Finite Group Databasebeta

← #8115575

Subgroups — #8115575

Order 512.

4587 conjugacy classes of subgroups.

The subgroup lattice has 1533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58309C214yesmaximal, complemented
2#58217C214yesmaximal, complemented
3#58135C214yesmaximal, complemented
4#57479C214yesmaximal, complemented
5#57208C214yesmaximal, complemented
6#57186C214yesmaximal, complemented
7#54334C214yesmaximal, complemented
8#54006C214yesmaximal, complemented
9#52979C212yesmaximal, complemented
10#52973C212yesmaximal, complemented
11#45139C211yesmaximal, characteristic, complemented
12#44963C211yesmaximal, characteristic, complemented
13#44947C211yesmaximal, characteristic, complemented
14#44931C211yesmaximal, characteristic, complemented
15#42875C211yesmaximal, characteristic, complemented
16#42651C211yesmaximal, characteristic, complemented
17#42529C212yesmaximal, complemented
18#42498C212yesmaximal, complemented
19#42429C211yesmaximal, characteristic, complemented
20#42425C211yesmaximal, characteristic, complemented
21#39174C211yesmaximal, characteristic, complemented
22#39169C211yesmaximal, characteristic, complemented
23#39142C212yesmaximal, complemented
24#38971C211yesmaximal, characteristic, complemented
25#38969C211yesmaximal, characteristic, complemented
26#38942C212yesmaximal, complemented
27#37368C212yesmaximal, complemented
28#37336C212yesmaximal, complemented
29#35276C211yesmaximal, characteristic, complemented
30#35268C211yesmaximal, characteristic, complemented
31#34644C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#540C2211yescharacteristic
38#2864C2211yescharacteristic
39#2861C2211yescharacteristic
40#2860C2212yes—
41#2858C2211yescharacteristic
42#2858C2211yescharacteristic
43#2856C2211yescharacteristic
44#2850C2211yescharacteristic
45#2841C2214yes—
46#2830C2214yes—
47#2829C2214yes—
48#2829C2214yes—
49#2828C2214yes—
50#2827C2214yes—
51#2826C2214yes—
52#2824C2214yes—
53#2821C2212yes—
54#2816C2212yes—
55#2813C2214yes—
56#2813C2212yes—
57#2813C2214yes—
58#2813C2212yes—
59#2801C2214yes—
60#2795C2214yes—
61#2790C2214yes—
62#2790C2214yes—
63#2788C2214yes—
64#2782C2214yes—
65#2781C2214yes—
66#2779C2214yes—
67#2778C2214yes—
68#2771C2214yes—
69#2756C2214yes—
70#2756C2214yes—
71#2756C2214yes—
72#2751C2214yes—
73#2750C2214yes—
74#2748C2214yes—
75#2746C2214yes—
76#2745C2214yes—
77#2741C2214yes—
78#2730C2214yes—
79#2729C2214yes—
80#2720C2214yes—
81#2720C2214yes—
82#2718C2214yes—
83#2712C2214yes—
84#2711C2214yes—
85#2711C2214yes—
86#2711C2214yes—
87#2710C2214yes—
88#2708C2214yes—
89#2708C2214yes—
90#2705C2214yes—
91#2703C2214yes—
92#2702C2214yes—
93#2701C2214yes—
94#2701C2214yes—
95#2699C2214yes—
96#2699C2214yes—
97#2699C2214yes—
98#2694C2214yes—
99#2694C2214yes—
100#2694C2214yes—
101#2692C2214yes—
102#2691C2214yes—
103#2691C2214yes—
104#2690C2214yes—
105#2688C2214yes—
106#2687C2214yes—
107#2686C2214yes—
108#2686C2214yes—
109#2682C2214yes—
110#2681C2214yes—
111#2680C2214yes—
112#2676C2214yes—
113#2676C2214yes—
114#2676C2214yes—
115#2676C2214yes—
116#2675C2214yes—
117#2672C2214yes—
118#2672C2214yes—
119#2671C2214yes—
120#2671C2214yes—
121#2671C2214yes—
122#2671C2214yes—
123#2667C2212yes—
124#2667C2212yes—
125#2666C2212yes—
126#2666C2212yes—
127#2666C2212yes—
128#2666C2212yes—
129#2665C2212yes—
130#2665C2212yes—
131#2663C2212yes—
132#2661C2214yes—
133#2660C2211yescharacteristic
134#2657C2211yescharacteristic
135#2656C2212yes—
