Finite Group Databasebeta

← #8095973

Subgroups — #8095973

Order 512.

5517 conjugacy classes of subgroups.

The subgroup lattice has 1466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53098C213yesmaximal, complemented
2#53087C213yesmaximal, complemented
3#53045C213yesmaximal, complemented
4#53041C213yesmaximal, complemented
5#53014C213yesmaximal, complemented
6#52956C213yesmaximal, complemented
7#52299C213yesmaximal, complemented
8#45721C213yesmaximal, complemented
9#45708C213yesmaximal, complemented
10#45687C213yesmaximal, complemented
11#45677C213yesmaximal, complemented
12#45628C213yesmaximal, complemented
13#45616C213yesmaximal, complemented
14#45608C213yesmaximal, complemented
15#45522C213yesmaximal, complemented
16#45497C213yesmaximal, complemented
17#36576C211yesmaximal, characteristic, complemented
18Q8×#123C211yesmaximal, characteristic, complemented
19Q8×#121C211yesmaximal, characteristic, complemented
20#36482C211yesmaximal, characteristic, complemented
21#36444C211yesmaximal, characteristic, complemented
22#36434C211yesmaximal, characteristic, complemented
23#36434C211yesmaximal, characteristic, complemented
24#36432C211yesmaximal, characteristic, complemented
25#36430C211yesmaximal, characteristic, complemented
26#35927C211yesmaximal, characteristic, complemented
27#35898C211yesmaximal, characteristic, complemented
28#35883C211yesmaximal, characteristic, complemented
29#35757C211yesmaximal, characteristic, complemented
30#35687C211yesmaximal, characteristic, complemented
31#35687C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#548C2211yescharacteristic
42C2×#548C2211yescharacteristic
43C2×#548C2211yescharacteristic
44C2×#548C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47C22×C4×Q8C2211yescharacteristic
48#2857C2213yes—
49#2857C2213yes—
50#2856C2213yes—
51#2855C2213yes—
52#2855C2213yes—
53#2855C2213yes—
54#2850C2213yes—
55#2850C2213yes—
56#2850C2213yes—
57#2841C2216yes—
58#2838C2216yes—
59#2838C2216yes—
60#2837C2216yes—
61#2829C2216yes—
62#2829C2216yes—
63#2829C2216yes—
64#2827C2216yes—
65#2826C2216yes—
66#2825C2216yes—
67#2813C2216yes—
68#2803C2216yes—
69#2801C2213yes—
70#2801C2213yes—
71#2796C2216yes—
72#2796C2216yes—
73#2795C2216yes—
74#2792C2216yes—
75#2790C2216yes—
76#2784C2216yes—
77#2780C2216yes—
78#2780C2216yes—
79#2780C2216yes—
80#2760C2213yes—
81#2756C2216yes—
82#2752C2213yes—
83#2752C2213yes—
84#2752C2213yes—
85#2749C2216yes—
86#2746C2216yes—
87#2746C2216yes—
88#2746C2216yes—
89#2742C2213yes—
90#2742C2213yes—
91#2742C2213yes—
92#2737C2216yes—
93#2714C2216yes—
94#2705C2216yes—
95#2703C2213yes—
96#2703C2211yescharacteristic
97#2703C2213yes—
98#2703C2213yes—
99#2703C2213yes—
100#2703C2213yes—
101#2699C2216yes—
102#2691C2216yes—
103#2688C2216yes—
104#2675C2213yes—
105#2658C2213yes—
106#2645C2213yes—
107#2644C2213yes—
108#2616C2213yes—
109#2616C2213yes—
110#2615C2213yes—
