Finite Group Databasebeta

← #8125440

Subgroups — #8125440

Order 512.

4289 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58861C214yesmaximal, complemented
2#58400C214yesmaximal, complemented
3#55810C214yesmaximal, complemented
4#54177C214yesmaximal, complemented
5#53023C212yesmaximal, complemented
6#53010C212yesmaximal, complemented
7#47467C214yesmaximal, complemented
8#47007C214yesmaximal, complemented
9#46889C214yesmaximal, complemented
10#46839C214yesmaximal, complemented
11#45288C212yesmaximal, complemented
12#45185C212yesmaximal, complemented
13#40219C212yesmaximal, complemented
14#39890C212yesmaximal, complemented
15#39603C212yesmaximal, complemented
16#39564C212yesmaximal, complemented
17#39022C212yesmaximal, complemented
18#38929C212yesmaximal, complemented
19#37853C212yesmaximal, complemented
20#37837C212yesmaximal
21#37427C211yesmaximal, characteristic, complemented
22#37394C211yesmaximal, characteristic, complemented
23#35334C211yesmaximal, characteristic, complemented
24#35309C211yesmaximal, characteristic, complemented
25#35086C211yesmaximal, characteristic, complemented
26#35020C211yesmaximal, characteristic, complemented
27#34742C211yesmaximal, characteristic
28C2×#552C2212yes—
29C2×#541C2211yescharacteristic, complemented
30C2×#533C2211yescharacteristic, complemented
31C2×#525C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2857C2211yescharacteristic
34#2855C2212yescomplemented
35#2851C2211yescharacteristic
36#2851C2211yescharacteristic
37#2851C2211yescharacteristic
38#2851C2212yes—
39#2851C2211yescharacteristic, complemented
40#2851C2211yescharacteristic, complemented
41#2848C2212yes—
42#2843C2214yescomplemented
43#2841C2214yes—
44#2839C2214yescomplemented
45#2839C2214yescomplemented
46#2836C2214yescomplemented
47#2836C2214yescomplemented
48#2831C2214yescomplemented
49#2814C2214yes—
50#2802C2214yescomplemented
51#2792C2214yescomplemented
52#2791C2214yescomplemented
53#2791C2214yescomplemented
54#2791C2214yescomplemented
55#2790C2214yes—
56#2790C2214yes—
57#2790C2214yescomplemented
58#2788C2214yes—
59#2787C2214yes—
60#2787C2214yescomplemented
61#2786C2214yescomplemented
62#2782C2214yes—
63#2776C2214yescomplemented
64#2776C2214yescomplemented
65#2776C2214yescomplemented
66#2775C2214yescomplemented
67#2770C2214yes—
68#2769C2214yescomplemented
69#2768C2214yes—
70#2767C2214yescomplemented
71#2767C2214yescomplemented
72#2765C2214yes—
73#2765C2214yescomplemented
74#2758C2214yescomplemented
75#2757C2214yes—
76#2755C2214yescomplemented
77#2751C2214yes—
78#2747C2214yes—
79#2747C2214yescomplemented
80#2746C2214yes—
81#2745C2214yes—
82#2744C2214yes—
83#2744C2214yes—
84#2744C2214yes—
85#2742C2214yes—
86#2740C2214yes—
87#2738C2214yes—
88#2738C2214yes—
89#2738C2214yes—
90#2738C2214yes—
91#2726C2214yescomplemented
92#2724C2214yes—
93#2722C2214yescomplemented
94#2719C2214yescomplemented
95#2718C2214yes—
96#2707C2214yes—
97#2704C2214yes—
98#2698C2214yes—
99#2698C2214yescomplemented
100#2695C2214yes—
101#2695C2214yes—
102#2691C2214yes—
103#2689C2214yescomplemented
104#2687C2214yes—
105#2680C2214yes—
106#2655C2214yescomplemented
107#2652C2214yes—
108#2652C2214yescomplemented
109#2646C2214yes—
110#2646C2214yescomplemented
111#2634C2214yescomplemented
112#2629C2212yes—
113#2629C2211yescharacteristic, complemented
114#2628C2212yes—
115#2628C2212yescomplemented
116#2625C2212yes—
117#2621C2211yescharacteristic, complemented
118#2616C2212yes—
119#2599C2214yes—
120#2597C2214yes—
121#2595C2214yescomplemented
122#2590C2214yescomplemented
123#2590C2214yescomplemented
124#2581C2214yescomplemented
125#2580C2214yes—
