Finite Group Databasebeta

← #8115468

Subgroups — #8115468

Order 512.

4385 conjugacy classes of subgroups.

The subgroup lattice has 1495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58146C214yesmaximal, complemented
2#57903C214yesmaximal, complemented
3#57832C214yesmaximal, complemented
4#57629C214yesmaximal, complemented
5#57252C214yesmaximal, complemented
6#57123C214yesmaximal, complemented
7#54608C214yesmaximal, complemented
8#54015C214yesmaximal, complemented
9#53087C212yesmaximal, complemented
10#52999C212yesmaximal, complemented
11#45299C211yesmaximal, characteristic, complemented
12#45143C211yesmaximal, characteristic, complemented
13#45083C211yesmaximal, characteristic, complemented
14#44935C211yesmaximal, characteristic, complemented
15#42880C211yesmaximal, characteristic, complemented
16#42879C211yesmaximal, characteristic, complemented
17#42794C211yesmaximal, characteristic, complemented
18#42706C212yesmaximal, complemented
19#42565C212yesmaximal, complemented
20#42429C211yesmaximal, characteristic, complemented
21#39187C211yesmaximal, characteristic, complemented
22#39174C211yesmaximal, characteristic, complemented
23#38970C211yesmaximal, characteristic, complemented
24#38952C211yesmaximal, characteristic, complemented
25#38288C212yesmaximal, complemented
26#38248C212yesmaximal, complemented
27#37361C212yesmaximal, complemented
28#37341C212yesmaximal, complemented
29#35318C211yesmaximal, characteristic, complemented
30#35296C211yesmaximal, characteristic, complemented
31#34640C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#541C2211yescharacteristic
38#2864C2211yescharacteristic
39#2862C2211yescharacteristic
40#2861C2211yescharacteristic
41#2858C2211yescharacteristic
42#2857C2211yescharacteristic
43#2854C2212yes—
44#2850C2211yescharacteristic
45#2838C2214yes—
46#2837C2214yes—
47#2836C2214yes—
48#2834C2214yes—
49#2829C2214yes—
50#2829C2214yes—
51#2827C2214yes—
52#2827C2214yes—
53#2826C2214yes—
54#2821C2212yes—
55#2820C2212yes—
56#2818C2212yes—
57#2814C2214yes—
58#2813C2212yes—
59#2803C2214yes—
60#2800C2214yes—
61#2797C2214yes—
62#2797C2214yes—
63#2796C2214yes—
64#2795C2214yes—
65#2787C2214yes—
66#2782C2214yes—
67#2781C2214yes—
68#2781C2214yes—
69#2781C2214yes—
70#2780C2214yes—
71#2780C2214yes—
72#2778C2214yes—
73#2778C2214yes—
74#2777C2214yes—
75#2776C2214yes—
76#2774C2214yes—
77#2768C2214yes—
78#2765C2214yes—
79#2761C2214yes—
80#2761C2214yes—
81#2757C2214yes—
82#2756C2214yes—
83#2756C2214yes—
84#2753C2214yes—
85#2752C2214yes—
86#2752C2214yes—
87#2750C2214yes—
88#2748C2214yes—
89#2746C2214yes—
90#2745C2214yes—
91#2744C2214yes—
92#2738C2214yes—
93#2729C2214yes—
94#2728C2214yes—
95#2724C2214yes—
96#2721C2214yes—
97#2720C2214yes—
98#2719C2214yes—
99#2719C2214yes—
100#2714C2214yes—
101#2711C2214yes—
102#2711C2214yes—
103#2711C2214yes—
104#2708C2214yes—
105#2707C2214yes—
106#2707C2214yes—
107#2707C2214yes—
108#2706C2214yes—
109#2703C2214yes—
110#2701C2214yes—
111#2691C2214yes—
112#2690C2214yes—
113#2688C2214yes—
114#2688C2214yes—
115#2683C2214yes—
116#2681C2214yes—
117#2680C2214yes—
118#2676C2214yes—
119#2673C2214yes—
120#2672C2214yes—
121#2672C2214yes—
122#2671C2214yes—
123#2664C2212yes—
124#2661C2214yes—
125#2660C2211yescharacteristic
126#2660C2212yes—
127#2658C2211yescharacteristic
