Finite Group Databasebeta

← #7900946

Subgroups — #7900946

Order 512.

5071 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59409C212yesmaximal, complemented
3#52160C211yesmaximal, characteristic, complemented
4#50971C214yesmaximal, complemented
5#50002C214yesmaximal, complemented
6#48642C214yesmaximal, complemented
7#46530C214yesmaximal, complemented
8#46091C212yesmaximal, complemented
9#45385C212yesmaximal, complemented
10#45310C212yesmaximal, complemented
11#45267C212yesmaximal, complemented
12#43214C214yesmaximal, complemented
13#42862C212yesmaximal, complemented
14#42510C212yesmaximal, complemented
15#40804C214yesmaximal, complemented
16#39666C212yesmaximal, complemented
17#39629C211yesmaximal, characteristic, complemented
18#39501C211yesmaximal, characteristic, complemented
19#39260C212yesmaximal, complemented
20#38802C212yesmaximal, complemented
21#38445C212yesmaximal, complemented
22#38027C212yesmaximal, complemented
23#37209C212yesmaximal, complemented
24#36415C211yesmaximal, characteristic, complemented
25#35737C212yesmaximal, complemented
26#35521C212yesmaximal, complemented
27#35206C211yesmaximal, characteristic, complemented
28#34475C212yesmaximal, complemented
29#34308C211yesmaximal, characteristic, complemented
30C2×#555C2211yescharacteristic
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2212yes—
33C2×#548C2212yes—
34C2×#548C2212yes—
35C2×#547C2211yescharacteristic
36C2×#547C2211yescharacteristic
37C2×#529C2212yes—
38C2×#520C2212yes—
39#2862C2211yescharacteristic
40#2855C2212yes—
41#2855C2212yes—
42#2851C2212yes—
43#2850C2212yes—
44#2836C2214yes—
45#2831C2214yes—
46#2809C2212yes—
47#2809C2212yes—
48#2808C2212yes—
49#2808C2212yes—
50#2806C2214yes—
51#2806C2212yes—
52#2806C2212yes—
53#2805C2212yes—
54#2805C2212yes—
55#2804C2214yes—
56#2800C2214yes—
57#2786C2214yes—
58#2784C2214yes—
59#2780C2214yes—
60#2774C2214yes—
61#2772C2214yes—
62#2770C2214yes—
63#2768C2214yes—
64#2761C2214yes—
65#2751C2214yes—
66#2750C2214yes—
67#2749C2214yes—
68#2749C2214yes—
69#2738C2214yes—
70#2733C2211yescharacteristic
71#2732C2211yescharacteristic
72#2730C2212yes—
73#2727C2211yescharacteristic
74#2725C2214yes—
75#2721C2212yes—
76#2716C2214yes—
77#2715C2214yes—
78#2714C2212yes—
79#2713C2214yes—
80#2712C2214yes—
81#2706C2214yes—
82#2705C2212yes—
83#2700C2214yes—
84#2700C2214yes—
85#2700C2214yes—
86#2699C2214yes—
87#2698C2214yes—
88#2695C2214yes—
89#2694C2212yes—
90#2687C2214yes—
91#2686C2214yes—
92#2683C2212yes—
93#2683C2212yes—
94#2682C2211yescharacteristic
95#2676C2214yes—
96#2676C2214yes—
97#2674C2214yes—
98#2674C2214yes—
99#2673C2212yes—
100#2667C2214yes—
101#2665C2214yes—
102#2665C2214yes—
103#2652C2214yes—
104#2652C2214yes—
105#2647C2212yes—
106#2630C2214yes—
107#2625C2212yes—
108#2621C2212yes—
109#2621C2214yes—
110#2608C2214yes—
111#2603C2214yes—
112#2589C2214yes—
113#2585C2214yes—
114#2581C2212yes—
115#2579C2214yes—
116#2574C2214yes—
117#2568C2211yescharacteristic
118#2563C2211yescharacteristic
119#2558C2214yes—
120#2557C2214yes—
121#2557C2214yes—
122#2557C2214yes—
123#2557C2214yes—
124#2554C2214yes—
125#2552C2211yescharacteristic
126#2551C2212yes—
127#2549C2214yes—
128#2549C2214yes—
129#2547C2214yes—
130#2547C2211yescharacteristic
131#2547C2211yescharacteristic
