Finite Group Databasebeta

← #7895474

Subgroups — #7895474

Order 512.

5141 conjugacy classes of subgroups.

The subgroup lattice has 1517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59815C212yesmaximal, complemented
3#52287C211yesmaximal, characteristic, complemented
4#51924C214yesmaximal, complemented
5#49414C214yesmaximal, complemented
6#48619C214yesmaximal, complemented
7#46983C214yesmaximal, complemented
8#46090C212yesmaximal, complemented
9#45354C212yesmaximal, complemented
10#44966C212yesmaximal, complemented
11#44964C212yesmaximal, complemented
12#43119C214yesmaximal, complemented
13#42699C212yesmaximal, complemented
14#42524C212yesmaximal, complemented
15#42130C214yesmaximal, complemented
16#40023C212yesmaximal, complemented
17#39808C212yesmaximal, complemented
18#39765C211yesmaximal, characteristic, complemented
19#39739C211yesmaximal, characteristic, complemented
20#39161C212yesmaximal, complemented
21#38820C212yesmaximal, complemented
22#38425C212yesmaximal, complemented
23#37219C212yesmaximal, complemented
24#36419C211yesmaximal, characteristic, complemented
25#35930C212yesmaximal, complemented
26#35561C212yesmaximal, complemented
27#35197C211yesmaximal, characteristic, complemented
28#34498C212yesmaximal, complemented
29#34332C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×#559C2212yes—
32C2×#556C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#554C2212yes—
35C2×#550C2212yes—
36C2×#550C2211yescharacteristic
37C2×#547C2214yes—
38#2861C2212yes—
39#2858C2211yescharacteristic
40#2854C2212yes—
41#2850C2212yes—
42#2850C2212yes—
43#2837C2214yes—
44#2829C2214yes—
45#2811C2211yescharacteristic
46#2808C2212yes—
47#2808C2212yes—
48#2806C2211yescharacteristic
49#2806C2211yescharacteristic
50#2806C2212yes—
51#2806C2212yes—
52#2804C2212yes—
53#2803C2214yes—
54#2803C2214yes—
55#2797C2214yes—
56#2793C2214yes—
57#2792C2212yes—
58#2792C2212yes—
59#2792C2212yes—
60#2790C2214yes—
61#2788C2214yes—
62#2772C2214yes—
63#2768C2214yes—
64#2739C2214yes—
65#2734C2211yescharacteristic
66#2734C2212yes—
67#2733C2212yes—
68#2733C2212yes—
69#2732C2212yes—
70#2732C2212yes—
71#2730C2214yes—
72#2730C2214yes—
73#2729C2214yes—
74#2724C2212yes—
75#2720C2214yes—
76#2718C2214yes—
77#2715C2214yes—
78#2710C2214yes—
79#2708C2214yes—
80#2708C2214yes—
81#2702C2214yes—
82#2701C2214yes—
83#2700C2214yes—
84#2695C2214yes—
85#2692C2214yes—
86#2691C2214yes—
87#2687C2214yes—
88#2686C2214yes—
89#2686C2214yes—
90#2686C2214yes—
91#2682C2212yes—
92#2682C2212yes—
93#2682C2214yes—
94#2682C2214yes—
95#2681C2214yes—
96#2681C2214yes—
97#2680C2214yes—
98#2672C2214yes—
99#2663C2214yes—
100#2662C2214yes—
101#2661C2214yes—
102#2657C2212yes—
103#2651C2214yes—
104#2650C2214yes—
105#2648C2214yes—
106#2641C2212yes—
107#2640C2212yes—
108#2630C2214yes—
109#2602C2214yes—
110#2600C2214yes—
111#2597C2214yes—
112#2592C2212yes—
113#2592C2212yes—
114#2587C2214yes—
115#2583C2214yes—
116#2582C2212yes—
117#2581C2212yes—
118#2580C2212yes—
119#2574C2214yes—
120#2571C2211yescharacteristic
121#2568C2211yescharacteristic
122#2566C2212yes—
123#2565C2212yes—
124#2560C2214yes—
125#2559C2214yes—
126#2559C2214yes—
127#2558C2214yes—
128#2555C2214yes—
129#2555C2214yes—
130#2552C2212yes—
131#2548C2211yescharacteristic
132#2548C2212yes—
133#2548C2211yescharacteristic
134#2545C2212yes—
135#2544C2212yes—
136#2544C2212yes—
137#2544C2212yes—
138#2544C2212yes—
139#2543C2214yes—
140#2542C2212yes—
141#2541C2212yes—
142#2541C2211yescharacteristic
143#2541C2212yes—
144#2538C2212yes—
145#2538C2212yes—
146#2538C2211yescharacteristic
147#2538C2212yes—
148#2538C2212yes—
149#2537C2214yes—
150#2531C2214yes—
151#2530C2214yes—
152#2529C2214yes—
