Finite Group Databasebeta

← #8108352

Subgroups — #8108352

Order 512.

4882 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#59008C214yesmaximal, complemented
2#53216C212yesmaximal, complemented
3#53205C212yesmaximal, complemented
4#53197C212yesmaximal, complemented
5#53195C212yesmaximal, complemented
6#45808C212yesmaximal, complemented
7#45807C212yesmaximal, complemented
8#45795C212yesmaximal, complemented
9#45793C212yesmaximal, complemented
10#45475C214yesmaximal, complemented
11#40453C214yesmaximal, complemented
12#40423C214yesmaximal, complemented
13#38484C212yesmaximal, complemented
14#38467C212yesmaximal, complemented
15#38444C212yesmaximal, complemented
16#38427C212yesmaximal, complemented
17#37877C212yesmaximal, complemented
18#37867C212yesmaximal, complemented
19#37708C212yesmaximal, complemented
20#37698C212yesmaximal, complemented
21#36896C214yesmaximal, complemented
22#36894C214yesmaximal, complemented
23#36729C212yesmaximal, complemented
24#36719C212yesmaximal, complemented
25#36625C211yesmaximal, characteristic, complemented
26#36624C211yesmaximal, characteristic
27C2×#2855C211yesmaximal, characteristic, complemented
28C2×#552C2214yes—
29C2×#539C2212yes—
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C2×#525C2212yes—
33C22×C22⋊Q8C2211yescharacteristic
34C23×C42C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2856C2211yescharacteristic
42#2856C2211yescharacteristic
43#2855C2212yes—
44#2855C2212yes—
45#2855C2212yes—
46#2855C2212yes—
47#2855C2212yes—
48#2855C2212yes—
49#2855C2212yes—
50#2855C2212yes—
51#2855C2212yes—
52#2855C2212yes—
53#2854C2212yes—
54#2854C2212yes—
55#2851C2212yes—
56#2851C2212yes—
57#2850C2212yes—
58#2850C2212yes—
59#2848C2212yes—
60#2848C2212yes—
61#2847C2212yes—
62#2847C2212yes—
63#2841C2214yes—
64#2816C2214yes—
65#2811C2212yescomplemented
66#2809C2212yescomplemented
67#2808C2212yescomplemented
68#2808C2212yescomplemented
69#2806C2212yescomplemented
70#2806C2212yescomplemented
71#2805C2212yescomplemented
72#2805C2212yescomplemented
73#2804C2212yescomplemented
74#2800C2214yescomplemented
75#2799C2214yescomplemented
76#2798C2214yescomplemented
77#2792C2214yescomplemented
78#2791C2214yescomplemented
79#2774C2214yescomplemented
80#2774C2214yescomplemented
81#2761C2214yes—
82#2755C2214yescomplemented
83#2751C2214yes—
84#2750C2214yes—
85#2747C2214yes—
86#2744C2214yes—
87#2743C2214yes—
88#2743C2214yes—
89#2742C2214yes—
90#2741C2214yes—
91#2740C2214yes—
92#2739C2214yes—
93#2732C2212yescomplemented
94#2732C2212yescomplemented
95#2729C2214yescomplemented
96#2727C2212yescomplemented
97#2727C2212yescomplemented
98#2726C2212yescomplemented
99#2726C2212yescomplemented
100#2725C2214yescomplemented
101#2723C2214yescomplemented
102#2721C2214yescomplemented
103#2720C2214yescomplemented
104#2719C2214yescomplemented
105#2719C2214yescomplemented
106#2717C2214yes—
107#2716C2214yescomplemented
108#2715C2214yescomplemented
109#2713C2214yescomplemented
110#2709C2214yescomplemented
111#2707C2214yescomplemented
112#2704C2214yes—
113#2704C2214yes—
114#2704C2214yes—
115#2704C2214yescomplemented
116#2702C2214yes—
117#2702C2214yes—
118#2702C2214yes—
119#2701C2214yes—
120#2700C2214yes—
121#2700C2214yescomplemented
122#2692C2214yes—
123#2692C2214yescomplemented
124#2691C2214yes—
125#2691C2214yes—
126#2690C2214yes—
127#2689C2214yescomplemented
128#2687C2214yes—
129#2686C2214yes—
130#2683C2214yes—
131#2683C2214yes—
132#2683C2212yescomplemented
133#2681C2214yes—
134#2681C2214yes—
135#2672C2214yes—
136#2672C2214yes—
137#2665C2214yescomplemented
138#2664C2214yescomplemented
139#2659C2212yes—
140#2652C2214yescomplemented