128#2655C2212yes—
129#2654C2212yes—
130#2653C2212yes—
131#2652C2212yes—
132#2651C2212yes—
133#2650C2212yes—
134#2649C2212yes—
135#2648C2212yes—
136#2648C2214yes—
137#2645C2212yes—
138#2644C2212yes—
139#2643C2214yes—
140#2641C2212yes—
141#2641C2212yes—
142#2639C2212yes—
143#2636C2212yes—
144#2634C2212yes—
145#2633C2212yes—
146#2628C2211yescharacteristic
147#2625C2212yes—
148#2624C2214yes—
149#2621C2211yescharacteristic
150#2620C2212yes—
151#2620C2211yescharacteristic
152#2619C2211yescharacteristic
153#2616C2212yes—
154#2611C2214yes—
155#2609C2214yes—
156#2604C2212yes—
157#2603C2212yes—
158#2597C2214yes—
159#2595C2214yes—
160#2581C2211yescharacteristic
161#2581C2211yescharacteristic
162#2576C2214yes—
163#2567C2211yescharacteristic
164#2566C2212yes—
165#2557C2214yes—
166#2556C2214yes—
167#2553C2214yes—
168#2552C2212yes—
169#2552C2212yes—
170#2548C2212yes—
171#2548C2211yescharacteristic
172#2548C2211yescharacteristic
173#2545C2212yes—
174#2544C2212yes—
175#2542C2211yescharacteristic
176#2540C2212yes—
177#2540C2212yes—
178#2538C2212yes—
179#2536C2211yescharacteristic
180#2535C2211yescharacteristic
181#2531C2214yes—
182#2528C2214yes—
183#2526C2214yes—
184#2524C2214yes—
185#2521C2214yes—
186#2519C2214yes—
187#2518C2214yes—
188#2513C2212yes—
189#2511C2212yes—
190#2510C2214yes—
191#2507C2212yes—
192#2505C2214yes—
193#2505C2214yes—
194#2501C2212yes—
195#2500C2214yes—
196#2494C2212yes—
197#2490C2212yes—
198#2489C2212yes—
199#2489C2212yes—
200#2477C2214yes—
201#2476C2214yes—
202#2474C2214yes—
203#2471C2214yes—
204#2471C2214yes—
205#2460C2214yes—
206#2454C2214yes—
207#2452C2212yes—
208#2447C2212yes—
209#2447C2212yes—
210#2446C2212yes—
211#2446C2212yes—
212#2445C2214yes—
213#2444C2214yes—
214#2442C2212yes—
215#2440C2212yes—
216#2438C2214yes—
217#2438C2214yes—
218#2432C2214yes—
219#2432C2212yes—
220#2432C2212yes—
221#2431C2212yes—
222#2430C2214yes—
223#2430C2212yes—
224#2429C2212yes—
225#2428C2212yes—
226#2428C2212yes—
227#2427C2212yes—
228#2427C2212yes—
229#2426C2214yes—
230#2426C2212yes—
231#2423C2212yes—
232#2422C2212yes—
233#2421C2214yes—
234#2416C2212yes—
235#2407C2212yes—
236#2402C2211yescharacteristic
237#2401C2212yes—
238#2398C2211yescharacteristic
239#2396C2211yescharacteristic
240#2395C2212yes—
241#2392C2211yescharacteristic
242#2367C2212yes—
243#2360C2212yes—
244#2356C2211yescharacteristic
245#2356C2211yescharacteristic
246#2354C2212yes—
247#2351C2211yescharacteristic
248#2349C2211yescharacteristic
249#2339C2212yes—
250#2331C2211yescharacteristic
251#2328C2211yescharacteristic
252#2327C2211yescharacteristic
253#2326C2212yes—
254#2326C2211yescharacteristic
255#2324C2212yes—
256#2324C2212yes—
257#2320C2212yes—
258#2311C2212yes—
259C4×C4⋊Q8C2211yescharacteristic
260C4×#124C2211yescharacteristic
261#2298C2212yes—
262#2295C2211yescharacteristic
263#2293C2211yescharacteristic
264#2293C2212yes—
265#2290C2212yes—
266C4×#117C2211yescharacteristic
267C22×#41C2312yes—
268C22×#41C2312yes—
269#557—44no—
270#554—44no—
271#550—44no—
272#550—44no—
273#542—44no—
274#541—44no—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2311yescharacteristic
281C2×#127C2311yescharacteristic
282C2×#127C2312yes—
283C2×#127C2312yes—
284C2×#126C2312yes—
285C2×#126C2312yes—
286C2×#126C2312yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2311yescharacteristic
