Finite Group Databasebeta

← #8901131

Subgroups — #8901131

Order 512.

4510 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58711C214yesmaximal, complemented
2#58571C214yesmaximal, complemented
3#58107C214yesmaximal, complemented
4#51840C212yesmaximal, complemented
5#51681C212yesmaximal, complemented
6#51258C214yesmaximal, complemented
7#51187C214yesmaximal, complemented
8#47725C214yesmaximal, complemented
9#47313C214yesmaximal, complemented
10#47225C212yesmaximal, complemented
11#46858C212yesmaximal, complemented
12#46475C212yesmaximal, complemented
13#46426C212yesmaximal, complemented
14#46357C212yesmaximal, complemented
15#40362C214yesmaximal, complemented
16#39657C214yesmaximal, complemented
17#38391C214yesmaximal, complemented
18#37388C212yesmaximal, complemented
19#36707C211yesmaximal, characteristic
20#35644C211yesmaximal, characteristic, complemented
21#35435C212yesmaximal, complemented
22#35408C212yesmaximal, complemented
23#35391C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#543C2211yescharacteristic
26C2×#537C2211yescharacteristic
27C2×#536C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29#2857C2212yescomplemented
30#2850C2212yescomplemented
31#2847C2212yes—
32#2843C2214yescomplemented
33#2836C2214yescomplemented
34#2834C2212yes—
35#2832C2214yescomplemented
36#2824C2212yes—
37#2817C2212yes—
38#2811C2212yescomplemented
39#2809C2212yescomplemented
40#2799C2214yescomplemented
41#2794C2214yescomplemented
42#2789C2214yescomplemented
43#2788C2214yescomplemented
44#2788C2214yescomplemented
45#2786C2214yes—
46#2786C2214yes—
47#2778C2214yes—
48#2775C2214yescomplemented
49#2775C2214yescomplemented
50#2766C2214yescomplemented
51#2762C2214yescomplemented
52#2759C2214yescomplemented
53#2759C2214yescomplemented
54#2755C2214yescomplemented
55#2755C2214yescomplemented
56#2747C2214yes—
57#2746C2214yescomplemented
58#2745C2214yes—
59#2742C2214yes—
60#2742C2214yes—
61#2742C2212yes—
62#2738C2214yes—
63#2731C2212yescomplemented
64#2731C2212yescomplemented
65#2729C2214yescomplemented
66#2729C2214yescomplemented
67#2729C2214yescomplemented
68#2729C2214yescomplemented
69#2728C2214yes—
70#2723C2214yes—
71#2720C2214yescomplemented
72#2716C2214yescomplemented
73#2713C2214yescomplemented
74#2712C2212yes—
75#2708C2214yescomplemented
76#2708C2214yescomplemented
77#2702C2214yescomplemented
78#2701C2214yes—
79#2701C2214yes—
80#2700C2214yes—
81#2700C2214yescomplemented
82#2696C2214yes—
83#2693C2212yes—
84#2692C2214yes—
85#2692C2214yes—
86#2692C2214yes—
87#2692C2214yes—
88#2691C2214yes—
89#2687C2214yes—
90#2686C2214yes—
91#2686C2214yes—
92#2680C2214yes—
93#2677C2212yes—
94#2677C2214yes—
95#2676C2214yes—
96#2676C2214yes—
97#2674C2214yes—
98#2674C2214yescomplemented
99#2672C2214yes—
100#2665C2214yescomplemented
101#2665C2214yescomplemented
102#2653C2214yes—
103#2650C2214yescomplemented
104#2649C2214yes—
105#2637C2214yescomplemented
106#2621C2212yescomplemented
107#2620C2212yescomplemented
108#2618C2212yes—
109#2607C2212yes—
110#2605C2214yescomplemented
111#2605C2214yescomplemented
112#2591C2214yes—
113#2589C2214yescomplemented
114#2589C2214yescomplemented
115#2583C2212yes—
116#2583C2212yes—
117#2578C2214yes—
118#2575C2214yes—
119#2572C2214yes—
120#2564C2214yes—
121#2563C2214yes—
122#2561C2212yes—
123#2561C2212yes—
124#2560C2214yescomplemented
125#2558C2214yescomplemented
126#2557C2214yes—
127#2553C2214yes—
128#2551C2214yescomplemented
129#2549C2214yes—
130#2549C2214yes—
131#2549C2214yes—
132#2539C2211yescharacteristic
133#2539C2211yescharacteristic
134#2531C2214yes—
135#2528C2214yescomplemented
136#2527C2214yes—
137#2523C2214yes—
138#2521C2214yescomplemented
139#2521C2214yescomplemented
140#2520C2214yescomplemented
141#2520C2214yescomplemented
142#2518C2214yescomplemented
143#2517C2212yes—
144#2516C2214yes—
145#2511C2214yescomplemented
146#2510C2214yes—
147#2503C2212yes—
148#2503C2212yes—
149#2502C2212yes—
150#2500C2212yescomplemented
151#2499C2212yescomplemented
152#2497C2214yescomplemented
153#2492C2214yes—
154#2492C2214yes—
