Finite Group Databasebeta

← #8751561

Subgroups — #8751561

Order 512.

4224 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59202C211yesmaximal, characteristic, complemented
2#59027C212yesmaximal, complemented
3#58797C212yesmaximal, complemented
4#58492C214yesmaximal, complemented
5#57495C214yesmaximal, complemented
6#56646C214yesmaximal, complemented
7#55944C214yesmaximal, complemented
8#53137C211yesmaximal, characteristic, complemented
9#53093C212yesmaximal, complemented
10#52868C214yesmaximal, complemented
11#52717C212yesmaximal, complemented
12#47419C212yesmaximal, complemented
13#45396C212yesmaximal, complemented
14#45351C211yesmaximal, characteristic, complemented
15#45288C212yesmaximal, complemented
16#45157C212yesmaximal, complemented
17#45133C212yesmaximal, complemented
18#42978C211yesmaximal, characteristic, complemented
19#42828C212yesmaximal, complemented
20#42714C212yesmaximal, complemented
21#42684C212yesmaximal, complemented
22#42675C212yesmaximal, complemented
23#42669C212yesmaximal, complemented
24#41537C214yesmaximal, complemented
25#39911C212yesmaximal, complemented
26#38917C211yesmaximal, characteristic, complemented
27#36676C211yesmaximal, characteristic
28#35926C211yesmaximal, characteristic, complemented
29#35899C212yesmaximal, complemented
30C2×#554C2211yescharacteristic, complemented
31C2×#552C2211yescharacteristic
32C2×#552C2212yes—
33C2×#544C2211yescharacteristic, complemented
34C22×C22⋊Q8C2211yescharacteristic
35#2848C2211yescharacteristic
36#2842C2211yescharacteristic
37#2838C2214yes—
38#2838C2214yescomplemented
39#2837C2214yes—
40#2837C2214yes—
41#2836C2214yes—
42#2834C2211yescharacteristic
43#2833C2214yescomplemented
44#2833C2214yescomplemented
45#2831C2214yes—
46#2827C2212yes—
47#2827C2212yes—
48#2827C2212yes—
49#2826C2212yes—
50#2826C2211yescharacteristic
51#2826C2212yes—
52#2825C2212yes—
53#2824C2212yescomplemented
54#2822C2212yescomplemented
55#2814C2214yes—
56#2812C2212yes—
57#2812C2211yescharacteristic
58#2808C2214yes—
59#2807C2212yes—
60#2806C2214yescomplemented
61#2803C2214yes—
62#2803C2214yes—
63#2801C2214yes—
64#2799C2212yescomplemented
65#2799C2214yescomplemented
66#2793C2214yescomplemented
67#2793C2214yescomplemented
68#2791C2214yescomplemented
69#2789C2214yescomplemented
70#2787C2214yescomplemented
71#2785C2214yescomplemented
72#2783C2214yes—
73#2779C2214yes—
74#2778C2214yes—
75#2777C2214yes—
76#2777C2214yescomplemented
77#2776C2214yescomplemented
78#2775C2214yes—
79#2770C2214yes—
80#2766C2214yescomplemented
81#2765C2214yes—
82#2759C2214yes—
83#2759C2214yescomplemented
84#2756C2214yes—
85#2754C2214yescomplemented
86#2752C2214yes—
87#2751C2214yes—
88#2747C2214yescomplemented
89#2742C2212yescomplemented
90#2741C2214yescomplemented
91#2740C2214yes—
92#2738C2214yes—
93#2736C2214yes—
94#2735C2212yes—
95#2726C2214yescomplemented
96#2725C2214yes—
97#2723C2214yes—
98#2722C2212yes—
99#2720C2214yes—
100#2719C2214yescomplemented
101#2716C2214yes—
102#2704C2214yescomplemented
103#2702C2214yes—
104#2702C2214yes—
105#2698C2214yes—
106#2696C2214yes—
107#2689C2214yescomplemented
108#2687C2214yes—
109#2687C2214yes—
110#2685C2214yes—
111#2684C2212yes—
112#2667C2214yescomplemented
113#2664C2212yescomplemented
114#2660C2211yescharacteristic, complemented
115#2654C2214yes—
116#2654C2214yes—
117#2653C2214yes—
118#2653C2214yes—
119#2651C2214yes—
120#2651C2214yescomplemented
121#2650C2214yescomplemented
122#2645C2212yescomplemented
123#2642C2212yescomplemented
124#2630C2214yes—
125#2628C2212yes—
126#2625C2214yescomplemented
127#2625C2211yescharacteristic, complemented
128#2623C2212yes—
129#2621C2212yescomplemented
130#2611C2212yes—
131#2611C2212yes—
132#2606C2214yescomplemented
133#2603C2212yescomplemented
134#2597C2214yes—
135#2596C2214yes—
136#2594C2214yes—
137#2594C2214yescomplemented
138#2593C2214yes—