141#2650C2214yescomplemented
142#2639C2212yes—
143#2627C2212yes—
144#2618C2212yes—
145#2607C2214yescomplemented
146#2601C2214yescomplemented
147#2590C2214yescomplemented
148#2589C2214yescomplemented
149#2588C2214yescomplemented
150#2588C2214yescomplemented
151#2587C2214yescomplemented
152#2586C2214yescomplemented
153#2585C2214yescomplemented
154#2584C2214yescomplemented
155#2569C2214yes—
156#2564C2214yes—
157#2560C2214yescomplemented
158#2559C2214yes—
159#2556C2214yes—
160#2549C2214yescomplemented
161#2534C2214yes—
162#2498C2214yes—
163#2498C2214yes—
164#2488C2214yes—
165#2481C2214yes—
166#2479C2214yescomplemented
167#2476C2214yes—
168#2475C2214yescomplemented
169#2472C2214yes—
170#2469C2214yescomplemented
171#2469C2214yescomplemented
172#2468C2214yes—
173#2466C2214yes—
174#2466C2214yescomplemented
175#2465C2214yes—
176#2462C2214yescomplemented
177#2460C2214yes—
178#2460C2214yes—
179#2460C2214yescomplemented
180#2458C2214yescomplemented
181#2454C2214yes—
182#2453C2214yescomplemented
183#2450C2214yes—
184#2450C2214yes—
185#2450C2214yescomplemented
186#2449C2214yes—
187#2444C2214yes—
188#2438C2214yes—
189#2438C2214yes—
190#2425C2214yes—
191#2421C2214yescomplemented
192#2419C2214yescomplemented
193#2418C2214yes—
194#2413C2214yes—
195#2413C2214yes—
196#2411C2214yes—
197#2409C2214yes—
198#2406C2214yes—
199#2378C2214yes—
200#2377C2214yes—
201#2367C2214yes—
202#2359C2214yes—
203#2359C2214yes—
204#2344C2214yes—
205#2339C2214yes—
206#2334C2214yescomplemented
207#2332C2214yescomplemented
208#2329C2212yes—
209#2329C2214yescomplemented
210#2325C2212yes—
211#2323C2214yescomplemented
212#2316C2212yes—
213C4×C22⋊Q8C2212yes—
214C4×C22⋊Q8C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×C22⋊Q8C2212yes—
217C4×#121C2212yes—
218C4×#121C2212yes—
219C4×#121C2212yes—
220C4×#121C2212yes—
221#2297C2212yes—
222#2296C2212yes—
223C2×#391C2211yescharacteristic
224C2×#391C2211yescharacteristic
225C2×#389C2211yescharacteristic
226C2×#389C2211yescharacteristic
227C2×#387C2212yes—
228C2×#387C2212yes—
229C2×#385C2212yes—
230#2285C2211yescharacteristic
231#2285C2211yescharacteristic
232#2280C2212yes—
233C2×#381C2212yes—
234C2×#380C2211yescharacteristic
235C22×#41C2312yes—
236C23×Q8C2311yescharacteristic
237C24×C4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239C24×C4C2311yescharacteristic
240#552—416no—
241#539—48no—
242#533—44no—
243#532—44no—
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2311yescharacteristic
246C2×C4⋊Q8C2311yescharacteristic
247C2×#127C2311yescharacteristic
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#125C2314yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#124C2312yes—
258C2×#124C2314yes—
259#525—48no—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×C22⋊Q8—44no—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×#121C2312yes—
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#120C2314yes—
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×#117C2312yes—
303C2×#117C2314yes—
304C2×#117C2314yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2311yescharacteristic
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2312yes—
315C22×C42—44no—
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2312yes—
430#391C2314yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
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#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
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#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
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#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#384C2311yescharacteristic
