Finite Group Databasebeta

← #7898472

Subgroups — #7898472

Order 512.

4489 conjugacy classes of subgroups.

The subgroup lattice has 1410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic
2#59113C212yesmaximal, complemented
3#52273C211yesmaximal, characteristic
4#51110C214yesmaximal, complemented
5#49940C214yesmaximal, complemented
6#48594C214yesmaximal, complemented
7#47271C214yesmaximal, complemented
8#45949C212yesmaximal, complemented
9#45326C212yesmaximal, complemented
10#45222C212yesmaximal, complemented
11#45143C212yesmaximal, complemented
12#43238C214yesmaximal
13#42859C214yesmaximal, complemented
14#42640C212yesmaximal, complemented
15#42513C212yesmaximal, complemented
16#40192C212yesmaximal, complemented
17#39702C212yesmaximal, complemented
18#39629C211yesmaximal, characteristic, complemented
19#39621C211yesmaximal, characteristic, complemented
20#38788C212yesmaximal, complemented
21#38101C212yesmaximal, complemented
22#37765C212yesmaximal, complemented
23#37265C212yesmaximal, complemented
24#36534C211yesmaximal, characteristic
25#35911C212yesmaximal, complemented
26#35637C212yesmaximal, complemented
27#35187C211yesmaximal, characteristic, complemented
28#34464C212yesmaximal, complemented
29#34337C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#554C2212yes—
33C2×#554C2211yescharacteristic
34C2×#541C2212yes—
35C2×#533C2212yes—
36#2864C2212yes—
37#2863C2212yes—
38#2862C2211yescharacteristic
39#2861C2212yes—
40#2851C2212yes—
41#2838C2214yes—
42#2838C2214yes—
43#2811C2212yes—
44#2808C2211yescharacteristic
45#2808C2211yescharacteristic
46#2806C2212yes—
47#2806C2212yes—
48#2806C2212yes—
49#2806C2212yes—
50#2805C2212yes—
51#2805C2214yes—
52#2805C2212yes—
53#2804C2211yescharacteristic
54#2802C2214yes—
55#2796C2212yes—
56#2796C2212yes—
57#2796C2214yes—
58#2794C2212yes—
59#2794C2214yes—
60#2774C2214yes—
61#2773C2214yes—
62#2768C2214yes—
63#2767C2214yes—
64#2766C2214yes—
65#2765C2214yes—
66#2762C2214yes—
67#2757C2214yes—
68#2754C2214yes—
69#2751C2212yes—
70#2751C2212yes—
71#2747C2214yes—
72#2745C2214yes—
73#2742C2214yes—
74#2737C2214yes—
75#2734C2212yes—
76#2732C2212yes—
77#2732C2212yes—
78#2729C2214yes—
79#2729C2214yes—
80#2726C2214yes—
81#2725C2214yes—
82#2724C2211yescharacteristic
83#2723C2214yes—
84#2723C2214yes—
85#2722C2214yes—
86#2721C2214yes—
87#2721C2214yes—
88#2720C2214yes—
89#2720C2214yes—
90#2719C2214yes—
91#2719C2214yes—
92#2719C2214yes—
93#2717C2214yes—
94#2716C2214yes—
95#2715C2214yes—
96#2709C2212yes—
97#2666C2214yes—
98#2660C2212yes—
99#2655C2214yes—
100#2655C2214yes—
101#2652C2214yes—
102#2652C2214yes—
103#2647C2212yes—
104#2637C2214yes—
105#2628C2214yes—
106#2628C2212yes—
107#2611C2214yes—
108#2604C2214yes—
109#2601C2214yes—
110#2595C2214yes—
111#2589C2214yes—
112#2589C2214yes—
113#2586C2214yes—
114#2585C2214yes—
115#2583C2214yes—
116#2582C2211yescharacteristic
117#2581C2212yes—
118#2571C2211yescharacteristic
119#2570C2214yes—
120#2568C2211yescharacteristic
121#2565C2214yes—
122#2565C2212yes—
123#2563C2211yescharacteristic
124#2560C2214yes—
125#2560C2214yes—
126#2560C2214yes—
127#2556C2214yes—
128#2552C2212yes—
129#2551C2212yes—
130#2550C2212yes—
131#2550C2212yes—
132#2547C2211yescharacteristic
133#2546C2211yescharacteristic
134#2544C2212yes—
135#2542C2212yes—
136#2538C2212yes—
137#2538C2214yes—
138#2536C2212yes—
139#2536C2212yes—
140#2530C2214yes—
141#2527C2214yes—
142#2524C2214yes—
143#2521C2214yes—
144#2520C2214yes—
145#2520C2214yes—
146#2520C2214yes—
147#2519C2214yes—
148#2517C2214yes—
149#2514C2212yes—
150#2514C2212yes—
151#2508C2212yes—
152#2506C2214yes—
153#2505C2214yes—
154#2502C2212yes—
155#2499C2212yes—
