Finite Group Databasebeta

← #8096607

Subgroups — #8096607

Order 512.

4009 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53124C212yesmaximal, complemented
2#53049C212yesmaximal
3#53029C212yesmaximal, complemented
4#52523C214yesmaximal, complemented
5#52516C214yesmaximal, complemented
6#52447C214yesmaximal, complemented
7#52306C211yesmaximal, characteristic, complemented
8#52281C212yesmaximal, complemented
9#46341C212yesmaximal, complemented
10#46295C212yesmaximal, complemented
11#46177C214yesmaximal, complemented
12#46153C211yesmaximal, characteristic, complemented
13#46109C212yesmaximal, complemented
14#46079C212yesmaximal, complemented
15#46023C211yesmaximal, characteristic, complemented
16#46022C211yesmaximal, characteristic, complemented
17#45963C214yesmaximal, complemented
18#45911C214yesmaximal, complemented
19#45807C212yesmaximal, complemented
20#45794C212yesmaximal, complemented
21#36554C212yesmaximal, complemented
22#36535C212yesmaximal, complemented
23#36454C211yesmaximal, characteristic, complemented
24#36453C211yesmaximal, characteristic
25#36407C211yesmaximal, characteristic, complemented
26#36298C212yesmaximal, complemented
27#35838C212yesmaximal, complemented
28#35788C212yesmaximal, complemented
29#35720C212yesmaximal, complemented
30#2865C2214yes—
31#2864C2214yes—
32#2863C2212yes—
33#2863C2214yes—
34#2862C2211yescharacteristic
35#2860C2212yes—
36#2859C2212yes—
37#2859C2211yescharacteristic
38#2859C2211yescharacteristic
39#2857C2212yes—
40#2855C2212yes—
41#2855C2212yes—
42#2845C2212yes—
43#2841C2214yes—
44#2839C2214yes—
45#2838C2214yes—
46#2837C2214yes—
47#2837C2214yes—
48#2837C2214yes—
49#2837C2214yes—
50#2836C2214yes—
51#2836C2214yes—
52#2836C2214yes—
53#2833C2214yes—
54#2830C2214yes—
55#2830C2214yes—
56#2822C2212yes—
57#2821C2214yes—
58#2820C2212yes—
59#2816C2214yes—
60#2809C2211yescharacteristic
61#2809C2212yes—
62#2808C2212yes—
63#2808C2214yes—
64#2806C2212yes—
65#2805C2212yes—
66#2793C2214yes—
67#2791C2214yes—
68#2786C2214yes—
69#2777C2214yes—
70#2777C2214yes—
71#2776C2214yes—
72#2775C2214yes—
73#2775C2212yes—
74#2775C2212yes—
75#2773C2214yes—
76#2773C2214yes—
77#2773C2214yes—
78#2772C2214yes—
79#2772C2214yes—
80#2770C2214yes—
81#2769C2212yes—
82#2766C2214yes—
83#2766C2214yes—
84#2762C2214yes—
85#2762C2214yes—
86#2754C2214yes—
87#2744C2214yes—
88#2741C2214yes—
89#2739C2214yes—
90#2734C2211yescharacteristic
91#2734C2214yes—
92#2731C2212yes—
93#2727C2214yes—
94#2727C2211yescharacteristic
95#2727C2211yescharacteristic
96#2726C2214yes—
97#2726C2214yes—
98#2726C2212yes—
99#2726C2212yes—
100#2723C2214yes—
101#2721C2212yes—
102#2721C2214yes—
103#2721C2212yes—
104#2716C2214yes—
105#2716C2214yes—
106#2711C2214yes—
107#2704C2214yes—
108#2702C2214yes—
109#2698C2214yes—
110#2689C2214yes—
111#2677C2214yes—
112#2667C2214yes—
113#2653C2214yes—
114#2652C2214yes—
115#2628C2212yes—
116#2625C2212yes—
117#2620C2212yes—
118#2607C2214yes—
119#2594C2214yes—
120#2592C2212yes—
121#2590C2214yes—
122#2590C2214yes—
123#2590C2214yes—
124#2590C2214yes—
125#2589C2214yes—
126#2588C2214yes—
127#2588C2214yes—
128#2588C2214yes—
129#2585C2214yes—
130#2585C2214yes—
131#2581C2212yes—
132#2581C2212yes—
133#2576C2214yes—
134#2575C2214yes—
135#2575C2214yes—
136#2574C2214yes—
137#2574C2214yes—
138#2574C2214yes—
139#2571C2212yes—
140#2570C2214yes—
141#2565C2212yes—
142#2565C2212yes—
143#2556C2214yes—
144#2552C2211yescharacteristic
145#2552C2212yes—
146#2552C2212yes—
147#2551C2211yescharacteristic
148#2550C2212yes—
149#2550C2214yes—
150#2547C2211yescharacteristic
151#2546C2212yes—
