Finite Group Databasebeta

← #7658365

Subgroups — #7658365

Order 512.

5358 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42903C213yesmaximal, complemented
2#42893C213yesmaximal, complemented
3#42874C213yesmaximal, complemented
4#42855C213yesmaximal, complemented
5#42852C213yesmaximal, complemented
6#42844C213yesmaximal, complemented
7#42835C213yesmaximal, complemented
8#42834C213yesmaximal, complemented
9#42520C213yesmaximal, complemented
10#42503C213yesmaximal, complemented
11#42462C213yesmaximal, complemented
12#42449C213yesmaximal, complemented
13#37516C213yesmaximal, complemented
14#37500C213yesmaximal, complemented
15#37498C213yesmaximal, complemented
16#36670C213yesmaximal, complemented
17#36049C211yesmaximal, characteristic, complemented
18#35983C211yesmaximal, characteristic, complemented
19#35920C211yesmaximal, characteristic, complemented
20#35910C211yesmaximal, characteristic, complemented
21#35898C211yesmaximal, characteristic, complemented
22#35845C211yesmaximal, characteristic, complemented
23#35831C211yesmaximal, characteristic, complemented
24#35801C211yesmaximal, characteristic, complemented
25#35771C211yesmaximal, characteristic, complemented
26#35771C211yesmaximal, characteristic, complemented
27#35757C211yesmaximal, characteristic, complemented
28#35687C211yesmaximal, characteristic, complemented
29#34294C211yesmaximal, characteristic, complemented
30#34291C211yesmaximal, characteristic, complemented
31#34257C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#520C2211yescharacteristic
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#2826C2213yes—
56#2826C2211yescharacteristic
57#2826C2216yes—
58#2825C2213yes—
59#2825C2213yes—
60#2824C2213yes—
61#2824C2213yes—
62#2808C2216yes—
63#2803C2216yes—
64#2797C2216yes—
65#2788C2216yes—
66#2788C2216yes—
67#2781C2216yes—
68#2780C2216yes—
69#2779C2216yes—
70#2774C2216yes—
71#2750C2216yes—
72#2750C2216yes—
73#2745C2216yes—
74#2727C2216yes—
75#2715C2216yes—
76#2714C2216yes—
77#2686C2216yes—
78#2665C2216yes—
79#2662C2216yes—
80#2652C2216yes—
81#2650C2216yes—
82#2649C2216yes—
83#2649C2216yes—
84#2649C2216yes—
85#2648C2216yes—
86#2648C2216yes—
87#2648C2216yes—
88#2645C2213yes—
89#2644C2213yes—
90#2642C2213yes—
91#2641C2213yes—
92#2636C2216yes—
93#2635C2216yes—
94#2628C2213yes—
95#2625C2213yes—
96#2624C2213yes—
97#2620C2213yes—
98#2620C2213yes—
99#2620C2213yes—
100#2616C2213yes—
101#2615C2213yes—
102#2597C2216yes—
103#2587C2216yes—
104#2581C2213yes—
105#2576C2216yes—
106#2568C2213yes—
107#2567C2213yes—
108#2562C2213yes—
109#2562C2213yes—
110#2559C2216yes—
111#2548C2213yes—
112#2545C2213yes—
113#2545C2213yes—
114#2544C2213yes—
115#2538C2213yes—
116#2538C2213yes—
117#2537C2213yes—
118#2513C2213yes—
119#2512C2213yes—
120#2512C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2511C2213yes—
124#2503C2213yes—
125#2500C2213yes—
126#2497C2213yes—
127#2496C2213yes—
128#2496C2213yes—
129#2496C2213yes—
130#2496C2213yes—
131#2494C2213yes—
132#2492C2213yes—
133#2492C2213yes—
134#2491C2213yes—
135#2491C2213yes—
136#2490C2213yes—
137#2490C2213yes—
138#2489C2213yes—
139#2489C2213yes—
140#2487C2213yes—
141#2485C2213yes—
142#2467C2216yes—
143#2459C2216yes—
144#2453C2213yes—
145#2453C2213yes—
146#2448C2213yes—
147#2448C2213yes—
148#2447C2213yes—
149#2447C2213yes—
150#2441C2213yes—
151#2441C2213yes—
152#2436C2213yes—
153#2434C2213yes—
154#2432C2213yes—
155#2432C2213yes—
156#2431C2213yes—
