Finite Group Databasebeta

← #8094937

Subgroups — #8094937

Order 512.

4757 conjugacy classes of subgroups.

The subgroup lattice has 1552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53127C212yesmaximal, complemented
2#53100C211yesmaximal, characteristic, complemented
3#53098C212yesmaximal, complemented
4#53080C211yesmaximal, characteristic, complemented
5#52989C211yesmaximal, characteristic, complemented
6#52987C211yesmaximal, characteristic, complemented
7#52762C212yesmaximal, complemented
8#52760C212yesmaximal, complemented
9#52757C214yesmaximal, complemented
10#52702C212yesmaximal, complemented
11#52693C212yesmaximal, complemented
12#52628C214yesmaximal, complemented
13#46303C212yesmaximal, complemented
14#46293C212yesmaximal, complemented
15#46274C212yesmaximal, complemented
16#46236C212yesmaximal, complemented
17#45930C214yesmaximal, complemented
18#45760C214yesmaximal, complemented
19#45716C212yesmaximal, complemented
20#45631C212yesmaximal, complemented
21#45616C212yesmaximal, complemented
22#45482C212yesmaximal, complemented
23#35600C212yesmaximal, complemented
24#35526C212yesmaximal, complemented
25#35520C212yesmaximal, complemented
26#35270C212yesmaximal, complemented
27#35228C212yesmaximal, complemented
28#35164C212yesmaximal, complemented
29#34979C211yesmaximal, characteristic, complemented
30#34937C211yesmaximal, characteristic, complemented
31#34876C211yesmaximal, characteristic, complemented
32C2×#562C2214yes—
33C2×#533C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#532C2212yes—
36C2×#529C2211yescharacteristic
37C2×#520C2212yes—
38C2×C4×#41C2211yescharacteristic
39#2866C2214yes—
40#2861C2214yes—
41#2857C2212yes—
42#2855C2212yes—
43#2855C2214yes—
44#2854C2212yes—
45#2853C2214yes—
46#2850C2212yes—
47#2839C2214yes—
48#2837C2214yes—
49#2836C2214yes—
50#2836C2214yes—
51#2834C2214yes—
52#2833C2212yes—
53#2833C2212yes—
54#2833C2212yes—
55#2832C2214yes—
56#2832C2212yes—
57#2830C2212yes—
58#2828C2214yes—
59#2828C2212yes—
60#2827C2214yes—
61#2827C2214yes—
62#2827C2214yes—
63#2826C2214yes—
64#2825C2214yes—
65#2824C2214yes—
66#2822C2212yes—
67#2819C2212yes—
68#2816C2214yes—
69#2814C2214yes—
70#2813C2214yes—
71#2806C2214yes—
72#2804C2212yes—
73#2803C2214yes—
74#2799C2212yes—
75#2795C2214yes—
76#2790C2214yes—
77#2789C2212yes—
78#2788C2214yes—
79#2782C2212yes—
80#2780C2214yes—
81#2778C2214yes—
82#2778C2214yes—
83#2752C2214yes—
84#2751C2214yes—
85#2751C2214yes—
86#2747C2214yes—
87#2746C2214yes—
88#2746C2214yes—
89#2746C2214yes—
90#2728C2212yes—
91#2728C2212yes—
92#2728C2212yes—
93#2724C2212yes—
94#2713C2214yes—
95#2712C2214yes—
96#2709C2214yes—
97#2708C2214yes—
98#2704C2214yes—
99#2703C2214yes—
100#2703C2214yes—
101#2701C2214yes—
102#2701C2214yes—
103#2700C2214yes—
104#2700C2214yes—
105#2699C2214yes—
106#2688C2214yes—
107#2687C2214yes—
108#2687C2214yes—
109#2687C2214yes—
110#2686C2214yes—
111#2677C2214yes—
112#2674C2214yes—
113#2673C2214yes—
114#2672C2214yes—
115#2655C2214yes—
116#2653C2214yes—
117#2650C2214yes—
118#2648C2214yes—
119#2647C2212yes—
120#2645C2212yes—
121#2644C2212yes—
122#2640C2212yes—
123#2611C2211yescharacteristic
124#2611C2211yescharacteristic
125#2611C2212yes—
126#2611C2212yes—
127#2610C2211yescharacteristic
128#2610C2211yescharacteristic
129#2609C2214yes—
130#2604C2212yes—
131#2603C2212yes—