136#2646C2214yes—
137#2645C2212yes—
138#2644C2212yes—
139#2641C2212yes—
140#2641C2212yes—
141#2640C2212yes—
142#2639C2212yes—
143#2635C2214yes—
144#2632C2212yes—
145#2629C2214yes—
146#2628C2211yescharacteristic
147#2624C2212yes—
148#2623C2212yes—
149#2620C2211yescharacteristic
150#2619C2211yescharacteristic
151#2619C2211yescharacteristic
152#2616C2212yes—
153#2615C2212yes—
154#2610C2214yes—
155#2604C2212yes—
156#2592C2212yes—
157#2581C2211yescharacteristic
158#2580C2211yescharacteristic
159#2580C2211yescharacteristic
160#2580C2211yescharacteristic
161#2580C2212yes—
162#2578C2214yes—
163#2570C2212yes—
164#2566C2212yes—
165#2566C2212yes—
166#2564C2214yes—
167#2563C2211yescharacteristic
168#2555C2214yes—
169#2554C2214yes—
170#2552C2212yes—
171#2552C2212yes—
172#2550C2212yes—
173#2548C2212yes—
174#2548C2211yescharacteristic
175#2548C2212yes—
176#2544C2212yes—
177#2544C2212yes—
178#2542C2211yescharacteristic
179#2541C2212yes—
180#2541C2211yescharacteristic
181#2541C2212yes—
182#2541C2212yes—
183#2538C2212yes—
184#2537C2214yes—
185#2530C2214yes—
186#2521C2214yes—
187#2516C2214yes—
188#2510C2214yes—
189#2509C2212yes—
190#2506C2212yes—
191#2501C2212yes—
192#2500C2214yes—
193#2493C2214yes—
194#2490C2212yes—
195#2490C2212yes—
196#2476C2214yes—
197#2473C2214yes—
198#2467C2214yes—
199#2464C2214yes—
200#2464C2214yes—
201#2461C2214yes—
202#2460C2214yes—
203#2459C2214yes—
204#2457C2214yes—
205#2454C2212yes—
206#2454C2212yes—
207#2453C2212yes—
208#2452C2212yes—
209#2450C2214yes—
210#2448C2212yes—
211#2447C2212yes—
212#2445C2212yes—
213#2445C2212yes—
214#2445C2212yes—
215#2445C2212yes—
216#2444C2214yes—
217#2438C2214yes—
218#2432C2214yes—
219#2430C2214yes—
220#2430C2212yes—
221#2430C2214yes—
222#2430C2212yes—
223#2428C2212yes—
224#2428C2212yes—
225#2428C2212yes—
226#2427C2212yes—
227#2426C2214yes—
228#2423C2214yes—
229#2422C2212yes—
230#2421C2212yes—
231#2420C2214yes—
232#2419C2214yes—
233#2416C2214yes—
234#2414C2214yes—
235#2407C2214yes—
236#2402C2212yes—
237#2399C2211yescharacteristic
238#2399C2211yescharacteristic
239#2396C2211yescharacteristic
240#2396C2211yescharacteristic
241#2396C2212yes—
242#2367C2212yes—
243#2366C2212yes—
244#2357C2211yescharacteristic
245#2356C2211yescharacteristic
246#2354C2212yes—
247#2349C2212yes—
248#2349C2211yescharacteristic
249#2349C2211yescharacteristic
250#2331C2211yescharacteristic
251#2328C2212yes—
252#2328C2211yescharacteristic
253#2328C2211yescharacteristic
254#2326C2212yes—
255#2326C2211yescharacteristic
256#2319C2212yes—
257#2319C2212yes—
258#2319C2212yes—
259C4×#127C2211yescharacteristic
260C4×#124C2211yescharacteristic
261C4×#121C2212yes—
262#2295C2211yescharacteristic
263#2295C2211yescharacteristic
264#2295C2212yes—
265#2283C2212yes—
266C4×#117C2211yescharacteristic
267C22×#41C2312yes—
268C22×#41C2312yes—
269#557—44no—
270#554—44no—
271#550—44no—
272#550—44no—
273#542—44no—
274#540—44no—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×#127C2311yescharacteristic
279C2×#127C2311yescharacteristic
280C2×#127C2311yescharacteristic
281C2×#127C2312yes—
282C2×#127C2311yescharacteristic
283C2×#127C2312yes—
284C2×#127C2312yes—
285C2×#126C2312yes—
286C2×#126C2314yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2311yescharacteristic
290C2×#125C2314yes—
291C2×#125C2314yes—
292C2×#124C2311yescharacteristic
293C2×#124C2312yes—
294C2×#124C2311yescharacteristic
295C2×#124C2311yescharacteristic