126#2578C2214yes—
127#2574C2214yes—
128#2573C2214yes—
129#2570C2212yescomplemented
130#2570C2212yescomplemented
131#2569C2214yes—
132#2569C2214yes—
133#2565C2212yescomplemented
134#2565C2214yescomplemented
135#2564C2214yes—
136#2564C2214yescomplemented
137#2562C2212yes—
138#2561C2214yes—
139#2553C2214yes—
140#2552C2212yescomplemented
141#2552C2212yescomplemented
142#2550C2212yescomplemented
143#2538C2212yes—
144#2534C2214yes—
145#2522C2214yes—
146#2520C2214yescomplemented
147#2520C2214yescomplemented
148#2515C2214yescomplemented
149#2514C2212yescomplemented
150#2508C2212yescomplemented
151#2508C2214yescomplemented
152#2507C2212yescomplemented
153#2507C2212yescomplemented
154#2505C2214yes—
155#2503C2212yes—
156#2499C2212yescomplemented
157#2497C2212yescomplemented
158#2496C2212yes—
159#2496C2214yescomplemented
160#2495C2212yes—
161#2495C2212yescomplemented
162#2494C2212yes—
163#2493C2214yes—
164#2493C2214yescomplemented
165#2492C2212yes—
166#2489C2212yes—
167#2489C2212yescomplemented
168#2486C2212yes—
169#2485C2214yes—
170#2485C2212yes—
171#2482C2214yes—
172#2480C2214yes—
173#2478C2214yes—
174#2475C2214yes—
175#2470C2214yes—
176#2468C2214yes—
177#2468C2214yes—
178#2466C2214yescomplemented
179#2462C2214yescomplemented
180#2460C2214yes—
181#2453C2212yescomplemented
182#2453C2212yescomplemented
183#2451C2212yescomplemented
184#2446C2212yescomplemented
185#2442C2212yes—
186#2442C2212yes—
187#2442C2212yes—
188#2442C2212yes—
189#2442C2212yescomplemented
190#2441C2214yes—
191#2440C2212yes—
192#2438C2214yes—
193#2438C2214yes—
194#2429C2212yes—
195#2425C2214yes—
196#2423C2212yes—
197#2423C2212yes—
198#2422C2212yes—
199#2421C2212yes—
200#2421C2212yes—
201#2421C2212yescomplemented
202#2420C2212yes—
203#2419C2212yes—
204#2419C2214yes—
205#2419C2212yes—
206#2418C2212yes—
207#2418C2212yes—
208#2417C2212yes—
209#2417C2212yes—
210#2411C2214yes—
211#2395C2212yes—
212#2395C2212yes—
213#2370C2212yescomplemented
214#2360C2212yes—
215#2360C2212yescomplemented
216#2351C2212yescomplemented
217D4×C4⋊C4C2212yes—
218#2347C2212yescomplemented
219#2344C2212yes—
220#2335C2214yes—
221#2334C2214yes—
222#2323C2212yes—
223#2323C2214yes—
224#2323C2212yes—
225#2318C2214yes—
226#2316C2212yescomplemented
227#2315C2214yes—
228#2314C2212yes—
229#2314C2214yes—
230#2314C2211yescharacteristic, complemented
231#2311C2212yes—
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2212yescomplemented
234C4×#123C2212yes—
235C4×#123C2212yes—
236#2297C2211yescharacteristic
237#2296C2211yescharacteristic
238#2285C2211yescharacteristic
239C2×#382C2211yescharacteristic, complemented
240#2280C2211yescharacteristic
241C2×#380C2212yes—
242C2×C4×C22⋊C4C2211yescharacteristic
243C22×#41C2311yescharacteristic
244C24×C4C2311yescharacteristic
245#552—48no—
246#541—44no—
247#533—44no—
248C2×C4⋊Q8C2311yescharacteristic
249C2×C4⋊Q8C2312yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2314yes—
256C2×#125C2311yescharacteristic
257C2×#125C2311yescharacteristic
258C2×#125C2311yescharacteristic
259C2×#125C2314yes—
260#525—44no—
261C2×#123C2314yes—
262C2×#123C2311yescharacteristic
263C2×#123C2311yescharacteristic
264C2×#123C2312yes—
265C2×#123C2312yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×#121C2312yes—
276C2×#120C2311yescharacteristic
277C2×#120C2311yescharacteristic
278C4×#41—44no—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×#117C2312yes—
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C2×#117C2314yes—
294C2×#117C2311yescharacteristic
295C2×#117C2311yescharacteristic
296C2×#117C2314yes—
297C2×#117C2311yescharacteristic