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#124C2312yes—
295C2×#124C2311yescharacteristic
296C2×#124C2312yes—
297C2×#124C2311yescharacteristic
298C2×#124C2312yes—
299C2×#124C2311yescharacteristic
300C2×#124C2314yes—
301C2×#123C2312yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×C22⋊Q8C2311yescharacteristic
307C2×C22⋊Q8C2311yescharacteristic
308C2×C22⋊Q8C2311yescharacteristic
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2311yescharacteristic
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2314yes—
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×#117C2311yescharacteristic
342C2×#117C2312yes—
343C2×#117C2311yescharacteristic
344C2×#117C2314yes—
345C2×#117C2314yes—
346C22×C4⋊C4C2312yes—
347C22×C42C2311yescharacteristic
348#401C2314yes—
349#401C2312yes—
350#401C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2312yes—
361#400C2312yes—
362#400C2312yes—
363#400C2312yes—
364#400C2314yes—
365#400C2311yescharacteristic
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2312yes—
372#400C2312yes—
373#399C2312yes—
374#399C2312yes—
375#399C2314yes—
376#399C2314yes—
377#399C2312yes—
378#399C2314yes—
379#399C2314yes—
380#399C2314yes—
381#399C2314yes—
382#399C2311yescharacteristic
383#399C2312yes—
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#398C2312yes—
400#398C2314yes—
401#398C2311yescharacteristic
402#398C2312yes—
403#398C2312yes—
404#398C2312yes—
405#397C2311yescharacteristic
406#397C2312yes—
407#397C2314yes—
408#397C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2312yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2312yes—
427#397C2314yes—
428#397C2314yes—
429#397C2312yes—
430#397C2312yes—
431#397C2312yes—
432#397C2312yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2312yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2312yes—
449#396C2312yes—
450#395C2314yes—
451#395C2312yes—
452#395C2312yes—
453#395C2312yes—
454#395C2312yes—
455#395C2314yes—
456#395C2311yescharacteristic
457#395C2312yes—
458#394C2314yes—
459#394C2312yes—
460#394C2312yes—
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#394C2312yes—
476#394C2312yes—
477#394C2314yes—
478#394C2312yes—
479#394C2312yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2311yescharacteristic
484#394C2312yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2312yes—
489#394C2312yes—
490#394C2312yes—
491#394C2312yes—
492#394C2314yes—
493#394C2314yes—
494#393C2311yescharacteristic
495#393C2312yes—
496#393C2314yes—
497#393C2312yes—
498#392C2311yescharacteristic
499#392C2312yes—
500#392C2314yes—
501#392C2314yes—
502#392C2314yes—
503#392C2314yes—
504#392C2312yes—
505#392C2312yes—
506#392C2314yes—
507#392C2314yes—
508#391C2311yescharacteristic
509#391C2311yescharacteristic
510#391C2312yes—
511#391C2312yes—
512#391C2312yes—
513#391C2311yescharacteristic
514#391C2311yescharacteristic
515#391C2311yescharacteristic
516#391C2311yescharacteristic
517#391C2314yes—
518#391C2314yes—
519#391C2312yes—
520#391C2312yes—
521#391C2312yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2312yes—
526#390C2314yes—
527#390C2314yes—
528#390C2311yescharacteristic
529#390C2314yes—
530#390C2314yes—
531#390C2311yescharacteristic
532#390C2312yes—
533#390C2314yes—
534#390C2314yes—
