Finite Group Databasebeta

← #8115386

Subgroups — #8115386

Order 512.

3979 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58358C214yesmaximal, complemented
2#58115C214yesmaximal, complemented
3#57956C214yesmaximal, complemented
4#57092C214yesmaximal, complemented
5#56148C214yesmaximal, complemented
6#56135C214yesmaximal, complemented
7#56002C214yesmaximal, complemented
8#54696C214yesmaximal, complemented
9#53154C211yesmaximal, characteristic, complemented
10#53121C211yesmaximal, characteristic, complemented
11#53077C211yesmaximal, characteristic, complemented
12#52985C211yesmaximal, characteristic, complemented
13#45080C212yesmaximal, complemented
14#45015C212yesmaximal, complemented
15#42871C212yesmaximal, complemented
16#42741C212yesmaximal, complemented
17#42620C212yesmaximal, complemented
18#42577C212yesmaximal, complemented
19#39281C212yesmaximal, complemented
20#39080C212yesmaximal, complemented
21#38230C212yesmaximal, complemented
22#38212C212yesmaximal, complemented
23#37407C212yesmaximal, complemented
24#37348C212yesmaximal, complemented
25#35321C211yesmaximal, characteristic, complemented
26#35295C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic, complemented
28#2863C2212yes—
29#2860C2212yes—
30#2856C2211yescharacteristic
31#2855C2212yes—
32#2851C2211yescharacteristic
33#2839C2214yes—
34#2837C2214yes—
35#2837C2214yes—
36#2837C2214yes—
37#2836C2214yes—
38#2836C2214yes—
39#2829C2214yes—
40#2827C2214yes—
41#2827C2214yes—
42#2827C2214yes—
43#2824C2214yes—
44#2822C2214yes—
45#2808C2214yes—
46#2807C2214yes—
47#2803C2214yes—
48#2802C2214yes—
49#2801C2214yes—
50#2800C2214yes—
51#2798C2214yes—
52#2797C2214yes—
53#2796C2214yes—
54#2795C2214yes—
55#2794C2214yes—
56#2793C2214yes—
57#2791C2214yes—
58#2790C2214yes—
59#2790C2214yes—
60#2787C2214yes—
61#2787C2214yes—
62#2786C2214yes—
63#2786C2214yes—
64#2782C2214yes—
65#2781C2214yes—
66#2780C2214yes—
67#2779C2214yes—
68#2776C2214yes—
69#2773C2214yes—
70#2772C2214yes—
71#2770C2214yes—
72#2767C2214yes—
73#2765C2214yes—
74#2764C2214yes—
75#2750C2214yes—
76#2750C2214yes—
77#2749C2214yes—
78#2749C2214yes—
79#2748C2214yes—
80#2747C2214yes—
81#2747C2214yes—
82#2743C2214yes—
83#2743C2214yes—
84#2740C2214yes—
85#2740C2214yes—
86#2738C2214yes—
87#2738C2214yes—
88#2738C2214yes—
89#2726C2214yes—
90#2725C2214yes—
91#2721C2214yes—
92#2719C2214yes—
93#2719C2214yes—
94#2718C2214yes—
95#2718C2214yes—
96#2711C2214yes—
97#2711C2214yes—
98#2711C2214yes—
99#2711C2214yes—
100#2708C2214yes—
101#2707C2214yes—
102#2701C2214yes—
103#2699C2214yes—
104#2699C2214yes—
105#2694C2214yes—
106#2691C2214yes—
107#2671C2214yes—
108#2671C2214yes—
109#2667C2214yes—
110#2655C2212yes—
111#2654C2212yes—
112#2653C2212yes—
113#2652C2212yes—
114#2652C2214yes—
115#2651C2212yes—
116#2650C2212yes—
117#2650C2214yes—
118#2649C2214yes—
119#2649C2212yes—
120#2648C2214yes—
121#2648C2212yes—
122#2647C2212yes—
123#2647C2211yescharacteristic
124#2647C2211yescharacteristic
125#2645C2212yes—
126#2644C2214yes—
127#2642C2211yescharacteristic
128#2641C2211yescharacteristic
129#2629C2211yescharacteristic
130#2624C2214yes—
131#2624C2212yes—
132#2624C2212yes—
133#2621C2211yescharacteristic
134#2620C2212yes—
135#2618C2214yes—
136#2611C2214yes—
137#2611C2214yes—
138#2601C2214yes—
139#2597C2214yes—
140#2594C2214yes—
141#2593C2214yes—
142#2587C2214yes—
143#2585C2214yes—
144#2582C2212yes—
145#2580C2212yes—
146#2578C2214yes—
147#2578C2214yes—
148#2576C2214yes—
149#2575C2214yes—
150#2573C2214yes—
151#2559C2214yes—
152#2558C2214yes—
153#2558C2214yes—
154#2552C2212yes—
155#2552C2212yes—
156#2545C2212yes—
157#2544C2212yes—
158#2540C2212yes—
159#2537C2212yes—
160#2533C2214yes—
161#2531C2214yes—
162#2527C2214yes—
163#2524C2214yes—
164#2518C2214yes—
165#2515C2214yes—
166#2515C2214yes—
167#2512C2212yes—
