Finite Group Databasebeta

← #8751559

Subgroups — #8751559

Order 512.

4384 conjugacy classes of subgroups.

The subgroup lattice has 1466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59202C211yesmaximal, characteristic, complemented
2#59027C212yesmaximal, complemented
3#58380C212yesmaximal, complemented
4#55218C214yesmaximal, complemented
5#54585C214yesmaximal, complemented
6#54384C214yesmaximal, complemented
7#54242C214yesmaximal, complemented
8#53120C212yesmaximal, complemented
9#52991C211yesmaximal, characteristic, complemented
10#52941C212yesmaximal, complemented
11#52874C214yesmaximal, complemented
12#46912C212yesmaximal, complemented
13#45406C212yesmaximal, complemented
14#45402C212yesmaximal, complemented
15#45330C211yesmaximal, characteristic, complemented
16#45282C212yesmaximal, complemented
17#45236C212yesmaximal, complemented
18#42920C212yesmaximal, complemented
19#42908C211yesmaximal, characteristic, complemented
20#42813C212yesmaximal, complemented
21#42691C212yesmaximal, complemented
22#42514C212yesmaximal, complemented
23#41660C212yesmaximal, complemented
24#41545C214yesmaximal, complemented
25#39934C212yesmaximal, complemented
26#39133C211yesmaximal, characteristic, complemented
27#36675C211yesmaximal, characteristic, complemented
28#36050C212yesmaximal, complemented
29#35948C211yesmaximal, characteristic, complemented
30C2×Q82C2211yescharacteristic, complemented
31C2×#552C2212yes—
32C2×#548C2211yescharacteristic
33C2×#537C2211yescharacteristic, complemented
34C22×C22⋊Q8C2211yescharacteristic
35#2847C2211yescharacteristic
36#2841C2212yes—
37#2840C2211yescharacteristic
38#2839C2214yescomplemented
39#2838C2214yescomplemented
40#2835C2211yescharacteristic
41#2835C2212yes—
42#2835C2212yescomplemented
43#2831C2214yes—
44#2831C2214yes—
45#2831C2214yescomplemented
46#2830C2214yes—
47#2826C2214yes—
48#2824C2212yes—
49#2824C2212yes—
50#2824C2212yes—
51#2824C2211yescharacteristic
52#2824C2212yes—
53#2821C2214yes—
54#2817C2212yescomplemented
55#2814C2214yes—
56#2812C2211yescharacteristic
57#2812C2212yes—
58#2803C2214yes—
59#2797C2214yes—
60#2786C2214yescomplemented
61#2785C2214yescomplemented
62#2779C2214yescomplemented
63#2771C2212yes—
64#2767C2214yescomplemented
65#2764C2212yes—
66#2762C2214yescomplemented
67#2761C2214yes—
68#2761C2214yescomplemented
69#2759C2214yescomplemented
70#2758C2214yescomplemented
71#2757C2214yescomplemented
72#2756C2214yes—
73#2756C2214yes—
74#2754C2214yescomplemented
75#2751C2214yes—
76#2749C2214yes—
77#2747C2214yescomplemented
78#2746C2214yescomplemented
79#2741C2214yes—
80#2740C2214yes—
81#2737C2214yes—
82#2737C2214yes—
83#2735C2212yes—
84#2732C2214yes—
85#2730C2214yes—
86#2730C2214yes—
87#2728C2212yescomplemented
88#2722C2212yescomplemented
89#2717C2214yes—
90#2714C2214yes—
91#2713C2214yescomplemented
92#2713C2214yescomplemented
93#2705C2214yes—
94#2703C2214yes—
95#2703C2214yes—
96#2702C2214yescomplemented
97#2698C2214yes—
98#2697C2214yes—
99#2696C2214yes—
100#2695C2214yes—
101#2692C2214yescomplemented
102#2692C2214yescomplemented
103#2690C2214yescomplemented
104#2688C2214yes—
105#2687C2214yes—
106#2687C2214yes—
107#2686C2214yescomplemented
108#2684C2212yes—
109#2674C2214yes—
110#2674C2214yes—
111#2670C2214yes—
112#2665C2214yescomplemented
113#2662C2214yes—
114#2660C2212yescomplemented
115#2654C2214yescomplemented
116#2651C2214yes—
117#2651C2214yescomplemented
118#2650C2214yes—
119#2648C2214yes—
120#2647C2212yescomplemented
121#2640C2212yescomplemented
122#2640C2211yescharacteristic, complemented
123#2639C2212yescomplemented
124#2637C2214yes—
125#2635C2212yes—
126#2630C2214yes—
127#2621C2214yescomplemented
128#2618C2212yes—
129#2616C2211yescharacteristic, complemented
130#2600C2212yes—
131#2599C2214yescomplemented
132#2596C2214yes—
133#2595C2214yes—
134#2593C2214yes—
135#2592C2212yescomplemented
136#2592C2211yescharacteristic, complemented
137#2588C2214yescomplemented
138#2586C2212yescomplemented
139#2586C2214yescomplemented
