Finite Group Databasebeta

← #7658467

Subgroups — #7658467

Order 512.

4865 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42784C213yesmaximal, complemented
2#42778C213yesmaximal, complemented
3#42776C213yesmaximal, complemented
4#42771C213yesmaximal, complemented
5#42769C213yesmaximal, complemented
6#42761C213yesmaximal, complemented
7#42714C213yesmaximal, complemented
8#42708C213yesmaximal, complemented
9#42702C213yesmaximal, complemented
10#42690C213yesmaximal, complemented
11#42669C213yesmaximal, complemented
12#42664C213yesmaximal, complemented
13#37628C213yesmaximal, complemented
14#37594C213yesmaximal, complemented
15#37579C213yesmaximal, complemented
16#36692C213yesmaximal, complemented
17#35983C211yesmaximal, characteristic, complemented
18#35971C211yesmaximal, characteristic, complemented
19#35927C211yesmaximal, characteristic, complemented
20#35801C211yesmaximal, characteristic, complemented
21#35771C211yesmaximal, characteristic, complemented
22#35771C211yesmaximal, characteristic, complemented
23#35737C211yesmaximal, characteristic, complemented
24#35723C211yesmaximal, characteristic, complemented
25#35723C211yesmaximal, characteristic, complemented
26#35700C211yesmaximal, characteristic, complemented
27#35700C211yesmaximal, characteristic, complemented
28#35700C211yesmaximal, characteristic, complemented
29#34312C211yesmaximal, characteristic, complemented
30#34311C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#548C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#519C2211yescharacteristic
44C2×#519C2211yescharacteristic
45C2×#519C2211yescharacteristic
46C2×#519C2211yescharacteristic
47#2837C2213yes—
48#2837C2213yes—
49#2837C2213yes—
50#2837C2213yes—
51#2836C2213yes—
52#2836C2213yes—
53#2836C2213yes—
54#2836C2213yes—
55#2836C2216yes—
56#2829C2213yes—
57#2829C2213yes—
58#2829C2213yes—
59#2829C2213yes—
60#2828C2213yes—
61#2828C2213yes—
62#2828C2211yescharacteristic
63#2828C2213yes—
64#2803C2216yes—
65#2800C2216yes—
66#2793C2216yes—
67#2791C2216yes—
68#2777C2216yes—
69#2777C2216yes—
70#2773C2216yes—
71#2773C2216yes—
72#2768C2216yes—
73#2761C2216yes—
74#2756C2216yes—
75#2753C2216yes—
76#2753C2216yes—
77#2752C2216yes—
78#2740C2216yes—
79#2738C2216yes—
80#2667C2216yes—
81#2667C2216yes—
82#2658C2213yes—
83#2654C2216yes—
84#2654C2216yes—
85#2654C2216yes—
86#2651C2216yes—
87#2651C2216yes—
88#2651C2216yes—
89#2649C2216yes—
90#2648C2216yes—
91#2647C2216yes—
92#2647C2213yes—
93#2644C2216yes—
94#2625C2213yes—
95#2625C2213yes—
96#2625C2213yes—
97#2624C2213yes—
98#2621C2213yes—
99#2621C2213yes—
100#2621C2213yes—
101#2621C2213yes—
102#2620C2213yes—
103#2620C2213yes—
104#2571C2213yes—
105#2570C2213yes—
106#2547C2213yes—
107#2546C2213yes—
108#2546C2213yes—
109#2546C2213yes—
110#2545C2213yes—
111#2545C2213yes—
112#2542C2213yes—
113#2542C2213yes—
114#2542C2213yes—
115#2540C2213yes—
116#2540C2213yes—
117#2540C2213yes—
118#2538C2213yes—
119#2538C2213yes—
120#2536C2213yes—
121#2536C2213yes—
122#2536C2213yes—
123#2535C2213yes—
124#2531C2216yes—
125#2526C2216yes—
126#2522C2216yes—
127#2516C2216yes—
128#2513C2216yes—
129#2509C2213yes—
130#2508C2213yes—
131#2508C2213yes—
132#2507C2213yes—
133#2507C2216yes—
134#2503C2213yes—
135#2500C2213yes—
136#2499C2213yes—
137#2499C2213yes—
138#2487C2213yes—
139#2485C2213yes—
140#2485C2213yes—
141#2485C2213yes—
142#2448C2213yes—
143#2448C2213yes—