535#390C2314yes—
536#390C2312yes—
537#390C2312yes—
538#390C2314yes—
539#390C2314yes—
540#390C2312yes—
541#390C2314yes—
542#390C2314yes—
543#390C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2314yes—
550#389C2312yes—
551#389C2314yes—
552#389C2314yes—
553#389C2312yes—
554#389C2314yes—
555#389C2312yes—
556#389C2312yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
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#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2312yes—
588#388C2312yes—
589#388C2314yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2312yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
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#387C2312yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2312yes—
622#387C2314yes—
623#387C2312yes—
624#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2312yes—
629#387C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2312yes—
650#386C2312yes—
651#386C2314yes—
652#386C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2312yes—
674#385C2312yes—
675#385C2314yes—
676#384C2311yescharacteristic
677#384C2312yes—
678#384C2312yes—
679#384C2311yescharacteristic
680#384C2314yes—
681#383C2312yes—
682#383C2312yes—
683#383C2314yes—
684#382C2312yes—
685#382C2311yescharacteristic
686#382C2314yes—
687#382C2314yes—
688#382C2311yescharacteristic
689#382C2311yescharacteristic
690#382C2311yescharacteristic
691#382C2314yes—
692#382C2314yes—
693#381C2314yes—
694#381C2314yes—
695#381C2314yes—
696#380C2314yes—
697#380C2314yes—
698#380C2312yes—
699#380C2312yes—
700#380C2312yes—
701#380C2314yes—
702#380C2312yes—
703#380C2314yes—
704#380C2314yes—
705#380C2314yes—
706#380C2314yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2311yescharacteristic
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C22⋊C4C2314yes—
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#376C2311yescharacteristic
736C2×#95C2314yes—
737C2×#95C2312yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C2×#41—44no—
741C2×#41—44no—
742C2×#41—44no—
743C2×#41—44no—
744C2×#41—84no—
745C22×Q8C2411yescharacteristic
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2411yescharacteristic
750C22×Q8C2412yes—
751C22×D4C2411yescharacteristic
752C22×D4C2412yes—
753C22×D4C2411yescharacteristic
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2412yes—
757C22×D4C2412yes—
758C22×D4C2414yes—
759C22×D4C2414yes—
760C22×D4C2414yes—
761C22×D4C2414yes—
762C22×D4C2414yes—
763C22×D4C2414yes—
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2412yes—
767C23×C4C2414yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C23×C4C2414yes—
772C23×C4C2412yes—
773C4⋊Q8—24no—
774C4⋊Q8—42no—
775C4⋊Q8—42no—
776C4⋊Q8—42no—
777C4⋊Q8—42no—
778C4⋊Q8—44no—
779#127—24no—
780#127—44no—
781#127—44no—
782#126—44no—
783#126—44no—
784#126—44no—
785#125—42no—
786#125—44no—
787#125—44no—
788#125—44no—
789#125—44no—
790#125—48no—
791#125—84no—
792#124—44no—
793#124—42no—
794#124—44no—
795#124—42no—
796#124—44no—
797#124—42no—
798#124—84no—
799#123—44no—
800#123—84no—
801#123—84no—
802#123—84no—
803#123—84no—
804C22⋊Q8—48no—
805C22⋊Q8—44no—
806C22⋊Q8—44no—
807C22⋊Q8—42no—
808C22⋊Q8—42no—
809C22⋊Q8—42no—
810C22⋊Q8—44no—
811C22⋊Q8—84no—
812C22⋊Q8—84no—
813C22⋊Q8—84no—
814#121—48no—
815#121—48no—
