Finite Group Databasebeta

← #7715913

Subgroups — #7715913

Order 512.

4942 conjugacy classes of subgroups.

The subgroup lattice has 1448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50493C214yesmaximal, complemented
2#50353C214yesmaximal, complemented
3#49331C214yesmaximal, complemented
4#49135C214yesmaximal, complemented
5#44836C214yesmaximal, complemented
6#44799C214yesmaximal, complemented
7#44155C214yesmaximal, complemented
8#43982C214yesmaximal, complemented
9#39796C212yesmaximal, complemented
10#39632C212yesmaximal, complemented
11#37942C212yesmaximal, complemented
12#37940C212yesmaximal, complemented
13#37762C212yesmaximal, complemented
14#37703C212yesmaximal, complemented
15#36957C212yesmaximal, complemented
16#36765C212yesmaximal, complemented
17#36203C212yesmaximal, complemented
18#36108C212yesmaximal, complemented
19#35270C212yesmaximal, complemented
20#35120C211yesmaximal, characteristic, complemented
21#35119C211yesmaximal, characteristic, complemented
22#35011C211yesmaximal, characteristic, complemented
23#35003C211yesmaximal, characteristic, complemented
24#35003C211yesmaximal, characteristic, complemented
25#34578C211yesmaximal, characteristic, complemented
26#34426C212yesmaximal, complemented
27C2×#2372C211yesmaximal, characteristic, complemented
28C2×#538C2212yes—
29C2×#538C2212yes—
30C2×#529C2212yes—
31C22×#124C2211yescharacteristic
32C22×C22⋊Q8C2212yes—
33#2857C2212yes—
34#2857C2212yes—
35#2855C2212yes—
36#2855C2212yes—
37#2854C2212yes—
38#2854C2212yes—
39#2850C2212yes—
40#2850C2212yes—
41#2847C2212yes—
42#2847C2212yes—
43#2806C2214yescomplemented
44#2804C2214yescomplemented
45#2800C2214yescomplemented
46#2798C2214yescomplemented
47#2788C2214yescomplemented
48#2788C2214yescomplemented
49#2782C2214yescomplemented
50#2781C2214yescomplemented
51#2779C2214yescomplemented
52#2778C2214yes—
53#2770C2214yescomplemented
54#2762C2214yescomplemented
55#2759C2214yescomplemented
56#2754C2214yescomplemented
57#2749C2214yescomplemented
58#2746C2214yes—
59#2731C2214yescomplemented
60#2730C2214yes—
61#2721C2214yescomplemented
62#2718C2214yescomplemented
63#2718C2214yescomplemented
64#2715C2214yes—
65#2715C2214yes—
66#2715C2214yescomplemented
67#2712C2214yes—
68#2712C2214yes—
69#2712C2214yescomplemented
70#2708C2214yes—
71#2705C2214yescomplemented
72#2702C2214yes—
73#2700C2214yescomplemented
74#2696C2214yes—
75#2689C2214yescomplemented
76#2688C2214yes—
77#2686C2214yescomplemented
78#2676C2214yes—
79#2676C2214yes—
80#2676C2214yes—
81#2672C2214yes—
82#2672C2214yes—
83#2667C2214yescomplemented
84#2665C2214yescomplemented
85#2659C2211yescharacteristic
86#2659C2211yescharacteristic
87#2659C2211yescharacteristic
88#2659C2212yes—
89#2656C2211yescharacteristic
90#2647C2212yescomplemented
91#2646C2212yes—
92#2646C2212yes—
93#2645C2212yescomplemented
94#2644C2212yescomplemented
95#2640C2212yescomplemented
96#2639C2212yes—
97#2626C2212yes—
98#2626C2212yes—
99#2617C2212yes—
100#2617C2212yes—
101#2612C2214yescomplemented
102#2612C2214yescomplemented
103#2611C2214yescomplemented
104#2610C2214yescomplemented
105#2606C2214yescomplemented
106#2605C2214yescomplemented
107#2605C2214yescomplemented
108#2604C2214yescomplemented
109#2603C2214yescomplemented
110#2603C2214yescomplemented
111#2598C2214yes—
112#2595C2214yescomplemented
113#2583C2214yescomplemented
114#2583C2214yescomplemented
115#2578C2214yes—
116#2572C2214yescomplemented
117#2560C2214yescomplemented
118#2560C2214yescomplemented
