Finite Group Databasebeta

← #7658309

Subgroups — #7658309

Order 512.

5222 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42906C213yesmaximal, complemented
2#42900C213yesmaximal, complemented
3#42867C213yesmaximal, complemented
4#42866C213yesmaximal, complemented
5#42860C213yesmaximal, complemented
6#42857C213yesmaximal, complemented
7#42853C213yesmaximal, complemented
8#42851C213yesmaximal, complemented
9#42696C213yesmaximal, complemented
10#42685C213yesmaximal, complemented
11#42654C213yesmaximal, complemented
12#42653C213yesmaximal, complemented
13#37519C213yesmaximal, complemented
14#37500C213yesmaximal, complemented
15#37499C213yesmaximal, complemented
16#36670C213yesmaximal, complemented
17#36059C211yesmaximal, characteristic, complemented
18#35910C211yesmaximal, characteristic, complemented
19#35883C211yesmaximal, characteristic, complemented
20#35854C211yesmaximal, characteristic, complemented
21#35801C211yesmaximal, characteristic, complemented
22#35786C211yesmaximal, characteristic, complemented
23#35771C211yesmaximal, characteristic, complemented
24#35723C211yesmaximal, characteristic, complemented
25#35700C211yesmaximal, characteristic, complemented
26#35700C211yesmaximal, characteristic, complemented
27#35687C211yesmaximal, characteristic, complemented
28#35687C211yesmaximal, characteristic, complemented
29#34291C211yesmaximal, characteristic, complemented
30#34291C211yesmaximal, characteristic, complemented
31#34257C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C2×#519C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2833C2213yes—
46#2832C2213yes—
47#2831C2213yes—
48#2831C2213yes—
49#2830C2213yes—
50#2829C2213yes—
51#2829C2213yes—
52#2828C2213yes—
53#2827C2213yes—
54#2827C2213yes—
55#2827C2216yes—
56#2826C2213yes—
57#2826C2213yes—
58#2825C2211yescharacteristic
59#2825C2213yes—
60#2824C2213yes—
61#2824C2213yes—
62#2808C2216yes—
63#2805C2216yes—
64#2803C2216yes—
65#2803C2216yes—
66#2800C2216yes—
67#2788C2216yes—
68#2787C2216yes—
69#2787C2216yes—
70#2786C2216yes—
71#2781C2216yes—
72#2775C2216yes—
73#2774C2216yes—
74#2770C2216yes—
75#2768C2216yes—
76#2759C2216yes—
77#2756C2216yes—
78#2666C2216yes—
79#2666C2216yes—
80#2653C2216yes—
81#2653C2216yes—
82#2652C2216yes—
83#2652C2216yes—
84#2651C2216yes—
85#2651C2216yes—
86#2649C2216yes—
87#2649C2216yes—
88#2648C2216yes—
89#2648C2216yes—
90#2645C2213yes—
91#2644C2213yes—
92#2642C2213yes—
93#2640C2213yes—
94#2629C2213yes—
95#2625C2213yes—
96#2624C2213yes—
97#2621C2213yes—
98#2621C2213yes—
99#2620C2213yes—
100#2616C2213yes—
101#2616C2213yes—
102#2597C2216yes—
103#2595C2216yes—
104#2592C2213yes—
105#2589C2216yes—
106#2587C2216yes—
107#2582C2213yes—
108#2568C2213yes—
109#2565C2213yes—
110#2563C2213yes—
111#2562C2213yes—
112#2546C2213yes—
113#2546C2213yes—
114#2545C2213yes—
115#2538C2213yes—
116#2536C2213yes—
117#2536C2213yes—
118#2518C2216yes—
119#2518C2216yes—
120#2514C2213yes—
121#2514C2213yes—
122#2513C2213yes—
123#2513C2213yes—
124#2513C2213yes—
125#2511C2213yes—
126#2500C2213yes—
127#2499C2213yes—
128#2497C2213yes—
129#2495C2213yes—
130#2495C2213yes—
131#2495C2213yes—
132#2495C2213yes—
133#2494C2213yes—
134#2492C2213yes—
135#2492C2213yes—
136#2490C2213yes—
137#2490C2213yes—
138#2489C2213yes—
139#2489C2213yes—
