×Q8—41no—
1041C2×Q8—42no—
1042C2×Q8C2×#4114yes—
1043C2×Q8H(5,𝔽2)14yes—
1044C2×Q82−1+414yes—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C22×C4—28no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2514yes—
1073C22×C4C2514yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2511yescharacteristic
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—22no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—22no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—22no—
1113C4⋊C4—22no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—41no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—41no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—42no—
1137C4⋊C4—41no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—41no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—41no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—41no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4C2×#4118yes—
1173C4⋊C4C2×#4114yes—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—28no—
1178C22⋊C4—28no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C42—28no—
1200C42—28no—
1201C42—28no—
1202C42—24no—
1203C42—28no—
1204C42—24no—
1205C42—24no—
1206C42—24no—
1207C42—24no—
1208C42—22no—
1209C42—24no—
1210C42—24no—
1211C42—24no—
1212C42—24no—
1213C42—22no—
1214C42—24no—
1215C42—41no—
1216C42—42no—
1217C42—42no—
1218C42—41no—
1219C42—42no—
1220C42—44no—
1221C42—42no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—41no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42C2×#4118yes—
1231C42C2×#4114yes—
1232C422−1+414yes—
1233C23—24no—
1234C23—24no—
1235C23—24no—
1236C23—24no—
1237C23—24no—
1238C23—24no—
1239C23—24no—
1240C23C2611yescharacteristic
1241Q8—28no—
1242Q8—44no—
1243Q8—44no—
1244Q8—48no—
1245Q8—48no—
1246Q8—48no—
1247Q8—48no—
1248Q8—82no—
1249Q8—82no—
1250Q8—84no—
1251D4—48no—
1252D4—84no—
1253D4—162no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—416no—
1327C2×C4—88no—
1328C2×C4—164no—
1329C2×C4C22×#4112yes—
1330C2×C4C22×#4114yes—
1331C2×C4C22×#4112yes—
1332C2×C4C22×#4114yes—
1333C2×C4C22×#4112yes—
1334C2×C4C2×H(5,𝔽2)14yes—
1335C2×C4C2×H(5,𝔽2)12yes—
1336C2×C4C2×2−1+412yes—
1337C2×C4C2×2−1+412yes—
1338C2×C4C2×2−1+414yes—
1339C2×C4C2×2−1+412yes—
1340C2×C4C2×2−1+412yes—
1341C22—44no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22—44no—
1348C22C23×#4111yescharacteristic
1349C22C22×H(5,𝔽2)11yescharacteristic
1350C22C22×2−1+411yescharacteristic
1351C22C22×2−1+411yescharacteristic
1352C22H(7,𝔽2)11yescharacteristic
1353C222−1+611yescharacteristic
1354C222−1+611yescharacteristic
1355C4—22no—
1356C4—24no—
1357C4—24no—
1358C4—24no—
1359C4—22no—
1360C4—22no—
1361C4—22no—
1362C4—24no—
1363C4—22no—
1364C4—42no—
1365C4—44no—
1366C4—44no—
1367C4—42no—
1368C4—44no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—41no—
1373C4—42no—
1374C4—44no—
1375C4—44no—
1376C4—42no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4#352214yes—
1383C2—84no—
1384C2C2×#352211yescharacteristic
1385C2#6284511yescharacteristic
1386C2#6288911yescharacteristic
1387C2#6289311yescharacteristic
1388C2#6294311yescharacteristic
1389C2#6300111yescharacteristic
1390C2#6305211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59828C2semidirect
3. #52287C2semidirect
4. #51654C2semidirect
5. #50604C2semidirect
6. #50138C2semidirect
7. #47642C2semidirect
8. #45965C2semidirect
9. #45394C2semidirect
10. #44966C2semidirect
12. #44264C2semidirect
13. #42701C2semidirect
14. #42526C2semidirect
15. #42126C2semidirect
17. #39809C2semidirect
20. #39702C2semidirect
21. #39162C2semidirect
22. #38811C2semidirect
23. #37265C2semidirect
25. #35938C2semidirect
26. #35610C2semidirect
27. #35187C2semidirect
28. #34481C2semidirect
29. #34337C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#598282
#522872
#516542
#506042
#501382
#476422
#459652
#453942
#449662
#449642
#442642
#427012
#425262
#421262
#400212
#398092
#397652
#397402
#397022
#391622
#388112
#372652
#365382
#359382
#356102
#351872
#344812
#343372