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C22⋊C4C2314yes—
302C22×C22⋊C4C2312yes—
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307#401C2314yes—
308#401C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2312yes—
341#399C2312yes—
342#399C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
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#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2312yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2312yes—
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2312yes—
420#394C2312yes—
421#394C2312yes—
422#394C2312yes—
423#394C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2312yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2312yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2312yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2312yes—
505#388C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2312yes—
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#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#387C2312yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2312yes—
559#386C2314yes—
560#386C2312yes—
561#386C2312yes—
562#386C2312yes—
563#386C2314yes—
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#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2312yes—
586#385C2312yes—
587#385C2312yes—
588#385C2312yes—
589#385C2314yes—
590#385C2314yes—
591#384C2314yes—
592#384C2312yes—
593#384C2312yes—
594#384C2311yescharacteristic
595#384C2314yes—
596#384C2312yes—
597#383C2314yes—
598#383C2314yes—
599#383C2314yes—
600#383C2314yes—
601#382C2314yes—
602#382C2312yes—
603#382C2312yes—
604#382C2314yes—
605#382C2311yescharacteristic
606#382C2311yescharacteristic
607#382C2314yes—
608#382C2314yes—
609#382C2314yes—
610#382C2311yescharacteristic
611#382C2312yes—
612#382C2312yes—
613#381C2314yes—
614#381C2314yes—
615#381C2314yes—
616#381C2314yes—
617#381C2314yes—
618#381C2312yes—
619#381C2312yes—
620#381C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2314yes—
626#380C2314yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2314yes—
631#380C2314yes—
632#380C2314yes—
633#380C2314yes—
634#380C2314yes—
635#380C2312yes—
636#380C2314yes—
637#380C2312yes—
638#380C2312yes—
639#380C2314yes—
640#380C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#379C2312yes—
649#379C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C2×#95C2314yes—
677C2×#95C2314yes—
678C2×#95C2312yes—
679C25C2411yescharacteristic
680C2×#41—24no—
681C2×#41—24no—
682C2×#41—42no—
683C22×Q8C2412yes—
684C22×Q8C2411yescharacteristic
685C22×Q8C2414yes—
686C22×D4C2412yes—
687C22×D4C2411yescharacteristic
688C22×D4C2411yescharacteristic
689C22×D4C2411yescharacteristic
690C22×D4C2412yes—
691C23×C4—24no—
692C23×C4—42no—
693C23×C4—42no—
694C23×C4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2414yes—
706C23×C4C2412yes—
707C4⋊Q8—44no—
708C4⋊Q8—42no—
709#126—48no—
710#126—48no—
711#126—48no—
712#125—44no—
713#125—42no—
714#125—42no—
715#125—42no—
716#125—48no—
717#125—44no—
718#125—48no—
719#123—44no—
720#123—44no—
721#123—42no—
722#123—48no—
723#123—48no—
724#123—42no—
725C22⋊Q8—28no—
726C22⋊Q8—28no—
727C22⋊Q8—48no—
728C22⋊Q8—48no—
729C22⋊Q8—44no—
730C22⋊Q8—44no—
731C22⋊Q8—44no—
732C22⋊Q8—44no—
733#121—44no—
734#120—42no—
735#120—42no—
736C4×Q8—48no—
737C4×Q8—44no—
738C4×Q8—44no—
739C4×Q8—44no—
740C4×Q8—44no—
741C4×D4—28no—
742C4×D4—44no—
743C4×D4—44no—
744C4×D4—48no—
745C4×D4—44no—
746C4×D4—44no—
747#117—24no—
748#117—28no—
749#117—24no—
750#117—42no—
751#117—42no—
752#117—42no—
753#117—48no—
754#117—48no—
755C2×C4⋊C4—44no—
756C2×C4⋊C4—44no—
