Finite Group Databasebeta

← #8701610

Subgroups — #8701610

Order 512.

4615 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#59885C212yesmaximal, complemented
2#59549C212yesmaximal, complemented
3#59281C212yesmaximal, complemented
4#59236C212yesmaximal, complemented
5#57586C214yesmaximal, complemented
6#56266C214yesmaximal, complemented
7#55403C214yesmaximal, complemented
8#52303C211yesmaximal, characteristic, complemented
9#50964C214yesmaximal, complemented
10#50452C214yesmaximal, complemented
11#49350C214yesmaximal, complemented
12#46022C211yesmaximal, characteristic, complemented
13#46016C211yesmaximal, characteristic, complemented
14#46015C211yesmaximal, characteristic, complemented
15#45150C212yesmaximal, complemented
16#44895C212yesmaximal, complemented
17#44889C212yesmaximal, complemented
18#42785C212yesmaximal, complemented
19#42503C212yesmaximal, complemented
20#42431C212yesmaximal, complemented
21#40145C212yesmaximal, complemented
22#39961C212yesmaximal, complemented
23#39905C212yesmaximal, complemented
24#37217C212yesmaximal, complemented
25#37165C212yesmaximal, complemented
26#37140C212yesmaximal, complemented
27#36463C211yesmaximal, characteristic, complemented
28#36453C211yesmaximal, characteristic, complemented
29#36303C211yesmaximal, characteristic, complemented
30C2×#550C2212yes—
31C2×D4×Q8C2211yescharacteristic
32C2×#547C2211yescharacteristic
33C2×#540C2212yes—
34#2862C2211yescharacteristic
35#2859C2211yescharacteristic
36#2858C2211yescharacteristic
37#2855C2212yes—
38#2854C2212yes—
39#2850C2212yes—
40#2850C2212yes—
41#2832C2214yes—
42#2824C2214yes—
43#2822C2212yes—
44#2819C2212yes—
45#2819C2212yes—
46#2816C2214yes—
47#2809C2212yes—
48#2808C2212yes—
49#2808C2211yescharacteristic
50#2806C2211yescharacteristic
51#2805C2212yes—
52#2804C2212yes—
53#2801C2214yes—
54#2788C2214yes—
55#2783C2212yes—
56#2781C2212yes—
57#2779C2214yes—
58#2778C2214yes—
59#2778C2214yes—
60#2775C2214yes—
61#2774C2214yes—
62#2770C2214yes—
63#2766C2214yes—
64#2762C2214yes—
65#2760C2214yes—
66#2760C2214yes—
67#2759C2214yes—
68#2759C2214yes—
69#2756C2214yes—
70#2754C2214yes—
71#2753C2214yes—
72#2751C2214yes—
73#2750C2214yes—
74#2750C2214yes—
75#2749C2214yes—
76#2746C2214yes—
77#2745C2214yes—
78#2744C2212yes—
79#2743C2214yes—
80#2738C2214yes—
81#2737C2214yes—
82#2733C2212yes—
83#2732C2211yescharacteristic
84#2730C2212yes—
85#2712C2214yes—
86#2711C2214yes—
87#2710C2214yes—
88#2709C2214yes—
89#2709C2214yes—
90#2708C2214yes—
91#2703C2214yes—
92#2703C2214yes—
93#2701C2214yes—
94#2699C2214yes—
95#2694C2212yes—
96#2688C2214yes—
97#2688C2214yes—
98#2687C2214yes—
99#2687C2214yes—
100#2687C2214yes—
101#2686C2214yes—
102#2686C2212yes—
103#2682C2212yes—
104#2682C2211yescharacteristic
105#2673C2214yes—
106#2673C2214yes—
107#2673C2214yes—
108#2672C2214yes—
109#2672C2214yes—
110#2671C2214yes—
111#2663C2214yes—
112#2661C2214yes—
113#2654C2214yes—
114#2653C2214yes—
115#2649C2214yes—
116#2645C2214yes—
117#2635C2214yes—
118#2631C2214yes—
119#2628C2212yes—
120#2614C2214yes—
121#2602C2214yes—
122#2592C2212yes—
123#2591C2214yes—
124#2580C2212yes—
125#2576C2214yes—
126#2576C2214yes—
127#2576C2214yes—
128#2572C2214yes—
129#2572C2214yes—
130#2572C2214yes—
131#2568C2211yescharacteristic
132#2565C2212yes—
133#2563C2211yescharacteristic
134#2563C2212yes—
135#2562C2212yes—
136#2557C2214yes—
137#2555C2214yes—
138#2550C2212yes—
139#2550C2212yes—
140#2547C2211yescharacteristic
141#2543C2214yes—
142#2543C2214yes—
143#2541C2211yescharacteristic
144#2538C2211yescharacteristic
145#2537C2211yescharacteristic