296C2×#124C2312yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#124C2314yes—
300C2×#123C2312yes—
301C2×#123C2312yes—
302C2×#123C2312yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2311yescharacteristic
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×#121C2312yes—
316C2×#121C2311yescharacteristic
317C2×#121C2311yescharacteristic
318C2×#121C2311yescharacteristic
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2312yes—
345C2×C4×D4C2311yescharacteristic
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2314yes—
354C2×#117C2311yescharacteristic
355C2×#117C2311yescharacteristic
356C2×#117C2314yes—
357C22×C4⋊C4C2312yes—
358C22×C42C2311yescharacteristic
359#401C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2312yes—
365#400C2314yes—
366#400C2312yes—
367#400C2314yes—
368#400C2312yes—
369#400C2314yes—
370#400C2311yescharacteristic
371#400C2311yescharacteristic
372#400C2312yes—
373#400C2312yes—
374#400C2314yes—
375#400C2314yes—
376#400C2312yes—
377#400C2312yes—
378#399C2312yes—
379#399C2312yes—
380#399C2314yes—
381#399C2314yes—
382#399C2314yes—
383#399C2314yes—
384#399C2312yes—
385#399C2312yes—
386#399C2312yes—
387#399C2314yes—
388#399C2311yescharacteristic
389#399C2312yes—
390#399C2311yescharacteristic
391#399C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2312yes—
396#398C2314yes—
397#398C2312yes—
398#398C2314yes—
399#398C2312yes—
400#398C2314yes—
401#398C2314yes—
402#398C2312yes—
403#398C2314yes—
404#398C2314yes—
405#398C2312yes—
406#398C2312yes—
407#398C2312yes—
408#398C2312yes—
409#398C2312yes—
410#398C2312yes—
411#398C2312yes—
412#398C2312yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2312yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2312yes—
439#396C2312yes—
440#396C2312yes—
441#395C2312yes—
442#395C2311yescharacteristic
443#395C2312yes—
444#395C2312yes—
445#395C2312yes—
446#395C2314yes—
447#395C2314yes—
448#395C2312yes—
449#395C2311yescharacteristic
450#395C2312yes—
451#395C2312yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
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#394C2312yes—
475#394C2312yes—
476#394C2312yes—
477#394C2314yes—
478#394C2314yes—
479#394C2312yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#393C2311yescharacteristic
492#393C2312yes—
493#393C2312yes—
494#393C2312yes—
495#393C2314yes—
496#393C2312yes—
497#393C2312yes—
498#393C2314yes—
499#393C2312yes—
500#393C2314yes—
501#393C2311yescharacteristic
502#393C2312yes—
503#392C2314yes—
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#392C2314yes—
508#392C2314yes—
509#392C2312yes—
510#392C2312yes—
511#392C2312yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2312yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#391C2312yes—
520#391C2311yescharacteristic
521#391C2311yescharacteristic
522#391C2314yes—
523#391C2312yes—
524#391C2314yes—
525#391C2312yes—
526#391C2312yes—
527#391C2312yes—
528#391C2312yes—
529#390C2311yescharacteristic
530#390C2311yescharacteristic
531#390C2314yes—
532#390C2312yes—
533#390C2312yes—
534#390C2312yes—
535#390C2312yes—
536#390C2314yes—
537#390C2314yes—
538#390C2314yes—
539#390C2314yes—
540#390C2311yescharacteristic
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2311yescharacteristic
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2311yescharacteristic
549#390C2312yes—
550#390C2311yescharacteristic
551#390C2314yes—
552#390C2314yes—
553#390C2314yes—
554#390C2314yes—
555#390C2312yes—
556#390C2314yes—
