Finite Group Databasebeta

← #7697419

Subgroups — #7697419

Order 512.

5529 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59834C211yesmaximal, characteristic, complemented
2#59814C212yesmaximal, complemented
3#59803C212yesmaximal, complemented
4#59568C214yesmaximal, complemented
5#52301C211yesmaximal, characteristic, complemented
6#52278C212yesmaximal, complemented
7#44168C214yesmaximal, complemented
8#43791C212yesmaximal, complemented
9#43772C214yesmaximal, complemented
10#43364C214yesmaximal, complemented
11#43118C214yesmaximal, complemented
12#39708C212yesmaximal, complemented
13#39208C214yesmaximal, complemented
14#38789C212yesmaximal, complemented
15#38636C214yesmaximal, complemented
16#38540C214yesmaximal, complemented
17#38466C212yesmaximal, complemented
18#36536C211yesmaximal, characteristic, complemented
19#36530C212yesmaximal, complemented
20#36074C212yesmaximal, complemented
21#35944C214yesmaximal, complemented
22#34320C212yesmaximal, complemented
23#34302C214yesmaximal, complemented
24C2×#555C2212yescomplemented
25C2×#546C2212yes—
26C2×#546C2214yes—
27C2×#546C2214yescomplemented
28#2864C2211yescharacteristic, complemented
29#2855C2212yescomplemented
30#2852C2214yescomplemented
31#2847C2212yescomplemented
32#2808C2212yescomplemented
33#2805C2212yescomplemented
34#2804C2212yescomplemented
35#2804C2211yescharacteristic, complemented
36#2797C2214yescomplemented
37#2784C2214yescomplemented
38#2782C2214yescomplemented
39#2782C2212yescomplemented
40#2779C2214yescomplemented
41#2778C2214yescomplemented
42#2778C2214yescomplemented
43#2775C2214yescomplemented
44#2771C2214yescomplemented
45#2757C2214yescomplemented
46#2751C2214yescomplemented
47#2745C2214yescomplemented
48#2745C2214yescomplemented
49#2734C2211yescharacteristic, complemented
50#2733C2211yescharacteristic, complemented
51#2728C2212yescomplemented
52#2714C2214yescomplemented
53#2712C2212yescomplemented
54#2708C2214yescomplemented
55#2697C2214yescomplemented
56#2696C2214yescomplemented
57#2693C2212yescomplemented
58#2692C2214yescomplemented
59#2689C2214yescomplemented
60#2688C2214yescomplemented
61#2688C2214yescomplemented
62#2686C2214yescomplemented
63#2684C2214yescomplemented
64#2684C2212yescomplemented
65#2684C2214yescomplemented
66#2683C2212yescomplemented
67#2682C2212yes—
68#2682C2212yescomplemented
69#2679C2212yes—
70#2679C2211yescharacteristic
71#2668C2214yes—
72#2665C2214yescomplemented
73#2650C2214yescomplemented
74#2648C2214yescomplemented
75#2648C2214yescomplemented
76#2631C2212yes—
77#2609C2212yescomplemented
78#2605C2212yescomplemented
79#2600C2214yescomplemented
80#2593C2212yescomplemented
81#2588C2214yescomplemented
82#2578C2214yescomplemented
83#2578C2214yescomplemented
84#2578C2214yescomplemented
85#2578C2214yescomplemented
86#2577C2214yescomplemented
87#2573C2214yescomplemented
88#2572C2212yescomplemented
89#2569C2212yescomplemented
90#2564C2214yescomplemented
91#2559C2214yescomplemented
92#2557C2214yescomplemented
93#2557C2214yescomplemented
94#2557C2214yescomplemented
95#2557C2214yescomplemented
96#2555C2214yescomplemented
97#2555C2214yescomplemented
98#2545C2212yescomplemented
99#2543C2212yescomplemented
100#2536C2211yescharacteristic, complemented
101#2535C2211yescharacteristic
102#2534C2214yescomplemented
103#2534C2214yescomplemented
104#2527C2214yescomplemented
