Finite Group Databasebeta

← #8096593

Subgroups — #8096593

Order 512.

4757 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52641C214yesmaximal, complemented
2#52563C214yesmaximal, complemented
3#52559C214yesmaximal, complemented
4#52498C214yesmaximal, complemented
5#52406C212yesmaximal, complemented
6#52162C212yesmaximal, complemented
7#52103C211yesmaximal, characteristic
8#46282C211yesmaximal, characteristic, complemented
9#46281C212yesmaximal, complemented
10#46227C214yesmaximal, complemented
11#46115C214yesmaximal, complemented
12#45963C212yesmaximal, complemented
13#45958C212yesmaximal, complemented
14#45947C212yesmaximal, complemented
15#45821C214yesmaximal, complemented
16#45491C212yesmaximal, complemented
17#45453C214yesmaximal, complemented
18#36371C212yesmaximal, complemented
19#36370C211yesmaximal, characteristic, complemented
20#36338C212yesmaximal, complemented
21#36148C214yesmaximal, complemented
22#35933C212yesmaximal, complemented
23#35917C214yesmaximal, complemented
24C2×#563C2214yescomplemented
25C2×#533C2214yescomplemented
26C2×#525C2214yes—
27#2864C2211yescharacteristic, complemented
28#2863C2212yescomplemented
29#2861C2212yes—
30#2860C2212yes—
31#2860C2212yescomplemented
32#2854C2214yes—
33#2851C2214yescomplemented
34#2850C2214yes—
35#2848C2214yescomplemented
36#2848C2212yescomplemented
37#2843C2212yescomplemented
38#2842C2212yescomplemented
39#2840C2212yescomplemented
40#2839C2214yescomplemented
41#2837C2214yes—
42#2832C2214yescomplemented
43#2831C2214yescomplemented
44#2831C2214yescomplemented
45#2830C2214yes—
46#2830C2214yescomplemented
47#2826C2214yes—
48#2826C2212yes—
49#2824C2214yes—
50#2824C2212yes—
51#2823C2214yescomplemented
52#2822C2214yescomplemented
53#2820C2214yescomplemented
54#2814C2214yes—
55#2814C2214yes—
56#2808C2212yes—
57#2804C2211yescharacteristic, complemented
58#2797C2214yescomplemented
59#2788C2214yescomplemented
60#2784C2214yes—
61#2781C2214yescomplemented
62#2780C2214yescomplemented
63#2779C2214yes—
64#2777C2214yescomplemented
65#2775C2214yescomplemented
66#2772C2214yescomplemented
67#2763C2212yescomplemented
68#2742C2212yescomplemented
69#2734C2212yescomplemented
70#2732C2212yes—
71#2730C2214yescomplemented
72#2729C2214yescomplemented
73#2729C2214yescomplemented
74#2727C2212yes—
75#2726C2212yescomplemented
76#2725C2214yescomplemented
77#2720C2214yescomplemented
78#2716C2214yescomplemented
79#2716C2214yescomplemented
80#2713C2214yescomplemented
81#2704C2214yescomplemented
82#2704C2214yescomplemented
83#2702C2214yes—
84#2702C2214yescomplemented
85#2697C2214yescomplemented
86#2692C2214yes—
87#2692C2214yes—
88#2692C2214yescomplemented
89#2691C2214yes—
90#2691C2214yes—
91#2685C2214yes—
92#2685C2214yes—
93#2684C2214yescomplemented
94#2683C2211yescharacteristic
95#2683C2211yescharacteristic, complemented
96#2682C2212yes—
97#2681C2214yes—
98#2681C2214yes—
99#2681C2214yes—
100#2680C2212yes—
101#2679C2211yescharacteristic
102#2678C2214yes—
103#2677C2214yescomplemented
104#2677C2214yescomplemented
105#2677C2212yescomplemented
106#2677C2212yescomplemented
107#2669C2212yes—
108#2665C2212yescomplemented
109#2662C2214yes—
110#2654C2214yescomplemented
111#2652C2214yescomplemented
112#2650C2214yescomplemented
113#2610C2214yescomplemented
114#2601C2214yescomplemented
115#2593C2214yes—
116#2592C2212yes—
117#2590C2214yescomplemented
118#2589C2214yescomplemented
119#2588C2214yescomplemented
120#2584C2212yescomplemented
121#2580C2211yescharacteristic
122#2580C2211yescharacteristic, complemented
123#2579C2212yescomplemented
124#2574C2214yescomplemented
125#2569C2212yescomplemented
126#2564C2212yes—
127#2560C2214yescomplemented
128#2558C2214yes—
129#2558C2214yes—
130#2558C2214yescomplemented
