Finite Group Databasebeta

← #8108456

Subgroups — #8108456

Order 512.

4602 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#59369C212yesmaximal, complemented
2#59367C212yesmaximal, complemented
3#53274C214yesmaximal, complemented
4#53272C214yesmaximal, complemented
5#45845C214yesmaximal, complemented
6#45823C214yesmaximal, complemented
7#45569C212yesmaximal, complemented
8#45539C212yesmaximal, complemented
9#39988C214yesmaximal, complemented
10#39964C214yesmaximal, complemented
11#38606C214yesmaximal, complemented
12#38605C214yesmaximal, complemented
13#37959C212yesmaximal, complemented
14#37951C212yesmaximal, complemented
15#37755C212yesmaximal, complemented
16#37747C212yesmaximal, complemented
17#36850C214yesmaximal, complemented
18#36848C214yesmaximal, complemented
19#36729C212yesmaximal, complemented
20#36708C211yesmaximal, characteristic, complemented
21#36707C211yesmaximal, characteristic
22#36621C212yesmaximal, complemented
23C2×#2855C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#529C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2855C2214yes—
30#2855C2214yes—
31#2855C2214yes—
32#2855C2214yes—
33#2855C2212yes—
34#2854C2212yes—
35#2853C2214yes—
36#2852C2214yes—
37#2852C2214yes—
38#2851C2212yes—
39#2851C2212yes—
40#2850C2212yes—
41#2850C2212yes—
42#2849C2214yes—
43#2848C2212yes—
44#2847C2212yes—
45#2835C2212yes—
46#2834C2212yes—
47#2826C2212yes—
48#2824C2212yes—
49#2807C2214yes—
50#2807C2212yes—
51#2805C2214yescomplemented
52#2804C2214yes—
53#2799C2214yescomplemented
54#2789C2214yescomplemented
55#2788C2214yescomplemented
56#2787C2214yescomplemented
57#2782C2214yes—
58#2782C2214yes—
59#2779C2214yescomplemented
60#2778C2214yes—
61#2775C2214yescomplemented
62#2775C2214yescomplemented
63#2774C2214yescomplemented
64#2771C2212yes—
65#2771C2214yescomplemented
66#2769C2214yescomplemented
67#2767C2214yescomplemented
68#2765C2214yescomplemented
69#2764C2212yes—
70#2763C2214yes—
71#2763C2212yes—
72#2762C2214yescomplemented
73#2760C2212yes—
74#2758C2214yescomplemented
75#2758C2214yescomplemented
76#2757C2214yes—
77#2757C2214yes—
78#2754C2214yescomplemented
79#2753C2214yes—
80#2752C2212yes—
81#2751C2214yes—
82#2748C2214yes—
83#2747C2214yes—
84#2745C2214yescomplemented
85#2744C2214yescomplemented
86#2743C2214yes—
87#2742C2214yes—
88#2741C2214yes—
89#2737C2214yescomplemented
90#2731C2214yescomplemented
91#2731C2214yescomplemented
92#2725C2214yescomplemented
93#2719C2214yescomplemented
94#2717C2214yes—
95#2716C2214yescomplemented
96#2716C2214yescomplemented
97#2712C2212yes—
98#2702C2214yes—
99#2702C2214yescomplemented
100#2700C2214yescomplemented
101#2693C2212yes—
102#2692C2214yes—
103#2692C2214yes—
104#2692C2214yes—
105#2691C2214yes—
106#2691C2214yescomplemented
107#2690C2214yes—
108#2690C2214yes—
109#2690C2214yescomplemented
110#2689C2214yescomplemented
111#2686C2214yescomplemented
112#2677C2214yes—
113#2677C2214yes—
114#2676C2214yes—
115#2676C2214yes—
116#2672C2214yes—
117#2666C2214yescomplemented
118#2665C2214yescomplemented
119#2659C2212yes—
120#2650C2214yescomplemented
121#2649C2214yescomplemented
122#2639C2212yes—
123#2627C2212yes—
124#2618C2212yes—
125#2612C2214yescomplemented
126#2607C2212yes—
127#2607C2212yes—
128#2605C2214yescomplemented
129#2600C2212yes—
130#2600C2212yes—
131#2588C2214yescomplemented
132#2587C2214yescomplemented
133#2586C2214yescomplemented