119#2555C2214yescomplemented
120#2555C2214yescomplemented
121#2553C2214yescomplemented
122#2553C2214yescomplemented
123#2534C2214yes—
124#2532C2214yescomplemented
125#2532C2214yescomplemented
126#2530C2214yescomplemented
127#2530C2214yescomplemented
128#2529C2214yescomplemented
129#2527C2214yescomplemented
130#2526C2214yescomplemented
131#2521C2214yescomplemented
132#2521C2214yescomplemented
133#2518C2214yescomplemented
134#2511C2214yescomplemented
135#2510C2214yes—
136#2502C2214yescomplemented
137#2502C2214yescomplemented
138#2500C2212yescomplemented
139#2497C2212yescomplemented
140#2495C2212yescomplemented
141#2492C2214yescomplemented
142#2491C2212yescomplemented
143#2489C2212yescomplemented
144#2488C2214yes—
145#2481C2214yes—
146#2481C2214yes—
147#2481C2214yescomplemented
148#2477C2214yescomplemented
149#2476C2214yes—
150#2474C2214yescomplemented
151#2472C2214yes—
152#2469C2214yescomplemented
153#2468C2214yescomplemented
154#2465C2214yescomplemented
155#2464C2214yes—
156#2464C2214yescomplemented
157#2464C2214yescomplemented
158#2450C2214yes—
159#2450C2214yes—
160#2443C2214yes—
161#2443C2214yescomplemented
162#2442C2212yescomplemented
163#2439C2212yescomplemented
164#2436C2214yes—
165#2436C2212yescomplemented
166#2434C2214yescomplemented
167#2427C2212yescomplemented
168#2426C2212yescomplemented
169#2421C2212yescomplemented
170#2420C2212yescomplemented
171#2419C2214yes—
172#2418C2214yes—
173#2417C2214yescomplemented
174#2416C2214yes—
175#2413C2214yescomplemented
176#2412C2214yes—
177#2410C2214yes—
178#2409C2214yes—
179#2396C2214yescomplemented
180#2396C2214yescomplemented
181#2383C2214yescomplemented
182#2377C2214yescomplemented
183#2373C2214yescomplemented
184#2372C2214yes—
185#2372C2214yes—
186#2372C2214yes—
187#2372C2214yes—
188#2372C2214yescomplemented
189#2363C2212yescomplemented
190#2361C2212yescomplemented
191#2361C2214yescomplemented
192#2358C2214yes—
193#2358C2214yes—
194#2353C2214yes—
195#2352C2214yescomplemented
196D4×C4⋊C4C2214yes—
197#2346C2212yescomplemented
198Q8×C22⋊C4C2212yescomplemented
199#2337C2214yescomplemented
200#2335C2214yescomplemented
201#2331C2212yescomplemented
202#2329C2212yes—
203#2329C2212yes—
204#2326C2212yescomplemented
205#2326C2214yescomplemented
206#2325C2212yes—
207#2325C2212yes—
208#2325C2212yes—
209#2325C2212yes—
210#2322C2214yescomplemented
211#2320C2212yescomplemented
212#2319C2212yescomplemented
213#2315C2212yes—
214#2315C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×C22⋊Q8C2212yes—
217C4×#121C2212yes—
218C4×#121C2212yes—
219C2×#391C2211yescharacteristic
220C2×#391C2211yescharacteristic
221C2×#388C2211yescharacteristic
222C2×#388C2211yescharacteristic
223C2×#388C2211yescharacteristic
224C2×#388C2211yescharacteristic
225C2×#386C2211yescharacteristic
226C2×#386C2211yescharacteristic
227#2283C2212yes—
228#2280C2212yes—
229C2×C4×C22⋊C4C2211yescharacteristic
230C2×C4×C22⋊C4C2211yescharacteristic
231C2×C4×C22⋊C4C2211yescharacteristic
232C2×C4×C22⋊C4C2211yescharacteristic
233C2×#376C2211yescharacteristic
234C2×#376C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×Q8C2312yes—
237C23×D4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239C24×C4C2311yescharacteristic
240#538—216no—
241#538—48no—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244#529—48no—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125C2312yes—
250C2×#124—28no—
251C2×#124C2314yes—
252C2×#124C2314yes—