601#384C2311yescharacteristic
602#384C2311yescharacteristic
603#384C2311yescharacteristic
604#382C2314yes—
605#382C2312yes—
606#382C2312yes—
607#381C2314yes—
608#381C2314yes—
609#381C2314yes—
610#381C2314yes—
611#381C2314yes—
612#381C2314yes—
613#381C2314yes—
614#381C2314yes—
615#380C2312yes—
616#380C2314yes—
617#380C2312yes—
618#380C2314yes—
619#380C2312yes—
620#380C2312yes—
621#380C2314yes—
622#380C2314yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#379C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C2×#95C2314yes—
661C2×#95C2312yes—
662C2×#95C2312yes—
663C2×#95C2312yes—
664C2×#95C2312yes—
665C25C2411yescharacteristic
666C2×#41—28no—
667C2×#41—44no—
668C2×#41—44no—
669C22×Q8—42no—
670C22×Q8—42no—
671C22×Q8—42no—
672C22×Q8C2412yes—
673C22×Q8C2412yes—
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×Q8C2412yes—
677C22×Q8C2414yes—
678C22×D4C2414yes—
679C22×D4C2414yes—
680C22×D4C2414yes—
681C22×D4C2412yes—
682C22×D4C2412yes—
683C22×D4C2412yes—
684C23×C4—24no—
685C23×C4—24no—
686C23×C4—24no—
687C23×C4—24no—
688C23×C4—42no—
689C23×C4—42no—
690C23×C4—42no—
691C23×C4—42no—
692C23×C4—42no—
693C23×C4C2412yes—
694C23×C4C2411yescharacteristic
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C23×C4C2411yescharacteristic
708C23×C4C2411yescharacteristic
709C23×C4C2412yes—
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2414yes—
713C23×C4C2411yescharacteristic
714C23×C4C2414yes—
715C23×C4C2414yes—
716C23×C4C2411yescharacteristic
717C23×C4C2411yescharacteristic
718C4⋊Q8—42no—
719C4⋊Q8—42no—
720C4⋊Q8—42no—
721#127—42no—
722#126—48no—
723#126—48no—
724#126—48no—
725#126—48no—
726#125—44no—
727#125—48no—
728#125—48no—
729#125—48no—
730#125—48no—
731#124—44no—
732#124—48no—
733#123—216no—
734#123—48no—
735#123—48no—
736#123—48no—
737#123—48no—
738C22⋊Q8—28no—
739C22⋊Q8—28no—
740C22⋊Q8—44no—
741C22⋊Q8—44no—
742C22⋊Q8—48no—
743C22⋊Q8—48no—
744C22⋊Q8—48no—
745C22⋊Q8—48no—
746C22⋊Q8—48no—
747C22⋊Q8—48no—
748C22⋊Q8—44no—
749C22⋊Q8—44no—
750C22⋊Q8—44no—
751C22⋊Q8—44no—
752C22⋊Q8—44no—
753C22⋊Q8—44no—
754C22⋊Q8—44no—
755C22⋊Q8—44no—
756#121—28no—
757#121—28no—
758#121—44no—
759#121—44no—
760#121—44no—
761#121—44no—
762#121—44no—
763#121—44no—
764#120—48no—
765C4×Q8—44no—
766C4×Q8—48no—
767C4×Q8—44no—
768C4×D4—44no—
769C4×D4—44no—
770C4×D4—48no—
771C4×D4—48no—
772C4×D4—48no—
773C4×D4—48no—
774#117—28no—
775#117—48no—
776#117—44no—
777#117—44no—
778#117—48no—
779C2×C4⋊C4—28no—
780C2×C4⋊C4—28no—
781C2×C4⋊C4—28no—
782C2×C4⋊C4—42no—
783C2×C4⋊C4—42no—
784C2×C4⋊C4—42no—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
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×C22⋊C4—44no—
843C2×C22⋊C4—44no—
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⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
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×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C42—24no—
880C2×C42—24no—
881C2×C42—42no—
882C2×C42—42no—
883C2×C42—42no—
884C2×C42—42no—
885C2×C42—42no—
886C2×C42—42no—
887C2×C42—42no—
888C2×C42—42no—
889C2×C42—42no—
890C2×C42—42no—
891C2×C42C2414yes—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894C2×C42C2411yescharacteristic
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
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—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968C24—22no—
969C24—22no—
970C24—22no—
971C24—22no—
972C24—22no—
973C24—41no—
974C24—41no—
975C24C2514yes—
976C24C2511yescharacteristic
977C24C2511yescharacteristic
978C24C2511yescharacteristic
979#41—816no—
980C2×Q8—24no—
981C2×Q8—24no—
982C2×Q8—24no—
983C2×Q8—24no—
984C2×Q8—24no—
985C2×Q8—44no—
