Finite Group Databasebeta

← #8115448

Subgroups — #8115448

Order 512.

4298 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58955C214yesmaximal, complemented
2#58939C214yesmaximal, complemented
3#58107C214yesmaximal, complemented
4#56247C214yesmaximal, complemented
5#55839C214yesmaximal, complemented
6#55744C214yesmaximal, complemented
7#54468C214yesmaximal, complemented
8#54189C214yesmaximal, complemented
9#53147C211yesmaximal, characteristic, complemented
10#53125C211yesmaximal, characteristic, complemented
11#53077C211yesmaximal, characteristic, complemented
12#52985C211yesmaximal, characteristic, complemented
13#45003C212yesmaximal, complemented
14#44918C212yesmaximal, complemented
15#42930C212yesmaximal, complemented
16#42747C212yesmaximal, complemented
17#42588C212yesmaximal, complemented
18#42503C212yesmaximal, complemented
19#39801C212yesmaximal, complemented
20#39424C212yesmaximal, complemented
21#37699C212yesmaximal, complemented
22#37687C212yesmaximal, complemented
23#37423C212yesmaximal, complemented
24#37327C212yesmaximal, complemented
25#35341C211yesmaximal, characteristic, complemented
26#35283C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic, complemented
28C2×#544C2212yes—
29C2×#542C2212yes—
30C2×#532C2211yescharacteristic
31C22×#125C2211yescharacteristic
32#2868C2211yescharacteristic
33#2862C2211yescharacteristic
34#2861C2212yes—
35#2861C2212yes—
36#2857C2212yes—
37#2841C2214yes—
38#2839C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2837C2214yes—
42#2836C2214yes—
43#2832C2214yes—
44#2829C2214yes—
45#2827C2214yes—
46#2824C2214yes—
47#2824C2214yes—
48#2814C2214yes—
49#2804C2214yes—
50#2802C2214yes—
51#2799C2214yes—
52#2798C2214yes—
53#2795C2214yes—
54#2795C2214yes—
55#2794C2214yes—
56#2793C2214yes—
57#2791C2214yes—
58#2790C2214yes—
59#2788C2214yes—
60#2788C2214yes—
61#2787C2214yes—
62#2786C2214yes—
63#2780C2214yes—
64#2779C2214yes—
65#2778C2214yes—
66#2777C2214yes—
67#2764C2214yes—
68#2759C2214yes—
69#2758C2214yes—
70#2757C2214yes—
71#2750C2214yes—
72#2748C2214yes—
73#2745C2214yes—
74#2739C2214yes—
75#2737C2214yes—
76#2732C2214yes—
77#2731C2214yes—
78#2731C2214yes—
79#2729C2214yes—
80#2728C2214yes—
81#2726C2214yes—
82#2725C2214yes—
83#2722C2214yes—
84#2720C2214yes—
85#2718C2214yes—
86#2716C2214yes—
87#2716C2214yes—
88#2716C2214yes—
89#2713C2214yes—
90#2710C2214yes—
91#2708C2214yes—
92#2704C2214yes—
93#2703C2214yes—
94#2702C2214yes—
95#2702C2214yes—
96#2700C2214yes—
97#2700C2214yes—
98#2696C2214yes—
99#2695C2214yes—
100#2692C2214yes—
101#2691C2214yes—
102#2691C2214yes—
103#2690C2214yes—
104#2690C2214yes—
105#2687C2214yes—
106#2687C2214yes—
107#2686C2214yes—
108#2681C2214yes—
109#2681C2214yes—
110#2676C2214yes—
111#2674C2214yes—
112#2671C2214yes—
113#2665C2214yes—
114#2665C2214yes—
115#2660C2212yes—
116#2655C2212yes—
117#2654C2212yes—
118#2653C2214yes—
119#2653C2212yes—
120#2652C2212yes—
121#2651C2212yes—
122#2650C2212yes—
123#2649C2214yes—
124#2649C2212yes—
125#2648C2212yes—
126#2647C2211yescharacteristic
127#2647C2211yescharacteristic
128#2646C2214yes—
129#2645C2214yes—
130#2642C2211yescharacteristic
131#2642C2211yescharacteristic
132#2641C2211yescharacteristic
133#2641C2211yescharacteristic
134#2640C2212yes—
135#2635C2214yes—
136#2629C2212yes—
137#2628C2212yes—
138#2620C2212yes—
139#2620C2214yes—
140#2604C2214yes—
141#2603C2214yes—
142#2599C2214yes—
143#2591C2214yes—
144#2591C2214yes—
145#2582C2212yes—
146#2580C2212yes—
147#2578C2214yes—
148#2578C2214yes—
149#2569C2214yes—
150#2568C2212yes—
151#2566C2212yes—
152#2565C2212yes—
153#2563C2212yes—
154#2562C2214yes—
155#2562C2214yes—
156#2560C2214yes—
157#2558C2214yes—
158#2552C2212yes—
159#2550C2212yes—
160#2549C2214yes—
161#2532C2214yes—
162#2530C2214yes—
163#2527C2214yes—
164#2514C2212yes—
165#2513C2212yes—
166#2512C2212yes—
167#2512C2212yes—