134#2575C2214yes—
135#2574C2214yescomplemented
136#2572C2214yes—
137#2561C2212yes—
138#2539C2212yes—
139#2531C2214yescomplemented
140#2529C2214yescomplemented
141#2528C2214yescomplemented
142#2527C2214yes—
143#2527C2214yescomplemented
144#2524C2214yescomplemented
145#2521C2214yescomplemented
146#2520C2214yescomplemented
147#2518C2214yescomplemented
148#2516C2214yes—
149#2505C2214yescomplemented
150#2503C2214yes—
151#2493C2214yes—
152#2493C2214yes—
153#2492C2214yescomplemented
154#2488C2214yes—
155#2488C2214yes—
156#2488C2214yes—
157#2486C2214yes—
158#2484C2212yes—
159#2482C2212yes—
160#2481C2214yes—
161#2476C2214yescomplemented
162#2475C2214yescomplemented
163#2472C2214yes—
164#2465C2214yescomplemented
165#2460C2214yescomplemented
166#2459C2214yes—
167#2457C2214yes—
168#2450C2214yes—
169#2449C2214yes—
170#2447C2214yes—
171#2446C2214yescomplemented
172#2444C2214yes—
173#2444C2214yescomplemented
174#2439C2214yescomplemented
175#2438C2214yescomplemented
176#2436C2212yes—
177#2434C2212yes—
178#2425C2214yes—
179#2419C2214yes—
180#2418C2214yes—
181#2413C2214yes—
182#2406C2212yes—
183#2406C2214yes—
184#2404C2212yes—
185#2379C2214yes—
186#2376C2214yes—
187#2368C2214yes—
188#2359C2214yes—
189#2357C2214yes—
190#2353C2214yes—
191#2353C2214yes—
192#2339C2214yes—
193#2337C2214yescomplemented
194#2334C2214yescomplemented
195#2331C2214yescomplemented
196#2329C2212yes—
197#2329C2214yescomplemented
198#2325C2212yes—
199#2313C2211yescharacteristic
200#2313C2211yescharacteristic
201C4×C22⋊Q8C2212yes—
202C4×C22⋊Q8C2212yes—
203C4×#123C2214yes—
204C4×#121C2212yes—
205C4×#121C2212yes—
206C4×#120C2214yes—
207C2×#391C2212yes—
208C2×#389C2212yes—
209#2290C2214yes—
210#2290C2214yes—
211C2×#387C2212yes—
212C2×#387C2212yes—
213C2×#385C2211yescharacteristic
214C2×#385C2211yescharacteristic
215#2283C2212yes—
216C2×#381C2211yescharacteristic
217C2×#381C2211yescharacteristic
218C2×#380C2211yescharacteristic
219C22×#41C2312yes—
220C23×Q8C2311yescharacteristic
221C24×C4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224#544—44no—
225#537—44no—
226C2×C4⋊Q8C2314yes—
227C2×C4⋊Q8C2314yes—
228#529—48no—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#125C2312yes—
232C2×#125C2314yes—
233C2×#124C2314yes—
234C2×#124C2312yes—
235C2×#124C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×C22⋊Q8—44no—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2314yes—
254C2×#121C2312yes—
255C2×#120C2314yes—
256C2×C4×Q8C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×#117C2312yes—
263C2×#117C2314yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2311yescharacteristic
272C22×C22⋊C4C2311yescharacteristic
273C22×C22⋊C4C2311yescharacteristic
274C22×C42—44no—
275C22×C42C2312yes—
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2312yes—
279C22×C42C2312yes—
280C22×C42C2312yes—
281#401C2314yes—
282#401C2314yes—
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#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#399C2312yes—
307#399C2312yes—
308#399C2314yes—
309#399C2312yes—
310#399C2312yes—
311#399C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#397C2312yes—
326#397C2312yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2312yes—
332#397C2312yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#393C2312yes—
370#393C2312yes—
371#393C2314yes—
372#393C2314yes—
373#393C2314yes—