157#2431C2213yes—
158#2429C2213yes—
159#2429C2213yes—
160#2428C2213yes—
161#2427C2213yes—
162#2426C2213yes—
163#2426C2213yes—
164#2423C2213yes—
165#2421C2213yes—
166#2420C2213yes—
167#2420C2213yes—
168#2417C2213yes—
169#2416C2213yes—
170#2415C2213yes—
171#2415C2213yes—
172#2414C2213yes—
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#2367C2213yes—
193#2365C2213yes—
194#2362C2213yes—
195#2361C2213yes—
196#2360C2213yes—
197#2360C2213yes—
198#2352C2213yes—
199#2351C2211yescharacteristic
200#2351C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205D4×C4⋊C4C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2213yes—
210#2341C2213yes—
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2213yes—
223Q8×C22⋊C4C2213yes—
224#2327C2213yes—
225#2326C2213yes—
226#2323C2213yes—
227#2323C2213yes—
228#2311C2213yes—
229#2311C2213yes—
230C4×C22⋊Q8C2213yes—
231C4×#121C2213yes—
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×#41C2311yescharacteristic
243C22×#41C2313yes—
244C22×#41C2313yes—
245C22×#41C2313yes—
246C23×Q8C2311yescharacteristic
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249C23×Q8C2313yes—
250#557—44no—
251#550—44no—
252D4×Q8—28no—
253D4×Q8—44no—
254#548—28no—
255#548—44no—
256#548—44no—
257#548—44no—
258C2×C4⋊Q8C2313yes—
259C2×C4⋊Q8C2313yes—
260C2×C4⋊Q8C2313yes—
261C2×#127C2313yes—
262C2×#126C2316yes—
263C2×#126C2316yes—
264C2×#125C2313yes—
265C2×#125C2313yes—
266C2×#124C2313yes—
267C2×#124C2313yes—
268C2×#124C2313yes—
269C2×#124C2313yes—
270C2×#124C2316yes—
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—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2316yes—
286#520—44no—
287#519—44no—
288#519—44no—
289C2×C4×Q8—44no—
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×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2313yes—
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
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×D4C2316yes—
317C2×#117C2313yes—
318C2×#117C2313yes—
319C2×#117C2313yes—
320C2×#117C2313yes—
321C2×#117C2313yes—
322C22×C4⋊C4C2313yes—
323C22×C4⋊C4C2313yes—
324C22×C42C2313yes—
325#401C2313yes—
326#401C2313yes—
327#400C2313yes—
328#400C2316yes—
329#400C2313yes—
330#400C2313yes—
331#400C2313yes—
332#400C2313yes—
333#400C2313yes—
334#400C2311yescharacteristic
335#400C2313yes—
336#400C2311yescharacteristic
337#400C2316yes—
338#400C2316yes—
339#400C2313yes—
340#400C2313yes—
341#400C2313yes—
342#400C2313yes—
343#400C2316yes—
344#400C2316yes—
345#400C2316yes—
346#400C2316yes—
347#400C2316yes—
348#399C2311yescharacteristic
349#399C2316yes—
350#399C2313yes—
351#399C2313yes—
352#399C2316yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2311yescharacteristic
371#397C2313yes—
372#397C2316yes—
373#397C2311yescharacteristic
374#397C2313yes—
375#397C2316yes—
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#397C2313yes—
381#397C2316yes—
382#397C2316yes—
383#397C2316yes—
384#396C2313yes—
385#396C2313yes—
386#396C2311yescharacteristic
387#396C2313yes—
388#396C2311yescharacteristic
389#396C2313yes—
390#396C2316yes—
391#396C2316yes—
392#396C2313yes—
393#396C2313yes—
394#396C2313yes—
395#396C2313yes—
396#396C2316yes—
397#396C2316yes—
398#396C2316yes—
399#396C2316yes—
400#395C2313yes—
401#395C2316yes—
402#395C2313yes—
403#395C2313yes—
404#395C2316yes—
405#394C2313yes—
406#394C2316yes—
407#394C2311yescharacteristic
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2313yes—
