Finite Group Databasebeta

← #8115467

Subgroups — #8115467

Order 512.

4097 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58770C214yesmaximal, complemented
2#58492C214yesmaximal, complemented
3#57922C214yesmaximal, complemented
4#57257C214yesmaximal, complemented
5#56910C214yesmaximal, complemented
6#56169C214yesmaximal, complemented
7#55656C214yesmaximal, complemented
8#54637C214yesmaximal, complemented
9#53093C212yesmaximal, complemented
10#53041C212yesmaximal, complemented
11#45344C211yesmaximal, characteristic, complemented
12#45338C211yesmaximal, characteristic, complemented
13#45268C211yesmaximal, characteristic, complemented
14#45231C211yesmaximal, characteristic, complemented
15#42882C211yesmaximal, characteristic
16#42828C212yesmaximal, complemented
17#42793C211yesmaximal, characteristic, complemented
18#42792C211yesmaximal, characteristic, complemented
19#42719C212yesmaximal, complemented
20#42649C211yesmaximal, characteristic, complemented
21#39187C211yesmaximal, characteristic, complemented
22#39172C211yesmaximal, characteristic, complemented
23#38970C211yesmaximal, characteristic, complemented
24#38954C211yesmaximal, characteristic, complemented
25#38291C212yesmaximal, complemented
26#38251C212yesmaximal, complemented
27#37414C212yesmaximal, complemented
28#37399C212yesmaximal, complemented
29#35324C211yesmaximal, characteristic, complemented
30#35318C211yesmaximal, characteristic, complemented
31#34640C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#541C2211yescharacteristic
38#2864C2211yescharacteristic
39#2862C2211yescharacteristic
40#2862C2211yescharacteristic
41#2861C2211yescharacteristic
42#2857C2211yescharacteristic
43#2855C2212yes—
44#2850C2211yescharacteristic
45#2841C2214yes—
46#2838C2214yes—
47#2838C2214yes—
48#2838C2214yes—
49#2837C2214yes—
50#2836C2214yes—
51#2833C2214yes—
52#2833C2214yes—
53#2831C2214yes—
54#2827C2214yes—
55#2821C2212yes—
56#2821C2212yes—
57#2819C2212yes—
58#2814C2212yes—
59#2808C2214yes—
60#2806C2214yes—
61#2804C2214yes—
62#2803C2214yes—
63#2799C2214yes—
64#2799C2214yes—
65#2797C2214yes—
66#2796C2214yes—
67#2793C2214yes—
68#2791C2214yes—
69#2791C2214yes—
70#2789C2214yes—
71#2789C2214yes—
72#2787C2214yes—
73#2786C2214yes—
74#2783C2214yes—
75#2780C2214yes—
76#2779C2214yes—
77#2777C2214yes—
78#2776C2214yes—
79#2776C2214yes—
80#2774C2214yes—
81#2773C2214yes—
82#2770C2214yes—
83#2768C2214yes—
84#2766C2214yes—
85#2766C2214yes—
86#2764C2214yes—
87#2760C2214yes—
88#2759C2214yes—
89#2759C2214yes—
90#2759C2214yes—
91#2751C2214yes—
92#2751C2214yes—
93#2750C2214yes—
94#2749C2214yes—
95#2747C2214yes—
96#2746C2214yes—
97#2745C2214yes—
98#2745C2214yes—
99#2744C2214yes—
100#2744C2214yes—
101#2742C2214yes—
102#2740C2214yes—
103#2740C2214yes—
104#2740C2214yes—
105#2738C2214yes—
106#2737C2214yes—
107#2731C2214yes—
108#2723C2214yes—
109#2722C2214yes—
110#2720C2214yes—
111#2716C2214yes—
112#2716C2214yes—
113#2716C2214yes—
114#2716C2214yes—
115#2716C2214yes—
116#2715C2214yes—
117#2713C2214yes—
118#2705C2214yes—
119#2702C2214yes—
120#2698C2214yes—
121#2698C2214yes—
122#2692C2214yes—
123#2662C2212yes—
124#2660C2212yes—
125#2660C2211yescharacteristic
126#2659C2212yes—
127#2658C2211yescharacteristic
128#2655C2212yes—
129#2654C2212yes—
130#2653C2214yes—
131#2653C2212yes—
132#2652C2212yes—
133#2651C2212yes—
134#2651C2214yes—
135#2650C2214yes—
136#2650C2212yes—
137#2649C2212yes—
138#2648C2212yes—
139#2648C2214yes—
140#2645C2212yes—
141#2645C2212yes—
142#2642C2212yes—
143#2640C2212yes—
144#2637C2212yes—
145#2634C2212yes—
146#2633C2212yes—
147#2628C2211yescharacteristic
