Finite Group Databasebeta

← #8750681

Subgroups — #8750681

Order 512.

4401 conjugacy classes of subgroups.

The subgroup lattice has 1460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59865C211yesmaximal, characteristic, complemented
2#59507C212yesmaximal, complemented
3#58749C212yesmaximal, complemented
4#57803C214yesmaximal, complemented
5#57291C214yesmaximal, complemented
6#56116C214yesmaximal, complemented
7#55620C214yesmaximal, complemented
8#52982C212yesmaximal, complemented
9#52968C211yesmaximal, characteristic, complemented
10#52754C212yesmaximal, complemented
11#52612C214yesmaximal, complemented
12#47657C212yesmaximal, complemented
13#45234C212yesmaximal, complemented
14#45158C212yesmaximal, complemented
15#45115C211yesmaximal, characteristic, complemented
16#44928C212yesmaximal, complemented
17#44885C212yesmaximal, complemented
18#42921C212yesmaximal, complemented
19#42919C212yesmaximal, complemented
20#42916C211yesmaximal, characteristic, complemented
21#42726C212yesmaximal, complemented
22#42591C212yesmaximal, complemented
23#42201C212yesmaximal, complemented
24#42097C214yesmaximal, complemented
25#40074C212yesmaximal, complemented
26#38951C211yesmaximal, characteristic, complemented
27#36696C211yesmaximal, characteristic, complemented
28#36067C211yesmaximal, characteristic, complemented
29#36011C212yesmaximal, complemented
30C2×#555C2212yes—
31C2×#547C2211yescharacteristic
32C2×#547C2211yescharacteristic
33C2×#537C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2862C2211yescharacteristic
36#2843C2211yescharacteristic
37#2841C2214yes—
38#2839C2214yes—
39#2839C2214yes—
40#2838C2214yes—
41#2836C2214yes—
42#2833C2214yes—
43#2833C2212yes—
44#2831C2214yes—
45#2830C2211yescharacteristic
46#2830C2212yes—
47#2829C2212yes—
48#2829C2212yes—
49#2829C2212yes—
50#2828C2212yes—
51#2828C2211yescharacteristic
52#2827C2214yes—
53#2826C2214yes—
54#2823C2211yescharacteristic
55#2818C2212yes—
56#2817C2212yes—
57#2814C2212yes—
58#2800C2214yes—
59#2799C2212yes—
60#2796C2214yes—
61#2794C2212yes—
62#2791C2214yes—
63#2787C2214yes—
64#2782C2214yes—
65#2781C2214yes—
66#2781C2214yes—
67#2779C2214yes—
68#2778C2214yes—
69#2778C2214yes—
70#2776C2214yes—
71#2775C2214yes—
72#2772C2214yes—
73#2771C2212yes—
74#2770C2214yes—
75#2767C2214yes—
76#2761C2214yes—
77#2758C2214yes—
78#2756C2214yes—
79#2752C2214yes—
80#2750C2214yes—
81#2750C2214yes—
82#2749C2214yes—
83#2743C2214yes—
84#2741C2214yes—
85#2741C2214yes—
86#2741C2214yes—
87#2740C2214yes—
88#2738C2214yes—
89#2734C2212yes—
90#2728C2214yes—
91#2717C2214yes—
92#2716C2214yes—
93#2709C2212yes—
94#2706C2214yes—
95#2706C2214yes—
96#2704C2214yes—
97#2703C2214yes—
98#2701C2214yes—
99#2701C2214yes—
100#2700C2214yes—
101#2696C2214yes—
102#2694C2214yes—
103#2693C2212yes—
104#2690C2214yes—
105#2688C2214yes—
106#2686C2214yes—
107#2682C2214yes—
108#2676C2214yes—
109#2674C2214yes—
110#2674C2214yes—
111#2672C2214yes—
112#2666C2214yes—
113#2661C2212yes—
114#2654C2214yes—
115#2652C2214yes—
116#2651C2214yes—
117#2650C2214yes—
118#2648C2214yes—
119#2648C2214yes—
120#2646C2214yes—
121#2635C2214yes—
122#2630C2214yes—
123#2628C2212yes—
124#2625C2212yes—
125#2625C2211yescharacteristic
126#2623C2212yes—
127#2620C2212yes—
128#2618C2212yes—
129#2616C2211yescharacteristic
130#2608C2214yes—
131#2595C2214yes—
132#2593C2212yes—
133#2591C2214yes—
134#2583C2212yes—
135#2576C2214yes—
136#2575C2214yes—
137#2574C2214yes—
138#2572C2212yes—
139#2571C2212yes—
140#2568C2212yes—
141#2562C2214yes—
142#2562C2212yes—
143#2562C2212yes—
144#2557C2214yes—
145#2556C2214yes—
146#2553C2214yes—
147#2551C2212yes—
148#2547C2211yescharacteristic
149#2543C2214yes—
150#2542C2211yescharacteristic
151#2538C2212yes—
152#2537C2212yes—
153#2536C2212yes—
154#2530C2214yes—
155#2529C2214yes—
156#2526C2214yes—
157#2526C2214yes—
158#2526C2214yes—
159#2523C2212yes—
160#2520C2214yes—
161#2516C2214yes—
162#2511C2212yes—
163#2510C2214yes—
164#2509C2212yes—
165#2506C2212yes—
166#2503C2211yescharacteristic
167#2502C2212yes—
168#2502C2211yescharacteristic
169#2499C2212yes—
170#2498C2212yes—
171#2497C2212yes—
172#2497C2214yes—
173#2495C2212yes—