111#2548C2213yes—
112#2547C2213yes—
113#2546C2213yes—
114#2545C2213yes—
115#2545C2213yes—
116#2544C2213yes—
117#2542C2213yes—
118#2542C2213yes—
119#2542C2213yes—
120#2540C2213yes—
121#2540C2213yes—
122#2540C2213yes—
123#2538C2213yes—
124#2538C2213yes—
125#2537C2213yes—
126#2536C2213yes—
127#2536C2213yes—
128#2535C2213yes—
129#2514C2213yes—
130#2514C2213yes—
131#2513C2213yes—
132#2512C2213yes—
133#2512C2213yes—
134#2511C2213yes—
135#2503C2213yes—
136#2502C2213yes—
137#2499C2213yes—
138#2497C2213yes—
139#2497C2213yes—
140#2496C2213yes—
141#2495C2213yes—
142#2494C2213yes—
143#2494C2213yes—
144#2487C2213yes—
145#2486C2213yes—
146#2485C2213yes—
147#2447C2213yes—
148#2447C2213yes—
149#2446C2213yes—
150#2446C2213yes—
151#2446C2213yes—
152#2446C2213yes—
153#2436C2213yes—
154#2434C2213yes—
155#2434C2213yes—
156#2432C2213yes—
157#2432C2213yes—
158#2432C2213yes—
159#2432C2213yes—
160#2431C2213yes—
161#2431C2213yes—
162#2429C2213yes—
163#2429C2213yes—
164#2429C2213yes—
165#2429C2213yes—
166#2428C2213yes—
167#2427C2213yes—
168#2427C2213yes—
169#2427C2213yes—
170#2426C2213yes—
171#2426C2213yes—
172#2426C2213yes—
173#2426C2213yes—
174#2423C2213yes—
175#2423C2213yes—
176#2422C2213yes—
177#2421C2213yes—
178#2421C2213yes—
179#2420C2213yes—
180#2417C2213yes—
181#2417C2213yes—
182#2417C2213yes—
183#2417C2213yes—
184#2416C2213yes—
185#2416C2213yes—
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#2401C2213yes—
202#2401C2213yes—
203#2397C2213yes—
204#2388C2213yes—
205#2388C2213yes—
206#2388C2213yes—
207#2383C2216yes—
208#2377C2216yes—
209#2377C2216yes—
210#2351C2211yescharacteristic
211#2351C2211yescharacteristic
212#2351C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214Q8×C4⋊C4C2211yescharacteristic
215Q8×C4⋊C4C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
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×#123C2213yes—
229C4×#123C2213yes—
230C4×#123C2213yes—
231C4×#121C2213yes—
232C4×#121C2213yes—
233C4×#121C2213yes—
234C4×#121C2213yes—
235C4×#121C2213yes—
236C4×#121C2213yes—
237#2276C2211yescharacteristic
238C2×2−1+4—44no—
239C2×2−1+4—44no—
240C2×2−1+4—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2313yes—
244C22×#41C2313yes—
245C22×#41C2313yes—
246C23×Q8C2311yescharacteristic
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249C23×Q8C2311yescharacteristic
250C23×Q8C2313yes—
251#550—44no—
252D4×Q8—44no—
253D4×Q8—44no—
254D4×Q8—44no—
255D4×Q8—44no—
256D4×Q8—44no—
257#548—44no—
258#548—44no—
259#548—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×#127C2313yes—
269C2×#126C2316yes—
270C2×#124C2313yes—
271C2×#124C2313yes—
272C2×#124C2313yes—
273C2×#124C2313yes—
274C2×#124C2313yes—
275C2×#124C2313yes—
276C2×#123C2311yescharacteristic
277C2×#123C2313yes—
278C2×#123C2313yes—
279C2×C22⋊Q8C2313yes—
280C2×C22⋊Q8C2313yes—
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×#121C2313yes—
