Finite Group Databasebeta

← #7657610

Subgroups — #7657610

Order 512.

4927 conjugacy classes of subgroups.

The subgroup lattice has 1413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42144C214yesmaximal, complemented
2#42136C214yesmaximal, complemented
3#41240C214yesmaximal, complemented
4#41220C214yesmaximal, complemented
5#40794C214yesmaximal, complemented
6#40773C214yesmaximal, complemented
7#39750C211yesmaximal, characteristic, complemented
8#39739C211yesmaximal, characteristic, complemented
9#39285C212yesmaximal, complemented
10#39282C212yesmaximal, complemented
11#39130C212yesmaximal, complemented
12#37772C212yesmaximal, complemented
13#37766C212yesmaximal, complemented
14#37626C212yesmaximal, complemented
15#37579C212yesmaximal, complemented
16#37570C212yesmaximal, complemented
17#36502C212yesmaximal, complemented
18#36149C211yesmaximal, characteristic, complemented
19#36136C211yesmaximal, characteristic, complemented
20#35766C214yesmaximal, complemented
21#35719C214yesmaximal, complemented
22#35331C211yesmaximal, characteristic, complemented
23#35299C212yesmaximal, complemented
24#34624C212yesmaximal, complemented
25#34621C211yesmaximal, characteristic, complemented
26#34331C212yesmaximal, complemented
27#34151C211yesmaximal, characteristic, complemented
28C2×#559C2212yes—
29C2×#542C2212yes—
30C2×#532C2212yes—
31C2×#529C2211yescharacteristic
32C2×#529C2212yes—
33#2863C2212yes—
34#2862C2211yescharacteristic
35#2860C2212yes—
36#2858C2211yescharacteristic
37#2857C2212yes—
38#2850C2212yes—
39#2850C2212yes—
40#2837C2214yes—
41#2836C2214yes—
42#2829C2214yes—
43#2828C2214yes—
44#2828C2214yes—
45#2828C2214yes—
46#2800C2214yes—
47#2799C2214yes—
48#2797C2214yes—
49#2795C2214yes—
50#2793C2214yes—
51#2772C2214yes—
52#2755C2214yes—
53#2733C2214yes—
54#2733C2214yes—
55#2733C2214yes—
56#2730C2214yes—
57#2730C2214yes—
58#2722C2214yes—
59#2718C2214yes—
60#2714C2214yes—
61#2714C2214yes—
62#2703C2214yes—
63#2694C2214yes—
64#2691C2214yes—
65#2682C2214yes—
66#2680C2214yes—
67#2673C2214yes—
68#2673C2214yes—
69#2672C2214yes—
70#2667C2214yes—
71#2662C2214yes—
72#2662C2214yes—
73#2661C2214yes—
74#2661C2214yes—
75#2661C2214yes—
76#2660C2212yes—
77#2657C2212yes—
78#2651C2214yes—
79#2651C2214yes—
80#2651C2214yes—
81#2649C2214yes—
82#2648C2214yes—
83#2648C2214yes—
84#2648C2214yes—
85#2648C2214yes—
86#2647C2211yescharacteristic
87#2644C2212yes—
88#2641C2211yescharacteristic
89#2640C2212yes—
90#2635C2214yes—
91#2635C2214yes—
92#2629C2211yescharacteristic
93#2625C2212yes—
94#2624C2214yes—
95#2624C2212yes—
96#2624C2212yes—
97#2621C2211yescharacteristic
98#2620C2212yes—
99#2620C2212yes—
100#2619C2211yescharacteristic
101#2619C2214yes—
102#2619C2211yescharacteristic
103#2619C2212yes—
104#2619C2212yes—
105#2608C2214yes—
106#2600C2214yes—
107#2598C2214yes—
108#2596C2214yes—
109#2595C2214yes—
110#2595C2214yes—
111#2589C2214yes—
112#2588C2214yes—
113#2578C2214yes—
114#2573C2214yes—
115#2571C2212yes—
116#2570C2212yes—
117#2570C2212yes—
118#2560C2214yes—
119#2560C2214yes—
120#2560C2214yes—
121#2557C2214yes—
122#2557C2214yes—
123#2554C2214yes—
124#2554C2214yes—
125#2545C2212yes—
126#2544C2212yes—
127#2543C2214yes—
128#2541C2212yes—
129#2541C2212yes—
130#2540C2212yes—
131#2540C2212yes—
132#2537C2212yes—
133#2536C2212yes—
134#2535C2212yes—
135#2532C2214yes—
136#2531C2214yes—
137#2531C2214yes—
138#2531C2214yes—
139#2526C2214yes—
140#2520C2214yes—
141#2518C2214yes—
142#2479C2214yes—
143#2478C2214yes—
144#2477C2214yes—
145#2476C2214yes—
146#2476C2214yes—
147#2474C2214yes—
148#2471C2214yes—
149#2468C2214yes—
150#2468C2214yes—
151#2467C2214yes—
152#2467C2214yes—
153#2467C2214yes—
154#2456C2214yes—
155#2456C2214yes—
156#2456C2214yes—
157#2456C2214yes—
158#2456C2214yes—
159#2456C2214yes—
160#2447C2214yes—
161#2445C2214yes—
162#2444C2214yes—
163#2438C2214yes—
164#2431C2214yes—
165#2429C2212yes—
166#2428C2214yes—
167#2428C2212yes—
168#2428C2212yes—
169#2428C2212yes—