153#2526C2214yes—
154#2521C2214yes—
155#2513C2212yes—
156#2512C2212yes—
157#2511C2212yes—
158#2500C2212yes—
159#2474C2214yes—
160#2473C2214yes—
161#2468C2214yes—
162#2466C2214yes—
163#2464C2214yes—
164#2464C2214yes—
165#2463C2214yes—
166#2463C2214yes—
167#2461C2214yes—
168#2460C2214yes—
169#2459C2214yes—
170#2458C2214yes—
171#2457C2214yes—
172#2456C2214yes—
173#2456C2214yes—
174#2455C2214yes—
175#2454C2214yes—
176#2450C2214yes—
177#2449C2214yes—
178#2448C2212yes—
179#2447C2212yes—
180#2447C2212yes—
181#2446C2212yes—
182#2445C2212yes—
183#2445C2212yes—
184#2445C2212yes—
185#2445C2212yes—
186#2445C2212yes—
187#2443C2214yes—
188#2443C2214yes—
189#2443C2214yes—
190#2443C2214yes—
191#2432C2212yes—
192#2430C2214yes—
193#2427C2212yes—
194#2420C2212yes—
195#2419C2214yes—
196#2417C2214yes—
197#2416C2214yes—
198#2416C2214yes—
199#2413C2214yes—
200#2407C2214yes—
201#2407C2214yes—
202#2406C2214yes—
203#2406C2214yes—
204#2399C2212yes—
205#2399C2212yes—
206#2399C2212yes—
207#2388C2214yes—
208#2376C2214yes—
209#2376C2214yes—
210#2370C2212yes—
211#2369C2211yescharacteristic
212#2367C2212yes—
213#2367C2212yes—
214#2367C2212yes—
215#2367C2212yes—
216#2367C2214yes—
217#2366C2212yes—
218#2366C2212yes—
219#2360C2214yes—
220#2360C2212yes—
221Q8×C4⋊C4C2211yescharacteristic
222Q8×C4⋊C4C2212yes—
223D4×C4⋊C4C2211yescharacteristic
224D4×C4⋊C4C2212yes—
225D4×C4⋊C4C2212yes—
226D4×C4⋊C4C2214yes—
227D4×C4⋊C4C2212yes—
228#2345C2212yes—
229#2332C2214yes—
230#2330C2212yes—
231#2329C2214yes—
232#2328C2212yes—
233#2326C2212yes—
234#2326C2212yes—
235#2326C2214yes—
236#2326C2212yes—
237#2326C2212yes—
238#2322C2214yes—
239#2322C2214yes—
240#2319C2212yes—
241#2319C2212yes—
242#2319C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2212yes—
246C4×#127C2211yescharacteristic
247C4×#127C2212yes—
248C4×#127C2212yes—
249C4×C22⋊Q8C2212yes—
250#2297C2212yes—
251#2295C2211yescharacteristic
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2295C2212yes—
255#2295C2212yes—
256C2×#389C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2314yes—
261#559—216no—
262#559—48no—
263#556—44no—
264#554—28no—
265#554—48no—
266#550—44no—
267#550—48no—
268#547—416no—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×#127C2311yescharacteristic
274C2×#127C2312yes—
275C2×#127C2312yes—
276C2×#127C2312yes—
277C2×#127C2311yescharacteristic
278C2×#127C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2314yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×#121C2312yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2314yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2314yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×#117C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2314yes—
357C22×C4⋊C4C2314yes—
358C22×C4⋊C4C2314yes—
359C22×C4⋊C4C2312yes—
360C22×C42C2312yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#395C2312yes—
415#395C2314yes—
416#395C2312yes—
417#395C2312yes—
418#395C2312yes—
419#395C2312yes—
420#395C2312yes—
421#395C2312yes—
422#395C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#393C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2314yes—
464#392C2314yes—
465#392C2314yes—
466#392C2314yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2311yescharacteristic
471#391C2312yes—
472#391C2311yescharacteristic
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2311yescharacteristic
484#391C2311yescharacteristic
485#391C2312yes—
486#391C2311yescharacteristic
487#391C2312yes—
488#391C2311yescharacteristic
489#390C2314yes—
490#390C2312yes—
491#390C2314yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2314yes—
497#390C2312yes—