156#2496C2214yes—
157#2496C2212yes—
158#2494C2212yes—
159#2494C2214yes—
160#2492C2212yes—
161#2489C2212yes—
162#2489C2212yes—
163#2489C2212yes—
164#2487C2214yes—
165#2479C2214yes—
166#2479C2214yes—
167#2478C2214yes—
168#2475C2214yes—
169#2469C2214yes—
170#2468C2214yes—
171#2465C2214yes—
172#2462C2214yes—
173#2462C2214yes—
174#2462C2214yes—
175#2460C2214yes—
176#2460C2214yes—
177#2454C2214yes—
178#2453C2214yes—
179#2451C2212yes—
180#2451C2214yes—
181#2451C2212yes—
182#2450C2214yes—
183#2449C2214yes—
184#2446C2212yes—
185#2442C2212yes—
186#2442C2212yes—
187#2441C2212yes—
188#2440C2212yes—
189#2440C2214yes—
190#2438C2214yes—
191#2429C2212yes—
192#2429C2214yes—
193#2429C2212yes—
194#2423C2212yes—
195#2423C2212yes—
196#2421C2212yes—
197#2421C2212yes—
198#2421C2214yes—
199#2421C2214yes—
200#2417C2212yes—
201#2417C2212yes—
202#2398C2212yes—
203#2398C2212yes—
204#2395C2212yes—
205#2395C2214yes—
206#2382C2214yes—
207#2378C2214yes—
208#2370C2212yes—
209#2370C2214yes—
210#2366C2212yes—
211#2365C2211yescharacteristic
212#2365C2212yes—
213#2362C2212yes—
214#2360C2212yes—
215#2360C2214yes—
216#2360C2212yes—
217#2360C2212yes—
218#2359C2214yes—
219#2355C2212yes—
220#2352C2212yes—
221#2352C2214yes—
222#2352C2212yes—
223#2351C2212yes—
224Q8×C4⋊C4C2212yes—
225Q8×C4⋊C4C2211yescharacteristic
226Q8×C4⋊C4C2212yes—
227Q8×C4⋊C4C2211yescharacteristic
228D4×C4⋊C4C2212yes—
229#2345C2212yes—
230#2344C2212yes—
231#2337C2214yes—
232#2336C2214yes—
233#2331C2212yes—
234#2330C2214yes—
235#2330C2212yes—
236#2329C2214yes—
237#2327C2212yes—
238#2327C2212yes—
239#2323C2212yes—
240#2323C2214yes—
241#2320C2212yes—
242#2318C2214yes—
243#2316C2212yes—
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×#127C2211yescharacteristic
248C4×#124C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×#123C2212yes—
251#2295C2211yescharacteristic
252#2295C2212yes—
253#2295C2211yescharacteristic
254C2×#389C2212yes—
255#2290C2212yes—
256#2290C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259#557—28no—
260#556—44no—
261#554—216no—
262#554—44no—
263#541—48no—
264#533—48no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×#127C2311yescharacteristic
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#123C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C2×#117C2314yes—
326C2×#117C2314yes—
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2314yes—
331C22×C42C2312yes—
332#401C2314yes—
333#401C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2312yes—
362#399C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2312yes—
400#397C2312yes—
401#397C2312yes—
402#397C2314yes—
403#397C2312yes—
404#397C2312yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2312yes—
426#394C2312yes—
427#394C2312yes—
428#394C2312yes—
429#394C2312yes—
430#394C2312yes—
431#393C2314yes—
432#393C2314yes—
433#393C2312yes—
434#393C2314yes—
435#393C2312yes—
436#393C2312yes—
437#393C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2312yes—
442#391C2311yescharacteristic
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2312yes—
462#391C2311yescharacteristic
463#391C2311yescharacteristic
464#391C2314yes—
465#391C2311yescharacteristic
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#390C2311yescharacteristic
470#390C2311yescharacteristic
471#390C2312yes—
472#390C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2311yescharacteristic
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2311yescharacteristic
520#389C2311yescharacteristic
521#388C2314yes—
522#388C2314yes—
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#388C2312yes—
542#388C2314yes—
543#388C2312yes—
544#388C2314yes—
545#388C2312yes—
