Finite Group Databasebeta

← #8678559

Subgroups — #8678559

Order 512.

4321 conjugacy classes of subgroups.

The subgroup lattice has 1387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59454C212yesmaximal, complemented
2#59264C212yesmaximal, complemented
3#59209C212yesmaximal, complemented
4#58533C214yesmaximal, complemented
5#58311C214yesmaximal, complemented
6#55262C214yesmaximal, complemented
7#53219C212yesmaximal, complemented
8#52304C211yesmaximal, characteristic, complemented
9#50139C214yesmaximal, complemented
10#49277C214yesmaximal, complemented
11#47875C214yesmaximal, complemented
12#46157C211yesmaximal, characteristic, complemented
13#46153C211yesmaximal, characteristic, complemented
14#46147C211yesmaximal, characteristic, complemented
15#45426C212yesmaximal, complemented
16#45181C212yesmaximal, complemented
17#45027C212yesmaximal, complemented
18#42728C212yesmaximal, complemented
19#42587C212yesmaximal, complemented
20#42496C212yesmaximal, complemented
21#39623C212yesmaximal, complemented
22#39400C212yesmaximal
23#39376C212yesmaximal, complemented
24#39157C212yesmaximal, complemented
25#38781C212yesmaximal, complemented
26#38447C212yesmaximal, complemented
27#36453C211yesmaximal, characteristic
28#36407C211yesmaximal, characteristic, complemented
29#36290C211yesmaximal, characteristic, complemented
30C2×#563C2212yes—
31C2×#539C2214yes—
32#2859C2211yescharacteristic
33#2859C2211yescharacteristic
34#2859C2211yescharacteristic
35#2857C2212yes—
36#2857C2212yes—
37#2855C2212yes—
38#2851C2212yes—
39#2845C2212yes—
40#2841C2214yes—
41#2839C2214yes—
42#2833C2214yes—
43#2822C2212yes—
44#2822C2212yes—
45#2810C2212yes—
46#2806C2214yes—
47#2805C2211yescharacteristic
48#2805C2211yescharacteristic
49#2802C2214yes—
50#2794C2214yes—
51#2792C2214yes—
52#2792C2214yes—
53#2791C2214yes—
54#2790C2214yes—
55#2790C2214yes—
56#2789C2212yes—
57#2788C2214yes—
58#2787C2214yes—
59#2776C2214yes—
60#2771C2214yes—
61#2770C2214yes—
62#2767C2214yes—
63#2766C2214yes—
64#2765C2212yes—
65#2765C2212yes—
66#2765C2214yes—
67#2765C2214yes—
68#2764C2214yes—
69#2762C2214yes—
70#2762C2214yes—
71#2755C2214yes—
72#2755C2214yes—
73#2747C2214yes—
74#2745C2214yes—
75#2742C2214yes—
76#2738C2214yes—
77#2734C2212yes—
78#2734C2214yes—
79#2729C2214yes—
80#2726C2214yes—
81#2726C2212yes—
82#2726C2212yes—
83#2726C2214yes—
84#2726C2212yes—
85#2724C2212yes—
86#2724C2211yescharacteristic
87#2722C2214yes—
88#2722C2214yes—
89#2719C2214yes—
90#2717C2212yes—
91#2713C2214yes—
92#2713C2214yes—
93#2708C2214yes—
94#2698C2214yes—
95#2698C2214yes—
96#2698C2214yes—
97#2695C2214yes—
98#2695C2214yes—
99#2690C2212yes—
100#2690C2212yes—
101#2690C2214yes—
102#2689C2214yes—
103#2689C2214yes—
104#2689C2214yes—
105#2687C2214yes—
106#2687C2214yes—
107#2683C2211yescharacteristic
108#2677C2214yes—
109#2666C2214yes—
110#2665C2214yes—
111#2659C2214yes—
112#2655C2214yes—
113#2652C2214yes—
114#2647C2212yes—
115#2645C2214yes—
116#2638C2214yes—
117#2627C2214yes—
118#2621C2214yes—
119#2609C2214yes—
120#2606C2214yes—
121#2589C2214yes—
122#2588C2214yes—
123#2583C2214yes—
124#2580C2212yes—
125#2576C2214yes—
126#2574C2214yes—
127#2571C2212yes—
128#2571C2211yescharacteristic
129#2570C2212yes—
130#2570C2212yes—
131#2567C2212yes—
132#2567C2212yes—
133#2564C2214yes—
134#2556C2214yes—
135#2553C2214yes—
136#2553C2214yes—
137#2552C2211yescharacteristic
138#2552C2212yes—
139#2552C2212yes—
140#2552C2211yescharacteristic
141#2551C2212yes—
142#2551C2211yescharacteristic
143#2550C2214yes—
144#2546C2212yes—
145#2538C2211yescharacteristic
146#2537C2211yescharacteristic
147#2530C2214yes—