174#2494C2212yes—
175#2494C2212yes—
176#2493C2214yes—
177#2493C2214yes—
178#2492C2212yes—
179#2489C2212yes—
180#2487C2211yescharacteristic
181#2487C2212yes—
182#2486C2212yes—
183#2486C2211yescharacteristic
184#2485C2212yes—
185#2484C2214yes—
186#2484C2212yes—
187#2476C2214yes—
188#2475C2214yes—
189#2474C2214yes—
190#2474C2214yes—
191#2470C2214yes—
192#2459C2214yes—
193#2459C2214yes—
194#2454C2212yes—
195#2453C2212yes—
196#2446C2212yes—
197#2444C2214yes—
198#2444C2214yes—
199#2442C2212yes—
200#2440C2212yes—
201#2440C2212yes—
202#2439C2212yes—
203#2438C2214yes—
204#2438C2214yes—
205#2432C2214yes—
206#2431C2212yes—
207#2430C2214yes—
208#2429C2212yes—
209#2427C2214yes—
210#2422C2212yes—
211#2421C2212yes—
212#2421C2212yes—
213#2420C2212yes—
214#2420C2212yes—
215#2419C2214yes—
216#2417C2212yes—
217#2417C2212yes—
218#2417C2212yes—
219#2417C2212yes—
220#2415C2212yes—
221#2407C2212yes—
222#2407C2212yes—
223#2407C2212yes—
224#2395C2212yes—
225#2395C2211yescharacteristic
226#2395C2214yes—
227C2×#400C2212yes—
228#2392C2212yes—
229#2392C2212yes—
230#2392C2212yes—
231#2388C2211yescharacteristic
232#2388C2212yes—
233#2374C2212yes—
234#2362C2212yes—
235#2362C2212yes—
236#2361C2212yes—
237#2359C2214yes—
238#2357C2212yes—
239#2356C2212yes—
240#2352C2212yes—
241#2352C2212yes—
242#2352C2212yes—
243#2352C2212yes—
244#2349C2212yes—
245#2345C2212yes—
246#2341C2211yescharacteristic
247#2339C2212yes—
248#2339C2211yescharacteristic
249#2331C2214yes—
250#2324C2212yes—
251#2323C2212yes—
252#2317C2212yes—
253#2311C2212yes—
254#2311C2212yes—
255C4×#127C2211yescharacteristic
256C4×#125C2212yes—
257C4×#126C2212yes—
258#2293C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C22×#41C2311yescharacteristic
262C22×#41C2312yes—
263#555—48no—
264#547—44no—
265#547—44no—
266#537—44no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#126C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#124C2314yes—
276C2×#124C2314yes—
277C2×#124C2312yes—
278C2×#123C2314yes—
279C2×#123C2312yes—
280C2×#123C2312yes—
281C2×#123C2312yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301#520—44no—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2311yescharacteristic
320C2×#117C2314yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329#401C2314yes—
330#401C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2311yescharacteristic
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2312yes—
360#399C2314yes—
361#399C2314yes—
362#399C2311yescharacteristic
363#399C2312yes—
364#399C2314yes—
365#399C2314yes—
366#399C2312yes—
367#398C2312yes—
368#398C2311yescharacteristic
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2312yes—
390#397C2311yescharacteristic
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2312yes—
398#397C2312yes—
399#397C2312yes—
400#397C2312yes—
401#397C2312yes—
402#397C2312yes—
403#397C2312yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2312yes—
408#397C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#396C2312yes—
419#396C2312yes—
420#396C2312yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2312yes—
426#396C2312yes—
427#396C2312yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2312yes—
437#395C2312yes—
438#395C2311yescharacteristic
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2312yes—
447#394C2312yes—
448#394C2312yes—
449#394C2312yes—
450#394C2312yes—
451#394C2312yes—
452#394C2311yescharacteristic
453#394C2312yes—
454#394C2314yes—
455#394C2314yes—
456#394C2312yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2314yes—
466#394C2314yes—
467#394C2312yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#393C2314yes—
475#393C2312yes—
476#393C2311yescharacteristic
477#393C2314yes—
478#393C2314yes—
479#392C2312yes—
480#392C2312yes—
481#392C2312yes—
482#392C2312yes—
483#392C2312yes—
484#392C2312yes—
485#392C2314yes—
486#392C2311yescharacteristic
487#392C2312yes—
488#392C2314yes—
489#392C2314yes—
490#391C2312yes—
491#391C2314yes—
492#391C2312yes—
493#391C2314yes—
494#391C2312yes—
495#391C2312yes—
496#391C2314yes—
497#391C2314yes—
498#391C2312yes—
499#391C2314yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#390C2311yescharacteristic