132#2600C2214yes—
133#2599C2214yes—
134#2598C2214yes—
135#2582C2212yes—
136#2580C2212yes—
137#2579C2214yes—
138#2568C2211yescharacteristic
139#2564C2211yescharacteristic
140#2564C2211yescharacteristic
141#2548C2211yescharacteristic
142#2547C2211yescharacteristic
143#2547C2211yescharacteristic
144#2546C2211yescharacteristic
145#2546C2211yescharacteristic
146#2545C2212yes—
147#2544C2212yes—
148#2543C2212yes—
149#2543C2211yescharacteristic
150#2543C2211yescharacteristic
151#2543C2212yes—
152#2542C2211yescharacteristic
153#2541C2211yescharacteristic
154#2537C2212yes—
155#2536C2212yes—
156#2536C2214yes—
157#2532C2214yes—
158#2531C2214yes—
159#2530C2214yes—
160#2529C2214yes—
161#2527C2214yes—
162#2527C2214yes—
163#2525C2214yes—
164#2520C2214yes—
165#2513C2212yes—
166#2511C2212yes—
167#2510C2214yes—
168#2509C2212yes—
169#2506C2212yes—
170#2503C2212yes—
171#2500C2212yes—
172#2499C2212yes—
173#2498C2212yes—
174#2494C2212yes—
175#2494C2212yes—
176#2493C2214yes—
177#2492C2212yes—
178#2491C2212yes—
179#2488C2214yes—
180#2488C2214yes—
181#2487C2212yes—
182#2486C2212yes—
183#2486C2212yes—
184#2485C2212yes—
185#2479C2214yes—
186#2477C2214yes—
187#2476C2214yes—
188#2474C2214yes—
189#2473C2214yes—
190#2473C2214yes—
191#2468C2214yes—
192#2464C2214yes—
193#2464C2214yes—
194#2463C2214yes—
195#2461C2214yes—
196#2460C2214yes—
197#2460C2214yes—
198#2459C2214yes—
199#2459C2214yes—
200#2455C2214yes—
201#2452C2212yes—
202#2451C2212yes—
203#2450C2214yes—
204#2449C2214yes—
205#2446C2212yes—
206#2445C2212yes—
207#2443C2214yes—
208#2440C2212yes—
209#2440C2212yes—
210#2440C2212yes—
211#2439C2212yes—
212#2432C2212yes—
213#2432C2212yes—
214#2431C2212yes—
215#2430C2212yes—
216#2427C2212yes—
217#2426C2212yes—
218#2423C2212yes—
219#2422C2212yes—
220#2419C2214yes—
221#2417C2212yes—
222#2417C2212yes—
223#2416C2212yes—
224#2416C2212yes—
225#2416C2212yes—
226#2415C2212yes—
227#2415C2212yes—
228#2414C2212yes—
229#2407C2212yes—
230#2407C2214yes—
231#2407C2212yes—
232#2407C2212yes—
233#2407C2212yes—
234#2406C2214yes—
235#2399C2211yescharacteristic
236#2398C2211yescharacteristic
237#2398C2211yescharacteristic
238#2397C2211yescharacteristic
239#2395C2212yes—
240#2395C2212yes—
241#2392C2212yes—
242#2392C2212yes—
243#2378C2214yes—
244#2377C2214yes—
245#2376C2214yes—
246#2331C2212yes—
247#2326C2212yes—
248#2324C2212yes—
249#2323C2212yes—
250#2320C2212yes—
251#2319C2212yes—
252#2314C2212yes—
253C4×C4⋊Q8C2212yes—
254C4×#124C2212yes—
255C4×C22⋊Q8C2212yes—
256C4×C22⋊Q8C2212yes—
257C4×#121C2212yes—
258C4×#121C2212yes—
259C4×#121C2212yes—
260C4×#121C2212yes—
261#2297C2212yes—
262#2290C2212yes—
263#2290C2212yes—
264C4×#117C2211yescharacteristic
265C2×C4×C4⋊C4C2211yescharacteristic
266C2×#376C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2312yes—
269C22×#41C2312yes—
270#562—416no—
271#533—44no—
272#532—44no—
273#532—48no—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×#127C2312yes—
281C2×#127C2311yescharacteristic
282#529—44no—
283C2×#126C2312yes—
284C2×#125C2314yes—
285C2×#125C2311yescharacteristic
286C2×#125C2312yes—
287C2×#124C2312yes—
288C2×#124C2314yes—
289C2×#124C2312yes—
290C2×#124C2311yescharacteristic
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2312yes—
299C2×#123C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2311yescharacteristic