105#2526C2214yescomplemented
106#2526C2214yescomplemented
107#2522C2214yescomplemented
108#2518C2214yescomplemented
109#2510C2214yescomplemented
110#2495C2212yescomplemented
111#2492C2214yescomplemented
112#2488C2214yescomplemented
113#2485C2214yescomplemented
114#2483C2212yescomplemented
115#2481C2214yescomplemented
116#2480C2214yescomplemented
117#2474C2214yescomplemented
118#2472C2214yescomplemented
119#2472C2214yescomplemented
120#2472C2214yescomplemented
121#2472C2214yescomplemented
122#2470C2214yescomplemented
123#2470C2214yescomplemented
124#2467C2214yescomplemented
125#2465C2214yescomplemented
126#2465C2214yescomplemented
127#2464C2214yescomplemented
128#2463C2214yescomplemented
129#2461C2214yescomplemented
130#2461C2214yescomplemented
131#2457C2214yescomplemented
132#2456C2214yescomplemented
133#2452C2214yescomplemented
134#2450C2214yescomplemented
135#2447C2214yescomplemented
136#2444C2214yescomplemented
137#2444C2214yescomplemented
138#2427C2214yescomplemented
139#2427C2214yescomplemented
140#2427C2212yescomplemented
141#2424C2214yes—
142#2424C2214yescomplemented
143#2424C2214yescomplemented
144#2424C2214yescomplemented
145#2418C2214yescomplemented
146#2415C2214yescomplemented
147#2412C2214yescomplemented
148#2410C2214yescomplemented
149#2408C2214yescomplemented
150#2407C2214yes—
151#2406C2214yescomplemented
152#2404C2214yes—
153#2404C2214yescomplemented
154#2403C2212yescomplemented
155#2403C2214yescomplemented
156#2401C2214yescomplemented
157#2398C2212yescomplemented
158#2398C2214yescomplemented
159#2398C2214yescomplemented
160#2388C2214yescomplemented
161#2374C2214yescomplemented
162#2374C2214yescomplemented
163#2372C2212yescomplemented
164#2372C2214yescomplemented
165#2368C2214yescomplemented
166#2367C2212yescomplemented
167#2364C2212yescomplemented
168#2364C2214yescomplemented
169#2364C2214yescomplemented
170#2363C2212yes—
171#2363C2214yescomplemented
172#2360C2212yescomplemented
173#2359C2214yescomplemented
174#2358C2214yescomplemented
175#2358C2214yescomplemented
176#2358C2214yescomplemented
177#2357C2212yescomplemented
178#2356C2211yescharacteristic, complemented
179#2353C2214yescomplemented
180#2353C2214yescomplemented
181#2352C2212yescomplemented
182#2349C2211yescharacteristic, complemented
183#2342C2214yescomplemented
184#2342C2214yescomplemented
185#2342C2214yescomplemented
186#2341C2212yescomplemented
187#2339C2214yescomplemented
188D4×C22⋊C4C2212yescomplemented
189D4×C22⋊C4C2214yescomplemented
190#2337C2214yescomplemented
191#2335C2214yescomplemented
192#2335C2214yescomplemented
193#2333C2214yes—
194#2333C2214yescomplemented
195#2333C2214yescomplemented
196#2329C2214yescomplemented
197#2321C2214yescomplemented
198#2321C2214yescomplemented
199C4×#124C2212yescomplemented
200C4×#124C2211yescharacteristic, complemented
201C4×C22⋊Q8C2212yescomplemented
202C4×#123C2214yescomplemented
203C4×#121C2212yes—
204C4×#121C2214yescomplemented
205C4×#121C2212yescomplemented
206C4×#121C2214yescomplemented
207C4×#120C2214yescomplemented
208C4×#120C2212yescomplemented
209#2297C2212yescomplemented
210#2297C2214yescomplemented
211#2293C2212yescomplemented
212C2×#390C2212yescomplemented
213#2290C2214yescomplemented
214C2×#386C2214yescomplemented
215#2275C2212yescomplemented
216#2273C2214yescomplemented
217C42×D4C2211yescharacteristic, complemented
218C2×C4×C22⋊C4C2212yescomplemented
