Finite Group Databasebeta

← #8726700

Subgroups — #8726700

Order 512.

4098 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59433C213yesmaximal, complemented
2#59202C213yesmaximal, complemented
3#59197C213yesmaximal, complemented
4#57646C216yesmaximal, complemented
5#57400C212yesmaximal
6#55887C216yesmaximal, complemented
7#53133C213yesmaximal, complemented
8#52301C211yesmaximal, characteristic
9#47222C216yesmaximal, complemented
10#45058C213yesmaximal, complemented
11#44491C216yesmaximal, complemented
12#42743C213yesmaximal, complemented
13#41839C216yesmaximal, complemented
14#39935C213yesmaximal, complemented
15#39154C213yesmaximal, complemented
16#39026C213yesmaximal, complemented
17#35855C213yesmaximal, complemented
18#2863C2211yescharacteristic, complemented
19#2848C2211yescharacteristic, complemented
20#2848C2211yescharacteristic, complemented
21#2838C2216yescomplemented
22#2838C2216yescomplemented
23#2833C2216yescomplemented
24#2831C2216yescomplemented
25#2814C2216yes—
26#2804C2213yes—
27#2798C2216yescomplemented
28#2793C2216yescomplemented
29#2793C2216yescomplemented
30#2791C2216yescomplemented
31#2789C2216yescomplemented
32#2789C2216yescomplemented
33#2788C2216yescomplemented
34#2787C2216yescomplemented
35#2786C2216yes—
36#2786C2216yes—
37#2782C2213yes—
38#2782C2213yes—
39#2779C2216yes—
40#2767C2216yescomplemented
41#2765C2216yescomplemented
42#2763C2216yescomplemented
43#2762C2216yescomplemented
44#2759C2216yescomplemented
45#2747C2216yescomplemented
46#2745C2216yescomplemented
47#2745C2216yescomplemented
48#2743C2216yes—
49#2741C2216yes—
50#2737C2216yes—
51#2735C2216yescomplemented
52#2735C2216yescomplemented
53#2718C2216yes—
54#2715C2216yes—
55#2700C2216yes—
56#2697C2216yes—
57#2689C2216yescomplemented
58#2684C2213yes—
59#2684C2216yes—
60#2684C2213yes—
61#2679C2211yescharacteristic
62#2653C2216yes—
63#2652C2216yescomplemented
64#2650C2216yescomplemented
65#2650C2216yescomplemented
66#2647C2213yescomplemented
67#2645C2216yescomplemented
68#2645C2211yescharacteristic, complemented
69#2643C2216yes—
70#2605C2216yescomplemented
71#2597C2216yes—
72#2596C2216yescomplemented
73#2594C2216yescomplemented
74#2587C2216yescomplemented
75#2584C2213yescomplemented
76#2581C2213yescomplemented
77#2576C2216yes—
78#2576C2216yes—
79#2576C2216yes—
80#2574C2216yescomplemented
81#2569C2216yescomplemented
82#2567C2213yescomplemented
83#2562C2213yes—
84#2547C2213yes—
85#2538C2213yes—
86#2533C2216yescomplemented
87#2531C2216yes—
88#2530C2216yescomplemented
89#2528C2216yescomplemented
90#2528C2216yescomplemented
91#2527C2216yescomplemented
92#2527C2216yescomplemented
93#2527C2216yescomplemented
94#2525C2216yescomplemented
95#2521C2216yes—
96#2520C2216yescomplemented
