Finite Group Databasebeta

← #7656253

Subgroups — #7656253

Order 512.

5365 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42857C213yesmaximal, complemented
2#42844C213yesmaximal, complemented
3#42839C213yesmaximal, complemented
4#42828C213yesmaximal, complemented
5#42696C213yesmaximal, complemented
6#42654C213yesmaximal, complemented
7#42503C213yesmaximal, complemented
8#42446C213yesmaximal, complemented
9#40218C213yesmaximal, complemented
10#40196C213yesmaximal, complemented
11#39783C213yesmaximal, complemented
12#39663C213yesmaximal, complemented
13#37514C213yesmaximal, complemented
14#37499C213yesmaximal, complemented
15#36585C211yesmaximal, characteristic, complemented
16Q8×#124C211yesmaximal, characteristic, complemented
17#36482C211yesmaximal, characteristic, complemented
18#36434C211yesmaximal, characteristic, complemented
19#35948C211yesmaximal, characteristic, complemented
20#35883C211yesmaximal, characteristic, complemented
21#35801C211yesmaximal, characteristic, complemented
22#35711C211yesmaximal, characteristic, complemented
23#35700C211yesmaximal, characteristic, complemented
24#35700C211yesmaximal, characteristic, complemented
25#35687C211yesmaximal, characteristic, complemented
26#35687C211yesmaximal, characteristic, complemented
27#35046C213yesmaximal, complemented
28#34589C213yesmaximal, complemented
29#34291C211yesmaximal, characteristic, complemented
30#34257C211yesmaximal, characteristic, complemented
31C4×D4×Q8C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2862C2213yes—
46#2860C2213yes—
47#2855C2213yes—
48#2850C2213yes—
49#2833C2216yes—
50#2830C2216yes—
51#2827C2216yes—
52#2824C2216yes—
53#2808C2216yes—
54#2806C2216yes—
55#2803C2216yes—
56#2800C2216yes—
57#2788C2216yes—
58#2788C2216yes—
59#2787C2216yes—
60#2779C2216yes—
61#2774C2216yes—
62#2770C2216yes—
63#2768C2216yes—
64#2759C2216yes—
65#2750C2216yes—
66#2745C2216yes—
67#2710C2216yes—
68#2686C2216yes—
69#2666C2213yes—
70#2665C2213yes—
71#2662C2213yes—
72#2661C2213yes—
73#2653C2213yes—
74#2653C2213yes—
75#2653C2216yes—
76#2653C2216yes—
77#2653C2216yes—
78#2652C2216yes—
79#2651C2213yes—
80#2650C2213yes—
81#2649C2216yes—
82#2649C2213yes—
83#2648C2213yes—
84#2648C2213yes—
85#2648C2213yes—
86#2645C2213yes—
87#2640C2213yes—
88#2636C2213yes—
89#2635C2213yes—
90#2631C2211yescharacteristic
91#2630C2213yes—
92#2628C2213yes—
93#2624C2213yes—
94#2621C2213yes—
95#2621C2213yes—
96#2616C2213yes—
97#2616C2213yes—
98#2595C2216yes—
99#2593C2216yes—
100#2592C2213yes—
101#2589C2216yes—
102#2589C2216yes—
103#2586C2216yes—
104#2581C2213yes—
105#2576C2216yes—
106#2568C2213yes—
107#2568C2213yes—
108#2563C2213yes—
109#2547C2213yes—
110#2546C2213yes—
111#2546C2213yes—
112#2545C2213yes—
113#2536C2213yes—
114#2536C2213yes—
115#2536C2213yes—
116#2518C2216yes—
117#2514C2213yes—
118#2514C2213yes—
119#2513C2213yes—
120#2513C2213yes—
121#2513C2213yes—
122#2511C2213yes—
123#2503C2213yes—
124#2500C2213yes—
125#2497C2213yes—
126#2495C2213yes—
127#2494C2213yes—
128#2494C2213yes—
129#2494C2213yes—
130#2494C2213yes—
131#2492C2213yes—
132#2492C2213yes—
133#2492C2213yes—
134#2492C2213yes—
135#2492C2213yes—
136#2492C2213yes—
137#2491C2213yes—
138#2491C2213yes—
139#2486C2213yes—
140#2485C2213yes—
141#2459C2216yes—
142#2451C2213yes—
143#2451C2213yes—
144#2448C2213yes—
145#2448C2213yes—
146#2446C2213yes—
147#2446C2213yes—
148#2439C2213yes—
149#2439C2213yes—
150#2434C2213yes—
151#2434C2213yes—
152#2432C2213yes—
153#2432C2213yes—