152#2542C2211yescharacteristic
153#2538C2211yescharacteristic
154#2537C2211yescharacteristic
155#2525C2214yes—
156#2525C2214yes—
157#2522C2214yes—
158#2522C2214yes—
159#2520C2214yes—
160#2520C2214yes—
161#2518C2214yes—
162#2517C2214yes—
163#2517C2214yes—
164#2516C2214yes—
165#2514C2212yes—
166#2513C2212yes—
167#2511C2212yes—
168#2511C2212yes—
169#2509C2214yes—
170#2508C2212yes—
171#2507C2212yes—
172#2507C2212yes—
173#2507C2212yes—
174#2507C2212yes—
175#2500C2212yes—
176#2499C2212yes—
177#2496C2212yes—
178#2494C2212yes—
179#2494C2212yes—
180#2492C2212yes—
181#2490C2212yes—
182#2489C2212yes—
183#2489C2212yes—
184#2479C2214yes—
185#2478C2214yes—
186#2478C2214yes—
187#2475C2214yes—
188#2468C2214yes—
189#2466C2214yes—
190#2460C2214yes—
191#2460C2214yes—
192#2454C2212yes—
193#2453C2212yes—
194#2452C2212yes—
195#2451C2212yes—
196#2451C2214yes—
197#2448C2212yes—
198#2447C2212yes—
199#2446C2212yes—
200#2441C2212yes—
201#2441C2212yes—
202#2441C2212yes—
203#2439C2212yes—
204#2439C2214yes—
205#2439C2212yes—
206#2429C2212yes—
207#2427C2212yes—
208#2426C2212yes—
209#2423C2212yes—
210#2423C2212yes—
211#2421C2212yes—
212#2420C2212yes—
213#2415C2212yes—
214#2396C2212yes—
215#2396C2214yes—
216#2396C2212yes—
217#2395C2214yes—
218#2395C2214yes—
219#2395C2212yes—
220#2382C2212yes—
221#2382C2212yes—
222#2382C2212yes—
223#2382C2214yes—
224#2378C2214yes—
225#2378C2214yes—
226#2370C2212yes—
227#2370C2212yes—
228#2369C2212yes—
229#2367C2212yes—
230#2365C2211yescharacteristic
231#2365C2211yescharacteristic
232#2361C2212yes—
233#2360C2212yes—
234#2360C2212yes—
235#2355C2211yescharacteristic
236#2355C2212yes—
237#2355C2212yes—
238#2355C2212yes—
239#2354C2211yescharacteristic
240#2354C2211yescharacteristic
241D4×C4⋊C4C2211yescharacteristic
242#2345C2212yes—
243#2344C2212yes—
244C4×C4⋊Q8C2212yes—
245C4×#125C2211yescharacteristic
246C4×#125C2214yes—
247C4×#125C2211yescharacteristic
248C4×#126C2212yes—
249C4×#126C2214yes—
250C4×#126C2212yes—
251C4×#124C2211yescharacteristic
252C4×C22⋊Q8C2212yes—
253C4×#121C2212yes—
254#2296C2212yes—
255#2293C2214yes—
256#2274C2212yes—
257C42×Q8C2212yes—
258C42×D4C2211yescharacteristic
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2314yes—
264C2×C4⋊Q8C2312yes—
265C2×#126C2312yes—
266C2×#126C2312yes—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#125C2311yescharacteristic
270C2×#125C2311yescharacteristic
271C2×#125C2314yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#124C2311yescharacteristic
278C2×#124C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2314yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2312yes—
299C2×#117C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2314yes—
303C2×#117C2312yes—
304C22×C4⋊C4C2312yes—
305C22×C42C2312yes—
306#401C2314yes—
307#401C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2312yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2312yes—
337#399C2312yes—
338#399C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2312yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2312yes—
403#396C2312yes—
404#396C2312yes—
405#396C2312yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2314yes—
412#395C2312yes—
413#395C2314yes—
414#394C2312yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2312yes—
425#393C2314yes—
426#393C2314yes—
427#393C2312yes—
428#393C2314yes—
429#393C2314yes—
430#393C2312yes—
431#393C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2314yes—
444#391C2312yes—
445#391C2311yescharacteristic
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#390C2314yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2311yescharacteristic