168#2511C2212yes—
169#2511C2214yes—
170#2511C2212yes—
171#2504C2212yes—
172#2503C2212yes—
173#2500C2212yes—
174#2499C2212yes—
175#2498C2214yes—
176#2492C2212yes—
177#2492C2212yes—
178#2492C2214yes—
179#2491C2212yes—
180#2490C2212yes—
181#2478C2214yes—
182#2477C2214yes—
183#2473C2214yes—
184#2470C2214yes—
185#2467C2214yes—
186#2466C2214yes—
187#2459C2214yes—
188#2459C2214yes—
189#2453C2212yes—
190#2452C2212yes—
191#2452C2212yes—
192#2451C2214yes—
193#2451C2212yes—
194#2450C2214yes—
195#2449C2214yes—
196#2446C2212yes—
197#2445C2212yes—
198#2442C2212yes—
199#2442C2212yes—
200#2441C2212yes—
201#2440C2214yes—
202#2440C2212yes—
203#2429C2214yes—
204#2429C2212yes—
205#2428C2212yes—
206#2426C2214yes—
207#2425C2214yes—
208#2423C2212yes—
209#2423C2214yes—
210#2422C2212yes—
211#2417C2214yes—
212#2416C2212yes—
213#2415C2212yes—
214#2407C2212yes—
215#2407C2212yes—
216#2402C2211yescharacteristic
217#2401C2212yes—
218#2398C2211yescharacteristic
219#2396C2211yescharacteristic
220#2395C2212yes—
221#2392C2211yescharacteristic
222#2363C2212yes—
223#2360C2212yes—
224#2356C2212yes—
225#2354C2212yes—
226#2352C2212yes—
227D4×C4⋊C4C2212yes—
228#2341C2212yes—
229#2339C2212yes—
230#2331C2212yes—
231#2330C2212yes—
232#2326C2212yes—
233#2314C2211yescharacteristic
234#2314C2211yescharacteristic
235#2311C2212yes—
236#2311C2212yes—
237C4×C4⋊Q8C2212yes—
238#2298C2212yes—
239#2295C2211yescharacteristic
240#2293C2211yescharacteristic
241#2290C2212yes—
242C4×#117C2211yescharacteristic
243C22×#41C2312yes—
244#544—48no—
245#542—48no—
246#532—44no—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2314yes—
252C2×C4⋊Q8C2314yes—
253C2×#127C2311yescharacteristic
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#125—44no—
258C2×#125C2312yes—
259C2×#125C2314yes—
260C2×#125C2312yes—
261C2×#125C2311yescharacteristic
262C2×#125C2311yescharacteristic
263C2×#125C2314yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2314yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2314yes—
294C2×#117C2311yescharacteristic
295C2×#117C2312yes—
296C2×#117C2311yescharacteristic
297C2×#117C2312yes—
298C2×#117C2314yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2312yes—
302C22×C42C2311yescharacteristic
303#401C2312yes—
304#401C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2312yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2312yes—
325#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2311yescharacteristic
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
335#399C2314yes—
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2311yescharacteristic
340#399C2312yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2312yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
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#398C2312yes—
361#398C2314yes—
362#398C2314yes—
363#398C2311yescharacteristic
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2312yes—
373#397C2314yes—
374#397C2314yes—
375#397C2312yes—
376#397C2312yes—
377#397C2312yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2311yescharacteristic
384#397C2312yes—
385#397C2312yes—
386#397C2312yes—
387#397C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2312yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2312yes—
402#396C2312yes—
403#396C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2311yescharacteristic
410#395C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2312yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2312yes—
430#394C2314yes—
431#394C2311yescharacteristic
432#394C2312yes—
433#394C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2312yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2311yescharacteristic
446#393C2314yes—
447#392C2314yes—
448#392C2314yes—
449#392C2311yescharacteristic
450#392C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2312yes—
