Finite Group Databasebeta

← #8656899

Subgroups — #8656899

Order 512.

4607 conjugacy classes of subgroups.

The subgroup lattice has 1484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59483C212yesmaximal, complemented
2#57545C214yesmaximal, complemented
3#56571C212yesmaximal, complemented
4#56200C214yesmaximal, complemented
5#52957C211yesmaximal, characteristic, complemented
6#51119C214yesmaximal, complemented
7#50281C214yesmaximal, complemented
8#48403C214yesmaximal, complemented
9#47173C212yesmaximal, complemented
10#47012C214yesmaximal, complemented
11#46190C211yesmaximal, characteristic, complemented
12#45682C212yesmaximal, complemented
13#45315C211yesmaximal, characteristic, complemented
14#44880C212yesmaximal, complemented
15#43621C212yesmaximal, complemented
16#42916C211yesmaximal, characteristic, complemented
17#42713C212yesmaximal, complemented
18#42201C212yesmaximal, complemented
19#40048C212yesmaximal, complemented
20#39436C212yesmaximal, complemented
21#39193C212yesmaximal, complemented
22#38997C212yesmaximal, complemented
23#38956C211yesmaximal, characteristic, complemented
24#37431C212yesmaximal, complemented
25#36372C212yesmaximal, complemented
26#36067C211yesmaximal, characteristic, complemented
27#35601C212yesmaximal, complemented
28#35136C212yesmaximal, complemented
29#34871C211yesmaximal, characteristic, complemented
30C2×#550C2211yescharacteristic
31C2×#547C2211yescharacteristic
32C2×#540C2212yes—
33C2×#537C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2864C2212yes—
36#2859C2212yes—
37#2858C2211yescharacteristic
38#2851C2212yes—
39#2850C2212yes—
40#2850C2212yes—
41#2839C2214yes—
42#2833C2212yes—
43#2828C2212yes—
44#2827C2214yes—
45#2824C2212yes—
46#2814C2212yes—
47#2813C2214yes—
48#2803C2214yes—
49#2797C2214yes—
50#2797C2214yes—
51#2797C2214yes—
52#2787C2214yes—
53#2784C2212yes—
54#2783C2214yes—
55#2782C2214yes—
56#2779C2214yes—
57#2779C2214yes—
58#2778C2214yes—
59#2775C2214yes—
60#2774C2214yes—
61#2772C2214yes—
62#2772C2214yes—
63#2770C2214yes—
64#2769C2212yes—
65#2767C2214yes—
66#2761C2214yes—
67#2757C2214yes—
68#2757C2214yes—
69#2753C2214yes—
70#2753C2214yes—
71#2753C2214yes—
72#2752C2212yes—
73#2750C2214yes—
74#2750C2214yes—
75#2749C2214yes—
76#2749C2214yes—
77#2745C2214yes—
78#2744C2214yes—
79#2743C2214yes—
80#2740C2214yes—
81#2739C2214yes—
82#2738C2214yes—
83#2724C2212yes—
84#2717C2212yes—
85#2708C2214yes—
86#2703C2214yes—
87#2703C2214yes—
88#2703C2214yes—
89#2701C2214yes—
90#2701C2214yes—
91#2701C2214yes—
92#2695C2214yes—
93#2688C2214yes—
94#2688C2214yes—
95#2688C2214yes—
96#2687C2214yes—
97#2682C2214yes—
98#2682C2214yes—
99#2675C2212yes—
100#2673C2214yes—
101#2671C2214yes—
102#2661C2212yes—
103#2654C2214yes—
104#2652C2214yes—
105#2651C2214yes—
106#2650C2214yes—
107#2648C2214yes—
108#2648C2214yes—
109#2625C2212yes—
110#2625C2211yescharacteristic
111#2623C2212yes—
112#2619C2212yes—
113#2618C2212yes—
114#2616C2211yescharacteristic
115#2615C2212yes—
116#2612C2211yescharacteristic
117#2610C2212yes—
118#2609C2214yes—
119#2609C2211yescharacteristic
120#2602C2214yes—
121#2602C2214yes—
122#2600C2212yes—
123#2593C2212yes—
124#2591C2214yes—
125#2586C2211yescharacteristic
126#2584C2212yes—
127#2583C2212yes—
128#2576C2214yes—
129#2573C2214yes—
130#2572C2211yescharacteristic
131#2570C2212yes—
132#2568C2211yescharacteristic
133#2566C2212yes—
134#2566C2212yes—
135#2554C2212yes—
136#2554C2214yes—
137#2543C2214yes—
138#2541C2211yescharacteristic
139#2538C2212yes—
140#2537C2212yes—
141#2535C2214yes—
142#2532C2212yes—
143#2531C2214yes—
144#2530C2214yes—
145#2526C2212yes—
146#2526C2214yes—
147#2511C2212yes—
148#2510C2214yes—