757C2×C4⋊C4—44no—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C22⋊C4—44no—
821C2×C22⋊C4—48no—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2411yescharacteristic
844C2×C22⋊C4C2411yescharacteristic
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C42—24no—
862C2×C42—42no—
863C2×C42—42no—
864C2×C42—42no—
865C2×C42C2414yes—
866C2×C42C2411yescharacteristic
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2411yescharacteristic
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2411yescharacteristic
884C2×C42C2414yes—
885C2×C42C2411yescharacteristic
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
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—
957C24—22no—
958C24—24no—
959C24—41no—
960C24—41no—
961C24—42no—
962C24C2511yescharacteristic
963C24C2511yescharacteristic
964C24C2511yescharacteristic
965C24C2512yes—
966#41—416no—
967C2×Q8—24no—
968C2×Q8—22no—
969C2×Q8—24no—
970C2×Q8—22no—
971C2×Q8—24no—
972C2×Q8—41no—
973C2×Q8—44no—
974C2×Q8—44no—
975C2×Q8—44no—
976C2×D4—24no—
977C2×D4—22no—
978C2×D4—22no—
979C2×D4—22no—
980C2×D4—22no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—22no—
984C2×D4—22no—
985C2×D4—42no—
986C2×D4—41no—
987C2×D4—41no—
988C2×D4—41no—
989C2×D4—42no—
990C2×D4—42no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—24no—
996C22×C4—22no—
997C22×C4—28no—
998C22×C4—28no—
999C22×C4—22no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—22no—
1003C22×C4—24no—
1004C22×C4—22no—
1005C22×C4—24no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—42no—
1014C22×C4—41no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—41no—
1019C22×C4—44no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—44no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—88no—
1029C22×C4H(5,𝔽2)14yes—
1030C22×C42−1+414yes—
1031C22×C4C2512yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—28no—
1059C4⋊C4—24no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—42no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—42no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—44no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—44no—
1141C22⋊C4—42no—
1142C22⋊C4—42no—
1143C22⋊C4—41no—
1144C22⋊C4—41no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—42no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C42—22no—
1156C42—22no—
1157C42—24no—
1158C42—22no—
1159C42—22no—
1160C42—28no—
1161C42—24no—
1162C42—24no—
1163C42—24no—
1164C42—41no—
1165C42—41no—
1166C42—42no—
1167C42—42no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42—44no—
1176C23—28no—
1177C23—22no—
1178C23—21no—
1179C23—22no—
1180C23—21no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—21no—
1186C23—21no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—21no—
1192C23—21no—
1193C23—22no—
1194C23—21no—
1195C23—22no—
1196C23—82no—
1197C23—82no—
1198C23—84no—
1199C23—84no—
1200C23C2×H(5,𝔽2)12yes—
1201C23C2×2−1+412yes—
1202C23#58514yes—
1203C23C2611yescharacteristic
1204Q8—44no—
1205Q8—48no—
1206Q8—88no—
1207D4—44no—
1208D4—44no—
1209D4—48no—
1210D4—44no—
1211D4—84no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—28no—
1217C2×C4—28no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—21no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—48no—
1279C2×C4—44no—
1280C2×C4—84no—
1281C2×C4—88no—
1282C2×C4—84no—
1283C2×C4—88no—
1284C2×C4—82no—
1285C2×C4—84no—
1286C2×C4—84no—
1287C2×C4—84no—
1288C2×C4—164no—
1289C2×C4C2×H(5,𝔽2)12yes—
1290C2×C4C2×H(5,𝔽2)12yes—
1291C2×C4C2×2−1+412yes—
1292C2×C4C2×2−1+412yes—
1293C2×C4#58512yes—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—24no—
1298C22—22no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—42no—