131#2557C2214yes—
132#2556C2214yescomplemented
133#2554C2214yescomplemented
134#2553C2214yes—
135#2532C2214yescomplemented
136#2530C2214yescomplemented
137#2525C2214yescomplemented
138#2517C2214yescomplemented
139#2512C2212yes—
140#2511C2212yescomplemented
141#2507C2212yescomplemented
142#2491C2214yes—
143#2480C2214yescomplemented
144#2479C2214yes—
145#2479C2214yescomplemented
146#2478C2214yescomplemented
147#2478C2214yescomplemented
148#2477C2214yes—
149#2477C2214yescomplemented
150#2475C2214yescomplemented
151#2474C2214yescomplemented
152#2472C2214yes—
153#2472C2214yescomplemented
154#2471C2214yes—
155#2470C2214yescomplemented
156#2469C2214yescomplemented
157#2469C2214yescomplemented
158#2469C2214yescomplemented
159#2468C2214yescomplemented
160#2468C2214yescomplemented
161#2465C2214yescomplemented
162#2460C2214yes—
163#2460C2214yes—
164#2460C2214yescomplemented
165#2458C2214yes—
166#2458C2214yescomplemented
167#2458C2214yescomplemented
168#2458C2214yescomplemented
169#2452C2212yes—
170#2452C2214yes—
171#2451C2212yescomplemented
172#2451C2214yescomplemented
173#2450C2214yes—
174#2450C2214yescomplemented
175#2449C2214yescomplemented
176#2449C2214yescomplemented
177#2445C2212yes—
178#2439C2214yescomplemented
179#2432C2214yes—
180#2429C2214yescomplemented
181#2429C2214yescomplemented
182#2426C2214yes—
183#2421C2214yescomplemented
184#2418C2214yes—
185#2411C2214yes—
186#2411C2214yescomplemented
187#2406C2212yes—
188#2399C2214yescomplemented
189#2396C2214yescomplemented
190#2396C2214yescomplemented
191#2392C2214yes—
192#2388C2212yes—
193#2382C2214yescomplemented
194#2380C2212yes—
195#2376C2214yescomplemented
196#2375C2214yes—
197#2373C2214yescomplemented
198#2370C2212yescomplemented
199#2368C2212yescomplemented
200#2367C2212yes—
201#2367C2214yescomplemented
202#2362C2214yescomplemented
203#2359C2214yes—
204#2359C2214yescomplemented
205#2357C2211yescharacteristic, complemented
206#2349C2211yescharacteristic
207#2341C2212yes—
208C4×C4⋊Q8C2212yescomplemented
209C4×#127C2211yescharacteristic
210C4×C22⋊Q8C2214yescomplemented
211C4×#120C2212yes—
212#2295C2212yescomplemented
213#2293C2212yes—
214#2293C2212yes—
215#2290C2214yes—
216#2274C2212yescomplemented
217C42×Q8C2211yescharacteristic, complemented
218C2×C4×C22⋊C4C2212yescomplemented
219C22×#41C2312yes—
220C24×C4C2312yes—
221#563—416no—
222#533—416no—
223C2×C4⋊Q8C2312yes—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2314yes—
227C2×#127C2311yescharacteristic
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#125C2314yes—
234C2×#125C2314yes—
235C2×#125C2314yes—
236C2×#125C2312yes—
237C2×#124C2314yes—
238C2×#124C2312yes—
239C2×#124C2314yes—
240#525—416no—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×#121C2314yes—
258C2×#121C2314yes—
259C2×#120C2312yes—
260C2×#120C2314yes—
261C2×#120C2314yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×#117C2314yes—
276C2×#117C2314yes—
277C2×#117C2314yes—
278C2×#117C2314yes—
279C22×C4⋊C4C2312yes—
280C22×C22⋊C4C2314yes—
281C22×C42C2314yes—
282#400C2312yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#399C2312yes—
296#399C2312yes—
297#399C2314yes—
298#399C2314yes—
299#399C2312yes—
300#399C2314yes—
301#399C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#395C2312yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2312yes—
363#395C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2312yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#393C2314yes—
385#393C2312yes—
386#393C2314yes—
387#393C2312yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2312yes—
396#393C2312yes—
397#393C2314yes—
398#393C2314yes—
399#392C2312yes—
400#392C2314yes—
401#392C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2312yes—
408#391C2312yes—