374#393C2312yes—
375#393C2312yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#392C2312yes—
382#392C2312yes—
383#392C2312yes—
384#392C2312yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2312yes—
397#391C2312yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#390C2312yes—
405#390C2312yes—
406#390C2314yes—
407#390C2314yes—
408#390C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
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#387C2314yes—
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#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
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#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#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#385C2312yes—
524#385C2312yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2312yes—
545#385C2312yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#383C2314yes—
552#383C2314yes—
553#383C2314yes—
554#383C2314yes—
555#382C2314yes—
556#382C2314yes—
557#382C2314yes—
558#382C2312yes—
559#382C2312yes—
560#382C2314yes—
561#382C2314yes—
562#381C2314yes—
563#381C2312yes—
564#381C2312yes—
565#381C2314yes—
566#381C2314yes—
567#381C2314yes—
568#381C2314yes—
569#381C2314yes—
570#381C2312yes—
571#381C2312yes—
572#381C2312yes—
573#381C2312yes—
574#381C2314yes—
575#381C2314yes—
576#380C2312yes—
577#380C2312yes—
578#380C2314yes—
579#380C2312yes—
580#380C2312yes—
581#380C2312yes—
582#380C2312yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#379C2314yes—
591C4×C4⋊C4C2312yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609#376C2314yes—
610#376C2314yes—
611C2×#95C2312yes—
612C2×#95C2314yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C25C2411yescharacteristic
620C2×#41—44no—
621C2×#41—48no—
622C22×Q8—42no—
623C22×Q8—44no—
624C22×Q8C2412yes—
625C22×Q8C2414yes—
626C22×Q8C2414yes—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×D4C2414yes—
630C22×D4C2414yes—
631C22×D4C2414yes—
632C22×D4C2412yes—
633C22×D4C2412yes—
634C22×D4C2412yes—
635C23×C4—24no—
636C23×C4—24no—
637C23×C4—44no—
638C23×C4—44no—
639C23×C4—42no—
640C23×C4—42no—
641C23×C4—42no—
642C23×C4C2411yescharacteristic
643C23×C4C2411yescharacteristic
644C23×C4C2411yescharacteristic
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2411yescharacteristic
653C23×C4C2411yescharacteristic
654C23×C4C2414yes—
655C23×C4C2411yescharacteristic
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2412yes—
659C23×C4C2411yescharacteristic
660C23×C4C2411yescharacteristic
661C23×C4C2411yescharacteristic
662C23×C4C2411yescharacteristic
663C4⋊Q8—48no—
664C4⋊Q8—48no—
665#126—48no—
666#126—48no—
667#125—44no—
668#125—48no—
669#124—44no—
670#124—48no—
671#124—48no—
672#123—48no—
673#123—48no—
674#123—48no—
675#123—48no—
676C22⋊Q8—28no—
677C22⋊Q8—48no—
678C22⋊Q8—44no—
679C22⋊Q8—48no—
680C22⋊Q8—48no—
681C22⋊Q8—48no—
682C22⋊Q8—48no—
683C22⋊Q8—44no—
684C22⋊Q8—44no—
685#121—28no—
686#121—44no—
687#121—44no—
688#121—48no—
689#121—44no—
690#120—48no—
691C4×Q8—44no—
692C4×D4—216no—
693C4×D4—44no—
694C4×D4—48no—
695C4×D4—48no—
696C4×D4—48no—
697#117—48no—
698#117—44no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—24no—
701C2×C4⋊C4—44no—
702C2×C4⋊C4—44no—
703C2×C4⋊C4—44no—
704C2×C4⋊C4—42no—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C22⋊C4—42no—
748C2×C22⋊C4—42no—
749C2×C22⋊C4—42no—