505#390C2312yes—
506#390C2311yescharacteristic
507#390C2312yes—
508#390C2312yes—
509#390C2314yes—
510#390C2312yes—
511#390C2314yes—
512#390C2314yes—
513#390C2312yes—
514#390C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#388C2312yes—
536#388C2312yes—
537#388C2312yes—
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#387C2312yes—
571#387C2312yes—
572#387C2312yes—
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#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2312yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#384C2311yescharacteristic
642#384C2312yes—
643#384C2312yes—
644#384C2312yes—
645#383C2312yes—
646#383C2314yes—
647#383C2314yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#382C2314yes—
654#382C2312yes—
655#381C2312yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2312yes—
660#381C2314yes—
661#381C2314yes—
662#381C2314yes—
663#380C2312yes—
664#380C2311yescharacteristic
665#380C2311yescharacteristic
666#380C2312yes—
667#380C2312yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2312yes—
672#380C2312yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2314yes—
678#380C2312yes—
679#380C2314yes—
680#380C2312yes—
681#380C2312yes—
682#380C2312yes—
683#380C2314yes—
684#380C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2314yes—
713C2×#95C2312yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C2×#41—24no—
718C2×#41—24no—
719C2×#41—42no—
720C2×#41—44no—
721C2×#41—44no—
722C2×#41—44no—
723C2×#41—44no—
724C2×#41—44no—
725C2×#41—82no—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2414yes—
730C22×Q8C2411yescharacteristic
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2411yescharacteristic
735C22×D4C2411yescharacteristic
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2412yes—
741C22×D4C2412yes—
742C22×D4C2412yes—
743C22×D4C2411yescharacteristic
744C22×D4C2412yes—
745C23×C4C2412yes—
746C23×C4C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C23×C4C2414yes—
755C23×C4C2412yes—
756C23×C4C2414yes—
757C23×C4C2414yes—
758C4⋊Q8—42no—
759C4⋊Q8—44no—
760C4⋊Q8—42no—
761C4⋊Q8—48no—
762#127—42no—
763#126—44no—
764#125—44no—
765#125—84no—
766#124—48no—
767#124—48no—
768#124—82no—
769#123—48no—
770#123—48no—
771#123—44no—
772#123—44no—
773#123—44no—
774#123—84no—
775C22⋊Q8—44no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—42no—
782C22⋊Q8—42no—
783C22⋊Q8—84no—
784C22⋊Q8—84no—
785#121—28no—
786#121—28no—
787#121—48no—
788#121—44no—
789#121—44no—
790#121—48no—
791#121—84no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×D4—28no—
795C4×D4—24no—
796C4×D4—44no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—44no—
801C4×D4—42no—
802C4×D4—42no—
803C4×D4—44no—
804C4×D4—48no—
805C4×D4—84no—
806#117—44no—
807#117—42no—
808#117—44no—
809#117—48no—
810#117—44no—
811#117—44no—
812#117—82no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4—42no—
815C2×C4⋊C4—42no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—44no—
818C2×C4⋊C4—44no—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2411yescharacteristic
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2411yescharacteristic
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949#95C2412yes—
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2411yescharacteristic
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2411yescharacteristic
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2411yescharacteristic
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24C2511yescharacteristic
1017C24C2512yes—
1018C24C2512yes—
1019C24C2511yescharacteristic
1020C24C2512yes—
1021#41—416no—
1022#41—88no—
1023#41—88no—
1024#41—816no—
1025C2×Q8—22no—
1026C2×Q8—22no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—41no—
1031C2×Q8—42no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×D4—24no—
1038C2×D4—28no—
1039C2×D4—28no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—41no—
1045C2×D4—44no—
1046C2×D4—41no—
1047C2×D4—41no—
1048C2×D4—42no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—44no—
1054C2×D4—42no—
1055C2×D4—41no—
1056C2×D4—42no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—42no—