149#2508C2214yes—
150#2504C2214yes—
151#2504C2212yes—
152#2503C2211yescharacteristic
153#2502C2211yescharacteristic
154#2498C2212yes—
155#2497C2212yes—
156#2495C2212yes—
157#2495C2212yes—
158#2495C2214yes—
159#2494C2212yes—
160#2490C2212yes—
161#2490C2212yes—
162#2490C2214yes—
163#2489C2212yes—
164#2489C2212yes—
165#2488C2214yes—
166#2487C2211yescharacteristic
167#2486C2211yescharacteristic
168#2484C2212yes—
169#2479C2212yes—
170#2476C2214yes—
171#2476C2214yes—
172#2475C2214yes—
173#2473C2214yes—
174#2471C2212yes—
175#2471C2214yes—
176#2471C2214yes—
177#2470C2214yes—
178#2470C2214yes—
179#2464C2214yes—
180#2464C2214yes—
181#2460C2214yes—
182#2460C2214yes—
183#2457C2214yes—
184#2456C2214yes—
185#2453C2212yes—
186#2453C2212yes—
187#2448C2212yes—
188#2447C2212yes—
189#2446C2212yes—
190#2445C2214yes—
191#2445C2212yes—
192#2445C2212yes—
193#2444C2214yes—
194#2444C2214yes—
195#2442C2212yes—
196#2442C2212yes—
197#2442C2214yes—
198#2431C2212yes—
199#2431C2212yes—
200#2431C2212yes—
201#2430C2214yes—
202#2429C2212yes—
203#2428C2212yes—
204#2428C2212yes—
205#2427C2212yes—
206#2427C2212yes—
207#2427C2212yes—
208#2426C2212yes—
209#2425C2214yes—
210#2422C2212yes—
211#2422C2212yes—
212#2421C2212yes—
213#2420C2212yes—
214#2420C2212yes—
215#2419C2214yes—
216#2416C2212yes—
217#2416C2214yes—
218#2414C2214yes—
219#2413C2214yes—
220#2407C2212yes—
221#2406C2214yes—
222#2396C2212yes—
223#2395C2211yescharacteristic
224C2×#400C2212yes—
225#2388C2211yescharacteristic
226#2377C2214yes—
227#2376C2212yes—
228#2370C2212yes—
229#2366C2212yes—
230#2361C2212yes—
231#2359C2214yes—
232#2359C2214yes—
233#2355C2212yes—
234#2349C2212yes—
235D4×C4⋊C4C2212yes—
236#2343C2214yes—
237#2341C2211yescharacteristic
238#2339C2212yes—
239#2339C2211yescharacteristic
240#2335C2214yes—
241#2333C2214yes—
242#2324C2212yes—
243#2324C2212yes—
244#2323C2212yes—
245#2322C2214yes—
246#2318C2214yes—
247#2311C2212yes—
248C4×#126C2212yes—
249C4×#124C2212yes—
250C4×#124C2212yes—
251C4×#124C2211yescharacteristic
252C4×#123C2212yes—
253C4×#121C2212yes—
254#2297C2212yes—
255#2293C2212yes—
256#2293C2212yes—
257#2293C2211yescharacteristic
258C4×#117C2212yes—
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C22×#41C2311yescharacteristic
262C22×#41C2312yes—
263#550—44no—
264#547—44no—
265#540—48no—
266#537—44no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×#127C2312yes—
269C2×#127C2311yescharacteristic
270C2×#127C2312yes—
271C2×#126C2312yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#124C2312yes—
276C2×#124C2312yes—
277C2×#124C2311yescharacteristic
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2312yes—
284C2×#123C2312yes—
285C2×#123C2312yes—
286C2×#123C2314yes—
287C2×#123C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2311yescharacteristic
292C2×C22⋊Q8C2311yescharacteristic
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309#520—44no—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×#117C2312yes—
326C2×#117C2311yescharacteristic
327C2×#117C2314yes—
328C2×#117C2312yes—
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2314yes—
337C22×C42C2312yes—
338#401C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
343#400C2311yescharacteristic
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#399C2314yes—
362#399C2311yescharacteristic
363#399C2312yes—
364#399C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2311yescharacteristic
376#398C2312yes—
377#398C2312yes—
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2311yescharacteristic
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2312yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2312yes—
415#396C2314yes—
416#396C2314yes—