473#390C2314yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2314yes—
482#390C2312yes—
483#390C2314yes—
484#390C2314yes—
485#390C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#388C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2312yes—
536#388C2312yes—
537#388C2312yes—
538#388C2314yes—
539#388C2314yes—
540#388C2312yes—
541#388C2312yes—
542#388C2312yes—
543#388C2312yes—
544#388C2314yes—
545#388C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2312yes—
564#387C2314yes—
565#387C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2312yes—
592#386C2312yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2312yes—
613#385C2312yes—
614#385C2314yes—
615#384C2312yes—
616#384C2312yes—
617#384C2312yes—
618#384C2311yescharacteristic
619#384C2311yescharacteristic
620#384C2314yes—
621#384C2314yes—
622#383C2314yes—
623#383C2314yes—
624#382C2311yescharacteristic
625#382C2312yes—
626#382C2311yescharacteristic
627#382C2312yes—
628#382C2312yes—
629#381C2314yes—
630#381C2314yes—
631#381C2314yes—
632#380C2314yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2312yes—
640#380C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2312yes—
644#380C2312yes—
645#380C2314yes—
646#380C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671#376C2312yes—
672#376C2311yescharacteristic
673#376C2314yes—
674#376C2311yescharacteristic
675C2×#95C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C2×#41—28no—
679C2×#41—44no—
680C2×#41—44no—
681C22×Q8C2412yes—
682C22×Q8C2414yes—
683C22×Q8C2411yescharacteristic
684C22×Q8C2414yes—
685C22×Q8C2414yes—
686C22×D4C2412yes—
687C22×D4C2412yes—
688C22×D4C2414yes—
689C22×D4C2411yescharacteristic
690C22×D4C2414yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C23×C4C2412yes—
694C23×C4C2411yescharacteristic
695C23×C4C2412yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2414yes—
701C4⋊Q8—28no—
702C4⋊Q8—44no—
703C4⋊Q8—44no—
704C4⋊Q8—42no—
705C4⋊Q8—48no—
706C4⋊Q8—84no—
707#127—42no—
708#126—48no—
709#126—84no—
710#126—84no—
711#125—28no—
712#125—48no—
713#125—42no—
714#125—42no—
715#125—44no—
716#125—48no—
717#124—28no—
718#124—48no—
719#124—84no—
720#123—48no—
721#123—84no—
722#123—84no—
723C22⋊Q8—48no—
724C22⋊Q8—48no—
725C22⋊Q8—48no—
726C22⋊Q8—44no—
727C22⋊Q8—44no—
728C22⋊Q8—84no—
729C22⋊Q8—84no—
730C22⋊Q8—84no—
731C22⋊Q8—84no—
732#121—48no—
733#121—44no—
734#121—44no—
735#121—84no—
736#121—84no—
737C4×Q8—42no—
738C4×Q8—44no—
739C4×Q8—44no—
740C4×Q8—84no—
741C4×D4—28no—
742C4×D4—48no—
743C4×D4—44no—
744C4×D4—44no—
745C4×D4—42no—
746C4×D4—84no—
747#117—24no—
748#117—28no—
749#117—42no—
750#117—44no—
751#117—84no—
752C2×C4⋊C4—44no—
753C2×C4⋊C4—48no—
754C2×C4⋊C4—44no—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C42—24no—
860C2×C42C2412yes—
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2411yescharacteristic
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2411yescharacteristic
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2411yescharacteristic
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2411yescharacteristic
925#95C2412yes—
926#95C2411yescharacteristic
927#95C2412yes—
928#95C2411yescharacteristic
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951C24C2512yes—
952C24C2514yes—
953C24C2511yescharacteristic
954#41—816no—
955C2×Q8—24no—
956C2×Q8—28no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—41no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—42no—
963C2×Q8—44no—
964C2×Q8—44no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×D4—24no—
970C2×D4—28no—
971C2×D4—24no—
972C2×D4—24no—
973C2×D4—24no—
974C2×D4—42no—
975C2×D4—42no—
976C2×D4—44no—
977C2×D4—41no—
978C2×D4—44no—
979C2×D4—42no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—28no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C42−1+414yes—
1013C22×C4C2512yes—
