Finite Group Databasebeta

← #7658025

Subgroups — #7658025

Order 512.

5066 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41589C214yesmaximal, complemented
2#41586C214yesmaximal, complemented
3#41314C214yesmaximal, complemented
4#41306C214yesmaximal, complemented
5#41302C214yesmaximal, complemented
6#41291C214yesmaximal, complemented
7#39494C211yesmaximal, characteristic, complemented
8#39436C212yesmaximal, complemented
9#39435C212yesmaximal, complemented
10#39356C211yesmaximal, characteristic, complemented
11#39335C212yesmaximal, complemented
12#37945C212yesmaximal, complemented
13#37750C212yesmaximal, complemented
14#37579C212yesmaximal, complemented
15#37498C212yesmaximal, complemented
16#37495C212yesmaximal, complemented
17#36605C212yesmaximal, complemented
18#36209C211yesmaximal, characteristic, complemented
19#36136C211yesmaximal, characteristic, complemented
20#36003C214yesmaximal, complemented
21#35827C214yesmaximal, complemented
22#35332C211yesmaximal, characteristic, complemented
23#35308C212yesmaximal, complemented
24#34629C211yesmaximal, characteristic, complemented
25#34614C212yesmaximal, complemented
26#34327C212yesmaximal, complemented
27#34141C211yesmaximal, characteristic, complemented
28C2×#548C2212yes—
29C2×#541C2211yescharacteristic
30C2×#540C2211yescharacteristic
31C2×#537C2212yes—
32C2×#536C2212yes—
33C2×#536C2212yes—
34C2×#532C2211yescharacteristic
35C2×#529C2212yes—
36C2×C4×#41C2212yes—
37#2859C2211yescharacteristic
38#2858C2211yescharacteristic
39#2857C2212yes—
40#2857C2212yes—
41#2850C2212yes—
42#2850C2212yes—
43#2850C2212yes—
44#2836C2214yes—
45#2833C2214yes—
46#2831C2214yes—
47#2829C2214yes—
48#2826C2214yes—
49#2825C2214yes—
50#2802C2214yes—
51#2781C2214yes—
52#2780C2214yes—
53#2780C2214yes—
54#2778C2214yes—
55#2765C2214yes—
56#2715C2214yes—
57#2713C2214yes—
58#2703C2214yes—
59#2695C2214yes—
60#2695C2214yes—
61#2694C2214yes—
62#2693C2214yes—
63#2689C2214yes—
64#2688C2214yes—
65#2688C2214yes—
66#2687C2214yes—
67#2687C2214yes—
68#2683C2214yes—
69#2682C2214yes—
70#2677C2214yes—
71#2676C2214yes—
72#2673C2214yes—
73#2671C2214yes—
74#2667C2214yes—
75#2666C2214yes—
76#2655C2214yes—
77#2652C2214yes—
78#2651C2214yes—
79#2651C2214yes—
80#2650C2214yes—
81#2649C2214yes—
82#2648C2214yes—
83#2648C2214yes—
84#2647C2211yescharacteristic
85#2646C2214yes—
86#2645C2212yes—
87#2643C2214yes—
88#2642C2211yescharacteristic
89#2642C2211yescharacteristic
90#2641C2211yescharacteristic
91#2637C2214yes—
92#2636C2214yes—
93#2636C2214yes—
94#2635C2214yes—
95#2630C2214yes—
96#2630C2214yes—
97#2629C2211yescharacteristic
98#2629C2212yes—
99#2625C2212yes—
100#2625C2212yes—
101#2624C2212yes—
102#2621C2211yescharacteristic
103#2621C2212yes—
104#2620C2212yes—
105#2620C2212yes—
106#2620C2212yes—
107#2616C2212yes—
108#2615C2212yes—
109#2601C2214yes—
110#2598C2214yes—
111#2594C2214yes—
112#2587C2214yes—
113#2579C2214yes—
114#2576C2214yes—
115#2573C2214yes—
116#2570C2212yes—
117#2559C2214yes—
118#2559C2214yes—
119#2559C2214yes—
120#2558C2214yes—
121#2558C2214yes—
122#2558C2214yes—
123#2555C2214yes—
124#2554C2214yes—
125#2553C2214yes—
126#2550C2214yes—
127#2545C2212yes—
128#2543C2214yes—
129#2540C2212yes—
130#2536C2212yes—
131#2535C2214yes—
