Finite Group Databasebeta

← #7657543

Subgroups — #7657543

Order 512.

4427 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42284C214yesmaximal, complemented
2#42140C214yesmaximal, complemented
3#41245C214yesmaximal, complemented
4#41225C214yesmaximal, complemented
5#40799C214yesmaximal, complemented
6#40776C214yesmaximal, complemented
7#39622C211yesmaximal, characteristic, complemented
8#39611C211yesmaximal, characteristic, complemented
9#39298C212yesmaximal, complemented
10#39292C212yesmaximal, complemented
11#39118C212yesmaximal, complemented
12#37960C212yesmaximal, complemented
13#37954C212yesmaximal, complemented
14#37627C212yesmaximal, complemented
15#37573C212yesmaximal, complemented
16#37573C212yesmaximal, complemented
17#36503C212yesmaximal, complemented
18#36211C211yesmaximal, characteristic, complemented
19#36196C211yesmaximal, characteristic, complemented
20#35893C214yesmaximal, complemented
21#35866C214yesmaximal, complemented
22#35336C211yesmaximal, characteristic, complemented
23#35295C212yesmaximal, complemented
24#34625C212yesmaximal, complemented
25#34621C211yesmaximal, characteristic, complemented
26#34317C212yesmaximal, complemented
27#34151C211yesmaximal, characteristic, complemented
28C2×#554C2212yes—
29C2×#529C2211yescharacteristic
30#2860C2212yes—
31#2860C2212yes—
32#2859C2211yescharacteristic
33#2859C2211yescharacteristic
34#2856C2212yes—
35#2851C2212yes—
36#2851C2212yes—
37#2838C2214yes—
38#2838C2214yes—
39#2837C2214yes—
40#2837C2214yes—
41#2829C2214yes—
42#2829C2214yes—
43#2806C2214yes—
44#2800C2214yes—
45#2798C2214yes—
46#2793C2214yes—
47#2792C2214yes—
48#2789C2214yes—
49#2787C2214yes—
50#2787C2214yes—
51#2786C2214yes—
52#2783C2214yes—
53#2756C2214yes—
54#2737C2214yes—
55#2732C2214yes—
56#2730C2214yes—
57#2728C2214yes—
58#2727C2214yes—
59#2715C2214yes—
60#2700C2214yes—
61#2699C2214yes—
62#2690C2214yes—
63#2689C2214yes—
64#2686C2214yes—
65#2683C2214yes—
66#2676C2214yes—
67#2667C2214yes—
68#2666C2214yes—
69#2666C2214yes—
70#2665C2214yes—
71#2662C2214yes—
72#2662C2214yes—
73#2660C2212yes—
74#2660C2212yes—
75#2654C2214yes—
76#2654C2214yes—
77#2653C2214yes—
78#2653C2214yes—
79#2651C2214yes—
80#2651C2214yes—
81#2651C2214yes—
82#2649C2214yes—
83#2649C2214yes—
84#2648C2214yes—
85#2647C2212yes—
86#2647C2211yescharacteristic
87#2644C2212yes—
88#2641C2211yescharacteristic
89#2629C2211yescharacteristic
90#2629C2211yescharacteristic
91#2629C2211yescharacteristic
92#2629C2212yes—
93#2629C2212yes—
94#2628C2212yes—
95#2628C2212yes—
96#2625C2214yes—
97#2624C2212yes—
98#2624C2212yes—
99#2624C2212yes—
100#2620C2214yes—
101#2619C2211yescharacteristic
102#2610C2214yes—
103#2601C2214yes—
104#2601C2214yes—
105#2597C2214yes—
106#2597C2214yes—
107#2596C2214yes—
108#2594C2214yes—
109#2594C2214yes—
110#2594C2214yes—
111#2590C2214yes—
112#2590C2214yes—
113#2588C2214yes—
114#2587C2214yes—
115#2587C2214yes—
116#2586C2214yes—
117#2573C2214yes—
118#2566C2212yes—
119#2566C2212yes—
120#2562C2212yes—
121#2562C2212yes—
122#2560C2214yes—
123#2560C2214yes—
124#2559C2214yes—
125#2559C2214yes—
126#2555C2214yes—
127#2552C2212yes—
128#2550C2212yes—
129#2550C2212yes—
130#2547C2212yes—
131#2542C2212yes—
132#2537C2212yes—
133#2535C2212yes—
134#2535C2212yes—
135#2533C2214yes—
136#2531C2214yes—
137#2527C2214yes—
138#2513C2214yes—
139#2512C2214yes—
140#2507C2214yes—
141#2497C2212yes—
142#2497C2212yes—
143#2496C2212yes—
144#2496C2212yes—
145#2494C2212yes—
146#2494C2212yes—
147#2491C2212yes—
148#2491C2212yes—
149#2490C2212yes—
150#2490C2212yes—
151#2490C2212yes—
152#2490C2212yes—
153#2481C2214yes—
154#2479C2214yes—
155#2479C2214yes—
156#2479C2214yes—
157#2479C2214yes—
158#2478C2214yes—
159#2478C2214yes—
160#2476C2214yes—
161#2476C2214yes—
162#2476C2214yes—
163#2474C2214yes—
164#2474C2214yes—
165#2474C2214yes—
166#2474C2214yes—
167#2469C2214yes—
168#2466C2214yes—
169#2466C2214yes—