462#389C2312yes—
463#389C2311yescharacteristic
464#389C2311yescharacteristic
465#389C2314yes—
466#389C2311yescharacteristic
467#389C2311yescharacteristic
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#388C2312yes—
515#388C2314yes—
516#388C2312yes—
517#388C2312yes—
518#388C2314yes—
519#388C2312yes—
520#388C2314yes—
521#388C2312yes—
522#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2312yes—
546#388C2314yes—
547#387C2312yes—
548#387C2314yes—
549#387C2312yes—
550#387C2314yes—
551#387C2312yes—
552#387C2312yes—
553#387C2314yes—
554#387C2312yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2312yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2312yes—
564#387C2314yes—
565#387C2314yes—
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#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#386C2314yes—
611#386C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2312yes—
623#384C2312yes—
624#384C2312yes—
625#384C2311yescharacteristic
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#384C2312yes—
629#383C2314yes—
630#383C2312yes—
631#383C2312yes—
632#383C2314yes—
633#382C2314yes—
634#382C2311yescharacteristic
635#382C2311yescharacteristic
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2314yes—
641#382C2312yes—
642#382C2314yes—
643#382C2312yes—
644#382C2312yes—
645#382C2311yescharacteristic
646#382C2314yes—
647#382C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2314yes—
651#380C2312yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C43C2312yes—
710C43C2314yes—
711C43C2311yescharacteristic
712C22×Q8C2412yes—
713C22×Q8C2411yescharacteristic
714C22×Q8C2412yes—
715C22×Q8C2412yes—
716C22×Q8C2414yes—
717C22×D4C2411yescharacteristic
718C22×D4C2411yescharacteristic
719C22×D4C2414yes—
720C23×C4C2412yes—
721C23×C4C2412yes—
722C23×C4C2414yes—
723C23×C4C2412yes—
724C23×C4C2412yes—
725C4⋊Q8—44no—
726C4⋊Q8—42no—
727C4⋊Q8—42no—
728C4⋊Q8—44no—
729C4⋊Q8—82no—
730C4⋊Q8—84no—
731#126—28no—
732#126—44no—
733#126—84no—
734#126—84no—
735#125—24no—
736#125—44no—
737#125—44no—
738#125—44no—
739#125—42no—
740#125—44no—
741#125—48no—
742#125—48no—
743#124—44no—
744#124—42no—
745C22⋊Q8—28no—
746C22⋊Q8—48no—
747C22⋊Q8—44no—
748C22⋊Q8—44no—
749C22⋊Q8—82no—
750C22⋊Q8—82no—
751#121—44no—
752#121—44no—
753C4×Q8—28no—
754C4×Q8—44no—
755C4×Q8—42no—
756C4×Q8—44no—
757C4×Q8—44no—
758C4×Q8—82no—
759C4×D4—24no—
760C4×D4—42no—
761C4×D4—42no—
762C4×D4—42no—
763C4×D4—48no—
764C4×D4—82no—
765#117—44no—
766#117—44no—
767#117—44no—
768#117—82no—
769#117—84no—
770C2×C4⋊C4—28no—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2411yescharacteristic
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C42—82no—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2411yescharacteristic
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2412yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988C24C2512yes—
989C24C2512yes—
990C2×Q8—24no—
991C2×Q8—24no—
992C2×Q8—24no—
993C2×Q8—24no—
994C2×Q8—22no—
995C2×Q8—41no—
996C2×Q8—42no—
997C2×Q8—42no—
998C2×Q8—41no—
999C2×Q8—42no—
1000C2×Q8—42no—
1001C2×Q8—42no—
1002C2×Q8—44no—
1003C2×Q8—44no—
1004C2×Q8—44no—
1005C2×D4—22no—
1006C2×D4—22no—
1007C2×D4—22no—
1008C2×D4—22no—
1009C2×D4—41no—
1010C2×D4—41no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—28no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—44no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4C2511yescharacteristic
1030C22×C4C2514yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C4⋊C4—28no—
