Finite Group Databasebeta

← #7715099

Subgroups — #7715099

Order 512.

4326 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51944C214yesmaximal, complemented
2#51928C214yesmaximal, complemented
3#51677C214yesmaximal, complemented
4#51644C214yesmaximal, complemented
5#46977C214yesmaximal, complemented
6#46865C214yesmaximal, complemented
7#46737C214yesmaximal, complemented
8#46487C214yesmaximal, complemented
9#39297C212yesmaximal, complemented
10#39296C212yesmaximal, complemented
11#39281C212yesmaximal, complemented
12#39280C212yesmaximal, complemented
13#38937C212yesmaximal, complemented
14#38936C212yesmaximal, complemented
15#38933C212yesmaximal, complemented
16#38932C212yesmaximal, complemented
17#37519C211yesmaximal, characteristic, complemented
18#37515C211yesmaximal, characteristic
19#37421C211yesmaximal, characteristic, complemented
20#37325C212yesmaximal, complemented
21#37309C211yesmaximal, characteristic, complemented
22#35321C211yesmaximal, characteristic, complemented
23#35287C211yesmaximal, characteristic, complemented
24#35270C212yesmaximal, complemented
25#35258C212yesmaximal, complemented
26#34422C212yesmaximal, complemented
27#34056C211yesmaximal, characteristic, complemented
28C2×#542C2212yes—
29C2×C4×#41C2211yescharacteristic
30#2863C2212yes—
31#2860C2212yes—
32#2857C2212yes—
33#2857C2212yes—
34#2855C2212yes—
35#2854C2212yes—
36#2850C2212yes—
37#2850C2212yes—
38#2827C2214yes—
39#2825C2214yes—
40#2810C2214yes—
41#2808C2214yes—
42#2806C2214yes—
43#2803C2214yes—
44#2801C2214yes—
45#2798C2214yes—
46#2790C2214yes—
47#2788C2214yes—
48#2786C2214yes—
49#2785C2214yes—
50#2784C2214yes—
51#2781C2214yes—
52#2781C2214yes—
53#2778C2214yes—
54#2775C2214yes—
55#2766C2214yes—
56#2766C2214yes—
57#2764C2214yes—
58#2764C2214yes—
59#2762C2214yes—
60#2759C2214yes—
61#2759C2214yes—
62#2759C2214yes—
63#2757C2214yes—
64#2756C2214yes—
65#2756C2214yes—
66#2756C2214yes—
67#2745C2214yes—
68#2744C2214yes—
69#2740C2214yes—
70#2738C2214yes—
71#2738C2214yes—
72#2730C2214yes—
73#2726C2214yes—
74#2725C2214yes—
75#2718C2214yes—
76#2712C2214yes—
77#2711C2214yes—
78#2710C2214yes—
79#2704C2214yes—
80#2704C2214yes—
81#2702C2214yes—
82#2702C2214yes—
83#2696C2214yes—
84#2693C2214yes—
85#2687C2214yes—
86#2687C2214yes—
87#2686C2214yes—
88#2666C2214yes—
89#2661C2214yes—
90#2653C2214yes—
91#2651C2214yes—
92#2647C2211yescharacteristic
93#2647C2212yes—
94#2647C2211yescharacteristic
95#2645C2212yes—
96#2644C2212yes—
97#2642C2211yescharacteristic
98#2641C2211yescharacteristic
99#2640C2212yes—
100#2629C2211yescharacteristic
101#2629C2211yescharacteristic
102#2628C2212yes—
103#2621C2211yescharacteristic
104#2620C2212yes—
105#2619C2211yescharacteristic
106#2616C2212yes—
107#2615C2212yes—
108#2605C2214yes—
109#2602C2214yes—
110#2596C2214yes—
111#2594C2214yes—
112#2593C2214yes—
113#2593C2214yes—
114#2592C2214yes—
115#2587C2214yes—
116#2585C2214yes—
117#2579C2214yes—
118#2577C2214yes—
119#2573C2214yes—
120#2572C2214yes—
121#2572C2214yes—
122#2568C2212yes—
123#2565C2214yes—
124#2563C2212yes—
125#2562C2214yes—
126#2558C2214yes—
127#2554C2214yes—
128#2552C2212yes—
129#2552C2212yes—
130#2550C2212yes—
131#2550C2212yes—
132#2545C2212yes—
133#2544C2212yes—
134#2532C2214yes—
135#2532C2214yes—
136#2532C2214yes—
137#2530C2214yes—
138#2529C2214yes—
139#2527C2214yes—
140#2526C2214yes—
141#2524C2214yes—
142#2521C2214yes—
143#2518C2214yes—
144#2518C2214yes—
145#2515C2214yes—
146#2514C2214yes—
147#2514C2214yes—
148#2510C2214yes—
149#2495C2214yes—
150#2495C2212yes—
151#2495C2212yes—
152#2495C2214yes—
153#2494C2212yes—
154#2494C2212yes—
155#2492C2212yes—
156#2491C2212yes—
157#2490C2212yes—
158#2489C2214yes—
159#2489C2212yes—
160#2488C2214yes—
161#2486C2214yes—