170#2465C2214yes—
171#2461C2214yes—
172#2449C2214yes—
173#2449C2214yes—
174#2448C2214yes—
175#2443C2214yes—
176#2426C2214yes—
177#2423C2214yes—
178#2420C2214yes—
179#2414C2214yes—
180#2402C2214yes—
181#2399C2214yes—
182#2396C2214yes—
183#2396C2214yes—
184#2395C2214yes—
185#2392C2214yes—
186#2374C2212yes—
187#2374C2212yes—
188#2373C2214yes—
189#2373C2212yes—
190#2373C2214yes—
191#2373C2212yes—
192#2370C2212yes—
193#2370C2212yes—
194#2370C2212yes—
195#2369C2212yes—
196#2367C2214yes—
197#2367C2212yes—
198#2363C2214yes—
199#2363C2212yes—
200#2362C2214yes—
201#2362C2214yes—
202#2362C2214yes—
203#2362C2212yes—
204#2357C2212yes—
205#2357C2212yes—
206#2355C2212yes—
207#2354C2212yes—
208#2344C2214yes—
209#2332C2214yes—
210#2332C2214yes—
211#2330C2211yescharacteristic
212#2330C2211yescharacteristic
213#2330C2212yes—
214#2328C2212yes—
215#2324C2212yes—
216#2324C2212yes—
217#2323C2214yes—
218#2314C2212yes—
219C4×C4⋊Q8C2212yes—
220C4×C4⋊Q8C2212yes—
221C4×#127C2211yescharacteristic
222C4×#125C2212yes—
223C4×#125C2212yes—
224C4×#125C2211yescharacteristic
225C4×#125C2212yes—
226C4×#121C2212yes—
227#2298C2212yes—
228#2295C2211yescharacteristic
229#2293C2212yes—
230#2293C2212yes—
231#2293C2212yes—
232#2293C2211yescharacteristic
233#2293C2212yes—
234#2290C2212yes—
235#2285C2212yes—
236#2283C2212yes—
237#2274C2214yes—
238C42×Q8C2211yescharacteristic
239C42×D4C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2212yes—
242C4×#117C2211yescharacteristic
243#554—216no—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2312yes—
246C2×#127C2311yescharacteristic
247#529—28no—
248C2×#126C2312yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2311yescharacteristic
256C2×#125C2311yescharacteristic
257C2×#125C2312yes—
258C2×#125C2311yescharacteristic
259C2×#125C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2314yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264C2×#123C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2311yescharacteristic
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×#121C2311yescharacteristic
272C2×#121C2312yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×D4C2312yes—
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×#117C2311yescharacteristic
291C2×#117C2312yes—
292C2×#117C2314yes—
293C2×#117C2312yes—
294C2×#117C2314yes—
295C2×#117C2312yes—
296C2×#117C2311yescharacteristic
297C2×#117C2314yes—
298C2×#117C2314yes—
299C2×#117C2314yes—
300C22×C4⋊C4C2314yes—
301C22×C42C2311yescharacteristic
302C22×C42C2312yes—
303#401C2314yes—
304#401C2314yes—
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#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
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#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2312yes—
416#390C2314yes—
417#390C2314yes—
418#390C2312yes—
419#390C2314yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#390C2312yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2312yes—
429#390C2312yes—
430#390C2314yes—
431#390C2314yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#390C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#388C2312yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2312yes—
486#388C2312yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2312yes—
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#388C2312yes—
507#388C2314yes—
508#388C2314yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2312yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
516#388C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2312yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2314yes—
550#387C2312yes—
551#387C2312yes—
552#387C2312yes—
553#387C2312yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2312yes—
564#386C2312yes—
565#386C2314yes—
566#386C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2312yes—
578#385C2312yes—
579#384C2311yescharacteristic