146#2535C2212yes—
147#2532C2214yes—
148#2532C2214yes—
149#2531C2214yes—
150#2530C2214yes—
151#2527C2214yes—
152#2526C2214yes—
153#2526C2214yes—
154#2514C2212yes—
155#2514C2212yes—
156#2514C2212yes—
157#2513C2212yes—
158#2511C2212yes—
159#2510C2214yes—
160#2505C2214yes—
161#2503C2212yes—
162#2503C2212yes—
163#2500C2212yes—
164#2494C2212yes—
165#2494C2212yes—
166#2493C2214yes—
167#2493C2214yes—
168#2492C2212yes—
169#2492C2212yes—
170#2492C2212yes—
171#2491C2212yes—
172#2491C2212yes—
173#2490C2212yes—
174#2490C2212yes—
175#2488C2214yes—
176#2488C2214yes—
177#2488C2214yes—
178#2463C2214yes—
179#2460C2214yes—
180#2459C2214yes—
181#2459C2214yes—
182#2459C2214yes—
183#2459C2214yes—
184#2457C2214yes—
185#2457C2214yes—
186#2457C2214yes—
187#2453C2212yes—
188#2447C2212yes—
189#2446C2212yes—
190#2445C2212yes—
191#2445C2212yes—
192#2444C2214yes—
193#2439C2212yes—
194#2436C2212yes—
195#2436C2214yes—
196#2432C2212yes—
197#2431C2212yes—
198#2431C2212yes—
199#2428C2214yes—
200#2428C2212yes—
201#2427C2212yes—
202#2425C2214yes—
203#2425C2214yes—
204#2422C2212yes—
205#2421C2212yes—
206#2420C2212yes—
207#2420C2214yes—
208#2420C2212yes—
209#2420C2212yes—
210#2419C2214yes—
211#2416C2212yes—
212#2415C2212yes—
213#2414C2212yes—
214#2407C2212yes—
215#2407C2212yes—
216#2407C2212yes—
217#2396C2212yes—
218#2395C2212yes—
219#2392C2212yes—
220#2382C2212yes—
221#2379C2212yes—
222#2379C2212yes—
223#2372C2214yes—
224#2369C2211yescharacteristic
225#2367C2212yes—
226#2366C2212yes—
227#2366C2211yescharacteristic
228#2361C2212yes—
229#2357C2212yes—
230#2357C2212yes—
231#2355C2211yescharacteristic
232#2353C2214yes—
233#2353C2214yes—
234#2352C2212yes—
235D4×C4⋊C4C2211yescharacteristic
236#2346C2212yes—
237#2345C2212yes—
238#2339C2212yes—
239#2339C2212yes—
240#2339C2212yes—
241#2335C2214yes—
242#2325C2214yes—
243#2323C2212yes—
244#2322C2214yes—
245#2311C2212yes—
246C4×#125C2211yescharacteristic
247C4×#124C2211yescharacteristic
248C4×#124C2211yescharacteristic
249C4×C22⋊Q8C2212yes—
250C4×#123C2212yes—
251C4×#121C2212yes—
252C4×#121C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255#2297C2212yes—
256C2×#391C2212yes—
257#2283C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261C23×Q8C2312yes—
262#550—48no—
263D4×Q8—44no—
264#547—44no—
265#540—48no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2312yes—
271C2×#127C2311yescharacteristic
272C2×#127C2314yes—
273C2×#125C2311yescharacteristic
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#124C2311yescharacteristic
277C2×#124C2311yescharacteristic
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2314yes—
282C2×#124C2312yes—
283C2×#124C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2312yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×#121C2312yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×D4C2312yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2314yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×#117C2312yes—
332C2×#117C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2312yes—
335C22×C42C2312yes—
336C22×C42C2312yes—
337#401C2314yes—
338#401C2314yes—
339#401C2314yes—
340#401C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#399C2312yes—
360#399C2314yes—
361#399C2314yes—
362#399C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2312yes—
382#397C2314yes—
383#397C2312yes—
384#397C2312yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#396C2312yes—
392#396C2314yes—
393#396C2312yes—
394#396C2312yes—
395#396C2314yes—
396#396C2312yes—
397#396C2314yes—
398#395C2314yes—
399#395C2312yes—
400#395C2314yes—