986C2×Q8—42no—
987C2×Q8—42no—
988C2×Q8—42no—
989C2×Q8—42no—
990C2×Q8—42no—
991C2×Q8—42no—
992C2×Q8—42no—
993C2×Q8—44no—
994C2×Q8—42no—
995C2×Q8—44no—
996C2×Q8—42no—
997C2×Q8—42no—
998C2×Q8—88no—
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—44no—
1008C2×D4—44no—
1009C2×D4—42no—
1010C2×D4—42no—
1011C2×D4—42no—
1012C2×D4—42no—
1013C2×D4—42no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—42no—
1017C22×C4—22no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—22no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—28no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—41no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—41no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—41no—
1074C22×C4—416no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—416no—
1090C22×C4—416no—
1091C22×C4H(5,𝔽2)14yes—
1092C22×C4H(5,𝔽2)14yes—
1093C22×C42−1+414yes—
1094C22×C42−1+414yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2514yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2514yes—
1103C22×C4C2514yes—
1104C22×C4C2514yes—
1105C22×C4C2514yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C22×C4C2511yescharacteristic
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—28no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—28no—
1178C22⋊C4—28no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
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⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—22no—
1216C42—22no—
1217C42—22no—
1218C42—28no—
1219C42—41no—
1220C42—41no—
1221C42—41no—
1222C42—41no—
1223C42—41no—
1224C42—41no—
1225C42—41no—
1226C42—41no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C23—21no—
1236C23—21no—
1237C23—21no—
1238C23—21no—
1239C23—28no—
1240C23—21no—
1241C23—21no—
1242C23—21no—
1243C23—21no—
1244C23—21no—
1245C23—21no—
1246C23—21no—
1247C23—21no—
1248C23—21no—
1249C23—21no—
1250C23—21no—
1251C23—21no—
1252C23—24no—
1253C23—24no—
1254C23—24no—
1255C23—24no—
1256C23—24no—
1257C23—24no—
1258C23—24no—
1259C23—44no—
1260C23—44no—
1261C23—44no—
1262C23—44no—
1263C23—44no—
1264C23—44no—
1265C23C2×H(5,𝔽2)12yes—
1266C23C2×H(5,𝔽2)12yes—
1267C23C2×2−1+412yes—
1268C23C2×2−1+412yes—
1269C23#58512yes—
1270C23C2611yescharacteristic
1271Q8—84no—
1272Q8—84no—
1273Q8—84no—
1274Q8—84no—
1275Q8—84no—
1276Q8—88no—
1277D4—416no—
1278D4—84no—
1279D4—84no—
1280D4—84no—
1281D4—88no—
1282D4—88no—
1283C2×C4—28no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—28no—
1305C2×C4—28no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
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—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—21no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—21no—
1345C2×C4—44no—
1346C2×C4—44no—
1347C2×C4—44no—
1348C2×C4—44no—
1349C2×C4—44no—
1350C2×C4—44no—
1351C2×C4—44no—
1352C2×C4—44no—
1353C2×C4—44no—
1354C2×C4—44no—
1355C2×C4—44no—
1356C2×C4—44no—
1357C2×C4—44no—
1358C2×C4—44no—
1359C2×C4—44no—
1360C2×C4—48no—
1361C2×C4—88no—
1362C2×C4—84no—
1363C2×C4—84no—
1364C2×C4—84no—
1365C2×C4—88no—
1366C2×C4—164no—
1367C2×C4C2×H(5,𝔽2)12yes—
1368C2×C4C2×H(5,𝔽2)12yes—
1369C2×C4C2×H(5,𝔽2)12yes—
1370C2×C4C2×H(5,𝔽2)12yes—
1371C2×C4C2×2−1+412yes—
1372C2×C4C2×2−1+412yes—
1373C2×C4C2×2−1+412yes—
1374C2×C4C2×2−1+412yes—
1375C2×C4#58512yes—
1376C2×C4#58512yes—
1377C22—22no—
1378C22—22no—
1379C22—22no—
1380C22—22no—
1381C22—22no—
1382C22—22no—
1383C22—22no—
1384C22—22no—
1385C22—22no—
1386C22—22no—
1387C22—22no—
1388C22—22no—
1389C22—416no—
1390C22—41no—
1391C22—41no—
1392C22—41no—
1393C22—41no—
1394C22—41no—
1395C22—41no—
1396C22—41no—
1397C22—41no—
1398C22—44no—
1399C22—44no—