417#394C2313yes—
418#394C2313yes—
419#394C2313yes—
420#394C2311yescharacteristic
421#394C2313yes—
422#394C2311yescharacteristic
423#394C2313yes—
424#394C2311yescharacteristic
425#394C2313yes—
426#394C2316yes—
427#394C2316yes—
428#394C2316yes—
429#394C2316yes—
430#394C2313yes—
431#394C2313yes—
432#394C2313yes—
433#394C2316yes—
434#394C2316yes—
435#394C2316yes—
436#394C2316yes—
437#394C2316yes—
438#393C2313yes—
439#393C2313yes—
440#393C2313yes—
441#393C2313yes—
442#393C2313yes—
443#393C2313yes—
444#393C2313yes—
445#393C2316yes—
446#392C2313yes—
447#392C2313yes—
448#392C2311yescharacteristic
449#392C2313yes—
450#392C2313yes—
451#392C2313yes—
452#392C2313yes—
453#392C2316yes—
454#392C2313yes—
455#392C2313yes—
456#392C2316yes—
457#391C2313yes—
458#391C2313yes—
459#391C2316yes—
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#390C2313yes—
478#390C2313yes—
479#390C2316yes—
480#390C2313yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2313yes—
490#390C2313yes—
491#390C2313yes—
492#390C2316yes—
493#390C2316yes—
494#390C2316yes—
495#389C2316yes—
496#389C2316yes—
497#389C2316yes—
498#389C2313yes—
499#389C2313yes—
500#389C2316yes—
501#389C2313yes—
502#389C2313yes—
503#389C2316yes—
504#389C2316yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2313yes—
512#389C2313yes—
513#388C2316yes—
514#388C2316yes—
515#388C2316yes—
516#388C2316yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
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#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2313yes—
537#387C2316yes—
538#387C2316yes—
539#387C2316yes—
540#387C2316yes—
541#387C2316yes—
542#387C2316yes—
543#387C2316yes—
544#387C2316yes—
545#387C2316yes—
546#387C2316yes—
547#386C2313yes—
548#386C2313yes—
549#386C2316yes—
550#386C2311yescharacteristic
551#386C2313yes—
552#386C2313yes—
553#386C2311yescharacteristic
554#386C2313yes—
555#386C2313yes—
556#386C2316yes—
557#386C2316yes—
558#386C2316yes—
559#386C2316yes—
560#386C2316yes—
561#386C2316yes—
562#386C2316yes—
563#385C2313yes—
564#385C2313yes—
565#385C2311yescharacteristic
566#385C2313yes—
567#385C2316yes—
568#385C2316yes—
569#385C2316yes—
570#385C2316yes—
571#385C2316yes—
572#385C2316yes—
573#385C2316yes—
574#384C2313yes—
575#384C2313yes—
576#384C2313yes—
577#384C2313yes—
578#382C2316yes—
579#382C2313yes—
580#382C2313yes—
581#381C2316yes—
582#381C2316yes—
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—
599#380C2316yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
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⋊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⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2316yes—
631#376C2313yes—
632#376C2313yes—
6332−1+4—464no—
634C2×#41—24no—
635C2×#41—212no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—212no—
642C2×#41—212no—
643C2×#41—46no—
644C2×#41—46no—
645C2×#41—46no—
646C2×#41—46no—
647C2×#41—46no—
648C2×#41—46no—
649C22×Q8—24no—
650C22×Q8—24no—
651C22×Q8—24no—
652C22×Q8—212no—
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×Q8C2411yescharacteristic
667C22×D4C2413yes—
668C22×D4C2413yes—
669C22×D4C2413yes—
670C22×D4C2411yescharacteristic
671C22×D4C2411yescharacteristic
672C22×D4C2413yes—
673C22×D4C2413yes—
674C22×D4C2411yescharacteristic
675C22×D4C2413yes—
676C22×D4C2413yes—
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2416yes—
680C23×C4C2413yes—
681C23×C4C2413yes—
682C23×C4C2413yes—
683C23×C4C2413yes—