219C22×#41C2314yes—
220C22×#41C2312yes—
221C23×D4C2314yes—
222C23×D4C2312yes—
223C24×C4C2312yes—
224#555—48no—
225#546—232no—
226#546—216no—
227#546—416no—
228C2×C4⋊Q8C2312yes—
229C2×#126C2314yes—
230C2×#124C2314yes—
231C2×#124C2312yes—
232C2×#124C2311yescharacteristic
233C2×#124C2312yes—
234C2×#124C2314yes—
235C2×#124C2314yes—
236C2×#124C2312yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2314yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2314yes—
251C2×#121C2314yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2314yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#120C2314yes—
259C2×#120C2314yes—
260C2×#120C2314yes—
261C2×#120C2312yes—
262C2×#120C2314yes—
263C2×#120C2314yes—
264C2×#120C2314yes—
265C2×#120C2314yes—
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2311yescharacteristic
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×#117C2314yes—
287C2×#117C2314yes—
288C2×#117C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C22⋊C4C2314yes—
291C22×C22⋊C4C2314yes—
292C22×C22⋊C4C2314yes—
293C22×C22⋊C4C2314yes—
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2314yes—
296C22×C22⋊C4C2314yes—
297C22×C42C2314yes—
298C22×C42C2312yes—
299#401C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2312yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2312yes—
311#400C2314yes—
312#399C2314yes—
313#398C2314yes—
314#398C2312yes—
315#398C2312yes—
316#397C2314yes—
317#397C2312yes—
318#397C2314yes—
319#397C2312yes—
320#397C2314yes—
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#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2314yes—
344#395C2314yes—
345#394C2312yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2312yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2312yes—
359#394C2312yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#393C2314yes—
366#393C2314yes—
367#393C2314yes—
368#393C2314yes—
369#393C2314yes—
370#393C2314yes—
371#393C2314yes—
372#393C2314yes—
373#392C2312yes—
374#392C2314yes—
375#392C2314yes—
376#392C2314yes—
377#392C2314yes—
378#392C2314yes—
379#392C2314yes—
380#392C2314yes—
381#392C2314yes—
382#392C2312yes—
383#391C2312yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2311yescharacteristic
389#391C2312yes—
390#391C2312yes—
391#391C2314yes—
392#391C2314yes—
393#391C2312yes—
394#390C2314yes—
395#390C2314yes—
396#390C2314yes—
397#390C2314yes—
398#390C2314yes—
399#390C2312yes—
400#390C2314yes—
401#390C2314yes—
402#390C2312yes—
403#390C2312yes—
404#390C2312yes—
405#390C2312yes—
406#390C2314yes—
407#390C2314yes—
408#390C2312yes—
409#390C2311yescharacteristic
410#390C2312yes—
411#389C2314yes—
412#389C2312yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2314yes—
420#389C2312yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2312yes—
519#386C2314yes—
520#386C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2312yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#383C2314yes—
541#383C2314yes—
542#383C2312yes—
543#382C2311yescharacteristic
544#382C2312yes—
545#382C2311yescharacteristic
546#382C2311yescharacteristic
547#381C2314yes—
548#381C2314yes—
549#381C2314yes—
550#381C2314yes—
551#381C2314yes—
552#381C2314yes—
553#380C2314yes—
554#380C2314yes—
555#380C2312yes—
556#380C2314yes—
557#380C2314yes—
558#380C2314yes—
559#380C2314yes—
560#380C2314yes—
561#380C2312yes—
562#380C2312yes—
