Finite Group Databasebeta

← #8750945

Subgroups — #8750945

Order 512.

4405 conjugacy classes of subgroups.

The subgroup lattice has 1434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59946C211yesmaximal, characteristic, complemented
2#59563C212yesmaximal, complemented
3#58787C212yesmaximal, complemented
4#57973C214yesmaximal, complemented
5#57670C214yesmaximal, complemented
6#55967C214yesmaximal, complemented
7#55841C214yesmaximal, complemented
8#53138C212yesmaximal, complemented
9#52960C211yesmaximal, characteristic, complemented
10#52628C214yesmaximal, complemented
11#52431C212yesmaximal, complemented
12#47173C212yesmaximal, complemented
13#45354C212yesmaximal, complemented
14#45315C211yesmaximal, characteristic, complemented
15#45220C212yesmaximal, complemented
16#45146C212yesmaximal, complemented
17#45053C212yesmaximal, complemented
18#42917C211yesmaximal, characteristic, complemented
19#42834C212yesmaximal, complemented
20#42749C212yesmaximal, complemented
21#42701C212yesmaximal, complemented
22#42572C212yesmaximal, complemented
23#42191C212yesmaximal, complemented
24#40800C214yesmaximal, complemented
25#40025C212yesmaximal, complemented
26#38956C211yesmaximal, characteristic
27#36698C211yesmaximal, characteristic, complemented
28#35998C211yesmaximal, characteristic, complemented
29#35778C212yesmaximal, complemented
30C2×#559C2212yes—
31C2×#550C2211yescharacteristic
32C2×#547C2211yescharacteristic
33C2×#536C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2858C2211yescharacteristic
36#2844C2211yescharacteristic
37#2839C2214yes—
38#2838C2212yes—
39#2838C2212yes—
40#2837C2214yes—
41#2836C2212yes—
42#2836C2214yes—
43#2836C2212yes—
44#2834C2214yes—
45#2833C2211yescharacteristic
46#2833C2211yescharacteristic
47#2831C2214yes—
48#2831C2214yes—
49#2830C2212yes—
50#2830C2212yes—
51#2827C2214yes—
52#2826C2212yes—
53#2826C2214yes—
54#2824C2214yes—
55#2822C2211yescharacteristic
56#2820C2212yes—
57#2814C2212yes—
58#2808C2214yes—
59#2800C2214yes—
60#2797C2214yes—
61#2797C2214yes—
62#2789C2212yes—
63#2788C2214yes—
64#2787C2214yes—
65#2784C2212yes—
66#2782C2214yes—
67#2780C2214yes—
68#2780C2214yes—
69#2778C2214yes—
70#2774C2214yes—
71#2770C2214yes—
72#2770C2214yes—
73#2768C2214yes—
74#2767C2214yes—
75#2766C2214yes—
76#2761C2214yes—
77#2761C2214yes—
78#2758C2214yes—
79#2757C2214yes—
80#2756C2214yes—
81#2752C2212yes—
82#2750C2214yes—
83#2750C2214yes—
84#2749C2214yes—
85#2747C2214yes—
86#2747C2214yes—
87#2746C2214yes—
88#2745C2214yes—
89#2745C2214yes—
90#2743C2214yes—
91#2739C2214yes—
92#2739C2214yes—
93#2724C2212yes—
94#2724C2214yes—
95#2717C2212yes—
96#2709C2214yes—
97#2708C2214yes—
98#2708C2214yes—
99#2707C2214yes—
100#2706C2214yes—
101#2706C2214yes—
102#2703C2214yes—
103#2703C2214yes—
104#2701C2214yes—
105#2700C2214yes—
106#2694C2214yes—
107#2693C2212yes—
108#2693C2214yes—
109#2687C2214yes—
110#2686C2214yes—
111#2686C2214yes—
112#2666C2214yes—
113#2663C2212yes—
114#2655C2214yes—
115#2653C2214yes—
116#2651C2214yes—
117#2650C2214yes—
118#2649C2214yes—
119#2648C2214yes—
120#2643C2214yes—
121#2642C2212yes—
122#2630C2214yes—
123#2627C2212yes—
124#2625C2211yescharacteristic
125#2625C2211yescharacteristic
126#2623C2212yes—
127#2623C2214yes—
128#2620C2212yes—
129#2619C2212yes—
130#2611C2214yes—
131#2600C2212yes—
132#2597C2214yes—
133#2593C2212yes—
134#2586C2212yes—
135#2583C2212yes—
136#2582C2212yes—
137#2581C2212yes—
138#2580C2212yes—
139#2579C2214yes—
140#2579C2214yes—
141#2578C2214yes—
142#2576C2214yes—
143#2575C2214yes—
144#2568C2211yescharacteristic
145#2568C2212yes—
146#2565C2212yes—
147#2557C2214yes—
148#2547C2212yes—
149#2546C2212yes—
150#2545C2212yes—
151#2545C2212yes—
152#2545C2212yes—
153#2544C2212yes—
154#2544C2212yes—
155#2541C2211yescharacteristic
156#2531C2214yes—
157#2530C2214yes—
158#2530C2214yes—
159#2527C2214yes—
160#2526C2214yes—
161#2520C2214yes—
162#2514C2212yes—
163#2511C2212yes—
164#2511C2212yes—
165#2510C2214yes—
166#2510C2214yes—
167#2507C2212yes—
168#2506C2212yes—
169#2504C2212yes—
170#2502C2211yescharacteristic
171#2498C2212yes—
172#2498C2214yes—
173#2494C2212yes—