296C2×#121C2311yescharacteristic
297C2×#121C2313yes—
298C2×#121C2313yes—
299C2×#121C2313yes—
300C2×#121C2313yes—
301C2×#121C2316yes—
302C2×#121C2313yes—
303C2×#121C2313yes—
304C2×#121C2313yes—
305C2×#121C2313yes—
306C2×#121C2313yes—
307C2×#121C2313yes—
308C2×#121C2313yes—
309C2×#121C2313yes—
310C4×#41—44no—
311C2×C4×Q8—44no—
312C2×C4×Q8—44no—
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×Q8C2311yescharacteristic
322C2×C4×Q8C2313yes—
323C2×C4×Q8C2313yes—
324C2×C4×Q8C2313yes—
325C2×C4×Q8C2313yes—
326C2×C4×D4C2313yes—
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×C4×D4C2313yes—
340C2×#117C2313yes—
341C22×C4⋊C4C2313yes—
342C22×C4⋊C4C2313yes—
343C22×C42C2313yes—
344C22×C42C2313yes—
345C22×C42C2313yes—
346#401C2316yes—
347#401C2313yes—
348#401C2313yes—
349#400C2316yes—
350#400C2316yes—
351#400C2313yes—
352#400C2316yes—
353#400C2313yes—
354#400C2316yes—
355#400C2313yes—
356#400C2316yes—
357#400C2311yescharacteristic
358#400C2313yes—
359#400C2313yes—
360#399C2316yes—
361#399C2313yes—
362#399C2316yes—
363#399C2316yes—
364#399C2316yes—
365#399C2313yes—
366#399C2313yes—
367#399C2313yes—
368#398C2316yes—
369#398C2316yes—
370#398C2316yes—
371#398C2316yes—
372#398C2316yes—
373#398C2316yes—
374#398C2316yes—
375#397C2316yes—
376#397C2316yes—
377#397C2316yes—
378#397C2313yes—
379#397C2313yes—
380#397C2316yes—
381#397C2313yes—
382#397C2316yes—
383#397C2316yes—
384#397C2316yes—
385#397C2316yes—
386#397C2316yes—
387#397C2311yescharacteristic
388#397C2313yes—
389#397C2313yes—
390#396C2316yes—
391#396C2316yes—
392#396C2316yes—
393#396C2316yes—
394#396C2316yes—
395#396C2313yes—
396#396C2316yes—
397#396C2316yes—
398#396C2316yes—
399#396C2316yes—
400#396C2313yes—
401#395C2316yes—
402#395C2313yes—
403#395C2316yes—
404#395C2313yes—
405#395C2313yes—
406#394C2316yes—
407#394C2316yes—
408#394C2316yes—
409#394C2313yes—
410#394C2316yes—
411#394C2316yes—
412#394C2316yes—
413#394C2316yes—
414#394C2313yes—
415#394C2313yes—
416#394C2316yes—
417#394C2313yes—
418#394C2316yes—
419#394C2316yes—
420#394C2313yes—
421#394C2316yes—
422#394C2311yescharacteristic
423#394C2313yes—
424#394C2313yes—
425#394C2313yes—
426#394C2316yes—
427#394C2316yes—
428#393C2313yes—
429#393C2316yes—
430#393C2313yes—
431#393C2313yes—
432#392C2313yes—
433#392C2313yes—
434#392C2316yes—
435#392C2316yes—
436#392C2316yes—
437#392C2313yes—
438#392C2313yes—
439#392C2311yescharacteristic
440#392C2311yescharacteristic
441#392C2313yes—
442#392C2313yes—
443#392C2313yes—
444#392C2313yes—
445#392C2311yescharacteristic
446#392C2313yes—
447#392C2313yes—
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#390C2313yes—
465#390C2316yes—
466#390C2316yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2316yes—
476#390C2313yes—
477#390C2316yes—
478#390C2316yes—
479#390C2313yes—
480#390C2313yes—
481#390C2311yescharacteristic
482#390C2313yes—
483#389C2316yes—
484#389C2313yes—