162#2469C2214yes—
163#2469C2214yes—
164#2468C2214yes—
165#2467C2214yes—
166#2465C2214yes—
167#2463C2214yes—
168#2461C2214yes—
169#2460C2214yes—
170#2459C2214yes—
171#2459C2214yes—
172#2457C2214yes—
173#2457C2214yes—
174#2456C2214yes—
175#2455C2214yes—
176#2450C2214yes—
177#2443C2214yes—
178#2442C2214yes—
179#2429C2212yes—
180#2428C2212yes—
181#2427C2212yes—
182#2426C2212yes—
183#2423C2212yes—
184#2423C2212yes—
185#2423C2214yes—
186#2422C2212yes—
187#2422C2212yes—
188#2420C2214yes—
189#2419C2214yes—
190#2383C2214yes—
191#2378C2214yes—
192#2373C2214yes—
193#2369C2212yes—
194#2367C2212yes—
195#2367C2212yes—
196#2365C2212yes—
197#2360C2214yes—
198#2357C2212yes—
199#2356C2212yes—
200Q8×C4⋊C4C2212yes—
201D4×C4⋊C4C2212yes—
202#2337C2214yes—
203#2335C2214yes—
204#2331C2212yes—
205#2326C2212yes—
206#2326C2214yes—
207#2324C2212yes—
208#2324C2212yes—
209#2323C2212yes—
210#2323C2212yes—
211#2322C2214yes—
212#2320C2212yes—
213#2320C2212yes—
214#2320C2212yes—
215#2320C2212yes—
216#2319C2212yes—
217#2319C2212yes—
218#2319C2212yes—
219#2319C2212yes—
220#2318C2212yes—
221#2318C2212yes—
222#2318C2212yes—
223#2318C2212yes—
224#2314C2212yes—
225C4×C4⋊Q8C2211yescharacteristic
226C4×#127C2211yescharacteristic
227C4×#125C2211yescharacteristic
228C4×#125C2211yescharacteristic
229C4×C22⋊Q8C2212yes—
230C4×C22⋊Q8C2212yes—
231C4×#121C2212yes—
232C4×#121C2212yes—
233#2298C2212yes—
234#2298C2212yes—
235#2297C2211yescharacteristic
236#2297C2211yescharacteristic
237#2296C2211yescharacteristic
238#2296C2211yescharacteristic
239#2283C2212yes—
240#2283C2212yes—
241C4×#117C2211yescharacteristic
242C2×#376C2211yescharacteristic
243C22×#41C2311yescharacteristic
244#542—216no—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2312yes—
248C2×#127C2311yescharacteristic
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#125C2311yescharacteristic
252C2×#125C2311yescharacteristic
253C2×#125C2314yes—
254C2×#125C2314yes—
255C2×#124C2314yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C4×#41—28no—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×#117C2312yes—
289C2×#117C2311yescharacteristic
290C2×#117C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C22×C4⋊C4C2314yes—
293C22×C42C2312yes—
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297#401C2314yes—
298#401C2314yes—
299#401C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#392C2314yes—
389#392C2314yes—
390#392C2314yes—
391#392C2314yes—
392#392C2314yes—
393#391C2312yes—
394#391C2314yes—
395#391C2314yes—
396#391C2312yes—
397#391C2312yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2312yes—
402#391C2312yes—
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2312yes—
414#390C2312yes—
415#390C2314yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#390C2314yes—
423#390C2314yes—
424#390C2312yes—
425#390C2314yes—
426#390C2314yes—
427#390C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2314yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2312yes—
469#388C2312yes—
470#388C2312yes—
471#388C2312yes—
472#388C2312yes—
473#388C2312yes—
474#388C2312yes—
475#388C2312yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2312yes—
521#387C2312yes—
522#387C2312yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2312yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#386C2312yes—
546#386C2314yes—
547#386C2312yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2312yes—
553#386C2312yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2311yescharacteristic
565#385C2311yescharacteristic
566#385C2311yescharacteristic
567#385C2311yescharacteristic
568#385C2312yes—
569#385C2312yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#384C2311yescharacteristic
582#384C2311yescharacteristic