132#2531C2214yes—
133#2526C2214yes—
134#2525C2214yes—
135#2525C2214yes—
136#2522C2214yes—
137#2521C2214yes—
138#2514C2212yes—
139#2512C2212yes—
140#2510C2214yes—
141#2510C2214yes—
142#2508C2214yes—
143#2505C2214yes—
144#2495C2214yes—
145#2491C2214yes—
146#2489C2212yes—
147#2489C2212yes—
148#2488C2214yes—
149#2485C2214yes—
150#2481C2214yes—
151#2479C2214yes—
152#2470C2214yes—
153#2468C2214yes—
154#2464C2214yes—
155#2464C2214yes—
156#2461C2214yes—
157#2461C2214yes—
158#2461C2214yes—
159#2457C2214yes—
160#2456C2214yes—
161#2450C2214yes—
162#2447C2212yes—
163#2446C2212yes—
164#2442C2212yes—
165#2441C2212yes—
166#2438C2214yes—
167#2434C2212yes—
168#2431C2212yes—
169#2429C2212yes—
170#2429C2212yes—
171#2429C2214yes—
172#2429C2214yes—
173#2428C2212yes—
174#2427C2212yes—
175#2427C2214yes—
176#2427C2214yes—
177#2425C2214yes—
178#2425C2214yes—
179#2425C2214yes—
180#2425C2214yes—
181#2423C2212yes—
182#2420C2212yes—
183#2417C2212yes—
184#2414C2212yes—
185#2409C2212yes—
186#2407C2212yes—
187#2402C2214yes—
188#2401C2214yes—
189#2396C2214yes—
190#2392C2214yes—
191#2392C2214yes—
192#2392C2214yes—
193#2373C2214yes—
194#2372C2214yes—
195#2368C2214yes—
196#2367C2212yes—
197#2367C2212yes—
198#2367C2212yes—
199#2366C2212yes—
200#2365C2212yes—
201#2364C2214yes—
202#2364C2212yes—
203#2364C2212yes—
204#2363C2214yes—
205#2362C2212yes—
206#2361C2212yes—
207#2361C2212yes—
208#2361C2212yes—
209#2356C2212yes—
210#2353C2214yes—
211#2353C2214yes—
212#2352C2212yes—
213#2346C2214yes—
214Q8×C22⋊C4C2212yes—
215#2339C2212yes—
216#2337C2214yes—
217#2332C2214yes—
218#2326C2212yes—
219#2325C2214yes—
220#2317C2212yes—
221C4×C4⋊Q8C2211yescharacteristic
222C4×#125C2211yescharacteristic
223C4×#124C2212yes—
224C4×C22⋊Q8C2212yes—
225C4×C22⋊Q8C2212yes—
226C4×C22⋊Q8C2212yes—
227C4×#121C2212yes—
228C4×#121C2212yes—
229#2297C2212yes—
230#2297C2212yes—
231#2295C2212yes—
232C2×#391C2212yes—
233#2293C2211yescharacteristic
234#2293C2211yescharacteristic
235#2290C2212yes—
236#2290C2212yes—
237#2285C2212yes—
238#2275C2214yes—
239C42×D4C2211yescharacteristic
240C42×D4C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C2×C4×C4⋊C4C2211yescharacteristic
243C22×#41C2312yes—
244C22×#41C2312yes—
245C23×Q8C2312yes—
246#548—216no—
247#541—44no—
248#540—44no—
249#537—48no—
250#536—48no—
251#536—48no—
252#532—28no—
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2314yes—
258C2×#127C2311yescharacteristic
259C2×#127C2311yescharacteristic
260#529—48no—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#126C2314yes—
264C2×#125C2311yescharacteristic
265C2×#125C2311yescharacteristic
266C2×#125C2311yescharacteristic
267C2×#125C2314yes—
268C2×#124C2312yes—
269C2×#124C2314yes—
270C2×#124C2312yes—
271C2×#124C2312yes—
272C2×#124C2312yes—
273C2×#124C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2314yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2311yescharacteristic
295C2×#121C2311yescharacteristic
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C4×#41—48no—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×#117C2312yes—
329C2×#117C2311yescharacteristic
330C2×#117C2311yescharacteristic
331C2×#117C2312yes—
332C2×#117C2314yes—
333C2×#117C2314yes—
334C2×#117C2312yes—
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2312yes—
