Finite Group Databasebeta

← #8096108

Subgroups — #8096108

Order 512.

5437 conjugacy classes of subgroups.

The subgroup lattice has 1458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53095C213yesmaximal, complemented
2#53047C213yesmaximal, complemented
3#53045C213yesmaximal, complemented
4#53011C213yesmaximal, complemented
5#53007C213yesmaximal, complemented
6#53006C213yesmaximal, complemented
7#52297C213yesmaximal, complemented
8#46339C213yesmaximal, complemented
9#46020C213yesmaximal, complemented
10#46002C213yesmaximal, complemented
11#45721C213yesmaximal, complemented
12#45677C213yesmaximal, complemented
13#45628C213yesmaximal, complemented
14#45628C213yesmaximal, complemented
15#45616C213yesmaximal, complemented
16#45497C213yesmaximal, complemented
17Q8×#127C211yesmaximal, characteristic, complemented
18Q8×#123C211yesmaximal, characteristic, complemented
19Q8×#121C211yesmaximal, characteristic, complemented
20Q8×#121C211yesmaximal, characteristic, complemented
21#36482C211yesmaximal, characteristic, complemented
22#36458C211yesmaximal, characteristic, complemented
23#36448C211yesmaximal, characteristic, complemented
24#36434C211yesmaximal, characteristic, complemented
25#36434C211yesmaximal, characteristic, complemented
26#35771C211yesmaximal, characteristic, complemented
27#35723C211yesmaximal, characteristic, complemented
28#35700C211yesmaximal, characteristic, complemented
29#35687C211yesmaximal, characteristic, complemented
30#35687C211yesmaximal, characteristic, complemented
31#35687C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×D4×Q8C2211yescharacteristic
40C2×D4×Q8C2211yescharacteristic
41C2×D4×Q8C2211yescharacteristic
42C2×#548C2211yescharacteristic
43C2×#548C2211yescharacteristic
44C2×#548C2211yescharacteristic
45C2×#519C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47C22×C4×Q8C2211yescharacteristic
48#2868C2213yes—
49#2863C2213yes—
50#2860C2213yes—
51#2857C2213yes—
52#2857C2213yes—
53#2855C2213yes—
54#2855C2213yes—
55#2850C2213yes—
56#2850C2213yes—
57#2843C2216yes—
58#2841C2216yes—
59#2838C2216yes—
60#2837C2216yes—
61#2837C2216yes—
62#2837C2216yes—
63#2829C2216yes—
64#2829C2216yes—
65#2827C2216yes—
66#2826C2216yes—
67#2823C2216yes—
68#2803C2213yes—
69#2803C2213yes—
70#2801C2216yes—
71#2796C2216yes—
72#2795C2216yes—
73#2795C2216yes—
74#2795C2213yes—
75#2792C2216yes—
76#2792C2216yes—
77#2792C2213yes—
78#2790C2216yes—
79#2790C2216yes—
80#2790C2216yes—
81#2790C2216yes—
82#2790C2216yes—
83#2784C2213yes—
84#2780C2216yes—
85#2780C2216yes—
86#2756C2216yes—
87#2756C2213yes—
88#2756C2213yes—
89#2752C2216yes—
90#2749C2216yes—
91#2746C2216yes—
92#2746C2216yes—
93#2742C2216yes—
94#2737C2213yes—
95#2737C2213yes—
96#2714C2213yes—
97#2714C2213yes—
98#2705C2216yes—
99#2705C2213yes—
100#2705C2213yes—
101#2699C2213yes—
102#2691C2216yes—
103#2673C2213yes—
104#2673C2211yescharacteristic
105#2625C2213yes—
106#2621C2213yes—
107#2620C2213yes—
108#2616C2213yes—
109#2616C2213yes—
110#2616C2213yes—
111#2546C2213yes—
112#2546C2213yes—
113#2546C2213yes—
114#2545C2213yes—
115#2545C2213yes—
116#2545C2213yes—
117#2542C2213yes—
118#2542C2213yes—
119#2542C2213yes—
120#2542C2213yes—
121#2542C2213yes—
122#2542C2213yes—
123#2538C2213yes—