485#389C2316yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2316yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#388C2313yes—
505#388C2316yes—
506#388C2316yes—
507#388C2313yes—
508#388C2316yes—
509#388C2313yes—
510#388C2316yes—
511#388C2313yes—
512#388C2316yes—
513#388C2316yes—
514#388C2313yes—
515#388C2316yes—
516#388C2316yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2311yescharacteristic
526#388C2313yes—
527#388C2311yescharacteristic
528#388C2313yes—
529#388C2313yes—
530#387C2316yes—
531#387C2316yes—
532#387C2316yes—
533#387C2316yes—
534#387C2316yes—
535#387C2313yes—
536#387C2316yes—
537#387C2316yes—
538#387C2316yes—
539#387C2313yes—
540#387C2313yes—
541#387C2313yes—
542#387C2313yes—
543#387C2313yes—
544#386C2313yes—
545#386C2316yes—
546#386C2316yes—
547#386C2313yes—
548#386C2316yes—
549#386C2316yes—
550#386C2313yes—
551#386C2313yes—
552#386C2316yes—
553#386C2313yes—
554#386C2316yes—
555#386C2316yes—
556#386C2316yes—
557#386C2316yes—
558#386C2313yes—
559#386C2313yes—
560#386C2313yes—
561#386C2313yes—
562#386C2313yes—
563#386C2311yescharacteristic
564#386C2311yescharacteristic
565#386C2313yes—
566#386C2311yescharacteristic
567#386C2313yes—
568#385C2316yes—
569#385C2316yes—
570#385C2316yes—
571#385C2313yes—
572#385C2316yes—
573#385C2313yes—
574#385C2316yes—
575#385C2316yes—
576#385C2316yes—
577#385C2316yes—
578#385C2316yes—
579#385C2313yes—
580#384C2313yes—
581#384C2313yes—
582#384C2313yes—
583#384C2316yes—
584#383C2316yes—
585#382C2313yes—
586#382C2313yes—
587#382C2313yes—
588#381C2316yes—
589#381C2313yes—
590#381C2316yes—
591#381C2313yes—
592#381C2313yes—
593#380C2313yes—
594#380C2316yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599#380C2313yes—
600#380C2313yes—
601#380C2313yes—
602#380C2313yes—
603#380C2313yes—
604#380C2313yes—
605#380C2313yes—
606#380C2313yes—
607#380C2313yes—
608#380C2316yes—
609#380C2316yes—
610#380C2313yes—
611#380C2313yes—
612#380C2311yescharacteristic
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—
635#376C2313yes—
6362−1+4—464no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—24no—
642C2×#41—24no—
643C2×#41—46no—
644C2×#41—46no—
645C2×#41—46no—
646C2×#41—46no—
647C2×#41—46no—
648C2×#41—46no—
649C2×#41—46no—
650C2×#41—46no—
651C2×#41—46no—
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×Q8C2411yescharacteristic
673C22×D4C2413yes—
674C22×D4C2413yes—
675C22×D4C2411yescharacteristic
676C22×D4C2411yescharacteristic
677C22×D4C2411yescharacteristic
678C22×D4C2411yescharacteristic
679C22×D4C2411yescharacteristic
680C22×D4C2413yes—
681C22×D4C2413yes—
682C22×D4C2413yes—
683C22×D4C2413yes—
684C22×D4C2413yes—
685C22×D4C2413yes—
686C22×D4C2413yes—
687C22×D4C2416yes—
688C22×D4C2411yescharacteristic
689C22×D4C2413yes—
690C22×D4C2413yes—
691C23×C4C2413yes—
692C23×C4C2413yes—
693C23×C4C2413yes—
694C23×C4C2413yes—
695C23×C4C2413yes—
696C23×C4C2413yes—
697C23×C4C2411yescharacteristic