563#380C2312yes—
564#380C2312yes—
565#379C2314yes—
566#379C2314yes—
567#379C2314yes—
568#379C2312yes—
569#379C2314yes—
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2311yescharacteristic
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2314yes—
580C4×C22⋊C4C2312yes—
581C4×C22⋊C4C2314yes—
582C4×C22⋊C4C2314yes—
583C4×C22⋊C4C2314yes—
584C4×C22⋊C4C2314yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2312yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610#376C2312yes—
611#376C2312yes—
612#376C2314yes—
613C2×#95C2314yes—
614C2×#95C2312yes—
615C2×#95C2314yes—
616C2×#95C2312yes—
617C43C2311yescharacteristic
618C25C2412yes—
619C25C2414yes—
620C2×#41—216no—
621C2×#41—28no—
622C2×#41—48no—
623C2×#41—84no—
624C2×#41—82no—
625C2×#41—82no—
626C22×Q8C2412yes—
627C22×Q8C2411yescharacteristic
628C22×Q8C2414yes—
629C22×Q8C2412yes—
630C22×D4—28no—
631C22×D4—216no—
632C22×D4—48no—
633C22×D4—82no—
634C22×D4—82no—
635C22×D4—84no—
636C22×D4C2411yescharacteristic
637C22×D4C2412yes—
638C22×D4C2414yes—
639C22×D4C2414yes—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2412yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2412yes—
648C22×D4C2412yes—
649C22×D4C2412yes—
650C22×D4C2414yes—
651C22×D4C2411yescharacteristic
652C23×C4—44no—
653C23×C4—84no—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2412yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2414yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2414yes—
665C23×C4C2414yes—
666C23×C4C2414yes—
667C23×C4C2412yes—
668C23×C4C2412yes—
669C4⋊Q8—44no—
670#126—84no—
671#124—28no—
672#124—24no—
673#124—216no—
674#124—44no—
675#124—48no—
676#124—48no—
677#124—44no—
678#123—216no—
679#123—216no—
680#123—216no—
681#123—48no—
682#123—48no—
683C22⋊Q8—216no—
684C22⋊Q8—28no—
685C22⋊Q8—48no—
686C22⋊Q8—84no—
687C22⋊Q8—82no—
688C22⋊Q8—84no—
689#121—216no—
690#121—216no—
691#121—28no—
692#121—216no—
693#121—216no—
694#121—44no—
695#121—48no—
696#121—48no—
697#121—84no—
698#121#41116yescomplemented
699#120—216no—
700#120—216no—
701#120—216no—
702#120—28no—
703#120—48no—
704#120—84no—
705#120—84no—
706#120—84no—
707C4×Q8—42no—
708C4×Q8—82no—
709C4×Q8—82no—
710C4×D4—216no—
711C4×D4—28no—
712C4×D4—28no—
713C4×D4—216no—
714C4×D4—42no—
715C4×D4—42no—
716C4×D4—44no—
717C4×D4—48no—
718C4×D4—48no—
719C4×D4—48no—
720C4×D4—84no—
721C4×D4—84no—
722C4×D4—82no—
723C4×D4—82no—
724C4×D4—82no—
725C4×D4—84no—
726C4×D4—84no—
727#117—48no—
728#117—48no—
729#117—82no—
730C2×C4⋊C4—82no—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C22⋊C4—216no—
764C2×C22⋊C4—216no—
765C2×C22⋊C4—216no—
766C2×C22⋊C4—48no—
767C2×C22⋊C4—48no—
768C2×C22⋊C4—48no—
769C2×C22⋊C4—84no—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C42—82no—
826C2×C42—84no—
827C2×C42C2411yescharacteristic
828C2×C42C2411yescharacteristic
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2412yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2414yes—
846C2×C42C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2412yes—
849#95C2414yes—
850#95C2414yes—
851#95C2412yes—
852#95C2412yes—
853#95C2414yes—
854#95C2412yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2412yes—
863#95C2414yes—
864#95C2412yes—
865#95C2414yes—
866#95C2414yes—
867#95C2412yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2411yescharacteristic
874#95C2412yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2412yes—