170#2427C2214yes—
171#2427C2212yes—
172#2426C2212yes—
173#2425C2214yes—
174#2423C2212yes—
175#2422C2212yes—
176#2421C2212yes—
177#2420C2214yes—
178#2420C2212yes—
179#2420C2212yes—
180#2420C2212yes—
181#2407C2214yes—
182#2407C2214yes—
183#2395C2214yes—
184#2392C2214yes—
185#2392C2214yes—
186#2392C2214yes—
187#2388C2214yes—
188#2388C2214yes—
189#2374C2212yes—
190#2374C2212yes—
191#2373C2212yes—
192#2373C2212yes—
193#2370C2212yes—
194#2367C2212yes—
195#2367C2212yes—
196#2367C2214yes—
197#2367C2212yes—
198#2366C2212yes—
199#2364C2214yes—
200#2363C2212yes—
201#2363C2214yes—
202#2362C2212yes—
203#2359C2214yes—
204#2359C2214yes—
205#2355C2212yes—
206#2354C2214yes—
207#2353C2214yes—
208Q8×C4⋊C4C2212yes—
209#2349C2212yes—
210#2349C2212yes—
211#2339C2214yes—
212#2335C2214yes—
213#2335C2214yes—
214#2331C2212yes—
215#2328C2211yescharacteristic
216#2327C2211yescharacteristic
217#2326C2214yes—
218#2326C2212yes—
219#2324C2212yes—
220#2323C2212yes—
221C4×#127C2212yes—
222C4×#127C2211yescharacteristic
223C4×#127C2212yes—
224C4×#125C2211yescharacteristic
225C4×#124C2212yes—
226C4×#124C2212yes—
227C4×#124C2212yes—
228C4×#121C2212yes—
229#2298C2212yes—
230#2295C2212yes—
231#2295C2211yescharacteristic
232#2293C2212yes—
233#2293C2212yes—
234#2293C2211yescharacteristic
235#2293C2212yes—
236#2290C2212yes—
237#2275C2214yes—
238C42×Q8C2211yescharacteristic
239C42×D4C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2212yes—
242C4×#117C2211yescharacteristic
243C22×#41C2314yes—
244#559—216no—
245#542—48no—
246#532—48no—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2311yescharacteristic
249C2×#127C2312yes—
250C2×#127C2311yescharacteristic
251C2×#127C2312yes—
252C2×#127C2311yescharacteristic
253C2×#127C2314yes—
254#529—28no—
255#529—48no—
256C2×#126C2312yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#125C2311yescharacteristic
261C2×#125C2311yescharacteristic
262C2×#124C2312yes—
263C2×#124C2314yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2311yescharacteristic
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#124C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2312yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×C22⋊Q8C2311yescharacteristic
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×#121C2311yescharacteristic
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×#117C2312yes—
321C2×#117C2311yescharacteristic
322C2×#117C2312yes—
323C2×#117C2314yes—
324C2×#117C2312yes—
325C2×#117C2311yescharacteristic
326C2×#117C2314yes—
327C2×#117C2314yes—
328C22×C42C2311yescharacteristic
329C22×C42C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#395C2314yes—
381#395C2314yes—
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#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#393C2314yes—
413#393C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2312yes—
450#390C2314yes—
451#390C2314yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2314yes—
462#390C2312yes—
463#390C2314yes—
464#390C2312yes—
465#390C2314yes—
466#390C2314yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2312yes—
497#388C2312yes—
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#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2312yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2314yes—
528#388C2312yes—
529#388C2312yes—
530#388C2312yes—
531#388C2312yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2312yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2312yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2312yes—
583#386C2312yes—
584#386C2314yes—
585#386C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2312yes—
597#385C2312yes—
598#384C2312yes—
599#384C2312yes—
600#384C2311yescharacteristic
601#384C2314yes—
602#383C2314yes—
603#382C2311yescharacteristic
604#382C2311yescharacteristic
605#382C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2311yescharacteristic
609#382C2314yes—
610#381C2314yes—
611#381C2314yes—
612#381C2314yes—