132#2538C2212yes—
133#2538C2212yes—
134#2538C2211yescharacteristic
135#2538C2212yes—
136#2538C2212yes—
137#2536C2212yes—
138#2535C2214yes—
139#2535C2212yes—
140#2535C2212yes—
141#2532C2214yes—
142#2532C2214yes—
143#2530C2214yes—
144#2520C2214yes—
145#2520C2214yes—
146#2515C2214yes—
147#2511C2212yes—
148#2499C2212yes—
149#2497C2212yes—
150#2496C2212yes—
151#2495C2212yes—
152#2492C2212yes—
153#2492C2212yes—
154#2489C2212yes—
155#2488C2214yes—
156#2487C2212yes—
157#2486C2212yes—
158#2486C2212yes—
159#2485C2212yes—
160#2481C2214yes—
161#2481C2214yes—
162#2475C2214yes—
163#2474C2214yes—
164#2471C2214yes—
165#2466C2214yes—
166#2461C2214yes—
167#2457C2214yes—
168#2457C2214yes—
169#2456C2214yes—
170#2456C2214yes—
171#2456C2214yes—
172#2452C2214yes—
173#2452C2214yes—
174#2451C2212yes—
175#2451C2212yes—
176#2449C2214yes—
177#2449C2214yes—
178#2449C2214yes—
179#2447C2212yes—
180#2447C2214yes—
181#2444C2214yes—
182#2444C2214yes—
183#2438C2214yes—
184#2431C2212yes—
185#2430C2214yes—
186#2427C2212yes—
187#2427C2214yes—
188#2427C2212yes—
189#2427C2214yes—
190#2425C2214yes—
191#2419C2214yes—
192#2419C2214yes—
193#2417C2214yes—
194#2417C2212yes—
195#2417C2212yes—
196#2417C2212yes—
197#2417C2214yes—
198#2415C2212yes—
199#2409C2212yes—
200#2409C2212yes—
201#2409C2212yes—
202#2409C2212yes—
203#2407C2212yes—
204#2407C2212yes—
205#2397C2212yes—
206#2392C2212yes—
207#2392C2214yes—
208#2392C2212yes—
209#2381C2214yes—
210#2378C2214yes—
211#2368C2214yes—
212#2366C2212yes—
213#2365C2211yescharacteristic
214#2362C2212yes—
215#2361C2212yes—
216#2360C2212yes—
217#2360C2212yes—
218#2359C2214yes—
219#2356C2212yes—
220#2353C2214yes—
221#2352C2212yes—
222#2352C2212yes—
223#2351C2212yes—
224D4×C4⋊C4C2211yescharacteristic
225D4×C4⋊C4C2211yescharacteristic
226#2344C2212yes—
227Q8×C22⋊C4C2212yes—
228Q8×C22⋊C4C2212yes—
229#2339C2212yes—
230#2339C2214yes—
231#2333C2214yes—
232#2332C2214yes—
233#2331C2214yes—
234#2329C2214yes—
235#2327C2212yes—
236#2326C2212yes—
237#2324C2212yes—
238#2323C2212yes—
239#2323C2212yes—
240#2322C2214yes—
241#2320C2212yes—
242#2318C2214yes—
243#2314C2212yes—
244#2310C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×#127C2211yescharacteristic
248C4×C22⋊Q8C2212yes—
249C4×#121C2212yes—
250C4×#121C2212yes—
251C4×#121C2212yes—
252#2297C2212yes—
253#2295C2211yescharacteristic
254C2×#391C2212yes—
255#2293C2211yescharacteristic
256C2×#389C2212yes—
257#2290C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261C23×Q8C2312yes—
262C23×Q8C2312yes—
263#555—44no—
264D4×Q8—216no—
265D4×Q8—48no—
266#548—48no—
267#548—48no—
268#547—28no—
269#547—44no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×#127C2311yescharacteristic
277#529—48no—
278C2×#126C2312yes—
279C2×#126C2312yes—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2314yes—
287C2×#124C2314yes—
288C2×#124C2312yes—
289C2×#123C2314yes—
290C2×#123C2312yes—
291C2×#123C2312yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2312yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C2×#121C2312yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×#121C2312yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319#520—48no—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2314yes—
351C2×#117C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C42C2312yes—