1060C2×D4—41no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4H(5,𝔽2)14yes—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—28no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—22no—
1081C22×C4—22no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—42no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2514yes—
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2514yes—
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2514yes—
1124C22×C4C2511yescharacteristic
1125C22×C4C2512yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2514yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—41no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—41no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—28no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—41no—
1223C22⋊C4—41no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C42—24no—
1247C42—22no—
1248C42—24no—
1249C42—24no—
1250C42—24no—
1251C42—22no—
1252C42—44no—
1253C42—42no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—41no—
1259C42—42no—
1260C42—44no—
1261C42—44no—
1262C42—44no—
1263C23—22no—
1264C23—24no—
1265C23—22no—
1266C23—24no—
1267C23—21no—
1268C23—22no—
1269C23—22no—
1270C23—21no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—21no—
1275C23—22no—
1276C23—22no—
1277C23—21no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—21no—
1282C23—21no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23C2×H(5,𝔽2)14yes—
1292C23C2611yescharacteristic
1293Q8—44no—
1294Q8—44no—
1295Q8—84no—
1296Q8—82no—
1297Q8—164no—
1298D4—28no—
1299D4—44no—
1300D4—48no—
1301D4—82no—
1302D4—88no—
1303D4—84no—
1304D4—88no—
1305D4—84no—
1306D4—84no—
1307D4—84no—
1308D4—84no—
1309D4—84no—
1310D4—82no—
1311D4—84no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—48no—
1376C2×C4—48no—
1377C2×C4—48no—
1378C2×C4—44no—
1379C2×C4—48no—
1380C2×C4—44no—
1381C2×C4—88no—
1382C2×C4—84no—
1383C2×C4—88no—
1384C2×C4—162no—
1385C2×C4—164no—
1386C2×C4—164no—
1387C2×C4—162no—
1388C2×C4C2×H(5,𝔽2)12yes—
1389C2×C4#58512yes—
1390C2×C4#58514yes—
1391C22—24no—
1392C22—24no—
1393C22—24no—
1394C22—44no—
1395C22—44no—
1396C22—41no—
1397C22—41no—
1398C22—42no—
1399C22—42no—
1400C22—41no—
1401C22—42no—
1402C22—42no—
1403C22—41no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—41no—
1412C22—42no—
1413C22—41no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22C22×H(5,𝔽2)11yescharacteristic
1421C22C2×#58512yes—
1422C22C2×#58511yescharacteristic
1423C22H(7,𝔽2)11yescharacteristic
1424C222−1+612yes—
1425C4—22no—
1426C4—42no—
1427C4—41no—
1428C4—41no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—41no—
1433C4—42no—
1434C4—44no—
1435C4—42no—
1436C4—44no—
1437C4—44no—
1438C4—42no—
1439C4—42no—
1440C4—42no—
1441C4—44no—
1442C4—44no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—44no—
1447C4—42no—
1448C4#353314yes—
1449C2—44no—
1450C2—81no—
1451C2—81no—
1452C2—82no—
1453C2—82no—
1454C2C2×#353311yescharacteristic
1455C2#6291811yescharacteristic
1456C2#6293912yes—
1457C2#6306311yescharacteristic
1458C2#6306512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59865C2semidirect
2. #59507C2semidirect
3. #58749C2semidirect
4. #57803C2semidirect
5. #57291C2semidirect
6. #56116C2semidirect
7. #55620C2semidirect
8. #52982C2semidirect
9. #52968C2semidirect
10. #52754C2semidirect
11. #52612C2semidirect
12. #47657C2semidirect
13. #45234C2semidirect
14. #45158C2semidirect
15. #45115C2semidirect
16. #44928C2semidirect
17. #44885C2semidirect
18. #42921C2semidirect
19. #42919C2semidirect
20. #42916C2semidirect
21. #42726C2semidirect
22. #42591C2semidirect
23. #42201C2semidirect
24. #42097C2semidirect
25. #40074C2semidirect
26. #38951C2semidirect
27. #36696C2semidirect
28. #36067C2semidirect
29. #36011C2semidirect

Maximal subgroups

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

subgroupindex
#598652
#595072
#587492
#578032
#572912
#561162
#556202
#529822
#529682
#527542
#526122
#476572
#452342
#451582
#451152
#449282
#448852
#429212
#429192
#429162
#427262
#425912
#422012
#420972
#400742
#389512
#366962
#360672
#360112