140#2489C2213yes—
141#2489C2213yes—
142#2485C2213yes—
143#2485C2213yes—
144#2453C2213yes—
145#2451C2213yes—
146#2448C2213yes—
147#2448C2213yes—
148#2446C2213yes—
149#2446C2213yes—
150#2441C2213yes—
151#2439C2213yes—
152#2434C2213yes—
153#2434C2213yes—
154#2432C2213yes—
155#2432C2213yes—
156#2432C2213yes—
157#2432C2213yes—
158#2429C2213yes—
159#2429C2213yes—
160#2429C2213yes—
161#2429C2213yes—
162#2429C2213yes—
163#2426C2213yes—
164#2423C2213yes—
165#2423C2213yes—
166#2421C2213yes—
167#2421C2213yes—
168#2415C2213yes—
169#2415C2213yes—
170#2415C2213yes—
171#2415C2213yes—
172#2415C2213yes—
173#2414C2213yes—
174#2409C2213yes—
175#2409C2213yes—
176#2407C2213yes—
177#2407C2213yes—
178#2407C2213yes—
179#2407C2213yes—
180#2401C2213yes—
181#2401C2213yes—
182#2398C2213yes—
183#2398C2213yes—
184#2396C2213yes—
185#2395C2213yes—
186#2395C2213yes—
187#2392C2213yes—
188#2392C2213yes—
189#2392C2213yes—
190#2388C2213yes—
191#2388C2213yes—
192#2365C2213yes—
193#2365C2213yes—
194#2362C2213yes—
195#2362C2213yes—
196#2360C2213yes—
197#2360C2213yes—
198#2352C2213yes—
199#2352C2213yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2213yes—
210#2341C2213yes—
211#2341C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2213yes—
221Q8×C22⋊C4C2213yes—
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224#2327C2213yes—
225#2327C2213yes—
226#2323C2213yes—
227#2323C2213yes—
228#2311C2213yes—
229#2311C2213yes—
230C4×C22⋊Q8C2213yes—
231C4×C22⋊Q8C2213yes—
232#2297C2213yes—
233#2297C2213yes—
234#2290C2213yes—
235#2290C2213yes—
236#2276C2211yescharacteristic
237#2276C2211yescharacteristic
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—
250#557—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×#125C2313yes—
265C2×#125C2313yes—
266C2×#124C2313yes—
267C2×#124C2313yes—
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×C22⋊Q8C2313yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282#519—44no—
283#519—44no—
284#519—44no—
285C2×C4×Q8—44no—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2313yes—
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×#117C2313yes—
313C2×#117C2313yes—
314C2×#117C2313yes—
315C2×#117C2313yes—
316C2×#117C2313yes—
317C2×#117C2313yes—
318C22×C4⋊C4C2313yes—
319C22×C42C2313yes—
320#401C2311yescharacteristic
321#401C2313yes—
322#401C2316yes—
323#400C2316yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#400C2313yes—
329#400C2313yes—
330#400C2313yes—
331#400C2313yes—
332#400C2313yes—
333#400C2313yes—
334#400C2313yes—
335#400C2313yes—
336#400C2316yes—
337#400C2316yes—
338#400C2313yes—
339#400C2316yes—
340#400C2316yes—
341#400C2316yes—
342#399C2313yes—
343#399C2313yes—
344#399C2313yes—
345#399C2316yes—
346#398C2313yes—
347#398C2316yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2316yes—
353#398C2316yes—
354#398C2313yes—
355#398C2313yes—
356#398C2316yes—
357#398C2316yes—
358#398C2316yes—
359#398C2316yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2311yescharacteristic
365#397C2313yes—
366#397C2311yescharacteristic
367#397C2311yescharacteristic
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2316yes—
380#397C2316yes—
381#397C2316yes—
382#397C2316yes—
383#397C2316yes—
384#397C2316yes—
385#397C2316yes—
386#397C2316yes—
387#397C2316yes—
388#396C2311yescharacteristic
