Finite Group Databasebeta

← #8115387

Subgroups — #8115387

Order 512.

4393 conjugacy classes of subgroups.

The subgroup lattice has 1502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57609C214yesmaximal, complemented
2#57537C214yesmaximal, complemented
3#57471C214yesmaximal, complemented
4#57440C214yesmaximal, complemented
5#57221C214yesmaximal, complemented
6#56286C214yesmaximal, complemented
7#54720C214yesmaximal, complemented
8#54705C214yesmaximal, complemented
9#53091C212yesmaximal, complemented
10#53004C212yesmaximal, complemented
11#45268C211yesmaximal, characteristic, complemented
12#45200C211yesmaximal, characteristic, complemented
13#45083C211yesmaximal, characteristic, complemented
14#44938C211yesmaximal, characteristic, complemented
15#42874C212yesmaximal, complemented
16#42788C211yesmaximal, characteristic, complemented
17#42646C211yesmaximal, characteristic, complemented
18#42645C211yesmaximal, characteristic, complemented
19#42629C212yesmaximal, complemented
20#42427C211yesmaximal, characteristic, complemented
21#39185C211yesmaximal, characteristic, complemented
22#39167C211yesmaximal, characteristic, complemented
23#38971C211yesmaximal, characteristic, complemented
24#38958C211yesmaximal, characteristic, complemented
25#38285C212yesmaximal, complemented
26#38255C212yesmaximal, complemented
27#37414C212yesmaximal, complemented
28#37348C212yesmaximal, complemented
29#35324C211yesmaximal, characteristic, complemented
30#35276C211yesmaximal, characteristic, complemented
31#34640C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#555C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#540C2211yescharacteristic
38#2864C2211yescharacteristic
39#2862C2211yescharacteristic
40#2861C2211yescharacteristic
41#2858C2211yescharacteristic
42#2856C2211yescharacteristic
43#2855C2212yes—
44#2850C2211yescharacteristic
45#2838C2214yes—
46#2838C2214yes—
47#2833C2214yes—
48#2832C2214yes—
49#2828C2214yes—
50#2825C2214yes—
51#2824C2214yes—
52#2824C2214yes—
53#2824C2214yes—
54#2821C2212yes—
55#2821C2214yes—
56#2817C2212yes—
57#2814C2212yes—
58#2813C2212yes—
59#2808C2214yes—
60#2805C2214yes—
61#2804C2214yes—
62#2803C2214yes—
63#2803C2214yes—
64#2803C2214yes—
65#2798C2214yes—
66#2798C2214yes—
67#2797C2214yes—
68#2796C2214yes—
69#2788C2214yes—
70#2784C2214yes—
71#2776C2214yes—
72#2771C2214yes—
73#2760C2214yes—
74#2760C2214yes—
75#2759C2214yes—
76#2751C2214yes—
77#2751C2214yes—
78#2750C2214yes—
79#2749C2214yes—
80#2748C2214yes—
81#2746C2214yes—
82#2746C2214yes—
83#2745C2214yes—
84#2745C2214yes—
85#2743C2214yes—
86#2741C2214yes—
87#2741C2214yes—
88#2740C2214yes—
89#2738C2214yes—
90#2731C2214yes—
91#2730C2214yes—
92#2725C2214yes—
93#2723C2214yes—
94#2723C2214yes—
95#2716C2214yes—
96#2715C2214yes—
97#2714C2214yes—
98#2713C2214yes—
99#2711C2214yes—
100#2711C2214yes—
101#2703C2214yes—
102#2701C2214yes—
103#2700C2214yes—
104#2700C2214yes—
105#2699C2214yes—
106#2696C2214yes—
107#2695C2214yes—
108#2692C2214yes—
109#2692C2214yes—
110#2691C2214yes—
111#2690C2214yes—
112#2689C2214yes—
113#2688C2214yes—
114#2688C2214yes—
115#2688C2214yes—
116#2686C2214yes—
117#2686C2214yes—
118#2676C2214yes—
119#2676C2214yes—
120#2674C2214yes—
121#2672C2214yes—
122#2671C2214yes—
123#2665C2214yes—
124#2663C2212yes—
125#2660C2211yescharacteristic
126#2657C2211yescharacteristic
127#2656C2212yes—
128#2655C2212yes—
129#2654C2212yes—
130#2653C2212yes—
131#2652C2212yes—