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2314yes—
319C2×#121C2311yescharacteristic
320C2×#121C2312yes—
321C2×#121C2314yes—
322C2×#121C2312yes—
323#520—48no—
324C4×#41—44no—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2314yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2311yescharacteristic
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2312yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2314yes—
351C2×#117C2311yescharacteristic
352C2×#117C2311yescharacteristic
353C2×#117C2311yescharacteristic
354C2×#117C2312yes—
355C22×C4⋊C4C2314yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C42C2311yescharacteristic
359C22×C42C2311yescharacteristic
360C22×C42C2311yescharacteristic
361C22×C42C2312yes—
362C22×C42C2312yes—
363#401C2314yes—
364#401C2314yes—
365#401C2314yes—
366#400C2311yescharacteristic
367#400C2311yescharacteristic
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2312yes—
384#400C2314yes—
385#400C2314yes—
386#399C2314yes—
387#399C2314yes—
388#399C2311yescharacteristic
389#399C2311yescharacteristic
390#399C2312yes—
391#399C2314yes—
392#399C2312yes—
393#399C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2311yescharacteristic
397#398C2314yes—
398#398C2312yes—
399#398C2314yes—
400#398C2314yes—
401#398C2312yes—
402#398C2312yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2312yes—
407#398C2311yescharacteristic
408#398C2314yes—
409#398C2314yes—
410#398C2312yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2311yescharacteristic
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2312yes—
434#397C2314yes—
435#397C2312yes—
436#397C2312yes—
437#397C2311yescharacteristic
438#397C2312yes—
439#397C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#395C2311yescharacteristic
450#395C2311yescharacteristic
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2312yes—
456#394C2312yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2311yescharacteristic
463#394C2312yes—
464#394C2314yes—
465#394C2312yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2311yescharacteristic
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#393C2314yes—
489#393C2311yescharacteristic
490#393C2311yescharacteristic
491#393C2314yes—
492#393C2314yes—
493#393C2314yes—
494#393C2312yes—
495#392C2314yes—
496#392C2314yes—
497#392C2311yescharacteristic
498#392C2314yes—
499#392C2314yes—
500#392C2314yes—
501#392C2312yes—
502#392C2314yes—
503#392C2312yes—
504#392C2311yescharacteristic
505#392C2312yes—
506#392C2314yes—
507#391C2312yes—
508#391C2312yes—
509#391C2312yes—
510#391C2312yes—
511#391C2312yes—
512#391C2312yes—
513#391C2312yes—
514#391C2314yes—
515#391C2312yes—
516#391C2312yes—
517#391C2312yes—
518#391C2314yes—
519#391C2314yes—
520#391C2314yes—
521#391C2314yes—
522#391C2314yes—
523#391C2312yes—
524#391C2314yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2314yes—
531#390C2312yes—
532#390C2312yes—
533#390C2312yes—
534#390C2314yes—
535#390C2312yes—
536#390C2312yes—
537#390C2314yes—
538#390C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2312yes—
548#389C2312yes—
549#389C2314yes—
550#389C2314yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#388C2312yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2314yes—
589#388C2314yes—
590#388C2312yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2312yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2312yes—