144#2447C2213yes—
145#2447C2213yes—
146#2446C2213yes—
147#2446C2213yes—
148#2446C2213yes—
149#2446C2213yes—
150#2429C2213yes—
151#2429C2213yes—
152#2429C2213yes—
153#2429C2213yes—
154#2429C2213yes—
155#2429C2213yes—
156#2429C2213yes—
157#2429C2213yes—
158#2427C2213yes—
159#2427C2213yes—
160#2426C2213yes—
161#2426C2213yes—
162#2423C2213yes—
163#2423C2213yes—
164#2423C2213yes—
165#2421C2213yes—
166#2421C2213yes—
167#2421C2213yes—
168#2420C2213yes—
169#2420C2213yes—
170#2417C2213yes—
171#2417C2213yes—
172#2415C2213yes—
173#2415C2213yes—
174#2415C2213yes—
175#2415C2213yes—
176#2415C2213yes—
177#2415C2213yes—
178#2415C2213yes—
179#2415C2213yes—
180#2414C2213yes—
181#2414C2213yes—
182#2402C2213yes—
183#2397C2213yes—
184#2395C2213yes—
185#2395C2213yes—
186#2395C2213yes—
187#2395C2213yes—
188#2392C2213yes—
189#2392C2213yes—
190#2392C2213yes—
191#2392C2213yes—
192#2392C2213yes—
193#2392C2213yes—
194#2367C2213yes—
195#2365C2213yes—
196#2363C2213yes—
197#2362C2213yes—
198#2362C2213yes—
199#2360C2213yes—
200#2356C2213yes—
201#2355C2213yes—
202#2354C2213yes—
203#2352C2213yes—
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207#2351C2211yescharacteristic
208#2351C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212#2347C2213yes—
213#2346C2213yes—
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224#2324C2213yes—
225#2323C2213yes—
226#2323C2213yes—
227#2323C2213yes—
228#2320C2213yes—
229#2314C2213yes—
230C4×C4⋊Q8C2213yes—
231C4×#124C2213yes—
232#2298C2213yes—
233#2295C2213yes—
234#2293C2213yes—
235#2293C2213yes—
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242C23×Q8C2311yescharacteristic
243D4×Q8—28no—
244D4×Q8—44no—
245D4×Q8—44no—
246D4×Q8—44no—
247D4×Q8—44no—
248D4×Q8—44no—
249#548—28no—
250#548—44no—
251#548—44no—
252#548—44no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×C4⋊Q8C2313yes—
257C2×C4⋊Q8C2313yes—
258C2×C4⋊Q8C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283#520—44no—
284#519—28no—
285#519—44no—
286#519—44no—
287#519—44no—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2313yes—
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×#117C2313yes—
319C2×#117C2313yes—
320C2×#117C2313yes—
321C2×#117C2313yes—
322C2×#117C2313yes—
323C2×#117C2313yes—
324C2×#117C2313yes—
325C2×#117C2313yes—
326C2×#117C2313yes—
327C22×C4⋊C4C2313yes—
328#400C2316yes—
329#400C2313yes—
330#400C2311yescharacteristic
331#400C2313yes—
332#400C2313yes—
333#400C2313yes—
334#400C2313yes—
335#400C2313yes—
336#400C2313yes—
337#400C2316yes—
338#400C2316yes—
339#400C2316yes—
340#400C2316yes—
341#399C2313yes—
342#399C2313yes—
343#399C2313yes—
344#399C2313yes—
345#399C2313yes—
346#399C2313yes—
347#399C2313yes—
348#399C2313yes—
349#399C2316yes—
350#399C2316yes—
351#399C2316yes—
352#399C2316yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#398C2313yes—
361#398C2313yes—
362#398C2313yes—
363#398C2313yes—
364#398C2313yes—
365#398C2313yes—
366#398C2313yes—
367#398C2316yes—
368#398C2316yes—
369#398C2316yes—
370#398C2316yes—
371#398C2316yes—
372#398C2316yes—
373#398C2316yes—
374#398C2316yes—
375#398C2316yes—
376#398C2316yes—
377#397C2311yescharacteristic
378#397C2311yescharacteristic
379#397C2313yes—
380#397C2313yes—
381#397C2313yes—
382#397C2313yes—
383#397C2313yes—
384#397C2313yes—
385#397C2313yes—
386#397C2313yes—
387#397C2313yes—
388#397C2313yes—
389#397C2313yes—
390#397C2313yes—
391#397C2313yes—