124#2538C2213yes—
125#2538C2213yes—
126#2536C2213yes—
127#2536C2213yes—
128#2536C2213yes—
129#2514C2213yes—
130#2514C2213yes—
131#2513C2213yes—
132#2512C2213yes—
133#2512C2213yes—
134#2511C2213yes—
135#2503C2213yes—
136#2502C2213yes—
137#2499C2213yes—
138#2497C2213yes—
139#2496C2213yes—
140#2496C2213yes—
141#2495C2213yes—
142#2495C2213yes—
143#2494C2213yes—
144#2487C2213yes—
145#2486C2213yes—
146#2485C2213yes—
147#2446C2213yes—
148#2446C2213yes—
149#2446C2213yes—
150#2446C2213yes—
151#2446C2213yes—
152#2446C2213yes—
153#2434C2213yes—
154#2434C2213yes—
155#2434C2213yes—
156#2432C2213yes—
157#2432C2213yes—
158#2432C2213yes—
159#2432C2213yes—
160#2432C2213yes—
161#2432C2213yes—
162#2429C2213yes—
163#2429C2213yes—
164#2429C2213yes—
165#2429C2213yes—
166#2429C2213yes—
167#2429C2213yes—
168#2429C2213yes—
169#2429C2213yes—
170#2429C2213yes—
171#2426C2213yes—
172#2426C2213yes—
173#2426C2213yes—
174#2423C2213yes—
175#2423C2213yes—
176#2423C2213yes—
177#2421C2213yes—
178#2421C2213yes—
179#2421C2213yes—
180#2417C2213yes—
181#2417C2213yes—
182#2417C2213yes—
183#2417C2213yes—
184#2417C2213yes—
185#2417C2213yes—
186#2416C2213yes—
187#2416C2213yes—
188#2415C2213yes—
189#2415C2213yes—
190#2415C2213yes—
191#2414C2213yes—
192#2409C2213yes—
193#2409C2213yes—
194#2409C2213yes—
195#2407C2213yes—
196#2407C2213yes—
197#2407C2213yes—
198#2407C2213yes—
199#2407C2213yes—
200#2407C2213yes—
201#2395C2213yes—
202#2392C2213yes—
203#2392C2213yes—
204#2388C2213yes—
205#2388C2213yes—
206#2388C2213yes—
207#2383C2216yes—
208#2383C2216yes—
209#2377C2216yes—
210#2351C2211yescharacteristic
211#2351C2211yescharacteristic
212#2351C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214Q8×C4⋊C4C2211yescharacteristic
215Q8×C4⋊C4C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226Q8×C22⋊C4C2211yescharacteristic
227Q8×C22⋊C4C2211yescharacteristic
228C4×#127C2213yes—
229C4×#126C2213yes—
230C4×#126C2213yes—
231C4×#123C2213yes—
232C4×#123C2213yes—
233C4×#121C2213yes—
234C4×#121C2213yes—
235C4×#121C2213yes—
236C4×#121C2213yes—
237C42×Q8C2211yescharacteristic
238C2×2−1+4—44no—
239C2×2−1+4—44no—
240C2×2−1+4—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2313yes—
243C22×#41C2313yes—
244C22×#41C2313yes—
245C23×Q8C2311yescharacteristic
246C23×Q8C2311yescharacteristic
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249C23×Q8C2311yescharacteristic
250C23×Q8C2313yes—
251D4×Q8—44no—
252D4×Q8—44no—
253D4×Q8—44no—
254D4×Q8—44no—
255D4×Q8—44no—
256D4×Q8—44no—
257D4×Q8—44no—
258D4×Q8—44no—
259D4×Q8—44no—
260#548—44no—
261#548—44no—
262#548—44no—
263C2×C4⋊Q8C2313yes—
264C2×C4⋊Q8C2313yes—
265C2×C4⋊Q8C2313yes—
266C2×C4⋊Q8C2313yes—
267C2×C4⋊Q8C2313yes—
268C2×C4⋊Q8C2313yes—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×#127C2311yescharacteristic
273C2×#126C2313yes—
274C2×#126C2313yes—
275C2×#126C2316yes—
276C2×#124C2313yes—
277C2×#124C2313yes—
278C2×#124C2313yes—
279C2×#123C2311yescharacteristic
280C2×#123C2313yes—
281C2×C22⋊Q8C2313yes—
282C2×C22⋊Q8C2313yes—
283C2×C22⋊Q8C2313yes—
284C2×C22⋊Q8C2313yes—
285C2×C22⋊Q8C2313yes—
286C2×C22⋊Q8C2313yes—
287C2×C22⋊Q8C2313yes—
288C2×C22⋊Q8C2313yes—
289C2×C22⋊Q8C2313yes—
290C2×C22⋊Q8C2313yes—
291C2×C22⋊Q8C2313yes—
292C2×C22⋊Q8C2313yes—