97#2517C2216yescomplemented
98#2510C2216yes—
99#2499C2216yescomplemented
100#2498C2216yes—
101#2497C2213yescomplemented
102#2496C2213yescomplemented
103#2495C2213yescomplemented
104#2494C2213yescomplemented
105#2494C2213yescomplemented
106#2494C2213yescomplemented
107#2494C2216yescomplemented
108#2494C2213yescomplemented
109#2494C2213yescomplemented
110#2493C2216yescomplemented
111#2492C2213yescomplemented
112#2489C2213yescomplemented
113#2487C2213yes—
114#2486C2213yes—
115#2485C2213yes—
116#2485C2213yes—
117#2480C2216yescomplemented
118#2474C2216yes—
119#2474C2216yes—
120#2472C2216yes—
121#2442C2213yescomplemented
122#2442C2213yescomplemented
123#2441C2213yescomplemented
124#2440C2213yescomplemented
125#2439C2213yescomplemented
126#2439C2213yescomplemented
127#2421C2213yescomplemented
128#2421C2213yescomplemented
129#2417C2213yes—
130#2415C2213yes—
131#2412C2216yes—
132#2401C2216yescomplemented
133#2398C2213yes—
134#2398C2213yes—
135#2373C2216yescomplemented
136#2372C2216yes—
137#2362C2213yescomplemented
138#2360C2213yescomplemented
139#2355C2213yescomplemented
140#2352C2213yes—
141#2352C2213yes—
142#2352C2213yes—
143#2346C2213yescomplemented
144#2346C2213yescomplemented
145#2345C2213yescomplemented
146#2344C2213yescomplemented
147#2342C2216yescomplemented
148#2335C2216yes—
149#2331C2213yescomplemented
150#2329C2216yescomplemented
151#2314C2216yescomplemented
152C4×#125C2213yescomplemented
153C4×#124C2213yes—
154C4×#120C2213yes—
155C4×#120C2213yes—
156#2280C2213yescomplemented
157C2×#380C2213yescomplemented
158#2276C2211yescharacteristic, complemented
159C24×C4C2311yescharacteristic
160C24×C4C2311yescharacteristic
161C2×C4⋊Q8C2313yes—
162C2×#126C2316yes—
163C2×#125C2313yes—
164C2×#124C2316yes—
165C2×#124C2313yes—
166C2×#123C2316yes—
167C2×C22⋊Q8C2316yes—
168C2×C22⋊Q8C2313yes—
169C2×C22⋊Q8C2313yes—
170C2×#120C2313yes—
171C2×#120C2313yes—
172C2×C4×Q8C2313yes—
173C2×C4×Q8C2313yes—
174C2×C4×D4C2313yes—
175C2×C4×D4C2313yes—
176C2×C4×D4C2313yes—
177C2×#117C2316yes—
178C2×#117C2313yes—
179C2×#117C2313yes—
180C22×C4⋊C4C2313yes—
181C22×C4⋊C4C2313yes—
182C22×C22⋊C4C2316yes—
183#401C2316yes—
184#401C2316yes—
185#401C2316yes—
186#401C2316yes—
187#401C2316yes—
188#401C2312yes—
189#400C2316yes—
190#400C2316yes—
191#400C2316yes—
192#400C2316yes—
193#400C2316yes—
194#400C2313yes—
195#400C2316yes—
196#400C2316yes—
197#400C2316yes—
198#400C2316yes—
199#400C2316yes—
200#400C2316yes—
201#400C2316yes—
202#400C2313yes—
203#400C2316yes—
204#400C2316yes—
205#400C2316yes—
206#400C2313yes—
207#400C2313yes—
208#399C2316yes—
209#399C2316yes—
210#398C2316yes—
211#398C2316yes—
212#398C2316yes—
213#398C2316yes—
214#398C2316yes—
215#398C2316yes—
216#398C2316yes—
217#398C2316yes—
218#397C2316yes—