392#397C2313yes—
393#397C2316yes—
394#397C2316yes—
395#397C2316yes—
396#397C2313yes—
397#397C2313yes—
398#397C2316yes—
399#397C2316yes—
400#397C2316yes—
401#397C2316yes—
402#397C2316yes—
403#397C2316yes—
404#397C2316yes—
405#396C2313yes—
406#396C2313yes—
407#396C2313yes—
408#396C2313yes—
409#396C2313yes—
410#396C2313yes—
411#396C2313yes—
412#396C2313yes—
413#396C2316yes—
414#396C2316yes—
415#396C2313yes—
416#396C2313yes—
417#396C2313yes—
418#396C2313yes—
419#396C2316yes—
420#396C2316yes—
421#394C2311yescharacteristic
422#394C2311yescharacteristic
423#394C2313yes—
424#394C2313yes—
425#394C2313yes—
426#394C2313yes—
427#394C2313yes—
428#394C2313yes—
429#394C2311yescharacteristic
430#394C2311yescharacteristic
431#394C2311yescharacteristic
432#394C2313yes—
433#394C2313yes—
434#394C2313yes—
435#394C2313yes—
436#394C2313yes—
437#394C2313yes—
438#394C2313yes—
439#394C2313yes—
440#394C2313yes—
441#394C2313yes—
442#394C2313yes—
443#394C2313yes—
444#394C2313yes—
445#394C2313yes—
446#394C2313yes—
447#394C2316yes—
448#394C2316yes—
449#394C2316yes—
450#392C2311yescharacteristic
451#392C2311yescharacteristic
452#392C2311yescharacteristic
453#392C2313yes—
454#392C2313yes—
455#392C2313yes—
456#392C2311yescharacteristic
457#392C2313yes—
458#392C2313yes—
459#392C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#391C2313yes—
464#391C2313yes—
465#391C2313yes—
466#391C2313yes—
467#391C2313yes—
468#391C2313yes—
469#391C2313yes—
470#391C2313yes—
471#391C2313yes—
472#391C2313yes—
473#391C2313yes—
474#391C2313yes—
475#391C2313yes—
476#390C2311yescharacteristic
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2316yes—
485#390C2316yes—
486#390C2316yes—
487#390C2316yes—
488#390C2316yes—
489#389C2313yes—
490#389C2316yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2316yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2316yes—
512#389C2316yes—
513#389C2316yes—
514#389C2316yes—
515#389C2316yes—
516#389C2316yes—
517#389C2316yes—
518#389C2316yes—
519#388C2313yes—
520#388C2316yes—
521#388C2313yes—
522#388C2311yescharacteristic
523#388C2313yes—
524#388C2313yes—
525#388C2311yescharacteristic
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2316yes—
533#388C2316yes—
534#388C2316yes—
535#388C2316yes—
536#388C2316yes—
537#388C2316yes—
538#388C2316yes—
539#388C2316yes—
540#388C2316yes—
541#388C2316yes—
542#388C2316yes—
543#388C2316yes—
544#388C2316yes—
545#388C2316yes—
546#388C2316yes—
547#388C2316yes—
548#388C2316yes—
549#388C2316yes—
550#388C2316yes—
551#387C2316yes—
552#387C2316yes—
553#387C2316yes—
554#387C2316yes—
555#387C2313yes—
556#387C2313yes—
557#387C2313yes—
558#387C2313yes—
559#387C2316yes—
560#387C2316yes—
561#387C2316yes—
562#387C2316yes—
563#387C2316yes—
564#387C2316yes—
565#387C2316yes—
566#387C2316yes—
567#387C2316yes—
568#387C2316yes—
569#386C2316yes—
570#386C2316yes—
571#386C2316yes—
572#386C2316yes—
573#385C2316yes—
574#385C2316yes—
575#384C2313yes—
576#384C2313yes—
577#384C2313yes—
578#384C2316yes—
579#383C2316yes—
580#382C2313yes—
581#382C2313yes—
582#382C2313yes—
583#382C2313yes—
584#382C2313yes—
585#382C2316yes—
586#382C2316yes—
587#381C2316yes—
588#381C2316yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599#380C2316yes—
600#380C2316yes—
601C4×C4⋊C4C2316yes—
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×C4⋊C4C2316yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊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⋊C4C2316yes—