401#395C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2312yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2312yes—
425#394C2312yes—
426#394C2312yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2312yes—
441#393C2314yes—
442#393C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#392C2314yes—
450#392C2312yes—
451#392C2314yes—
452#392C2314yes—
453#392C2314yes—
454#392C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2311yescharacteristic
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2314yes—
473#391C2312yes—
474#391C2314yes—
475#391C2314yes—
476#391C2312yes—
477#391C2311yescharacteristic
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2314yes—
485#390C2312yes—
486#390C2311yescharacteristic
487#390C2312yes—
488#390C2312yes—
489#390C2314yes—
490#390C2312yes—
491#390C2312yes—
492#390C2314yes—
493#390C2312yes—
494#390C2311yescharacteristic
495#389C2311yescharacteristic
496#389C2311yescharacteristic
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2312yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2312yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2312yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2312yes—
551#388C2312yes—
552#388C2314yes—
553#388C2312yes—
554#388C2314yes—
555#387C2312yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2312yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2312yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2312yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#384C2311yescharacteristic
631#384C2311yescharacteristic
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#382C2311yescharacteristic
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2314yes—
645#382C2312yes—
646#382C2311yescharacteristic
647#382C2311yescharacteristic
648#381C2314yes—
649#381C2312yes—
650#381C2314yes—
651#381C2314yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2314yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2314yes—
665#380C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2314yes—
711#376C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C43C2311yescharacteristic
716C2×#41—28no—
717C2×#41—44no—
718C2×#41—44no—
719C2×#41—44no—
720C2×#41—44no—
721C2×#41—44no—
722C22×Q8—44no—
723C22×Q8—44no—
724C22×Q8—82no—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2414yes—
730C22×Q8C2412yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2411yescharacteristic
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2412yes—
741C22×D4C2414yes—
742C22×D4C2412yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2414yes—
746C22×D4C2412yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2414yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2414yes—
754C23×C4C2414yes—
755C23×C4C2414yes—
756C23×C4C2412yes—
757C23×C4C2414yes—
758C23×C4C2414yes—
759C23×C4C2412yes—
760C4⋊Q8—42no—
761C4⋊Q8—44no—
762C4⋊Q8—42no—
763C4⋊Q8—42no—
764#127—28no—
765#127—42no—
766#127—48no—
767#125—44no—
768#125—42no—
769#125—44no—
770#124—44no—
771#124—44no—
772#124—44no—
773#124—42no—
774#124—42no—
775#124—48no—
776#124—82no—
777#124—84no—
778#123—44no—
779#123—48no—
780#123—48no—
781#123—48no—
782#123—48no—
783#123—48no—
784#123—84no—
785C22⋊Q8—44no—
786C22⋊Q8—48no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789C22⋊Q8—44no—
790C22⋊Q8—82no—
791#121—28no—
792#121—48no—
793#121—44no—
794#121—48no—
795#121—48no—
796#121—44no—
797#121—44no—
798#121—44no—
799#121—44no—
800#121—44no—
801#121—48no—
802#121—44no—
803#121—48no—
804#121—82no—
805#121—84no—
806C4×Q8—42no—
807C4×Q8—42no—
808C4×Q8—44no—
809C4×D4—28no—
810C4×D4—24no—