154#2432C2213yes—
155#2432C2213yes—
156#2429C2213yes—
157#2429C2213yes—
158#2429C2213yes—
159#2429C2213yes—
160#2429C2213yes—
161#2426C2213yes—
162#2423C2213yes—
163#2421C2213yes—
164#2421C2213yes—
165#2421C2213yes—
166#2417C2213yes—
167#2416C2213yes—
168#2415C2213yes—
169#2415C2213yes—
170#2415C2213yes—
171#2415C2213yes—
172#2409C2213yes—
173#2409C2213yes—
174#2407C2213yes—
175#2407C2213yes—
176#2407C2213yes—
177#2407C2213yes—
178#2401C2213yes—
179#2398C2213yes—
180#2396C2213yes—
181#2395C2213yes—
182#2392C2213yes—
183#2392C2213yes—
184#2388C2213yes—
185#2388C2213yes—
186#2365C2213yes—
187#2365C2213yes—
188#2362C2213yes—
189#2360C2213yes—
190#2360C2213yes—
191#2360C2213yes—
192#2352C2213yes—
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199D4×C4⋊C4C2213yes—
200#2341C2213yes—
201#2341C2211yescharacteristic
202#2341C2213yes—
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206Q8×C22⋊C4C2213yes—
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2213yes—
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2337C2216yes—
219#2334C2216yes—
220#2327C2213yes—
221#2323C2213yes—
222#2311C2213yes—
223#2311C2213yes—
224C4×C4⋊Q8C2213yes—
225C4×#126C2213yes—
226C4×#124C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×#123C2213yes—
231C4×#121C2213yes—
232#2297C2213yes—
233#2297C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C2×2−1+4—28no—
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×Q8C2313yes—
250Q82—44no—
251D4×Q8—28no—
252D4×Q8—28no—
253D4×Q8—44no—
254D4×Q8—44no—
255D4×Q8—44no—
256#548—44no—
257#548—44no—
258C2×C4⋊Q8C2313yes—
259C2×C4⋊Q8C2313yes—
260C2×C4⋊Q8C2313yes—
261C2×C4⋊Q8C2313yes—
262C2×C4⋊Q8C2313yes—
263C2×C4⋊Q8C2313yes—
264C2×C4⋊Q8C2313yes—
265C2×C4⋊Q8C2313yes—
266C2×#126C2313yes—
267C2×#124C2311yescharacteristic
268C2×#124C2313yes—
269C2×#124C2316yes—
270C2×#124C2313yes—
271C2×#123C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2313yes—
279C2×C22⋊Q8C2313yes—
280C2×C22⋊Q8C2313yes—
281C2×C22⋊Q8C2313yes—
282C2×C22⋊Q8C2313yes—
283C2×C22⋊Q8C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287#519—44no—
288#519—44no—
289C2×C4×Q8—44no—
290C2×C4×Q8—44no—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2313yes—
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
307C2×C4×Q8C2313yes—
308C2×C4×Q8C2313yes—
309C2×C4×Q8C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×#117C2313yes—
320C2×#117C2313yes—
321C2×#117C2313yes—
322C2×#117C2313yes—
323C22×C4⋊C4C2313yes—
324C22×C4⋊C4C2313yes—
325C22×C42C2313yes—
326C22×C42C2313yes—
327#401C2316yes—
328#401C2316yes—
329#401C2313yes—
330#400C2313yes—
331#400C2316yes—
332#400C2316yes—
333#400C2316yes—
334#400C2316yes—
335#400C2316yes—
336#400C2316yes—
337#400C2313yes—
338#400C2313yes—
339#400C2316yes—
340#400C2313yes—
341#400C2313yes—
342#400C2313yes—
343#400C2313yes—
344#399C2316yes—
345#399C2313yes—
346#399C2313yes—
347#398C2316yes—
348#398C2316yes—
349#398C2316yes—
350#398C2316yes—
351#398C2316yes—
352#398C2316yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2316yes—
362#397C2316yes—
363#397C2313yes—
364#397C2316yes—
365#397C2316yes—
366#397C2316yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2311yescharacteristic
371#397C2311yescharacteristic
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#396C2313yes—
377#396C2316yes—
378#396C2313yes—
379#396C2316yes—
380#396C2313yes—
381#396C2313yes—
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#395C2316yes—
386#395C2316yes—