409#391C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2314yes—
414#390C2314yes—
415#390C2311yescharacteristic
416#390C2314yes—
417#390C2311yescharacteristic
418#390C2312yes—
419#390C2314yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2312yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#390C2314yes—
431#390C2314yes—
432#389C2312yes—
433#389C2314yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2312yes—
533#386C2312yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2312yes—
540#386C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2312yes—
544#385C2312yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2312yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#384C2311yescharacteristic
564#384C2312yes—
565#383C2314yes—
566#382C2314yes—
567#382C2314yes—
568#382C2311yescharacteristic
569#382C2311yescharacteristic
570#381C2312yes—
571#380C2314yes—
572#380C2312yes—
573#380C2314yes—
574#380C2314yes—
575#380C2312yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#379C2312yes—
580#379C2314yes—
581#379C2314yes—
582#379C2314yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2311yescharacteristic
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612#376C2314yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C43C2311yescharacteristic
616C43C2312yes—
617C25C2412yes—
618C2×#41—44no—
619C2×#41—48no—
620C22×Q8C2412yes—
621C22×Q8C2414yes—
622C22×Q8C2412yes—
623C22×Q8C2411yescharacteristic
624C22×Q8C2414yes—
625C22×Q8C2412yes—
626C22×D4C2412yes—
627C22×D4C2414yes—
628C22×D4C2414yes—
629C22×D4C2411yescharacteristic
630C22×D4C2414yes—
631C22×D4C2414yes—
632C22×D4C2412yes—
633C22×D4C2411yescharacteristic
634C23×C4—48no—
635C23×C4—44no—
636C23×C4C2414yes—
637C23×C4C2414yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2412yes—
641C23×C4C2414yes—
642C23×C4C2414yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C4⋊Q8—28no—
646C4⋊Q8—48no—
647C4⋊Q8—48no—
648C4⋊Q8—48no—
649#127—24no—
650#126—48no—
651#126—48no—
652#126—48no—
653#126—48no—
654#126—48no—
655#125—216no—
656#125—44no—
657#125—48no—
658#125—48no—
659#124—48no—
660#124—44no—
661#124—48no—
662#123—216no—
663#123—48no—
664#123—48no—
665#123—48no—
666#123—48no—
667C22⋊Q8—216no—
668C22⋊Q8—48no—
669C22⋊Q8—48no—
670C22⋊Q8—48no—
671C22⋊Q8—48no—
672C22⋊Q8—48no—
673C22⋊Q8—44no—
674C22⋊Q8—48no—
675C22⋊Q8—48no—
676C22⋊Q8—48no—
677C22⋊Q8—48no—
678#121—48no—
679#121—48no—
680#120—28no—
681#120—48no—
682#120—48no—
683C4×Q8—28no—
684C4×Q8—42no—
685C4×Q8—44no—
686C4×Q8—48no—
687C4×Q8—48no—
688C4×Q8—48no—
689C4×D4—28no—
690C4×D4—28no—
691C4×D4—48no—
692C4×D4—42no—
693C4×D4—42no—
694C4×D4—48no—
695C4×D4—48no—
696#117—48no—
697#117—48no—
698#117—48no—
699#117—48no—
700C2×C4⋊C4—44no—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C22⋊C4—48no—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2412yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C42—48no—
800C2×C42C2412yes—
801C2×C42C2412yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2411yescharacteristic
805C2×C42C2412yes—
806C2×C42C2412yes—
807C2×C42C2414yes—
808C2×C42C2412yes—
809C2×C42C2411yescharacteristic
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2414yes—
823#95C2412yes—
824#95C2414yes—
825#95C2412yes—
826#95C2412yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2412yes—
832#95C2414yes—
833#95C2412yes—
834#95C2414yes—
835#95C2412yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2411yescharacteristic
845#95C2412yes—
846#95C2412yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2412yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2412yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874C24—24no—
875C24—44no—
876C24—42no—
877C24—44no—
878C24—42no—
879C24C2514yes—