358C22×C42C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#399C2312yes—
372#399C2314yes—
373#399C2312yes—
374#399C2312yes—
375#399C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2312yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2312yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2312yes—
422#396C2312yes—
423#396C2314yes—
424#396C2312yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2312yes—
440#394C2312yes—
441#394C2312yes—
442#394C2314yes—
443#394C2312yes—
444#394C2312yes—
445#394C2312yes—
446#394C2314yes—
447#394C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#392C2314yes—
456#392C2312yes—
457#392C2312yes—
458#392C2312yes—
459#392C2314yes—
460#392C2312yes—
461#392C2312yes—
462#392C2312yes—
463#392C2314yes—
464#392C2314yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2314yes—
471#391C2312yes—
472#391C2314yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2314yes—
486#391C2314yes—
487#391C2312yes—
488#391C2311yescharacteristic
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2314yes—
493#391C2312yes—
494#391C2311yescharacteristic
495#390C2311yescharacteristic
496#390C2311yescharacteristic
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2314yes—
502#390C2314yes—
503#390C2314yes—
504#390C2311yescharacteristic
505#390C2314yes—
506#390C2314yes—
507#390C2311yescharacteristic
508#390C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2311yescharacteristic
527#389C2312yes—
528#389C2311yescharacteristic
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2311yescharacteristic
536#389C2314yes—
537#389C2312yes—
538#389C2311yescharacteristic
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2314yes—
545#388C2312yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
557#388C2314yes—
558#388C2312yes—
559#388C2312yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2314yes—
599#387C2312yes—
600#386C2312yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2312yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2312yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#384C2311yescharacteristic
646#384C2311yescharacteristic
647#384C2311yescharacteristic
648#384C2312yes—
649#383C2314yes—
650#383C2314yes—
651#382C2312yes—
652#382C2312yes—
653#382C2312yes—
654#382C2314yes—
655#382C2312yes—
656#382C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2314yes—
660#381C2314yes—
661#381C2314yes—
662#381C2314yes—
663#381C2314yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2312yes—
674#380C2314yes—
675#380C2314yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2312yes—
681#380C2312yes—
682#380C2312yes—
683#380C2314yes—
684#380C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715#376C2312yes—
716#376C2314yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C2×#95C2314yes—
720C43C2311yescharacteristic
721C2×#41—28no—
722C2×#41—28no—
723C2×#41—28no—
724C2×#41—44no—
725C2×#41—44no—
726C2×#41—82no—
727C22×Q8—28no—
728C22×Q8—28no—
729C22×Q8—44no—
730C22×Q8—44no—
731C22×Q8—44no—
732C22×Q8—44no—
733C22×Q8C2412yes—
734C22×Q8C2412yes—
735C22×Q8C2411yescharacteristic
736C22×Q8C2414yes—
737C22×Q8C2414yes—
738C22×Q8C2412yes—
739C22×Q8C2412yes—
740C22×D4C2412yes—
741C22×D4C2412yes—
742C22×D4C2414yes—