630#376C2313yes—
631#376C2316yes—
632C43C2313yes—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C22×Q8—24no—
637C22×Q8—24no—
638C22×Q8—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8—24no—
643C22×Q8—24no—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8C2413yes—
649C22×Q8C2413yes—
650C22×Q8C2413yes—
651C22×Q8C2413yes—
652C22×Q8C2411yescharacteristic
653C22×D4C2413yes—
654C22×D4C2411yescharacteristic
655C22×D4C2413yes—
656C22×D4C2411yescharacteristic
657C22×D4C2411yescharacteristic
658C22×D4C2411yescharacteristic
659C22×D4C2411yescharacteristic
660C22×D4C2411yescharacteristic
661C22×D4C2413yes—
662C22×D4C2413yes—
663C22×D4C2413yes—
664C23×C4C2413yes—
665C23×C4C2413yes—
666C23×C4C2413yes—
667C23×C4C2413yes—
668C23×C4C2413yes—
669C23×C4C2416yes—
670C4⋊Q8—212no—
671C4⋊Q8—46no—
672C4⋊Q8—46no—
673C4⋊Q8—46no—
674C4⋊Q8—46no—
675C4⋊Q8—46no—
676#124—212no—
677#124—46no—
678#124—46no—
679#124—46no—
680C22⋊Q8—212no—
681C22⋊Q8—212no—
682C22⋊Q8—212no—
683C22⋊Q8—46no—
684C22⋊Q8—46no—
685C22⋊Q8—46no—
686C22⋊Q8—46no—
687C22⋊Q8—46no—
688C22⋊Q8—46no—
689C22⋊Q8—46no—
690C22⋊Q8—46no—
691C22⋊Q8—46no—
692C22⋊Q8—46no—
693C22⋊Q8—46no—
694C22⋊Q8—46no—
695C22⋊Q8—46no—
696#121—212no—
697#121—46no—
698#121—46no—
699#121—46no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—212no—
710C4×Q8—212no—
711C4×Q8—46no—
712C4×Q8—46no—
713C4×Q8—46no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×Q8—46no—
717C4×Q8#4118yes—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—46no—
721C4×D4—46no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4—46no—
727C4×D4—46no—
728C4×D4—46no—
729C4×D4—46no—
730#117—212no—
731#117—212no—
732#117—46no—
733#117—46no—
734#117—46no—
735#117—46no—
736#117—46no—
737#117—46no—
738#117—46no—
739C2×C4⋊C4—46no—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2416yes—
785C2×C4⋊C4C2416yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2416yes—
794C2×C4⋊C4C2413yes—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
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⋊C4C2416yes—
827C2×C22⋊C4C2416yes—
828C2×C22⋊C4C2416yes—
829C2×C22⋊C4C2411yescharacteristic
830C2×C22⋊C4C2411yescharacteristic
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2411yescharacteristic
836C2×C22⋊C4C2411yescharacteristic
837C2×C22⋊C4C2411yescharacteristic
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2416yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2416yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2416yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2416yes—
862C2×C42C2416yes—
863C2×C42C2416yes—
864C2×C42C2411yescharacteristic
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2416yes—
869C2×C42C2413yes—
870#95C2411yescharacteristic
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2416yes—
877#95C2416yes—
878#95C2411yescharacteristic
879#95C2413yes—
880#95C2411yescharacteristic
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2416yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2416yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2416yes—
901#95C2411yescharacteristic
902#95C2411yescharacteristic
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2411yescharacteristic
906#95C2416yes—
907#95C2416yes—
908#95C2416yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2416yes—
919#95C2416yes—