148#2530C2214yes—
149#2520C2214yes—
150#2509C2212yes—
151#2509C2212yes—
152#2509C2212yes—
153#2508C2212yes—
154#2508C2212yes—
155#2507C2212yes—
156#2507C2212yes—
157#2507C2212yes—
158#2507C2212yes—
159#2507C2212yes—
160#2507C2212yes—
161#2507C2212yes—
162#2506C2212yes—
163#2506C2214yes—
164#2505C2214yes—
165#2496C2214yes—
166#2496C2212yes—
167#2496C2212yes—
168#2496C2212yes—
169#2496C2214yes—
170#2496C2212yes—
171#2495C2212yes—
172#2494C2212yes—
173#2494C2212yes—
174#2494C2212yes—
175#2493C2214yes—
176#2489C2214yes—
177#2486C2214yes—
178#2486C2212yes—
179#2486C2214yes—
180#2484C2214yes—
181#2477C2214yes—
182#2475C2214yes—
183#2473C2214yes—
184#2473C2214yes—
185#2473C2214yes—
186#2468C2214yes—
187#2466C2214yes—
188#2460C2214yes—
189#2460C2214yes—
190#2454C2212yes—
191#2452C2212yes—
192#2452C2212yes—
193#2450C2214yes—
194#2449C2214yes—
195#2442C2212yes—
196#2442C2212yes—
197#2442C2212yes—
198#2442C2212yes—
199#2441C2212yes—
200#2440C2214yes—
201#2440C2214yes—
202#2440C2212yes—
203#2440C2212yes—
204#2440C2212yes—
205#2440C2214yes—
206#2439C2212yes—
207#2438C2214yes—
208#2427C2212yes—
209#2422C2212yes—
210#2422C2212yes—
211#2420C2212yes—
212#2419C2214yes—
213#2419C2214yes—
214#2415C2214yes—
215#2401C2212yes—
216#2401C2212yes—
217#2399C2212yes—
218#2382C2212yes—
219#2382C2212yes—
220#2370C2212yes—
221#2370C2212yes—
222#2369C2212yes—
223#2361C2212yes—
224#2361C2212yes—
225#2359C2214yes—
226#2357C2212yes—
227#2355C2211yescharacteristic
228#2355C2212yes—
229#2354C2211yescharacteristic
230#2354C2211yescharacteristic
231#2349C2212yes—
232D4×C4⋊C4C2212yes—
233D4×C4⋊C4C2211yescharacteristic
234D4×C4⋊C4C2214yes—
235D4×C4⋊C4C2211yescharacteristic
236D4×C4⋊C4C2211yescharacteristic
237#2345C2212yes—
238#2345C2212yes—
239#2344C2212yes—
240#2343C2214yes—
241#2331C2212yes—
242#2330C2214yes—
243#2330C2212yes—
244#2329C2214yes—
245#2319C2212yes—
246C4×#125C2211yescharacteristic
247C4×#125C2211yescharacteristic
248C4×#124C2211yescharacteristic
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×#123C2212yes—
252C4×#121C2212yes—
253C4×#121C2212yes—
254#2296C2212yes—
255C2×#389C2212yes—
256C2×#389C2212yes—
257#2283C2212yes—
258C42×D4C2211yescharacteristic
259#563—48no—
260#539—416no—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2314yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2314yes—
266C2×#126C2314yes—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#125C2311yescharacteristic
271C2×#125C2312yes—
272C2×#125C2311yescharacteristic
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#124C2311yescharacteristic
281C2×#123C2314yes—
282C2×#123C2312yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×D4C2312yes—
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×#117C2312yes—
309C2×#117C2314yes—
310C2×#117C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2314yes—
317C22×C42C2312yes—
318C22×C42C2312yes—
319#401C2314yes—
320#401C2312yes—
321#401C2314yes—
322#401C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2312yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#399C2314yes—
353#399C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#397C2314yes—
394#397C2312yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2312yes—
403#397C2312yes—
404#397C2312yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2312yes—
414#396C2312yes—
415#396C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#395C2312yes—
428#395C2314yes—
429#395C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2312yes—
445#391C2311yescharacteristic
446#391C2312yes—
447#391C2314yes—
448#391C2314yes—