155#2492C2214yes—
156#2492C2214yes—
157#2492C2214yescomplemented
158#2489C2214yes—
159#2489C2214yes—
160#2481C2214yes—
161#2479C2214yes—
162#2478C2214yescomplemented
163#2477C2214yes—
164#2477C2214yes—
165#2477C2214yes—
166#2475C2214yescomplemented
167#2474C2214yes—
168#2472C2214yes—
169#2472C2214yes—
170#2470C2214yes—
171#2467C2214yes—
172#2463C2212yes—
173#2461C2214yes—
174#2459C2214yes—
175#2458C2214yes—
176#2451C2214yescomplemented
177#2451C2214yescomplemented
178#2440C2214yes—
179#2440C2214yes—
180#2436C2211yescharacteristic
181#2436C2211yescharacteristic
182#2436C2212yescomplemented
183#2434C2212yes—
184#2434C2212yescomplemented
185#2434C2214yescomplemented
186#2432C2212yes—
187#2432C2212yes—
188#2423C2214yes—
189#2418C2214yes—
190#2418C2214yes—
191#2417C2214yes—
192#2409C2214yes—
193#2406C2212yes—
194#2404C2212yes—
195#2381C2212yescomplemented
196#2379C2212yescomplemented
197#2372C2212yescomplemented
198#2369C2212yescomplemented
199#2364C2214yes—
200#2345C2214yes—
201#2337C2214yes—
202#2337C2214yes—
203#2335C2214yes—
204#2335C2214yes—
205#2334C2214yescomplemented
206#2332C2212yes—
207#2332C2212yes—
208#2326C2214yes—
209#2315C2212yes—
210#2313C2211yescharacteristic
211#2310C2212yes—
212C4×C22⋊Q8C2214yescomplemented
213C4×#123C2214yes—
214#2297C2212yes—
215C2×#385C2212yes—
216#2280C2212yes—
217#2274C2211yescharacteristic
218#2273C2211yescharacteristic
219C22×#41C2312yes—
220C23×Q8C2311yescharacteristic
221C23×Q8C2312yes—
222C24×C4C2311yescharacteristic
223#544—44no—
224#543—44no—
225#537—44no—
226#536—48no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#125C2314yes—
237C2×#124C2314yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2312yes—
247C2×#123C2312yes—
248C2×C22⋊Q8—44no—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×#121C2314yes—
266C2×#121C2312yes—
267C2×#121C2312yes—
268C2×#121C2312yes—
269C2×#121C2311yescharacteristic
270C2×#121C2311yescharacteristic
271C2×#120C2312yes—
272C2×#120C2312yes—
273C2×C4×Q8C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×#117C2312yes—
277C2×#117C2312yes—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2314yes—
284C22×C22⋊C4C2311yescharacteristic
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2312yes—
288C22×C42C2312yes—
289#401C2314yes—
290#401C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#399C2314yes—
310#399C2314yes—
311#399C2312yes—
312#399C2314yes—
313#399C2314yes—
314#399C2312yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#397C2314yes—
332#397C2312yes—
333#397C2312yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#393C2314yes—
384#393C2312yes—
385#393C2312yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#392C2312yes—
399#392C2314yes—
400#392C2312yes—
401#391C2314yes—
402#391C2314yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2314yes—
421#391C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#390C2312yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2312yes—
437#390C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
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#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
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#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2312yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2312yes—
530#386C2312yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2312yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2312yes—
542#385C2314yes—
543#385C2312yes—
544#385C2312yes—
545#385C2314yes—
546#385C2312yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#384C2314yes—
563#384C2312yes—
564#384C2312yes—
565#383C2314yes—
566#383C2314yes—
567#383C2314yes—
568#382C2314yes—
569#382C2314yes—
570#382C2312yes—
571#382C2312yes—
572#382C2314yes—
573#381C2314yes—
574#381C2314yes—
575#381C2312yes—
576#381C2314yes—
577#381C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2314yes—
582#380C2314yes—
583#380C2312yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#379C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2312yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2311yescharacteristic