625#386C2312yes—
626#386C2312yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2312yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2312yes—
640#386C2314yes—
641#386C2312yes—
642#386C2314yes—
643#386C2314yes—
644#386C2312yes—
645#386C2312yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2312yes—
652#386C2314yes—
653#385C2312yes—
654#385C2312yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2312yes—
674#385C2314yes—
675#385C2312yes—
676#385C2314yes—
677#384C2312yes—
678#384C2312yes—
679#384C2312yes—
680#383C2314yes—
681#382C2312yes—
682#382C2312yes—
683#382C2314yes—
684#382C2312yes—
685#381C2314yes—
686#381C2314yes—
687#381C2314yes—
688#381C2314yes—
689#381C2314yes—
690#381C2314yes—
691#380C2312yes—
692#380C2312yes—
693#380C2312yes—
694#380C2312yes—
695#380C2314yes—
696#380C2312yes—
697#380C2312yes—
698#380C2312yes—
699#380C2312yes—
700#380C2314yes—
701#380C2314yes—
702#380C2314yes—
703#380C2314yes—
704#380C2314yes—
705#380C2312yes—
706#380C2312yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2311yescharacteristic
716C4×C4⋊C4C2311yescharacteristic
717C4×C4⋊C4C2311yescharacteristic
718C4×C4⋊C4C2312yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729#376C2312yes—
730#376C2312yes—
731#376C2311yescharacteristic
732#376C2311yescharacteristic
733#376C2312yes—
734#376C2311yescharacteristic
735#376C2311yescharacteristic
736C2×#95C2311yescharacteristic
737C2×#95C2311yescharacteristic
738C2×#95C2312yes—
739C2×#95C2312yes—
740C43C2312yes—
741C2×#41—24no—
742C2×#41—42no—
743C2×#41—44no—
744C2×#41—44no—
745C2×#41—44no—
746C2×#41—42no—
747C2×#41—44no—
748C2×#41—44no—
749C2×#41—44no—
750C22×Q8C2412yes—
751C22×Q8C2411yescharacteristic
752C22×Q8C2412yes—
753C22×Q8C2412yes—
754C22×Q8C2411yescharacteristic
755C22×Q8C2414yes—
756C22×D4C2412yes—
757C22×D4C2411yescharacteristic
758C22×D4C2411yescharacteristic
759C22×D4C2412yes—
760C22×D4C2412yes—
761C22×D4C2414yes—
762C22×D4C2414yes—
763C22×D4C2412yes—
764C22×D4C2414yes—
765C22×D4C2414yes—
766C22×D4C2411yescharacteristic
767C22×D4C2412yes—
768C22×D4C2412yes—
769C22×D4C2414yes—
770C22×D4C2411yescharacteristic
771C23×C4C2411yescharacteristic
772C23×C4C2412yes—
773C23×C4C2411yescharacteristic
774C23×C4C2411yescharacteristic
775C23×C4C2411yescharacteristic
776C23×C4C2411yescharacteristic
777C23×C4C2411yescharacteristic
778C23×C4C2414yes—
779C23×C4C2414yes—
780C23×C4C2411yescharacteristic
781C23×C4C2411yescharacteristic
782C23×C4C2411yescharacteristic
783C23×C4C2412yes—
784C23×C4C2414yes—
785C23×C4C2414yes—
786C23×C4C2414yes—
787C23×C4C2412yes—
788C4⋊Q8—44no—
789C4⋊Q8—42no—
790C4⋊Q8—42no—
791C4⋊Q8—42no—
792C4⋊Q8—44no—
793C4⋊Q8—44no—
794#127—42no—
795#127—44no—
796#126—44no—
797#125—42no—
798#125—44no—
799#125—48no—
800#124—28no—
801#124—42no—
802#124—44no—
803#124—48no—
804#124—44no—
805#124—44no—
806#124—44no—
807#123—48no—
808#123—48no—
809#123—44no—
810#123—48no—
811#123—48no—
812#123—48no—
813C22⋊Q8—48no—
814C22⋊Q8—48no—
815C22⋊Q8—48no—
816C22⋊Q8—48no—
817C22⋊Q8—48no—
818C22⋊Q8—42no—
819C22⋊Q8—44no—
820C22⋊Q8—44no—
821C22⋊Q8—44no—
822C22⋊Q8—44no—
823C22⋊Q8—44no—
824#121—216no—
825#121—28no—
826#121—42no—
827#121—44no—
828#121—44no—
829#121—48no—
830#121—48no—
831#121—44no—
832#121—44no—
833#121—44no—
834#121—44no—
835#121—48no—
836C4×Q8—28no—