293C2×C22⋊Q8C2313yes—
294C2×C22⋊Q8C2313yes—
295C2×C22⋊Q8C2313yes—
296C2×C22⋊Q8C2313yes—
297C2×C22⋊Q8C2313yes—
298C2×C22⋊Q8C2313yes—
299C2×C22⋊Q8C2313yes—
300C2×C22⋊Q8C2313yes—
301C2×C22⋊Q8C2313yes—
302C2×#121C2313yes—
303C2×#121C2311yescharacteristic
304C2×#121C2311yescharacteristic
305C2×#121C2313yes—
306C2×#121C2313yes—
307C2×#121C2313yes—
308C2×#121C2313yes—
309#519—44no—
310C2×C4×Q8—44no—
311C2×C4×Q8—44no—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2313yes—
322C2×C4×Q8C2313yes—
323C2×C4×Q8C2313yes—
324C2×C4×Q8C2313yes—
325C2×C4×Q8C2313yes—
326C2×C4×Q8C2313yes—
327C2×C4×D4C2313yes—
328C2×C4×D4C2313yes—
329C2×C4×D4C2313yes—
330C2×C4×D4C2313yes—
331C2×C4×D4C2313yes—
332C2×C4×D4C2313yes—
333C2×C4×D4C2313yes—
334C2×C4×D4C2313yes—
335C2×C4×D4C2313yes—
336C2×C4×D4C2313yes—
337C2×C4×D4C2313yes—
338C2×C4×D4C2313yes—
339C2×#117C2313yes—
340C2×#117C2313yes—
341C22×C4⋊C4C2313yes—
342C22×C4⋊C4C2313yes—
343C22×C42C2313yes—
344C22×C42C2313yes—
345#401C2316yes—
346#400C2316yes—
347#400C2316yes—
348#400C2316yes—
349#400C2316yes—
350#400C2316yes—
351#400C2316yes—
352#400C2316yes—
353#400C2313yes—
354#399C2316yes—
355#399C2316yes—
356#399C2316yes—
357#399C2316yes—
358#399C2313yes—
359#399C2316yes—
360#398C2316yes—
361#398C2316yes—
362#398C2316yes—
363#398C2316yes—
364#398C2316yes—
365#398C2316yes—
366#398C2316yes—
367#398C2316yes—
368#398C2316yes—
369#398C2316yes—
370#398C2316yes—
371#398C2313yes—
372#398C2316yes—
373#398C2313yes—
374#398C2313yes—
375#397C2316yes—
376#397C2316yes—
377#397C2313yes—
378#397C2313yes—
379#397C2316yes—
380#397C2316yes—
381#397C2316yes—
382#397C2313yes—
383#397C2316yes—
384#397C2313yes—
385#397C2313yes—
386#396C2313yes—
387#396C2316yes—
388#396C2316yes—
389#396C2316yes—
390#396C2316yes—
391#396C2316yes—
392#396C2316yes—
393#396C2316yes—
394#396C2316yes—
395#396C2316yes—
396#396C2316yes—
397#396C2313yes—
398#396C2316yes—
399#396C2313yes—
400#396C2313yes—
401#395C2316yes—
402#395C2316yes—
403#395C2316yes—
404#395C2313yes—
405#395C2313yes—
406#395C2313yes—
407#394C2313yes—
408#394C2316yes—
409#394C2316yes—
410#394C2313yes—
411#394C2316yes—
412#394C2316yes—
413#394C2313yes—
414#394C2316yes—
415#394C2316yes—
416#394C2313yes—
417#394C2313yes—
418#394C2316yes—
419#394C2316yes—
420#394C2313yes—
421#394C2313yes—
422#394C2313yes—
423#394C2316yes—
424#394C2313yes—
425#394C2313yes—
426#394C2313yes—
427#394C2313yes—
428#394C2313yes—
429#394C2311yescharacteristic
430#394C2313yes—
431#394C2313yes—
432#394C2311yescharacteristic
433#393C2313yes—
434#393C2313yes—
435#393C2313yes—
436#392C2313yes—
437#392C2313yes—
438#392C2313yes—
439#392C2311yescharacteristic
440#392C2311yescharacteristic
441#392C2311yescharacteristic
442#392C2313yes—
443#392C2313yes—
444#392C2313yes—
445#392C2311yescharacteristic
446#392C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#391C2313yes—
457#391C2313yes—
458#391C2313yes—
459#391C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#391C2313yes—
464#391C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2313yes—
477#390C2313yes—
478#390C2316yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#389C2316yes—
483#389C2316yes—
484#389C2316yes—