139#2590C2214yescomplemented
140#2589C2214yes—
141#2589C2214yes—
142#2586C2212yescomplemented
143#2576C2214yes—
144#2570C2212yescomplemented
145#2568C2212yescomplemented
146#2563C2212yes—
147#2562C2211yescharacteristic, complemented
148#2558C2214yes—
149#2556C2214yes—
150#2556C2214yescomplemented
151#2550C2212yescomplemented
152#2547C2211yescharacteristic
153#2542C2212yes—
154#2538C2212yescomplemented
155#2536C2212yes—
156#2536C2212yes—
157#2532C2214yescomplemented
158#2531C2214yes—
159#2529C2214yes—
160#2529C2214yescomplemented
161#2528C2214yescomplemented
162#2528C2214yescomplemented
163#2527C2214yes—
164#2521C2214yes—
165#2517C2212yes—
166#2517C2212yes—
167#2516C2214yescomplemented
168#2514C2212yescomplemented
169#2508C2214yescomplemented
170#2508C2214yescomplemented
171#2507C2212yescomplemented
172#2507C2214yescomplemented
173#2507C2212yescomplemented
174#2503C2211yescharacteristic, complemented
175#2499C2212yes—
176#2496C2212yes—
177#2494C2212yes—
178#2494C2212yes—
179#2494C2214yescomplemented
180#2492C2212yes—
181#2492C2212yescomplemented
182#2489C2212yes—
183#2489C2212yes—
184#2489C2214yescomplemented
185#2487C2211yescharacteristic
186#2485C2212yes—
187#2485C2212yes—
188#2485C2214yes—
189#2485C2214yescomplemented
190#2482C2212yes—
191#2480C2214yes—
192#2478C2214yes—
193#2477C2214yes—
194#2477C2214yescomplemented
195#2473C2214yes—
196#2468C2214yes—
197#2461C2214yes—
198#2453C2212yescomplemented
199#2451C2212yescomplemented
200#2446C2212yescomplemented
201#2442C2212yes—
202#2442C2212yescomplemented
203#2439C2212yes—
204#2439C2212yes—
205#2439C2214yescomplemented
206#2434C2211yescharacteristic
207#2429C2212yes—
208#2429C2212yescomplemented
209#2423C2212yes—
210#2423C2212yes—
211#2423C2212yescomplemented
212#2418C2214yes—
213#2417C2212yes—
214#2417C2212yescomplemented
215#2415C2212yes—
216#2415C2212yes—
217#2415C2212yes—
218#2415C2212yes—
219#2415C2212yescomplemented
220#2415C2212yescomplemented
221#2411C2212yes—
222#2409C2211yescharacteristic
223#2409C2212yes—
224#2402C2214yescomplemented
225#2401C2212yes—
226#2397C2211yescharacteristic
227#2395C2211yescharacteristic
228#2395C2212yes—
229#2392C2212yes—
230#2392C2212yes—
231#2392C2212yes—
232#2392C2212yes—
233#2372C2212yes—
234#2370C2212yescomplemented
235#2365C2212yescomplemented
236#2362C2212yes—
237#2362C2212yes—
238#2355C2212yescomplemented
239#2354C2212yes—
240#2352C2214yes—
241#2352C2212yes—
242#2352C2212yescomplemented
243D4×C4⋊C4C2212yes—
244#2347C2212yescomplemented
245#2346C2212yes—
246#2346C2211yescharacteristic, complemented
247#2344C2211yescharacteristic
248Q8×C22⋊C4C2212yes—
249#2334C2214yes—
250#2323C2212yescomplemented
251#2323C2212yescomplemented
252#2317C2212yes—
253#2316C2212yescomplemented
254#2314C2212yescomplemented
255C4×#120C2211yescharacteristic
256C4×#120C2212yes—
257#2280C2212yes—
258#2276C2211yescharacteristic, complemented
259C23×Q8C2311yescharacteristic
260C24×C4C2311yescharacteristic
261#554—44no—
262#552—44no—
263#552—48no—
264#544—44no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×#126C2314yes—
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#125C2312yes—
273C2×#125C2311yescharacteristic
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#124C2312yes—
279C2×#123C2312yes—
280C2×#123C2314yes—
281C2×C22⋊Q8—44no—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×#120C2311yescharacteristic
295C2×#120C2312yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2314yes—
317C2×#117C2312yes—
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2311yescharacteristic
322C22×C22⋊C4C2312yes—
323#401C2312yes—
324#401C2314yes—
325#401C2314yes—
326#401C2314yes—
327#401C2314yes—
328#400C2312yes—
329#400C2314yes—
330#400C2312yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2312yes—
339#400C2314yes—
340#400C2312yes—
341#400C2311yescharacteristic