337C22×C42C2311yescharacteristic
338C22×C42C2312yes—
339C22×C42C2312yes—
340C22×C42C2312yes—
341#401C2314yes—
342#401C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#393C2314yes—
435#393C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#391C2312yes—
446#391C2314yes—
447#391C2312yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2314yes—
460#391C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2314yes—
526#388C2312yes—
527#388C2312yes—
528#388C2312yes—
529#388C2314yes—
530#388C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2314yes—
541#387C2312yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#386C2312yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2312yes—
568#386C2314yes—
569#386C2314yes—
570#386C2312yes—
571#386C2312yes—
572#386C2312yes—
573#386C2312yes—
574#386C2312yes—
575#386C2312yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#385C2312yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2312yes—
596#385C2312yes—
597#385C2312yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#384C2311yescharacteristic
602#384C2312yes—
603#384C2312yes—
604#383C2314yes—
605#383C2314yes—
606#382C2311yescharacteristic
607#382C2312yes—
608#382C2312yes—
609#382C2314yes—
610#382C2314yes—
611#382C2314yes—
612#381C2314yes—
613#381C2314yes—
614#381C2314yes—
615#380C2314yes—
616#380C2314yes—
617#380C2312yes—
618#380C2312yes—
619#380C2314yes—
620#380C2314yes—
621#380C2314yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2314yes—
626#380C2314yes—
627#380C2314yes—
628#380C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2311yescharacteristic
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2311yescharacteristic
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2311yescharacteristic
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672#376C2311yescharacteristic
673#376C2314yes—
674#376C2314yes—
675#376C2311yescharacteristic
676C2×#95C2314yes—
677C2×#95C2314yes—
678C2×#95C2311yescharacteristic
679C2×#95C2314yes—
680C2×#95C2311yescharacteristic
681C43C2311yescharacteristic
682C43C2311yescharacteristic
683C2×#41—28no—
684C2×#41—28no—
685C2×#41—28no—
686C2×#41—44no—
687C2×#41—44no—
688C2×#41—44no—
689C22×Q8—28no—
690C22×Q8—44no—
691C22×Q8—44no—
692C22×Q8C2412yes—
693C22×Q8C2412yes—
694C22×Q8C2412yes—
695C22×Q8C2414yes—
696C22×D4C2412yes—
697C22×D4C2412yes—
698C22×D4C2412yes—
699C22×D4C2412yes—
700C22×D4C2414yes—
701C22×D4C2411yescharacteristic
702C22×D4C2414yes—
703C22×D4C2412yes—
704C22×D4C2414yes—
705C22×D4C2414yes—
706C22×D4C2414yes—
707C22×D4C2414yes—
708C22×D4C2411yescharacteristic
709C23×C4C2412yes—
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2411yescharacteristic
713C23×C4C2411yescharacteristic
714C23×C4C2412yes—
715C23×C4C2414yes—
716C23×C4C2412yes—
717C23×C4C2412yes—
718C23×C4C2414yes—
719C23×C4C2414yes—
720C23×C4C2411yescharacteristic
721C23×C4C2412yes—
722C23×C4C2414yes—
723C23×C4C2412yes—
724C23×C4C2414yes—
725C4⋊Q8—24no—
726C4⋊Q8—24no—
727C4⋊Q8—44no—
728C4⋊Q8—42no—
729C4⋊Q8—48no—
730#127—24no—
731#127—42no—
732#126—48no—
733#126—48no—
734#126—48no—
735#125—24no—
736#125—42no—
737#125—42no—
738#125—48no—
739#124—28no—
740#124—216no—
741#124—28no—
742#124—28no—
743#124—44no—