498#390C2314yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2314yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2312yes—
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2312yes—
514#390C2314yes—
515#390C2314yes—
516#390C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2311yescharacteristic
543#389C2311yescharacteristic
544#389C2312yes—
545#389C2314yes—
546#389C2311yescharacteristic
547#389C2311yescharacteristic
548#389C2312yes—
549#389C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
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#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2312yes—
594#387C2314yes—
595#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2312yes—
600#387C2314yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2314yes—
606#387C2312yes—
607#387C2314yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#384C2312yes—
658#384C2311yescharacteristic
659#384C2312yes—
660#384C2311yescharacteristic
661#384C2311yescharacteristic
662#384C2312yes—
663#384C2312yes—
664#384C2314yes—
665#382C2312yes—
666#382C2312yes—
667#382C2312yes—
668#381C2314yes—
669#381C2314yes—
670#381C2314yes—
671#381C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2312yes—
679#380C2312yes—
680#380C2314yes—
681#380C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2312yes—
715#376C2314yes—
716#376C2312yes—
717C2×#95C2314yes—
718C43C2312yes—
719C43C2311yescharacteristic
720C2×#41—28no—
721C2×#41—44no—
722C2×#41—48no—
723C2×#41—48no—
724C2×#41—82no—
725C2×#41—84no—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×Q8C2411yescharacteristic
733C22×Q8C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2411yescharacteristic
738C22×D4C2414yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2414yes—
743C22×D4C2412yes—
744C22×D4C2414yes—
745C22×D4C2412yes—
746C22×D4C2412yes—
747C22×D4C2414yes—
748C22×D4C2414yes—
749C23×C4C2412yes—
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2414yes—
754C23×C4C2414yes—
755C23×C4C2414yes—
756C23×C4C2414yes—
757C23×C4C2412yes—
758C23×C4C2414yes—
759C23×C4C2414yes—
760C4⋊Q8—28no—
761C4⋊Q8—24no—
762C4⋊Q8—24no—
763C4⋊Q8—42no—
764#127—28no—
765#127—28no—
766#127—28no—
767#127—24no—
768#127—44no—
769#127—42no—
770#126—48no—
771#126—84no—
772#125—28no—
773#125—48no—
774#124—216no—
775#124—28no—
776#124—28no—
777#124—28no—
778#124—28no—
779#124—44no—
780#124—48no—
781#124—82no—
782#124—82no—
783#124—84no—
784#123—216no—
785#123—216no—
786#123—48no—
787#123—48no—
788#123—48no—
789#123—48no—
790#123—48no—
791#123—48no—
792#123—84no—
793C22⋊Q8—28no—
794C22⋊Q8—216no—
795C22⋊Q8—216no—
796C22⋊Q8—44no—
797C22⋊Q8—48no—
798C22⋊Q8—48no—
799C22⋊Q8—48no—
800C22⋊Q8—82no—
801C22⋊Q8—84no—
802#121—48no—
803#121—48no—
804#121—48no—
805#121—48no—
806#121—48no—
807#121—44no—
808#121—48no—
809#121—82no—
810#121—84no—
811#121—84no—
812#121—82no—
813C4×Q8—28no—
814C4×Q8—24no—
815C4×Q8—44no—
816C4×Q8—42no—
817C4×Q8—42no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×Q8—44no—
821C4×Q8—44no—
822C4×Q8—82no—
823C4×Q8#4118yescomplemented
824C4×D4—24no—
825C4×D4—28no—
826C4×D4—216no—
827C4×D4—24no—
828C4×D4—28no—
829C4×D4—28no—
830C4×D4—28no—
831C4×D4—24no—
832C4×D4—44no—
833C4×D4—48no—
834C4×D4—44no—
835C4×D4—44no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—48no—
839C4×D4—48no—
840C4×D4—48no—
841C4×D4—82no—
842C4×D4—84no—
843C4×D4—84no—
844C4×D4—84no—
845#117—44no—
846C2×C4⋊C4—28no—
847C2×C4⋊C4—48no—
848C2×C4⋊C4—48no—
849C2×C4⋊C4—48no—
850C2×C4⋊C4—82no—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2411yescharacteristic
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2411yescharacteristic
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