837C4×Q8—42no—
838C4×Q8—42no—
839C4×Q8—42no—
840C4×Q8—44no—
841C4×Q8—44no—
842C4×D4—28no—
843C4×D4—48no—
844C4×D4—44no—
845C4×D4—44no—
846C4×D4—44no—
847C4×D4—42no—
848C4×D4—42no—
849C4×D4—42no—
850C4×D4—42no—
851C4×D4—42no—
852C4×D4—42no—
853C4×D4—42no—
854C4×D4—44no—
855C4×D4—44no—
856C4×D4—48no—
857C4×D4—48no—
858C4×D4—48no—
859#117—28no—
860#117—42no—
861#117—42no—
862#117—42no—
863#117—44no—
864#117—48no—
865#117—44no—
866C2×C4⋊C4—44no—
867C2×C4⋊C4—48no—
868C2×C4⋊C4—44no—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2411yescharacteristic
933C2×C22⋊C4C2411yescharacteristic
934C2×C22⋊C4C2411yescharacteristic
935C2×C22⋊C4C2411yescharacteristic
936C2×C22⋊C4C2411yescharacteristic
937C2×C22⋊C4C2411yescharacteristic
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C42—24no—
979C2×C42—24no—
980C2×C42—24no—
981C2×C42—44no—
982C2×C42—44no—
983C2×C42C2411yescharacteristic
984C2×C42C2414yes—
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994C2×C42C2411yescharacteristic
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2414yes—
998C2×C42C2414yes—
999C2×C42C2414yes—
1000C2×C42C2412yes—
1001C2×C42C2412yes—
1002C2×C42C2412yes—
1003C2×C42C2414yes—
1004C2×C42C2412yes—
1005C2×C42C2412yes—
1006C2×C42C2411yescharacteristic
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2411yescharacteristic
1013#95C2411yescharacteristic
1014#95C2411yescharacteristic
1015#95C2412yes—
1016#95C2411yescharacteristic
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2414yes—
1070#95C2414yes—
1071C24C2512yes—
1072C24C2514yes—
1073C24C2511yescharacteristic
1074C24C2511yescharacteristic
1075C24C2511yescharacteristic
1076#41—416no—
1077#41—432no—
1078#41—816no—
1079C2×Q8—24no—
1080C2×Q8—22no—
1081C2×Q8—24no—
1082C2×Q8—24no—
1083C2×Q8—24no—
1084C2×Q8—22no—
1085C2×Q8—24no—
1086C2×Q8—41no—
1087C2×Q8—41no—
1088C2×Q8—42no—
1089C2×Q8—42no—
1090C2×Q8—42no—
1091C2×Q8—42no—
1092C2×Q8—42no—
1093C2×Q8—44no—
1094C2×Q8—44no—
1095C2×Q8—44no—
1096C2×D4—22no—
1097C2×D4—22no—
1098C2×D4—28no—
1099C2×D4—24no—
1100C2×D4—24no—
1101C2×D4—28no—
1102C2×D4—24no—
1103C2×D4—22no—
1104C2×D4—24no—
1105C2×D4—24no—
1106C2×D4—24no—
1107C2×D4—41no—
1108C2×D4—41no—
1109C2×D4—41no—
1110C2×D4—44no—
1111C2×D4—41no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—41no—
1115C2×D4—42no—
1116C2×D4—41no—
1117C2×D4—42no—
1118C2×D4—44no—
1119C2×D4—42no—
1120C2×D4—42no—
1121C2×D4—44no—
1122C2×D4—42no—
1123C2×D4—42no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—42no—
1127C2×D4—42no—
1128C2×D4—42no—
1129C2×D4—42no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—42no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4H(5,𝔽2)14yes—
1139C22×C4—22no—
1140C22×C4—22no—
1141C22×C4—22no—
1142C22×C4—22no—
1143C22×C4—28no—
1144C22×C4—24no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—22no—
1149C22×C4—22no—
1150C22×C4—22no—
1151C22×C4—24no—
1152C22×C4—22no—
1153C22×C4—24no—
1154C22×C4—24no—
1155C22×C4—24no—
1156C22×C4—24no—
1157C22×C4—24no—
1158C22×C4—22no—
1159C22×C4—22no—
1160C22×C4—28no—
1161C22×C4—44no—
1162C22×C4—42no—
1163C22×C4—41no—
1164C22×C4—41no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—42no—
1168C22×C4—42no—
1169C22×C4—44no—
1170C22×C4—44no—
1171C22×C4—42no—
1172C22×C4—42no—
1173C22×C4—42no—
1174C22×C4—42no—
1175C22×C4—42no—
1176C22×C4—44no—
1177C22×C4—44no—