880C24C2512yes—
881C24C2512yes—
882#41—816no—
883C2×Q8—28no—
884C2×Q8—24no—
885C2×Q8—28no—
886C2×Q8—41no—
887C2×Q8—42no—
888C2×Q8—42no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—42no—
893C2×Q8—44no—
894C2×Q8—42no—
895C2×Q8—44no—
896C2×Q8—44no—
897C2×Q8—42no—
898C2×D4—28no—
899C2×D4—28no—
900C2×D4—24no—
901C2×D4—28no—
902C2×D4—22no—
903C2×D4—41no—
904C2×D4—41no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—41no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—42no—
914C2×D4—44no—
915C2×D4—41no—
916C2×D4—42no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D42−1+414yes—
921C22×C4—28no—
922C22×C4—28no—
923C22×C4—28no—
924C22×C4—28no—
925C22×C4—28no—
926C22×C4—28no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—44no—
930C22×C4—42no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—42no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—42no—
942C22×C4—44no—
943C22×C4—816no—
944C22×C4C2512yes—
945C22×C4C2514yes—
946C22×C4C2511yescharacteristic
947C22×C4C2512yes—
948C22×C4C2514yes—
949C22×C4C2514yes—
950C22×C4C2514yes—
951C22×C4C2514yes—
952C22×C4C2512yes—
953C22×C4C2514yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2514yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2512yes—
964C4⋊C4—28no—
965C4⋊C4—28no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—24no—
974C4⋊C4—28no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—44no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—44no—
993C4⋊C4—41no—
994C4⋊C4—42no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—42no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4H(5,𝔽2)18yes—
1015C22⋊C4—28no—
1016C22⋊C4—24no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—42no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C42—28no—
1062C42—28no—
1063C42—24no—
1064C42—24no—
1065C42—24no—
1066C42—24no—
1067C42—22no—
1068C42—28no—
1069C42—22no—
1070C42—24no—
1071C42—44no—
1072C42—44no—
1073C42—41no—
1074C42—44no—
1075C42—44no—
1076C42—44no—
1077C42—44no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—44no—
1082C23—24no—
1083C23—22no—
1084C23—24no—
1085C23—22no—
1086C23—24no—
1087C23—24no—
1088C23—24no—
1089C23—24no—
1090C23—22no—
1091C23—24no—
1092C23—24no—
1093C23—24no—
1094C23—24no—
1095C23—22no—
1096C23—22no—
1097C23—24no—
1098C23—48no—
1099C23—88no—
1100C23—84no—
1101C23—84no—
1102C23—88no—
1103C23C2×2−1+414yes—
1104C23C2611yescharacteristic
1105Q8—48no—
1106Q8—44no—
1107Q8—88no—
1108Q8—84no—
1109Q8—88no—
1110Q8—162no—
1111D4—44no—
1112D4—82no—
1113D4—84no—
1114D4—88no—
1115D4—88no—
1116D4—88no—
1117D4—88no—
1118D4—84no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—48no—
1171C2×C4—416no—
1172C2×C4—416no—
1173C2×C4—48no—
1174C2×C4—84no—
1175C2×C4—88no—
1176C2×C4—84no—
1177C2×C4—88no—
1178C2×C4—162no—
1179C2×C4C2×H(5,𝔽2)14yes—
1180C2×C4C2×H(5,𝔽2)18yes—
1181C2×C4C2×2−1+412yes—
1182C2×C4#58514yes—
1183C2×C4#58512yes—
1184C22—28no—
1185C22—24no—
1186C22—42no—
1187C22—42no—
1188C22—44no—
1189C22—44no—
1190C22—42no—
1191C22—44no—
1192C22—44no—
1193C22—44no—
1194C22—42no—
1195C22—44no—
1196C22—42no—
1197C22—44no—
1198C22—44no—
1199C22—44no—
1200C22—44no—
1201C22—816no—
1202C22C22×H(5,𝔽2)12yes—
1203C22C22×2−1+411yescharacteristic
1204C22C2×#58511yescharacteristic
1205C22C2×#58512yes—
1206C222−1+611yescharacteristic
1207C4—22no—
1208C4—28no—
1209C4—24no—
1210C4—22no—
1211C4—24no—
1212C4—42no—
1213C4—42no—
1214C4—44no—
1215C4—42no—
1216C4—42no—
1217C4—44no—
1218C4—44no—
1219C4—42no—
1220C4—44no—
1221C4—41no—
1222C4—42no—
1223C4—44no—
1224C4—44no—
1225C4—44no—
1226C4—44no—
1227C2—44no—
1228C2—82no—
1229C2—84no—
1230C2#6269411yescharacteristic
1231C2#6290411yescharacteristic
1232C2#6296012yes—
1233C2#6301211yescharacteristic