1303C22—41no—
1304C22—41no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—42no—
1315C22—42no—
1316C22—88no—
1317C22C22×H(5,𝔽2)11yescharacteristic
1318C22C22×2−1+411yescharacteristic
1319C22C2×#58511yescharacteristic
1320C22C2×#58512yes—
1321C222−1+612yes—
1322C4—22no—
1323C4—22no—
1324C4—42no—
1325C4—41no—
1326C4—44no—
1327C4—42no—
1328C4—44no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—44no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4—44no—
1343C4—44no—
1344C4#353514yes—
1345C2—42no—
1346C2—42no—
1347C2—44no—
1348C2—81no—
1349C2C2×#353511yescharacteristic
1350C2#6282511yescharacteristic
1351C2#6288911yescharacteristic
1352C2#6292712yes—
1353C2#6294012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58861C2semidirect
2. #58400C2semidirect
3. #55810C2semidirect
4. #54177C2semidirect
5. #53023C2semidirect
6. #53010C2semidirect
7. #47467C2semidirect
8. #47007C2semidirect
9. #46889C2semidirect
10. #46839C2semidirect
11. #45288C2semidirect
12. #45185C2semidirect
13. #40219C2semidirect
14. #39890C2semidirect
15. #39603C2semidirect
16. #39564C2semidirect
17. #39022C2semidirect
18. #38929C2semidirect
19. #37853C2semidirect
21. #37427C2semidirect
22. #37394C2semidirect
23. #35334C2semidirect
24. #35309C2semidirect
25. #35086C2semidirect
26. #35020C2semidirect
29. C2×#541C22semidirect
30. C2×#533C22semidirect
34. #2855C22semidirect
39. #2851C22semidirect
40. #2851C22semidirect
42. #2843C22semidirect
44. #2839C22semidirect
45. #2839C22semidirect
46. #2836C22semidirect
47. #2836C22semidirect
48. #2831C22semidirect
50. #2802C22semidirect
51. #2792C22semidirect
52. #2791C22semidirect
53. #2791C22semidirect
54. #2791C22semidirect
57. #2790C22semidirect
60. #2787C22semidirect
61. #2786C22semidirect
63. #2776C22semidirect
64. #2776C22semidirect
65. #2776C22semidirect
66. #2775C22semidirect
68. #2769C22semidirect
70. #2767C22semidirect
71. #2767C22semidirect
73. #2765C22semidirect
74. #2758C22semidirect
76. #2755C22semidirect
79. #2747C22semidirect
91. #2726C22semidirect
93. #2722C22semidirect
94. #2719C22semidirect
99. #2698C22semidirect
103. #2689C22semidirect
106. #2655C22semidirect
108. #2652C22semidirect
110. #2646C22semidirect
111. #2634C22semidirect
113. #2629C22semidirect
115. #2628C22semidirect
117. #2621C22semidirect
121. #2595C22semidirect
122. #2590C22semidirect
123. #2590C22semidirect
124. #2581C22semidirect
129. #2570C22semidirect
130. #2570C22semidirect
133. #2565C22semidirect
134. #2565C22semidirect
136. #2564C22semidirect
140. #2552C22semidirect
141. #2552C22semidirect
142. #2550C22semidirect
146. #2520C22semidirect
147. #2520C22semidirect
148. #2515C22semidirect
149. #2514C22semidirect
150. #2508C22semidirect
151. #2508C22semidirect
152. #2507C22semidirect
153. #2507C22semidirect
156. #2499C22semidirect
157. #2497C22semidirect
159. #2496C22semidirect
161. #2495C22semidirect
164. #2493C22semidirect
167. #2489C22semidirect
178. #2466C22semidirect
179. #2462C22semidirect
181. #2453C22semidirect
182. #2453C22semidirect
183. #2451C22semidirect
184. #2446C22semidirect
189. #2442C22semidirect
201. #2421C22semidirect
213. #2370C22semidirect
215. #2360C22semidirect
216. #2351C22semidirect
218. #2347C22semidirect
226. #2316C22semidirect
230. #2314C22semidirect
233. C4×C22⋊Q8C22semidirect
239. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#588612
#584002
#558102
#541772
#530232
#530102
#474672
#470072
#468892
#468392
#452882
#451852
#402192
#398902
#396032
#395642
#390222
#389292
#378532
#378372
#374272
#373942
#353342
#353092
#350862
#350202
#347422