583#384C2314yes—
584#384C2312yes—
585#384C2312yes—
586#383C2312yes—
587#383C2314yes—
588#383C2314yes—
589#383C2314yes—
590#383C2314yes—
591#383C2312yes—
592#383C2312yes—
593#383C2312yes—
594#383C2314yes—
595#383C2314yes—
596#382C2311yescharacteristic
597#382C2311yescharacteristic
598#382C2312yes—
599#382C2312yes—
600#382C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2312yes—
604#382C2314yes—
605#382C2314yes—
606#382C2314yes—
607#381C2312yes—
608#381C2314yes—
609#381C2314yes—
610#381C2314yes—
611#381C2314yes—
612#381C2312yes—
613#381C2312yes—
614#381C2312yes—
615#380C2312yes—
616#380C2314yes—
617#380C2314yes—
618#380C2314yes—
619#380C2314yes—
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2314yes—
626#380C2314yes—
627#380C2312yes—
628#380C2314yes—
629#380C2312yes—
630#380C2314yes—
631#380C2312yes—
632#380C2312yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665#376C2311yescharacteristic
666#376C2312yes—
667#376C2312yes—
668#376C2312yes—
669#376C2311yescharacteristic
670#376C2312yes—
671#376C2314yes—
672C2×#95C2312yes—
673C2×#95C2312yes—
674C43C2311yescharacteristic
675C43C2311yescharacteristic
676C2×#41—24no—
677C2×#41—42no—
678C2×#41—42no—
679C22×Q8C2412yes—
680C22×Q8C2411yescharacteristic
681C22×Q8C2414yes—
682C22×Q8C2414yes—
683C22×D4C2412yes—
684C22×D4C2412yes—
685C22×D4C2411yescharacteristic
686C22×D4C2414yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2414yes—
690C23×C4C2412yes—
691C23×C4C2411yescharacteristic
692C23×C4C2414yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C23×C4C2411yescharacteristic
699C23×C4C2412yes—
700C23×C4C2411yescharacteristic
701C4⋊Q8—28no—
702C4⋊Q8—44no—
703C4⋊Q8—42no—
704#127—42no—
705#126—216no—
706#126—84no—
707#125—42no—
708#125—42no—
709#125—84no—
710#125—84no—
711#124—216no—
712#124—28no—
713#124—44no—
714#124—84no—
715#123—216no—
716#123—84no—
717#123—84no—
718#123—84no—
719C22⋊Q8—28no—
720C22⋊Q8—216no—
721C22⋊Q8—44no—
722C22⋊Q8—44no—
723C22⋊Q8—84no—
724C22⋊Q8—84no—
725#121—28no—
726#121—44no—
727#121—44no—
728#121—84no—
729C4×Q8—28no—
730C4×Q8—28no—
731C4×Q8—44no—
732C4×Q8—44no—
733C4×Q8—84no—
734C4×D4—28no—
735C4×D4—28no—
736C4×D4—28no—
737C4×D4—28no—
738C4×D4—44no—
739C4×D4—44no—
740C4×D4—84no—
741C4×D4—84no—
742C4×D4—84no—
743#117—28no—
744#117—42no—
745#117—42no—
746#117#4118yes—
747C2×C4⋊C4—84no—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2411yescharacteristic
843C2×C42—24no—
844C2×C42—28no—
845C2×C42—42no—
846C2×C42—42no—
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849C2×C42C2411yescharacteristic
850C2×C42C2411yescharacteristic
851C2×C42C2411yescharacteristic
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2411yescharacteristic
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945C24C2514yes—
946C24C2512yes—
947C24C2511yescharacteristic
948#41—416no—
949C2×Q8—22no—
950C2×Q8—24no—
951C2×Q8—28no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—41no—
955C2×Q8—41no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×Q8—44no—
959C2×Q8—44no—
960C2×Q8—44no—
961C2×D4—24no—
962C2×D4—28no—
963C2×D4—22no—
964C2×D4—24no—
965C2×D4—24no—
966C2×D4—24no—
967C2×D4—41no—
968C2×D4—41no—
969C2×D4—42no—
970C2×D4—42no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—28no—
991C22×C4—41no—
992C22×C4—42no—
993C22×C4—41no—
994C22×C4—44no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—44no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4C2×#4114yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2514yes—
1020C22×C4C2514yes—
1021C22×C4C2512yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2514yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2512yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2512yes—