253C2×#124C2314yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2314yes—
257C2×#124C2314yes—
258C2×#124C2312yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×C22⋊Q8—48no—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#120C2314yes—
285C2×#120C2314yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×#117C2312yes—
298C2×#117C2314yes—
299C2×#117C2312yes—
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2314yes—
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2311yescharacteristic
313C22×C22⋊C4C2311yescharacteristic
314C22×C22⋊C4C2311yescharacteristic
315C22×C22⋊C4C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323#401C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#398C2314yes—
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#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
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#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#392C2314yes—
407#392C2314yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2312yes—
415#391C2312yes—
416#391C2314yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#390C2312yes—
433#390C2314yes—
434#390C2312yes—
435#390C2312yes—
436#390C2314yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#390C2312yes—
442#390C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
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#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#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#384C2312yes—
580#384C2314yes—
581#384C2312yes—
582#383C2314yes—
583#383C2314yes—
584#383C2314yes—
585#382C2314yes—
586#382C2312yes—
587#382C2312yes—
588#382C2312yes—
589#382C2312yes—
590#381C2314yes—
591#381C2314yes—
592#381C2314yes—
593#381C2314yes—
594#380C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2312yes—
602#380C2312yes—
603#380C2314yes—
604#380C2312yes—
605#380C2312yes—
606#380C2312yes—
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610#380C2312yes—
611#380C2312yes—
612#380C2312yes—
613#379C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C22⋊C4C2312yes—
624C4×C22⋊C4C2314yes—
625C4×C22⋊C4C2312yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2312yes—
634C4×C22⋊C4C2312yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2312yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2312yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643#376C2312yes—
644#376C2312yes—
645#376C2314yes—
646#376C2314yes—
647#376C2314yes—
648#376C2314yes—
649#376C2312yes—
650#376C2312yes—
651C2×#95C2311yescharacteristic
652C2×#95C2311yescharacteristic
653C2×#95C2311yescharacteristic
654C2×#95C2311yescharacteristic
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2311yescharacteristic
660C2×#95C2311yescharacteristic
661C2×#95C2311yescharacteristic
662C2×#95C2311yescharacteristic
663C25C2411yescharacteristic
664C25C2411yescharacteristic
665C22×Q8—24no—
666C22×Q8—44no—
667C22×Q8—44no—
668C22×Q8—81no—
669C22×Q8—81no—
670C22×Q8—82no—
671C22×Q8C2412yes—
672C22×Q8C2412yes—
673C22×Q8C2412yes—
674C22×Q8C2414yes—
675C22×Q8C2414yes—
676C22×D4—24no—
677C22×D4—81no—
678C22×D4—81no—
679C22×D4C2414yes—
680C22×D4C2414yes—
681C22×D4C2414yes—
682C22×D4C2412yes—
683C22×D4C2412yes—
684C22×D4C2412yes—
685C22×D4C2414yes—
686C22×D4C2414yes—
687C22×D4C2414yes—
688C23×C4—24no—
689C23×C4—24no—
690C23×C4—42no—
691C23×C4—42no—
692C23×C4—81no—
693C23×C4—81no—
694C23×C4C2411yescharacteristic
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2412yes—
698C23×C4C2412yes—