603C4×C22⋊C4C2311yescharacteristic
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617#376C2314yes—
618C2×#95C2314yes—
619C25C2411yescharacteristic
620C2×#41—28no—
621C2×#41—82no—
622C2×#41—82no—
623C22×Q8—42no—
624C22×Q8—44no—
625C22×Q8—44no—
626C22×Q8—82no—
627C22×Q8—82no—
628C22×Q8C2414yes—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2414yes—
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C22×D4C2412yes—
643C22×D4C2411yescharacteristic
644C22×D4C2411yescharacteristic
645C23×C4—44no—
646C23×C4—42no—
647C23×C4C2411yescharacteristic
648C23×C4C2411yescharacteristic
649C23×C4C2414yes—
650C23×C4C2411yescharacteristic
651C23×C4C2411yescharacteristic
652C23×C4C2411yescharacteristic
653C23×C4C2414yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2414yes—
660C23×C4C2411yescharacteristic
661C4⋊Q8—44no—
662C4⋊Q8—44no—
663C4⋊Q8—48no—
664C4⋊Q8—48no—
665C4⋊Q8—82no—
666C4⋊Q8—82no—
667C4⋊Q8—84no—
668#126—48no—
669#126—84no—
670#125—48no—
671#124—216no—
672#124—48no—
673#124—44no—
674#124—44no—
675#124—82no—
676#124—82no—
677#123—216no—
678#123—48no—
679#123—48no—
680#123—82no—
681#123—82no—
682C22⋊Q8—28no—
683C22⋊Q8—28no—
684C22⋊Q8—44no—
685C22⋊Q8—44no—
686C22⋊Q8—48no—
687C22⋊Q8—48no—
688C22⋊Q8—48no—
689C22⋊Q8—48no—
690C22⋊Q8—48no—
691C22⋊Q8—44no—
692C22⋊Q8—44no—
693C22⋊Q8—44no—
694C22⋊Q8—44no—
695C22⋊Q8—84no—
696C22⋊Q8—84no—
697C22⋊Q8—84no—
698#121—48no—
699#121—44no—
700#121—44no—
701#121—42no—
702#121—42no—
703#121—44no—
704#120—82no—
705#120—82no—
706C4×Q8—84no—
707C4×D4—84no—
708C4×D4—84no—
709#117—44no—
710#117—44no—
711#117—44no—
712#117—82no—
713C2×C4⋊C4—24no—
714C2×C4⋊C4—24no—
715C2×C4⋊C4—48no—
716C2×C4⋊C4—42no—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C22⋊C4—24no—
763C2×C22⋊C4—28no—
764C2×C22⋊C4—44no—
765C2×C22⋊C4—42no—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C42—82no—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2412yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2412yes—
838#95C2414yes—
839#95C2412yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2412yes—
854#95C2414yes—
855#95C2412yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885C24—22no—
886C24—24no—
887C24—42no—
888C24—42no—
889C24C2512yes—
890C24C2512yes—
891C24C2511yescharacteristic
892C24C2512yes—
893#41—816no—
894C2×Q8—24no—
895C2×Q8—24no—
896C2×Q8—24no—
897C2×Q8—28no—
898C2×Q8—24no—
899C2×Q8—24no—
900C2×Q8—44no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—44no—
904C2×Q8—44no—
905C2×Q8—44no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8—42no—
910C2×Q8—44no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—42no—
917C2×Q8—44no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—88no—
921C2×Q8—816no—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—28no—
925C2×D4—28no—
926C2×D4—24no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—41no—
938C2×D4—41no—
939C2×D4—42no—
940C2×D4—44no—
941C2×D4—42no—
942C2×D4—42no—
943C22×C4—22no—
944C22×C4—24no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—28no—
952C22×C4—28no—
953C22×C4—28no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—42no—
968C22×C4—44no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—88no—
977C22×C4H(5,𝔽2)14yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2514yes—
996C22×C4C2512yes—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—41no—
1022C4⋊C4—42no—
1023C4⋊C4—41no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—24no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—44no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C42−1+418yes—
1084C42—28no—
1085C42—44no—
1086C42—42no—
1087C42—42no—
1088C42—42no—
1089C42—42no—
1090C42—44no—
1091C42—44no—
1092C42—42no—
1093C42—42no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—42no—
1098C42—42no—
1099C42—44no—
1100C42—42no—
1101C42—42no—
1102C23—28no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—24no—
