Finite Group Databasebeta

← #8932442

Subgroups — #8932442

Order 512.

4424 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#55979C214yesmaximal, complemented
2#55869C214yesmaximal, complemented
3#53917C214yesmaximal, complemented
4#53709C214yesmaximal, complemented
5#53644C214yesmaximal, complemented
6#53582C214yesmaximal, complemented
7#51993C212yesmaximal, complemented
8#51945C212yesmaximal, complemented
9#51378C214yesmaximal, complemented
10#49886C214yesmaximal, complemented
11#46816C212yesmaximal, complemented
12#46814C212yesmaximal, complemented
13#46455C212yesmaximal, complemented
14#46294C212yesmaximal, complemented
15#46290C212yesmaximal, complemented
16#46064C214yesmaximal, complemented
17#45929C214yesmaximal, complemented
18#37020C212yesmaximal, complemented
19#37010C212yesmaximal, complemented
20#36967C211yesmaximal, characteristic
21#36966C211yesmaximal, characteristic, complemented
22#35679C211yesmaximal, characteristic, complemented
23#35669C212yesmaximal, complemented
24C2×#543C2211yescharacteristic, complemented
25C2×#542C2212yes—
26C2×#534C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C2×#519C2211yescharacteristic, complemented
29#2866C2214yescomplemented
30#2861C2214yescomplemented
31#2855C2212yescomplemented
32#2854C2212yes—
33#2838C2214yescomplemented
34#2838C2214yescomplemented
35#2837C2214yescomplemented
36#2837C2214yescomplemented
37#2836C2214yescomplemented
38#2832C2214yescomplemented
39#2832C2214yescomplemented
40#2829C2214yescomplemented
41#2816C2212yes—
42#2810C2212yescomplemented
43#2808C2212yescomplemented
44#2805C2212yescomplemented
45#2804C2212yescomplemented
46#2803C2214yes—
47#2800C2214yescomplemented
48#2799C2214yescomplemented
49#2798C2214yescomplemented
50#2798C2214yescomplemented
51#2798C2214yescomplemented
52#2796C2214yescomplemented
53#2795C2214yescomplemented
54#2793C2214yescomplemented
55#2778C2214yescomplemented
56#2759C2214yescomplemented
57#2754C2214yescomplemented
58#2754C2214yescomplemented
59#2752C2214yescomplemented
60#2751C2214yescomplemented
61#2749C2214yescomplemented
62#2745C2214yescomplemented
63#2743C2214yescomplemented
64#2743C2214yescomplemented
65#2741C2214yescomplemented
66#2740C2214yescomplemented
67#2738C2214yescomplemented
68#2736C2214yes—
69#2735C2214yes—
70#2735C2214yescomplemented
71#2735C2214yescomplemented
72#2734C2212yescomplemented
73#2732C2212yescomplemented
74#2730C2214yes—
75#2730C2214yescomplemented
76#2730C2214yescomplemented
77#2729C2214yescomplemented
78#2727C2212yescomplemented
79#2726C2212yescomplemented
80#2723C2214yescomplemented
81#2721C2214yescomplemented
82#2720C2214yescomplemented
83#2716C2214yescomplemented
84#2715C2214yescomplemented
85#2710C2214yes—
86#2710C2214yes—
87#2710C2214yes—
88#2701C2214yes—
89#2700C2214yescomplemented
90#2700C2214yescomplemented
91#2700C2214yescomplemented
92#2700C2214yescomplemented
93#2697C2212yescomplemented
94#2697C2212yescomplemented
95#2696C2214yes—
96#2694C2214yescomplemented
97#2692C2214yescomplemented
98#2689C2214yescomplemented
99#2687C2214yescomplemented
100#2686C2214yes—
101#2685C2214yescomplemented
102#2685C2214yescomplemented
103#2685C2214yescomplemented
104#2684C2214yescomplemented
105#2684C2214yescomplemented
106#2683C2212yescomplemented
107#2683C2212yescomplemented
108#2680C2214yescomplemented
109#2680C2214yescomplemented
110#2677C2214yescomplemented
111#2674C2214yescomplemented
112#2674C2214yescomplemented
113#2674C2214yescomplemented
114#2674C2214yescomplemented
115#2674C2214yescomplemented
116#2670C2214yes—
117#2670C2214yes—
118#2662C2214yes—
119#2652C2214yescomplemented
120#2651C2214yescomplemented
121#2650C2214yescomplemented
122#2649C2214yescomplemented
123#2648C2214yes—
124#2638C2214yescomplemented
125#2626C2212yes—
126#2626C2214yescomplemented
127#2617C2212yes—
128#2607C2214yescomplemented