485#389C2316yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2316yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2316yes—
501#389C2316yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#388C2311yescharacteristic
506#388C2313yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2316yes—
512#388C2316yes—
513#388C2313yes—
514#388C2313yes—
515#388C2316yes—
516#388C2316yes—
517#388C2316yes—
518#388C2316yes—
519#388C2313yes—
520#388C2316yes—
521#388C2316yes—
522#388C2316yes—
523#388C2313yes—
524#388C2316yes—
525#388C2316yes—
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2313yes—
533#388C2313yes—
534#387C2311yescharacteristic
535#387C2313yes—
536#387C2313yes—
537#387C2313yes—
538#387C2313yes—
539#387C2313yes—
540#387C2316yes—
541#387C2316yes—
542#387C2316yes—
543#387C2316yes—
544#387C2316yes—
545#387C2316yes—
546#387C2316yes—
547#387C2313yes—
548#387C2313yes—
549#387C2316yes—
550#387C2316yes—
551#387C2313yes—
552#387C2313yes—
553#386C2313yes—
554#386C2316yes—
555#386C2316yes—
556#386C2313yes—
557#386C2313yes—
558#386C2316yes—
559#386C2313yes—
560#386C2316yes—
561#386C2316yes—
562#386C2313yes—
563#386C2313yes—
564#386C2311yescharacteristic
565#386C2313yes—
566#386C2311yescharacteristic
567#386C2311yescharacteristic
568#385C2316yes—
569#385C2316yes—
570#385C2316yes—
571#385C2313yes—
572#385C2316yes—
573#385C2316yes—
574#385C2316yes—
575#385C2316yes—
576#385C2316yes—
577#385C2316yes—
578#385C2316yes—
579#385C2313yes—
580#384C2313yes—
581#384C2316yes—
582#384C2316yes—
583#384C2313yes—
584#384C2313yes—
585#384C2313yes—
586#384C2316yes—
587#383C2313yes—
588#383C2313yes—
589#383C2316yes—
590#382C2313yes—
591#382C2313yes—
592#382C2313yes—
593#381C2316yes—
594#381C2313yes—
595#381C2313yes—
596#380C2313yes—
597#380C2316yes—
598#380C2313yes—
599#380C2313yes—
600#380C2313yes—
601#380C2313yes—
602#380C2313yes—
603#380C2313yes—
604#380C2313yes—
605#380C2313yes—
606#380C2313yes—
607#380C2313yes—
608#380C2313yes—
609#380C2313yes—
610#380C2313yes—
611#380C2313yes—
612#380C2316yes—
613#380C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊C4C2313yes—
618C4×C4⋊C4C2313yes—
619C4×C4⋊C4C2313yes—
620C4×C4⋊C4C2313yes—
621C4×C4⋊C4C2313yes—
622C4×C4⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2313yes—
631C4×C22⋊C4C2313yes—
632C4×C22⋊C4C2313yes—
633C4×C22⋊C4C2313yes—
634C4×C22⋊C4C2313yes—
635C43C2313yes—
6362−1+4—464no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—46no—
641C2×#41—46no—
642C2×#41—46no—
643C2×#41—46no—
644C2×#41—46no—
645C2×#41—46no—
646C2×#41—46no—
647C2×#41—46no—
648C2×#41—46no—
649C22×Q8—24no—
650C22×Q8—24no—
651C22×Q8—24no—
652C22×Q8—24no—
653C22×Q8—24no—
654C22×Q8—24no—
655C22×Q8—24no—
656C22×Q8—24no—
657C22×Q8—24no—
658C22×Q8—24no—
659C22×Q8—24no—
660C22×Q8—24no—
661C22×Q8—24no—
662C22×Q8—24no—
663C22×Q8—24no—
664C22×Q8—46no—
665C22×Q8—46no—
666C22×Q8—46no—
667C22×Q8C2413yes—
668C22×Q8C2413yes—
669C22×Q8C2413yes—
670C22×Q8C2413yes—
671C22×Q8C2413yes—
672C22×Q8C2413yes—
673C22×Q8C2411yescharacteristic
674C22×D4C2413yes—
675C22×D4C2411yescharacteristic
676C22×D4C2411yescharacteristic
677C22×D4C2411yescharacteristic
678C22×D4C2411yescharacteristic
679C22×D4C2411yescharacteristic
680C22×D4C2411yescharacteristic
681C22×D4C2411yescharacteristic
682C22×D4C2411yescharacteristic