684C23×C4C2413yes—
685C23×C4C2416yes—
686C23×C4C2413yes—
687C23×C4C2416yes—
688C23×C4C2411yescharacteristic
689C4⋊Q8—212no—
690C4⋊Q8—46no—
691C4⋊Q8—46no—
692#127—46no—
693#126—86no—
694#126—86no—
695#125—46no—
696#125—46no—
697#124—212no—
698#124—46no—
699#124—46no—
700#124—46no—
701#124—86no—
702C22⋊Q8—212no—
703C22⋊Q8—212no—
704C22⋊Q8—212no—
705C22⋊Q8—46no—
706C22⋊Q8—46no—
707C22⋊Q8—46no—
708C22⋊Q8—46no—
709C22⋊Q8—46no—
710#121—212no—
711#121—46no—
712#121—46no—
713#121—46no—
714#121—46no—
715#121—46no—
716#121—86no—
717C4×Q8—24no—
718C4×Q8—24no—
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—46no—
728C4×Q8—46no—
729C4×Q8—46no—
730C4×Q8—46no—
731C4×Q8—46no—
732C4×Q8—46no—
733C4×Q8—46no—
734C4×D4—212no—
735C4×D4—212no—
736C4×D4—46no—
737C4×D4—46no—
738C4×D4—46no—
739C4×D4—46no—
740C4×D4—46no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—86no—
744#117—46no—
745#117—46no—
746#117—46no—
747#117—46no—
748#117—46no—
749C2×C4⋊C4—46no—
750C2×C4⋊C4—46no—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2416yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2416yes—
782C2×C4⋊C4C2416yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2416yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2416yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2416yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2416yes—
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2416yes—
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2416yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2411yescharacteristic
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2411yescharacteristic
839C2×C22⋊C4C2411yescharacteristic
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2411yescharacteristic
843C2×C22⋊C4C2411yescharacteristic
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2416yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2416yes—
854C2×C22⋊C4C2416yes—
855C2×C42—46no—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2416yes—
867C2×C42C2416yes—
868C2×C42C2416yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2416yes—
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2413yes—
883#95C2411yescharacteristic
884#95C2413yes—
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2416yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2416yes—
897#95C2416yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2416yes—
902#95C2413yes—
903#95C2416yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2411yescharacteristic
915#95C2411yescharacteristic
916#95C2416yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2416yes—
927#95C2416yes—
928#95C2416yes—
929#95C2416yes—
930C24C2511yescharacteristic
931C24C2513yes—
932C24C2511yescharacteristic
933C24C2513yes—
934C24C2511yescharacteristic
935#41—448no—
936#41—448no—
937#41—448no—
938#41—416no—
939#41—416no—
940C2×Q8—232no—
941C2×Q8—26no—
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—43no—
951C2×Q8—43no—
952C2×Q8—43no—
953C2×Q8—43no—
954C2×Q8—43no—
955C2×Q8—448no—
956C2×Q8—416no—
957C2×Q8—416no—
958C2×Q8C2×#41112yes—
959C2×Q8C2×#4114yes—
960C2×Q8H(5,𝔽2)14yes—
961C2×Q8H(5,𝔽2)14yes—
962C2×D4—22no—
963C2×D4—26no—
964C2×D4—22no—
965C2×D4—26no—
966C2×D4—26no—
967C2×D4—26no—
968C2×D4—26no—
969C2×D4—26no—
970C2×D4—26no—
971C2×D4—26no—
972C2×D4—26no—
973C2×D4—41no—
974C2×D4—43no—
975C2×D4—41no—
976C2×D4—41no—
977C2×D4—41no—
978C2×D4—43no—
979C2×D4—41no—
980C2×D4—43no—