698C23×C4C2413yes—
699C23×C4C2413yes—
700C23×C4C2411yescharacteristic
701C23×C4C2413yes—
702C23×C4C2413yes—
703C23×C4C2416yes—
704C4⋊Q8—46no—
705C4⋊Q8—46no—
706C4⋊Q8—46no—
707C4⋊Q8—46no—
708C4⋊Q8—46no—
709#127—46no—
710#126—412no—
711#124—46no—
712#124—46no—
713#124—46no—
714#124—46no—
715#124—46no—
716#124—46no—
717#123—24no—
718#123—46no—
719#123—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—
736#121—24no—
737#121—212no—
738#121—46no—
739#121—46no—
740#121—46no—
741#121—46no—
742#121—46no—
743#121—46no—
744#121—46no—
745#121—46no—
746#121—46no—
747#121—46no—
748#121—46no—
749#121—46no—
750#121—412no—
751C4×Q8—24no—
752C4×Q8—24no—
753C4×Q8—24no—
754C4×Q8—24no—
755C4×Q8—24no—
756C4×Q8—24no—
757C4×Q8—24no—
758C4×Q8—24no—
759C4×Q8—24no—
760C4×Q8—46no—
761C4×Q8—46no—
762C4×Q8—46no—
763C4×Q8—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—
774C4×D4—46no—
775C4×D4—46no—
776C4×D4—46no—
777C4×D4—46no—
778#117—46no—
779C2×C4⋊C4—46no—
780C2×C4⋊C4—46no—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2416yes—
797C2×C4⋊C4C2416yes—
798C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
822C2×C4⋊C4C2416yes—
823C2×C4⋊C4C2416yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2411yescharacteristic
830C2×C22⋊C4C2411yescharacteristic
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2416yes—
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2411yescharacteristic
836C2×C22⋊C4C2411yescharacteristic
837C2×C22⋊C4C2411yescharacteristic
838C2×C22⋊C4C2411yescharacteristic
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
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⋊C4C2416yes—
858C2×C22⋊C4C2416yes—
859C2×C22⋊C4C2416yes—
860C2×C22⋊C4C2416yes—
861C2×C22⋊C4C2416yes—
862C2×C22⋊C4C2416yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2416yes—
867C2×C22⋊C4C2416yes—
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2416yes—
872C2×C22⋊C4C2416yes—
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2411yescharacteristic
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2411yescharacteristic
883C2×C42—46no—
884C2×C42—46no—
885C2×C42—46no—
886C2×C42C2413yes—
887C2×C42C2413yes—
888C2×C42C2413yes—
889C2×C42C2413yes—
890C2×C42C2413yes—
891C2×C42C2413yes—
892C2×C42C2413yes—
893C2×C42C2413yes—
894C2×C42C2413yes—
895C2×C42C2413yes—
896C2×C42C2413yes—
897C2×C42C2413yes—
898C2×C42C2413yes—
899C2×C42C2413yes—
900C2×C42C2416yes—
901C2×C42C2411yescharacteristic
902#95C2411yescharacteristic
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2411yescharacteristic
907#95C2411yescharacteristic
908#95C2411yescharacteristic
909#95C2411yescharacteristic
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#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2411yescharacteristic
931#95C2411yescharacteristic
932#95C2411yescharacteristic
933#95C2413yes—
934#95C2413yes—
935#95C2413yes—