920#95C2416yes—
921#95C2416yes—
922#95C2416yes—
923#95C2416yes—
924C24C2511yescharacteristic
925C24C2511yescharacteristic
926C24C2511yescharacteristic
927C24C2513yes—
928C24C2511yescharacteristic
929#41—416no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—26no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—26no—
939C2×Q8—26no—
940C2×Q8—26no—
941C2×Q8—26no—
942C2×Q8—416no—
943C2×Q8—416no—
944C2×Q8—416no—
945C2×Q8—416no—
946C2×Q8C2×#4114yes—
947C2×Q8H(5,𝔽2)14yes—
948C2×Q8H(5,𝔽2)14yes—
949C2×D4—22no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—41no—
955C2×D4—41no—
956C2×D4—41no—
957C2×D4—41no—
958C2×D4—41no—
959C2×D4—41no—
960C2×D4—41no—
961C2×D4—41no—
962C2×D4—41no—
963C2×D4—41no—
964C2×D4—41no—
965C2×D4—41no—
966C2×D4—41no—
967C2×D4—41no—
968C2×D4—41no—
969C2×D4—41no—
970C2×D4—41no—
971C2×D4—43no—
972C2×D4—43no—
973C2×D4—43no—
974C2×D4—43no—
975C2×D4—43no—
976C2×D4—43no—
977C2×D4—43no—
978C2×D4—43no—
979C2×D4—43no—
980C2×D4—43no—
981C2×D4—43no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—26no—
989C22×C4—26no—
990C22×C4—26no—
991C22×C4—26no—
992C22×C4—26no—
993C22×C4—26no—
994C22×C4—26no—
995C22×C4—26no—
996C22×C4—26no—
997C22×C4—46no—
998C22×C4—46no—
999C22×C4—46no—
1000C22×C4C2513yes—
1001C22×C4C2513yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2513yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C22×C4C2513yes—
1010C22×C4C2513yes—
1011C22×C4C2513yes—
1012C22×C4C2511yescharacteristic
1013C22×C4C2511yescharacteristic
1014C22×C4C2513yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2513yes—
1017C22×C4C2513yes—
1018C22×C4C2513yes—
1019C22×C4C2513yes—
1020C22×C4C2513yes—
1021C22×C4C2513yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2513yes—
1024C22×C4C2511yescharacteristic
1025C22×C4C2513yes—
1026C4⋊C4—26no—
1027C4⋊C4—26no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—212no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—43no—
1041C4⋊C4—41no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—46no—
1045C4⋊C4—43no—
1046C4⋊C4—41no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—46no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—41no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—46no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—41no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C4⋊C4—46no—
1076C4⋊C4—46no—
1077C4⋊C4—46no—
1078C4⋊C4—46no—
1079C4⋊C4—46no—
1080C4⋊C4C2×#41112yes—
1081C22⋊C4—26no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—26no—
1085C22⋊C4—26no—
1086C22⋊C4—26no—
1087C22⋊C4—212no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—41no—
1094C22⋊C4—46no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—41no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—46no—
1103C22⋊C4—43no—
1104C22⋊C4—41no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—41no—
1108C22⋊C4—43no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—41no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—43no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—43no—
1134C22⋊C4—46no—
1135C22⋊C4—46no—
1136C22⋊C4—46no—
1137C42—26no—
1138C42—212no—
1139C42—26no—
1140C42—26no—
1141C42—26no—
1142C42—26no—
1143C42—26no—
1144C42—26no—
1145C42—26no—
1146C42—26no—
1147C42—43no—
1148C42—46no—
1149C42—43no—
1150C42—43no—
1151C42—41no—
1152C42—46no—
1153C42—46no—
1154C42—46no—