546#388C2312yes—
547#388C2312yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
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#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#387C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2314yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#387C2312yes—
603#387C2314yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#386C2312yes—
608#386C2314yes—
609#386C2314yes—
610#386C2312yes—
611#386C2312yes—
612#386C2314yes—
613#386C2312yes—
614#386C2312yes—
615#386C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2312yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2312yes—
631#385C2314yes—
632#385C2312yes—
633#385C2314yes—
634#384C2311yescharacteristic
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#384C2312yes—
638#384C2314yes—
639#384C2312yes—
640#384C2314yes—
641#384C2312yes—
642#383C2314yes—
643#383C2314yes—
644#382C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2314yes—
648#382C2314yes—
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#382C2312yes—
654#382C2312yes—
655#382C2312yes—
656#381C2314yes—
657#381C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2312yes—
714#376C2314yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C43C2312yes—
718C22×Q8C2412yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2414yes—
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2411yescharacteristic
729C22×D4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2412yes—
732C23×C4C2414yes—
733C23×C4C2414yes—
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2412yes—
737C4⋊Q8—28no—
738C4⋊Q8—28no—
739C4⋊Q8—24no—
740C4⋊Q8—44no—
741C4⋊Q8—42no—
742C4⋊Q8—42no—
743C4⋊Q8—84no—
744C4⋊Q8#4118yes—
745#127—24no—
746#126—48no—
747#126—48no—
748#126—48no—
749#126—84no—
750#125—216no—
751#125—216no—
752#125—28no—
753#125—44no—
754#125—48no—
755#125—44no—
756#125—48no—
757#125—48no—
758#124—28no—
759#124—44no—
760#123—28no—
761C22⋊Q8—216no—
762C22⋊Q8—216no—
763C22⋊Q8—28no—
764C22⋊Q8—28no—
765C22⋊Q8—28no—
766C22⋊Q8—28no—
767C22⋊Q8—48no—
768C22⋊Q8—48no—
769C22⋊Q8—44no—
770C22⋊Q8—44no—
771C22⋊Q8—84no—
772C4×Q8—28no—
773C4×Q8—28no—
774C4×Q8—24no—
775C4×Q8—28no—
776C4×Q8—28no—
777C4×Q8—24no—
778C4×Q8—24no—
779C4×Q8—24no—
780C4×Q8—24no—
781C4×Q8—48no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×Q8—44no—
785C4×Q8—82no—
786C4×Q8—82no—
787C4×Q8—82no—
788C4×D4—216no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—44no—
792C4×D4—42no—
793C4×D4—42no—
794C4×D4—84no—
795#117—44no—
796#117—48no—
797#117—44no—
798#117—84no—
799C2×C4⋊C4—28no—
800C2×C4⋊C4—28no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4—84no—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C42—44no—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2414yes—
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014C24C2512yes—
1015C24C2512yes—
1016C2×Q8—22no—
1017C2×Q8—24no—
1018C2×Q8—22no—
1019C2×Q8—24no—
1020C2×Q8—22no—
1021C2×Q8—24no—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—42no—
1025C2×Q8—41no—
1026C2×Q8—42no—
1027C2×Q8—41no—
1028C2×Q8—44no—
1029C2×Q8—42no—
1030C2×Q8—44no—
1031C2×Q8—41no—
1032C2×Q8—41no—
1033C2×Q8—42no—
1034C2×Q8—44no—
1035C2×Q8—42no—
1036C2×Q8—42no—
1037C2×Q8—42no—
1038C2×Q8C2×#4118yes—
1039C2×Q8H(5,𝔽2)14yes—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—22no—
1045C2×D4—41no—
1046C2×D4—42no—
1047C2×D4—42no—
1048C2×D4—41no—
1049C2×D4—41no—
1050C2×D4—41no—
1051C2×D42−1+414yes—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—28no—