387#395C2316yes—
388#395C2313yes—
389#395C2313yes—
390#395C2313yes—
391#394C2313yes—
392#394C2316yes—
393#394C2316yes—
394#394C2316yes—
395#394C2313yes—
396#394C2316yes—
397#394C2316yes—
398#394C2316yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#393C2316yes—
414#393C2316yes—
415#393C2316yes—
416#393C2316yes—
417#393C2316yes—
418#393C2313yes—
419#393C2311yescharacteristic
420#393C2311yescharacteristic
421#393C2313yes—
422#393C2313yes—
423#392C2313yes—
424#392C2311yescharacteristic
425#392C2311yescharacteristic
426#392C2311yescharacteristic
427#392C2311yescharacteristic
428#392C2313yes—
429#392C2313yes—
430#392C2313yes—
431#391C2313yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2316yes—
436#391C2313yes—
437#391C2313yes—
438#391C2313yes—
439#391C2316yes—
440#391C2316yes—
441#391C2313yes—
442#391C2313yes—
443#391C2313yes—
444#391C2313yes—
445#391C2313yes—
446#391C2313yes—
447#391C2316yes—
448#391C2316yes—
449#391C2316yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#391C2313yes—
457#391C2313yes—
458#391C2313yes—
459#391C2313yes—
460#390C2313yes—
461#390C2313yes—
462#390C2313yes—
463#390C2316yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#389C2316yes—
474#389C2316yes—
475#389C2313yes—
476#389C2316yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2316yes—
481#389C2316yes—
482#389C2316yes—
483#389C2316yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2316yes—
497#388C2316yes—
498#388C2313yes—
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#388C2316yes—
503#388C2316yes—
504#388C2316yes—
505#388C2316yes—
506#388C2316yes—
507#388C2316yes—
508#388C2316yes—
509#388C2313yes—
510#388C2313yes—
511#388C2316yes—
512#388C2316yes—
513#388C2316yes—
514#388C2313yes—
515#388C2313yes—
516#388C2316yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2313yes—
530#387C2316yes—
531#387C2316yes—
532#387C2316yes—
533#387C2316yes—
534#387C2316yes—
535#387C2313yes—
536#387C2313yes—
537#387C2316yes—
538#387C2316yes—
539#387C2316yes—
540#387C2313yes—
541#386C2316yes—
542#386C2313yes—
543#386C2313yes—
544#386C2313yes—
545#386C2316yes—
546#386C2316yes—
547#386C2313yes—
548#386C2316yes—
549#386C2311yescharacteristic
550#386C2311yescharacteristic
551#386C2311yescharacteristic
552#386C2311yescharacteristic
553#386C2313yes—
554#385C2316yes—
555#385C2313yes—
556#385C2316yes—
557#385C2316yes—
558#385C2316yes—
559#385C2316yes—
560#385C2316yes—
561#385C2313yes—
562#385C2316yes—
563#385C2316yes—
564#385C2313yes—
565#384C2313yes—
566#383C2311yescharacteristic
567#383C2316yes—
568#382C2316yes—
569#382C2313yes—
570#382C2313yes—
571#382C2313yes—
572#382C2313yes—
573#382C2313yes—
574#382C2313yes—
575#381C2316yes—
576#381C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2316yes—
585#380C2316yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2316yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2316yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2316yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2313yes—
631#376C2313yes—
632C43C2313yes—
6332−1+4—464no—
634C2×#41—212no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—212no—
639C2×#41—212no—
640C2×#41—46no—
641C2×#41—46no—
642C2×#41—46no—
643C2×#41—46no—
644C2×#41—46no—
645C2×#41—46no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8—24no—
649C22×Q8—24no—
650C22×Q8—212no—
651C22×Q8—24no—
652C22×Q8—24no—
653C22×Q8—24no—
654C22×Q8—24no—
655C22×Q8—24no—
656C22×Q8—24no—
657C22×Q8—24no—
658C22×Q8—46no—