811C4×D4—44no—
812C4×D4—42no—
813C4×D4—42no—
814C4×D4—44no—
815C4×D4—44no—
816C4×D4—42no—
817C4×D4—42no—
818C4×D4—44no—
819C4×D4—48no—
820C4×D4—48no—
821C4×D4—48no—
822C4×D4—82no—
823C4×D4—82no—
824C4×D4—84no—
825#117—44no—
826#117—44no—
827C2×C4⋊C4—44no—
828C2×C4⋊C4—44no—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C42—44no—
937C2×C42—82no—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2412yes—
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2414yes—
956C2×C42C2412yes—
957C2×C42C2411yescharacteristic
958C2×C42C2412yes—
959C2×C42C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025C24C2512yes—
1026C24C2512yes—
1027C24C2514yes—
1028C24C2512yes—
1029#41—816no—
1030#41—816no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—22no—
1034C2×Q8—24no—
1035C2×Q8—22no—
1036C2×Q8—24no—
1037C2×Q8—41no—
1038C2×Q8—41no—
1039C2×Q8—41no—
1040C2×Q8—42no—
1041C2×Q8—44no—
1042C2×Q8—41no—
1043C2×Q8—42no—
1044C2×Q8—44no—
1045C2×Q8—44no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—816no—
1050C2×D4—28no—
1051C2×D4—28no—
1052C2×D4—28no—
1053C2×D4—28no—
1054C2×D4—24no—
1055C2×D4—22no—
1056C2×D4—22no—
1057C2×D4—24no—
1058C2×D4—22no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—22no—
1062C2×D4—41no—
1063C2×D4—41no—
1064C2×D4—41no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—42no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—42no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—42no—
1078C2×D4—42no—
1079C2×D4—44no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4—41no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—42no—
1094C2×D4—42no—
1095C2×D4—44no—
1096C2×D4—42no—
1097C2×D4H(5,𝔽2)14yes—
1098C22×C4—24no—
1099C22×C4—28no—
1100C22×C4—28no—
1101C22×C4—24no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—24no—
1109C22×C4—24no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—42no—
1114C22×C4—42no—
1115C22×C4—44no—
1116C22×C4—42no—
1117C22×C4—42no—
1118C22×C4—42no—
1119C22×C4—42no—
1120C22×C4—42no—
1121C22×C4—42no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4C2511yescharacteristic
1138C22×C4C2514yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2514yes—
1147C22×C4C2512yes—
1148C22×C4C2514yes—
1149C22×C4C2514yes—
1150C22×C4C2514yes—
1151C22×C4C2512yes—
1152C22×C4C2511yescharacteristic
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2511yescharacteristic
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C4⋊C4—24no—
1163C4⋊C4—22no—
1164C4⋊C4—24no—
1165C4⋊C4—22no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—22no—
1169C4⋊C4—24no—
1170C4⋊C4—28no—
1171C4⋊C4—22no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—22no—
1175C4⋊C4—41no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—41no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—41no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—41no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—41no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—41no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4—44no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C22⋊C4—28no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—24no—
1216C22⋊C4—28no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—28no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—42no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—42no—
1263C22⋊C4—42no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—42no—
1269C42—24no—
1270C42—24no—
1271C42—22no—
1272C42—24no—
1273C42—24no—
1274C42—22no—
1275C42—22no—
1276C42—22no—
1277C42—22no—
1278C42—22no—