168#2509C2212yes—
169#2509C2212yes—
170#2508C2212yes—
171#2507C2212yes—
172#2506C2212yes—
173#2506C2212yes—
174#2504C2214yes—
175#2504C2212yes—
176#2499C2212yes—
177#2497C2212yes—
178#2497C2212yes—
179#2496C2214yes—
180#2485C2212yes—
181#2484C2214yes—
182#2481C2214yes—
183#2479C2214yes—
184#2479C2214yes—
185#2476C2214yes—
186#2476C2214yes—
187#2476C2214yes—
188#2473C2214yes—
189#2473C2214yes—
190#2454C2212yes—
191#2453C2212yes—
192#2448C2212yes—
193#2447C2212yes—
194#2447C2212yes—
195#2442C2212yes—
196#2441C2214yes—
197#2441C2214yes—
198#2441C2212yes—
199#2429C2212yes—
200#2428C2212yes—
201#2427C2212yes—
202#2426C2212yes—
203#2426C2212yes—
204#2423C2212yes—
205#2423C2212yes—
206#2422C2212yes—
207#2422C2212yes—
208#2421C2212yes—
209#2417C2212yes—
210#2416C2212yes—
211#2415C2212yes—
212#2402C2211yescharacteristic
213#2401C2212yes—
214#2398C2211yescharacteristic
215#2396C2211yescharacteristic
216#2395C2212yes—
217#2392C2211yescharacteristic
218#2367C2212yes—
219#2363C2212yes—
220#2363C2212yes—
221#2360C2212yes—
222#2356C2212yes—
223Q8×C4⋊C4C2212yes—
224D4×C4⋊C4C2212yes—
225#2344C2212yes—
226#2330C2211yescharacteristic
227#2328C2211yescharacteristic
228#2326C2212yes—
229#2324C2212yes—
230#2323C2212yes—
231#2323C2212yes—
232#2320C2212yes—
233#2319C2212yes—
234#2317C2212yes—
235C4×C4⋊Q8C2211yescharacteristic
236C4×#125C2211yescharacteristic
237#2298C2212yes—
238#2295C2211yescharacteristic
239#2293C2211yescharacteristic
240#2293C2212yes—
241#2290C2212yes—
242C4×#117C2211yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×#127C2311yescharacteristic
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#125C2311yescharacteristic
248C2×#125C2311yescharacteristic
249C2×#125C2314yes—
250C2×#125C2314yes—
251C2×#125C2314yes—
252C2×#125C2314yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2311yescharacteristic
276C2×#117C2312yes—
277C2×#117C2312yes—
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2314yes—
281C2×#117C2314yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2314yes—
284C22×C42C2311yescharacteristic
285#401C2312yes—
286#401C2314yes—
287#400C2312yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2312yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2312yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2312yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2312yes—
311#400C2314yes—
312#400C2312yes—
313#400C2312yes—
314#400C2311yescharacteristic
315#400C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2311yescharacteristic
326#399C2312yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2312yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2312yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2311yescharacteristic
353#398C2312yes—
354#398C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2312yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2312yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2312yes—
376#397C2312yes—
377#397C2314yes—
378#397C2311yescharacteristic
379#397C2312yes—
380#397C2312yes—
381#397C2312yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2312yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2312yes—
398#396C2312yes—
399#396C2314yes—
400#395C2311yescharacteristic
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2312yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2312yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2312yes—
421#394C2314yes—
422#394C2311yescharacteristic
423#394C2314yes—
424#394C2314yes—
425#394C2312yes—
426#394C2314yes—
427#393C2314yes—
428#393C2312yes—
429#393C2311yescharacteristic
430#392C2314yes—
431#392C2314yes—
432#392C2311yescharacteristic
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#390C2314yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2314yes—
446#390C2312yes—