132#2651C2212yes—
133#2650C2212yes—
134#2649C2212yes—
135#2649C2214yes—
136#2649C2214yes—
137#2648C2212yes—
138#2645C2212yes—
139#2645C2212yes—
140#2640C2212yes—
141#2640C2212yes—
142#2639C2212yes—
143#2631C2212yes—
144#2628C2211yescharacteristic
145#2624C2212yes—
146#2624C2214yes—
147#2624C2212yes—
148#2624C2212yes—
149#2621C2211yescharacteristic
150#2620C2212yes—
151#2620C2211yescharacteristic
152#2619C2211yescharacteristic
153#2614C2212yes—
154#2611C2214yes—
155#2610C2214yes—
156#2603C2212yes—
157#2589C2214yes—
158#2588C2214yes—
159#2581C2211yescharacteristic
160#2580C2211yescharacteristic
161#2578C2214yes—
162#2575C2214yes—
163#2567C2211yescharacteristic
164#2567C2212yes—
165#2559C2214yes—
166#2555C2214yes—
167#2554C2214yes—
168#2552C2212yes—
169#2551C2212yes—
170#2547C2211yescharacteristic
171#2547C2211yescharacteristic
172#2544C2212yes—
173#2544C2212yes—
174#2544C2212yes—
175#2542C2211yescharacteristic
176#2540C2212yes—
177#2537C2212yes—
178#2535C2211yescharacteristic
179#2535C2211yescharacteristic
180#2530C2214yes—
181#2528C2214yes—
182#2527C2214yes—
183#2527C2214yes—
184#2526C2214yes—
185#2526C2214yes—
186#2516C2214yes—
187#2514C2212yes—
188#2511C2212yes—
189#2510C2214yes—
190#2509C2212yes—
191#2499C2212yes—
192#2498C2212yes—
193#2498C2212yes—
194#2496C2212yes—
195#2493C2214yes—
196#2492C2212yes—
197#2492C2212yes—
198#2491C2212yes—
199#2491C2214yes—
200#2477C2214yes—
201#2477C2214yes—
202#2474C2214yes—
203#2471C2214yes—
204#2467C2214yes—
205#2467C2214yes—
206#2464C2214yes—
207#2461C2214yes—
208#2453C2212yes—
209#2448C2212yes—
210#2447C2212yes—
211#2447C2212yes—
212#2447C2212yes—
213#2444C2214yes—
214#2441C2212yes—
215#2439C2212yes—
216#2439C2214yes—
217#2438C2214yes—
218#2436C2214yes—
219#2436C2212yes—
220#2436C2212yes—
221#2436C2212yes—
222#2434C2212yes—
223#2428C2212yes—
224#2428C2212yes—
225#2428C2212yes—
226#2427C2212yes—
227#2426C2212yes—
228#2426C2212yes—
229#2423C2212yes—
230#2422C2212yes—
231#2420C2214yes—
232#2415C2214yes—
233#2414C2212yes—
234#2409C2214yes—
235#2409C2212yes—
236#2402C2211yescharacteristic
237#2401C2212yes—
238#2398C2211yescharacteristic
239#2396C2211yescharacteristic
240#2395C2212yes—
241#2392C2211yescharacteristic
242#2367C2212yes—
243#2363C2212yes—
244#2357C2211yescharacteristic
245#2356C2211yescharacteristic
246#2354C2212yes—
247#2349C2211yescharacteristic
248#2349C2211yescharacteristic
249Q8×C22⋊C4C2212yes—
250#2331C2211yescharacteristic
251#2328C2211yescharacteristic
252#2327C2211yescharacteristic
253#2326C2211yescharacteristic
254#2326C2212yes—
255#2324C2212yes—
256#2323C2212yes—
257#2319C2212yes—
258#2310C2212yes—
259C4×#127C2211yescharacteristic
260C4×#124C2211yescharacteristic
261#2298C2212yes—
262#2295C2211yescharacteristic
263#2295C2212yes—
264#2293C2211yescharacteristic
265#2290C2212yes—
266C4×#117C2211yescharacteristic
267C23×Q8C2312yes—
268C23×Q8C2312yes—
269#556—44no—
270#555—44no—
271D4×Q8—44no—
272D4×Q8—44no—
273#542—44no—
274#540—44no—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2314yes—
281C2×#127C2311yescharacteristic
282C2×#127C2311yescharacteristic
283C2×#127C2311yescharacteristic
284C2×#126C2312yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#125C2311yescharacteristic
288C2×#125C2314yes—
289C2×#124C2311yescharacteristic
290C2×#124C2312yes—
291C2×#124C2311yescharacteristic
292C2×#124C2312yes—
293C2×#124C2311yescharacteristic