140#2584C2212yescomplemented
141#2582C2212yescomplemented
142#2581C2212yescomplemented
143#2577C2214yes—
144#2576C2214yes—
145#2574C2214yes—
146#2573C2214yescomplemented
147#2569C2214yescomplemented
148#2564C2212yes—
149#2560C2214yes—
150#2560C2214yescomplemented
151#2557C2214yes—
152#2556C2214yes—
153#2547C2212yes—
154#2547C2211yescharacteristic
155#2547C2212yes—
156#2539C2212yes—
157#2538C2212yes—
158#2538C2212yescomplemented
159#2536C2212yes—
160#2535C2212yes—
161#2534C2212yes—
162#2532C2214yes—
163#2532C2214yescomplemented
164#2529C2214yescomplemented
165#2529C2214yescomplemented
166#2527C2214yes—
167#2526C2214yescomplemented
168#2524C2214yescomplemented
169#2518C2214yes—
170#2517C2212yes—
171#2515C2214yescomplemented
172#2513C2214yes—
173#2504C2212yescomplemented
174#2503C2211yescharacteristic, complemented
175#2501C2211yescharacteristic
176#2499C2212yes—
177#2497C2212yes—
178#2497C2212yescomplemented
179#2497C2212yescomplemented
180#2496C2212yescomplemented
181#2495C2212yes—
182#2495C2214yescomplemented
183#2494C2212yes—
184#2492C2214yescomplemented
185#2492C2212yescomplemented
186#2491C2212yes—
187#2491C2214yes—
188#2490C2212yescomplemented
189#2490C2214yescomplemented
190#2489C2212yes—
191#2488C2214yes—
192#2487C2211yescharacteristic
193#2486C2211yescharacteristic
194#2485C2212yes—
195#2485C2212yes—
196#2480C2214yes—
197#2477C2214yes—
198#2476C2214yescomplemented
199#2476C2214yescomplemented
200#2473C2214yes—
201#2461C2214yes—
202#2461C2214yes—
203#2442C2212yes—
204#2442C2212yescomplemented
205#2440C2212yescomplemented
206#2440C2212yescomplemented
207#2439C2212yes—
208#2439C2212yes—
209#2427C2212yescomplemented
210#2426C2212yes—
211#2423C2212yes—
212#2423C2212yes—
213#2423C2212yescomplemented
214#2422C2212yes—
215#2421C2212yescomplemented
216#2421C2212yescomplemented
217#2418C2214yes—
218#2417C2212yes—
219#2415C2212yes—
220#2414C2212yes—
221#2414C2212yes—
222#2409C2212yes—
223#2407C2212yes—
224#2402C2214yescomplemented
225#2398C2212yes—
226#2398C2212yes—
227#2398C2212yes—
228#2398C2211yescharacteristic
229#2398C2212yes—
230#2398C2212yes—
231#2388C2211yescharacteristic
232#2388C2212yes—
233#2372C2212yes—
234#2363C2212yes—
235#2362C2212yes—
236#2362C2212yescomplemented
237#2362C2212yescomplemented
238#2355C2212yescomplemented
239#2354C2212yes—
240#2352C2212yes—
241#2352C2214yes—
242D4×C4⋊C4C2212yes—
243#2347C2212yescomplemented
244#2346C2212yes—
245#2341C2212yescomplemented
246Q8×C22⋊C4C2212yes—
247Q8×C22⋊C4C2211yescharacteristic
248#2339C2211yescharacteristic, complemented
249#2337C2214yes—
250#2322C2212yes—
251#2320C2212yescomplemented
252#2320C2212yescomplemented
253#2319C2212yescomplemented
254#2311C2212yescomplemented
255C4×#120C2211yescharacteristic
256C4×#120C2212yes—
257#2280C2212yes—
258#2276C2211yescharacteristic, complemented
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262C24×C4C2311yescharacteristic
263Q82—44no—
264#552—48no—
265#548—44no—
266#537—44no—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#124C2311yescharacteristic
276C2×#124C2312yes—
277C2×#124C2314yes—
278C2×#124C2312yes—
279C2×#124C2314yes—
280C2×#123C2312yes—
281C2×#123C2314yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×#123C2314yes—
285C2×C22⋊Q8—44no—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2311yescharacteristic
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×#121C2312yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#120C2312yes—
304C2×#120C2311yescharacteristic
305C2×#120C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2311yescharacteristic
321C2×#117C2312yes—
322C2×#117C2314yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C22⋊C4C2312yes—
330#401C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2312yes—
341#400C2312yes—
342#400C2312yes—
343#400C2312yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#399C2312yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2312yes—
384#397C2314yes—
385#397C2312yes—
386#397C2311yescharacteristic