683C22×D4C2413yes—
684C22×D4C2413yes—
685C22×D4C2413yes—
686C22×D4C2411yescharacteristic
687C22×D4C2413yes—
688C22×D4C2413yes—
689C22×D4C2411yescharacteristic
690C23×C4C2413yes—
691C23×C4C2413yes—
692C23×C4C2413yes—
693C23×C4C2413yes—
694C23×C4C2413yes—
695C23×C4C2413yes—
696C23×C4C2411yescharacteristic
697C23×C4C2413yes—
698C23×C4C2411yescharacteristic
699C23×C4C2413yes—
700C23×C4C2416yes—
701C4⋊Q8—46no—
702C4⋊Q8—46no—
703C4⋊Q8—46no—
704C4⋊Q8—46no—
705C4⋊Q8—46no—
706C4⋊Q8—46no—
707C4⋊Q8—46no—
708C4⋊Q8—46no—
709C4⋊Q8—46no—
710#127—24no—
711#126—212no—
712#126—412no—
713#126—46no—
714#124—46no—
715#124—46no—
716#124—46no—
717#123—24no—
718#123—46no—
719C22⋊Q8—46no—
720C22⋊Q8—46no—
721C22⋊Q8—46no—
722C22⋊Q8—46no—
723C22⋊Q8—46no—
724C22⋊Q8—46no—
725C22⋊Q8—46no—
726C22⋊Q8—46no—
727C22⋊Q8—46no—
728C22⋊Q8—46no—
729C22⋊Q8—46no—
730C22⋊Q8—46no—
731C22⋊Q8—46no—
732C22⋊Q8—46no—
733C22⋊Q8—46no—
734C22⋊Q8—46no—
735C22⋊Q8—46no—
736C22⋊Q8—46no—
737C22⋊Q8—46no—
738C22⋊Q8—46no—
739C22⋊Q8—46no—
740#121—24no—
741#121—212no—
742#121—24no—
743#121—46no—
744#121—46no—
745#121—46no—
746#121—46no—
747C4×Q8—24no—
748C4×Q8—24no—
749C4×Q8—24no—
750C4×Q8—24no—
751C4×Q8—24no—
752C4×Q8—24no—
753C4×Q8—24no—
754C4×Q8—24no—
755C4×Q8—24no—
756C4×Q8—46no—
757C4×Q8—46no—
758C4×Q8—46no—
759C4×Q8—46no—
760C4×Q8—46no—
761C4×Q8—46no—
762C4×D4—46no—
763C4×D4—46no—
764C4×D4—46no—
765C4×D4—46no—
766C4×D4—46no—
767C4×D4—46no—
768C4×D4—46no—
769C4×D4—46no—
770C4×D4—46no—
771C4×D4—46no—
772C4×D4—46no—
773C4×D4—46no—
774#117—46no—
775#117—46no—
776C2×C4⋊C4—46no—
777C2×C4⋊C4—46no—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2416yes—
795C2×C4⋊C4C2416yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2416yes—
811C2×C4⋊C4C2416yes—
812C2×C4⋊C4C2416yes—
813C2×C4⋊C4C2416yes—
814C2×C4⋊C4C2416yes—
815C2×C4⋊C4C2416yes—
816C2×C4⋊C4C2416yes—
817C2×C4⋊C4C2416yes—
818C2×C4⋊C4C2416yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2416yes—
822C2×C4⋊C4C2416yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2416yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2411yescharacteristic
829C2×C22⋊C4C2411yescharacteristic
830C2×C22⋊C4C2411yescharacteristic
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2411yescharacteristic
836C2×C22⋊C4C2411yescharacteristic
837C2×C22⋊C4C2411yescharacteristic
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2411yescharacteristic
844C2×C22⋊C4C2411yescharacteristic
845C2×C22⋊C4C2411yescharacteristic
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2416yes—
868C2×C22⋊C4C2416yes—
869C2×C22⋊C4C2416yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2413yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2416yes—
877C2×C22⋊C4C2416yes—
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2416yes—
883C2×C42—46no—
884C2×C42—46no—
885C2×C42C2413yes—
886C2×C42C2413yes—
887C2×C42C2413yes—
888C2×C42C2413yes—
889C2×C42C2413yes—
890C2×C42C2413yes—
891C2×C42C2413yes—
892C2×C42C2413yes—
893C2×C42C2413yes—
894C2×C42C2413yes—
895C2×C42C2413yes—
896C2×C42C2411yescharacteristic
897C2×C42C2416yes—
898C2×C42C2413yes—
899C2×C42C2413yes—
900C2×C42C2413yes—
901C2×C42C2413yes—
902C2×C42C2413yes—
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2411yescharacteristic