750C2×C22⋊C4—42no—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
763C2×C22⋊C4C2412yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
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⋊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×C42—28no—
791C2×C42—44no—
792C2×C42—44no—
793C2×C42—44no—
794C2×C42—44no—
795C2×C42—44no—
796C2×C42C2412yes—
797C2×C42C2412yes—
798C2×C42C2414yes—
799C2×C42C2412yes—
800C2×C42C2412yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2412yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2412yes—
848#95C2414yes—
849#95C2414yes—
850#95C2412yes—
851#95C2412yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2412yes—
862#95C2414yes—
863#95C2414yes—
864#95C2412yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2412yes—
869#95C2412yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877C24—22no—
878C24—22no—
879C24—22no—
880C24—24no—
881C24—42no—
882C24C2514yes—
883C24C2511yescharacteristic
884C24C2511yescharacteristic
885C24C2511yescharacteristic
886#41—816no—
887C2×Q8—24no—
888C2×Q8—28no—
889C2×Q8—44no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—42no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—42no—
896C2×Q8—44no—
897C2×Q8—44no—
898C2×Q8—44no—
899C2×Q8—44no—
900C2×Q8—88no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—42no—
916C2×D4—44no—
917C22×C4—22no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—28no—
940C22×C4—41no—
941C22×C4—42no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—42no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—41no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
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—42no—
964C22×C4—42no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—416no—
971C22×C4—416no—
972C22×C4—416no—
973C22×C4H(5,𝔽2)14yes—
974C22×C42−1+414yes—
975C22×C4C2512yes—
976C22×C4C2514yes—
977C22×C4C2512yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2514yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2514yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—24no—
1039C22⋊C4—24no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
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—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—
1075C42—24no—
1076C42—24no—
1077C42—24no—
1078C42—24no—
1079C42—28no—
1080C42—42no—
1081C42—42no—
1082C42—42no—
1083C42—42no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C23—21no—
1093C23—22no—
1094C23—21no—
1095C23—28no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—24no—
1105C23—24no—
1106C23—24no—
1107C23—24no—
1108C23—24no—
1109C23—24no—
1110C23—24no—
1111C23—48no—
1112C23—48no—
1113C23—44no—
1114C23—44no—
1115C23C2×H(5,𝔽2)12yes—
1116C23C2×2−1+412yes—
1117C23#58512yes—
1118C23#58514yes—
1119C23C2611yescharacteristic
1120Q8—84no—
1121Q8—88no—
1122Q8—84no—
1123Q8—162no—
1124Q8—164no—
1125D4—416no—
1126D4—84no—
1127D4—88no—
1128D4—88no—
1129D4—84no—
1130D4—162no—
1131C2×C4—28no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
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—24no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—44no—
1183C2×C4—44no—
1184C2×C4—48no—
1185C2×C4—48no—
1186C2×C4—48no—
1187C2×C4—48no—
1188C2×C4—44no—
1189C2×C4—44no—
1190C2×C4—48no—
1191C2×C4—44no—
1192C2×C4—44no—
1193C2×C4—48no—
1194C2×C4—44no—
1195C2×C4—88no—
1196C2×C4—84no—
1197C2×C4—84no—