898C24—28no—
899C24—24no—
900C24—28no—
901C24—28no—
902C24—42no—
903C24—44no—
904C24—44no—
905C24—42no—
906C24—44no—
907C24—44no—
908C24—44no—
909C24—44no—
910C24C2514yes—
911C24C2514yes—
912C24C2512yes—
913C24C2512yes—
914#41—832no—
915#41—816no—
916C2×Q8—24no—
917C2×Q8—28no—
918C2×Q8—22no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—41no—
922C2×Q8—44no—
923C2×Q8—41no—
924C2×Q8—44no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×D4—28no—
929C2×D4—24no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—28no—
936C2×D4—28no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—28no—
940C2×D4—24no—
941C2×D4—28no—
942C2×D4—44no—
943C2×D4—41no—
944C2×D4—41no—
945C2×D4—42no—
946C2×D4—41no—
947C2×D4—42no—
948C2×D4—44no—
949C2×D4—42no—
950C2×D4—44no—
951C2×D4—42no—
952C2×D4—44no—
953C2×D4—42no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—42no—
966C2×D4—44no—
967C2×D4—42no—
968C2×D4—42no—
969C2×D4—42no—
970C2×D4—816no—
971C2×D4—832no—
972C2×D4C2×#4118yes—
973C2×D4C2×#41116yes—
974C2×D4H(5,𝔽2)14yes—
975C22×C4—28no—
976C22×C4—28no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—24no—
980C22×C4—28no—
981C22×C4—28no—
982C22×C4—28no—
983C22×C4—28no—
984C22×C4—24no—
985C22×C4—28no—
986C22×C4—24no—
987C22×C4—44no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—42no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—42no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—816no—
1018C22×C4C2×#4118yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2514yes—
1022C22×C4C2512yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2514yes—
1025C22×C4C2512yes—
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2511yescharacteristic
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—24no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—42no—
1054C4⋊C4—44no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—41no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4C2×#4118yes—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—24no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—24no—
1080C22⋊C4—24no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—24no—
1093C22⋊C4—28no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—42no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—42no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4C2×#41116yes—
1125C42—24no—
1126C42—28no—
1127C42—22no—
1128C42—22no—
1129C42—24no—
1130C42—41no—
1131C42—44no—
1132C42—42no—
1133C42—44no—
1134C42—42no—
1135C42—44no—
1136C42—42no—
1137C42—44no—
1138C42—44no—
1139C42—42no—
1140C42—44no—
1141C42—42no—
1142C42—44no—
1143C42—42no—
1144C42—44no—
1145C23—24no—
1146C23—22no—
1147C23—24no—
1148C23—24no—
1149C23—22no—
1150C23—22no—
1151C23—24no—
1152C23—22no—
1153C23—22no—
1154C23—22no—
1155C23—24no—
1156C23—22no—
1157C23—24no—
1158C23—24no—
1159C23—24no—
1160C23—22no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—24no—
1168C23—416no—
1169C23—48no—
1170C23—416no—
1171C23—88no—
1172C23—84no—
1173C23—88no—
1174C23—88no—
1175C23—88no—
1176C23—88no—
1177C23—84no—
1178C23—164no—
1179C23—164no—
1180C23C22×#4118yes—
1181C23C22×#4114yes—
1182C23C2×H(5,𝔽2)14yes—
1183C23C2611yescharacteristic
1184Q8—48no—
1185Q8—82no—
1186Q8—88no—
1187Q8—162no—
1188D4—48no—
1189D4—416no—
1190D4—44no—
1191D4—416no—
1192D4—48no—
1193D4—48no—
1194D4—44no—
1195D4—416no—