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2411yescharacteristic
928#95C2411yescharacteristic
929#95C2411yescharacteristic
930#95C2416yes—
931#95C2413yes—
932#95C2413yes—
933#95C2413yes—
934#95C2413yes—
935#95C2413yes—
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2416yes—
941#95C2416yes—
942#95C2416yes—
943#95C2416yes—
944#95C2416yes—
945#95C2416yes—
946#95C2416yes—
947#95C2416yes—
948#95C2416yes—
949#95C2416yes—
950#95C2416yes—
951#95C2416yes—
952C24C2511yescharacteristic
953C24C2511yescharacteristic
954C24C2511yescharacteristic
955C24C2513yes—
956C24C2511yescharacteristic
957C24C2511yescharacteristic
958#41—448no—
959#41—448no—
960#41—448no—
961#41—416no—
962C2×Q8—26no—
963C2×Q8—26no—
964C2×Q8—26no—
965C2×Q8—26no—
966C2×Q8—26no—
967C2×Q8—26no—
968C2×Q8—26no—
969C2×Q8—26no—
970C2×Q8—26no—
971C2×Q8—26no—
972C2×Q8—26no—
973C2×Q8—26no—
974C2×Q8—26no—
975C2×Q8—26no—
976C2×Q8—26no—
977C2×Q8—43no—
978C2×Q8—43no—
979C2×Q8—43no—
980C2×Q8—448no—
981C2×Q8—416no—
982C2×Q8—416no—
983C2×Q8—416no—
984C2×Q8—416no—
985C2×Q8—416no—
986C2×Q8H(5,𝔽2)14yes—
987C2×Q8H(5,𝔽2)14yes—
988C2×Q8H(5,𝔽2)14yes—
989C2×D4—22no—
990C2×D4—22no—
991C2×D4—22no—
992C2×D4—22no—
993C2×D4—22no—
994C2×D4—22no—
995C2×D4—26no—
996C2×D4—26no—
997C2×D4—26no—
998C2×D4—26no—
999C2×D4—26no—
1000C2×D4—22no—
1001C2×D4—22no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—22no—
1005C2×D4—22no—
1006C2×D4—22no—
1007C2×D4—41no—
1008C2×D4—41no—
1009C2×D4—41no—
1010C2×D4—41no—
1011C2×D4—41no—
1012C2×D4—41no—
1013C2×D4—41no—
1014C2×D4—41no—
1015C2×D4—41no—
1016C2×D4—41no—
1017C2×D4—41no—
1018C2×D4—41no—
1019C2×D4—41no—
1020C2×D4—41no—
1021C2×D4—41no—
1022C2×D4—41no—
1023C2×D4—43no—
1024C2×D4—43no—
1025C2×D4—43no—
1026C2×D4—43no—
1027C2×D4—43no—
1028C2×D4—43no—
1029C2×D4—43no—
1030C2×D4—43no—
1031C2×D4—43no—
1032C2×D4—43no—
1033C2×D4—43no—
1034C2×D4—43no—
1035C2×D4—43no—
1036C2×D42−1+414yescomplemented
1037C22×C4—22no—
1038C22×C4—26no—
1039C22×C4—26no—
1040C22×C4—26no—
1041C22×C4—26no—
1042C22×C4—26no—
1043C22×C4—26no—
1044C22×C4—26no—
1045C22×C4—26no—
1046C22×C4—26no—
1047C22×C4—26no—
1048C22×C4—26no—
1049C22×C4—26no—
1050C22×C4—26no—
1051C22×C4—26no—
1052C22×C4—26no—
1053C22×C4—26no—
1054C22×C4—26no—
1055C22×C4—26no—
1056C22×C4—26no—
1057C22×C4—22no—
1058C22×C4—22no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—46no—
1063C22×C4—46no—
1064C22×C4—46no—
1065C22×C4—43no—
1066C22×C4—43no—
1067C22×C4—43no—
1068C22×C4—43no—
1069C22×C4—43no—
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2513yes—
1074C22×C4C2513yes—
1075C22×C4C2513yes—
1076C22×C4C2513yes—
1077C22×C4C2513yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2513yes—
1080C22×C4C2513yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2513yes—
1083C22×C4C2513yes—
1084C22×C4C2513yes—
1085C22×C4C2513yes—
1086C22×C4C2513yes—
1087C22×C4C2513yes—
1088C22×C4C2513yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2513yes—
1095C4⋊C4—26no—
1096C4⋊C4—26no—
1097C4⋊C4—26no—
1098C4⋊C4—26no—
1099C4⋊C4—26no—
1100C4⋊C4—26no—
1101C4⋊C4—26no—
1102C4⋊C4—26no—
1103C4⋊C4—26no—
1104C4⋊C4—22no—
1105C4⋊C4—26no—
1106C4⋊C4—22no—
1107C4⋊C4—26no—
1108C4⋊C4—26no—
1109C4⋊C4—26no—
1110C4⋊C4—26no—
1111C4⋊C4—46no—