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2413yes—
941#95C2413yes—
942#95C2416yes—
943#95C2416yes—
944#95C2416yes—
945#95C2416yes—
946#95C2416yes—
947#95C2416yes—
948#95C2416yes—
949#95C2416yes—
950#95C2416yes—
951#95C2416yes—
952#95C2416yes—
953C24C2513yes—
954C24C2511yescharacteristic
955C24C2511yescharacteristic
956C24C2513yes—
957C24C2511yescharacteristic
958C24C2511yescharacteristic
959#41—448no—
960#41—448no—
961#41—448no—
962#41—416no—
963#41—416no—
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—43no—
977C2×Q8—43no—
978C2×Q8—43no—
979C2×Q8—448no—
980C2×Q8—416no—
981C2×Q8—416no—
982C2×Q8—416no—
983C2×Q8—416no—
984C2×Q8H(5,𝔽2)14yes—
985C2×Q8H(5,𝔽2)14yes—
986C2×Q8H(5,𝔽2)14yes—
987C2×D4—22no—
988C2×D4—22no—
989C2×D4—22no—
990C2×D4—22no—
991C2×D4—22no—
992C2×D4—22no—
993C2×D4—26no—
994C2×D4—26no—
995C2×D4—26no—
996C2×D4—26no—
997C2×D4—26no—
998C2×D4—26no—
999C2×D4—26no—
1000C2×D4—26no—
1001C2×D4—26no—
1002C2×D4—26no—
1003C2×D4—22no—
1004C2×D4—26no—
1005C2×D4—22no—
1006C2×D4—41no—
1007C2×D4—41no—
1008C2×D4—41no—
1009C2×D4—41no—
1010C2×D4—41no—
1011C2×D4—41no—
1012C2×D4—41no—
1013C2×D4—41no—
1014C2×D4—43no—
1015C2×D4—43no—
1016C2×D4—41no—
1017C2×D4—41no—
1018C2×D4—43no—
1019C2×D4—43no—
1020C2×D4—43no—
1021C2×D4—43no—
1022C2×D4—43no—
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×D4—43no—
1037C2×D4—43no—
1038C2×D4—46no—
1039C2×D4—46no—
1040C2×D4—46no—
1041C22×C4—22no—
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—26no—
1058C22×C4—26no—
1059C22×C4—26no—
1060C22×C4—26no—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—26no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—46no—
1068C22×C4—46no—
1069C22×C4—46no—
1070C22×C4—43no—
1071C22×C4—43no—
1072C22×C4—43no—
1073C22×C4—43no—
1074C22×C4—43no—
1075C22×C4—43no—
1076C22×C4—43no—
1077C22×C4—43no—
1078C22×C4—43no—
1079C22×C4—43no—
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2513yes—
1085C22×C4C2513yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2513yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2513yes—
1090C22×C4C2513yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2513yes—
1093C22×C4C2513yes—
1094C22×C4C2513yes—
1095C22×C4C2513yes—
1096C22×C4C2513yes—
1097C22×C4C2513yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2513yes—
1100C22×C4C2513yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2513yes—
1105C4⋊C4—26no—
1106C4⋊C4—26no—
1107C4⋊C4—26no—
1108C4⋊C4—26no—
1109C4⋊C4—26no—
1110C4⋊C4—26no—
1111C4⋊C4—26no—
1112C4⋊C4—26no—
1113C4⋊C4—26no—
1114C4⋊C4—22no—
1115C4⋊C4—26no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—26no—
1119C4⋊C4—26no—
1120C4⋊C4—46no—
1121C4⋊C4—46no—
1122C4⋊C4—46no—
1123C4⋊C4—41no—
1124C4⋊C4—43no—
1125C4⋊C4—43no—
1126C4⋊C4—43no—
1127C4⋊C4—43no—
1128C4⋊C4—43no—
1129C4⋊C4—43no—
1130C4⋊C4—43no—
1131C4⋊C4—43no—
1132C4⋊C4—43no—
1133C4⋊C4—43no—
1134C4⋊C4—43no—
1135C4⋊C4—43no—
1136C4⋊C4—43no—