557#390C2314yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2312yes—
575#389C2314yes—
576#389C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
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#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
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#384C2311yescharacteristic
672#384C2312yes—
673#384C2311yescharacteristic
674#384C2314yes—
675#384C2314yes—
676#383C2312yes—
677#383C2312yes—
678#383C2312yes—
679#382C2312yes—
680#382C2311yescharacteristic
681#382C2311yescharacteristic
682#382C2311yescharacteristic
683#382C2311yescharacteristic
684#382C2312yes—
685#382C2312yes—
686#381C2312yes—
687#381C2314yes—
688#381C2314yes—
689#381C2314yes—
690#381C2314yes—
691#381C2312yes—
692#381C2312yes—
693#380C2314yes—
694#380C2314yes—
695#380C2314yes—
696#380C2314yes—
697#380C2314yes—
698#380C2314yes—
699#380C2314yes—
700#380C2312yes—
701#380C2312yes—
702#380C2314yes—
703#380C2314yes—
704#380C2312yes—
705#380C2312yes—
706#380C2312yes—
707#380C2314yes—
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2312yes—
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×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2314yes—
730#376C2311yescharacteristic
731#376C2312yes—
732#376C2312yes—
733#376C2311yescharacteristic
734#376C2312yes—
735C2×#95C2312yes—
736C2×#95C2314yes—
737C2×#95C2312yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C2×#41—44no—
741C2×#41—44no—
742C2×#41—84no—
743C2×#41—84no—
744C22×Q8C2411yescharacteristic
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2412yes—
750C22×D4C2411yescharacteristic
751C22×D4C2411yescharacteristic
752C22×D4C2411yescharacteristic
753C22×D4C2412yes—
754C22×D4C2414yes—
755C22×D4C2412yes—
756C22×D4C2412yes—
757C22×D4C2414yes—
758C22×D4C2414yes—
759C22×D4C2412yes—
760C22×D4C2412yes—
761C22×D4C2412yes—
762C22×D4C2414yes—
763C22×D4C2414yes—
764C22×D4C2414yes—
765C22×D4C2412yes—
766C22×D4C2412yes—
767C22×D4C2414yes—
768C22×D4C2414yes—
769C22×D4C2414yes—
770C23×C4C2411yescharacteristic
771C23×C4C2412yes—
772C23×C4C2414yes—
773C23×C4C2412yes—
774C23×C4C2412yes—
775C23×C4C2412yes—
776C23×C4C2414yes—
777C23×C4C2414yes—
778C23×C4C2414yes—
779C23×C4C2414yes—
780C23×C4C2414yes—
781C4⋊Q8—24no—
782C4⋊Q8—42no—
783C4⋊Q8—44no—
784#127—24no—
785#127—24no—
786#127—42no—
787#127—44no—
788#127—42no—
789#127—44no—
790#127—44no—
791#126—44no—
792#126—84no—
793#125—42no—
794#125—44no—
795#125—44no—
796#125—48no—
797#125—84no—
798#124—24no—
799#124—44no—
800#124—42no—
801#124—44no—
802#124—42no—
803#124—84no—
804#124—84no—
805#124—84no—
806#123—44no—
807#123—44no—
808#123—44no—
809#123—84no—
810#123—84no—
811#123—84no—
812#123—84no—
813#123—84no—
814C22⋊Q8—48no—
815C22⋊Q8—44no—
816C22⋊Q8—42no—
817C22⋊Q8—44no—
818C22⋊Q8—84no—
819C22⋊Q8—84no—
820C22⋊Q8—84no—
821#121—44no—
822#121—44no—
823#121—48no—
824#121—48no—
825#121—44no—
826#121—42no—
827#121—42no—
828#121—42no—
829#121—44no—
830#121—44no—
831#121—84no—
832#121—84no—
833#121—84no—
834#121—84no—
835#121—84no—
836#121—84no—
837#121—84no—
838#121—84no—
839#121—84no—
840#121—84no—
841#121—84no—
842C4×Q8—24no—
843C4×Q8—24no—
844C4×Q8—24no—
845C4×Q8—44no—
846C4×Q8—44no—
847C4×Q8—44no—
848C4×D4—24no—
849C4×D4—24no—
850C4×D4—24no—
851C4×D4—28no—
852C4×D4—44no—
853C4×D4—44no—
854C4×D4—44no—
855C4×D4—44no—
856C4×D4—44no—
857C4×D4—84no—
858C4×D4—84no—
859C4×D4—84no—
860#117—24no—
861#117—42no—
862#117—84no—