1155C42C2×#41112yes—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—23no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—23no—
1167C23—21no—
1168C23—23no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—23no—
1179C23—21no—
1180C23—23no—
1181C23—21no—
1182C23—23no—
1183C23—23no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23C2611yescharacteristic
1192Q8—412no—
1193Q8—412no—
1194Q8—412no—
1195Q8—412no—
1196Q8#540116yes—
1197D4—44no—
1198D4—44no—
1199D4—44no—
1200D4—44no—
1201D4—44no—
1202D4—44no—
1203D4—412no—
1204D4—86no—
1205D4—86no—
1206D4—86no—
1207D4—86no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—21no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—21no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—21no—
1266C2×C4—23no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—23no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—23no—
1279C2×C4—21no—
1280C2×C4—23no—
1281C2×C4—412no—
1282C2×C4—412no—
1283C2×C4—412no—
1284C2×C4—412no—
1285C2×C4—412no—
1286C2×C4—166no—
1287C2×C4C22×#4116yes—
1288C2×C4C22×#4112yes—
1289C2×C4C22×#4116yes—
1290C2×C4C2×H(5,𝔽2)16yes—
1291C2×C4C2×H(5,𝔽2)16yes—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—43no—
1302C22—43no—
1303C22—43no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—43no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—43no—
1316C22—41no—
1317C22—41no—
1318C22—43no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—43no—
1327C22C23×#4111yescharacteristic
1328C22C22×H(5,𝔽2)11yescharacteristic
1329C22C22×H(5,𝔽2)11yescharacteristic
1330C222−1+611yescharacteristic
1331C222−1+611yescharacteristic
1332C222−1+611yescharacteristic
1333C222−1+611yescharacteristic
1334C4—22no—
1335C4—26no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—43no—
1340C4—43no—
1341C4—43no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—43no—
1346C4—43no—
1347C4—43no—
1348C4—43no—
1349C4—43no—
1350C4—41no—
1351C4—41no—
1352C4—43no—
1353C4—41no—
1354C4—41no—
1355C4—43no—
1356C4—43no—
1357C4—43no—
1358C4—43no—
1359C4C2×#540112yes—
1360C2—81no—
1361C2—81no—
1362C2—81no—
1363C2—81no—
1364C2—83no—
1365C2C22×#54011yescharacteristic
1366C2#6285011yescharacteristic
1367C2#6286111yescharacteristic
1368C2#6304411yescharacteristic
1369C2#6304411yescharacteristic
1370C2#6304411yescharacteristic
1371C2#6304811yescharacteristic
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. #42784C2semidirect
2. #42778C2semidirect
3. #42776C2semidirect
4. #42771C2semidirect
5. #42769C2semidirect
6. #42761C2semidirect
7. #42714C2semidirect
8. #42708C2semidirect
9. #42702C2semidirect
10. #42690C2semidirect
11. #42669C2semidirect
12. #42664C2semidirect
13. #37628C2semidirect
14. #37594C2semidirect
15. #37579C2semidirect
16. #36692C2semidirect
17. #35983C2semidirect
18. #35971C2semidirect
19. #35927C2semidirect
20. #35801C2semidirect
21. #35771C2semidirect
22. #35771C2semidirect
23. #35737C2semidirect
24. #35723C2semidirect
25. #35723C2semidirect
26. #35700C2semidirect
27. #35700C2semidirect
28. #35700C2semidirect
29. #34312C2semidirect
30. #34311C2semidirect
31. #34262C2semidirect

Maximal subgroups

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

subgroupindex
#427842
#427782
#427762
#427712
#427692
#427612
#427142
#427082
#427022
#426902
#426692
#426642
#376282
#375942
#375792
#366922
#359832
#359712
#359272
#358012
#357712
#357372
#357232
#357002
#343122
#343112
#342622