148#2625C2212yes—
149#2625C2212yes—
150#2621C2212yes—
151#2621C2211yescharacteristic
152#2621C2211yescharacteristic
153#2620C2211yescharacteristic
154#2606C2214yes—
155#2605C2214yes—
156#2604C2212yes—
157#2603C2212yes—
158#2592C2212yes—
159#2589C2214yes—
160#2588C2214yes—
161#2585C2214yes—
162#2581C2211yescharacteristic
163#2581C2211yescharacteristic
164#2575C2214yes—
165#2574C2214yes—
166#2570C2212yes—
167#2568C2212yes—
168#2568C2211yescharacteristic
169#2563C2211yescharacteristic
170#2556C2214yes—
171#2553C2214yes—
172#2550C2212yes—
173#2547C2212yes—
174#2546C2211yescharacteristic
175#2546C2212yes—
176#2546C2211yescharacteristic
177#2545C2212yes—
178#2542C2212yes—
179#2536C2211yescharacteristic
180#2536C2212yes—
181#2535C2211yescharacteristic
182#2532C2214yes—
183#2531C2214yes—
184#2531C2214yes—
185#2528C2214yes—
186#2528C2214yes—
187#2527C2214yes—
188#2527C2214yes—
189#2527C2214yes—
190#2524C2214yes—
191#2521C2214yes—
192#2520C2214yes—
193#2519C2214yes—
194#2515C2214yes—
195#2514C2212yes—
196#2514C2212yes—
197#2513C2214yes—
198#2510C2214yes—
199#2507C2212yes—
200#2499C2212yes—
201#2498C2212yes—
202#2497C2214yes—
203#2494C2212yes—
204#2493C2214yes—
205#2492C2212yes—
206#2492C2212yes—
207#2489C2212yes—
208#2477C2214yes—
209#2469C2214yes—
210#2467C2214yes—
211#2451C2214yes—
212#2451C2212yes—
213#2447C2212yes—
214#2447C2214yes—
215#2446C2214yes—
216#2446C2212yes—
217#2446C2212yes—
218#2446C2212yes—
219#2439C2214yes—
220#2439C2212yes—
221#2439C2212yes—
222#2436C2212yes—
223#2434C2212yes—
224#2434C2212yes—
225#2429C2212yes—
226#2429C2212yes—
227#2427C2212yes—
228#2427C2212yes—
229#2426C2212yes—
230#2426C2212yes—
231#2423C2212yes—
232#2421C2214yes—
233#2421C2212yes—
234#2414C2212yes—
235#2409C2212yes—
236#2402C2211yescharacteristic
237#2401C2212yes—
238#2398C2211yescharacteristic
239#2396C2211yescharacteristic
240#2395C2212yes—
241#2392C2211yescharacteristic
242#2365C2212yes—
243#2362C2212yes—
244#2357C2212yes—
245#2356C2211yescharacteristic
246#2356C2211yescharacteristic
247#2351C2211yescharacteristic
248#2349C2211yescharacteristic
249Q8×C22⋊C4C2212yes—
250#2331C2211yescharacteristic
251#2327C2212yes—
252#2327C2211yescharacteristic
253#2327C2211yescharacteristic
254#2326C2211yescharacteristic
255#2324C2212yes—
256#2323C2212yes—
257#2320C2212yes—
258#2310C2212yes—
259C4×C4⋊Q8C2211yescharacteristic
260C4×#124C2211yescharacteristic
261#2298C2212yes—
262#2295C2211yescharacteristic
263#2295C2212yes—
264#2293C2211yescharacteristic
265#2290C2212yes—
266C4×#117C2211yescharacteristic
267C23×Q8C2312yes—
268Q82—44no—
269#556—44no—
270#556—44no—
271D4×Q8—44no—
272#542—44no—
273#541—44no—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2311yescharacteristic
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2312yes—
285C2×C4⋊Q8C2314yes—
286C2×#126C2312yes—
287C2×#126C2312yes—
288C2×#126C2312yes—
289C2×#126C2314yes—
290C2×#126C2314yes—
291C2×#125C2311yescharacteristic
292C2×#125C2312yes—
293C2×#125C2312yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2311yescharacteristic
297C2×#124C2311yescharacteristic
298C2×#124C2311yescharacteristic
299C2×#124C2312yes—
300C2×#123C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2311yescharacteristic
303C2×C22⋊Q8C2311yescharacteristic
304C2×C22⋊Q8C2311yescharacteristic
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×#121C2312yes—
312C2×#121C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×#117C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2311yescharacteristic
332C2×#117C2312yes—
333C22×C42C2311yescharacteristic