1178C22×C4—44no—
1179C22×C4—44no—
1180C22×C4—44no—
1181C22×C4—44no—
1182C22×C4—44no—
1183C22×C4—44no—
1184C22×C4C2512yes—
1185C22×C4C2511yescharacteristic
1186C22×C4C2511yescharacteristic
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2514yes—
1190C22×C4C2514yes—
1191C22×C4C2512yes—
1192C22×C4C2514yes—
1193C22×C4C2511yescharacteristic
1194C22×C4C2514yes—
1195C22×C4C2512yes—
1196C22×C4C2514yes—
1197C22×C4C2512yes—
1198C22×C4C2514yes—
1199C22×C4C2511yescharacteristic
1200C22×C4C2511yescharacteristic
1201C22×C4C2511yescharacteristic
1202C22×C4C2511yescharacteristic
1203C22×C4C2514yes—
1204C22×C4C2512yes—
1205C22×C4C2511yescharacteristic
1206C22×C4C2511yescharacteristic
1207C22×C4C2511yescharacteristic
1208C22×C4C2511yescharacteristic
1209C22×C4C2511yescharacteristic
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—28no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—28no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—24no—
1221C4⋊C4—24no—
1222C4⋊C4—28no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—41no—
1231C4⋊C4—41no—
1232C4⋊C4—41no—
1233C4⋊C4—41no—
1234C4⋊C4—41no—
1235C4⋊C4—41no—
1236C4⋊C4—42no—
1237C4⋊C4—42no—
1238C4⋊C4—42no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—44no—
1242C4⋊C4—41no—
1243C4⋊C4—42no—
1244C4⋊C4—41no—
1245C4⋊C4—44no—
1246C4⋊C4—42no—
1247C4⋊C4—42no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—44no—
1259C4⋊C4—44no—
1260C4⋊C4—44no—
1261C4⋊C4—44no—
1262C4⋊C4—44no—
1263C22⋊C4—28no—
1264C22⋊C4—24no—
1265C22⋊C4—28no—
1266C22⋊C4—28no—
1267C22⋊C4—24no—
1268C22⋊C4—24no—
1269C22⋊C4—28no—
1270C22⋊C4—28no—
1271C22⋊C4—24no—
1272C22⋊C4—24no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—42no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—42no—
1283C22⋊C4—44no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—41no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—42no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—42no—
1300C22⋊C4—42no—
1301C22⋊C4—42no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—42no—
1306C22⋊C4—44no—
1307C22⋊C4—44no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—44no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C22⋊C4—44no—
1314C22⋊C4—44no—
1315C22⋊C4—44no—
1316C22⋊C4—44no—
1317C22⋊C4—44no—
1318C22⋊C4—44no—
1319C42—22no—
1320C42—22no—
1321C42—22no—
1322C42—22no—
1323C42—22no—
1324C42—22no—
1325C42—22no—
1326C42—22no—
1327C42—22no—
1328C42—24no—
1329C42—28no—
1330C42—24no—
1331C42—24no—
1332C42—24no—
1333C42—42no—
1334C42—42no—
1335C42—44no—
1336C42—42no—
1337C42—42no—
1338C42—44no—
1339C42—44no—
1340C42—44no—
1341C42—42no—
1342C42H(5,𝔽2)14yes—
1343C23—21no—
1344C23—21no—
1345C23—22no—
1346C23—22no—
1347C23—21no—
1348C23—21no—
1349C23—22no—
1350C23—22no—
1351C23—22no—
1352C23—22no—
1353C23—24no—
1354C23—24no—
1355C23—21no—
1356C23—21no—
1357C23—22no—
1358C23—22no—
1359C23—22no—
1360C23—24no—
1361C23—24no—
1362C23—21no—
1363C23—24no—
1364C23—22no—
1365C23—22no—
1366C23—24no—
1367C23—24no—
1368C23—22no—
1369C23—22no—
1370C23C2×H(5,𝔽2)12yes—
1371C23C2×H(5,𝔽2)12yes—
1372C23C2611yescharacteristic
1373Q8—44no—
1374Q8—48no—
1375Q8—84no—
1376Q8—84no—
1377Q8—82no—
1378Q8—164no—
1379D4—44no—
1380D4—44no—
1381D4—44no—
1382D4—416no—
1383D4—48no—
1384D4—84no—
1385D4—84no—
1386D4—84no—
1387D4—88no—
1388D4—88no—
1389D4—84no—
1390D4—82no—