219#397C2316yes—
220#397C2316yes—
221#397C2316yes—
222#397C2316yes—
223#397C2313yes—
224#397C2316yes—
225#397C2316yes—
226#397C2316yes—
227#397C2316yes—
228#397C2316yes—
229#397C2316yes—
230#397C2316yes—
231#397C2316yes—
232#397C2313yes—
233#397C2313yes—
234#397C2313yes—
235#397C2316yes—
236#397C2316yes—
237#397C2316yes—
238#396C2316yes—
239#396C2316yes—
240#396C2316yes—
241#396C2316yes—
242#396C2316yes—
243#396C2316yes—
244#396C2316yes—
245#395C2316yes—
246#395C2316yes—
247#395C2316yes—
248#395C2316yes—
249#395C2316yes—
250#394C2316yes—
251#394C2316yes—
252#394C2316yes—
253#394C2313yes—
254#394C2313yes—
255#394C2316yes—
256#394C2313yes—
257#394C2313yes—
258#393C2313yes—
259#393C2313yes—
260#393C2313yes—
261#393C2316yes—
262#393C2316yes—
263#393C2316yes—
264#393C2313yes—
265#391C2316yes—
266#391C2316yes—
267#391C2316yes—
268#391C2313yes—
269#391C2313yes—
270#391C2316yes—
271#391C2316yes—
272#391C2316yes—
273#391C2316yes—
274#391C2316yes—
275#391C2313yes—
276#390C2316yes—
277#390C2313yes—
278#389C2313yes—
279#389C2313yes—
280#389C2313yes—
281#389C2313yes—
282#389C2313yes—
283#389C2313yes—
284#389C2316yes—
285#389C2316yes—
286#389C2313yes—
287#389C2316yes—
288#389C2313yes—
289#389C2313yes—
290#389C2313yes—
291#389C2316yes—
292#389C2316yes—
293#389C2316yes—
294#388C2316yes—
295#388C2316yes—
296#388C2313yes—
297#388C2316yes—
298#388C2316yes—
299#388C2316yes—
300#388C2316yes—
301#388C2316yes—
302#388C2316yes—
303#388C2316yes—
304#388C2316yes—
305#388C2316yes—
306#388C2316yes—
307#388C2316yes—
308#388C2316yes—
309#388C2316yes—
310#388C2316yes—
311#388C2313yes—
312#388C2316yes—
313#388C2313yes—
314#388C2316yes—
315#388C2316yes—
316#388C2316yes—
317#388C2316yes—
318#388C2316yes—
319#388C2316yes—
320#388C2316yes—
321#388C2313yes—
322#388C2316yes—
323#387C2316yes—
324#387C2316yes—
325#387C2316yes—
326#387C2316yes—
327#387C2316yes—
328#387C2316yes—
329#387C2316yes—
330#387C2316yes—
331#387C2316yes—
332#387C2316yes—
333#387C2316yes—
334#387C2316yes—
335#387C2316yes—
336#387C2316yes—
337#387C2316yes—
338#387C2316yes—
339#387C2316yes—
340#387C2316yes—
341#387C2316yes—
342#387C2316yes—
343#387C2316yes—
344#387C2316yes—
345#387C2316yes—
346#387C2316yes—
347#387C2316yes—
348#387C2316yes—
349#387C2316yes—
350#387C2316yes—
351#387C2316yes—
352#387C2316yes—
353#387C2316yes—
354#387C2316yes—
355#386C2313yes—
356#386C2313yes—
357#386C2316yes—
358#386C2316yes—
359#386C2316yes—
360#386C2316yes—
361#386C2313yes—
362#386C2316yes—
363#386C2313yes—
364#386C2313yes—
365#386C2313yes—
366#385C2313yes—
367#385C2316yes—
368#385C2316yes—
369#385C2316yes—
370#385C2313yes—
371#385C2316yes—
372#385C2313yes—
373#385C2316yes—
374#385C2316yes—
375#385C2316yes—
376#385C2313yes—
377#385C2313yes—