816#121—44no—
817#121—44no—
818#121—42no—
819#121—44no—
820#121—44no—
821#121—84no—
822#121—84no—
823#121—84no—
824C4×Q8—24no—
825C4×Q8—24no—
826C4×Q8—24no—
827C4×Q8—24no—
828C4×Q8—44no—
829C4×Q8—44no—
830C4×Q8—44no—
831C4×D4—24no—
832C4×D4—24no—
833C4×D4—44no—
834C4×D4—44no—
835C4×D4—44no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—44no—
839#117—24no—
840#117—44no—
841#117—42no—
842#117—84no—
843#117—84no—
844C2×C4⋊C4—44no—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C22⋊C4C2411yescharacteristic
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C42—42no—
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2411yescharacteristic
976C2×C42C2412yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2414yes—
980C2×C42C2414yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2414yes—
985C2×C42C2412yes—
986C2×C42C2411yescharacteristic
987#95C2412yes—
988#95C2411yescharacteristic
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2411yescharacteristic
995#95C2411yescharacteristic
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2411yescharacteristic
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053C24C2511yescharacteristic
1054C24C2512yes—
1055C24C2512yes—
1056C24C2514yes—
1057#41—816no—
1058#41—816no—
1059C2×Q8—22no—
1060C2×Q8—22no—
1061C2×Q8—22no—
1062C2×Q8—22no—
1063C2×Q8—24no—
1064C2×Q8—22no—
1065C2×Q8—22no—
1066C2×Q8—22no—
1067C2×Q8—22no—
1068C2×Q8—22no—
1069C2×Q8—22no—
1070C2×Q8—42no—
1071C2×Q8—44no—
1072C2×Q8—42no—
1073C2×Q8—44no—
1074C2×D4—22no—
1075C2×D4—22no—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—22no—
1080C2×D4—24no—
1081C2×D4—22no—
1082C2×D4—24no—
1083C2×D4—42no—
1084C2×D4—42no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—42no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—42no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—42no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C22×C4—24no—
1110C22×C4—22no—
1111C22×C4—22no—
1112C22×C4—22no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—42no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—42no—
1126C22×C4—44no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2514yes—
1139C22×C4C2514yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2512yes—
1158C22×C4C2514yes—
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C4⋊C4—22no—
1163C4⋊C4—24no—
1164C4⋊C4—22no—
1165C4⋊C4—22no—
1166C4⋊C4—22no—
1167C4⋊C4—22no—
1168C4⋊C4—24no—
1169C4⋊C4—22no—
1170C4⋊C4—22no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—22no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—42no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—44no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C22⋊C4—22no—
1224C22⋊C4—22no—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—42no—
1254C22⋊C4—42no—
1255C22⋊C4—42no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—42no—
1263C22⋊C4—42no—
1264C22⋊C4—42no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—42no—
1268C22⋊C4—42no—
1269C22⋊C4—42no—
1270C22⋊C4—44no—
1271C22⋊C4—42no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C42—22no—
1282C42—24no—
1283C42—24no—
1284C42—24no—
1285C42—24no—
1286C42—22no—
1287C42—22no—
1288C42—22no—
1289C42—24no—
1290C42—22no—
1291C42—24no—
1292C42—42no—
1293C42—42no—
1294C42—42no—
1295C42—44no—
1296C42—42no—