744#124—48no—
745#123—48no—
746#123—48no—
747#123—48no—
748#123—48no—
749#123—48no—
750#123—48no—
751C22⋊Q8—28no—
752C22⋊Q8—28no—
753C22⋊Q8—28no—
754C22⋊Q8—216no—
755C22⋊Q8—48no—
756C22⋊Q8—48no—
757C22⋊Q8—48no—
758C22⋊Q8—44no—
759C22⋊Q8—44no—
760C22⋊Q8—44no—
761C22⋊Q8—44no—
762#121—24no—
763#121—216no—
764#121—28no—
765#121—28no—
766#121—24no—
767#121—28no—
768#121—48no—
769#121—48no—
770#121—48no—
771#121—48no—
772#121—48no—
773#121—44no—
774#121—44no—
775C4×Q8—28no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—44no—
780C4×D4—28no—
781C4×D4—216no—
782C4×D4—24no—
783C4×D4—48no—
784C4×D4—44no—
785C4×D4—44no—
786C4×D4—44no—
787C4×D4—44no—
788C4×D4—48no—
789C4×D4—48no—
790C4×D4—44no—
791C4×D4—44no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—44no—
796C4×D4—48no—
797C4×D4#4118yes—
798#117—24no—
799#117—24no—
800#117—28no—
801#117—48no—
802#117—44no—
803#117—48no—
804#117—44no—
805C2×C4⋊C4—44no—
806C2×C4⋊C4—44no—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C42—24no—
906C2×C42—28no—
907C2×C42—44no—
908C2×C42—44no—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936#95C2414yes—
937#95C2412yes—
938#95C2411yescharacteristic
939#95C2414yes—
940#95C2411yescharacteristic
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993C24C2514yes—
994C24C2512yes—
995C24C2512yes—
996C24C2511yescharacteristic
997#41—432no—
998#41—816no—
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—24no—
1002C2×Q8—28no—
1003C2×Q8—24no—
1004C2×Q8—24no—
1005C2×Q8—24no—
1006C2×Q8—24no—
1007C2×Q8—24no—
1008C2×Q8—42no—
1009C2×Q8—44no—
1010C2×Q8—44no—
1011C2×Q8—816no—
1012C2×D4—28no—
1013C2×D4—24no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—24no—
1017C2×D4—24no—
1018C2×D4—28no—
1019C2×D4—28no—
1020C2×D4—22no—
1021C2×D4—24no—
1022C2×D4—24no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—24no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4—42no—
1029C2×D4—42no—
1030C2×D4—42no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—42no—
1040C2×D4—42no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4C2×#4114yes—
1049C22×C4—22no—
1050C22×C4—22no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—28no—
1054C22×C4—22no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—22no—
1061C22×C4—28no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—28no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4C2×#4118yes—
1094C22×C4H(5,𝔽2)14yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2514yes—
1104C22×C4C2514yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2514yes—
1109C22×C4C2514yes—
1110C22×C4C2512yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C4⋊C4—24no—
1119C4⋊C4—22no—
1120C4⋊C4—28no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4C2×#4114yes—
1165C22⋊C4—24no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—28no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—28no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4C2×#4118yes—
1216C42—22no—
1217C42—22no—
1218C42—22no—
1219C42—28no—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—22no—
1224C42—24no—
1225C42—22no—
1226C42—22no—
1227C42—28no—
1228C42—28no—
1229C42—42no—
1230C42—42no—
1231C42—42no—
1232C42—42no—
1233C42—42no—