1036C22×C4C2511yescharacteristic
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—42no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—41no—
1058C4⋊C4—42no—
1059C4⋊C4—41no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4C2×#4118yes—
1086C22⋊C4—28no—
1087C22⋊C4—24no—
1088C22⋊C4—24no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—42no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—42no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—42no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—42no—
1129C22⋊C4—44no—
1130C22⋊C4C2×#4114yes—
1131C22⋊C4C2×#4114yes—
1132C42—22no—
1133C42—22no—
1134C42—24no—
1135C42—24no—
1136C42—24no—
1137C42—28no—
1138C42—24no—
1139C42—24no—
1140C42—22no—
1141C42—22no—
1142C42—22no—
1143C42—22no—
1144C42—42no—
1145C42—41no—
1146C42—41no—
1147C42—44no—
1148C42—42no—
1149C42—44no—
1150C42—42no—
1151C42—42no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—42no—
1159C42C2×#4118yes—
1160C23—21no—
1161C23—21no—
1162C23—22no—
1163C23—22no—
1164C23—24no—
1165C23—22no—
1166C23—24no—
1167C23—24no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—24no—
1172C23—22no—
1173C23—24no—
1174C23—22no—
1175C23—24no—
1176C23—22no—
1177C23—24no—
1178C23C22×#4112yes—
1179C23C2611yescharacteristic
1180Q8—44no—
1181Q8—48no—
1182Q8—88no—
1183Q8—164no—
1184D4—44no—
1185D4—48no—
1186D4—48no—
1187D4—88no—
1188D4—88no—
1189D4—88no—
1190D4—164no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—28no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—48no—
1255C2×C4—84no—
1256C2×C4—88no—
1257C2×C4—84no—
1258C2×C4—84no—
1259C2×C4—84no—
1260C2×C4—82no—
1261C2×C4—82no—
1262C2×C4—164no—
1263C2×C4—164no—
1264C2×C4C22×#4114yes—
1265C2×C4C22×#4112yes—
1266C2×C4C22×#4114yes—
1267C2×C4C22×#4112yes—
1268C2×C4#58512yes—
1269C2×C4#58512yes—
1270C22—22no—
1271C22—24no—
1272C22—42no—
1273C22—41no—
1274C22—41no—
1275C22—42no—
1276C22—44no—
1277C22—44no—
1278C22—42no—
1279C22—42no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—42no—
1284C22—42no—
1285C22—44no—
1286C22—42no—
1287C22—44no—
1288C22—42no—
1289C22C23×#4111yescharacteristic
1290C22C2×#58511yescharacteristic
1291C22C2×#58511yescharacteristic
1292C22H(7,𝔽2)12yes—
1293C222−1+612yes—
1294C4—22no—
1295C4—24no—
1296C4—24no—
1297C4—42no—
1298C4—44no—
1299C4—42no—
1300C4—42no—
1301C4—44no—
1302C4—44no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—44no—
1308C4—44no—
1309C4—41no—
1310C4—42no—
1311C4—44no—
1312C4—41no—
1313C4—44no—
1314C4—41no—
1315C4—41no—
1316C4—42no—
1317C4#349314yes—
1318C2—42no—
1319C2—82no—
1320C2—84no—
1321C2C2×#349311yescharacteristic
1322C2#6285712yes—
1323C2#6288212yes—
1324C2#6288311yescharacteristic
1325C2#6289011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37515C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51944C2semidirect
2. #51928C2semidirect
3. #51677C2semidirect
4. #51644C2semidirect
5. #46977C2semidirect
6. #46865C2semidirect
7. #46737C2semidirect
8. #46487C2semidirect
9. #39297C2semidirect
10. #39296C2semidirect
11. #39281C2semidirect
12. #39280C2semidirect
13. #38937C2semidirect
14. #38936C2semidirect
15. #38933C2semidirect
16. #38932C2semidirect
17. #37519C2semidirect
19. #37421C2semidirect
20. #37325C2semidirect
21. #37309C2semidirect
22. #35321C2semidirect
23. #35287C2semidirect
24. #35270C2semidirect
25. #35258C2semidirect
26. #34422C2semidirect
27. #34056C2semidirect

Maximal subgroups

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

subgroupindex
#519442
#519282
#516772
#516442
#469772
#468652
#467372
#464872
#392972
#392962
#392812
#392802
#389372
#389362
#389332
#389322
#375192
#375152
#374212
#373252
#373092
#353212
#352872
#352702
#352582
#344222
#340562