129#2607C2212yescomplemented
130#2602C2214yes—
131#2597C2214yescomplemented
132#2595C2214yescomplemented
133#2594C2214yescomplemented
134#2594C2214yescomplemented
135#2589C2214yescomplemented
136#2588C2214yescomplemented
137#2586C2214yescomplemented
138#2577C2214yescomplemented
139#2568C2212yescomplemented
140#2567C2212yescomplemented
141#2561C2212yes—
142#2561C2214yescomplemented
143#2560C2214yescomplemented
144#2560C2214yescomplemented
145#2560C2214yescomplemented
146#2558C2214yescomplemented
147#2556C2214yescomplemented
148#2554C2214yes—
149#2553C2214yescomplemented
150#2545C2212yescomplemented
151#2545C2212yescomplemented
152#2542C2214yescomplemented
153#2539C2212yes—
154#2532C2214yescomplemented
155#2526C2214yescomplemented
156#2525C2214yescomplemented
157#2521C2214yescomplemented
158#2516C2214yescomplemented
159#2507C2214yescomplemented
160#2500C2212yes—
161#2499C2212yescomplemented
162#2492C2214yescomplemented
163#2492C2214yescomplemented
164#2483C2212yescomplemented
165#2482C2212yes—
166#2482C2212yes—
167#2482C2212yescomplemented
168#2482C2212yescomplemented
169#2479C2214yescomplemented
170#2477C2214yescomplemented
171#2474C2214yescomplemented
172#2474C2214yescomplemented
173#2472C2214yescomplemented
174#2472C2214yescomplemented
175#2472C2214yescomplemented
176#2470C2214yescomplemented
177#2470C2214yescomplemented
178#2469C2214yescomplemented
179#2469C2214yescomplemented
180#2465C2214yescomplemented
181#2465C2214yescomplemented
182#2463C2214yescomplemented
183#2459C2214yescomplemented
184#2458C2214yescomplemented
185#2448C2214yescomplemented
186#2448C2214yescomplemented
187#2448C2214yescomplemented
188#2448C2214yescomplemented
189#2436C2212yes—
190#2435C2214yes—
191#2434C2212yescomplemented
192#2423C2214yescomplemented
193#2418C2214yescomplemented
194#2418C2214yescomplemented
195#2405C2212yes—
196#2405C2214yes—
197#2405C2212yes—
198#2403C2212yes—
199#2383C2214yescomplemented
200#2378C2214yescomplemented
201#2376C2212yescomplemented
202#2375C2212yescomplemented
203#2374C2212yescomplemented
204#2358C2212yescomplemented
205#2333C2212yes—
206#2332C2212yescomplemented
207#2327C2212yescomplemented
208#2326C2212yescomplemented
209#2312C2211yescharacteristic
210#2312C2211yescharacteristic, complemented
211#2310C2211yescharacteristic, complemented
212#2309C2211yescharacteristic
213#2309C2211yescharacteristic
214C4×C4⋊Q8C2212yescomplemented
215C4×#124C2212yescomplemented
216#2298C2212yescomplemented
217#2296C2211yescharacteristic, complemented
218#2296C2211yescharacteristic, complemented
219C23×Q8C2311yescharacteristic
220C23×D4C2311yescharacteristic
221C23×D4C2312yes—
222#543—44no—
223#542—48no—
224#534—44no—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2314yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#125C2314yes—
233C2×#124—44no—
234C2×#124C2312yes—
235C2×#124C2314yes—
236C2×#124C2314yes—
237C2×#124C2312yes—
238C2×#124C2314yes—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2314yes—
242C2×#123C2312yes—
243C2×#123C2312yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#120C2312yes—
261C2×#120C2312yes—
262C2×#120C2314yes—
263C2×#120C2314yes—
264#519—44no—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×#117C2312yes—
273C2×#117C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2312yes—
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2314yes—
284C22×C42C2311yescharacteristic
285#401C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#399C2314yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
306#399C2314yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
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#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
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#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2312yes—
409#391C2312yes—
410#391C2314yes—
411#391C2314yes—