387#397C2312yes—
388#397C2312yes—
389#397C2312yes—
390#397C2312yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2312yes—
400#397C2312yes—
401#397C2314yes—
402#397C2312yes—
403#397C2311yescharacteristic
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2312yes—
408#397C2314yes—
409#397C2312yes—
410#397C2314yes—
411#397C2314yes—
412#397C2312yes—
413#397C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#395C2311yescharacteristic
426#395C2312yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2312yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2311yescharacteristic
438#394C2312yes—
439#394C2312yes—
440#394C2312yes—
441#394C2312yes—
442#394C2312yes—
443#394C2312yes—
444#394C2312yes—
445#394C2312yes—
446#394C2312yes—
447#394C2312yes—
448#394C2312yes—
449#394C2312yes—
450#394C2312yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2312yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#393C2312yes—
464#393C2312yes—
465#393C2311yescharacteristic
466#393C2314yes—
467#393C2314yes—
468#393C2311yescharacteristic
469#393C2312yes—
470#393C2312yes—
471#393C2312yes—
472#393C2312yes—
473#393C2312yes—
474#393C2311yescharacteristic
475#393C2312yes—
476#393C2312yes—
477#393C2314yes—
478#393C2314yes—
479#393C2312yes—
480#393C2314yes—
481#393C2314yes—
482#392C2311yescharacteristic
483#392C2312yes—
484#392C2312yes—
485#392C2312yes—
486#392C2312yes—
487#392C2314yes—
488#392C2314yes—
489#392C2314yes—
490#392C2314yes—
491#391C2314yes—
492#391C2314yes—
493#391C2314yes—
494#391C2314yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#390C2314yes—
508#390C2314yes—
509#390C2314yes—
510#390C2314yes—
511#390C2312yes—
512#390C2312yes—
513#390C2314yes—
514#390C2314yes—
515#390C2312yes—
516#390C2314yes—
517#390C2314yes—
518#390C2314yes—
519#390C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
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#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#386C2312yes—
609#386C2312yes—
610#386C2311yescharacteristic
611#386C2312yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2312yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#385C2314yes—
625#385C2311yescharacteristic
626#385C2312yes—
627#385C2312yes—
628#385C2312yes—
629#385C2312yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#384C2312yes—
640#384C2312yes—
641#384C2312yes—
642#383C2314yes—
643#383C2314yes—
644#383C2314yes—
645#383C2314yes—
646#382C2314yes—
647#382C2314yes—
648#382C2314yes—
649#382C2312yes—
650#382C2314yes—
651#382C2312yes—
652#382C2312yes—
653#381C2312yes—
654#381C2314yes—
655#381C2314yes—
656#381C2312yes—
657#381C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2312yes—
667#380C2314yes—
668#380C2314yes—
669#380C2311yescharacteristic
670#380C2312yes—
671#380C2311yescharacteristic
672#380C2312yes—
673#380C2312yes—
674#380C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2314yes—
678#380C2312yes—
679#379C2312yes—
680#379C2311yescharacteristic
681#379C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2311yescharacteristic
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2311yescharacteristic
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2314yes—
714#376C2311yescharacteristic
715#376C2312yes—
716C2×#95C2312yes—
717C25C2411yescharacteristic
718C2×#41—24no—
719C2×#41—42no—
720C2×#41—44no—
721C2×#41—44no—
722C22×Q8—24no—
723C22×Q8—44no—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2412yes—
730C22×Q8C2411yescharacteristic
731C22×Q8C2414yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2411yescharacteristic
743C22×D4C2412yes—
744C23×C4—42no—
745C23×C4—44no—
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2411yescharacteristic
754C23×C4C2414yes—
755C23×C4C2412yes—
756C23×C4C2414yes—
757C23×C4C2412yes—
758C4⋊Q8—48no—
759C4⋊Q8—42no—
760C4⋊Q8—44no—
761C4⋊Q8—44no—
762#126—48no—
763#126—84no—
764#125—44no—
765#125—48no—
766#124—42no—
767#124—44no—
768#124—44no—
769#124—48no—
770#124—84no—
771#123—48no—
772#123—44no—