1060C22×C4—28no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2512yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C4⋊C4—24no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—22no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—22no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—22no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—41no—
1139C4⋊C4—41no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—41no—
1155C4⋊C4—41no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—41no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4C2×#4118yes—
1173C4⋊C4C2×#4118yes—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—28no—
1178C22⋊C4—28no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C42—28no—
1208C42—28no—
1209C42—24no—
1210C42—24no—
1211C42—24no—
1212C42—24no—
1213C42—28no—
1214C42—22no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—22no—
1220C42—42no—
1221C42—42no—
1222C42—41no—
1223C42—42no—
1224C42—41no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—41no—
1233C42—42no—
1234C42—44no—
1235C42C2×#4114yes—
1236C422−1+414yes—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23C2×2−1+414yes—
1251C23C2611yescharacteristic
1252Q8—28no—
1253Q8—48no—
1254Q8—44no—
1255Q8—48no—
1256Q8—82no—
1257Q8—84no—
1258Q8—88no—
1259Q8—162no—
1260D4—44no—
1261D4—48no—
1262D4—48no—
1263D4—82no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—24no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—24no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—21no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—21no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—48no—
1336C2×C4—48no—
1337C2×C4—48no—
1338C2×C4—88no—
1339C2×C4—88no—
1340C2×C4—84no—
1341C2×C4—164no—
1342C2×C4C22×#4112yes—
1343C2×C4C22×#4112yes—
1344C2×C4C22×#4118yes—
1345C2×C4C22×#4112yes—
1346C2×C4C2×H(5,𝔽2)14yes—
1347C2×C4C2×H(5,𝔽2)12yes—
1348C2×C4C2×2−1+412yes—
1349C2×C4C2×2−1+412yes—
1350C2×C4C2×2−1+412yes—
1351C2×C4C2×2−1+412yes—
1352C22—24no—
1353C22—24no—
1354C22—24no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—42no—
1366C22C23×#4111yescharacteristic
1367C22C22×H(5,𝔽2)11yescharacteristic
1368C22C22×2−1+411yescharacteristic
1369C22C22×2−1+411yescharacteristic
1370C22H(7,𝔽2)11yescharacteristic
1371C222−1+611yescharacteristic
1372C222−1+611yescharacteristic
1373C4—22no—
1374C4—24no—
1375C4—28no—
1376C4—22no—
1377C4—22no—
1378C4—22no—
1379C4—22no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—44no—
1389C4—44no—
1390C4—41no—
1391C4—44no—
1392C4—42no—
1393C4—42no—
1394C4—42no—
1395C4—42no—
1396C4—44no—
1397C4—42no—
1398C4—42no—
1399C4#352214yes—
1400C2—44no—
1401C2—82no—
1402C2C2×#352211yescharacteristic
1403C2#6284711yescharacteristic
1404C2#6288911yescharacteristic
1405C2#6289311yescharacteristic
1406C2#6294511yescharacteristic
1407C2#6299811yescharacteristic
1408C2#6305211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59113C2semidirect
4. #51110C2semidirect
5. #49940C2semidirect
6. #48594C2semidirect
7. #47271C2semidirect
8. #45949C2semidirect
9. #45326C2semidirect
10. #45222C2semidirect
11. #45143C2semidirect
13. #42859C2semidirect
14. #42640C2semidirect
15. #42513C2semidirect
16. #40192C2semidirect
17. #39702C2semidirect
18. #39629C2semidirect
19. #39621C2semidirect
20. #38788C2semidirect
21. #38101C2semidirect
22. #37765C2semidirect
23. #37265C2semidirect
25. #35911C2semidirect
26. #35637C2semidirect
27. #35187C2semidirect
28. #34464C2semidirect
29. #34337C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#591132
#522732
#511102
#499402
#485942
#472712
#459492
#453262
#452222
#451432
#432382
#428592
#426402
#425132
#401922
#397022
#396292
#396212
#387882
#381012
#377652
#372652
#365342
#359112
#356372
#351872
#344642
#343372