378#385C2313yes—
379#384C2316yes—
380#384C2313yes—
381#383C2316yes—
382#383C2312yes—
383#382C2313yes—
384#382C2316yes—
385#382C2316yes—
386#382C2316yes—
387#382C2313yes—
388#382C2313yes—
389#382C2313yes—
390#381C2316yes—
391#381C2316yes—
392#381C2316yes—
393#380C2313yes—
394#380C2313yes—
395#380C2313yes—
396#380C2313yes—
397#380C2316yes—
398#380C2316yes—
399#380C2316yes—
400#380C2316yes—
401#380C2313yes—
402#380C2316yes—
403#380C2313yes—
404#380C2313yes—
405#380C2313yes—
406#380C2313yes—
407#380C2313yes—
408#380C2316yes—
409#379C2312yes—
410#379C2312yes—
411#379C2313yes—
412#379C2316yes—
413#379C2313yes—
414C4×C4⋊C4C2313yes—
415C4×C4⋊C4C2316yes—
416C4×C4⋊C4C2313yes—
417C4×C4⋊C4C2316yes—
418C4×C4⋊C4C2313yes—
419C4×C4⋊C4C2316yes—
420C4×C4⋊C4C2316yes—
421C4×C4⋊C4C2313yes—
422C4×C4⋊C4C2316yes—
423C4×C4⋊C4C2313yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428C4×C22⋊C4C2316yes—
429C4×C22⋊C4C2316yes—
430C4×C22⋊C4C2316yes—
431C4×C22⋊C4C2313yes—
432C4×C22⋊C4C2313yes—
433C4×C22⋊C4C2313yes—
434C4×C22⋊C4C2313yes—
435C4×C22⋊C4C2313yes—
436C4×C22⋊C4C2313yes—
437#376C2311yescharacteristic
438#376C2316yes—
439#376C2316yes—
440#376C2311yescharacteristic
441#376C2312yes—
442C2×#95C2316yes—
443C43C2311yescharacteristic
444C25C2411yescharacteristic
445C25C2411yescharacteristic
446C22×Q8C2411yescharacteristic
447C22×Q8C2413yes—
448C22×Q8C2416yes—
449C22×D4C2413yes—
450C22×D4C2413yes—
451C22×D4C2413yes—
452C23×C4—46no—
453C23×C4—46no—
454C23×C4C2413yes—
455C23×C4C2413yes—
456C23×C4C2416yes—
457C23×C4C2416yes—
458C23×C4C2413yes—
459C23×C4C2413yes—
460C4⋊Q8—46no—
461#126—412no—
462#125—46no—
463#124—412no—
464#124—46no—
465#123—412no—
466C22⋊Q8—412no—
467C22⋊Q8—46no—
468C22⋊Q8—46no—
469#120—46no—
470#120—46no—
471C4×Q8—46no—
472C4×Q8—46no—
473C4×D4—46no—
474C4×D4—46no—
475C4×D4—46no—
476#117—412no—
477#117—46no—
478#117—46no—
479C2×C4⋊C4—46no—
480C2×C4⋊C4—46no—
481C2×C4⋊C4C2413yes—
482C2×C4⋊C4C2413yes—
483C2×C4⋊C4C2413yes—
484C2×C4⋊C4C2413yes—
485C2×C4⋊C4C2413yes—
486C2×C4⋊C4C2416yes—
487C2×C4⋊C4C2416yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C2416yes—
490C2×C4⋊C4C2413yes—
491C2×C4⋊C4C2413yes—
492C2×C4⋊C4C2413yes—
493C2×C4⋊C4C2416yes—
494C2×C4⋊C4C2413yes—
495C2×C4⋊C4C2413yes—
496C2×C4⋊C4C2413yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2416yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C2416yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C2416yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2416yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2416yes—
512C2×C22⋊C4—412no—
513C2×C22⋊C4C2416yes—
514C2×C22⋊C4C2416yes—
515C2×C22⋊C4C2413yes—
516C2×C22⋊C4C2413yes—
517C2×C22⋊C4C2416yes—
518C2×C22⋊C4C2413yes—
519C2×C22⋊C4C2416yes—