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#396C2313yes—
395#396C2313yes—
396#396C2316yes—
397#396C2316yes—
398#396C2313yes—
399#396C2313yes—
400#396C2316yes—
401#395C2313yes—
402#395C2313yes—
403#395C2313yes—
404#395C2316yes—
405#395C2316yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2311yescharacteristic
416#394C2311yescharacteristic
417#394C2313yes—
418#394C2313yes—
419#394C2311yescharacteristic
420#394C2313yes—
421#394C2313yes—
422#394C2313yes—
423#394C2313yes—
424#394C2313yes—
425#394C2313yes—
426#394C2316yes—
427#394C2316yes—
428#394C2313yes—
429#394C2313yes—
430#394C2313yes—
431#394C2316yes—
432#394C2316yes—
433#394C2316yes—
434#394C2316yes—
435#393C2313yes—
436#393C2316yes—
437#393C2313yes—
438#393C2313yes—
439#393C2313yes—
440#393C2313yes—
441#393C2313yes—
442#393C2313yes—
443#392C2311yescharacteristic
444#392C2313yes—
445#392C2311yescharacteristic
446#392C2311yescharacteristic
447#392C2313yes—
448#392C2311yescharacteristic
449#392C2313yes—
450#392C2313yes—
451#392C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#391C2316yes—
457#391C2313yes—
458#391C2316yes—
459#391C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#391C2313yes—
464#391C2313yes—
465#391C2316yes—
466#391C2313yes—
467#391C2313yes—
468#391C2313yes—
469#391C2313yes—
470#391C2313yes—
471#391C2313yes—
472#391C2313yes—
473#391C2313yes—
474#391C2313yes—
475#391C2313yes—
476#391C2313yes—
477#390C2316yes—
478#390C2313yes—
479#390C2313yes—
480#390C2316yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2316yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2316yes—
493#389C2316yes—
494#389C2316yes—
495#389C2313yes—
496#389C2313yes—
497#389C2316yes—
498#389C2316yes—
499#389C2316yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2316yes—
509#389C2316yes—
510#388C2316yes—
511#388C2316yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2313yes—
516#388C2316yes—
517#388C2316yes—
518#388C2316yes—
519#388C2316yes—
520#388C2316yes—
521#388C2316yes—
522#388C2316yes—
523#388C2316yes—
524#388C2316yes—
525#388C2316yes—
526#388C2316yes—
527#388C2316yes—
528#388C2316yes—
529#388C2316yes—
530#388C2316yes—
531#388C2316yes—
532#388C2316yes—
533#388C2316yes—
534#387C2316yes—
535#387C2316yes—
536#387C2313yes—
537#387C2313yes—
538#387C2313yes—
539#387C2313yes—
540#387C2316yes—
541#387C2316yes—
542#387C2316yes—
543#387C2316yes—
544#387C2316yes—
545#387C2316yes—
546#387C2316yes—
547#387C2316yes—
548#387C2316yes—
549#387C2316yes—
550#387C2316yes—
551#387C2316yes—
552#386C2313yes—
553#386C2313yes—
554#386C2316yes—
555#386C2311yescharacteristic
556#386C2313yes—
557#386C2313yes—
558#386C2311yescharacteristic
559#386C2313yes—
560#386C2311yescharacteristic
561#386C2316yes—
562#386C2316yes—
563#385C2313yes—
564#385C2313yes—
565#385C2313yes—
566#385C2313yes—
567#385C2316yes—
568#385C2316yes—
569#385C2316yes—
570#385C2316yes—
571#385C2316yes—
572#385C2316yes—
573#384C2313yes—
574#384C2313yes—
575#383C2316yes—
576#383C2316yes—
577#382C2316yes—
578#382C2313yes—
579#382C2316yes—
580#382C2313yes—
581#382C2313yes—
582#382C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2316yes—
594#380C2316yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2316yes—
605C4×C4⋊C4C2316yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2313yes—