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#399C2312yes—
355#399C2311yescharacteristic
356#399C2312yes—
357#399C2312yes—
358#399C2311yescharacteristic
359#399C2311yescharacteristic
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#398C2311yescharacteristic
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#397C2314yes—
396#397C2312yes—
397#397C2312yes—
398#397C2312yes—
399#397C2312yes—
400#397C2312yes—
401#397C2312yes—
402#397C2314yes—
403#397C2312yes—
404#397C2312yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2312yes—
410#397C2311yescharacteristic
411#397C2312yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#396C2312yes—
427#396C2312yes—
428#396C2312yes—
429#396C2312yes—
430#396C2314yes—
431#396C2312yes—
432#396C2312yes—
433#396C2312yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2312yes—
447#394C2312yes—
448#394C2314yes—
449#394C2314yes—
450#394C2312yes—
451#394C2312yes—
452#394C2312yes—
453#394C2312yes—
454#394C2312yes—
455#394C2312yes—
456#394C2314yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2312yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#392C2311yescharacteristic
479#392C2312yes—
480#392C2312yes—
481#392C2312yes—
482#392C2311yescharacteristic
483#392C2312yes—
484#391C2314yes—
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2314yes—
489#391C2314yes—
490#391C2312yes—
491#391C2312yes—
492#391C2314yes—
493#391C2314yes—
494#391C2314yes—
495#391C2312yes—
496#391C2314yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2314yes—
502#391C2314yes—
503#390C2314yes—
504#390C2314yes—
505#390C2314yes—
506#390C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
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#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#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#386C2314yes—
617#386C2312yes—
618#386C2312yes—
619#386C2312yes—
620#386C2312yes—
621#386C2311yescharacteristic
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2312yes—
626#386C2312yes—
627#386C2314yes—
628#385C2312yes—
629#385C2311yescharacteristic
630#385C2312yes—
631#385C2312yes—
632#385C2312yes—
633#385C2312yes—
634#385C2312yes—
635#385C2312yes—
636#385C2312yes—
637#385C2312yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#384C2312yes—
645#384C2312yes—
646#384C2314yes—
647#383C2314yes—
648#383C2314yes—
649#382C2314yes—
650#382C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2312yes—
654#382C2314yes—
655#382C2314yes—
656#382C2314yes—
657#382C2314yes—
658#381C2314yes—
659#381C2312yes—
660#381C2314yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2314yes—
668#380C2312yes—
669#380C2311yescharacteristic
670#380C2312yes—
671#380C2314yes—
672#380C2311yescharacteristic
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2314yes—
677#380C2312yes—
678#380C2314yes—
679#379C2311yescharacteristic
680#379C2312yes—
681#379C2312yes—
682#379C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2314yes—
714#376C2312yes—
715#376C2312yes—
716#376C2311yescharacteristic
717C25C2411yescharacteristic
718C22×Q8—42no—
719C22×Q8—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2414yes—
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2412yes—
732C23×C4—42no—
733C23×C4—44no—
734C23×C4C2412yes—
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2412yes—
743C23×C4C2412yes—
744C4⋊Q8—44no—
745C4⋊Q8—44no—
746C4⋊Q8—42no—
747C4⋊Q8—44no—
748#126—44no—
749#126—48no—
750#126—48no—
751#125—28no—
752#125—44no—
753#125—44no—
754#125—42no—
755#125—44no—
756#125—48no—
757#124—44no—
758#123—48no—
759#123—44no—
760C22⋊Q8—28no—
761C22⋊Q8—48no—
762C22⋊Q8—48no—
763C22⋊Q8—48no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766C22⋊Q8—44no—
767C22⋊Q8—44no—
768C22⋊Q8—44no—
769C22⋊Q8—42no—
770C22⋊Q8—42no—
771C22⋊Q8—44no—
772#120—42no—
773#120—44no—
774C4×Q8—24no—
775C4×Q8—44no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×D4—44no—