1279C42—42no—
1280C42—42no—
1281C42—41no—
1282C42—42no—
1283C42—42no—
1284C42—42no—
1285C42—44no—
1286C42—44no—
1287C42—44no—
1288C42—44no—
1289C42—44no—
1290C42—44no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23—24no—
1300C23—22no—
1301C23—24no—
1302C23—22no—
1303C23—24no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—24no—
1308C23—22no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—24no—
1313C23—22no—
1314C23—24no—
1315C23—22no—
1316C23—24no—
1317C23—22no—
1318C23C2×H(5,𝔽2)14yes—
1319C23C2611yescharacteristic
1320Q8—44no—
1321Q8—48no—
1322Q8—82no—
1323Q8—84no—
1324Q8—88no—
1325Q8—162no—
1326D4—28no—
1327D4—44no—
1328D4—48no—
1329D4—82no—
1330D4—84no—
1331D4—88no—
1332D4—88no—
1333D4—88no—
1334D4—88no—
1335D4—84no—
1336D4—84no—
1337D4—88no—
1338D4—88no—
1339D4—164no—
1340D4—162no—
1341D4—164no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
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—24no—
1382C2×C4—24no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—48no—
1412C2×C4—48no—
1413C2×C4—48no—
1414C2×C4—84no—
1415C2×C4—84no—
1416C2×C4—88no—
1417C2×C4—88no—
1418C2×C4—84no—
1419C2×C4—84no—
1420C2×C4—88no—
1421C2×C4—164no—
1422C2×C4—164no—
1423C2×C4—164no—
1424C2×C4C2×H(5,𝔽2)12yes—
1425C2×C4#58512yes—
1426C2×C4#58512yes—
1427C2×C4#58512yes—
1428C2×C4#58512yes—
1429C2×C4#58512yes—
1430C22—24no—
1431C22—24no—
1432C22—24no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—44no—
1440C22—44no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—44no—
1446C22—44no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—44no—
1452C22—42no—
1453C22—44no—
1454C22—42no—
1455C22—42no—
1456C22—44no—
1457C22—42no—
1458C22C22×H(5,𝔽2)11yescharacteristic
1459C22C2×#58511yescharacteristic
1460C22C2×#58511yescharacteristic
1461C22C2×#58511yescharacteristic
1462C22C2×#58511yescharacteristic
1463C22C2×#58511yescharacteristic
1464C22H(7,𝔽2)11yescharacteristic
1465C4—22no—
1466C4—22no—
1467C4—22no—
1468C4—42no—
1469C4—42no—
1470C4—44no—
1471C4—41no—
1472C4—42no—
1473C4—44no—
1474C4—42no—
1475C4—41no—
1476C4—42no—
1477C4—42no—
1478C4—41no—
1479C4—44no—
1480C4—42no—
1481C4—42no—
1482C4—44no—
1483C4—42no—
1484C4—42no—
1485C4—42no—
1486C4—42no—
1487C4—42no—
1488C4—44no—
1489C4#354514yes—
1490C2—44no—
1491C2—82no—
1492C2—82no—
1493C2—84no—
1494C2C2×#354511yescharacteristic
1495C2#6289611yescharacteristic
1496C2#6290811yescharacteristic
1497C2#6296511yescharacteristic
1498C2#6302411yescharacteristic
1499C2#6303111yescharacteristic
1500C2#6303611yescharacteristic
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. #59885C2semidirect
2. #59549C2semidirect
3. #59281C2semidirect
4. #59236C2semidirect
5. #57586C2semidirect
6. #56266C2semidirect
7. #55403C2semidirect
8. #52303C2semidirect
9. #50964C2semidirect
10. #50452C2semidirect
11. #49350C2semidirect
12. #46022C2semidirect
13. #46016C2semidirect
14. #46015C2semidirect
15. #45150C2semidirect
16. #44895C2semidirect
17. #44889C2semidirect
18. #42785C2semidirect
19. #42503C2semidirect
20. #42431C2semidirect
21. #40145C2semidirect
22. #39961C2semidirect
23. #39905C2semidirect
24. #37217C2semidirect
25. #37165C2semidirect
26. #37140C2semidirect
27. #36463C2semidirect
28. #36453C2semidirect
29. #36303C2semidirect

Maximal subgroups

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

subgroupindex
#598852
#595492
#592812
#592362
#575862
#562662
#554032
#523032
#509642
#504522
#493502
#460222
#460162
#460152
#451502
#448952
#448892
#427852
#425032
#424312
#401452
#399612
#399052
#372172
#371652
#371402
#364632
#364532
#363032