447#390C2312yes—
448#390C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2314yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2312yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2312yes—
527#388C2314yes—
528#388C2312yes—
529#388C2312yes—
530#388C2312yes—
531#388C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2312yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2312yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2312yes—
584#386C2312yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2312yes—
607#385C2312yes—
608#385C2314yes—
609#384C2311yescharacteristic
610#384C2314yes—
611#384C2312yes—
612#384C2312yes—
613#384C2311yescharacteristic
614#384C2312yes—
615#384C2314yes—
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#382C2311yescharacteristic
620#382C2314yes—
621#382C2314yes—
622#382C2314yes—
623#382C2312yes—
624#382C2311yescharacteristic
625#381C2314yes—
626#381C2314yes—
627#381C2314yes—
628#381C2314yes—
629#381C2314yes—
630#380C2314yes—
631#380C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2311yescharacteristic
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668#376C2312yes—
669#376C2311yescharacteristic
670#376C2314yes—
671#376C2311yescharacteristic
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C22×Q8C2412yes—
675C22×Q8C2411yescharacteristic
676C22×D4C2412yes—
677C22×D4C2411yescharacteristic
678C22×D4C2412yes—
679C22×D4C2414yes—
680C22×D4C2414yes—
681C22×D4C2414yes—
682C22×D4C2414yes—
683C23×C4C2412yes—
684C23×C4C2411yescharacteristic
685C23×C4C2414yes—
686C23×C4C2414yes—
687C23×C4C2414yes—
688C23×C4C2414yes—
689C23×C4C2412yes—
690C4⋊Q8—42no—
691#127—42no—
692#126—84no—
693#126—84no—
694#125—42no—
695#125—42no—
696#125—84no—
697#125—84no—
698#125—84no—
699#125—84no—
700#124—44no—
701#124—44no—
702#123—84no—
703#123—84no—
704C22⋊Q8—44no—
705C22⋊Q8—44no—
706C22⋊Q8—44no—
707#121—44no—
708#121—44no—
709#121—44no—
710#121—84no—
711#121—84no—
712#121—84no—
713#121—84no—
714C4×Q8—42no—
715C4×Q8—44no—
716C4×Q8—44no—
717C4×Q8—44no—
718C4×D4—44no—
719C4×D4—44no—
720C4×D4—44no—
721C4×D4—42no—
722C4×D4—44no—
723#117—44no—
724#117—42no—
725#117—42no—
726#117—44no—
727#117—84no—
728#117—84no—
729C2×C4⋊C4—44no—
730C2×C4⋊C4—84no—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C42—42no—
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842C2×C42C2411yescharacteristic
843C2×C42C2412yes—
844C2×C42C2411yescharacteristic
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2411yescharacteristic
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2412yes—
864#95C2412yes—
865#95C2412yes—
866#95C2412yes—
867#95C2414yes—
868#95C2412yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2412yes—
883#95C2414yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2414yes—
893#95C2411yescharacteristic
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2412yes—
906#95C2411yescharacteristic
907#95C2412yes—
908#95C2412yes—
909#95C2411yescharacteristic
910#95C2411yescharacteristic
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931C24C2512yes—
932C24C2511yescharacteristic
933C24C2514yes—
934C2×Q8—24no—
935C2×Q8—24no—
936C2×Q8—24no—
937C2×Q8—41no—
938C2×Q8—42no—
939C2×D4—24no—
940C2×D4—24no—
941C2×D4—24no—
942C2×D4—42no—
943C2×D4—41no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4—42no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C22×C4—22no—
960C22×C4—24no—
961C22×C4—22no—
962C22×C4—24no—
963C22×C4—22no—
964C22×C4—24no—
965C22×C4—42no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—42no—
973C22×C4—44no—
974C22×C4—42no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4C2512yes—
981C22×C4C2511yescharacteristic
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2511yescharacteristic
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2512yes—