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#123C2312yes—
300C2×#123C2312yes—
301C2×#123C2312yes—
302C2×#123C2314yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2311yescharacteristic
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×#121C2312yes—
313C2×#121C2311yescharacteristic
314C2×#121C2311yescharacteristic
315C2×#121C2311yescharacteristic
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2314yes—
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×#117C2311yescharacteristic
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2311yescharacteristic
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2314yes—
347C22×C42C2311yescharacteristic
348#401C2314yes—
349#401C2312yes—
350#401C2314yes—
351#401C2314yes—
352#400C2311yescharacteristic
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2312yes—
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
371#400C2314yes—
372#400C2314yes—
373#400C2312yes—
374#400C2312yes—
375#400C2312yes—
376#400C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2312yes—
381#399C2312yes—
382#399C2314yes—
383#399C2312yes—
384#399C2312yes—
385#399C2311yescharacteristic
386#399C2314yes—
387#399C2312yes—
388#398C2311yescharacteristic
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2312yes—
396#398C2312yes—
397#398C2312yes—
398#398C2312yes—
399#398C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2312yes—
413#397C2312yes—
414#397C2312yes—
415#397C2314yes—
416#397C2312yes—
417#397C2314yes—
418#397C2312yes—
419#397C2312yes—
420#397C2312yes—
421#397C2311yescharacteristic
422#397C2314yes—
423#397C2312yes—
424#397C2312yes—
425#397C2314yes—
426#397C2314yes—
427#397C2312yes—
428#397C2312yes—
429#397C2314yes—
430#397C2312yes—
431#396C2312yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2312yes—
438#396C2312yes—
439#396C2314yes—
440#396C2314yes—
441#395C2312yes—
442#395C2314yes—
443#395C2312yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2312yes—
449#395C2314yes—
450#395C2312yes—
451#395C2311yescharacteristic
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2312yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2311yescharacteristic
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2312yes—
476#394C2312yes—
477#394C2312yes—
478#394C2314yes—
479#394C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#393C2314yes—
489#393C2314yes—
490#393C2314yes—
491#393C2312yes—
492#393C2314yes—
493#393C2311yescharacteristic
494#393C2312yes—
495#393C2314yes—
496#393C2312yes—
497#392C2314yes—
498#392C2314yes—
499#392C2314yes—
500#392C2314yes—
501#392C2314yes—
502#392C2314yes—
503#392C2314yes—
504#392C2314yes—
505#392C2312yes—
506#392C2311yescharacteristic
507#392C2312yes—
508#391C2311yescharacteristic
509#391C2312yes—
510#391C2312yes—
511#391C2314yes—
512#391C2312yes—
513#391C2314yes—
514#391C2312yes—
515#391C2312yes—
516#391C2314yes—
517#391C2314yes—
518#391C2312yes—
519#391C2311yescharacteristic
520#391C2312yes—
521#391C2314yes—
522#391C2314yes—
523#391C2314yes—
524#391C2312yes—
525#391C2312yes—
526#391C2314yes—
527#391C2312yes—
528#391C2314yes—
529#390C2311yescharacteristic
530#390C2311yescharacteristic
531#390C2314yes—
532#390C2314yes—
533#390C2311yescharacteristic
534#390C2312yes—
535#390C2314yes—
536#390C2311yescharacteristic
537#390C2311yescharacteristic
538#390C2311yescharacteristic
539#390C2314yes—
540#390C2314yes—
541#390C2314yes—
542#390C2312yes—
543#390C2314yes—
544#390C2312yes—