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⋊C4C2313yes—
629C4×C22⋊C4C2316yes—
630C4×C22⋊C4C2316yes—
631#376C2313yes—
632#376C2313yes—
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×Q8C2413yes—
666C22×Q8C2413yes—
667C22×Q8C2411yescharacteristic
668C22×D4C2413yes—
669C22×D4C2411yescharacteristic
670C22×D4C2411yescharacteristic
671C22×D4C2411yescharacteristic
672C22×D4C2413yes—
673C22×D4C2413yes—
674C22×D4C2411yescharacteristic
675C22×D4C2411yescharacteristic
676C22×D4C2411yescharacteristic
677C22×D4C2413yes—
678C22×D4C2413yes—
679C23×C4C2413yes—
680C23×C4C2413yes—
681C23×C4C2413yes—
682C23×C4C2413yes—
683C23×C4C2413yes—
684C23×C4C2416yes—
685C23×C4C2413yes—
686C23×C4C2411yescharacteristic
687C4⋊Q8—212no—
688C4⋊Q8—212no—
689C4⋊Q8—46no—
690C4⋊Q8—46no—
691C4⋊Q8—46no—
692C4⋊Q8—46no—
693#125—46no—
694#125—46no—
695#124—46no—
696#124—46no—
697C22⋊Q8—212no—
698C22⋊Q8—212no—
699C22⋊Q8—212no—
700C22⋊Q8—212no—
701C22⋊Q8—46no—
702C22⋊Q8—46no—
703C22⋊Q8—46no—
704C22⋊Q8—46no—
705C22⋊Q8—46no—
706C22⋊Q8—46no—
707C22⋊Q8—46no—
708C22⋊Q8—46no—
709#121—46no—
710#121—46no—
711C4×Q8—24no—
712C4×Q8—24no—
713C4×Q8—24no—
714C4×Q8—24no—
715C4×Q8—24no—
716C4×Q8—24no—
717C4×Q8—24no—
718C4×Q8—24no—
719C4×Q8—24no—
720C4×Q8—24no—
721C4×Q8—46no—
722C4×Q8—46no—
723C4×Q8—46no—
724C4×Q8—46no—
725C4×Q8—46no—
726C4×Q8—46no—
727C4×Q8—46no—
728C4×Q8—46no—
729C4×Q8—46no—
730C4×D4—212no—
731C4×D4—212no—
732C4×D4—46no—
733C4×D4—46no—
734C4×D4—46no—
735C4×D4—46no—
736C4×D4—46no—
737#117—46no—
738#117—46no—
739#117—46no—
740#117—46no—
741#117—46no—
742#117—46no—
743C2×C4⋊C4—46no—
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⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2416yes—
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⋊C4C2411yescharacteristic
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2416yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
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⋊C4C2416yes—
790C2×C4⋊C4C2416yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2411yescharacteristic
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2416yes—
834C2×C22⋊C4C2416yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2416yes—
844C2×C22⋊C4C2416yes—
845C2×C42—46no—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2416yes—
857C2×C42C2416yes—
858C2×C42C2416yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2416yes—
862C2×C42C2416yes—
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2411yescharacteristic
873#95C2413yes—
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2416yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889#95C2413yes—
890#95C2416yes—
891#95C2416yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2411yescharacteristic
906#95C2411yescharacteristic
907#95C2411yescharacteristic
908#95C2411yescharacteristic
909#95C2416yes—
910#95C2416yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2416yes—
920#95C2416yes—
921#95C2416yes—
922#95C2416yes—
923#95C2416yes—
924#95C2416yes—
925C24C2511yescharacteristic
926C24C2511yescharacteristic
927C24C2511yescharacteristic
928C24C2513yes—
929C24C2511yescharacteristic
930#41—448no—
931#41—448no—
932#41—448no—
933#41—416no—
934C2×Q8—232no—
935C2×Q8—26no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—26no—