580#384C2312yes—
581#384C2312yes—
582#384C2311yescharacteristic
583#384C2312yes—
584#384C2311yescharacteristic
585#384C2314yes—
586#383C2314yes—
587#382C2312yes—
588#382C2312yes—
589#382C2312yes—
590#382C2311yescharacteristic
591#382C2312yes—
592#382C2314yes—
593#381C2314yes—
594#381C2314yes—
595#381C2314yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2312yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2312yes—
604#380C2314yes—
605#380C2314yes—
606#380C2312yes—
607#380C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2311yescharacteristic
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2311yescharacteristic
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2312yes—
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2311yescharacteristic
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2311yescharacteristic
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666#376C2312yes—
667#376C2311yescharacteristic
668#376C2314yes—
669#376C2311yescharacteristic
670#376C2311yescharacteristic
671#376C2311yescharacteristic
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C43C2312yes—
675C43C2312yes—
676C22×Q8C2414yes—
677C22×Q8C2414yes—
678C22×Q8C2411yescharacteristic
679C22×D4C2412yes—
680C22×D4C2411yescharacteristic
681C22×D4C2412yes—
682C22×D4C2414yes—
683C22×D4C2414yes—
684C22×D4C2414yes—
685C22×D4C2414yes—
686C23×C4C2411yescharacteristic
687C23×C4C2412yes—
688C23×C4C2412yes—
689C23×C4C2414yes—
690C23×C4C2414yes—
691C23×C4C2414yes—
692C23×C4C2411yescharacteristic
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C4⋊Q8—28no—
696C4⋊Q8—44no—
697#127—24no—
698#126—28no—
699#126—48no—
700#126—48no—
701#126—84no—
702#126—84no—
703#125—24no—
704#125—28no—
705#125—28no—
706#125—24no—
707#125—42no—
708#125—42no—
709#125—44no—
710#124—24no—
711#124—48no—
712#124—84no—
713#124—84no—
714#123—28no—
715C22⋊Q8—24no—
716C22⋊Q8—216no—
717C22⋊Q8—216no—
718C22⋊Q8—216no—
719C22⋊Q8—84no—
720C22⋊Q8—84no—
721#121—24no—
722#121—48no—
723#121—44no—
724#121—44no—
725#121—44no—
726#121—84no—
727#121—84no—
728C4×Q8—44no—
729C4×Q8—84no—
730C4×Q8—84no—
731C4×Q8#4118yes—
732C4×D4—24no—
733C4×D4—28no—
734C4×D4—28no—
735C4×D4—28no—
736C4×D4—28no—
737C4×D4—44no—
738C4×D4—84no—
739C4×D4—84no—
740#117—28no—
741#117—24no—
742#117—42no—
743#117—44no—
744#117—48no—
745#117—48no—
746#117—44no—
747#117—84no—
748#117—84no—
749#117—84no—
750C2×C4⋊C4—216no—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C42—24no—
853C2×C42—28no—
854C2×C42C2411yescharacteristic
855C2×C42C2412yes—
856C2×C42C2411yescharacteristic
857C2×C42C2414yes—
858C2×C42C2411yescharacteristic
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2412yes—
891#95C2412yes—
892#95C2414yes—
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
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#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949C24C2512yes—
950C24C2514yes—
951C24C2511yescharacteristic
952C2×Q8—28no—
953C2×Q8—42no—
954C2×Q8—44no—
955C2×Q8—44no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×Q8—44no—
959C2×Q8C2×#4114yes—
960C2×D4—24no—
961C2×D4—22no—
962C2×D4—24no—
963C2×D4—24no—
964C2×D4—28no—
965C2×D4—24no—
966C2×D4—42no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—42no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—28no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—22no—
991C22×C4—28no—
992C22×C4—28no—
993C22×C4—24no—
994C22×C4—44no—
995C22×C4—42no—
996C22×C4—44no—
997C22×C4—42no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—44no—
1003C22×C4—42no—
1004C22×C4—44no—
1005C22×C4C2511yescharacteristic
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2514yes—
1011C22×C4C2512yes—
1012C22×C4C2514yes—
1013C22×C4C2514yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2511yescharacteristic
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2511yescharacteristic