334#401C2314yes—
335#401C2314yes—
336#401C2314yes—
337#401C2312yes—
338#401C2314yes—
339#401C2314yes—
340#400C2312yes—
341#400C2314yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2312yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2311yescharacteristic
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2312yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#399C2311yescharacteristic
373#399C2312yes—
374#399C2314yes—
375#399C2314yes—
376#399C2314yes—
377#399C2312yes—
378#399C2314yes—
379#399C2314yes—
380#398C2312yes—
381#398C2314yes—
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2312yes—
399#398C2314yes—
400#398C2312yes—
401#398C2312yes—
402#398C2312yes—
403#398C2312yes—
404#398C2312yes—
405#398C2314yes—
406#398C2314yes—
407#398C2311yescharacteristic
408#398C2312yes—
409#398C2312yes—
410#398C2312yes—
411#397C2311yescharacteristic
412#397C2312yes—
413#397C2314yes—
414#397C2312yes—
415#397C2314yes—
416#397C2314yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2312yes—
422#397C2314yes—
423#397C2314yes—
424#397C2312yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2312yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2312yes—
437#397C2312yes—
438#397C2312yes—
439#397C2312yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2312yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2312yes—
449#396C2312yes—
450#396C2314yes—
451#396C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2312yes—
459#395C2312yes—
460#395C2314yes—
461#395C2314yes—
462#395C2312yes—
463#395C2311yescharacteristic
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2312yes—
470#394C2314yes—
471#394C2311yescharacteristic
472#394C2312yes—
473#394C2312yes—
474#394C2312yes—
475#394C2312yes—
476#394C2314yes—
477#393C2312yes—
478#393C2312yes—
479#393C2314yes—
480#393C2312yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#393C2311yescharacteristic
489#393C2314yes—
490#393C2312yes—
491#392C2311yescharacteristic
492#392C2314yes—
493#392C2312yes—
494#391C2311yescharacteristic
495#391C2311yescharacteristic
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2312yes—
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2312yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2312yes—
508#391C2314yes—
509#391C2314yes—
510#391C2312yes—
511#391C2311yescharacteristic
512#391C2311yescharacteristic
513#391C2312yes—
514#391C2311yescharacteristic
515#391C2311yescharacteristic
516#391C2314yes—
517#391C2314yes—
518#391C2314yes—
519#391C2314yes—
520#391C2314yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2314yes—
525#391C2314yes—
526#391C2312yes—
527#391C2314yes—
528#390C2312yes—
529#390C2311yescharacteristic
530#390C2314yes—
531#390C2311yescharacteristic
532#390C2314yes—
533#390C2314yes—
534#390C2312yes—
535#390C2314yes—
536#390C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2314yes—
543#389C2312yes—
544#389C2314yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#388C2312yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2314yes—
590#388C2312yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2312yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2312yes—
636#387C2314yes—
637#387C2312yes—
638#387C2314yes—
639#387C2314yes—
640#387C2312yes—
641#387C2314yes—
642#387C2312yes—
643#387C2312yes—
644#387C2312yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2312yes—
653#386C2312yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2312yes—
667#385C2312yes—
668#385C2314yes—
669#385C2314yes—
670#384C2311yescharacteristic
671#384C2311yescharacteristic
672#384C2314yes—
673#383C2312yes—