449#391C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2311yescharacteristic
454#389C2311yescharacteristic
455#389C2311yescharacteristic
456#389C2311yescharacteristic
457#389C2311yescharacteristic
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2312yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2312yes—
531#388C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2312yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2312yes—
608#385C2314yes—
609#385C2312yes—
610#385C2312yes—
611#385C2312yes—
612#385C2314yes—
613#384C2314yes—
614#384C2314yes—
615#384C2311yescharacteristic
616#384C2311yescharacteristic
617#384C2312yes—
618#384C2311yescharacteristic
619#384C2312yes—
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#384C2311yescharacteristic
624#384C2312yes—
625#383C2314yes—
626#383C2314yes—
627#382C2311yescharacteristic
628#382C2311yescharacteristic
629#382C2311yescharacteristic
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2314yes—
641#381C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2312yes—
646#381C2314yes—
647#381C2314yes—
648#380C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2314yes—
661#380C2314yes—
662#380C2312yes—
663#380C2312yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2312yes—
710#376C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C43C2311yescharacteristic
714C22×Q8C2411yescharacteristic
715C22×Q8C2412yes—
716C22×Q8C2414yes—
717C22×Q8C2414yes—
718C22×D4C2414yes—
719C22×D4C2411yescharacteristic
720C22×D4C2411yescharacteristic
721C23×C4C2412yes—
722C23×C4C2412yes—
723C23×C4C2412yes—
724C23×C4C2414yes—
725C23×C4C2412yes—
726C23×C4C2414yes—
727C23×C4C2412yes—
728C23×C4C2414yes—
729C23×C4C2412yes—
730C23×C4C2414yes—
731C4⋊Q8—44no—
732C4⋊Q8—44no—
733C4⋊Q8—48no—
734C4⋊Q8—82no—
735C4⋊Q8—84no—
736#126—48no—
737#126—48no—
738#126—48no—
739#126—48no—
740#125—28no—
741#125—24no—
742#125—42no—
743#125—44no—
744#125—44no—
745#125—44no—
746#125—48no—
747#125—48no—
748#125—48no—
749#125—82no—
750#124—24no—
751#123—28no—
752#123—216no—
753#123—48no—
754#123—48no—
755C22⋊Q8—28no—
756C22⋊Q8—48no—
757C22⋊Q8—48no—
758C22⋊Q8—48no—
759C22⋊Q8—48no—
760C22⋊Q8—44no—
761C22⋊Q8—48no—
762C22⋊Q8—84no—
763C22⋊Q8—82no—
764#121—28no—
765#121—28no—
766C4×Q8—44no—
767C4×Q8—42no—
768C4×D4—24no—
769C4×D4—28no—
770C4×D4—24no—
771C4×D4—44no—
772C4×D4—42no—
773C4×D4—42no—
774C4×D4—48no—
775C4×D4—48no—
776C4×D4—48no—
777C4×D4—82no—
778#117—28no—
779#117—82no—
780#117—84no—
781C2×C4⋊C4—28no—
782C2×C4⋊C4—44no—
783C2×C4⋊C4—44no—
784C2×C4⋊C4—48no—
785C2×C4⋊C4—82no—
786C2×C4⋊C4—84no—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C42—44no—
898C2×C42—82no—
899C2×C42C2414yes—
900C2×C42C2411yescharacteristic
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2411yescharacteristic
922C2×C42C2412yes—
923C2×C42C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001C24C2512yes—
1002C24C2512yes—
1003C2×Q8—22no—
1004C2×Q8—24no—
1005C2×Q8—42no—
1006C2×Q8—41no—
1007C2×Q8—42no—
1008C2×Q8—41no—
1009C2×Q8—44no—
1010C2×Q8—44no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—44no—
1015C2×D4—28no—
1016C2×D4—28no—
1017C2×D4—22no—
1018C2×D4—22no—
1019C2×D4—41no—
1020C2×D4—44no—
1021C2×D4—41no—
1022C2×D4H(5,𝔽2)14yes—
1023C2×D42−1+414yes—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—28no—
1027C22×C4—28no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—28no—
1036C22×C4—24no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—42no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—22no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—22no—
1099C4⋊C4—24no—