659C22×Q8—46no—
660C22×Q8#4118yes—
661C22×Q8C2413yes—
662C22×Q8C2413yes—
663C22×Q8C2413yes—
664C22×Q8C2413yes—
665C22×Q8C2411yescharacteristic
666C22×Q8C2413yes—
667C22×Q8C2416yes—
668C22×Q8C2411yescharacteristic
669C22×D4C2411yescharacteristic
670C22×D4C2413yes—
671C22×D4C2411yescharacteristic
672C22×D4C2411yescharacteristic
673C22×D4C2411yescharacteristic
674C22×D4C2411yescharacteristic
675C22×D4C2413yes—
676C22×D4C2411yescharacteristic
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2413yes—
680C23×C4C2413yes—
681C23×C4C2413yes—
682C23×C4C2413yes—
683C23×C4C2413yes—
684C23×C4C2413yes—
685C23×C4C2413yes—
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2416yes—
689C23×C4C2413yes—
690C4⋊Q8—212no—
691C4⋊Q8—212no—
692C4⋊Q8—46no—
693C4⋊Q8—46no—
694C4⋊Q8—46no—
695C4⋊Q8—46no—
696C4⋊Q8—46no—
697C4⋊Q8—46no—
698#126—212no—
699#124—24no—
700#124—46no—
701#124—46no—
702#124—412no—
703#123—46no—
704C22⋊Q8—212no—
705C22⋊Q8—212no—
706C22⋊Q8—212no—
707C22⋊Q8—212no—
708C22⋊Q8—46no—
709C22⋊Q8—46no—
710C22⋊Q8—46no—
711C22⋊Q8—46no—
712C22⋊Q8—46no—
713C22⋊Q8—46no—
714C22⋊Q8—46no—
715C22⋊Q8—46no—
716#121—46no—
717#121—46no—
718#121—46no—
719C4×Q8—24no—
720C4×Q8—24no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—24no—
724C4×Q8—24no—
725C4×Q8—24no—
726C4×Q8—24no—
727C4×Q8—24no—
728C4×Q8—24no—
729C4×Q8—46no—
730C4×Q8—46no—
731C4×Q8—46no—
732C4×Q8—46no—
733C4×Q8—46no—
734C4×Q8—46no—
735C4×Q8—46no—
736C4×Q8—46no—
737C4×Q8—46no—
738C4×D4—212no—
739C4×D4—212no—
740C4×D4—24no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747#117—46no—
748#117—46no—
749#117—46no—
750#117—46no—
751C2×C4⋊C4—46no—
752C2×C4⋊C4—46no—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
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⋊C4C2416yes—
788C2×C4⋊C4C2416yes—
789C2×C4⋊C4C2416yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2416yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2416yes—
828C2×C22⋊C4C2416yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2416yes—
834C2×C22⋊C4C2416yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2411yescharacteristic
837C2×C22⋊C4C2411yescharacteristic
838C2×C22⋊C4C2411yescharacteristic
839C2×C22⋊C4C2411yescharacteristic
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2416yes—
849C2×C42—46no—
850C2×C42—46no—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2416yes—
862C2×C42C2416yes—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2416yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2411yescharacteristic
872#95C2411yescharacteristic
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
891#95C2413yes—
892#95C2416yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2416yes—
898#95C2413yes—
899#95C2416yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2411yescharacteristic
911#95C2411yescharacteristic
912#95C2411yescharacteristic
913#95C2416yes—
914#95C2411yescharacteristic
915#95C2411yescharacteristic
916#95C2416yes—
917#95C2416yes—
918#95C2416yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2416yes—
925#95C2416yes—
926#95C2416yes—
927#95C2416yes—
928#95C2416yes—
929#95C2416yes—
930#95C2416yes—
931#95C2416yes—
932C24C2511yescharacteristic
933C24C2511yescharacteristic
934C24C2513yes—
935C24C2511yescharacteristic
936C24C2511yescharacteristic
937#41—448no—
938#41—448no—
939#41—448no—
940#41—416no—
941C2×Q8—232no—
942C2×Q8—26no—
943C2×Q8—26no—
944C2×Q8—26no—
945C2×Q8—26no—
946C2×Q8—26no—
947C2×Q8—26no—
948C2×Q8—26no—
949C2×Q8—26no—