174#2490C2212yes—
175#2490C2212yes—
176#2488C2214yes—
177#2486C2211yescharacteristic
178#2484C2212yes—
179#2475C2214yes—
180#2474C2214yes—
181#2473C2214yes—
182#2473C2214yes—
183#2471C2214yes—
184#2470C2214yes—
185#2460C2214yes—
186#2459C2214yes—
187#2457C2214yes—
188#2455C2214yes—
189#2454C2212yes—
190#2453C2212yes—
191#2450C2214yes—
192#2448C2212yes—
193#2447C2212yes—
194#2447C2212yes—
195#2447C2212yes—
196#2447C2212yes—
197#2446C2212yes—
198#2446C2212yes—
199#2445C2212yes—
200#2445C2214yes—
201#2445C2212yes—
202#2443C2214yes—
203#2443C2214yes—
204#2443C2214yes—
205#2442C2214yes—
206#2436C2212yes—
207#2434C2211yescharacteristic
208#2432C2212yes—
209#2431C2212yes—
210#2431C2212yes—
211#2431C2212yes—
212#2429C2212yes—
213#2427C2212yes—
214#2427C2212yes—
215#2427C2212yes—
216#2423C2212yes—
217#2422C2212yes—
218#2421C2212yes—
219#2419C2214yes—
220#2413C2214yes—
221#2409C2211yescharacteristic
222#2406C2214yes—
223#2406C2214yes—
224#2401C2212yes—
225#2401C2212yes—
226#2399C2212yes—
227#2396C2212yes—
228#2396C2212yes—
229#2395C2211yescharacteristic
230#2395C2211yescharacteristic
231#2392C2214yes—
232C2×#398C2212yes—
233#2374C2212yes—
234#2370C2212yes—
235#2367C2212yes—
236#2367C2212yes—
237#2367C2212yes—
238#2365C2212yes—
239#2361C2212yes—
240#2360C2212yes—
241#2354C2212yes—
242D4×C4⋊C4C2212yes—
243D4×C4⋊C4C2212yes—
244#2344C2214yes—
245#2341C2211yescharacteristic
246Q8×C22⋊C4C2212yes—
247#2339C2212yes—
248#2339C2211yescharacteristic
249#2335C2214yes—
250#2328C2212yes—
251#2326C2212yes—
252#2324C2212yes—
253#2320C2212yes—
254#2311C2212yes—
255C4×#125C2212yes—
256C4×#124C2211yescharacteristic
257#2295C2212yes—
258#2293C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C22×#41C2312yes—
262C23×Q8C2311yescharacteristic
263#559—48no—
264#550—44no—
265#547—44no—
266#536—44no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×#127C2312yes—
271C2×#127C2311yescharacteristic
272C2×#127C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#124C2312yes—
277C2×#124C2311yescharacteristic
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2314yes—
283C2×#123C2314yes—
284C2×#123C2312yes—
285C2×#123C2312yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2312yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302#520—44no—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2314yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2314yes—
319C2×#117C2311yescharacteristic
320C2×#117C2311yescharacteristic
321C2×#117C2312yes—
322C2×#117C2312yes—
323C2×#117C2314yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2314yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2314yes—
329#401C2312yes—
330#401C2312yes—
331#401C2314yes—
332#401C2314yes—
333#400C2312yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2311yescharacteristic
353#400C2311yescharacteristic
354#400C2314yes—
355#400C2312yes—
356#400C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#399C2312yes—
364#399C2312yes—
365#399C2311yescharacteristic
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2311yescharacteristic
370#399C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2311yescharacteristic
374#398C2312yes—
375#398C2311yescharacteristic
376#398C2312yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2312yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2312yes—
400#397C2312yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2312yes—
410#397C2312yes—
411#397C2312yes—
412#397C2312yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2311yescharacteristic
421#397C2311yescharacteristic
422#397C2312yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2312yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#396C2312yes—
433#396C2312yes—
434#396C2312yes—
435#396C2312yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2312yes—
442#396C2312yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#395C2312yes—
449#395C2312yes—
450#395C2312yes—
451#395C2312yes—
452#395C2312yes—
453#395C2312yes—
454#395C2314yes—
455#395C2312yes—
456#395C2312yes—
457#395C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#393C2312yes—