613#380C2314yes—
614#380C2312yes—
615#380C2312yes—
616#380C2314yes—
617#380C2314yes—
618#380C2314yes—
619#380C2312yes—
620#380C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2311yescharacteristic
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2311yescharacteristic
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2311yescharacteristic
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2311yescharacteristic
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667#376C2312yes—
668#376C2314yes—
669#376C2311yescharacteristic
670#376C2311yescharacteristic
671#376C2311yescharacteristic
672#376C2311yescharacteristic
673C2×#95C2314yes—
674C2×#95C2314yes—
675C43C2311yescharacteristic
676C43C2312yes—
677C43C2312yes—
678C43C2311yescharacteristic
679C2×#41—48no—
680C2×#41—48no—
681C2×#41—84no—
682C22×Q8C2412yes—
683C22×Q8C2414yes—
684C22×Q8C2411yescharacteristic
685C22×D4C2412yes—
686C22×D4C2412yes—
687C22×D4C2411yescharacteristic
688C22×D4C2414yes—
689C22×D4C2414yes—
690C22×D4C2412yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C22×D4C2414yes—
700C22×D4C2414yes—
701C23×C4C2411yescharacteristic
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2411yescharacteristic
705C23×C4C2414yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2411yescharacteristic
711C23×C4C2412yes—
712C23×C4C2414yes—
713C4⋊Q8—28no—
714C4⋊Q8—42no—
715#127—28no—
716#127—24no—
717#127—44no—
718#127—42no—
719#127—84no—
720#126—28no—
721#126—48no—
722#126—48no—
723#126—84no—
724#125—24no—
725#125—24no—
726#124—24no—
727#124—216no—
728#124—28no—
729#124—28no—
730#124—28no—
731#124—44no—
732#124—48no—
733#124—48no—
734#123—28no—
735#123—216no—
736#123—216no—
737#123—48no—
738#123—48no—
739#123—84no—
740C22⋊Q8—24no—
741C22⋊Q8—48no—
742C22⋊Q8—44no—
743C22⋊Q8—44no—
744C22⋊Q8—44no—
745C22⋊Q8—84no—
746#121—24no—
747#121—48no—
748#121—48no—
749#121—44no—
750#121—44no—
751#121—44no—
752#121—44no—
753#121—44no—
754#121—48no—
755#121—44no—
756#121—84no—
757#121—84no—
758#121—84no—
759#121—84no—
760C4×Q8—28no—
761C4×Q8—44no—
762C4×Q8—44no—
763C4×Q8—44no—
764C4×Q8#4118yescomplemented
765C4×D4—216no—
766C4×D4—24no—
767C4×D4—28no—
768C4×D4—28no—
769C4×D4—28no—
770C4×D4—44no—
771C4×D4—48no—
772C4×D4—44no—
773C4×D4—44no—
774C4×D4—44no—
775C4×D4—48no—
776C4×D4—48no—
777C4×D4—44no—
778C4×D4—48no—
779C4×D4—48no—
780C4×D4—84no—
781C4×D4—84no—
782C4×D4—84no—
783C4×D4—84no—
784#117—28no—
785#117—24no—
786#117—44no—
787#117—42no—
788#117—44no—
789#117—48no—
790#117—84no—
791#117—84no—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C42—24no—
893C2×C42—28no—
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2411yescharacteristic
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925#95C2411yescharacteristic
926#95C2414yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2411yescharacteristic
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978C24C2512yes—
979C24C2514yes—
980C24C2514yes—
981C24C2511yescharacteristic
982#41—832no—
983C2×Q8—24no—
984C2×Q8—24no—
985C2×Q8—28no—
986C2×Q8—24no—
987C2×Q8—42no—
988C2×Q8—44no—
989C2×Q8—44no—
990C2×Q8C2×#4114yes—
991C2×D4—22no—
992C2×D4—28no—
993C2×D4—24no—
994C2×D4—24no—
995C2×D4—24no—
996C2×D4—28no—
997C2×D4—24no—
998C2×D4—24no—
999C2×D4—28no—
1000C2×D4—24no—
1001C2×D4—24no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—42no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—42no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—22no—
1048C22×C4—28no—
1049C22×C4—28no—
1050C22×C4—24no—
1051C22×C4—28no—
1052C22×C4—28no—
1053C22×C4—28no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4C2511yescharacteristic
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2514yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2512yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—22no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4C2×#4118yes—