1198C2×C4—82no—
1199C2×C4—82no—
1200C2×C4—88no—
1201C2×C4—164no—
1202C2×C4C2×H(5,𝔽2)14yes—
1203C2×C4C2×2−1+414yes—
1204C2×C4#58514yes—
1205C22—24no—
1206C22—22no—
1207C22—22no—
1208C22—24no—
1209C22—24no—
1210C22—22no—
1211C22—22no—
1212C22—24no—
1213C22—416no—
1214C22—41no—
1215C22—41no—
1216C22—42no—
1217C22—41no—
1218C22—41no—
1219C22—42no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22#354014yes—
1228C22C22×H(5,𝔽2)11yescharacteristic
1229C22C22×2−1+411yescharacteristic
1230C22C2×#58512yes—
1231C22C2×#58512yes—
1232C22C2×#58511yescharacteristic
1233C4—24no—
1234C4—24no—
1235C4—24no—
1236C4—42no—
1237C4—42no—
1238C4—42no—
1239C4—42no—
1240C4—44no—
1241C4—44no—
1242C4—44no—
1243C4—42no—
1244C4—44no—
1245C4—42no—
1246C4—42no—
1247C4—44no—
1248C4—44no—
1249C4—44no—
1250C4—44no—
1251C4—44no—
1252C2—24no—
1253C2—42no—
1254C2—42no—
1255C2—84no—
1256C2C2×#354011yescharacteristic
1257C2#6275212yes—
1258C2#6281911yescharacteristic
1259C2#6282011yescharacteristic
1260C2#6282912yes—
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. #59369C2semidirect
2. #59367C2semidirect
3. #53274C2semidirect
4. #53272C2semidirect
5. #45845C2semidirect
6. #45823C2semidirect
7. #45569C2semidirect
8. #45539C2semidirect
9. #39988C2semidirect
10. #39964C2semidirect
11. #38606C2semidirect
12. #38605C2semidirect
13. #37959C2semidirect
14. #37951C2semidirect
15. #37755C2semidirect
16. #37747C2semidirect
17. #36850C2semidirect
18. #36848C2semidirect
19. #36729C2semidirect
20. #36708C2semidirect
22. #36621C2semidirect
23. C2×#2855C2semidirect
51. #2805C22semidirect
53. #2799C22semidirect
54. #2789C22semidirect
55. #2788C22semidirect
56. #2787C22semidirect
59. #2779C22semidirect
61. #2775C22semidirect
62. #2775C22semidirect
63. #2774C22semidirect
65. #2771C22semidirect
66. #2769C22semidirect
67. #2767C22semidirect
68. #2765C22semidirect
72. #2762C22semidirect
74. #2758C22semidirect
75. #2758C22semidirect
78. #2754C22semidirect
84. #2745C22semidirect
85. #2744C22semidirect
89. #2737C22semidirect
90. #2731C22semidirect
91. #2731C22semidirect
92. #2725C22semidirect
93. #2719C22semidirect
95. #2716C22semidirect
96. #2716C22semidirect
99. #2702C22semidirect
100. #2700C22semidirect
106. #2691C22semidirect
109. #2690C22semidirect
110. #2689C22semidirect
111. #2686C22semidirect
117. #2666C22semidirect
118. #2665C22semidirect
120. #2650C22semidirect
121. #2649C22semidirect
125. #2612C22semidirect
128. #2605C22semidirect
131. #2588C22semidirect
132. #2587C22semidirect
133. #2586C22semidirect
135. #2574C22semidirect
139. #2531C22semidirect
140. #2529C22semidirect
141. #2528C22semidirect
143. #2527C22semidirect
144. #2524C22semidirect
145. #2521C22semidirect
146. #2520C22semidirect
147. #2518C22semidirect
149. #2505C22semidirect
153. #2492C22semidirect
161. #2476C22semidirect
162. #2475C22semidirect
164. #2465C22semidirect
165. #2460C22semidirect
171. #2446C22semidirect
173. #2444C22semidirect
174. #2439C22semidirect
175. #2438C22semidirect
193. #2337C22semidirect
194. #2334C22semidirect
195. #2331C22semidirect
197. #2329C22semidirect

Maximal subgroups

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

subgroupindex
#593692
#593672
#532742
#532722
#458452
#458232
#455692
#455392
#399882
#399642
#386062
#386052
#379592
#379512
#377552
#377472
#368502
#368482
#367292
#367082
#367072
#366212
C2×#28552