1196D4—416no—
1197D4—88no—
1198D4—88no—
1199D4—88no—
1200D4—88no—
1201D4—88no—
1202D4—162no—
1203D4—162no—
1204C2×C4—24no—
1205C2×C4—21no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—48no—
1253C2×C4—416no—
1254C2×C4—48no—
1255C2×C4—48no—
1256C2×C4—88no—
1257C2×C4—88no—
1258C2×C4—84no—
1259C2×C4—88no—
1260C2×C4—84no—
1261C2×C4—88no—
1262C2×C4—88no—
1263C2×C4—88no—
1264C2×C4—88no—
1265C2×C4—88no—
1266C2×C4—164no—
1267C2×C4C22×#4114yes—
1268C2×C4C22×#4114yes—
1269C2×C4C22×#4118yes—
1270C2×C4C2×H(5,𝔽2)12yes—
1271C2×C4#58512yes—
1272C22—28no—
1273C22—24no—
1274C22—28no—
1275C22—24no—
1276C22—28no—
1277C22—24no—
1278C22—28no—
1279C22—24no—
1280C22—44no—
1281C22—42no—
1282C22—42no—
1283C22—44no—
1284C22—42no—
1285C22—42no—
1286C22—44no—
1287C22—44no—
1288C22—42no—
1289C22—44no—
1290C22—42no—
1291C22—44no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—816no—
1299C22—1616no—
1300C22C23×#4112yes—
1301C22C22×H(5,𝔽2)11yescharacteristic
1302C22C2×#58511yescharacteristic
1303C22H(7,𝔽2)12yes—
1304C22H(7,𝔽2)11yescharacteristic
1305C4—28no—
1306C4—22no—
1307C4—24no—
1308C4—24no—
1309C4—22no—
1310C4—44no—
1311C4—42no—
1312C4—44no—
1313C4—44no—
1314C4—44no—
1315C4—42no—
1316C4—42no—
1317C4—44no—
1318C4—44no—
1319C4—42no—
1320C4—44no—
1321C4—42no—
1322C4—42no—
1323C4—41no—
1324C2—44no—
1325C2—48no—
1326C2—44no—
1327C2—84no—
1328C2#41211yescharacteristic
1329C2#6284612yes—
1330C2#6290511yescharacteristic
1331C2#6298312yes—
1332C2#6304611yescharacteristic
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. #59834C2semidirect
2. #59814C2semidirect
3. #59803C2semidirect
4. #59568C2semidirect
5. #52301C2semidirect
6. #52278C2semidirect
7. #44168C2semidirect
8. #43791C2semidirect
9. #43772C2semidirect
10. #43364C2semidirect
11. #43118C2semidirect
12. #39708C2semidirect
13. #39208C2semidirect
14. #38789C2semidirect
15. #38636C2semidirect
16. #38540C2semidirect
17. #38466C2semidirect
18. #36536C2semidirect
19. #36530C2semidirect
20. #36074C2semidirect
21. #35944C2semidirect
22. #34320C2semidirect
23. #34302C2semidirect
24. C2×#555C22semidirect
27. C2×#546C22semidirect
28. #2864C22semidirect
29. #2855C22semidirect
30. #2852C22semidirect
31. #2847C22semidirect
32. #2808C22semidirect
33. #2805C22semidirect
34. #2804C22semidirect
35. #2804C22semidirect
36. #2797C22semidirect
37. #2784C22semidirect
38. #2782C22semidirect
39. #2782C22semidirect
40. #2779C22semidirect
41. #2778C22semidirect
42. #2778C22semidirect
43. #2775C22semidirect
44. #2771C22semidirect
45. #2757C22semidirect
46. #2751C22semidirect
47. #2745C22semidirect
48. #2745C22semidirect
49. #2734C22semidirect
50. #2733C22semidirect
51. #2728C22semidirect
52. #2714C22semidirect
53. #2712C22semidirect
54. #2708C22semidirect
55. #2697C22semidirect
56. #2696C22semidirect
57. #2693C22semidirect
58. #2692C22semidirect
59. #2689C22semidirect
60. #2688C22semidirect
61. #2688C22semidirect
62. #2686C22semidirect
63. #2684C22semidirect
64. #2684C22semidirect
65. #2684C22semidirect
66. #2683C22semidirect
68. #2682C22semidirect
72. #2665C22semidirect
73. #2650C22semidirect
74. #2648C22semidirect
75. #2648C22semidirect
77. #2609C22semidirect
78. #2605C22semidirect
79. #2600C22semidirect
80. #2593C22semidirect
81. #2588C22semidirect
82. #2578C22semidirect
83. #2578C22semidirect
84. #2578C22semidirect
85. #2578C22semidirect
86. #2577C22semidirect