1137C4⋊C4—43no—
1138C4⋊C4—46no—
1139C4⋊C4—46no—
1140C4⋊C4—46no—
1141C4⋊C4—46no—
1142C4⋊C4—46no—
1143C4⋊C4—46no—
1144C4⋊C4—43no—
1145C4⋊C4—43no—
1146C4⋊C4—43no—
1147C4⋊C4—46no—
1148C22⋊C4—26no—
1149C22⋊C4—26no—
1150C22⋊C4—22no—
1151C22⋊C4—22no—
1152C22⋊C4—22no—
1153C22⋊C4—26no—
1154C22⋊C4—26no—
1155C22⋊C4—22no—
1156C22⋊C4—41no—
1157C22⋊C4—43no—
1158C22⋊C4—43no—
1159C22⋊C4—41no—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—41no—
1163C22⋊C4—43no—
1164C22⋊C4—43no—
1165C22⋊C4—46no—
1166C22⋊C4—41no—
1167C22⋊C4—41no—
1168C22⋊C4—41no—
1169C22⋊C4—41no—
1170C22⋊C4—41no—
1171C22⋊C4—41no—
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—43no—
1191C22⋊C4—43no—
1192C22⋊C4—43no—
1193C22⋊C4—46no—
1194C22⋊C4—46no—
1195C22⋊C4—46no—
1196C22⋊C4—46no—
1197C22⋊C4—46no—
1198C22⋊C4—46no—
1199C22⋊C4—46no—
1200C22⋊C4—46no—
1201C22⋊C4—43no—
1202C22⋊C4—43no—
1203C22⋊C4—43no—
1204C22⋊C4—46no—
1205C22⋊C4—46no—
1206C22⋊C42−1+414yescomplemented
1207C42—26no—
1208C42—26no—
1209C42—26no—
1210C42—26no—
1211C42—26no—
1212C42—26no—
1213C42—26no—
1214C42—26no—
1215C42—26no—
1216C42—41no—
1217C42—43no—
1218C42—43no—
1219C42—43no—
1220C42—43no—
1221C42—43no—
1222C42—46no—
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—23no—
1236C23—23no—
1237C23—23no—
1238C23—21no—
1239C23—21no—
1240C23—21no—
1241C23—21no—
1242C23—23no—
1243C23—23no—
1244C23—21no—
1245C23—21no—
1246C23—23no—
1247C23—21no—
1248C23—21no—
1249C23—23no—
1250C23—23no—
1251C23—23no—
1252C23—21no—
1253C23—23no—
1254C23—21no—
1255C23—21no—
1256C23—21no—
1257C23—23no—
1258C23—23no—
1259C23—21no—
1260C23—23no—
1261C23—23no—
1262C23—21no—
1263C23C2×2−1+412yes—
1264C23#58512yes—
1265C23C2611yescharacteristic
1266Q8—412no—
1267Q8—412no—
1268Q8—412no—
1269Q8—412no—
1270Q8—412no—
1271Q8#560116yes—
1272D4—44no—
1273D4—44no—
1274D4—44no—
1275D4—44no—
1276D4—44no—
1277D4—44no—
1278D4—412no—
1279D4—412no—
1280D4—412no—
1281D4—412no—
1282D4—86no—
1283D4—86no—
1284D4—86no—
1285D4—86no—
1286D4—86no—
1287D4—86no—
1288D4—86no—
1289D4—166no—
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—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—21no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—21no—
1316C2×C4—23no—
1317C2×C4—23no—
1318C2×C4—21no—
1319C2×C4—23no—
1320C2×C4—23no—
1321C2×C4—21no—
1322C2×C4—23no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—23no—
1326C2×C4—23no—
1327C2×C4—23no—
1328C2×C4—23no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—23no—
1333C2×C4—21no—
1334C2×C4—23no—
1335C2×C4—23no—
1336C2×C4—23no—
1337C2×C4—23no—
1338C2×C4—23no—
1339C2×C4—23no—
1340C2×C4—23no—
1341C2×C4—21no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—21no—
1345C2×C4—23no—
1346C2×C4—23no—
1347C2×C4—23no—
1348C2×C4—23no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—23no—
1355C2×C4—23no—
1356C2×C4—23no—
1357C2×C4—21no—
1358C2×C4—23no—
1359C2×C4—44no—