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2412yes—
705C23×C4C2414yes—
706C23×C4C2412yes—
707C23×C4C2411yescharacteristic
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2414yes—
711C23×C4C2414yes—
712C23×C4C2411yescharacteristic
713C23×C4C2411yescharacteristic
714C23×C4C2411yescharacteristic
715C23×C4C2411yescharacteristic
716C4⋊Q8—44no—
717C4⋊Q8—82no—
718#126—216no—
719#126—48no—
720#126—48no—
721#126—84no—
722#125—44no—
723#124—216no—
724#124—216no—
725#124—216no—
726#124—44no—
727#124—44no—
728#124—48no—
729#124—48no—
730#124—82no—
731#123—216no—
732#123—48no—
733#123—48no—
734#123—84no—
735C22⋊Q8—28no—
736C22⋊Q8—28no—
737C22⋊Q8—28no—
738C22⋊Q8—48no—
739C22⋊Q8—48no—
740C22⋊Q8—44no—
741C22⋊Q8—44no—
742C22⋊Q8—84no—
743C22⋊Q8—84no—
744#121—28no—
745#121—28no—
746#121—28no—
747#121—216no—
748#121—44no—
749#121—44no—
750#121—48no—
751#121—84no—
752#121—82no—
753#121—84no—
754#121—82no—
755#120—216no—
756#120—48no—
757C4×Q8—44no—
758C4×Q8—44no—
759C4×Q8—82no—
760C4×D4—216no—
761C4×D4—44no—
762C4×D4—48no—
763C4×D4—44no—
764C4×D4—48no—
765C4×D4—48no—
766C4×D4—82no—
767C4×D4—84no—
768#117—44no—
769#117—48no—
770#117—82no—
771C2×C4⋊C4—48no—
772C2×C4⋊C4—44no—
773C2×C4⋊C4—81no—
774C2×C4⋊C4—84no—
775C2×C4⋊C4—81no—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C22⋊C4—24no—
820C2×C22⋊C4—24no—
821C2×C22⋊C4—24no—
822C2×C22⋊C4—24no—
823C2×C22⋊C4—24no—
824C2×C22⋊C4—42no—
825C2×C22⋊C4—42no—
826C2×C22⋊C4—48no—
827C2×C22⋊C4—81no—
828C2×C22⋊C4—81no—
829C2×C22⋊C4#4118yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C42—24no—
878C2×C42—24no—
879C2×C42—24no—
880C2×C42—42no—
881C2×C42—42no—
882C2×C42—81no—
883C2×C42—81no—
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905#95C2411yescharacteristic
906#95C2412yes—
907#95C2411yescharacteristic
908#95C2414yes—
909#95C2411yescharacteristic
910#95C2411yescharacteristic
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
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—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963C24—22no—
964C24—22no—
965C24—22no—
966C24—22no—
967C24—22no—
968C24—41no—
969C24—41no—
970C24—41no—
971C24—41no—
972C24—41no—
973C24—41no—
974C24—41no—
975C24—41no—
976C24C2×#4114yes—
977C24C2512yes—
978C24C2514yes—
979C24C2512yes—
980C24C2511yescharacteristic
981C2×Q8—24no—
982C2×Q8—28no—
983C2×Q8—24no—
984C2×Q8—24no—
985C2×Q8—28no—
986C2×Q8—42no—
987C2×Q8—42no—
988C2×Q8—42no—
989C2×Q8—44no—
990C2×Q8—44no—
991C2×Q8—44no—
992C2×Q8—42no—
993C2×Q8—42no—
994C2×Q8—44no—
995C2×Q8—42no—
996C2×Q8—88no—
997C2×Q8—816no—
998C2×D4—28no—
999C2×D4—28no—
1000C2×D4—28no—
1001C2×D4—28no—
1002C2×D4—28no—
1003C2×D4—28no—
1004C2×D4—24no—
1005C2×D4—24no—
1006C2×D4—24no—
1007C2×D4—42no—
1008C2×D4—44no—
1009C2×D4—42no—
1010C2×D4—44no—
1011C2×D4—42no—
1012C2×D4—42no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—42no—
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—88no—
1026C22×C4—22no—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—22no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—28no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—41no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—41no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—42no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—42no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—41no—
1067C22×C4—41no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—41no—
1071C22×C4—41no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—88no—