743C22×D4C2414yes—
744C22×D4C2411yescharacteristic
745C22×D4C2411yescharacteristic
746C22×D4C2412yes—
747C22×D4C2414yes—
748C22×D4C2412yes—
749C22×D4C2411yescharacteristic
750C22×D4C2412yes—
751C22×D4C2412yes—
752C22×D4C2411yescharacteristic
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2414yes—
757C23×C4C2412yes—
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2414yes—
761C23×C4C2414yes—
762C23×C4C2414yes—
763C23×C4C2412yes—
764C23×C4C2414yes—
765C23×C4C2414yes—
766C23×C4C2412yes—
767C4⋊Q8—216no—
768C4⋊Q8—24no—
769C4⋊Q8—42no—
770C4⋊Q8—48no—
771C4⋊Q8—42no—
772C4⋊Q8#4118yescomplemented
773#127—24no—
774#126—44no—
775#126—44no—
776#126—84no—
777#125—44no—
778#125—82no—
779#124—28no—
780#124—48no—
781#124—48no—
782#124—48no—
783#124—44no—
784#124—82no—
785#123—216no—
786#123—44no—
787#123—48no—
788#123—44no—
789#123—84no—
790#123—84no—
791C22⋊Q8—28no—
792C22⋊Q8—28no—
793C22⋊Q8—28no—
794C22⋊Q8—216no—
795C22⋊Q8—216no—
796C22⋊Q8—44no—
797C22⋊Q8—48no—
798C22⋊Q8—48no—
799C22⋊Q8—48no—
800C22⋊Q8—48no—
801C22⋊Q8—44no—
802C22⋊Q8—44no—
803C22⋊Q8—44no—
804C22⋊Q8—44no—
805C22⋊Q8—44no—
806C22⋊Q8—82no—
807#121—28no—
808#121—28no—
809#121—28no—
810#121—28no—
811#121—44no—
812#121—48no—
813#121—48no—
814#121—44no—
815C4×Q8—28no—
816C4×Q8—28no—
817C4×Q8—24no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×Q8—44no—
821C4×D4—24no—
822C4×D4—216no—
823C4×D4—24no—
824C4×D4—24no—
825C4×D4—28no—
826C4×D4—24no—
827C4×D4—28no—
828C4×D4—48no—
829C4×D4—44no—
830C4×D4—48no—
831C4×D4—44no—
832C4×D4—44no—
833C4×D4—42no—
834C4×D4—44no—
835C4×D4—44no—
836C4×D4—42no—
837C4×D4—48no—
838C4×D4—48no—
839C4×D4—48no—
840C4×D4—82no—
841C4×D4—84no—
842#117—28no—
843#117—44no—
844#117—48no—
845#117—44no—
846#117—44no—
847C2×C4⋊C4—28no—
848C2×C4⋊C4—48no—
849C2×C4⋊C4—44no—
850C2×C4⋊C4—44no—
851C2×C4⋊C4—82no—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2411yescharacteristic
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2411yescharacteristic
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2414yes—
965C2×C42—44no—
966C2×C42—82no—
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2412yes—
970C2×C42C2411yescharacteristic
971C2×C42C2412yes—
972C2×C42C2414yes—
973C2×C42C2411yescharacteristic
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987C2×C42C2414yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049C24C2512yes—
1050C24C2512yes—
1051C24C2512yes—
1052C24C2512yes—
1053#41—432no—
1054#41—816no—
1055C2×Q8—24no—
1056C2×Q8—28no—
1057C2×Q8—28no—
1058C2×Q8—24no—
1059C2×Q8—24no—
1060C2×Q8—24no—
1061C2×Q8—24no—
1062C2×Q8—22no—
1063C2×Q8—24no—
1064C2×Q8—44no—
1065C2×Q8—44no—
1066C2×Q8—44no—
1067C2×Q8—44no—
1068C2×Q8—42no—
1069C2×Q8—41no—
1070C2×Q8—42no—
1071C2×Q8—41no—
1072C2×Q8—42no—
1073C2×Q8—42no—
1074C2×Q8—42no—
1075C2×Q8—816no—
1076C2×Q8—816no—
1077C2×Q8C2×#4118yes—
1078C2×D4—28no—
1079C2×D4—28no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—28no—
1083C2×D4—28no—
1084C2×D4—24no—
1085C2×D4—24no—
1086C2×D4—22no—
1087C2×D4—24no—
1088C2×D4—22no—
1089C2×D4—28no—
1090C2×D4—22no—
1091C2×D4—24no—
1092C2×D4—22no—
1093C2×D4—44no—
1094C2×D4—41no—
1095C2×D4—41no—
1096C2×D4—44no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C2×D4—41no—
1100C2×D4—41no—
1101C2×D4—41no—
1102C2×D4—42no—