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—22no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—28no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—42no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
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—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4C2×#4118yes—
1083C4⋊C4C2×#4114yes—
1084C22⋊C4—24no—
1085C22⋊C4—24no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—24no—
1090C22⋊C4—24no—
1091C22⋊C4—24no—
1092C22⋊C4—24no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—24no—
1096C22⋊C4—24no—
1097C22⋊C4—44no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—42no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—42no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—42no—
1130C42—22no—
1131C42—22no—
1132C42—22no—
1133C42—24no—
1134C42—24no—
1135C42—24no—
1136C42—22no—
1137C42—22no—
1138C42—24no—
1139C42—28no—
1140C42—22no—
1141C42—24no—
1142C42—24no—
1143C42—44no—
1144C42—44no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—42no—
1156C42—42no—
1157C42—42no—
1158C42—44no—
1159C42—44no—
1160C42—42no—
1161C42C2×#4114yes—
1162C42C2×#4118yes—
1163C422−1+414yes—
1164C23—22no—
1165C23—24no—
1166C23—21no—
1167C23—21no—
1168C23—22no—
1169C23—24no—
1170C23—22no—
1171C23—24no—
1172C23—22no—
1173C23—24no—
1174C23—24no—
1175C23—21no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—22no—
1182C23—22no—
1183C23C2611yescharacteristic
1184Q8—44no—
1185Q8—88no—
1186Q8—88no—
1187D4—44no—
1188D4—48no—
1189D4—84no—
1190D4—88no—
1191D4—88no—
1192D4—164no—
1193D4—164no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—48no—
1254C2×C4—416no—
1255C2×C4—44no—
1256C2×C4—44no—
1257C2×C4—48no—
1258C2×C4—82no—
1259C2×C4—88no—
1260C2×C4—88no—
1261C2×C4—84no—
1262C2×C4C22×#4112yes—
1263C2×C4C22×#4112yes—
1264C2×C4C22×#4114yes—
1265C2×C4C22×#4114yes—
1266C2×C4C22×#4112yes—
1267C2×C4C2×2−1+414yes—
1268C2×C4C2×2−1+412yes—
1269C2×C4#58514yes—
1270C2×C4#58512yes—
1271C22—42no—
1272C22—41no—
1273C22—44no—
1274C22—44no—
1275C22—41no—
1276C22—42no—
1277C22—44no—
1278C22—41no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—44no—
1283C22—44no—
1284C22—42no—
1285C22—42no—
1286C22—44no—
1287C22—42no—
1288C22—44no—
1289C22—42no—
1290C22C23×#4111yescharacteristic
1291C22C22×2−1+411yescharacteristic
1292C22C2×#58511yescharacteristic
1293C22C2×#58512yes—
1294C22H(7,𝔽2)12yes—
1295C4—22no—
1296C4—24no—
1297C4—24no—
1298C4—22no—
1299C4—24no—
1300C4—24no—
1301C4—41no—
1302C4—42no—
1303C4—41no—
1304C4—44no—
1305C4—44no—
1306C4—41no—
1307C4—44no—
1308C4—42no—
1309C4—44no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—44no—
1315C4—44no—
1316C4—44no—
1317C4—42no—
1318C4#351814yes—
1319C2—81no—
1320C2—82no—
1321C2—84no—
1322C2#6268611yescharacteristic
1323C2C2×#351811yescharacteristic
1324C2#6285811yescharacteristic
1325C2#6295812yes—
1326C2#6296912yes—
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. #42284C2semidirect
2. #42140C2semidirect
3. #41245C2semidirect
4. #41225C2semidirect
5. #40799C2semidirect
6. #40776C2semidirect
7. #39622C2semidirect
8. #39611C2semidirect
9. #39298C2semidirect
10. #39292C2semidirect
11. #39118C2semidirect
12. #37960C2semidirect
13. #37954C2semidirect
14. #37627C2semidirect
15. #37573C2semidirect
16. #37573C2semidirect
17. #36503C2semidirect
18. #36211C2semidirect
19. #36196C2semidirect
20. #35893C2semidirect
21. #35866C2semidirect
22. #35336C2semidirect
23. #35295C2semidirect
24. #34625C2semidirect
25. #34621C2semidirect
26. #34317C2semidirect
27. #34151C2semidirect

Maximal subgroups

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

subgroupindex
#422842
#421402
#412452
#412252
#407992
#407762
#396222
#396112
#392982
#392922
#391182
#379602
#379542
#376272
#375732
#365032
#362112
#361962
#358932
#358662
#353362
#352952
#346252
#346212
#343172
#341512