1137C4⋊C4C2×#4114yes—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—24no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—24no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—24no—
1153C22⋊C4—28no—
1154C22⋊C4—24no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4—42no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—42no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C42—22no—
1196C42—22no—
1197C42—22no—
1198C42—28no—
1199C42—24no—
1200C42—24no—
1201C42—24no—
1202C42—22no—
1203C42—22no—
1204C42—24no—
1205C42—24no—
1206C42—22no—
1207C42—24no—
1208C42—42no—
1209C42—44no—
1210C42—42no—
1211C42—42no—
1212C42—44no—
1213C42—44no—
1214C42—44no—
1215C42—42no—
1216C42—42no—
1217C42—42no—
1218C42—42no—
1219C42—42no—
1220C42—42no—
1221C42—44no—
1222C42—42no—
1223C42C2×#4114yes—
1224C42C2×#4118yes—
1225C42H(5,𝔽2)14yes—
1226C23—22no—
1227C23—24no—
1228C23—24no—
1229C23—21no—
1230C23—21no—
1231C23—24no—
1232C23—24no—
1233C23—22no—
1234C23—22no—
1235C23—22no—
1236C23—24no—
1237C23—22no—
1238C23—24no—
1239C23—21no—
1240C23—24no—
1241C23—24no—
1242C23—22no—
1243C23—24no—
1244C23—24no—
1245C23—22no—
1246C23—24no—
1247C23—24no—
1248C23—24no—
1249C23—22no—
1250C23—24no—
1251C23—22no—
1252C23C2611yescharacteristic
1253Q8—44no—
1254Q8—48no—
1255Q8—88no—
1256D4—44no—
1257D4—416no—
1258D4—416no—
1259D4—48no—
1260D4—48no—
1261D4—84no—
1262D4—88no—
1263D4—88no—
1264D4—88no—
1265D4—88no—
1266D4—88no—
1267D4—88no—
1268D4—88no—
1269D4—164no—
1270D4—164no—
1271D4—164no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—21no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—21no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—48no—
1329C2×C4—44no—
1330C2×C4—44no—
1331C2×C4—48no—
1332C2×C4—82no—
1333C2×C4—88no—
1334C2×C4—88no—
1335C2×C4—88no—
1336C2×C4—84no—
1337C2×C4—88no—
1338C2×C4—88no—
1339C2×C4—164no—
1340C2×C4C22×#4114yes—
1341C2×C4C22×#4112yes—
1342C2×C4C22×#4112yes—
1343C2×C4C22×#4114yes—
1344C2×C4C22×#4112yes—
1345C2×C4C2×H(5,𝔽2)14yes—
1346C2×C4C2×H(5,𝔽2)12yes—
1347C2×C4#58514yes—
1348C2×C4#58512yes—
1349C22—42no—
1350C22—41no—
1351C22—44no—
1352C22—44no—
1353C22—41no—
1354C22—44no—
1355C22—44no—
1356C22—42no—
1357C22—42no—
1358C22—44no—
1359C22—44no—
1360C22—42no—
1361C22—44no—
1362C22—44no—
1363C22—42no—
1364C22—42no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—44no—
1369C22—42no—
1370C22—42no—
1371C22—41no—
1372C22—42no—
1373C22—44no—
1374C22—44no—
1375C22C23×#4111yescharacteristic
1376C22C22×H(5,𝔽2)11yescharacteristic
1377C22C2×#58511yescharacteristic
1378C22C2×#58512yes—
1379C22H(7,𝔽2)12yes—
1380C4—22no—
1381C4—24no—
1382C4—24no—
1383C4—24no—
1384C4—22no—
1385C4—24no—
1386C4—41no—
1387C4—42no—
1388C4—44no—
1389C4—41no—
1390C4—44no—
1391C4—42no—
1392C4—44no—
1393C4—44no—
1394C4—44no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—44no—
1400C4—42no—
1401C4—41no—
1402C4#351714yes—
1403C2—81no—
1404C2—82no—
1405C2—84no—
1406C2—84no—
1407C2#6268611yescharacteristic
1408C2C2×#351711yescharacteristic
1409C2#6285811yescharacteristic
1410C2#6292412yes—
1411C2#6293812yes—
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. #42144C2semidirect
2. #42136C2semidirect
3. #41240C2semidirect
4. #41220C2semidirect
5. #40794C2semidirect
6. #40773C2semidirect
7. #39750C2semidirect
8. #39739C2semidirect
9. #39285C2semidirect
10. #39282C2semidirect
11. #39130C2semidirect
12. #37772C2semidirect
13. #37766C2semidirect
14. #37626C2semidirect
15. #37579C2semidirect
16. #37570C2semidirect
17. #36502C2semidirect
18. #36149C2semidirect
19. #36136C2semidirect
20. #35766C2semidirect
21. #35719C2semidirect
22. #35331C2semidirect
23. #35299C2semidirect
24. #34624C2semidirect
25. #34621C2semidirect
26. #34331C2semidirect
27. #34151C2semidirect
764. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#421442
#421362
#412402
#412202
#407942
#407732
#397502
#397392
#392852
#392822
#391302
#377722
#377662
#376262
#375792
#375702
#365022
#361492
#361362
#357662
#357192
#353312
#352992
#346242
#346212
#343312
#341512