412#391C2312yes—
413#391C2312yes—
414#391C2314yes—
415#391C2312yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2314yes—
433#390C2312yes—
434#390C2314yes—
435#390C2312yes—
436#390C2312yes—
437#390C2314yes—
438#390C2312yes—
439#390C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
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#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
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#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#386C2312yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2312yes—
550#386C2312yes—
551#386C2314yes—
552#386C2314yes—
553#386C2312yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2312yes—
570#385C2312yes—
571#385C2312yes—
572#385C2312yes—
573#384C2312yes—
574#384C2312yes—
575#384C2314yes—
576#383C2314yes—
577#382C2312yes—
578#382C2312yes—
579#381C2312yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2312yes—
584#381C2314yes—
585#380C2312yes—
586#380C2312yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#379C2314yes—
591#379C2314yes—
592#379C2314yes—
593#379C2312yes—
594#379C2312yes—
595#379C2312yes—
596#379C2312yes—
597#379C2312yes—
598#379C2312yes—
599#379C2314yes—
600#379C2314yes—
601C4×C4⋊C4C2312yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617#376C2312yes—
618C43C2312yes—
619C25C2411yescharacteristic
620C25C2411yescharacteristic
621C25C2412yes—
622C22×Q8—24no—
623C22×Q8—42no—
624C22×Q8—42no—
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2414yes—
630C22×Q8C2414yes—
631C22×D4—42no—
632C22×D4—42no—
633C22×D4—42no—
634C22×D4—44no—
635C22×D4—84no—
636C22×D4C2412yes—
637C22×D4C2414yes—
638C22×D4C2412yes—
639C22×D4C2412yes—
640C22×D4C2414yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C23×C4C2411yescharacteristic
645C23×C4C2411yescharacteristic
646C23×C4C2411yescharacteristic
647C23×C4C2411yescharacteristic
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2412yes—
651C23×C4C2414yes—
652C23×C4C2412yes—
653C23×C4C2411yescharacteristic
654C4⋊Q8—44no—
655C4⋊Q8—44no—
656C4⋊Q8—44no—
657C4⋊Q8—84no—
658#126—48no—
659#126—48no—
660#126—84no—
661#125—84no—
662#124—44no—
663#124—48no—
664#124—48no—
665#124—48no—
666#124—44no—
667#124—44no—
668#124—84no—
669#124—84no—
670#123—48no—
671#123—48no—
672#123—44no—
673#123—44no—
674#123—84no—
675#123—84no—
676C22⋊Q8—28no—
677C22⋊Q8—44no—
678C22⋊Q8—48no—
679C22⋊Q8—48no—
680C22⋊Q8—48no—
681C22⋊Q8—48no—
682C22⋊Q8—84no—
683C22⋊Q8—84no—
684C22⋊Q8—84no—
685C22⋊Q8—84no—
686#121—28no—
687#121—44no—
688#120—44no—
689#120—44no—
690#120—48no—
691#120—84no—
692C4×Q8—44no—
693C4×Q8—44no—
694C4×Q8—44no—
695C4×Q8—44no—
696C4×Q8—44no—
697C4×D4—44no—
698C4×D4—84no—
699#117—28no—
700#117—42no—
701#117—44no—
702#117—42no—
703#117—42no—
704#117—42no—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C22⋊C4—24no—
752C2×C22⋊C4—24no—
753C2×C22⋊C4—44no—
754C2×C22⋊C4—42no—
755C2×C22⋊C4—42no—
756C2×C22⋊C4—84no—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C42—42no—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
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#95C2414yes—
854#95C2414yes—
855#95C2414yes—
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—
880C24—22no—
881C24—22no—
882C24—42no—
883C24—42no—
884C24—44no—
885C24—42no—
886C24—42no—
887C24—42no—
888C24—41no—
889C24—41no—
890C24—41no—
891C24—41no—
892C24—42no—
893C24—44no—
894C24—42no—
895C24C2512yes—
896C24C2512yes—
897C24C2514yes—
898C24C2511yescharacteristic
899C2×Q8—24no—
900C2×Q8—24no—
901C2×Q8—24no—
902C2×Q8—24no—
903C2×Q8—24no—
904C2×Q8—42no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8—44no—
910C2×Q8—44no—
911C2×Q8—42no—
912C2×Q8—44no—
913C2×Q8—44no—
914C2×Q8—44no—
915C2×Q8—42no—
916C2×Q8—44no—
917C2×Q8—416no—
918C2×D4—28no—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—44no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—44no—