545#390C2314yes—
546#390C2314yes—
547#390C2314yes—
548#390C2312yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2312yes—
556#389C2312yes—
557#389C2314yes—
558#389C2312yes—
559#389C2314yes—
560#389C2312yes—
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2314yes—
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#388C2312yes—
587#388C2314yes—
588#388C2314yes—
589#388C2312yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2314yes—
594#388C2314yes—
595#388C2312yes—
596#388C2312yes—
597#388C2312yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
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#387C2312yes—
619#387C2314yes—
620#387C2314yes—
621#387C2312yes—
622#387C2312yes—
623#387C2314yes—
624#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2312yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
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#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2312yes—
653#386C2312yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
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#385C2314yes—
675#385C2312yes—
676#384C2311yescharacteristic
677#384C2312yes—
678#384C2312yes—
679#384C2311yescharacteristic
680#383C2314yes—
681#383C2312yes—
682#382C2314yes—
683#382C2311yescharacteristic
684#382C2311yescharacteristic
685#382C2311yescharacteristic
686#382C2311yescharacteristic
687#381C2312yes—
688#381C2314yes—
689#381C2314yes—
690#381C2314yes—
691#381C2314yes—
692#381C2314yes—
693#381C2314yes—
694#381C2314yes—
695#380C2314yes—
696#380C2314yes—
697#380C2312yes—
698#380C2312yes—
699#380C2312yes—
700#380C2314yes—
701#380C2312yes—
702#380C2312yes—
703#380C2314yes—
704#380C2314yes—
705#380C2314yes—
706#380C2314yes—
707C4×C4⋊C4C2311yescharacteristic
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2311yescharacteristic
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2314yes—
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#376C2314yes—
735#376C2311yescharacteristic
736C2×#95C2312yes—
737C2×#95C2312yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C22×Q8—44no—
741C22×Q8—44no—
742C22×Q8—44no—
743C22×Q8—44no—
744C22×Q8—84no—
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2412yes—
750C22×Q8C2414yes—
751C22×Q8C2414yes—
752C22×D4C2411yescharacteristic
753C22×D4C2411yescharacteristic
754C22×D4C2411yescharacteristic
755C22×D4C2411yescharacteristic
756C22×D4C2412yes—
757C22×D4C2414yes—
758C22×D4C2412yes—
759C22×D4C2414yes—
760C22×D4C2412yes—
761C22×D4C2412yes—
762C22×D4C2412yes—
763C22×D4C2414yes—
764C22×D4C2414yes—
765C22×D4C2414yes—
766C22×D4C2412yes—
767C23×C4C2411yescharacteristic
768C23×C4C2412yes—
769C23×C4C2412yes—
770C23×C4C2412yes—
771C23×C4C2412yes—
772C23×C4C2414yes—
773C23×C4C2414yes—
774C23×C4C2414yes—
775C23×C4C2414yes—
776C23×C4C2412yes—
777C4⋊Q8—24no—
778C4⋊Q8—24no—
779C4⋊Q8—42no—
780C4⋊Q8—44no—
781C4⋊Q8—44no—
782C4⋊Q8—84no—
783#127—42no—
784#127—42no—
785#127—42no—
786#126—44no—
787#126—48no—
788#126—84no—
789#125—42no—
790#125—84no—
791#124—44no—
792#124—42no—
793#124—44no—
794#124—42no—
795#124—44no—
796#124—42no—
797#124—44no—
798#124—48no—
799#124—84no—
800#124—84no—
801#123—44no—
802#123—44no—
803#123—44no—
804#123—84no—
805C22⋊Q8—48no—
806C22⋊Q8—48no—
807C22⋊Q8—44no—
808C22⋊Q8—44no—
809C22⋊Q8—42no—
810C22⋊Q8—44no—
811C22⋊Q8—44no—
812C22⋊Q8—44no—
813C22⋊Q8—84no—
814#121—44no—
815#121—44no—
816#121—44no—
817#121—44no—
818#121—42no—