479#393C2314yes—
480#393C2314yes—
481#393C2312yes—
482#393C2312yes—
483#393C2314yes—
484#392C2312yes—
485#392C2314yes—
486#392C2312yes—
487#392C2314yes—
488#392C2314yes—
489#392C2314yes—
490#391C2312yes—
491#391C2312yes—
492#391C2311yescharacteristic
493#391C2312yes—
494#391C2314yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2314yes—
504#391C2314yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#390C2312yes—
509#390C2312yes—
510#390C2311yescharacteristic
511#390C2312yes—
512#390C2314yes—
513#390C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2314yes—
518#390C2314yes—
519#390C2312yes—
520#390C2314yes—
521#390C2312yes—
522#390C2314yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2312yes—
541#389C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2312yes—
551#388C2312yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
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#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2312yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2312yes—
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#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#384C2312yes—
654#384C2312yes—
655#383C2314yes—
656#383C2314yes—
657#382C2312yes—
658#382C2312yes—
659#382C2311yescharacteristic
660#382C2312yes—
661#382C2314yes—
662#382C2314yes—
663#381C2314yes—
664#381C2314yes—
665#381C2312yes—
666#381C2314yes—
667#381C2312yes—
668#381C2314yes—
669#381C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2314yes—
677#380C2311yescharacteristic
678#380C2314yes—
679#380C2311yescharacteristic
680#380C2312yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2314yes—
714C2×#95C2312yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C2×#41—24no—
718C2×#41—24no—
719C2×#41—44no—
720C2×#41—44no—
721C2×#41—44no—
722C2×#41—44no—
723C2×#41—82no—
724C22×Q8—42no—
725C22×Q8—44no—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×D4C2412yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2412yes—
742C22×D4C2414yes—
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2414yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C4⋊Q8—44no—
756C4⋊Q8—44no—
757C4⋊Q8—42no—
758#127—28no—
759#127—42no—
760#127—82no—
761#125—44no—
762#125—44no—
763#125—84no—
764#124—28no—
765#124—44no—
766#124—44no—
767#124—44no—
768#124—42no—
769#124—44no—
770#124—48no—
771#123—48no—
772#123—48no—
773#123—44no—
774#123—44no—
775#123—48no—
776#123—44no—
777#123—48no—
778#123—84no—
779#123—84no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—42no—
784C22⋊Q8—42no—
785#121—48no—
786#121—44no—
787#121—44no—
788#121—44no—
789#121—44no—
790C4×Q8—42no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×D4—28no—
797C4×D4—24no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—44no—
801C4×D4—44no—
802C4×D4—42no—
803C4×D4—48no—
804C4×D4—48no—
805C4×D4—84no—
806#117—42no—
807#117—42no—
808#117—44no—
809#117—82no—
810#117—84no—
811C2×C4⋊C4—48no—
812C2×C4⋊C4—42no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4—84no—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2414yes—
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2411yescharacteristic
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2411yescharacteristic
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2411yescharacteristic
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24C2511yescharacteristic
1017C24C2511yescharacteristic
1018C24C2514yes—
1019C24C2512yes—
1020#41—416no—
1021#41—88no—
1022#41—816no—
1023C2×Q8—22no—
1024C2×Q8—24no—
1025C2×Q8—22no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—22no—
1031C2×Q8—41no—
1032C2×Q8—41no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—42no—
1037C2×Q8—42no—
1038C2×Q8—88no—
1039C2×D4—24no—
1040C2×D4—28no—
1041C2×D4—24no—
1042C2×D4—28no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—22no—
1048C2×D4—24no—
1049C2×D4—44no—
1050C2×D4—41no—
1051C2×D4—44no—
1052C2×D4—42no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—41no—