1360C2×C4—44no—
1361C2×C4—424no—
1362C2×C4—412no—
1363C2×C4—412no—
1364C2×C4—412no—
1365C2×C4—412no—
1366C2×C4—412no—
1367C2×C4—412no—
1368C2×C4—86no—
1369C2×C4—86no—
1370C2×C4—86no—
1371C2×C4—86no—
1372C2×C4C2×H(5,𝔽2)16yes—
1373C2×C4C2×H(5,𝔽2)16yes—
1374C2×C4C2×H(5,𝔽2)16yes—
1375C2×C4C2×2−1+412yes—
1376C2×C4C2×2−1+412yes—
1377C2×C4#58512yes—
1378C22—22no—
1379C22—22no—
1380C22—22no—
1381C22—22no—
1382C22—22no—
1383C22—22no—
1384C22—41no—
1385C22—41no—
1386C22—41no—
1387C22—41no—
1388C22—41no—
1389C22—41no—
1390C22—41no—
1391C22—41no—
1392C22—43no—
1393C22—41no—
1394C22—41no—
1395C22—43no—
1396C22—43no—
1397C22—43no—
1398C22—41no—
1399C22—41no—
1400C22—41no—
1401C22—43no—
1402C22—43no—
1403C22—41no—
1404C22—41no—
1405C22—43no—
1406C22—43no—
1407C22—41no—
1408C22—41no—
1409C22—43no—
1410C22—43no—
1411C22—41no—
1412C22—43no—
1413C22—41no—
1414C22—41no—
1415C22—43no—
1416C22—43no—
1417C22—41no—
1418C22—41no—
1419C22—43no—
1420C22C22×H(5,𝔽2)11yescharacteristic
1421C22C22×H(5,𝔽2)11yescharacteristic
1422C22C22×H(5,𝔽2)11yescharacteristic
1423C22C22×2−1+411yescharacteristic
1424C22C2×#58511yescharacteristic
1425C22C2×#58511yescharacteristic
1426C222−1+611yescharacteristic
1427C4—22no—
1428C4—22no—
1429C4—22no—
1430C4—43no—
1431C4—41no—
1432C4—43no—
1433C4—43no—
1434C4—43no—
1435C4—43no—
1436C4—41no—
1437C4—41no—
1438C4—41no—
1439C4—43no—
1440C4—43no—
1441C4—41no—
1442C4—43no—
1443C4—41no—
1444C4—43no—
1445C4—41no—
1446C4—41no—
1447C4—43no—
1448C4—43no—
1449C4—43no—
1450C4—43no—
1451C4C2×#560112yes—
1452C2—42no—
1453C2—42no—
1454C2—83no—
1455C2—81no—
1456C2—83no—
1457C2—81no—
1458C2C22×#56011yescharacteristic
1459C2#6291311yescharacteristic
1460C2#6291911yescharacteristic
1461C2#6292211yescharacteristic
1462C2#6301511yescharacteristic
1463C2#6301511yescharacteristic
1464C2#6301911yescharacteristic
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. #53098C2semidirect
2. #53087C2semidirect
3. #53045C2semidirect
4. #53041C2semidirect
5. #53014C2semidirect
6. #52956C2semidirect
7. #52299C2semidirect
8. #45721C2semidirect
9. #45708C2semidirect
10. #45687C2semidirect
11. #45677C2semidirect
12. #45628C2semidirect
13. #45616C2semidirect
14. #45608C2semidirect
15. #45522C2semidirect
16. #45497C2semidirect
17. #36576C2semidirect
18. Q8×#123C2semidirect
19. Q8×#121C2semidirect
20. #36482C2semidirect
21. #36444C2semidirect
22. #36434C2semidirect
23. #36434C2semidirect
24. #36432C2semidirect
25. #36430C2semidirect
26. #35927C2semidirect
27. #35898C2semidirect
28. #35883C2semidirect
29. #35757C2semidirect
30. #35687C2semidirect
31. #35687C2semidirect
1206. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#530982
#530872
#530452
#530412
#530142
#529562
#522992
#457212
#457082
#456872
#456772
#456282
#456162
#456082
#455222
#454972
#365762
Q8×#1232
Q8×#1212
#364822
#364442
#364342
#364322
#364302
#359272
#358982
#358832
#357572
#356872