779C4×D4—44no—
780C4×D4—44no—
781C4×D4—44no—
782C4×D4—44no—
783C4×D4—42no—
784C4×D4—44no—
785C4×D4—42no—
786C4×D4—48no—
787#117—24no—
788#117—44no—
789#117—42no—
790#117—44no—
791#117—44no—
792#117—44no—
793#117—44no—
794#117—44no—
795#117—48no—
796C2×C4⋊C4—24no—
797C2×C4⋊C4—28no—
798C2×C4⋊C4—44no—
799C2×C4⋊C4—42no—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C22⋊C4—44no—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2411yescharacteristic
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2411yescharacteristic
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936#95C2411yescharacteristic
937#95C2412yes—
938#95C2411yescharacteristic
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2411yescharacteristic
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2411yescharacteristic
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
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#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007C24—22no—
1008C24—41no—
1009C24—42no—
1010C24—42no—
1011C24—41no—
1012C24C2512yes—
1013C24C2511yescharacteristic
1014C24C2512yes—
1015C24C2511yescharacteristic
1016C2×Q8—22no—
1017C2×Q8—24no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—42no—
1022C2×Q8—44no—
1023C2×Q8—42no—
1024C2×Q8—44no—
1025C2×Q8—42no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8—42no—
1029C2×Q8—88no—
1030C2×D4—24no—
1031C2×D4—22no—
1032C2×D4—41no—
1033C2×D4—42no—
1034C2×D4—42no—
1035C2×D4—42no—
1036C2×D4—41no—
1037C2×D4—42no—
1038C2×D4—42no—
1039C2×D4—42no—
1040C2×D4—42no—
1041C2×D4—42no—
1042C2×D4—42no—
1043C2×D4—42no—
1044C2×D4—42no—
1045C2×D4—42no—
1046C2×D4—42no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C2×D4—41no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—28no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—41no—
1066C22×C4—44no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—88no—
1076C22×C4C2512yes—
1077C22×C4C2511yescharacteristic
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C4⋊C4—24no—
1102C4⋊C4—22no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—22no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—41no—
1136C4⋊C4—42no—
1137C4⋊C4—41no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4H(5,𝔽2)14yes—
1164C22⋊C4—22no—
1165C22⋊C4—24no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—28no—
1169C22⋊C4—24no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—41no—
1179C22⋊C4—42no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—42no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—41no—
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—42no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—41no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—22no—
1221C42—24no—
1222C42—24no—
1223C42—24no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—42no—
1235C42—44no—
1236C23—21no—
1237C23—22no—
1238C23—22no—
1239C23—21no—
1240C23—21no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—21no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—21no—
1257C23—22no—
1258C23—22no—
1259C23—44no—
1260C23—82no—
1261C23—84no—
1262C23—82no—
1263C23—84no—
1264C23#58512yes—
1265C23C2611yescharacteristic
1266Q8—44no—
1267Q8—48no—
1268Q8—84no—
1269Q8—164no—
1270Q8—162no—
1271D4—48no—
1272D4—44no—
1273D4—82no—
1274D4—84no—
1275D4—84no—
1276D4—84no—
1277D4—84no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—48no—
1345C2×C4—48no—
1346C2×C4—44no—
1347C2×C4—48no—
1348C2×C4—44no—
1349C2×C4—88no—
1350C2×C4—82no—
1351C2×C4—84no—
1352C2×C4—84no—
1353C2×C4—162no—
1354C2×C4C2×H(5,𝔽2)14yes—
1355C2×C4C2×H(5,𝔽2)12yes—
1356C2×C4#58514yes—
1357C22—22no—
1358C22—24no—
1359C22—41no—
1360C22—41no—
1361C22—42no—
1362C22—42no—
1363C22—41no—
1364C22—42no—
1365C22—41no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—41no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—88no—