1100C4⋊C4—22no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—22no—
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—41no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—41no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—41no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—41no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—41no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C42−1+414yes—
1162C4⋊C42−1+414yes—
1163C22⋊C4—24no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—24no—
1167C22⋊C4—28no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—28no—
1172C22⋊C4—24no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—42no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C42—22no—
1192C42—28no—
1193C42—22no—
1194C42—22no—
1195C42—24no—
1196C42—22no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—22no—
1201C42—24no—
1202C42—22no—
1203C42—42no—
1204C42—42no—
1205C42—41no—
1206C42—42no—
1207C42—42no—
1208C42—42no—
1209C42—44no—
1210C42—44no—
1211C42—44no—
1212C42—44no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23C2×H(5,𝔽2)14yes—
1229C23C2×2−1+414yes—
1230C23C2611yescharacteristic
1231Q8—84no—
1232Q8—82no—
1233Q8—164no—
1234Q8—164no—
1235D4—28no—
1236D4—44no—
1237D4—416no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—48no—
1312C2×C4—48no—
1313C2×C4—48no—
1314C2×C4—84no—
1315C2×C4—84no—
1316C2×C4—88no—
1317C2×C4—88no—
1318C2×C4—84no—
1319C2×C4—88no—
1320C2×C4—164no—
1321C2×C4C2×H(5,𝔽2)12yes—
1322C2×C4C2×2−1+414yes—
1323C2×C4C2×2−1+412yes—
1324C2×C4C2×2−1+414yes—
1325C2×C4C2×2−1+412yes—
1326C2×C4C2×2−1+412yes—
1327C2×C4#58512yes—
1328C2×C4#58512yes—
1329C22—24no—
1330C22—24no—
1331C22—24no—
1332C22—24no—
1333C22—24no—
1334C22—24no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22C22×H(5,𝔽2)11yescharacteristic
1344C22C22×2−1+411yescharacteristic
1345C22C22×2−1+411yescharacteristic
1346C22C22×2−1+411yescharacteristic
1347C22C2×#58511yescharacteristic
1348C22C2×#58511yescharacteristic
1349C22H(7,𝔽2)11yescharacteristic
1350C4—24no—
1351C4—22no—
1352C4—22no—
1353C4—22no—
1354C4—24no—
1355C4—42no—
1356C4—41no—
1357C4—44no—
1358C4—42no—
1359C4—44no—
1360C4—41no—
1361C4—42no—
1362C4—42no—
1363C4—41no—
1364C4—42no—
1365C4—44no—
1366C4—42no—
1367C4—44no—
1368C4—42no—
1369C4—42no—
1370C4—44no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—44no—
1376C4#356314yes—
1377C2—44no—
1378C2—44no—
1379C2C2×#356311yescharacteristic
1380C2#6290511yescharacteristic
1381C2#6294511yescharacteristic
1382C2#6294811yescharacteristic
1383C2#6301311yescharacteristic
1384C2#6302511yescharacteristic
1385C2#6303711yescharacteristic
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. #59454C2semidirect
2. #59264C2semidirect
3. #59209C2semidirect
4. #58533C2semidirect
5. #58311C2semidirect
6. #55262C2semidirect
7. #53219C2semidirect
8. #52304C2semidirect
9. #50139C2semidirect
10. #49277C2semidirect
11. #47875C2semidirect
12. #46157C2semidirect
13. #46153C2semidirect
14. #46147C2semidirect
15. #45426C2semidirect
16. #45181C2semidirect
17. #45027C2semidirect
18. #42728C2semidirect
19. #42587C2semidirect
20. #42496C2semidirect
21. #39623C2semidirect
23. #39376C2semidirect
24. #39157C2semidirect
25. #38781C2semidirect
26. #38447C2semidirect
28. #36407C2semidirect
29. #36290C2semidirect

Maximal subgroups

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

subgroupindex
#594542
#592642
#592092
#585332
#583112
#552622
#532192
#523042
#501392
#492772
#478752
#461572
#461532
#461472
#454262
#451812
#450272
#427282
#425872
#424962
#396232
#394002
#393762
#391572
#387812
#384472
#364532
#364072
#362902