1057C4⋊C4—24no—
1058C4⋊C4—28no—
1059C4⋊C4—28no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—22no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—22no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—22no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—41no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—44no—
1086C4⋊C4—41no—
1087C4⋊C4—42no—
1088C4⋊C4—41no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—41no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—41no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—41no—
1132C4⋊C42−1+414yes—
1133C4⋊C42−1+414yes—
1134C22⋊C4—24no—
1135C22⋊C4—28no—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—42no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
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—42no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4—42no—
1166C22⋊C4—42no—
1167C42—22no—
1168C42—24no—
1169C42—28no—
1170C42—22no—
1171C42—24no—
1172C42—24no—
1173C42—24no—
1174C42—22no—
1175C42—22no—
1176C42—24no—
1177C42—24no—
1178C42—22no—
1179C42—22no—
1180C42—41no—
1181C42—42no—
1182C42—42no—
1183C42—42no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C42—42no—
1194C42—42no—
1195C42—44no—
1196C42—42no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23C2611yescharacteristic
1212Q8—48no—
1213Q8—82no—
1214Q8—84no—
1215Q8—84no—
1216Q8—164no—
1217D4—44no—
1218D4—44no—
1219D4—88no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—48no—
1294C2×C4—48no—
1295C2×C4—84no—
1296C2×C4—88no—
1297C2×C4—84no—
1298C2×C4C2×2−1+414yes—
1299C2×C4C2×2−1+414yes—
1300C2×C4C2×2−1+412yes—
1301C2×C4C2×2−1+412yes—
1302C2×C4#58512yes—
1303C2×C4#58512yes—
1304C2×C4#58512yes—
1305C2×C4#58512yes—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22C22×2−1+411yescharacteristic
1321C22C22×2−1+411yescharacteristic
1322C22C2×#58511yescharacteristic
1323C22C2×#58511yescharacteristic
1324C22C2×#58511yescharacteristic
1325C22C2×#58511yescharacteristic
1326C22H(7,𝔽2)11yescharacteristic
1327C4—24no—
1328C4—22no—
1329C4—22no—
1330C4—24no—
1331C4—22no—
1332C4—41no—
1333C4—42no—
1334C4—44no—
1335C4—44no—
1336C4—41no—
1337C4—42no—
1338C4—41no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—42no—
1345C4—44no—
1346C4—42no—
1347C4—44no—
1348C4—42no—
1349C4—44no—
1350C4—42no—
1351C4—42no—
1352C4—44no—
1353C4#353114yes—
1354C2—82no—
1355C2—82no—
1356C2C2×#353111yescharacteristic
1357C2#6290811yescharacteristic
1358C2#6294811yescharacteristic
1359C2#6296211yescharacteristic
1360C2#6303111yescharacteristic
1361C2#6303211yescharacteristic
1362C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53124C2semidirect
3. #53029C2semidirect
4. #52523C2semidirect
5. #52516C2semidirect
6. #52447C2semidirect
7. #52306C2semidirect
8. #52281C2semidirect
9. #46341C2semidirect
10. #46295C2semidirect
11. #46177C2semidirect
12. #46153C2semidirect
13. #46109C2semidirect
14. #46079C2semidirect
15. #46023C2semidirect
16. #46022C2semidirect
17. #45963C2semidirect
18. #45911C2semidirect
19. #45807C2semidirect
20. #45794C2semidirect
21. #36554C2semidirect
22. #36535C2semidirect
23. #36454C2semidirect
25. #36407C2semidirect
26. #36298C2semidirect
27. #35838C2semidirect
28. #35788C2semidirect
29. #35720C2semidirect

Maximal subgroups

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

subgroupindex
#531242
#530492
#530292
#525232
#525162
#524472
#523062
#522812
#463412
#462952
#461772
#461532
#461092
#460792
#460232
#460222
#459632
#459112
#458072
#457942
#365542
#365352
#364542
#364532
#364072
#362982
#358382
#357882
#357202