1103C2×D4—42no—
1104C2×D4—42no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—41no—
1109C2×D4—44no—
1110C2×D4—42no—
1111C2×D4—42no—
1112C2×D4—42no—
1113C2×D4—44no—
1114C2×D4—42no—
1115C2×D4H(5,𝔽2)14yes—
1116C2×D42−1+414yes—
1117C22×C4—24no—
1118C22×C4—28no—
1119C22×C4—24no—
1120C22×C4—28no—
1121C22×C4—24no—
1122C22×C4—28no—
1123C22×C4—24no—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—24no—
1127C22×C4—24no—
1128C22×C4—24no—
1129C22×C4—24no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—28no—
1134C22×C4—28no—
1135C22×C4—24no—
1136C22×C4—42no—
1137C22×C4—42no—
1138C22×C4—44no—
1139C22×C4—42no—
1140C22×C4—42no—
1141C22×C4—42no—
1142C22×C4—42no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—42no—
1149C22×C4—44no—
1150C22×C4—42no—
1151C22×C4—42no—
1152C22×C4—42no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2511yescharacteristic
1163C22×C4C2514yes—
1164C22×C4C2514yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2514yes—
1171C22×C4C2514yes—
1172C22×C4C2512yes—
1173C22×C4C2514yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2511yescharacteristic
1179C22×C4C2514yes—
1180C22×C4C2511yescharacteristic
1181C22×C4C2511yescharacteristic
1182C22×C4C2511yescharacteristic
1183C22×C4C2511yescharacteristic
1184C4⋊C4—22no—
1185C4⋊C4—28no—
1186C4⋊C4—22no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—28no—
1190C4⋊C4—28no—
1191C4⋊C4—28no—
1192C4⋊C4—24no—
1193C4⋊C4—22no—
1194C4⋊C4—22no—
1195C4⋊C4—28no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—22no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—41no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
1216C4⋊C4—44no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—41no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—42no—
1224C4⋊C4—41no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4—42no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—41no—
1242C4⋊C4—44no—
1243C4⋊C4C2×#4118yes—
1244C4⋊C4C2×#4118yes—
1245C22⋊C4—28no—
1246C22⋊C4—24no—
1247C22⋊C4—28no—
1248C22⋊C4—28no—
1249C22⋊C4—28no—
1250C22⋊C4—24no—
1251C22⋊C4—28no—
1252C22⋊C4—28no—
1253C22⋊C4—24no—
1254C22⋊C4—24no—
1255C22⋊C4—24no—
1256C22⋊C4—24no—
1257C22⋊C4—28no—
1258C22⋊C4—24no—
1259C22⋊C4—24no—
1260C22⋊C4—24no—
1261C22⋊C4—24no—
1262C22⋊C4—24no—
1263C22⋊C4—24no—
1264C22⋊C4—42no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—42no—
1269C22⋊C4—42no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—42no—
1280C22⋊C4—42no—
1281C22⋊C4—42no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—42no—
1297C42—28no—
1298C42—24no—
1299C42—24no—
1300C42—28no—
1301C42—22no—
1302C42—24no—
1303C42—22no—
1304C42—42no—
1305C42—42no—
1306C42—41no—
1307C42—42no—
1308C42—42no—
1309C42—42no—
1310C42—41no—
1311C42—41no—
1312C42—44no—
1313C42—44no—
1314C42—44no—
1315C42—44no—
1316C42—44no—
1317C42—44no—
1318C42C2×#4114yes—
1319C42H(5,𝔽2)14yes—
1320C23—22no—
1321C23—22no—
1322C23—22no—
1323C23—22no—
1324C23—22no—
1325C23—22no—
1326C23—22no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—22no—
1336C23—22no—
1337C23—22no—
1338C23—22no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23C2×H(5,𝔽2)14yes—
1347C23C2×2−1+414yes—
1348C23C2611yescharacteristic
1349Q8—216no—
1350Q8—48no—
1351Q8—82no—
1352Q8—88no—
1353Q8—88no—