773#123—82no—
774#123—82no—
775#123—84no—
776C22⋊Q8—28no—
777C22⋊Q8—28no—
778C22⋊Q8—48no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—42no—
783C22⋊Q8—44no—
784C22⋊Q8—84no—
785C22⋊Q8—84no—
786C22⋊Q8—84no—
787#121—44no—
788#121—48no—
789#121—44no—
790#121—44no—
791#121—42no—
792#121—44no—
793#120—42no—
794#120—44no—
795#120—82no—
796C4×Q8—24no—
797C4×Q8—28no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×Q8—42no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—42no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—48no—
811#117—48no—
812#117—44no—
813#117—44no—
814#117—44no—
815C2×C4⋊C4—42no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—42no—
818C2×C4⋊C4—44no—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C22⋊C4—44no—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2414yes—
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2411yescharacteristic
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2411yescharacteristic
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24—22no—
1017C24—41no—
1018C24—42no—
1019C24—41no—
1020C24—42no—
1021C24C2512yes—
1022C24C2512yes—
1023C24C2512yes—
1024C24C2511yescharacteristic
1025C24C2511yescharacteristic
1026#41—88no—
1027#41—88no—
1028C2×Q8—22no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—41no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—41no—
1036C2×Q8—42no—
1037C2×Q8—44no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—44no—
1042C2×Q8—42no—
1043C2×Q8—44no—
1044C2×Q8—42no—
1045C2×Q8—44no—
1046C2×Q8—88no—
1047C2×Q8H(5,𝔽2)14yes—
1048C2×D4—24no—
1049C2×D4—22no—
1050C2×D4—24no—
1051C2×D4—22no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—41no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—41no—
1067C2×D4—41no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—22no—
1084C22×C4—22no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—42no—
1095C22×C4—41no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—88no—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2514yes—
1119C22×C4C2514yes—
1120C22×C4C2512yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2514yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2514yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—41no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—41no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C22⋊C4—28no—
1186C22⋊C4—22no—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—41no—
1216C22⋊C4—42no—
1217C22⋊C4—41no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—41no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C42—28no—
1247C42—24no—
1248C42—22no—
1249C42—24no—
1250C42—24no—
1251C42—24no—
1252C42—24no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—42no—
1261C42—44no—
1262C42—44no—
1263C23—21no—
1264C23—22no—
1265C23—21no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—21no—
1271C23—22no—
1272C23—21no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—24no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—21no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—24no—
1290C23—22no—
1291C23—44no—
1292C23—82no—
1293C23—84no—
1294C23—82no—
1295C23—84no—
1296C23#58512yes—
1297C23C2611yescharacteristic
1298Q8—28no—
1299Q8—44no—
1300Q8—44no—
1301Q8—84no—
1302Q8—84no—
1303Q8—82no—
1304Q8—162no—
1305Q8—164no—
1306D4—48no—
1307D4—44no—
1308D4—84no—
1309D4—82no—
1310D4—84no—
1311D4—84no—
1312D4—84no—
1313D4—84no—
1314D4—82no—
1315D4—84no—
1316D4—164no—
1317D4—164no—
1318C2×C4—24no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—21no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—48no—
1382C2×C4—44no—
1383C2×C4—48no—
1384C2×C4—44no—
1385C2×C4—84no—
1386C2×C4—84no—
1387C2×C4—84no—
1388C2×C4—88no—
1389C2×C4—82no—
1390C2×C4—84no—
1391C2×C4—162no—
1392C2×C4—164no—
1393C2×C4C2×H(5,𝔽2)14yes—
1394C2×C4C2×H(5,𝔽2)12yes—
1395C2×C4#58514yes—
1396C22—22no—
1397C22—24no—
1398C22—41no—
1399C22—41no—
1400C22—42no—
1401C22—42no—
1402C22—41no—
1403C22—42no—