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×C42—82no—
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2411yescharacteristic
971C2×C42C2414yes—
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2411yescharacteristic
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2414yes—
980C2×C42C2412yes—
981C2×C42C2414yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047C24C2514yes—
1048C24C2514yes—
1049C24C2512yes—
1050#41—816no—
1051#41—832no—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—24no—
1056C2×Q8—22no—
1057C2×Q8—24no—
1058C2×Q8—22no—
1059C2×Q8—41no—
1060C2×Q8—42no—
1061C2×Q8—41no—
1062C2×Q8—41no—
1063C2×Q8—41no—
1064C2×Q8—42no—
1065C2×Q8—42no—
1066C2×Q8—41no—
1067C2×Q8—42no—
1068C2×Q8—41no—
1069C2×Q8—42no—
1070C2×Q8—41no—
1071C2×Q8—41no—
1072C2×Q8—42no—
1073C2×Q8—42no—
1074C2×Q8C2×#4114yes—
1075C2×Q8H(5,𝔽2)14yes—
1076C2×D4—28no—
1077C2×D4—28no—
1078C2×D4—28no—
1079C2×D4—28no—
1080C2×D4—22no—
1081C2×D4—28no—
1082C2×D4—24no—
1083C2×D4—24no—
1084C2×D4—28no—
1085C2×D4—24no—
1086C2×D4—24no—
1087C2×D4—28no—
1088C2×D4—24no—
1089C2×D4—22no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—24no—
1093C2×D4—24no—
1094C2×D4—42no—
1095C2×D4—44no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—42no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—42no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—42no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—42no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—42no—
1116C2×D4—42no—
1117C2×D4—44no—
1118C2×D4—42no—
1119C2×D4—44no—
1120C2×D4H(5,𝔽2)14yes—
1121C22×C4—24no—
1122C22×C4—28no—
1123C22×C4—24no—
1124C22×C4—24no—
1125C22×C4—28no—
1126C22×C4—28no—
1127C22×C4—28no—
1128C22×C4—28no—
1129C22×C4—28no—
1130C22×C4—24no—
1131C22×C4—42no—
1132C22×C4—42no—
1133C22×C4—42no—
1134C22×C4—42no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—42no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2514yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2514yes—
1167C22×C4C2514yes—
1168C22×C4C2514yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2511yescharacteristic
1177C22×C4C2511yescharacteristic
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C4⋊C4—28no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—22no—
1184C4⋊C4—24no—
1185C4⋊C4—28no—
1186C4⋊C4—28no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—28no—
1190C4⋊C4—24no—
1191C4⋊C4—28no—
1192C4⋊C4—24no—
1193C4⋊C4—22no—
1194C4⋊C4—24no—
1195C4⋊C4—28no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—24no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—41no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—41no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—41no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—44no—
1220C4⋊C4—42no—
1221C4⋊C4—44no—
1222C4⋊C4—41no—
1223C4⋊C4—42no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—44no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—44no—
1231C4⋊C4—42no—
1232C4⋊C4—41no—
1233C4⋊C4—41no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4C2×#4114yes—
1244C4⋊C4C2×#4118yes—
1245C22⋊C4—28no—
1246C22⋊C4—28no—
1247C22⋊C4—24no—
1248C22⋊C4—28no—
1249C22⋊C4—24no—
1250C22⋊C4—28no—
1251C22⋊C4—28no—
1252C22⋊C4—28no—
1253C22⋊C4—28no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—28no—
1259C22⋊C4—24no—
1260C22⋊C4—28no—
1261C22⋊C4—28no—
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—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
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—
1292C42—28no—
1293C42—24no—
1294C42—22no—
1295C42—24no—
1296C42—24no—
1297C42—22no—
1298C42—24no—
1299C42—24no—
1300C42—24no—
1301C42—41no—
1302C42—42no—
1303C42—42no—