819#121—42no—
820#121—42no—
821#121—44no—
822#121—44no—
823#121—84no—
824#121—84no—
825#121—84no—
826#121—84no—
827#121—84no—
828C4×Q8—24no—
829C4×Q8—24no—
830C4×Q8—44no—
831C4×Q8—44no—
832C4×D4—24no—
833C4×D4—24no—
834C4×D4—24no—
835C4×D4—24no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—44no—
839C4×D4—44no—
840C4×D4—44no—
841C4×D4—84no—
842#117—24no—
843#117—44no—
844#117—42no—
845#117—44no—
846#117—44no—
847#117—44no—
848#117—84no—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C22⋊C4C2411yescharacteristic
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C42—42no—
962C2×C42C2411yescharacteristic
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2411yescharacteristic
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2412yes—
976C2×C42C2414yes—
977C2×C42C2412yes—
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2411yescharacteristic
983#95C2411yescharacteristic
984#95C2411yescharacteristic
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2411yescharacteristic
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2411yescharacteristic
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
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—
1056C24C2512yes—
1057C24C2512yes—
1058C2×Q8—22no—
1059C2×Q8—22no—
1060C2×Q8—24no—
1061C2×Q8—24no—
1062C2×Q8—24no—
1063C2×Q8—24no—
1064C2×Q8—22no—
1065C2×Q8—22no—
1066C2×Q8—42no—
1067C2×Q8—44no—
1068C2×Q8—44no—
1069C2×Q8—44no—
1070C2×Q8—44no—
1071C2×Q8—44no—
1072C2×Q8—44no—
1073C2×Q8—44no—
1074C2×Q8—42no—
1075C2×Q8—44no—
1076C2×Q8—816no—
1077C2×Q8—816no—
1078C2×D4—22no—
1079C2×D4—22no—
1080C2×D4—22no—
1081C2×D4—22no—
1082C2×D4—22no—
1083C2×D4—22no—
1084C2×D4—22no—
1085C2×D4—22no—
1086C2×D4—22no—
1087C2×D4—22no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—44no—
1091C2×D4—42no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—42no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C22×C4—22no—
1118C22×C4—24no—
1119C22×C4—22no—
1120C22×C4—22no—
1121C22×C4—24no—
1122C22×C4—24no—
1123C22×C4—24no—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—42no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—42no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—42no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2514yes—
1151C22×C4C2514yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2514yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2514yes—
1164C22×C4C2511yescharacteristic
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2511yescharacteristic
1169C22×C4C2511yescharacteristic
1170C4⋊C4—22no—
1171C4⋊C4—22no—
1172C4⋊C4—22no—
1173C4⋊C4—22no—
1174C4⋊C4—22no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—22no—
1179C4⋊C4—22no—
1180C4⋊C4—24no—
1181C4⋊C4—22no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—42no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—44no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—42no—
1223C22⋊C4—22no—
1224C22⋊C4—22no—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—24no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
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—44no—
1254C22⋊C4—42no—
1255C22⋊C4—42no—
1256C22⋊C4—42no—
1257C22⋊C4—42no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—42no—
1268C22⋊C4—42no—
1269C22⋊C4—44no—
1270C22⋊C4—42no—
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—42no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C42—22no—
1283C42—24no—