950C2×Q8—26no—
951C2×Q8—26no—
952C2×Q8—26no—
953C2×Q8—26no—
954C2×Q8—22no—
955C2×Q8—41no—
956C2×Q8—43no—
957C2×Q8—43no—
958C2×Q8—41no—
959C2×Q8—46no—
960C2×Q8—46no—
961C2×Q8—46no—
962C2×Q8—448no—
963C2×Q8—416no—
964C2×Q8—416no—
965C2×Q8—416no—
966C2×Q8C2×#41112yes—
967C2×Q8C2×#4114yes—
968C2×Q8H(5,𝔽2)14yes—
969C2×Q8H(5,𝔽2)14yes—
970C2×D4—22no—
971C2×D4—22no—
972C2×D4—22no—
973C2×D4—22no—
974C2×D4—26no—
975C2×D4—22no—
976C2×D4—22no—
977C2×D4—26no—
978C2×D4—26no—
979C2×D4—26no—
980C2×D4—26no—
981C2×D4—26no—
982C2×D4—22no—
983C2×D4—22no—
984C2×D4—41no—
985C2×D4—41no—
986C2×D4—41no—
987C2×D4—41no—
988C2×D4—41no—
989C2×D4—41no—
990C2×D4—41no—
991C2×D4—41no—
992C2×D4—43no—
993C2×D4—43no—
994C2×D4—41no—
995C2×D4—41no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—43no—
999C2×D4—43no—
1000C2×D4—43no—
1001C2×D4—43no—
1002C2×D4—43no—
1003C22×C4—26no—
1004C22×C4—26no—
1005C22×C4—26no—
1006C22×C4—26no—
1007C22×C4—26no—
1008C22×C4—212no—
1009C22×C4—26no—
1010C22×C4—26no—
1011C22×C4—26no—
1012C22×C4—26no—
1013C22×C4—26no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—26no—
1017C22×C4—26no—
1018C22×C4—26no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—46no—
1026C22×C4—46no—
1027C22×C4—43no—
1028C22×C4—43no—
1029C22×C4—43no—
1030C22×C4—43no—
1031C22×C4—43no—
1032C22×C4C2×#41112yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2513yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2511yescharacteristic
1038C22×C4C2513yes—
1039C22×C4C2513yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2513yes—
1045C22×C4C2513yes—
1046C22×C4C2513yes—
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2513yes—
1053C22×C4C2513yes—
1054C22×C4C2513yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C22×C4C2513yes—
1059C4⋊C4—26no—
1060C4⋊C4—26no—
1061C4⋊C4—26no—
1062C4⋊C4—26no—
1063C4⋊C4—212no—
1064C4⋊C4—212no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—22no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—26no—
1077C4⋊C4—46no—
1078C4⋊C4—46no—
1079C4⋊C4—43no—
1080C4⋊C4—46no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—43no—
1097C4⋊C4—43no—
1098C4⋊C4—46no—
1099C4⋊C4—46no—
1100C4⋊C4—46no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C22⋊C4—26no—
1104C22⋊C4—26no—
1105C22⋊C4—26no—
1106C22⋊C4—26no—
1107C22⋊C4—26no—
1108C22⋊C4—26no—
1109C22⋊C4—22no—
1110C22⋊C4—22no—
1111C22⋊C4—22no—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—26no—
1116C22⋊C4—26no—
1117C22⋊C4—26no—
1118C22⋊C4—46no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—46no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—43no—
1129C22⋊C4—41no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—41no—
1133C22⋊C4—41no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—41no—
1138C22⋊C4—41no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—46no—
1150C22⋊C4—46no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—46no—
1154C22⋊C4—46no—
1155C42—26no—
1156C42—26no—
1157C42—26no—
1158C42—26no—
1159C42—26no—
1160C42—26no—
1161C42—26no—
1162C42—26no—
1163C42—26no—
1164C42—26no—
1165C42—43no—
1166C42—43no—
1167C42—43no—
1168C42—43no—
1169C42—43no—
1170C42—43no—
1171C42—46no—
1172C42—46no—
1173C42—43no—
1174C42—46no—
1175C422−1+414yescomplemented
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—23no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—23no—
1196C23—23no—
1197C23—23no—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23—23no—
1202C23—21no—
1203C23—21no—