674#383C2312yes—
675#383C2314yes—
676#383C2314yes—
677#383C2314yes—
678#382C2312yes—
679#382C2312yes—
680#382C2311yescharacteristic
681#382C2312yes—
682#382C2314yes—
683#382C2314yes—
684#382C2314yes—
685#382C2311yescharacteristic
686#382C2311yescharacteristic
687#382C2311yescharacteristic
688#382C2314yes—
689#381C2314yes—
690#381C2314yes—
691#381C2314yes—
692#381C2314yes—
693#381C2314yes—
694#380C2314yes—
695#380C2314yes—
696#380C2312yes—
697#380C2312yes—
698#380C2314yes—
699#380C2312yes—
700#380C2314yes—
701#380C2314yes—
702#380C2312yes—
703#380C2314yes—
704#380C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2311yescharacteristic
707C4×C4⋊C4C2311yescharacteristic
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2312yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2314yes—
731#376C2312yes—
732#376C2311yescharacteristic
733#376C2312yes—
734#376C2312yes—
735#376C2314yes—
736#376C2311yescharacteristic
737C2×#95C2312yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C22×Q8—44no—
741C22×Q8—44no—
742C22×Q8—44no—
743C22×Q8C2411yescharacteristic
744C22×Q8C2411yescharacteristic
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2412yes—
750C22×Q8C2414yes—
751C22×Q8C2414yes—
752C22×D4C2411yescharacteristic
753C22×D4C2411yescharacteristic
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2414yes—
757C23×C4C2411yescharacteristic
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2414yes—
761C23×C4C2414yes—
762C23×C4C2412yes—
763C4⋊Q8—24no—
764C4⋊Q8—24no—
765C4⋊Q8—42no—
766C4⋊Q8—44no—
767C4⋊Q8—44no—
768C4⋊Q8—44no—
769C4⋊Q8—42no—
770C4⋊Q8—44no—
771C4⋊Q8—42no—
772C4⋊Q8—44no—
773C4⋊Q8—42no—
774C4⋊Q8—48no—
775#126—44no—
776#126—44no—
777#126—44no—
778#126—48no—
779#126—48no—
780#125—42no—
781#125—44no—
782#125—44no—
783#124—44no—
784#124—42no—
785#124—42no—
786#124—42no—
787#124—44no—
788#124—44no—
789#123—44no—
790C22⋊Q8—48no—
791C22⋊Q8—44no—
792C22⋊Q8—44no—
793C22⋊Q8—44no—
794C22⋊Q8—42no—
795C22⋊Q8—42no—
796C22⋊Q8—42no—
797C22⋊Q8—44no—
798C22⋊Q8—44no—
799C22⋊Q8—44no—
800#121—44no—
801#121—42no—
802C4×Q8—24no—
803C4×Q8—24no—
804C4×Q8—24no—
805C4×Q8—24no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—44no—
810C4×Q8—44no—
811C4×Q8—44no—
812C4×D4—24no—
813C4×D4—24no—
814C4×D4—44no—
815C4×D4—44no—
816C4×D4—44no—
817#117—24no—
818#117—44no—
819#117—42no—
820#117—44no—
821#117—44no—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C22⋊C4C2411yescharacteristic
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C42—42no—
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956#95C2411yescharacteristic
957#95C2412yes—
958#95C2414yes—
959#95C2411yescharacteristic
960#95C2411yescharacteristic
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2411yescharacteristic
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038C24C2511yescharacteristic
1039C24C2512yes—
1040C24C2512yes—
1041C2×Q8—22no—
1042C2×Q8—22no—
1043C2×Q8—22no—
1044C2×Q8—22no—
1045C2×Q8—24no—
1046C2×Q8—24no—
1047C2×Q8—22no—
1048C2×Q8—24no—
1049C2×Q8—22no—
1050C2×Q8—24no—
1051C2×Q8—22no—
1052C2×Q8—22no—
1053C2×Q8—22no—
1054C2×Q8—22no—
1055C2×Q8—42no—
1056C2×Q8—44no—
1057C2×Q8—44no—
1058C2×Q8—44no—
1059C2×Q8—44no—
1060C2×Q8—42no—
1061C2×Q8—44no—
1062C2×Q8—44no—
1063C2×Q8—44no—
1064C2×Q8—44no—
1065C2×Q8—816no—
1066C2×D4—22no—
1067C2×D4—22no—
1068C2×D4—22no—
1069C2×D4—22no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C22×C4—22no—
1080C22×C4—24no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2511yescharacteristic
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—22no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—22no—