981C2×D4—43no—
982C2×D4—41no—
983C2×D4—43no—
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—
993C2×D4—43no—
994C2×D4—43no—
995C2×D4—43no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—46no—
999C2×D4—46no—
1000C2×D4—46no—
1001C22×C4—26no—
1002C22×C4—26no—
1003C22×C4—26no—
1004C22×C4—26no—
1005C22×C4—212no—
1006C22×C4—26no—
1007C22×C4—26no—
1008C22×C4—26no—
1009C22×C4—26no—
1010C22×C4—26no—
1011C22×C4—26no—
1012C22×C4—26no—
1013C22×C4—26no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—46no—
1020C22×C4—46no—
1021C22×C4—43no—
1022C22×C4—43no—
1023C22×C4—43no—
1024C22×C4—46no—
1025C22×C4—46no—
1026C22×C4—46no—
1027C22×C4C2×#41112yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2511yescharacteristic
1031C22×C4C2513yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2513yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2513yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2513yes—
1040C22×C4C2513yes—
1041C22×C4C2513yes—
1042C22×C4C2513yes—
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2513yes—
1046C22×C4C2513yes—
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2513yes—
1053C22×C4C2513yes—
1054C4⋊C4—26no—
1055C4⋊C4—26no—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—212no—
1059C4⋊C4—26no—
1060C4⋊C4—26no—
1061C4⋊C4—26no—
1062C4⋊C4—26no—
1063C4⋊C4—26no—
1064C4⋊C4—26no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—43no—
1068C4⋊C4—46no—
1069C4⋊C4—41no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—43no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—46no—
1078C4⋊C4—41no—
1079C4⋊C4—43no—
1080C4⋊C4—41no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—41no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—46no—
1091C4⋊C4—41no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—46no—
1095C4⋊C4—46no—
1096C4⋊C4—46no—
1097C4⋊C4—43no—
1098C4⋊C4—43no—
1099C4⋊C4—46no—
1100C22⋊C4—22no—
1101C22⋊C4—26no—
1102C22⋊C4—26no—
1103C22⋊C4—26no—
1104C22⋊C4—212no—
1105C22⋊C4—43no—
1106C22⋊C4—46no—
1107C22⋊C4—46no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—43no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—46no—
1124C22⋊C4—43no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—43no—
1134C22⋊C4—41no—
1135C22⋊C4—41no—
1136C22⋊C4—41no—
1137C22⋊C4—43no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—46no—
1146C22⋊C4—46no—
1147C22⋊C4—46no—
1148C22⋊C4—46no—
1149C22⋊C4—43no—
1150C22⋊C4—46no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—46no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—43no—
1157C22⋊C4—43no—
1158C42—26no—
1159C42—26no—
1160C42—26no—
1161C42—26no—
1162C42—26no—
1163C42—26no—
1164C42—26no—
1165C42—26no—
1166C42—26no—
1167C42—26no—
1168C42—43no—
1169C42—43no—
1170C42—46no—
1171C42—46no—
1172C42—46no—
1173C42—46no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—23no—
1182C23—21no—
1183C23—23no—
1184C23—21no—
1185C23—23no—
1186C23—21no—
1187C23—23no—
1188C23—21no—
1189C23—23no—
1190C23—21no—
1191C23—23no—
1192C23—21no—
1193C23—23no—
1194C23—23no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—23no—
1199C23—23no—
1200C23—23no—
1201C23—23no—
1202C23—21no—
1203C23—23no—
1204C23—21no—
1205C23—23no—
1206C23—21no—
1207C23—21no—
1208C23C22×#4112yes—
1209C23C2611yescharacteristic
1210Q8—224no—
1211Q8—412no—
1212Q8—412no—
1213Q8—412no—
1214Q8—86no—
1215Q8#538116yes—
1216D4—412no—
1217D4—44no—
1218D4—412no—
1219D4—44no—
1220D4—412no—
1221D4—44no—