1234C42—42no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—42no—
1239C42—42no—
1240C42—44no—
1241C42C2×#4114yes—
1242C42H(5,𝔽2)14yes—
1243C23—21no—
1244C23—22no—
1245C23—21no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—24no—
1254C23—22no—
1255C23—24no—
1256C23—24no—
1257C23—22no—
1258C23—22no—
1259C23—24no—
1260C23—22no—
1261C23—22no—
1262C23—24no—
1263C23—24no—
1264C23—22no—
1265C23—22no—
1266C23—24no—
1267C23C22×#4114yes—
1268C23C2×H(5,𝔽2)12yes—
1269C23C2611yescharacteristic
1270Q8—48no—
1271Q8—48no—
1272Q8—48no—
1273Q8—88no—
1274D4—44no—
1275D4—48no—
1276D4—48no—
1277D4—44no—
1278D4—48no—
1279D4—416no—
1280D4—48no—
1281D4—84no—
1282D4—88no—
1283D4—88no—
1284D4—88no—
1285D4—164no—
1286D4—164no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—216no—
1298C2×C4—28no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—48no—
1346C2×C4—44no—
1347C2×C4—48no—
1348C2×C4—82no—
1349C2×C4—84no—
1350C2×C4—84no—
1351C2×C4—88no—
1352C2×C4—84no—
1353C2×C4—88no—
1354C2×C4—88no—
1355C2×C4—84no—
1356C2×C4—84no—
1357C2×C4—164no—
1358C2×C4—164no—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C22×#4114yes—
1362C2×C4C22×#4112yes—
1363C2×C4C2×H(5,𝔽2)14yes—
1364C2×C4C2×H(5,𝔽2)12yes—
1365C2×C4C2×H(5,𝔽2)12yes—
1366C2×C4C2×H(5,𝔽2)12yes—
1367C2×C4#58514yes—
1368C22—24no—
1369C22—22no—
1370C22—24no—
1371C22—24no—
1372C22—24no—
1373C22—41no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—41no—
1380C22—42no—
1381C22—44no—
1382C22—42no—
1383C22—44no—
1384C22—42no—
1385C22—42no—
1386C22—44no—
1387C22—44no—
1388C22—44no—
1389C22—44no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22—44no—
1394C22C23×#4111yescharacteristic
1395C22C22×H(5,𝔽2)11yescharacteristic
1396C22C22×H(5,𝔽2)11yescharacteristic
1397C22C2×#58512yes—
1398C222−1+612yes—
1399C4—24no—
1400C4—22no—
1401C4—22no—
1402C4—24no—
1403C4—24no—
1404C4—22no—
1405C4—42no—
1406C4—44no—
1407C4—44no—
1408C4—41no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—44no—
1414C4—44no—
1415C4—42no—
1416C4—44no—
1417C4—44no—
1418C4—42no—
1419C4—41no—
1420C4—44no—
1421C4#351914yes—
1422C2—44no—
1423C2—42no—
1424C2—82no—
1425C2—84no—
1426C2#6268611yescharacteristic
1427C2C2×#351911yescharacteristic
1428C2#6286111yescharacteristic
1429C2#6292712yes—
1430C2#6293112yes—
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. #41589C2semidirect
2. #41586C2semidirect
3. #41314C2semidirect
4. #41306C2semidirect
5. #41302C2semidirect
6. #41291C2semidirect
7. #39494C2semidirect
8. #39436C2semidirect
9. #39435C2semidirect
10. #39356C2semidirect
11. #39335C2semidirect
12. #37945C2semidirect
13. #37750C2semidirect
14. #37579C2semidirect
15. #37498C2semidirect
16. #37495C2semidirect
17. #36605C2semidirect
18. #36209C2semidirect
19. #36136C2semidirect
20. #36003C2semidirect
21. #35827C2semidirect
22. #35332C2semidirect
23. #35308C2semidirect
24. #34629C2semidirect
25. #34614C2semidirect
26. #34327C2semidirect
27. #34141C2semidirect

Maximal subgroups

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

subgroupindex
#415892
#415862
#413142
#413062
#413022
#412912
#394942
#394362
#394352
#393562
#393352
#379452
#377502
#375792
#374982
#374952
#366052
#362092
#361362
#360032
#358272
#353322
#353082
#346292
#346142
#343272
#341412