1204C23—23no—
1205C23—23no—
1206C23—21no—
1207C23—21no—
1208C23—21no—
1209C23C22×#4112yes—
1210C23#58512yes—
1211C23C2611yescharacteristic
1212Q8—224no—
1213Q8—44no—
1214Q8—412no—
1215Q8—412no—
1216Q8—412no—
1217Q8—412no—
1218Q8—166no—
1219Q8#538116yes—
1220D4—28no—
1221D4—44no—
1222D4—412no—
1223D4—44no—
1224D4—44no—
1225D4—44no—
1226D4—44no—
1227D4—412no—
1228D4—412no—
1229D4—86no—
1230D4—86no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—224no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—21no—
1246C2×C4—23no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—23no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—23no—
1282C2×C4—21no—
1283C2×C4—23no—
1284C2×C4—21no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—23no—
1288C2×C4—23no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—23no—
1303C2×C4—44no—
1304C2×C4—44no—
1305C2×C4—424no—
1306C2×C4—412no—
1307C2×C4—412no—
1308C2×C4—412no—
1309C2×C4—412no—
1310C2×C4—86no—
1311C2×C4—86no—
1312C2×C4C22×#4116yes—
1313C2×C4C22×#4116yes—
1314C2×C4C2×H(5,𝔽2)16yes—
1315C2×C4C2×H(5,𝔽2)16yes—
1316C2×C4C2×2−1+412yes—
1317C2×C4C2×2−1+412yes—
1318C2×C4C2×2−1+412yes—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—22no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—43no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—43no—
1339C22—41no—
1340C22—41no—
1341C22—43no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—43no—
1347C22—43no—
1348C22—41no—
1349C22—43no—
1350C22—41no—
1351C22—43no—
1352C22—41no—
1353C22—41no—
1354C22C23×#4111yescharacteristic
1355C22C22×H(5,𝔽2)11yescharacteristic
1356C22C22×H(5,𝔽2)11yescharacteristic
1357C22C22×2−1+411yescharacteristic
1358C22C2×#58511yescharacteristic
1359C222−1+611yescharacteristic
1360C222−1+611yescharacteristic
1361C4—22no—
1362C4—22no—
1363C4—22no—
1364C4—26no—
1365C4—43no—
1366C4—43no—
1367C4—41no—
1368C4—43no—
1369C4—43no—
1370C4—43no—
1371C4—41no—
1372C4—43no—
1373C4—43no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—43no—
1380C4—43no—
1381C4—43no—
1382C4—41no—
1383C4—43no—
1384C4—43no—
1385C4—43no—
1386C4C2×#538112yes—
1387C2—42no—
1388C2—42no—
1389C2—81no—
1390C2—81no—
1391C2—83no—
1392C2C22×#53811yescharacteristic
1393C2#6278811yescharacteristic
1394C2#6285011yescharacteristic
1395C2#6289711yescharacteristic
1396C2#6291311yescharacteristic
1397C2#6291311yescharacteristic
1398C2#6291911yescharacteristic
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. #42857C2semidirect
2. #42844C2semidirect
3. #42839C2semidirect
4. #42828C2semidirect
5. #42696C2semidirect
6. #42654C2semidirect
7. #42503C2semidirect
8. #42446C2semidirect
9. #40218C2semidirect
10. #40196C2semidirect
11. #39783C2semidirect
12. #39663C2semidirect
13. #37514C2semidirect
14. #37499C2semidirect
15. #36585C2semidirect
16. Q8×#124C2semidirect
17. #36482C2semidirect
18. #36434C2semidirect
19. #35948C2semidirect
20. #35883C2semidirect
21. #35801C2semidirect
22. #35711C2semidirect
23. #35700C2semidirect
24. #35700C2semidirect
25. #35687C2semidirect
26. #35687C2semidirect
27. #35046C2semidirect
28. #34589C2semidirect
29. #34291C2semidirect
30. #34257C2semidirect
31. C4×D4×Q8C2semidirect
1175. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
#428572
#428442
#428392
#428282
#426962
#426542
#425032
#424462
#402182
#401962
#397832
#396632
#375142
#374992
#365852
Q8×#1242
#364822
#364342
#359482
#358832
#358012
#357112
#357002
#356872
#350462
#345892
#342912
#342572
C4×D4×Q82