520C2×C22⋊C4C2416yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2416yes—
523C2×C22⋊C4C2413yes—
524C2×C22⋊C4C2413yes—
525C2×C22⋊C4C2413yes—
526C2×C22⋊C4C2413yes—
527C2×C22⋊C4C2413yes—
528C2×C22⋊C4C2413yes—
529C2×C22⋊C4C2413yes—
530C2×C22⋊C4C2413yes—
531C2×C22⋊C4C2413yes—
532C2×C22⋊C4C2413yes—
533C2×C22⋊C4C2413yes—
534C2×C22⋊C4C2416yes—
535C2×C22⋊C4C2416yes—
536C2×C22⋊C4C2416yes—
537C2×C22⋊C4C2416yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2413yes—
541C2×C22⋊C4C2413yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2413yes—
544C2×C22⋊C4C2413yes—
545C2×C42C2413yes—
546C2×C42C2413yes—
547C2×C42C2413yes—
548C2×C42C2416yes—
549C2×C42C2416yes—
550C2×C42C2416yes—
551C2×C42C2416yes—
552C2×C42C2416yes—
553C2×C42C2413yes—
554C2×C42C2416yes—
555C2×C42C2416yes—
556C2×C42C2411yescharacteristic
557C2×C42C2416yes—
558#95C2416yes—
559#95C2416yes—
560#95C2416yes—
561#95C2416yes—
562#95C2411yescharacteristic
563#95C2413yes—
564#95C2413yes—
565#95C2416yes—
566#95C2416yes—
567#95C2416yes—
568#95C2416yes—
569#95C2413yes—
570#95C2416yes—
571#95C2416yes—
572#95C2416yes—
573#95C2413yes—
574#95C2411yescharacteristic
575#95C2413yes—
576#95C2416yes—
577#95C2416yes—
578#95C2416yes—
579#95C2416yes—
580#95C2416yes—
581#95C2416yes—
582#95C2413yes—
583#95C2413yes—
584#95C2413yes—
585#95C2413yes—
586#95C2416yes—
587#95C2413yes—
588#95C2413yes—
589#95C2413yes—
590#95C2413yes—
591#95C2413yes—
592#95C2416yes—
593#95C2416yes—
594#95C2416yes—
595#95C2416yes—
596#95C2416yes—
597#95C2416yes—
598#95C2416yes—
599#95C2416yes—
600#95C2416yes—
601#95C2416yes—
602#95C2416yes—
603#95C2416yes—
604#95C2416yes—
605#95C2416yes—
606#95C2416yes—
607#95C2416yes—
608#95C2416yes—
609C24—26no—
610C24—43no—
611C24—43no—
612C24—43no—
613C24—41no—
614C24—41no—
615C24C2513yes—
616C24C2513yes—
617C2×Q8—26no—
618C2×Q8—43no—
619C2×Q8—43no—
620C2×Q8—43no—
621C2×Q8—46no—
622C2×Q8—46no—
623C2×Q8—46no—
624C2×D4—26no—
625C2×D4—26no—
626C2×D4—26no—
627C2×D4—43no—
628C2×D4—43no—
629C2×D4—43no—
630C2×D4—43no—
631C2×D4—43no—
632C2×D4—43no—
633C22×C4—212no—
634C22×C4—26no—
635C22×C4—26no—
636C22×C4—26no—
637C22×C4—26no—
638C22×C4—26no—
639C22×C4—26no—
640C22×C4—46no—
641C22×C4—46no—
642C22×C4—43no—
643C22×C4—43no—
644C22×C4—43no—
645C22×C4—43no—
646C22×C4—43no—
647C22×C4—43no—
648C22×C4—46no—
649C22×C4—46no—
650C22×C4—46no—
651C22×C4—88no—
652C22×C4—88no—
653C22×C4C2513yes—
654C22×C4C2513yes—
655C22×C4C2513yes—
656C22×C4C2513yes—
657C22×C4C2516yes—
658C22×C4C2513yes—
659C22×C4C2513yes—
660C22×C4C2516yes—
661C22×C4C2516yes—
662C22×C4C2516yes—
663C22×C4C2512yes—
664C22×C4C2513yes—
665C22×C4C2516yes—
666C22×C4C2513yes—
667C22×C4C2511yescharacteristic
668C4⋊C4—26no—
669C4⋊C4—26no—
670C4⋊C4—26no—
671C4⋊C4—26no—
672C4⋊C4—26no—
673C4⋊C4—46no—