990C22×C4C2511yescharacteristic
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C22×C4C2512yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2514yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—44no—
1011C4⋊C4—42no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—41no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—41no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—42no—
1033C4⋊C4—41no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—41no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—44no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—42no—
1075C22⋊C4—41no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—41no—
1079C22⋊C4—42no—
1080C22⋊C4—44no—
1081C22⋊C4—42no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—42no—
1087C22⋊C4—44no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—42no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C42—22no—
1112C42—22no—
1113C42—22no—
1114C42—22no—
1115C42—22no—
1116C42—24no—
1117C42—22no—
1118C42—24no—
1119C42—24no—
1120C42—42no—
1121C42—42no—
1122C42—42no—
1123C42—44no—
1124C42—42no—
1125C42—44no—
1126C42—44no—
1127C42—44no—
1128C42—44no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—42no—
1133C23—22no—
1134C23—21no—
1135C23—21no—
1136C23—24no—
1137C23—22no—
1138C23—24no—
1139C23—24no—
1140C23—22no—
1141C23—21no—
1142C23—24no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—24no—
1147C23—22no—
1148C23—22no—
1149C23—24no—
1150C23—24no—
1151C23—22no—
1152C23C2611yescharacteristic
1153Q8—48no—
1154Q8—82no—
1155D4—48no—
1156D4—82no—
1157D4—84no—
1158D4—164no—
1159D4—164no—
1160D4—164no—
1161D4—164no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—21no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—44no—
1228C2×C4—48no—
1229C2×C4—88no—
1230C2×C4—84no—
1231C2×C4—88no—
1232C2×C4—88no—
1233C2×C4—164no—
1234C2×C4#58512yes—
1235C2×C4#58512yes—
1236C2×C4#58512yes—
1237C22—42no—
1238C22—41no—
1239C22—44no—
1240C22—42no—
1241C22—42no—
1242C22—44no—
1243C22—42no—
1244C22—44no—
1245C22—44no—
1246C22—42no—
1247C22—41no—
1248C22—44no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—44no—
1255C22—41no—
1256C22C2×#58511yescharacteristic
1257C22C2×#58511yescharacteristic
1258C22C2×#58511yescharacteristic
1259C22H(7,𝔽2)12yes—
1260C222−1+612yes—
1261C4—42no—
1262C4—41no—
1263C4—44no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—44no—
1268C4—44no—
1269C4—42no—
1270C4—41no—
1271C4—42no—
1272C4—44no—
1273C4—41no—
1274C4—44no—
1275C4—42no—
1276C4—42no—
1277C4—44no—
1278C4—42no—
1279C4—44no—
1280C4—42no—
1281C4—41no—
1282C4—42no—
1283C4—41no—
1284C4#356714yes—
1285C2—82no—
1286C2—81no—
1287C2—84no—
1288C2C2×#356711yescharacteristic
1289C2#6288212yes—
1290C2#6288311yescharacteristic
1291C2#6288412yes—
1292C2#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. #58358C2semidirect
2. #58115C2semidirect
3. #57956C2semidirect
4. #57092C2semidirect
5. #56148C2semidirect
6. #56135C2semidirect
7. #56002C2semidirect
8. #54696C2semidirect
9. #53154C2semidirect
10. #53121C2semidirect
11. #53077C2semidirect
12. #52985C2semidirect
13. #45080C2semidirect
14. #45015C2semidirect
15. #42871C2semidirect
16. #42741C2semidirect
17. #42620C2semidirect
18. #42577C2semidirect
19. #39281C2semidirect
20. #39080C2semidirect
21. #38230C2semidirect
22. #38212C2semidirect
23. #37407C2semidirect
24. #37348C2semidirect
25. #35321C2semidirect
26. #35295C2semidirect
27. #34640C2semidirect

Maximal subgroups

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

subgroupindex
#583582
#581152
#579562
#570922
#561482
#561352
#560022
#546962
#531542
#531212
#530772
#529852
#450802
#450152
#428712
#427412
#426202
#425772
#392812
#390802
#382302
#382122
#374072
#373482
#353212
#352952
#346402