936C2×D4—42no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—88no—
943C2×D4—816no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—44no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—44no—
969C22×C4H(5,𝔽2)14yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2514yes—
973C22×C4C2512yes—
974C22×C4C2514yes—
975C22×C4C2512yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—28no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—42no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—42no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—42no—
1013C4⋊C4—44no—
1014C4⋊C4—42no—
1015C4⋊C4—44no—
1016C4⋊C4—42no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C22⋊C4—28no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
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—42no—
1060C22⋊C4—42no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—42no—
1079C22⋊C4—44no—
1080C22⋊C4—42no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C42—24no—
1090C42—24no—
1091C42—42no—
1092C42—42no—
1093C42—44no—
1094C42—42no—
1095C42—42no—
1096C42—42no—
1097C42—42no—
1098C42—42no—
1099C42—42no—
1100C42—44no—
1101C42—44no—
1102C42—42no—
1103C42—42no—
1104C42—44no—
1105C42—44no—
1106C42—44no—
1107C42—42no—
1108C42—42no—
1109C23—21no—
1110C23—21no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—24no—
1123C23—24no—
1124C23—24no—
1125C23—24no—
1126C23—24no—
1127C23—24no—
1128C23—24no—
1129C23—24no—
1130C23—44no—
1131C23—44no—
1132C23—82no—
1133C23—82no—
1134C23—82no—
1135C23—82no—
1136C23—84no—
1137C23—88no—
1138C23—162no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23—164no—
1143C23—162no—
1144C23—162no—
1145C23C2×H(5,𝔽2)12yes—
1146C23C2611yescharacteristic
1147Q8—48no—
1148Q8—48no—
1149Q8—84no—
1150Q8—164no—
1151Q8—164no—
1152Q8—162no—
1153D4—84no—
1154D4—84no—
1155D4—84no—
1156D4—88no—
1157D4—88no—
1158D4—88no—
1159D4—164no—
1160D4—162no—
1161C2×C4—28no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—44no—
1213C2×C4—44no—
1214C2×C4—82no—
1215C2×C4—82no—
1216C2×C4—84no—
1217C2×C4—164no—
1218C2×C4—162no—
1219C2×C4—164no—
1220C2×C4—162no—
1221C2×C4C2×H(5,𝔽2)14yes—
1222C2×C4#58512yes—
1223C2×C4#58512yes—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—42no—
1228C22—42no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—42no—
1239C22—44no—
1240C22—42no—
1241C22—44no—
1242C22—42no—
1243C22—44no—
1244C22—42no—
1245C22—42no—
1246C22—164no—
1247C22—164no—
1248C22—168no—
1249C22C22×H(5,𝔽2)11yescharacteristic
1250C22C2×#58511yescharacteristic
1251C22C2×#58511yescharacteristic
1252C22H(7,𝔽2)12yes—
1253C222−1+612yes—
1254C4—22no—
1255C4—22no—
1256C4—24no—
1257C4—44no—
1258C4—44no—
1259C4—44no—
1260C4—44no—
1261C4—44no—
1262C4—44no—
1263C4—42no—
1264C4—44no—
1265C4—44no—
1266C4—42no—
1267C4—42no—
1268C4—44no—
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4—42no—
1273C2—42no—
1274C2—84no—
1275C2—82no—
1276C2—82no—
1277C2#6282011yescharacteristic
1278C2#6287611yescharacteristic
1279C2#6288711yescharacteristic
1280C2#6305612yes—
1281C2#6306912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36967C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #55979C2semidirect
2. #55869C2semidirect
3. #53917C2semidirect
4. #53709C2semidirect
5. #53644C2semidirect
6. #53582C2semidirect
7. #51993C2semidirect
8. #51945C2semidirect
9. #51378C2semidirect
10. #49886C2semidirect
11. #46816C2semidirect
12. #46814C2semidirect
13. #46455C2semidirect
14. #46294C2semidirect
15. #46290C2semidirect
16. #46064C2semidirect
17. #45929C2semidirect
18. #37020C2semidirect
19. #37010C2semidirect
21. #36966C2semidirect
22. #35679C2semidirect
23. #35669C2semidirect
24. C2×#543C22semidirect
28. C2×#519C22semidirect
29. #2866C22semidirect
30. #2861C22semidirect
31. #2855C22semidirect
33. #2838C22semidirect
34. #2838C22semidirect