1234C2#6301512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52103C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52641C2semidirect
2. #52563C2semidirect
3. #52559C2semidirect
4. #52498C2semidirect
5. #52406C2semidirect
6. #52162C2semidirect
8. #46282C2semidirect
9. #46281C2semidirect
10. #46227C2semidirect
11. #46115C2semidirect
12. #45963C2semidirect
13. #45958C2semidirect
14. #45947C2semidirect
15. #45821C2semidirect
16. #45491C2semidirect
17. #45453C2semidirect
18. #36371C2semidirect
19. #36370C2semidirect
20. #36338C2semidirect
21. #36148C2semidirect
22. #35933C2semidirect
23. #35917C2semidirect
24. C2×#563C22semidirect
25. C2×#533C22semidirect
27. #2864C22semidirect
28. #2863C22semidirect
31. #2860C22semidirect
33. #2851C22semidirect
35. #2848C22semidirect
36. #2848C22semidirect
37. #2843C22semidirect
38. #2842C22semidirect
39. #2840C22semidirect
40. #2839C22semidirect
42. #2832C22semidirect
43. #2831C22semidirect
44. #2831C22semidirect
46. #2830C22semidirect
51. #2823C22semidirect
52. #2822C22semidirect
53. #2820C22semidirect
57. #2804C22semidirect
58. #2797C22semidirect
59. #2788C22semidirect
61. #2781C22semidirect
62. #2780C22semidirect
64. #2777C22semidirect
65. #2775C22semidirect
66. #2772C22semidirect
67. #2763C22semidirect
68. #2742C22semidirect
69. #2734C22semidirect
71. #2730C22semidirect
72. #2729C22semidirect
73. #2729C22semidirect
75. #2726C22semidirect
76. #2725C22semidirect
77. #2720C22semidirect
78. #2716C22semidirect
79. #2716C22semidirect
80. #2713C22semidirect
81. #2704C22semidirect
82. #2704C22semidirect
84. #2702C22semidirect
85. #2697C22semidirect
88. #2692C22semidirect
93. #2684C22semidirect
95. #2683C22semidirect
103. #2677C22semidirect
104. #2677C22semidirect
105. #2677C22semidirect
106. #2677C22semidirect
108. #2665C22semidirect
110. #2654C22semidirect
111. #2652C22semidirect
112. #2650C22semidirect
113. #2610C22semidirect
114. #2601C22semidirect
117. #2590C22semidirect
118. #2589C22semidirect
119. #2588C22semidirect
120. #2584C22semidirect
122. #2580C22semidirect
123. #2579C22semidirect
124. #2574C22semidirect
125. #2569C22semidirect
127. #2560C22semidirect
130. #2558C22semidirect
132. #2556C22semidirect
133. #2554C22semidirect
135. #2532C22semidirect
136. #2530C22semidirect
137. #2525C22semidirect
138. #2517C22semidirect
140. #2511C22semidirect
141. #2507C22semidirect
143. #2480C22semidirect
145. #2479C22semidirect
146. #2478C22semidirect
147. #2478C22semidirect
149. #2477C22semidirect
150. #2475C22semidirect
151. #2474C22semidirect
153. #2472C22semidirect
155. #2470C22semidirect
156. #2469C22semidirect
157. #2469C22semidirect
158. #2469C22semidirect
159. #2468C22semidirect
160. #2468C22semidirect
161. #2465C22semidirect
164. #2460C22semidirect
166. #2458C22semidirect
167. #2458C22semidirect
168. #2458C22semidirect
171. #2451C22semidirect
172. #2451C22semidirect
174. #2450C22semidirect
175. #2449C22semidirect
176. #2449C22semidirect
178. #2439C22semidirect
180. #2429C22semidirect
181. #2429C22semidirect
183. #2421C22semidirect
186. #2411C22semidirect
188. #2399C22semidirect
189. #2396C22semidirect
190. #2396C22semidirect
193. #2382C22semidirect
195. #2376C22semidirect
197. #2373C22semidirect
198. #2370C22semidirect
199. #2368C22semidirect
201. #2367C22semidirect
202. #2362C22semidirect
204. #2359C22semidirect
205. #2357C22semidirect
208. C4×C4⋊Q8C22semidirect
210. C4×C22⋊Q8C22semidirect
212. #2295C22semidirect
216. #2274C22semidirect
217. C42×Q8C22semidirect
218. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#526412
#525632
#525592
#524982
#524062
#521622
#521032
#462822
#462812
#462272
#461152
#459632
#459582
#459472
#458212
#454912
#454532
#363712
#363702
#363382
#361482
#359332
#359172