1284C42—24no—
1285C42—22no—
1286C42—22no—
1287C42—24no—
1288C42—22no—
1289C42—22no—
1290C42—24no—
1291C42—42no—
1292C42—42no—
1293C42—42no—
1294C42—44no—
1295C42—44no—
1296C42—44no—
1297C42—44no—
1298C42—42no—
1299C42—44no—
1300C42—42no—
1301C42—44no—
1302C42H(5,𝔽2)14yes—
1303C23—21no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—21no—
1309C23—21no—
1310C23—22no—
1311C23—22no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—24no—
1320C23—22no—
1321C23—24no—
1322C23—22no—
1323C23—24no—
1324C23—24no—
1325C23—22no—
1326C23—24no—
1327C23—22no—
1328C23—22no—
1329C23—24no—
1330C23C2611yescharacteristic
1331Q8—44no—
1332Q8—48no—
1333Q8—44no—
1334Q8—84no—
1335Q8—88no—
1336Q8—88no—
1337Q8—162no—
1338D4—44no—
1339D4—44no—
1340D4—44no—
1341D4—44no—
1342D4—84no—
1343D4—88no—
1344D4—162no—
1345D4—164no—
1346D4—162no—
1347D4—162no—
1348D4—164no—
1349D4—164no—
1350D4—164no—
1351D4—162no—
1352D4—162no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—21no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—44no—
1419C2×C4—48no—
1420C2×C4—84no—
1421C2×C4—84no—
1422C2×C4—84no—
1423C2×C4—84no—
1424C2×C4—88no—
1425C2×C4—88no—
1426C2×C4—88no—
1427C2×C4—164no—
1428C2×C4C2×H(5,𝔽2)12yes—
1429C2×C4C2×H(5,𝔽2)12yes—
1430C2×C4C2×H(5,𝔽2)12yes—
1431C2×C4#58512yes—
1432C2×C4#58512yes—
1433C22—42no—
1434C22—41no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—41no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—44no—
1445C22—44no—
1446C22—44no—
1447C22—42no—
1448C22—44no—
1449C22—42no—
1450C22—42no—
1451C22—44no—
1452C22—42no—
1453C22—44no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—41no—
1458C22—42no—
1459C22—42no—
1460C22C22×H(5,𝔽2)11yescharacteristic
1461C22C2×#58511yescharacteristic
1462C22C2×#58511yescharacteristic
1463C22H(7,𝔽2)12yes—
1464C222−1+612yes—
1465C4—22no—
1466C4—22no—
1467C4—41no—
1468C4—42no—
1469C4—42no—
1470C4—44no—
1471C4—42no—
1472C4—42no—
1473C4—44no—
1474C4—42no—
1475C4—41no—
1476C4—42no—
1477C4—42no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—44no—
1483C4—42no—
1484C4—42no—
1485C4—44no—
1486C4—42no—
1487C4—42no—
1488C4—42no—
1489C4—41no—
1490C4#355114yes—
1491C2—82no—
1492C2—81no—
1493C2—82no—
1494C2—82no—
1495C2—82no—
1496C2C2×#355111yescharacteristic
1497C2#6287611yescharacteristic
1498C2#6288212yes—
1499C2#6288212yes—
1500C2#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. #57609C2semidirect
2. #57537C2semidirect
3. #57471C2semidirect
4. #57440C2semidirect
5. #57221C2semidirect
6. #56286C2semidirect
7. #54720C2semidirect
8. #54705C2semidirect
9. #53091C2semidirect
10. #53004C2semidirect
11. #45268C2semidirect
12. #45200C2semidirect
13. #45083C2semidirect
14. #44938C2semidirect
15. #42874C2semidirect
16. #42788C2semidirect
17. #42646C2semidirect
18. #42645C2semidirect
19. #42629C2semidirect
20. #42427C2semidirect
21. #39185C2semidirect
22. #39167C2semidirect
23. #38971C2semidirect
24. #38958C2semidirect
25. #38285C2semidirect
26. #38255C2semidirect
27. #37414C2semidirect
28. #37348C2semidirect
29. #35324C2semidirect
30. #35276C2semidirect
31. #34640C2semidirect

Maximal subgroups

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

subgroupindex
#576092
#575372
#574712
#574402
#572212
#562862
#547202
#547052
#530912
#530042
#452682
#452002
#450832
#449382
#428742
#427882
#426462
#426452
#426292
#424272
#391852
#391672
#389712
#389582
#382852
#382552
#374142
#373482
#353242
#352762
#346402