1354Q8—84no—
1355Q8—162no—
1356D4—28no—
1357D4—44no—
1358D4—48no—
1359D4—48no—
1360D4—416no—
1361D4—44no—
1362D4—416no—
1363D4—82no—
1364D4—88no—
1365D4—84no—
1366D4—84no—
1367D4—84no—
1368D4—84no—
1369C2×C4—24no—
1370C2×C4—21no—
1371C2×C4—24no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
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—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—21no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—24no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—24no—
1434C2×C4—22no—
1435C2×C4—416no—
1436C2×C4—48no—
1437C2×C4—48no—
1438C2×C4—48no—
1439C2×C4—48no—
1440C2×C4—48no—
1441C2×C4—84no—
1442C2×C4—88no—
1443C2×C4—88no—
1444C2×C4—84no—
1445C2×C4—88no—
1446C2×C4—84no—
1447C2×C4—164no—
1448C2×C4—164no—
1449C2×C4C22×#4112yes—
1450C2×C4C22×#4112yes—
1451C2×C4C22×#4118yes—
1452C2×C4C22×#4112yes—
1453C2×C4C2×H(5,𝔽2)12yes—
1454C2×C4C2×H(5,𝔽2)12yes—
1455C2×C4C2×H(5,𝔽2)12yes—
1456C2×C4C2×H(5,𝔽2)12yes—
1457C2×C4C2×2−1+412yes—
1458C22—24no—
1459C22—24no—
1460C22—24no—
1461C22—24no—
1462C22—24no—
1463C22—24no—
1464C22—42no—
1465C22—42no—
1466C22—42no—
1467C22—42no—
1468C22—42no—
1469C22—42no—
1470C22—42no—
1471C22—42no—
1472C22—42no—
1473C22—42no—
1474C22—42no—
1475C22—42no—
1476C22—42no—
1477C22—42no—
1478C22—42no—
1479C22—42no—
1480C22—42no—
1481C22—42no—
1482C22—42no—
1483C22—42no—
1484C22—42no—
1485C22—42no—
1486C22C23×#4111yescharacteristic
1487C22C22×H(5,𝔽2)11yescharacteristic
1488C22C22×H(5,𝔽2)11yescharacteristic
1489C22C22×2−1+411yescharacteristic
1490C22H(7,𝔽2)11yescharacteristic
1491C222−1+611yescharacteristic
1492C222−1+611yescharacteristic
1493C4—22no—
1494C4—28no—
1495C4—22no—
1496C4—22no—
1497C4—22no—
1498C4—22no—
1499C4—42no—
1500C4—42no—
1501C4—42no—
1502C4—44no—
1503C4—42no—
1504C4—44no—
1505C4—41no—
1506C4—44no—
1507C4—42no—
1508C4—42no—
1509C4—42no—
1510C4—42no—
1511C4—44no—
1512C4—42no—
1513C4—44no—
1514C4—42no—
1515C4—42no—
1516C4—42no—
1517C4#351914yes—
1518C2—44no—
1519C2—44no—
1520C2—82no—
1521C2—82no—
1522C2C2×#351911yescharacteristic
1523C2#6285111yescharacteristic
1524C2#6287811yescharacteristic
1525C2#6289411yescharacteristic
1526C2#6294211yescharacteristic
1527C2#6299811yescharacteristic
1528C2#6306311yescharacteristic
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. #59817C2semidirect
2. #59409C2semidirect
3. #52160C2semidirect
4. #50971C2semidirect
5. #50002C2semidirect
6. #48642C2semidirect
7. #46530C2semidirect
8. #46091C2semidirect
9. #45385C2semidirect
10. #45310C2semidirect
11. #45267C2semidirect
12. #43214C2semidirect
13. #42862C2semidirect
14. #42510C2semidirect
15. #40804C2semidirect
16. #39666C2semidirect
17. #39629C2semidirect
18. #39501C2semidirect
19. #39260C2semidirect
20. #38802C2semidirect
21. #38445C2semidirect
22. #38027C2semidirect
23. #37209C2semidirect
24. #36415C2semidirect
25. #35737C2semidirect
26. #35521C2semidirect
27. #35206C2semidirect
28. #34475C2semidirect
29. #34308C2semidirect
772. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598172
#594092
#521602
#509712
#500022
#486422
#465302
#460912
#453852
#453102
#452672
#432142
#428622
#425102
#408042
#396662
#396292
#395012
#392602
#388022
#384452
#380272
#372092
#364152
#357372
#355212
#352062
#344752
#343082