417#395C2314yes—
418#395C2311yescharacteristic
419#395C2312yes—
420#395C2312yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2311yescharacteristic
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2312yes—
435#394C2312yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2312yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#393C2311yescharacteristic
447#393C2314yes—
448#393C2312yes—
449#392C2312yes—
450#392C2314yes—
451#392C2314yes—
452#392C2312yes—
453#392C2314yes—
454#392C2314yes—
455#392C2312yes—
456#392C2314yes—
457#392C2314yes—
458#392C2311yescharacteristic
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#391C2311yescharacteristic
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2314yes—
481#390C2314yes—
482#390C2314yes—
483#390C2314yes—
484#390C2312yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2311yescharacteristic
490#390C2314yes—
491#390C2314yes—
492#390C2314yes—
493#390C2314yes—
494#390C2312yes—
495#390C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#388C2312yes—
519#388C2312yes—
520#388C2312yes—
521#388C2312yes—
522#388C2314yes—
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#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2314yes—
545#388C2314yes—
546#388C2312yes—
547#388C2312yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2312yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2312yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2312yes—
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#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2312yes—
611#386C2312yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2314yes—
618#386C2314yes—
619#386C2312yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2312yes—
625#385C2312yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#384C2312yes—
643#384C2312yes—
644#383C2312yes—
645#383C2314yes—
646#383C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#382C2314yes—
654#382C2311yescharacteristic
655#382C2314yes—
656#381C2312yes—
657#381C2314yes—
658#381C2314yes—
659#381C2314yes—
660#381C2312yes—
661#381C2312yes—
662#381C2314yes—
663#381C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2314yes—
671#380C2312yes—
672#380C2311yescharacteristic
673#380C2311yescharacteristic
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677#380C2312yes—
678#380C2314yes—
679#380C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2311yescharacteristic
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2312yes—
711#376C2312yes—
712C2×#95C2312yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C2×#41—24no—
718C2×#41—24no—
719C2×#41—42no—
720C2×#41—44no—
721C2×#41—44no—
722C2×#41—44no—
723C2×#41—44no—
724C2×#41—44no—
725C2×#41—82no—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2411yescharacteristic
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2411yescharacteristic
737C22×D4C2414yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2412yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2411yescharacteristic
746C22×D4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2414yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2414yes—
758C23×C4C2414yes—
759C23×C4C2412yes—
760C23×C4C2414yes—
761C23×C4C2412yes—
762C4⋊Q8—42no—
763#127—28no—
764#127—42no—
765#127—82no—
766#126—44no—
767#125—44no—
768#125—44no—
769#125—84no—
770#124—44no—
771#124—44no—
772#124—42no—
773#123—48no—
774#123—48no—
775#123—48no—
776#123—48no—
777#123—48no—
778#123—44no—
779#123—44no—
780#123—48no—
781#123—44no—
782#123—44no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—42no—
787C22⋊Q8—42no—
788#121—28no—
789#121—48no—
790#121—48no—
791#121—48no—