1089C22×C4—88no—
1090C22×C4C2×#4114yes—
1091C22×C4C2×#4114yes—
1092C22×C4H(5,𝔽2)14yes—
1093C22×C42−1+414yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2514yes—
1110C22×C4C2514yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—28no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—28no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4C2×#41116yes—
1207C42—24no—
1208C42—24no—
1209C42—28no—
1210C42—24no—
1211C42—24no—
1212C42—24no—
1213C42—24no—
1214C42—24no—
1215C42—24no—
1216C42—28no—
1217C42—42no—
1218C42—42no—
1219C42—42no—
1220C42—42no—
1221C42—42no—
1222C42—42no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C23—21no—
1229C23—21no—
1230C23—21no—
1231C23—21no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—28no—
1239C23—22no—
1240C23—24no—
1241C23—22no—
1242C23—24no—
1243C23—24no—
1244C23—22no—
1245C23—22no—
1246C23—24no—
1247C23—24no—
1248C23—22no—
1249C23—24no—
1250C23—24no—
1251C23—22no—
1252C23—22no—
1253C23—44no—
1254C23—44no—
1255C23—44no—
1256C23—44no—
1257C23—44no—
1258C23—82no—
1259C23—82no—
1260C23—82no—
1261C23—82no—
1262C23—82no—
1263C23—82no—
1264C23—82no—
1265C23—82no—
1266C23C22×#4114yes—
1267C23C22×#4112yes—
1268C23C2×H(5,𝔽2)12yes—
1269C23C2×2−1+412yes—
1270C23C2611yescharacteristic
1271Q8—48no—
1272Q8—84no—
1273Q8—88no—
1274Q8—88no—
1275Q8—84no—
1276D4—416no—
1277D4—84no—
1278D4—84no—
1279D4—84no—
1280D4—88no—
1281D4—88no—
1282D4—88no—
1283D4—164no—
1284D4—164no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—21no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—22no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—44no—
1349C2×C4—44no—
1350C2×C4—44no—
1351C2×C4—44no—
1352C2×C4—48no—
1353C2×C4—48no—
1354C2×C4—44no—
1355C2×C4—44no—
1356C2×C4—44no—
1357C2×C4—44no—
1358C2×C4—44no—
1359C2×C4—88no—
1360C2×C4—84no—
1361C2×C4—84no—
1362C2×C4—82no—
1363C2×C4—82no—
1364C2×C4—82no—
1365C2×C4—82no—
1366C2×C4—88no—
1367C2×C4—88no—
1368C2×C4—88no—
1369C2×C4—164no—
1370C2×C4C22×#4114yes—
1371C2×C4C22×#4114yes—
1372C2×C4C2×H(5,𝔽2)14yes—
1373C2×C4C2×2−1+414yes—
1374C2×C4#58512yes—
1375C2×C4#58512yes—
1376C22—22no—
1377C22—22no—
1378C22—22no—
1379C22—22no—
1380C22—22no—
1381C22—22no—
1382C22—24no—
1383C22—24no—
1384C22—24no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—44no—
1390C22—42no—
1391C22—44no—
1392C22—42no—
1393C22—44no—
1394C22—42no—
1395C22—44no—
1396C22—42no—
1397C22—42no—
1398C22—44no—
1399C22—44no—
1400C22—42no—
1401C22—44no—
1402C22—42no—
1403C22—88no—
1404C22—88no—
1405C22#351114yes—
1406C22C23×#4111yescharacteristic
1407C22C22×H(5,𝔽2)11yescharacteristic
1408C22C22×2−1+411yescharacteristic
1409C22C2×#58511yescharacteristic
1410C22C2×#58511yescharacteristic
1411C22H(7,𝔽2)11yescharacteristic
1412C22H(7,𝔽2)11yescharacteristic
1413C4—24no—
1414C4—24no—
1415C4—22no—
1416C4—24no—
1417C4—22no—
1418C4—24no—
1419C4—44no—
1420C4—41no—
1421C4—41no—
1422C4—44no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—41no—
1427C4—44no—
1428C4—44no—
1429C4—41no—
1430C4—42no—
1431C4—42no—
1432C4—44no—
1433C4—42no—
1434C4—42no—
1435C4—44no—
1436C2—24no—
1437C2—44no—
1438C2—84no—
1439C2—82no—
1440C2#6278111yescharacteristic
1441C2C2×#351111yescharacteristic
1442C2#6284611yescharacteristic
1443C2#6290011yescharacteristic
1444C2#6290311yescharacteristic
1445C2#6292911yescharacteristic
1446C2#6293011yescharacteristic
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. #50493C2semidirect
2. #50353C2semidirect