1056C2×D4—42no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—42no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4H(5,𝔽2)14yes—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—24no—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—42no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—42no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2514yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2514yes—
1112C22×C4C2514yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2512yes—
1117C22×C4C2514yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C4⋊C4—24no—
1125C4⋊C4—22no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—41no—
1133C4⋊C4—42no—
1134C4⋊C4—41no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—41no—
1154C4⋊C4—41no—
1155C4⋊C4—41no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—41no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—44no—
1188C22⋊C4—42no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—41no—
1206C22⋊C4—41no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C42—24no—
1234C42—24no—
1235C42—22no—
1236C42—24no—
1237C42—24no—
1238C42—24no—
1239C42—24no—
1240C42—22no—
1241C42—44no—
1242C42—42no—
1243C42—44no—
1244C42—41no—
1245C42—44no—
1246C42—44no—
1247C42—42no—
1248C42—44no—
1249C42—44no—
1250C42—44no—
1251C23—24no—
1252C23—22no—
1253C23—22no—
1254C23—24no—
1255C23—21no—
1256C23—21no—
1257C23—24no—
1258C23—21no—
1259C23—24no—
1260C23—21no—
1261C23—24no—
1262C23—24no—
1263C23—22no—
1264C23—22no—
1265C23—21no—
1266C23—24no—
1267C23—21no—
1268C23—22no—
1269C23—22no—
1270C23—24no—
1271C23—24no—
1272C23C2×H(5,𝔽2)14yes—
1273C23C2611yescharacteristic
1274Q8—44no—
1275Q8—48no—
1276Q8—44no—
1277Q8—44no—
1278Q8—84no—
1279Q8—84no—
1280D4—28no—
1281D4—48no—
1282D4—48no—
1283D4—82no—
1284D4—84no—
1285D4—88no—
1286D4—84no—
1287D4—88no—
1288D4—88no—
1289D4—164no—
1290D4—162no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—48no—
1358C2×C4—48no—
1359C2×C4—44no—
1360C2×C4—44no—
1361C2×C4—88no—
1362C2×C4—84no—
1363C2×C4—88no—
1364C2×C4—88no—
1365C2×C4—84no—
1366C2×C4—88no—
1367C2×C4—162no—
1368C2×C4—164no—
1369C2×C4C2×H(5,𝔽2)12yes—
1370C2×C4#58512yes—
1371C2×C4#58514yes—
1372C22—24no—
1373C22—24no—
1374C22—24no—
1375C22—44no—
1376C22—44no—
1377C22—41no—
1378C22—41no—
1379C22—44no—
1380C22—44no—
1381C22—42no—
1382C22—44no—
1383C22—42no—
1384C22—44no—
1385C22—41no—
1386C22—41no—
1387C22—44no—
1388C22—41no—
1389C22—41no—
1390C22—42no—
1391C22—44no—
1392C22—42no—
1393C22—44no—
1394C22C22×H(5,𝔽2)11yescharacteristic
1395C22C2×#58512yes—
1396C22C2×#58511yescharacteristic
1397C22H(7,𝔽2)11yescharacteristic
1398C222−1+612yes—
1399C4—22no—
1400C4—41no—
1401C4—41no—
1402C4—42no—
1403C4—42no—
1404C4—44no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—42no—
1409C4—44no—
1410C4—42no—
1411C4—41no—
1412C4—42no—
1413C4—42no—
1414C4—42no—
1415C4—42no—
1416C4—42no—
1417C4—44no—
1418C4—42no—
1419C4—42no—
1420C4—42no—
1421C4—44no—
1422C4—42no—
1423C4#353314yes—
1424C2—44no—
1425C2—81no—
1426C2—81no—
1427C2—84no—
1428C2C2×#353311yescharacteristic
1429C2#6291811yescharacteristic
1430C2#6296712yes—
1431C2#6305612yes—
1432C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#38956C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59946C2semidirect
2. #59563C2semidirect
3. #58787C2semidirect
4. #57973C2semidirect
5. #57670C2semidirect
6. #55967C2semidirect
7. #55841C2semidirect
8. #53138C2semidirect
9. #52960C2semidirect
10. #52628C2semidirect
11. #52431C2semidirect
12. #47173C2semidirect
13. #45354C2semidirect
14. #45315C2semidirect
15. #45220C2semidirect
16. #45146C2semidirect
17. #45053C2semidirect
18. #42917C2semidirect
19. #42834C2semidirect
20. #42749C2semidirect
21. #42701C2semidirect
22. #42572C2semidirect
23. #42191C2semidirect
24. #40800C2semidirect
25. #40025C2semidirect
27. #36698C2semidirect
28. #35998C2semidirect
29. #35778C2semidirect

Maximal subgroups

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

subgroupindex
#599462
#595632
#587872
#579732
#576702
#559672
#558412
#531382
#529602
#526282
#524312
#471732
#453542
#453152
#452202
#451462
#450532
#429172
#428342
#427492
#427012
#425722
#421912
#408002
#400252
#389562
#366982
#359982
#357782