674C4⋊C4—46no—
675C4⋊C4—46no—
676C4⋊C4—46no—
677C4⋊C4—46no—
678C4⋊C4—46no—
679C4⋊C4—43no—
680C4⋊C4—43no—
681C4⋊C4—43no—
682C4⋊C4—43no—
683C4⋊C4—43no—
684C4⋊C4—43no—
685C4⋊C4—46no—
686C4⋊C4—46no—
687C4⋊C4—46no—
688C4⋊C4—46no—
689C4⋊C4—46no—
690C4⋊C4—46no—
691C4⋊C4—46no—
692C4⋊C4—46no—
693C4⋊C4—46no—
694C4⋊C4—46no—
695C4⋊C4—46no—
696C4⋊C4—46no—
697C4⋊C4—46no—
698C4⋊C4—46no—
699C22⋊C4—212no—
700C22⋊C4—212no—
701C22⋊C4—26no—
702C22⋊C4—26no—
703C22⋊C4—212no—
704C22⋊C4—26no—
705C22⋊C4—46no—
706C22⋊C4—46no—
707C22⋊C4—43no—
708C22⋊C4—43no—
709C22⋊C4—46no—
710C22⋊C4—46no—
711C22⋊C4—46no—
712C22⋊C4—43no—
713C22⋊C4—43no—
714C22⋊C4—43no—
715C22⋊C4—43no—
716C22⋊C4—43no—
717C22⋊C4—43no—
718C22⋊C4—43no—
719C22⋊C4—43no—
720C22⋊C4—43no—
721C22⋊C4—43no—
722C22⋊C4—43no—
723C22⋊C4—46no—
724C22⋊C4—46no—
725C22⋊C4—46no—
726C22⋊C4—46no—
727C22⋊C4—43no—
728C22⋊C4—43no—
729C22⋊C4—46no—
730C22⋊C4—46no—
731C42—26no—
732C42—26no—
733C42—26no—
734C42—46no—
735C42—41no—
736C42—46no—
737C42—46no—
738C42—46no—
739C42—46no—
740C42—46no—
741C42—43no—
742C42—46no—
743C42—46no—
744C23—23no—
745C23—23no—
746C23—23no—
747C23—23no—
748C23—23no—
749C23—23no—
750C23—23no—
751C23—23no—
752C23—23no—
753C23—23no—
754C23—23no—
755C23—23no—
756C23—23no—
757C23—412no—
758C23—86no—
759C23—82no—
760C23—82no—
761C23—86no—
762C23—86no—
763C23#58516yes—
764C23C2611yescharacteristic
765Q8—44no—
766Q8—86no—
767Q8—166no—
768D4—86no—
769D4—86no—
770D4—86no—
771C2×C4—23no—
772C2×C4—23no—
773C2×C4—23no—
774C2×C4—23no—
775C2×C4—23no—
776C2×C4—23no—
777C2×C4—23no—
778C2×C4—23no—
779C2×C4—26no—
780C2×C4—23no—
781C2×C4—23no—
782C2×C4—26no—
783C2×C4—26no—
784C2×C4—23no—
785C2×C4—23no—
786C2×C4—26no—
787C2×C4—26no—
788C2×C4—26no—
789C2×C4—26no—
790C2×C4—23no—
791C2×C4—26no—
792C2×C4—26no—
793C2×C4—26no—
794C2×C4—26no—
795C2×C4—26no—
796C2×C4—23no—
797C2×C4—23no—
798C2×C4—23no—
799C2×C4—23no—
800C2×C4—26no—
801C2×C4—26no—
802C2×C4—23no—
803C2×C4—23no—
804C2×C4—23no—
805C2×C4—23no—
806C2×C4—23no—
807C2×C4—26no—
808C2×C4—23no—
809C2×C4—23no—
810C2×C4—26no—
811C2×C4—412no—
812C2×C4—412no—
813C2×C4—812no—
814C2×C4—86no—
815C2×C4—86no—
816C2×C4—166no—
817C2×C4#58516yes—
818C22—26no—
819C22—26no—
820C22—26no—
821C22—43no—
822C22—43no—
823C22—43no—
824C22—43no—
825C22—43no—
826C22—43no—
827C22—43no—
828C22—43no—
829C22—43no—
830C22—43no—
831C22—43no—
832C22—88no—
833C22—88no—
834C22C2×#58513yes—
835C22C2×#58513yes—
836C222−1+611yescharacteristic
837C4—43no—
838C4—43no—
839C4—42no—
840C4—43no—
841C4—46no—
842C4—46no—
843C4—43no—
844C4—43no—
845C4—46no—
846C4—46no—
847C4—46no—
848C4—43no—
849C4—43no—
850C4—43no—
851C4#356814yes—
852C2—46no—
853C2—83no—
854C2C2×#356811yescharacteristic
855C2#6291113yes—