1304C42—42no—
1305C42—41no—
1306C42—42no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—42no—
1311C42—41no—
1312C42—42no—
1313C42—44no—
1314C42—44no—
1315C42C2×#4114yes—
1316C42C2×#4118yes—
1317C422−1+414yes—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—22no—
1323C23—22no—
1324C23—24no—
1325C23—24no—
1326C23—24no—
1327C23—24no—
1328C23—24no—
1329C23—24no—
1330C23—24no—
1331C23—24no—
1332C23—24no—
1333C23—24no—
1334C23—24no—
1335C23—24no—
1336C23—24no—
1337C23—24no—
1338C23C2×H(5,𝔽2)14yes—
1339C23C2611yescharacteristic
1340Q8—44no—
1341Q8—44no—
1342Q8—48no—
1343Q8—48no—
1344Q8—84no—
1345Q8—82no—
1346Q8—82no—
1347Q8—84no—
1348D4—28no—
1349D4—416no—
1350D4—416no—
1351D4—48no—
1352D4—48no—
1353D4—48no—
1354D4—88no—
1355D4—84no—
1356D4—84no—
1357D4—88no—
1358D4—88no—
1359D4—88no—
1360D4—88no—
1361D4—162no—
1362D4—164no—
1363C2×C4—21no—
1364C2×C4—22no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—21no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—21no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—48no—
1431C2×C4—48no—
1432C2×C4—88no—
1433C2×C4—88no—
1434C2×C4—88no—
1435C2×C4—84no—
1436C2×C4—88no—
1437C2×C4—88no—
1438C2×C4—88no—
1439C2×C4—88no—
1440C2×C4—164no—
1441C2×C4C22×#4114yes—
1442C2×C4C22×#4112yes—
1443C2×C4C22×#4112yes—
1444C2×C4C22×#4114yes—
1445C2×C4C22×#4112yes—
1446C2×C4C2×H(5,𝔽2)12yes—
1447C2×C4C2×H(5,𝔽2)14yes—
1448C2×C4C2×H(5,𝔽2)12yes—
1449C2×C4C2×2−1+412yes—
1450C2×C4C2×2−1+412yes—
1451C2×C4C2×2−1+412yes—
1452C22—24no—
1453C22—24no—
1454C22—24no—
1455C22—42no—
1456C22—42no—
1457C22—42no—
1458C22—42no—
1459C22—44no—
1460C22—44no—
1461C22—44no—
1462C22—44no—
1463C22—44no—
1464C22—44no—
1465C22—44no—
1466C22—44no—
1467C22—44no—
1468C22—44no—
1469C22—44no—
1470C22—44no—
1471C22—44no—
1472C22—44no—
1473C22C23×#4111yescharacteristic
1474C22C22×H(5,𝔽2)11yescharacteristic
1475C22C22×H(5,𝔽2)11yescharacteristic
1476C22C22×2−1+411yescharacteristic
1477C22H(7,𝔽2)11yescharacteristic
1478C22H(7,𝔽2)11yescharacteristic
1479C222−1+611yescharacteristic
1480C4—24no—
1481C4—22no—
1482C4—22no—
1483C4—24no—
1484C4—22no—
1485C4—22no—
1486C4—24no—
1487C4—22no—
1488C4—44no—
1489C4—44no—
1490C4—44no—
1491C4—42no—
1492C4—42no—
1493C4—41no—
1494C4—42no—
1495C4—42no—
1496C4—42no—
1497C4—42no—
1498C4—42no—
1499C4—42no—
1500C4—44no—
1501C4—42no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4#352214yes—
1506C2—44no—
1507C2—84no—
1508C2—84no—
1509C2C2×#352211yescharacteristic
1510C2#6284511yescharacteristic
1511C2#6288111yescharacteristic
1512C2#6289211yescharacteristic
1513C2#6291311yescharacteristic
1514C2#6298611yescharacteristic
1515C2#6304911yescharacteristic
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. #59823C2semidirect
2. #59815C2semidirect
3. #52287C2semidirect
4. #51924C2semidirect
5. #49414C2semidirect
6. #48619C2semidirect
7. #46983C2semidirect
8. #46090C2semidirect
9. #45354C2semidirect
10. #44966C2semidirect
11. #44964C2semidirect
12. #43119C2semidirect
13. #42699C2semidirect
14. #42524C2semidirect
15. #42130C2semidirect
16. #40023C2semidirect
17. #39808C2semidirect
18. #39765C2semidirect
19. #39739C2semidirect
20. #39161C2semidirect
21. #38820C2semidirect
22. #38425C2semidirect
23. #37219C2semidirect
24. #36419C2semidirect
25. #35930C2semidirect
26. #35561C2semidirect
27. #35197C2semidirect
28. #34498C2semidirect
29. #34332C2semidirect
823. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598232
#598152
#522872
#519242
#494142
#486192
#469832
#460902
#453542
#449662
#449642
#431192
#426992
#425242
#421302
#400232
#398082
#397652
#397392
#391612
#388202
#384252
#372192
#364192
#359302
#355612
#351972
#344982
#343322