1112C4⋊C4—46no—
1113C4⋊C4—43no—
1114C4⋊C4—43no—
1115C4⋊C4—46no—
1116C4⋊C4—43no—
1117C4⋊C4—43no—
1118C4⋊C4—43no—
1119C4⋊C4—43no—
1120C4⋊C4—43no—
1121C4⋊C4—43no—
1122C4⋊C4—43no—
1123C4⋊C4—43no—
1124C4⋊C4—43no—
1125C4⋊C4—43no—
1126C4⋊C4—43no—
1127C4⋊C4—43no—
1128C4⋊C4—43no—
1129C4⋊C4—43no—
1130C4⋊C4—46no—
1131C4⋊C4—46no—
1132C4⋊C4—46no—
1133C4⋊C4—46no—
1134C4⋊C4—46no—
1135C4⋊C4—46no—
1136C4⋊C4—46no—
1137C4⋊C4—46no—
1138C4⋊C4—46no—
1139C4⋊C4—46no—
1140C4⋊C4—46no—
1141C4⋊C4—43no—
1142C4⋊C4—43no—
1143C4⋊C42−1+414yescomplemented
1144C22⋊C4—26no—
1145C22⋊C4—22no—
1146C22⋊C4—22no—
1147C22⋊C4—22no—
1148C22⋊C4—26no—
1149C22⋊C4—22no—
1150C22⋊C4—22no—
1151C22⋊C4—22no—
1152C22⋊C4—22no—
1153C22⋊C4—26no—
1154C22⋊C4—26no—
1155C22⋊C4—26no—
1156C22⋊C4—26no—
1157C22⋊C4—22no—
1158C22⋊C4—46no—
1159C22⋊C4—43no—
1160C22⋊C4—43no—
1161C22⋊C4—41no—
1162C22⋊C4—43no—
1163C22⋊C4—41no—
1164C22⋊C4—43no—
1165C22⋊C4—41no—
1166C22⋊C4—41no—
1167C22⋊C4—41no—
1168C22⋊C4—43no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—43no—
1172C22⋊C4—43no—
1173C22⋊C4—43no—
1174C22⋊C4—43no—
1175C22⋊C4—43no—
1176C22⋊C4—43no—
1177C22⋊C4—43no—
1178C22⋊C4—43no—
1179C22⋊C4—43no—
1180C22⋊C4—43no—
1181C22⋊C4—43no—
1182C22⋊C4—43no—
1183C22⋊C4—43no—
1184C22⋊C4—43no—
1185C22⋊C4—43no—
1186C22⋊C4—43no—
1187C22⋊C4—43no—
1188C22⋊C4—43no—
1189C22⋊C4—43no—
1190C22⋊C4—46no—
1191C22⋊C4—46no—
1192C22⋊C4—46no—
1193C22⋊C4—43no—
1194C22⋊C4—43no—
1195C22⋊C4—43no—
1196C22⋊C4—46no—
1197C22⋊C4—46no—
1198C22⋊C4—43no—
1199C22⋊C4—43no—
1200C42—26no—
1201C42—26no—
1202C42—26no—
1203C42—26no—
1204C42—26no—
1205C42—26no—
1206C42—26no—
1207C42—26no—
1208C42—26no—
1209C42—26no—
1210C42—22no—
1211C42—26no—
1212C42—43no—
1213C42—43no—
1214C42—43no—
1215C42—43no—
1216C42—43no—
1217C42—46no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—21no—
1222C23—21no—
1223C23—21no—
1224C23—21no—
1225C23—21no—
1226C23—21no—
1227C23—21no—
1228C23—21no—
1229C23—21no—
1230C23—21no—
1231C23—21no—
1232C23—21no—
1233C23—21no—
1234C23—21no—
1235C23—21no—
1236C23—21no—
1237C23—21no—
1238C23—21no—
1239C23—23no—
1240C23—23no—
1241C23—23no—
1242C23—23no—
1243C23—21no—
1244C23—23no—
1245C23—21no—
1246C23—21no—
1247C23—21no—
1248C23—21no—
1249C23—21no—
1250C23—21no—
1251C23—23no—
1252C23—21no—
1253C23—21no—
1254C23—21no—
1255C23—21no—
1256C23—23no—
1257C23—21no—
1258C23C2×2−1+412yes—
1259C23C2×2−1+412yes—
1260C23C2611yescharacteristic
1261Q8—412no—
1262Q8—412no—
1263Q8—412no—
1264Q8—412no—
1265Q8—412no—
1266Q8—412no—
1267Q8#560116yes—
1268D4—44no—
1269D4—44no—
1270D4—44no—
1271D4—44no—
1272D4—44no—
1273D4—44no—
1274D4—44no—
1275D4—44no—
1276D4—44no—
1277D4—44no—
1278D4—412no—
1279D4—412no—
1280D4—412no—
1281D4—86no—
1282D4—86no—
1283D4—86no—
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—23no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—23no—
1309C2×C4—23no—
1310C2×C4—23no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—23no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—23no—
1320C2×C4—23no—
1321C2×C4—23no—
1322C2×C4—23no—
1323C2×C4—23no—
1324C2×C4—23no—
1325C2×C4—23no—
1326C2×C4—23no—
1327C2×C4—21no—
1328C2×C4—23no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—23no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—23no—