1391D4—88no—
1392D4—84no—
1393D4—164no—
1394C2×C4—28no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—22no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—24no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—22no—
1421C2×C4—21no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—24no—
1431C2×C4—24no—
1432C2×C4—24no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—24no—
1438C2×C4—24no—
1439C2×C4—24no—
1440C2×C4—24no—
1441C2×C4—24no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—21no—
1446C2×C4—24no—
1447C2×C4—24no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—24no—
1453C2×C4—22no—
1454C2×C4—22no—
1455C2×C4—22no—
1456C2×C4—24no—
1457C2×C4—22no—
1458C2×C4—22no—
1459C2×C4—44no—
1460C2×C4—44no—
1461C2×C4—44no—
1462C2×C4—416no—
1463C2×C4—44no—
1464C2×C4—44no—
1465C2×C4—44no—
1466C2×C4—48no—
1467C2×C4—82no—
1468C2×C4—82no—
1469C2×C4—88no—
1470C2×C4—84no—
1471C2×C4—88no—
1472C2×C4—84no—
1473C2×C4—164no—
1474C2×C4—164no—
1475C2×C4C2×H(5,𝔽2)12yes—
1476C2×C4C2×H(5,𝔽2)12yes—
1477C2×C4C2×H(5,𝔽2)12yes—
1478C2×C4C2×H(5,𝔽2)12yes—
1479C2×C4#58512yes—
1480C2×C4#58514yes—
1481C22—22no—
1482C22—22no—
1483C22—24no—
1484C22—24no—
1485C22—41no—
1486C22—41no—
1487C22—41no—
1488C22—41no—
1489C22—42no—
1490C22—42no—
1491C22—41no—
1492C22—44no—
1493C22—42no—
1494C22—41no—
1495C22—42no—
1496C22—44no—
1497C22—42no—
1498C22—42no—
1499C22—44no—
1500C22—44no—
1501C22—42no—
1502C22—44no—
1503C22—42no—
1504C22—41no—
1505C22—42no—
1506C22—42no—
1507C22—42no—
1508C22—44no—
1509C22—44no—
1510C22C22×H(5,𝔽2)11yescharacteristic
1511C22C22×H(5,𝔽2)11yescharacteristic
1512C22C2×#58511yescharacteristic
1513C22C2×#58512yes—
1514C222−1+612yes—
1515C4—22no—
1516C4—22no—
1517C4—22no—
1518C4—22no—
1519C4—41no—
1520C4—44no—
1521C4—42no—
1522C4—44no—
1523C4—41no—
1524C4—41no—
1525C4—41no—
1526C4—42no—
1527C4—42no—
1528C4—44no—
1529C4—44no—
1530C4—42no—
1531C4—44no—
1532C4—41no—
1533C4—41no—
1534C4—41no—
1535C4—42no—
1536C4—44no—
1537C4—44no—
1538C4—42no—
1539C4—42no—
1540C4#352914yes—
1541C2—42no—
1542C2—42no—
1543C2—81no—
1544C2—84no—
1545C2—82no—
1546C2C2×#352911yescharacteristic
1547C2#6281811yescharacteristic
1548C2#6288611yescharacteristic
1549C2#6292112yes—
1550C2#6296712yes—
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. #53127C2semidirect
2. #53100C2semidirect
3. #53098C2semidirect
4. #53080C2semidirect
5. #52989C2semidirect
6. #52987C2semidirect
7. #52762C2semidirect
8. #52760C2semidirect
9. #52757C2semidirect
10. #52702C2semidirect
11. #52693C2semidirect
12. #52628C2semidirect
13. #46303C2semidirect
14. #46293C2semidirect
15. #46274C2semidirect
16. #46236C2semidirect
17. #45930C2semidirect
18. #45760C2semidirect
19. #45716C2semidirect
20. #45631C2semidirect
21. #45616C2semidirect
22. #45482C2semidirect
23. #35600C2semidirect
24. #35526C2semidirect
25. #35520C2semidirect
26. #35270C2semidirect
27. #35228C2semidirect
28. #35164C2semidirect
29. #34979C2semidirect
30. #34937C2semidirect
31. #34876C2semidirect

Maximal subgroups

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

subgroupindex
#531272
#531002
#530982
#530802
#529892
#529872
#527622
#527602
#527572
#527022
#526932
#526282
#463032
#462932
#462742
#462362
#459302
#457602
#457162
#456312
#456162
#454822
#356002
#355262
#355202
#352702
#352282
#351642
#349792
#349372
#348762