1404C22—42no—
1405C22—41no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—44no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—41no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—44no—
1425C22—88no—
1426C22C22×H(5,𝔽2)11yescharacteristic
1427C22C2×#58512yes—
1428C22C2×#58511yescharacteristic
1429C22H(7,𝔽2)11yescharacteristic
1430C222−1+612yes—
1431C4—24no—
1432C4—42no—
1433C4—41no—
1434C4—41no—
1435C4—42no—
1436C4—42no—
1437C4—44no—
1438C4—41no—
1439C4—42no—
1440C4—44no—
1441C4—42no—
1442C4—44no—
1443C4—42no—
1444C4—42no—
1445C4—44no—
1446C4—44no—
1447C4—41no—
1448C4—42no—
1449C4—42no—
1450C4—44no—
1451C4—42no—
1452C4—42no—
1453C4—42no—
1454C4#354514yes—
1455C2—42no—
1456C2—81no—
1457C2—82no—
1458C2—82no—
1459C2—82no—
1460C2C2×#354511yescharacteristic
1461C2#6289911yescharacteristic
1462C2#6290712yes—
1463C2#6304811yescharacteristic
1464C2#6306512yes—
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. #59202C2semidirect
2. #59027C2semidirect
3. #58380C2semidirect
4. #55218C2semidirect
5. #54585C2semidirect
6. #54384C2semidirect
7. #54242C2semidirect
8. #53120C2semidirect
9. #52991C2semidirect
10. #52941C2semidirect
11. #52874C2semidirect
12. #46912C2semidirect
13. #45406C2semidirect
14. #45402C2semidirect
15. #45330C2semidirect
16. #45282C2semidirect
17. #45236C2semidirect
18. #42920C2semidirect
19. #42908C2semidirect
20. #42813C2semidirect
21. #42691C2semidirect
22. #42514C2semidirect
23. #41660C2semidirect
24. #41545C2semidirect
25. #39934C2semidirect
26. #39133C2semidirect
27. #36675C2semidirect
28. #36050C2semidirect
29. #35948C2semidirect
30. C2×Q82C22semidirect
33. C2×#537C22semidirect
38. #2839C22semidirect
39. #2838C22semidirect
42. #2835C22semidirect
45. #2831C22semidirect
54. #2817C22semidirect
60. #2786C22semidirect
61. #2785C22semidirect
62. #2779C22semidirect
64. #2767C22semidirect
66. #2762C22semidirect
68. #2761C22semidirect
69. #2759C22semidirect
70. #2758C22semidirect
71. #2757C22semidirect
74. #2754C22semidirect
77. #2747C22semidirect
78. #2746C22semidirect
87. #2728C22semidirect
88. #2722C22semidirect
91. #2713C22semidirect
92. #2713C22semidirect
96. #2702C22semidirect
101. #2692C22semidirect
102. #2692C22semidirect
103. #2690C22semidirect
107. #2686C22semidirect
112. #2665C22semidirect
114. #2660C22semidirect
115. #2654C22semidirect
117. #2651C22semidirect
120. #2647C22semidirect
121. #2640C22semidirect
122. #2640C22semidirect
123. #2639C22semidirect
127. #2621C22semidirect
129. #2616C22semidirect
131. #2599C22semidirect
135. #2592C22semidirect
136. #2592C22semidirect
137. #2588C22semidirect
138. #2586C22semidirect
139. #2586C22semidirect
140. #2584C22semidirect
141. #2582C22semidirect
142. #2581C22semidirect
146. #2573C22semidirect
147. #2569C22semidirect
150. #2560C22semidirect
158. #2538C22semidirect
163. #2532C22semidirect
164. #2529C22semidirect
165. #2529C22semidirect
167. #2526C22semidirect
168. #2524C22semidirect
171. #2515C22semidirect
173. #2504C22semidirect
174. #2503C22semidirect
178. #2497C22semidirect
179. #2497C22semidirect
180. #2496C22semidirect
182. #2495C22semidirect
184. #2492C22semidirect
185. #2492C22semidirect
188. #2490C22semidirect
189. #2490C22semidirect
198. #2476C22semidirect
199. #2476C22semidirect
204. #2442C22semidirect
205. #2440C22semidirect
206. #2440C22semidirect
209. #2427C22semidirect
213. #2423C22semidirect
215. #2421C22semidirect
216. #2421C22semidirect
224. #2402C22semidirect
236. #2362C22semidirect
237. #2362C22semidirect
238. #2355C22semidirect
243. #2347C22semidirect
245. #2341C22semidirect
248. #2339C22semidirect
251. #2320C22semidirect
252. #2320C22semidirect
253. #2319C22semidirect
254. #2311C22semidirect
258. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#592022
#590272
#583802
#552182
#545852
#543842
#542422
#531202
#529912
#529412
#528742
#469122
#454062
#454022
#453302
#452822
#452362
#429202
#429082
#428132
#426912
#425142
#416602
#415452
#399342
#391332
#366752
#360502
#359482