1335C2×C4—23no—
1336C2×C4—23no—
1337C2×C4—23no—
1338C2×C4—23no—
1339C2×C4—21no—
1340C2×C4—23no—
1341C2×C4—23no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—23no—
1345C2×C4—23no—
1346C2×C4—21no—
1347C2×C4—23no—
1348C2×C4—23no—
1349C2×C4—21no—
1350C2×C4—23no—
1351C2×C4—44no—
1352C2×C4—44no—
1353C2×C4—424no—
1354C2×C4—412no—
1355C2×C4—412no—
1356C2×C4—412no—
1357C2×C4—412no—
1358C2×C4—412no—
1359C2×C4—412no—
1360C2×C4—86no—
1361C2×C4—86no—
1362C2×C4C2×H(5,𝔽2)16yes—
1363C2×C4C2×H(5,𝔽2)16yes—
1364C2×C4C2×H(5,𝔽2)16yes—
1365C2×C4C2×2−1+412yes—
1366C2×C4C2×2−1+412yes—
1367C2×C4C2×2−1+412yes—
1368C2×C4C2×2−1+412yes—
1369C2×C4#58512yes—
1370C22—22no—
1371C22—22no—
1372C22—22no—
1373C22—22no—
1374C22—22no—
1375C22—22no—
1376C22—41no—
1377C22—41no—
1378C22—41no—
1379C22—41no—
1380C22—41no—
1381C22—41no—
1382C22—41no—
1383C22—41no—
1384C22—41no—
1385C22—41no—
1386C22—43no—
1387C22—41no—
1388C22—41no—
1389C22—41no—
1390C22—41no—
1391C22—43no—
1392C22—41no—
1393C22—41no—
1394C22—41no—
1395C22—43no—
1396C22—41no—
1397C22—41no—
1398C22—41no—
1399C22—43no—
1400C22—41no—
1401C22—41no—
1402C22—41no—
1403C22—43no—
1404C22—41no—
1405C22—43no—
1406C22—41no—
1407C22—41no—
1408C22—43no—
1409C22—41no—
1410C22—41no—
1411C22—41no—
1412C22C22×H(5,𝔽2)11yescharacteristic
1413C22C22×H(5,𝔽2)11yescharacteristic
1414C22C22×H(5,𝔽2)11yescharacteristic
1415C22C22×2−1+411yescharacteristic
1416C22C22×2−1+411yescharacteristic
1417C22C2×#58511yescharacteristic
1418C222−1+611yescharacteristic
1419C4—22no—
1420C4—22no—
1421C4—22no—
1422C4—22no—
1423C4—22no—
1424C4—43no—
1425C4—43no—
1426C4—41no—
1427C4—41no—
1428C4—43no—
1429C4—43no—
1430C4—41no—
1431C4—43no—
1432C4—43no—
1433C4—41no—
1434C4—43no—
1435C4—43no—
1436C4—43no—
1437C4—41no—
1438C4—43no—
1439C4—43no—
1440C4—43no—
1441C4—43no—
1442C4—43no—
1443C4C2×#560112yes—
1444C2—42no—
1445C2—42no—
1446C2—81no—
1447C2—81no—
1448C2—83no—
1449C2—81no—
1450C2C22×#56011yescharacteristic
1451C2#6289311yescharacteristic
1452C2#6291311yescharacteristic
1453C2#6292211yescharacteristic
1454C2#6301511yescharacteristic
1455C2#6301611yescharacteristic
1456C2#6303911yescharacteristic
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. #53095C2semidirect
2. #53047C2semidirect
3. #53045C2semidirect
4. #53011C2semidirect
5. #53007C2semidirect
6. #53006C2semidirect
7. #52297C2semidirect
8. #46339C2semidirect
9. #46020C2semidirect
10. #46002C2semidirect
11. #45721C2semidirect
12. #45677C2semidirect
13. #45628C2semidirect
14. #45628C2semidirect
15. #45616C2semidirect
16. #45497C2semidirect
17. Q8×#127C2semidirect
18. Q8×#123C2semidirect
19. Q8×#121C2semidirect
20. Q8×#121C2semidirect
21. #36482C2semidirect
22. #36458C2semidirect
23. #36448C2semidirect
24. #36434C2semidirect
25. #36434C2semidirect
26. #35771C2semidirect
27. #35723C2semidirect
28. #35700C2semidirect
29. #35687C2semidirect
30. #35687C2semidirect
31. #35687C2semidirect
1036. C2×D42−1+4semidirect
1143. C4⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#530952
#530472
#530452
#530112
#530072
#530062
#522972
#463392
#460202
#460022
#457212
#456772
#456282
#456162
#454972
Q8×#1272
Q8×#1232
Q8×#1212
#364822
#364582
#364482
#364342
#357712
#357232
#357002
#356872