1108C23—24no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—24no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—82no—
1121C23—82no—
1122C23—88no—
1123C23C2×H(5,𝔽2)12yes—
1124C23C2×2−1+414yes—
1125C23C2611yescharacteristic
1126Q8—88no—
1127Q8—84no—
1128Q8—84no—
1129Q8—84no—
1130Q8—84no—
1131Q8—84no—
1132Q8—88no—
1133Q8—162no—
1134Q8—162no—
1135D4—84no—
1136D4—88no—
1137D4—88no—
1138D4—84no—
1139D4—84no—
1140D4—162no—
1141D4—161no—
1142D4—161no—
1143C2×C4—28no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—44no—
1195C2×C4—48no—
1196C2×C4—48no—
1197C2×C4—88no—
1198C2×C4—88no—
1199C2×C4—88no—
1200C2×C4—82no—
1201C2×C4—82no—
1202C2×C4—82no—
1203C2×C4—82no—
1204C2×C4—88no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4C2×H(5,𝔽2)14yes—
1208C2×C4C2×2−1+418yes—
1209C2×C4#58514yes—
1210C22—22no—
1211C22—22no—
1212C22—24no—
1213C22—22no—
1214C22—28no—
1215C22—42no—
1216C22—42no—
1217C22—44no—
1218C22—44no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—88no—
1230C22C22×H(5,𝔽2)11yescharacteristic
1231C22C22×2−1+412yes—
1232C22C2×#58512yes—
1233C22H(7,𝔽2)12yes—
1234C4—24no—
1235C4—24no—
1236C4—28no—
1237C4—42no—
1238C4—41no—
1239C4—41no—
1240C4—42no—
1241C4—44no—
1242C4—44no—
1243C4—42no—
1244C4—42no—
1245C4—44no—
1246C4—44no—
1247C4—42no—
1248C4—44no—
1249C4—44no—
1250C4—44no—
1251C4—44no—
1252C4—44no—
1253C2—42no—
1254C2—44no—
1255C2—82no—
1256C2—82no—
1257C2#6282411yescharacteristic
1258C2#6283311yescharacteristic
1259C2#6286211yescharacteristic
1260C2#6295114yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36707C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58711C2semidirect
2. #58571C2semidirect
3. #58107C2semidirect
4. #51840C2semidirect
5. #51681C2semidirect
6. #51258C2semidirect
7. #51187C2semidirect
8. #47725C2semidirect
9. #47313C2semidirect
10. #47225C2semidirect
11. #46858C2semidirect
12. #46475C2semidirect
13. #46426C2semidirect
14. #46357C2semidirect
15. #40362C2semidirect
16. #39657C2semidirect
17. #38391C2semidirect
18. #37388C2semidirect
20. #35644C2semidirect
21. #35435C2semidirect
22. #35408C2semidirect
23. #35391C2semidirect
29. #2857C22semidirect
30. #2850C22semidirect
32. #2843C22semidirect
33. #2836C22semidirect
35. #2832C22semidirect
38. #2811C22semidirect
39. #2809C22semidirect
40. #2799C22semidirect
41. #2794C22semidirect
42. #2789C22semidirect
43. #2788C22semidirect
44. #2788C22semidirect
48. #2775C22semidirect
49. #2775C22semidirect
50. #2766C22semidirect
51. #2762C22semidirect
52. #2759C22semidirect
53. #2759C22semidirect
54. #2755C22semidirect
55. #2755C22semidirect
57. #2746C22semidirect
63. #2731C22semidirect
64. #2731C22semidirect
65. #2729C22semidirect
66. #2729C22semidirect
67. #2729C22semidirect
68. #2729C22semidirect
71. #2720C22semidirect
72. #2716C22semidirect
73. #2713C22semidirect
75. #2708C22semidirect
76. #2708C22semidirect
77. #2702C22semidirect
81. #2700C22semidirect
98. #2674C22semidirect
100. #2665C22semidirect
101. #2665C22semidirect
103. #2650C22semidirect
105. #2637C22semidirect
106. #2621C22semidirect
107. #2620C22semidirect
110. #2605C22semidirect
111. #2605C22semidirect
113. #2589C22semidirect
114. #2589C22semidirect
124. #2560C22semidirect
125. #2558C22semidirect
128. #2551C22semidirect
135. #2528C22semidirect
138. #2521C22semidirect
139. #2521C22semidirect
140. #2520C22semidirect
141. #2520C22semidirect
142. #2518C22semidirect
145. #2511C22semidirect
150. #2500C22semidirect
151. #2499C22semidirect
152. #2497C22semidirect
157. #2492C22semidirect
162. #2478C22semidirect
166. #2475C22semidirect
176. #2451C22semidirect
177. #2451C22semidirect
182. #2436C22semidirect
184. #2434C22semidirect
185. #2434C22semidirect
195. #2381C22semidirect
196. #2379C22semidirect
197. #2372C22semidirect
198. #2369C22semidirect
205. #2334C22semidirect
212. C4×C22⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#587112
#585712
#581072
#518402
#516812
#512582
#511872
#477252
#473132
#472252
#468582
#464752
#464262
#463572
#403622
#396572
#383912
#373882
#367072
#356442
#354352
#354082
#353912