863C2×C4⋊C4—44no—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C22⋊C4C2411yescharacteristic
923C2×C22⋊C4C2411yescharacteristic
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2414yes—
980C2×C42—24no—
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990C2×C42C2412yes—
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2412yes—
994C2×C42C2414yes—
995C2×C42C2414yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001#95C2411yescharacteristic
1002#95C2412yes—
1003#95C2411yescharacteristic
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2411yescharacteristic
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2411yescharacteristic
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063C24C2511yescharacteristic
1064C24C2512yes—
1065C24C2512yes—
1066C24C2512yes—
1067C24C2514yes—
1068#41—816no—
1069#41—816no—
1070C2×Q8—22no—
1071C2×Q8—22no—
1072C2×Q8—22no—
1073C2×Q8—24no—
1074C2×Q8—22no—
1075C2×Q8—22no—
1076C2×Q8—42no—
1077C2×Q8—42no—
1078C2×Q8—42no—
1079C2×Q8—42no—
1080C2×Q8—44no—
1081C2×Q8—42no—
1082C2×Q8—42no—
1083C2×Q8—44no—
1084C2×D4—22no—
1085C2×D4—22no—
1086C2×D4—22no—
1087C2×D4—24no—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—22no—
1092C2×D4—22no—
1093C2×D4—22no—
1094C2×D4—28no—
1095C2×D4—22no—
1096C2×D4—22no—
1097C2×D4—24no—
1098C2×D4—22no—
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—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—42no—
1116C2×D4—42no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—42no—
1120C2×D4—42no—
1121C2×D4—42no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C22×C4—22no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—24no—
1141C22×C4—24no—
1142C22×C4—24no—
1143C22×C4—24no—
1144C22×C4—28no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—42no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—42no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2511yescharacteristic
1172C22×C4C2514yes—
1173C22×C4C2512yes—
1174C22×C4C2514yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2512yes—
1183C22×C4C2512yes—
1184C22×C4C2512yes—
1185C22×C4C2512yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2514yes—
1188C22×C4C2512yes—
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2512yes—
1192C22×C4C2511yescharacteristic
1193C4⋊C4—22no—
1194C4⋊C4—24no—
1195C4⋊C4—22no—
1196C4⋊C4—22no—
1197C4⋊C4—22no—
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—24no—
1201C4⋊C4—22no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—22no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—42no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—42no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—42no—
1251C22⋊C4—22no—
1252C22⋊C4—22no—
1253C22⋊C4—24no—
1254C22⋊C4—24no—
1255C22⋊C4—24no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—42no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—42no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—42no—
1298C22⋊C4—44no—
1299C22⋊C4—42no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—44no—
1308C22⋊C4—44no—
1309C42—22no—
1310C42—24no—
1311C42—24no—
1312C42—24no—
1313C42—24no—
1314C42—22no—
1315C42—22no—
1316C42—22no—
1317C42—24no—
1318C42—24no—
1319C42—44no—
1320C42—44no—
1321C42—44no—
1322C42—42no—
1323C42—44no—
1324C42—42no—
1325C42—42no—
1326C42—42no—
1327C42H(5,𝔽2)14yes—
1328C422−1+414yes—
1329C23—21no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—24no—
1334C23—22no—
1335C23—24no—
1336C23—21no—
1337C23—22no—
1338C23—22no—