1014C22×C4C2511yescharacteristic
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C22×C4C2512yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2511yescharacteristic
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—28no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—41no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—42no—
1068C4⋊C4—41no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—24no—
1097C22⋊C4—24no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—24no—
1101C22⋊C4—44no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—44no—
1106C22⋊C4—42no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—42no—
1111C22⋊C4—44no—
1112C22⋊C4—42no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—42no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—42no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—42no—
1140C22⋊C4—44no—
1141C42—24no—
1142C42—22no—
1143C42—24no—
1144C42—22no—
1145C42—22no—
1146C42—24no—
1147C42—22no—
1148C42—22no—
1149C42—24no—
1150C42—42no—
1151C42—42no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—42no—
1159C42—44no—
1160C42—42no—
1161C42H(5,𝔽2)14yes—
1162C23—21no—
1163C23—21no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—24no—
1168C23—22no—
1169C23—24no—
1170C23—22no—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23—22no—
1175C23—22no—
1176C23—24no—
1177C23—22no—
1178C23—24no—
1179C23—22no—
1180C23C2×2−1+412yes—
1181C23C2611yescharacteristic
1182Q8—48no—
1183Q8—88no—
1184Q8—82no—
1185Q8—164no—
1186Q8—164no—
1187D4—48no—
1188D4—48no—
1189D4—88no—
1190D4—88no—
1191D4—82no—
1192D4—164no—
1193D4—164no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—28no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—48no—
1259C2×C4—84no—
1260C2×C4—88no—
1261C2×C4—88no—
1262C2×C4—88no—
1263C2×C4—164no—
1264C2×C4—164no—
1265C2×C4C2×H(5,𝔽2)14yes—
1266C2×C4C2×H(5,𝔽2)12yes—
1267C2×C4C2×2−1+412yes—
1268C2×C4C2×2−1+412yes—
1269C2×C4#58512yes—
1270C22—22no—
1271C22—24no—
1272C22—42no—
1273C22—41no—
1274C22—41no—
1275C22—42no—
1276C22—44no—
1277C22—42no—
1278C22—42no—
1279C22—44no—
1280C22—44no—
1281C22—42no—
1282C22—44no—
1283C22—44no—
1284C22—42no—
1285C22—44no—
1286C22—42no—
1287C22—42no—
1288C22—44no—
1289C22C22×H(5,𝔽2)11yescharacteristic
1290C22C22×2−1+411yescharacteristic
1291C22C2×#58511yescharacteristic
1292C22H(7,𝔽2)12yes—
1293C222−1+612yes—
1294C4—22no—
1295C4—24no—
1296C4—42no—
1297C4—44no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—44no—
1303C4—44no—
1304C4—42no—
1305C4—42no—
1306C4—44no—
1307C4—44no—
1308C4—42no—
1309C4—42no—
1310C4—44no—
1311C4—41no—
1312C4—44no—
1313C4—41no—
1314C4—41no—
1315C4—42no—
1316C4—41no—
1317C4#356114yes—
1318C2—42no—
1319C2—82no—
1320C2—84no—
1321C2C2×#356111yescharacteristic
1322C2#6287712yes—
1323C2#6287812yes—
1324C2#6288311yescharacteristic
1325C2#6289011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58955C2semidirect
2. #58939C2semidirect
3. #58107C2semidirect
4. #56247C2semidirect
5. #55839C2semidirect
6. #55744C2semidirect
7. #54468C2semidirect
8. #54189C2semidirect
9. #53147C2semidirect
10. #53125C2semidirect
11. #53077C2semidirect
12. #52985C2semidirect
13. #45003C2semidirect
14. #44918C2semidirect
15. #42930C2semidirect
16. #42747C2semidirect
17. #42588C2semidirect
18. #42503C2semidirect
19. #39801C2semidirect
20. #39424C2semidirect
21. #37699C2semidirect
22. #37687C2semidirect
23. #37423C2semidirect
24. #37327C2semidirect
25. #35341C2semidirect
26. #35283C2semidirect
27. #34640C2semidirect

Maximal subgroups

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

subgroupindex
#589552
#589392
#581072
#562472
#558392
#557442
#544682
#541892
#531472
#531252
#530772
#529852
#450032
#449182
#429302
#427472
#425882
#425032
#398012
#394242
#376992
#376872
#374232
#373272
#353412
#352832
#346402