1222D4—412no—
1223D4—412no—
1224D4—86no—
1225D4—86no—
1226D4—86no—
1227D4—86no—
1228D4—166no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—224no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—21no—
1237C2×C4—23no—
1238C2×C4—21no—
1239C2×C4—23no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
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—23no—
1257C2×C4—21no—
1258C2×C4—23no—
1259C2×C4—21no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—23no—
1283C2×C4—21no—
1284C2×C4—23no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—23no—
1288C2×C4—23no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—23no—
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—23no—
1301C2×C4—21no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—424no—
1305C2×C4—44no—
1306C2×C4—412no—
1307C2×C4—412no—
1308C2×C4—412no—
1309C2×C4—412no—
1310C2×C4—86no—
1311C2×C4—166no—
1312C2×C4C22×#4116yes—
1313C2×C4C22×#4116yes—
1314C2×C4C2×H(5,𝔽2)16yes—
1315C2×C4C2×H(5,𝔽2)16yes—
1316C22—22no—
1317C22—22no—
1318C22—22no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—43no—
1327C22—43no—
1328C22—43no—
1329C22—41no—
1330C22—43no—
1331C22—43no—
1332C22—41no—
1333C22—41no—
1334C22—43no—
1335C22—43no—
1336C22—43no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—43no—
1341C22—41no—
1342C22—43no—
1343C22—43no—
1344C22—41no—
1345C22—41no—
1346C22—43no—
1347C22—43no—
1348C22—41no—
1349C22—41no—
1350C22—43no—
1351C22C23×#4111yescharacteristic
1352C22C22×H(5,𝔽2)11yescharacteristic
1353C22C22×H(5,𝔽2)11yescharacteristic
1354C22H(7,𝔽2)11yescharacteristic
1355C222−1+611yescharacteristic
1356C222−1+611yescharacteristic
1357C222−1+611yescharacteristic
1358C4—26no—
1359C4—41no—
1360C4—41no—
1361C4—43no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—43no—
1366C4—41no—
1367C4—41no—
1368C4—43no—
1369C4—43no—
1370C4—43no—
1371C4—43no—
1372C4—43no—
1373C4—43no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—43no—
1378C4—43no—
1379C4—41no—
1380C4—41no—
1381C4—43no—
1382C4—43no—
1383C4C2×#538112yes—
1384C2—42no—
1385C2—81no—
1386C2—81no—
1387C2—83no—
1388C2—83no—
1389C2C22×#53811yescharacteristic
1390C2#6285011yescharacteristic
1391C2#6285111yescharacteristic
1392C2#6304411yescharacteristic
1393C2#6304411yescharacteristic
1394C2#6305211yescharacteristic
1395C2#6305211yescharacteristic
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. #42903C2semidirect
2. #42893C2semidirect
3. #42874C2semidirect
4. #42855C2semidirect
5. #42852C2semidirect
6. #42844C2semidirect
7. #42835C2semidirect
8. #42834C2semidirect
9. #42520C2semidirect
10. #42503C2semidirect
11. #42462C2semidirect
12. #42449C2semidirect
13. #37516C2semidirect
14. #37500C2semidirect
15. #37498C2semidirect
16. #36670C2semidirect
17. #36049C2semidirect
18. #35983C2semidirect
19. #35920C2semidirect
20. #35910C2semidirect
21. #35898C2semidirect
22. #35845C2semidirect
23. #35831C2semidirect
24. #35801C2semidirect
25. #35771C2semidirect
26. #35771C2semidirect
27. #35757C2semidirect
28. #35687C2semidirect
29. #34294C2semidirect
30. #34291C2semidirect
31. #34257C2semidirect

Maximal subgroups

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

subgroupindex
#429032
#428932
#428742
#428552
#428522
#428442
#428352
#428342
#425202
#425032
#424622
#424492
#375162
#375002
#374982
#366702
#360492
#359832
#359202
#359102
#358982
#358452
#358312
#358012
#357712
#357572
#356872
#342942
#342912
#342572