1400C22—44no—
1401C22—44no—
1402C22—44no—
1403C22—44no—
1404C22—44no—
1405C22#353614yes—
1406C22C22×H(5,𝔽2)11yescharacteristic
1407C22C22×H(5,𝔽2)11yescharacteristic
1408C22C22×2−1+411yescharacteristic
1409C22C22×2−1+411yescharacteristic
1410C22C2×#58511yescharacteristic
1411C22C2×#58511yescharacteristic
1412C22C2×#58511yescharacteristic
1413C4—22no—
1414C4—22no—
1415C4—22no—
1416C4—22no—
1417C4—22no—
1418C4—22no—
1419C4—22no—
1420C4—22no—
1421C4—22no—
1422C4—22no—
1423C4—44no—
1424C4—44no—
1425C4—44no—
1426C4—44no—
1427C4—44no—
1428C4—44no—
1429C4—41no—
1430C4—41no—
1431C4—44no—
1432C4—44no—
1433C4—44no—
1434C4—44no—
1435C4—44no—
1436C2—24no—
1437C2—42no—
1438C2—42no—
1439C2—84no—
1440C2C2×#353611yescharacteristic
1441C2#6274811yescharacteristic
1442C2#6275211yescharacteristic
1443C2#6281911yescharacteristic
1444C2#6282011yescharacteristic
1445C2#6283511yescharacteristic
1446C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36624C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59008C2semidirect
2. #53216C2semidirect
3. #53205C2semidirect
4. #53197C2semidirect
5. #53195C2semidirect
6. #45808C2semidirect
7. #45807C2semidirect
8. #45795C2semidirect
9. #45793C2semidirect
10. #45475C2semidirect
11. #40453C2semidirect
12. #40423C2semidirect
13. #38484C2semidirect
14. #38467C2semidirect
15. #38444C2semidirect
16. #38427C2semidirect
17. #37877C2semidirect
18. #37867C2semidirect
19. #37708C2semidirect
20. #37698C2semidirect
21. #36896C2semidirect
22. #36894C2semidirect
23. #36729C2semidirect
24. #36719C2semidirect
25. #36625C2semidirect
27. C2×#2855C2semidirect
65. #2811C22semidirect
66. #2809C22semidirect
67. #2808C22semidirect
68. #2808C22semidirect
69. #2806C22semidirect
70. #2806C22semidirect
71. #2805C22semidirect
72. #2805C22semidirect
73. #2804C22semidirect
74. #2800C22semidirect
75. #2799C22semidirect
76. #2798C22semidirect
77. #2792C22semidirect
78. #2791C22semidirect
79. #2774C22semidirect
80. #2774C22semidirect
82. #2755C22semidirect
93. #2732C22semidirect
94. #2732C22semidirect
95. #2729C22semidirect
96. #2727C22semidirect
97. #2727C22semidirect
98. #2726C22semidirect
99. #2726C22semidirect
100. #2725C22semidirect
101. #2723C22semidirect
102. #2721C22semidirect
103. #2720C22semidirect
104. #2719C22semidirect
105. #2719C22semidirect
107. #2716C22semidirect
108. #2715C22semidirect
109. #2713C22semidirect
110. #2709C22semidirect
111. #2707C22semidirect
115. #2704C22semidirect
121. #2700C22semidirect
123. #2692C22semidirect
127. #2689C22semidirect
132. #2683C22semidirect
137. #2665C22semidirect
138. #2664C22semidirect
140. #2652C22semidirect
141. #2650C22semidirect
145. #2607C22semidirect
146. #2601C22semidirect
147. #2590C22semidirect
148. #2589C22semidirect
149. #2588C22semidirect
150. #2588C22semidirect
151. #2587C22semidirect
152. #2586C22semidirect
153. #2585C22semidirect
154. #2584C22semidirect
157. #2560C22semidirect
160. #2549C22semidirect
166. #2479C22semidirect
168. #2475C22semidirect
170. #2469C22semidirect
171. #2469C22semidirect
174. #2466C22semidirect
176. #2462C22semidirect
179. #2460C22semidirect
180. #2458C22semidirect
182. #2453C22semidirect
185. #2450C22semidirect
191. #2421C22semidirect
192. #2419C22semidirect
206. #2334C22semidirect
207. #2332C22semidirect
209. #2329C22semidirect
211. #2323C22semidirect

Maximal subgroups

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

subgroupindex
#590082
#532162
#532052
#531972
#531952
#458082
#458072
#457952
#457932
#454752
#404532
#404232
#384842
#384672
#384442
#384272
#378772
#378672
#377082
#376982
#368962
#368942
#367292
#367192
#366252
#366242
C2×#28552