87. #2573C22semidirect
88. #2572C22semidirect
89. #2569C22semidirect
90. #2564C22semidirect
91. #2559C22semidirect
92. #2557C22semidirect
93. #2557C22semidirect
94. #2557C22semidirect
95. #2557C22semidirect
96. #2555C22semidirect
97. #2555C22semidirect
98. #2545C22semidirect
99. #2543C22semidirect
100. #2536C22semidirect
102. #2534C22semidirect
103. #2534C22semidirect
104. #2527C22semidirect
105. #2526C22semidirect
106. #2526C22semidirect
107. #2522C22semidirect
108. #2518C22semidirect
109. #2510C22semidirect
110. #2495C22semidirect
111. #2492C22semidirect
112. #2488C22semidirect
113. #2485C22semidirect
114. #2483C22semidirect
115. #2481C22semidirect
116. #2480C22semidirect
117. #2474C22semidirect
118. #2472C22semidirect
119. #2472C22semidirect
120. #2472C22semidirect
121. #2472C22semidirect
122. #2470C22semidirect
123. #2470C22semidirect
124. #2467C22semidirect
125. #2465C22semidirect
126. #2465C22semidirect
127. #2464C22semidirect
128. #2463C22semidirect
129. #2461C22semidirect
130. #2461C22semidirect
131. #2457C22semidirect
132. #2456C22semidirect
133. #2452C22semidirect
134. #2450C22semidirect
135. #2447C22semidirect
136. #2444C22semidirect
137. #2444C22semidirect
138. #2427C22semidirect
139. #2427C22semidirect
140. #2427C22semidirect
142. #2424C22semidirect
143. #2424C22semidirect
144. #2424C22semidirect
145. #2418C22semidirect
146. #2415C22semidirect
147. #2412C22semidirect
148. #2410C22semidirect
149. #2408C22semidirect
151. #2406C22semidirect
153. #2404C22semidirect
154. #2403C22semidirect
155. #2403C22semidirect
156. #2401C22semidirect
157. #2398C22semidirect
158. #2398C22semidirect
159. #2398C22semidirect
160. #2388C22semidirect
161. #2374C22semidirect
162. #2374C22semidirect
163. #2372C22semidirect
164. #2372C22semidirect
165. #2368C22semidirect
166. #2367C22semidirect
167. #2364C22semidirect
168. #2364C22semidirect
169. #2364C22semidirect
171. #2363C22semidirect
172. #2360C22semidirect
173. #2359C22semidirect
174. #2358C22semidirect
175. #2358C22semidirect
176. #2358C22semidirect
177. #2357C22semidirect
178. #2356C22semidirect
179. #2353C22semidirect
180. #2353C22semidirect
181. #2352C22semidirect
182. #2349C22semidirect
183. #2342C22semidirect
184. #2342C22semidirect
185. #2342C22semidirect
186. #2341C22semidirect
187. #2339C22semidirect
188. D4×C22⋊C4C22semidirect
189. D4×C22⋊C4C22semidirect
190. #2337C22semidirect
191. #2335C22semidirect
192. #2335C22semidirect
194. #2333C22semidirect
195. #2333C22semidirect
196. #2329C22semidirect
197. #2321C22semidirect
198. #2321C22semidirect
199. C4×#124C22semidirect
200. C4×#124C22semidirect
201. C4×C22⋊Q8C22semidirect
202. C4×#123C22semidirect
204. C4×#121C22semidirect
205. C4×#121C22semidirect
206. C4×#121C22semidirect
207. C4×#120C22semidirect
208. C4×#120C22semidirect
209. #2297C22semidirect
210. #2297C22semidirect
211. #2293C22semidirect
212. C2×#390C22semidirect
213. #2290C22semidirect
214. C2×#386C22semidirect
215. #2275C22semidirect
216. #2273C22semidirect
217. C42×D4C22semidirect
218. C2×C4×C22⋊C4C22semidirect
698. #121#41semidirect

Maximal subgroups

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

subgroupindex
#598342
#598142
#598032
#595682
#523012
#522782
#441682
#437912
#437722
#433642
#431182
#397082
#392082
#387892
#386362
#385402
#384662
#365362
#365302
#360742
#359442
#343202
#343022