3. #49331C2semidirect
4. #49135C2semidirect
5. #44836C2semidirect
6. #44799C2semidirect
7. #44155C2semidirect
8. #43982C2semidirect
9. #39796C2semidirect
10. #39632C2semidirect
11. #37942C2semidirect
12. #37940C2semidirect
13. #37762C2semidirect
14. #37703C2semidirect
15. #36957C2semidirect
16. #36765C2semidirect
17. #36203C2semidirect
18. #36108C2semidirect
19. #35270C2semidirect
20. #35120C2semidirect
21. #35119C2semidirect
22. #35011C2semidirect
23. #35003C2semidirect
24. #35003C2semidirect
25. #34578C2semidirect
26. #34426C2semidirect
27. C2×#2372C2semidirect
43. #2806C22semidirect
44. #2804C22semidirect
45. #2800C22semidirect
46. #2798C22semidirect
47. #2788C22semidirect
48. #2788C22semidirect
49. #2782C22semidirect
50. #2781C22semidirect
51. #2779C22semidirect
53. #2770C22semidirect
54. #2762C22semidirect
55. #2759C22semidirect
56. #2754C22semidirect
57. #2749C22semidirect
59. #2731C22semidirect
61. #2721C22semidirect
62. #2718C22semidirect
63. #2718C22semidirect
66. #2715C22semidirect
69. #2712C22semidirect
71. #2705C22semidirect
73. #2700C22semidirect
75. #2689C22semidirect
77. #2686C22semidirect
83. #2667C22semidirect
84. #2665C22semidirect
90. #2647C22semidirect
93. #2645C22semidirect
94. #2644C22semidirect
95. #2640C22semidirect
101. #2612C22semidirect
102. #2612C22semidirect
103. #2611C22semidirect
104. #2610C22semidirect
105. #2606C22semidirect
106. #2605C22semidirect
107. #2605C22semidirect
108. #2604C22semidirect
109. #2603C22semidirect
110. #2603C22semidirect
112. #2595C22semidirect
113. #2583C22semidirect
114. #2583C22semidirect
116. #2572C22semidirect
117. #2560C22semidirect
118. #2560C22semidirect
119. #2555C22semidirect
120. #2555C22semidirect
121. #2553C22semidirect
122. #2553C22semidirect
124. #2532C22semidirect
125. #2532C22semidirect
126. #2530C22semidirect
127. #2530C22semidirect
128. #2529C22semidirect
129. #2527C22semidirect
130. #2526C22semidirect
131. #2521C22semidirect
132. #2521C22semidirect
133. #2518C22semidirect
134. #2511C22semidirect
136. #2502C22semidirect
137. #2502C22semidirect
138. #2500C22semidirect
139. #2497C22semidirect
140. #2495C22semidirect
141. #2492C22semidirect
142. #2491C22semidirect
143. #2489C22semidirect
147. #2481C22semidirect
148. #2477C22semidirect
150. #2474C22semidirect
152. #2469C22semidirect
153. #2468C22semidirect
154. #2465C22semidirect
156. #2464C22semidirect
157. #2464C22semidirect
161. #2443C22semidirect
162. #2442C22semidirect
163. #2439C22semidirect
165. #2436C22semidirect
166. #2434C22semidirect
167. #2427C22semidirect
168. #2426C22semidirect
169. #2421C22semidirect
170. #2420C22semidirect
173. #2417C22semidirect
175. #2413C22semidirect
179. #2396C22semidirect
180. #2396C22semidirect
181. #2383C22semidirect
182. #2377C22semidirect
183. #2373C22semidirect
188. #2372C22semidirect
189. #2363C22semidirect
190. #2361C22semidirect
191. #2361C22semidirect
195. #2352C22semidirect
197. #2346C22semidirect
198. Q8×C22⋊C4C22semidirect
199. #2337C22semidirect
200. #2335C22semidirect
201. #2331C22semidirect
204. #2326C22semidirect
205. #2326C22semidirect
210. #2322C22semidirect
211. #2320C22semidirect
212. #2319C22semidirect

Maximal subgroups

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

subgroupindex
#504932
#503532
#493312
#491352
#448362
#447992
#441552
#439822
#397962
#396322
#379422
#379402
#377622
#377032
#369572
#367652
#362032
#361082
#352702
#351202
#351192
#350112
#350032
#345782
#344262
C2×#23722