1297C42—44no—
1298C42—44no—
1299C42—44no—
1300C42—44no—
1301C42—42no—
1302C42H(5,𝔽2)14yes—
1303C23—21no—
1304C23—22no—
1305C23—22no—
1306C23—24no—
1307C23—22no—
1308C23—21no—
1309C23—22no—
1310C23—22no—
1311C23—24no—
1312C23—24no—
1313C23—22no—
1314C23—21no—
1315C23—22no—
1316C23—24no—
1317C23—24no—
1318C23—24no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—24no—
1323C23—22no—
1324C23—24no—
1325C23—24no—
1326C23—22no—
1327C23C2611yescharacteristic
1328Q8—44no—
1329Q8—44no—
1330Q8—44no—
1331Q8—44no—
1332Q8—84no—
1333Q8—162no—
1334D4—44no—
1335D4—44no—
1336D4—48no—
1337D4—84no—
1338D4—84no—
1339D4—84no—
1340D4—88no—
1341D4—88no—
1342D4—162no—
1343D4—164no—
1344D4—164no—
1345D4—164no—
1346D4—164no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—21no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—22no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—44no—
1416C2×C4—48no—
1417C2×C4—84no—
1418C2×C4—84no—
1419C2×C4—88no—
1420C2×C4—88no—
1421C2×C4—88no—
1422C2×C4—88no—
1423C2×C4—164no—
1424C2×C4C2×H(5,𝔽2)12yes—
1425C2×C4C2×H(5,𝔽2)12yes—
1426C2×C4C2×H(5,𝔽2)12yes—
1427C2×C4#58512yes—
1428C2×C4#58512yes—
1429C22—42no—
1430C22—41no—
1431C22—44no—
1432C22—42no—
1433C22—42no—
1434C22—44no—
1435C22—42no—
1436C22—41no—
1437C22—42no—
1438C22—44no—
1439C22—44no—
1440C22—42no—
1441C22—42no—
1442C22—44no—
1443C22—44no—
1444C22—42no—
1445C22—42no—
1446C22—44no—
1447C22—44no—
1448C22—42no—
1449C22—42no—
1450C22—44no—
1451C22—42no—
1452C22—41no—
1453C22C22×H(5,𝔽2)11yescharacteristic
1454C22C2×#58511yescharacteristic
1455C22C2×#58511yescharacteristic
1456C22H(7,𝔽2)12yes—
1457C222−1+612yes—
1458C4—22no—
1459C4—22no—
1460C4—41no—
1461C4—42no—
1462C4—42no—
1463C4—42no—
1464C4—42no—
1465C4—42no—
1466C4—42no—
1467C4—42no—
1468C4—44no—
1469C4—42no—
1470C4—41no—
1471C4—42no—
1472C4—42no—
1473C4—42no—
1474C4—42no—
1475C4—42no—
1476C4—42no—
1477C4—42no—
1478C4—44no—
1479C4—44no—
1480C4—42no—
1481C4—41no—
1482C4—42no—
1483C4—42no—
1484C4#355114yes—
1485C2—82no—
1486C2—81no—
1487C2—84no—
1488C2—82no—
1489C2C2×#355111yescharacteristic
1490C2#6287611yescharacteristic
1491C2#6288412yes—
1492C2#6288412yes—
1493C2#6288711yescharacteristic
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. #58146C2semidirect
2. #57903C2semidirect
3. #57832C2semidirect
4. #57629C2semidirect
5. #57252C2semidirect
6. #57123C2semidirect
7. #54608C2semidirect
8. #54015C2semidirect
9. #53087C2semidirect
10. #52999C2semidirect
11. #45299C2semidirect
12. #45143C2semidirect
13. #45083C2semidirect
14. #44935C2semidirect
15. #42880C2semidirect
16. #42879C2semidirect
17. #42794C2semidirect
18. #42706C2semidirect
19. #42565C2semidirect
20. #42429C2semidirect
21. #39187C2semidirect
22. #39174C2semidirect
23. #38970C2semidirect
24. #38952C2semidirect
25. #38288C2semidirect
26. #38248C2semidirect
27. #37361C2semidirect
28. #37341C2semidirect
29. #35318C2semidirect
30. #35296C2semidirect
31. #34640C2semidirect

Maximal subgroups

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

subgroupindex
#581462
#579032
#578322
#576292
#572522
#571232
#546082
#540152
#530872
#529992
#452992
#451432
#450832
#449352
#428802
#428792
#427942
#427062
#425652
#424292
#391872
#391742
#389702
#389522
#382882
#382482
#373612
#373412
#353182
#352962
#346402