939C2×Q8—26no—
940C2×Q8—26no—
941C2×Q8—26no—
942C2×Q8—26no—
943C2×Q8—26no—
944C2×Q8—26no—
945C2×Q8—26no—
946C2×Q8—26no—
947C2×Q8—43no—
948C2×Q8—43no—
949C2×Q8—43no—
950C2×Q8—43no—
951C2×Q8—43no—
952C2×Q8—448no—
953C2×Q8—416no—
954C2×Q8—416no—
955C2×Q8—416no—
956C2×Q8C2×#41112yes—
957C2×Q8C2×#4114yes—
958C2×Q8H(5,𝔽2)14yes—
959C2×Q8H(5,𝔽2)14yes—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—22no—
963C2×D4—26no—
964C2×D4—26no—
965C2×D4—26no—
966C2×D4—26no—
967C2×D4—26no—
968C2×D4—41no—
969C2×D4—41no—
970C2×D4—41no—
971C2×D4—41no—
972C2×D4—41no—
973C2×D4—41no—
974C2×D4—41no—
975C2×D4—41no—
976C2×D4—41no—
977C2×D4—41no—
978C2×D4—41no—
979C2×D4—41no—
980C2×D4—41no—
981C2×D4—43no—
982C2×D4—43no—
983C2×D4—41no—
984C2×D4—41no—
985C2×D4—43no—
986C2×D4—43no—
987C2×D4—43no—
988C2×D4—43no—
989C2×D4—43no—
990C2×D4—43no—
991C2×D4—43no—
992C2×D4—43no—
993C22×C4—26no—
994C22×C4—26no—
995C22×C4—26no—
996C22×C4—26no—
997C22×C4—212no—
998C22×C4—26no—
999C22×C4—26no—
1000C22×C4—26no—
1001C22×C4—26no—
1002C22×C4—26no—
1003C22×C4—26no—
1004C22×C4—26no—
1005C22×C4—26no—
1006C22×C4—26no—
1007C22×C4—26no—
1008C22×C4—41no—
1009C22×C4—41no—
1010C22×C4—41no—
1011C22×C4—46no—
1012C22×C4—46no—
1013C22×C4—43no—
1014C22×C4—43no—
1015C22×C4—43no—
1016C22×C4C2×#41112yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2513yes—
1022C22×C4C2513yes—
1023C22×C4C2513yes—
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2513yes—
1027C22×C4C2513yes—
1028C22×C4C2513yes—
1029C22×C4C2513yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C22×C4C2513yes—
1034C22×C4C2513yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2511yescharacteristic
1037C22×C4C2513yes—
1038C22×C4C2513yes—
1039C22×C4C2513yes—
1040C22×C4C2513yes—
1041C22×C4C2513yes—
1042C22×C4C2513yes—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—26no—
1047C4⋊C4—212no—
1048C4⋊C4—212no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—26no—
1056C4⋊C4—26no—
1057C4⋊C4—46no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—41no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—41no—
1069C4⋊C4—43no—
1070C4⋊C4—46no—
1071C4⋊C4—46no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—43no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—41no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—46no—
1087C4⋊C4—46no—
1088C4⋊C4—46no—
1089C4⋊C4—46no—
1090C22⋊C4—26no—
1091C22⋊C4—26no—
1092C22⋊C4—26no—
1093C22⋊C4—26no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C22⋊C4—46no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—41no—
1112C22⋊C4—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—43no—
1116C22⋊C4—41no—
1117C22⋊C4—46no—
1118C22⋊C4—46no—
1119C22⋊C4—46no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—41no—
1133C22⋊C4—41no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—46no—
1143C22⋊C4—46no—
1144C42—26no—
1145C42—26no—
1146C42—26no—
1147C42—26no—
1148C42—26no—
1149C42—26no—
1150C42—26no—
1151C42—26no—
1152C42—26no—
1153C42—26no—
1154C42—43no—
1155C42—43no—
1156C42—46no—
1157C42—46no—
1158C42—46no—
1159C42—46no—
1160C42—46no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—23no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—23no—
1178C23—23no—
1179C23—21no—