35. #2837C22semidirect
36. #2837C22semidirect
37. #2836C22semidirect
38. #2832C22semidirect
39. #2832C22semidirect
40. #2829C22semidirect
42. #2810C22semidirect
43. #2808C22semidirect
44. #2805C22semidirect
45. #2804C22semidirect
47. #2800C22semidirect
48. #2799C22semidirect
49. #2798C22semidirect
50. #2798C22semidirect
51. #2798C22semidirect
52. #2796C22semidirect
53. #2795C22semidirect
54. #2793C22semidirect
55. #2778C22semidirect
56. #2759C22semidirect
57. #2754C22semidirect
58. #2754C22semidirect
59. #2752C22semidirect
60. #2751C22semidirect
61. #2749C22semidirect
62. #2745C22semidirect
63. #2743C22semidirect
64. #2743C22semidirect
65. #2741C22semidirect
66. #2740C22semidirect
67. #2738C22semidirect
70. #2735C22semidirect
71. #2735C22semidirect
72. #2734C22semidirect
73. #2732C22semidirect
75. #2730C22semidirect
76. #2730C22semidirect
77. #2729C22semidirect
78. #2727C22semidirect
79. #2726C22semidirect
80. #2723C22semidirect
81. #2721C22semidirect
82. #2720C22semidirect
83. #2716C22semidirect
84. #2715C22semidirect
89. #2700C22semidirect
90. #2700C22semidirect
91. #2700C22semidirect
92. #2700C22semidirect
93. #2697C22semidirect
94. #2697C22semidirect
96. #2694C22semidirect
97. #2692C22semidirect
98. #2689C22semidirect
99. #2687C22semidirect
101. #2685C22semidirect
102. #2685C22semidirect
103. #2685C22semidirect
104. #2684C22semidirect
105. #2684C22semidirect
106. #2683C22semidirect
107. #2683C22semidirect
108. #2680C22semidirect
109. #2680C22semidirect
110. #2677C22semidirect
111. #2674C22semidirect
112. #2674C22semidirect
113. #2674C22semidirect
114. #2674C22semidirect
115. #2674C22semidirect
119. #2652C22semidirect
120. #2651C22semidirect
121. #2650C22semidirect
122. #2649C22semidirect
124. #2638C22semidirect
126. #2626C22semidirect
128. #2607C22semidirect
129. #2607C22semidirect
131. #2597C22semidirect
132. #2595C22semidirect
133. #2594C22semidirect
134. #2594C22semidirect
135. #2589C22semidirect
136. #2588C22semidirect
137. #2586C22semidirect
138. #2577C22semidirect
139. #2568C22semidirect
140. #2567C22semidirect
142. #2561C22semidirect
143. #2560C22semidirect
144. #2560C22semidirect
145. #2560C22semidirect
146. #2558C22semidirect
147. #2556C22semidirect
149. #2553C22semidirect
150. #2545C22semidirect
151. #2545C22semidirect
152. #2542C22semidirect
154. #2532C22semidirect
155. #2526C22semidirect
156. #2525C22semidirect
157. #2521C22semidirect
158. #2516C22semidirect
159. #2507C22semidirect
161. #2499C22semidirect
162. #2492C22semidirect
163. #2492C22semidirect
164. #2483C22semidirect
167. #2482C22semidirect
168. #2482C22semidirect
169. #2479C22semidirect
170. #2477C22semidirect
171. #2474C22semidirect
172. #2474C22semidirect
173. #2472C22semidirect
174. #2472C22semidirect
175. #2472C22semidirect
176. #2470C22semidirect
177. #2470C22semidirect
178. #2469C22semidirect
179. #2469C22semidirect
180. #2465C22semidirect
181. #2465C22semidirect
182. #2463C22semidirect
183. #2459C22semidirect
184. #2458C22semidirect
185. #2448C22semidirect
186. #2448C22semidirect
187. #2448C22semidirect
188. #2448C22semidirect
191. #2434C22semidirect
192. #2423C22semidirect
193. #2418C22semidirect
194. #2418C22semidirect
199. #2383C22semidirect
200. #2378C22semidirect
201. #2376C22semidirect
202. #2375C22semidirect
203. #2374C22semidirect
204. #2358C22semidirect
206. #2332C22semidirect
207. #2327C22semidirect
208. #2326C22semidirect
210. #2312C22semidirect
211. #2310C22semidirect
214. C4×C4⋊Q8C22semidirect
215. C4×#124C22semidirect
216. #2298C22semidirect
217. #2296C22semidirect
218. #2296C22semidirect

Maximal subgroups

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

subgroupindex
#559792
#558692
#539172
#537092
#536442
#535822
#519932
#519452
#513782
#498862
#468162
#468142
#464552
#462942
#462902
#460642
#459292
#370202
#370102
#369672
#369662
#356792
#356692