1382C22C22×H(5,𝔽2)11yescharacteristic
1383C22C2×#58512yes—
1384C22C2×#58511yescharacteristic
1385C222−1+612yes—
1386C222−1+611yescharacteristic
1387C4—24no—
1388C4—41no—
1389C4—42no—
1390C4—42no—
1391C4—41no—
1392C4—44no—
1393C4—42no—
1394C4—44no—
1395C4—41no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—44no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—42no—
1405C4—41no—
1406C4—44no—
1407C4—44no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4#355114yes—
1412C2—42no—
1413C2—81no—
1414C2—82no—
1415C2—82no—
1416C2C2×#355111yescharacteristic
1417C2#6289811yescharacteristic
1418C2#6290712yes—
1419C2#6304811yescharacteristic
1420C2#6305312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36676C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59202C2semidirect
2. #59027C2semidirect
3. #58797C2semidirect
4. #58492C2semidirect
5. #57495C2semidirect
6. #56646C2semidirect
7. #55944C2semidirect
8. #53137C2semidirect
9. #53093C2semidirect
10. #52868C2semidirect
11. #52717C2semidirect
12. #47419C2semidirect
13. #45396C2semidirect
14. #45351C2semidirect
15. #45288C2semidirect
16. #45157C2semidirect
17. #45133C2semidirect
18. #42978C2semidirect
19. #42828C2semidirect
20. #42714C2semidirect
21. #42684C2semidirect
22. #42675C2semidirect
23. #42669C2semidirect
24. #41537C2semidirect
25. #39911C2semidirect
26. #38917C2semidirect
28. #35926C2semidirect
29. #35899C2semidirect
30. C2×#554C22semidirect
33. C2×#544C22semidirect
38. #2838C22semidirect
43. #2833C22semidirect
44. #2833C22semidirect
53. #2824C22semidirect
54. #2822C22semidirect
60. #2806C22semidirect
64. #2799C22semidirect
65. #2799C22semidirect
66. #2793C22semidirect
67. #2793C22semidirect
68. #2791C22semidirect
69. #2789C22semidirect
70. #2787C22semidirect
71. #2785C22semidirect
76. #2777C22semidirect
77. #2776C22semidirect
80. #2766C22semidirect
83. #2759C22semidirect
85. #2754C22semidirect
88. #2747C22semidirect
89. #2742C22semidirect
90. #2741C22semidirect
95. #2726C22semidirect
100. #2719C22semidirect
102. #2704C22semidirect
107. #2689C22semidirect
112. #2667C22semidirect
113. #2664C22semidirect
114. #2660C22semidirect
120. #2651C22semidirect
121. #2650C22semidirect
122. #2645C22semidirect
123. #2642C22semidirect
126. #2625C22semidirect
127. #2625C22semidirect
129. #2621C22semidirect
132. #2606C22semidirect
133. #2603C22semidirect
137. #2594C22semidirect
139. #2590C22semidirect
142. #2586C22semidirect
144. #2570C22semidirect
145. #2568C22semidirect
147. #2562C22semidirect
150. #2556C22semidirect
151. #2550C22semidirect
154. #2538C22semidirect
157. #2532C22semidirect
160. #2529C22semidirect
161. #2528C22semidirect
162. #2528C22semidirect
167. #2516C22semidirect
168. #2514C22semidirect
169. #2508C22semidirect
170. #2508C22semidirect
171. #2507C22semidirect
172. #2507C22semidirect
173. #2507C22semidirect
174. #2503C22semidirect
179. #2494C22semidirect
181. #2492C22semidirect
184. #2489C22semidirect
189. #2485C22semidirect
194. #2477C22semidirect
198. #2453C22semidirect
199. #2451C22semidirect
200. #2446C22semidirect
202. #2442C22semidirect
205. #2439C22semidirect
208. #2429C22semidirect
211. #2423C22semidirect
214. #2417C22semidirect
219. #2415C22semidirect
220. #2415C22semidirect
224. #2402C22semidirect
234. #2370C22semidirect
235. #2365C22semidirect
238. #2355C22semidirect
242. #2352C22semidirect
244. #2347C22semidirect
246. #2346C22semidirect
250. #2323C22semidirect
251. #2323C22semidirect
253. #2316C22semidirect
254. #2314C22semidirect
258. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#592022
#590272
#587972
#584922
#574952
#566462
#559442
#531372
#530932
#528682
#527172
#474192
#453962
#453512
#452882
#451572
#451332
#429782
#428282
#427142
#426842
#426752
#426692
#415372
#399112
#389172
#366762
#359262
#358992