1180C23—23no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—23no—
1185C23—23no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—23no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23C22×#4112yes—
1196C23C2611yescharacteristic
1197Q8—224no—
1198Q8—412no—
1199Q8—412no—
1200Q8—412no—
1201Q8—412no—
1202Q8—86no—
1203Q8#538116yes—
1204D4—412no—
1205D4—44no—
1206D4—44no—
1207D4—44no—
1208D4—412no—
1209D4—44no—
1210D4—44no—
1211D4—44no—
1212D4—412no—
1213D4—86no—
1214D4—86no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—224no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—21no—
1225C2×C4—23no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—21no—
1257C2×C4—23no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—21no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—23no—
1290C2×C4—424no—
1291C2×C4—44no—
1292C2×C4—412no—
1293C2×C4—412no—
1294C2×C4—412no—
1295C2×C4—412no—
1296C2×C4—86no—
1297C2×C4C22×#4116yes—
1298C2×C4C22×#4116yes—
1299C2×C4C2×H(5,𝔽2)16yes—
1300C2×C4C2×H(5,𝔽2)16yes—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—43no—
1317C22—43no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—43no—
1323C22—43no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—43no—
1330C22—41no—
1331C22—43no—
1332C22—43no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22C23×#4111yescharacteristic
1337C22C22×H(5,𝔽2)11yescharacteristic
1338C22C22×H(5,𝔽2)11yescharacteristic
1339C222−1+611yescharacteristic
1340C222−1+611yescharacteristic
1341C222−1+611yescharacteristic
1342C222−1+611yescharacteristic
1343C4—26no—
1344C4—41no—
1345C4—41no—
1346C4—43no—
1347C4—43no—
1348C4—41no—
1349C4—41no—
1350C4—43no—
1351C4—43no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—43no—
1356C4—43no—
1357C4—43no—
1358C4—43no—
1359C4—41no—
1360C4—43no—
1361C4—43no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—43no—
1366C4—43no—
1367C4—43no—
1368C4C2×#538112yes—
1369C2—42no—
1370C2—81no—
1371C2—81no—
1372C2—81no—
1373C2—83no—
1374C2C22×#53811yescharacteristic
1375C2#6285011yescharacteristic
1376C2#6285011yescharacteristic
1377C2#6304411yescharacteristic
1378C2#6304411yescharacteristic
1379C2#6304411yescharacteristic
1380C2#6304411yescharacteristic
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. #42906C2semidirect
2. #42900C2semidirect
3. #42867C2semidirect
4. #42866C2semidirect
5. #42860C2semidirect
6. #42857C2semidirect
7. #42853C2semidirect
8. #42851C2semidirect
9. #42696C2semidirect
10. #42685C2semidirect
11. #42654C2semidirect
12. #42653C2semidirect
13. #37519C2semidirect
14. #37500C2semidirect
15. #37499C2semidirect
16. #36670C2semidirect
17. #36059C2semidirect
18. #35910C2semidirect
19. #35883C2semidirect
20. #35854C2semidirect
21. #35801C2semidirect
22. #35786C2semidirect
23. #35771C2semidirect
24. #35723C2semidirect
25. #35700C2semidirect
26. #35700C2semidirect
27. #35687C2semidirect
28. #35687C2semidirect
29. #34291C2semidirect
30. #34291C2semidirect
31. #34257C2semidirect

Maximal subgroups

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

subgroupindex
#429062
#429002
#428672
#428662
#428602
#428572
#428532
#428512
#426962
#426852
#426542
#426532
#375192
#375002
#374992
#366702
#360592
#359102
#358832
#358542
#358012
#357862
#357712
#357232
#357002
#356872
#342912
#342572