792#121—48no—
793#121—48no—
794#121—44no—
795#121—44no—
796#121—44no—
797#121—44no—
798#121—44no—
799#121—48no—
800#121—44no—
801#121—44no—
802#121—84no—
803#121—84no—
804C4×Q8—42no—
805C4×Q8—44no—
806C4×Q8—44no—
807C4×D4—28no—
808C4×D4—24no—
809C4×D4—44no—
810C4×D4—44no—
811C4×D4—44no—
812C4×D4—44no—
813C4×D4—44no—
814C4×D4—42no—
815C4×D4—48no—
816C4×D4—48no—
817C4×D4—84no—
818C4×D4—84no—
819#117—42no—
820#117—44no—
821#117—48no—
822#117—44no—
823#117—44no—
824#117—44no—
825#117—82no—
826C2×C4⋊C4—42no—
827C2×C4⋊C4—42no—
828C2×C4⋊C4—44no—
829C2×C4⋊C4—44no—
830C2×C4⋊C4—84no—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2411yescharacteristic
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C42—44no—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2412yes—
945C2×C42C2411yescharacteristic
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2411yescharacteristic
950C2×C42C2414yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962#95C2412yes—
963#95C2411yescharacteristic
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2411yescharacteristic
981#95C2412yes—
982#95C2414yes—
983#95C2411yescharacteristic
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2411yescharacteristic
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025C24C2511yescharacteristic
1026C24C2512yes—
1027C24C2511yescharacteristic
1028C24C2514yes—
1029C24C2512yes—
1030#41—416no—
1031#41—88no—
1032#41—88no—
1033#41—816no—
1034C2×Q8—22no—
1035C2×Q8—22no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—22no—
1039C2×Q8—41no—
1040C2×Q8—41no—
1041C2×Q8—41no—
1042C2×Q8—42no—
1043C2×D4—24no—
1044C2×D4—28no—
1045C2×D4—28no—
1046C2×D4—24no—
1047C2×D4—28no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—22no—
1054C2×D4—24no—
1055C2×D4—44no—
1056C2×D4—41no—
1057C2×D4—42no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—42no—
1062C2×D4—41no—
1063C2×D4—42no—
1064C2×D4—44no—
1065C2×D4—42no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—41no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—44no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4H(5,𝔽2)14yes—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—28no—
1092C22×C4—24no—
1093C22×C4—22no—
1094C22×C4—22no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—28no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—44no—
1107C22×C4—42no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—42no—
1114C22×C4—42no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—42no—
1119C22×C4—42no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—42no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—42no—
1129C22×C4C2511yescharacteristic
1130C22×C4C2512yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2514yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2514yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2512yes—
1147C22×C4C2514yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2512yes—
1152C22×C4C2511yescharacteristic
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—22no—
1156C4⋊C4—28no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—28no—
1164C4⋊C4—24no—
1165C4⋊C4—41no—
1166C4⋊C4—42no—
1167C4⋊C4—41no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—41no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—41no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C22⋊C4—28no—
1204C22⋊C4—24no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—28no—
1210C22⋊C4—24no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—41no—
1226C22⋊C4—41no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—42no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C42—24no—
1263C42—24no—