1339C23—22no—
1340C23—24no—
1341C23—21no—
1342C23—22no—
1343C23—22no—
1344C23—24no—
1345C23—24no—
1346C23—22no—
1347C23—24no—
1348C23—24no—
1349C23—24no—
1350C23—24no—
1351C23—24no—
1352C23—24no—
1353C23—24no—
1354C23—24no—
1355C23—22no—
1356C23C2611yescharacteristic
1357Q8—44no—
1358Q8—44no—
1359Q8—44no—
1360Q8—84no—
1361Q8—84no—
1362Q8—162no—
1363D4—44no—
1364D4—44no—
1365D4—44no—
1366D4—48no—
1367D4—88no—
1368D4—84no—
1369D4—84no—
1370D4—88no—
1371D4—88no—
1372D4—88no—
1373D4—88no—
1374D4—162no—
1375D4—162no—
1376D4—164no—
1377D4—162no—
1378D4—164no—
1379D4—162no—
1380D4—162no—
1381D4—164no—
1382D4—164no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—21no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—24no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—24no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—24no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—44no—
1448C2×C4—84no—
1449C2×C4—84no—
1450C2×C4—88no—
1451C2×C4—84no—
1452C2×C4—84no—
1453C2×C4—88no—
1454C2×C4—88no—
1455C2×C4—164no—
1456C2×C4—164no—
1457C2×C4—164no—
1458C2×C4C2×H(5,𝔽2)12yes—
1459C2×C4C2×H(5,𝔽2)12yes—
1460C2×C4C2×H(5,𝔽2)12yes—
1461C2×C4C2×2−1+414yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4#58512yes—
1464C22—41no—
1465C22—42no—
1466C22—42no—
1467C22—42no—
1468C22—44no—
1469C22—42no—
1470C22—42no—
1471C22—44no—
1472C22—44no—
1473C22—42no—
1474C22—42no—
1475C22—41no—
1476C22—42no—
1477C22—41no—
1478C22—42no—
1479C22—44no—
1480C22—42no—
1481C22—44no—
1482C22—44no—
1483C22—44no—
1484C22—44no—
1485C22—44no—
1486C22—44no—
1487C22—42no—
1488C22—44no—
1489C22—44no—
1490C22—44no—
1491C22C22×H(5,𝔽2)11yescharacteristic
1492C22C22×2−1+411yescharacteristic
1493C22C2×#58511yescharacteristic
1494C22H(7,𝔽2)12yes—
1495C22H(7,𝔽2)12yes—
1496C4—22no—
1497C4—22no—
1498C4—24no—
1499C4—41no—
1500C4—42no—
1501C4—42no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4—42no—
1506C4—42no—
1507C4—44no—
1508C4—42no—
1509C4—41no—
1510C4—41no—
1511C4—42no—
1512C4—42no—
1513C4—44no—
1514C4—42no—
1515C4—44no—
1516C4—42no—
1517C4—42no—
1518C4—42no—
1519C4—42no—
1520C4—42no—
1521C4#354714yes—
1522C2—81no—
1523C2—84no—
1524C2—82no—
1525C2—82no—
1526C2—82no—
1527C2C2×#354711yescharacteristic
1528C2#6287611yescharacteristic
1529C2#6287611yescharacteristic
1530C2#6288112yes—
1531C2#6288312yes—
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. #58309C2semidirect
2. #58217C2semidirect
3. #58135C2semidirect
4. #57479C2semidirect
5. #57208C2semidirect
6. #57186C2semidirect
7. #54334C2semidirect
8. #54006C2semidirect
9. #52979C2semidirect
10. #52973C2semidirect
11. #45139C2semidirect
12. #44963C2semidirect
13. #44947C2semidirect
14. #44931C2semidirect
15. #42875C2semidirect
16. #42651C2semidirect
17. #42529C2semidirect
18. #42498C2semidirect
19. #42429C2semidirect
20. #42425C2semidirect
21. #39174C2semidirect
22. #39169C2semidirect
23. #39142C2semidirect
24. #38971C2semidirect
25. #38969C2semidirect
26. #38942C2semidirect
27. #37368C2semidirect
28. #37336C2semidirect
29. #35276C2semidirect
30. #35268C2semidirect
31. #34644C2semidirect

Maximal subgroups

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

subgroupindex
#583092
#582172
#581352
#574792
#572082
#571862
#543342
#540062
#529792
#529732
#451392
#449632
#449472
#449312
#428752
#426512
#425292
#424982
#424292
#424252
#391742
#391692
#391422
#389712
#389692
#389422
#373682
#373362
#352762
#352682
#346442