1131C4⋊C4—22no—
1132C4⋊C4—24no—
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C22⋊C4—22no—
1190C22⋊C4—22no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C42—22no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—24no—
1237C42—22no—
1238C42—22no—
1239C42—24no—
1240C42—22no—
1241C42—22no—
1242C42—24no—
1243C42—42no—
1244C42—42no—
1245C42—42no—
1246C42—42no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—42no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42H(5,𝔽2)14yes—
1257C23—21no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—21no—
1262C23—21no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—24no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—24no—
1273C23—22no—
1274C23C2611yescharacteristic
1275Q8—44no—
1276Q8—44no—
1277Q8—44no—
1278Q8—48no—
1279Q8—44no—
1280Q8—84no—
1281Q8—88no—
1282Q8—162no—
1283Q8—164no—
1284D4—44no—
1285D4—44no—
1286D4—84no—
1287D4—162no—
1288D4—164no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—21no—
1306C2×C4—22no—
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—21no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—21no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
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—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—44no—
1361C2×C4—48no—
1362C2×C4—84no—
1363C2×C4—84no—
1364C2×C4—88no—
1365C2×C4—164no—
1366C2×C4C2×H(5,𝔽2)12yes—
1367C2×C4C2×H(5,𝔽2)12yes—
1368C2×C4C2×H(5,𝔽2)12yes—
1369C2×C4#58512yes—
1370C2×C4#58512yes—
1371C22—42no—
1372C22—41no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—41no—
1377C22—41no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—44no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—44no—
1386C22—42no—
1387C22—42no—
1388C22C22×H(5,𝔽2)11yescharacteristic
1389C22C2×#58511yescharacteristic
1390C22C2×#58511yescharacteristic
1391C222−1+612yes—
1392C222−1+612yes—
1393C4—22no—
1394C4—22no—
1395C4—41no—
1396C4—42no—
1397C4—42no—
1398C4—44no—
1399C4—42no—
1400C4—42no—
1401C4—41no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—42no—
1406C4—44no—
1407C4—42no—
1408C4—41no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4—42no—
1415C4—42no—
1416C4—44no—
1417C4—42no—
1418C4—42no—
1419C4—44no—
1420C4#355114yes—
1421C2—82no—
1422C2—81no—
1423C2—82no—
1424C2C2×#355111yescharacteristic
1425C2#6288711yescharacteristic
1426C2#6288711yescharacteristic
1427C2#6289112yes—
1428C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42882C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58770C2semidirect
2. #58492C2semidirect
3. #57922C2semidirect
4. #57257C2semidirect
5. #56910C2semidirect
6. #56169C2semidirect
7. #55656C2semidirect
8. #54637C2semidirect
9. #53093C2semidirect
10. #53041C2semidirect
11. #45344C2semidirect
12. #45338C2semidirect
13. #45268C2semidirect
14. #45231C2semidirect
16. #42828C2semidirect
17. #42793C2semidirect
18. #42792C2semidirect
19. #42719C2semidirect
20. #42649C2semidirect
21. #39187C2semidirect
22. #39172C2semidirect
23. #38970C2semidirect
24. #38954C2semidirect
25. #38291C2semidirect
26. #38251C2semidirect
27. #37414C2semidirect
28. #37399C2semidirect
29. #35324C2semidirect
30. #35318C2semidirect
31. #34640C2semidirect

Maximal subgroups

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

subgroupindex
#587702
#584922
#579222
#572572
#569102
#561692
#556562
#546372
#530932
#530412
#453442
#453382
#452682
#452312
#428822
#428282
#427932
#427922
#427192
#426492
#391872
#391722
#389702
#389542
#382912
#382512
#374142
#373992
#353242
#353182
#346402