1264C42—22no—
1265C42—24no—
1266C42—24no—
1267C42—24no—
1268C42—22no—
1269C42—24no—
1270C42—42no—
1271C42—42no—
1272C42—44no—
1273C42—42no—
1274C42—42no—
1275C42—44no—
1276C42—41no—
1277C42—42no—
1278C42—44no—
1279C42—44no—
1280C42—44no—
1281C42—42no—
1282C42—42no—
1283C23—24no—
1284C23—22no—
1285C23—24no—
1286C23—22no—
1287C23—21no—
1288C23—22no—
1289C23—21no—
1290C23—24no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—24no—
1295C23—21no—
1296C23—21no—
1297C23—24no—
1298C23—24no—
1299C23—24no—
1300C23—22no—
1301C23—22no—
1302C23—24no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—21no—
1309C23—21no—
1310C23—24no—
1311C23C2×H(5,𝔽2)14yes—
1312C23C2611yescharacteristic
1313Q8—44no—
1314Q8—44no—
1315Q8—44no—
1316Q8—82no—
1317D4—28no—
1318D4—48no—
1319D4—48no—
1320D4—82no—
1321D4—84no—
1322D4—84no—
1323D4—88no—
1324D4—88no—
1325D4—84no—
1326D4—88no—
1327D4—88no—
1328D4—82no—
1329D4—84no—
1330D4—164no—
1331D4—162no—
1332D4—164no—
1333D4—164no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—21no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—22no—
1352C2×C4—22no—
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—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—48no—
1397C2×C4—48no—
1398C2×C4—48no—
1399C2×C4—44no—
1400C2×C4—48no—
1401C2×C4—44no—
1402C2×C4—88no—
1403C2×C4—88no—
1404C2×C4—84no—
1405C2×C4—84no—
1406C2×C4—88no—
1407C2×C4—162no—
1408C2×C4—164no—
1409C2×C4—162no—
1410C2×C4—164no—
1411C2×C4C2×H(5,𝔽2)12yes—
1412C2×C4#58514yes—
1413C2×C4#58512yes—
1414C2×C4#58514yes—
1415C22—24no—
1416C22—24no—
1417C22—24no—
1418C22—44no—
1419C22—44no—
1420C22—41no—
1421C22—41no—
1422C22—42no—
1423C22—44no—
1424C22—41no—
1425C22—44no—
1426C22—42no—
1427C22—41no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—44no—
1432C22—42no—
1433C22—44no—
1434C22—44no—
1435C22—41no—
1436C22—42no—
1437C22—41no—
1438C22—44no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—44no—
1444C22C22×H(5,𝔽2)11yescharacteristic
1445C22C2×#58512yes—
1446C22C2×#58512yes—
1447C22C2×#58511yescharacteristic
1448C22H(7,𝔽2)11yescharacteristic
1449C4—22no—
1450C4—24no—
1451C4—41no—
1452C4—41no—
1453C4—42no—
1454C4—42no—
1455C4—42no—
1456C4—42no—
1457C4—44no—
1458C4—42no—
1459C4—41no—
1460C4—42no—
1461C4—44no—
1462C4—42no—
1463C4—42no—
1464C4—42no—
1465C4—42no—
1466C4—42no—
1467C4—44no—
1468C4—42no—
1469C4—42no—
1470C4—44no—
1471C4—44no—
1472C4#353314yes—
1473C2—44no—
1474C2—81no—
1475C2—81no—
1476C2—82no—
1477C2—84no—
1478C2C2×#353311yescharacteristic
1479C2#6284012yes—
1480C2#6291811yescharacteristic
1481C2#6297012yes—
1482C2#6302411yescharacteristic
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. #59483C2semidirect
2. #57545C2semidirect
3. #56571C2semidirect
4. #56200C2semidirect
5. #52957C2semidirect
6. #51119C2semidirect
7. #50281C2semidirect
8. #48403C2semidirect
9. #47173C2semidirect
10. #47012C2semidirect
11. #46190C2semidirect
12. #45682C2semidirect
13. #45315C2semidirect
14. #44880C2semidirect
15. #43621C2semidirect
16. #42916C2semidirect
17. #42713C2semidirect
18. #42201C2semidirect
19. #40048C2semidirect
20. #39436C2semidirect
21. #39193C2semidirect
22. #38997C2semidirect
23. #38956C2semidirect
24. #37431C2semidirect
25. #36372C2semidirect
26. #36067C2semidirect
27. #35601C2semidirect
28. #35136C2semidirect
29. #34871C2semidirect

Maximal subgroups

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

subgroupindex
#594832
#575452
#565712
#562002
#529572
#511192
#502812
#484032
#471732
#470122
#461902
#456822
#453152
#448802
#436212
#429162
#427132
#422012
#400482
#394362
#391932
#389972
#389562
#374312
#363722
#360672
#356012
#351362
#348712