856C2#6302713yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2679C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59433C2semidirect
2. #59202C2semidirect
3. #59197C2semidirect
4. #57646C2semidirect
6. #55887C2semidirect
7. #53133C2semidirect
9. #47222C2semidirect
10. #45058C2semidirect
11. #44491C2semidirect
12. #42743C2semidirect
13. #41839C2semidirect
14. #39935C2semidirect
15. #39154C2semidirect
16. #39026C2semidirect
17. #35855C2semidirect
18. #2863C22semidirect
19. #2848C22semidirect
20. #2848C22semidirect
21. #2838C22semidirect
22. #2838C22semidirect
23. #2833C22semidirect
24. #2831C22semidirect
27. #2798C22semidirect
28. #2793C22semidirect
29. #2793C22semidirect
30. #2791C22semidirect
31. #2789C22semidirect
32. #2789C22semidirect
33. #2788C22semidirect
34. #2787C22semidirect
40. #2767C22semidirect
41. #2765C22semidirect
42. #2763C22semidirect
43. #2762C22semidirect
44. #2759C22semidirect
45. #2747C22semidirect
46. #2745C22semidirect
47. #2745C22semidirect
51. #2735C22semidirect
52. #2735C22semidirect
57. #2689C22semidirect
63. #2652C22semidirect
64. #2650C22semidirect
65. #2650C22semidirect
66. #2647C22semidirect
67. #2645C22semidirect
68. #2645C22semidirect
70. #2605C22semidirect
72. #2596C22semidirect
73. #2594C22semidirect
74. #2587C22semidirect
75. #2584C22semidirect
76. #2581C22semidirect
80. #2574C22semidirect
81. #2569C22semidirect
82. #2567C22semidirect
86. #2533C22semidirect
88. #2530C22semidirect
89. #2528C22semidirect
90. #2528C22semidirect
91. #2527C22semidirect
92. #2527C22semidirect
93. #2527C22semidirect
94. #2525C22semidirect
96. #2520C22semidirect
97. #2517C22semidirect
99. #2499C22semidirect
101. #2497C22semidirect
102. #2496C22semidirect
103. #2495C22semidirect
104. #2494C22semidirect
105. #2494C22semidirect
106. #2494C22semidirect
107. #2494C22semidirect
108. #2494C22semidirect
109. #2494C22semidirect
110. #2493C22semidirect
111. #2492C22semidirect
112. #2489C22semidirect
117. #2480C22semidirect
121. #2442C22semidirect
122. #2442C22semidirect
123. #2441C22semidirect
124. #2440C22semidirect
125. #2439C22semidirect
126. #2439C22semidirect
127. #2421C22semidirect
128. #2421C22semidirect
132. #2401C22semidirect
135. #2373C22semidirect
137. #2362C22semidirect
138. #2360C22semidirect
139. #2355C22semidirect
143. #2346C22semidirect
144. #2346C22semidirect
145. #2345C22semidirect
146. #2344C22semidirect
147. #2342C22semidirect
149. #2331C22semidirect
150. #2329C22semidirect
151. #2314C22semidirect
152. C4×#125C22semidirect
156. #2280C22semidirect
157. C2×#380C22semidirect
158. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#594332
#592022
#591972
#576462
#574002
#558872
#531332
#523012
#472222
#450582
#444912
#427432
#418392
#399352
#391542
#390262
#358552