Finite Group Databasebeta

← #8942848

Subgroups — #8942848

Order 512.

4762 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57650C214yesmaximal, complemented
2#54899C214yesmaximal, complemented
3#54891C214yesmaximal, complemented
4#51840C212yesmaximal, complemented
5#51531C212yesmaximal, complemented
6#51042C212yesmaximal, complemented
7#50182C212yesmaximal, complemented
8#48776C212yesmaximal, complemented
9#48716C214yesmaximal, complemented
10#48090C214yesmaximal, complemented
11#46480C214yesmaximal, complemented
12#43810C214yesmaximal, complemented
13#43504C214yesmaximal, complemented
14#42944C212yesmaximal, complemented
15#41456C214yesmaximal, complemented
16#41450C214yesmaximal, complemented
17#37932C212yesmaximal, complemented
18#37761C212yesmaximal, complemented
19#36708C211yesmaximal, characteristic, complemented
20#36032C212yesmaximal, complemented
21#35851C212yesmaximal, complemented
22#35633C211yesmaximal, characteristic, complemented
23#35377C211yesmaximal, characteristic, complemented
24C2×#555C2212yescomplemented
25C2×#553C2212yes—
26C2×#544C2211yescharacteristic, complemented
27C2×#538C2212yescomplemented
28C2×#536C2211yescharacteristic, complemented
29C2×#534C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic, complemented
33#2848C2212yes—
34#2839C2214yescomplemented
35#2838C2214yescomplemented
36#2837C2214yescomplemented
37#2827C2214yes—
38#2821C2214yescomplemented
39#2809C2212yescomplemented
40#2807C2214yescomplemented
41#2788C2214yescomplemented
42#2787C2214yescomplemented
43#2784C2214yes—
44#2782C2214yescomplemented
45#2778C2214yes—
46#2774C2214yescomplemented
47#2773C2214yescomplemented
48#2770C2214yescomplemented
49#2768C2214yescomplemented
50#2767C2214yescomplemented
51#2766C2214yescomplemented
52#2757C2214yescomplemented
53#2755C2214yescomplemented
54#2750C2214yes—
55#2746C2214yescomplemented
56#2745C2214yescomplemented
57#2744C2214yescomplemented
58#2743C2214yescomplemented
59#2741C2214yes—
60#2741C2214yescomplemented
61#2741C2214yescomplemented
62#2740C2214yescomplemented
63#2740C2214yescomplemented
64#2739C2214yescomplemented
65#2735C2214yescomplemented
66#2734C2212yescomplemented
67#2731C2212yescomplemented
68#2731C2212yescomplemented
69#2723C2214yes—
70#2716C2214yescomplemented
71#2708C2214yes—
72#2708C2214yescomplemented
73#2706C2214yescomplemented
74#2701C2214yes—
75#2695C2214yes—
76#2695C2214yes—
77#2694C2214yes—
78#2690C2214yescomplemented
79#2690C2214yescomplemented
80#2687C2214yescomplemented
81#2687C2214yescomplemented
82#2686C2214yescomplemented
83#2686C2214yescomplemented
84#2685C2214yes—
85#2684C2214yescomplemented
86#2677C2214yescomplemented
87#2677C2214yescomplemented
88#2674C2214yescomplemented
89#2672C2214yescomplemented
90#2672C2214yescomplemented
91#2672C2214yescomplemented
92#2671C2214yes—
93#2671C2214yes—
94#2668C2214yes—
95#2667C2212yescomplemented
96#2664C2214yescomplemented
97#2659C2212yescomplemented
98#2652C2214yescomplemented
99#2650C2214yescomplemented
100#2649C2214yescomplemented
101#2646C2212yescomplemented
102#2646C2214yescomplemented
103#2635C2212yes—
104#2634C2212yescomplemented
105#2633C2214yescomplemented
106#2628C2214yescomplemented
107#2627C2212yescomplemented
108#2626C2212yescomplemented
109#2626C2212yescomplemented
110#2624C2212yes—
111#2618C2212yescomplemented
112#2611C2212yescomplemented
113#2609C2214yescomplemented
114#2602C2214yescomplemented
115#2598C2212yescomplemented
116#2594C2214yescomplemented
117#2591C2212yes—
118#2591C2212yes—
119#2590C2214yescomplemented
120#2589C2214yescomplemented
121#2578C2214yescomplemented
122#2575C2214yescomplemented
123#2575C2214yescomplemented
124#2561C2212yes—
125#2553C2214yes—
126#2553C2214yescomplemented
127#2550C2214yescomplemented
128#2547C2214yescomplemented
129#2543C2212yescomplemented
130#2534C2212yes—
131#2534C2212yes—
132#2529C2214yescomplemented
133#2522C2214yescomplemented
134#2522C2214yescomplemented
135#2521C2214yescomplemented
136#2516C2214yescomplemented
137#2505C2214yescomplemented
138#2504C2212yes—
139#2498C2214yescomplemented
140#2495C2214yescomplemented
141#2491C2214yescomplemented
142#2488C2214yes—
143#2488C2214yes—
144#2487C2212yescomplemented
145#2486C2212yescomplemented
146#2486C2212yescomplemented
147#2484C2212yescomplemented
148#2482C2212yes—
149#2481C2214yescomplemented
150#2480C2214yes—
151#2480C2214yescomplemented
152#2479C2214yescomplemented
153#2479C2214yescomplemented
154#2478C2214yescomplemented
155#2477C2214yes—
156#2474C2214yescomplemented
157#2472C2214yes—
158#2472C2214yes—
159#2470C2214yescomplemented
160#2470C2214yescomplemented
161#2469C2214yescomplemented
162#2468C2214yescomplemented
163#2461C2214yes—
164#2459C2214yes—
165#2457C2214yescomplemented
166#2457C2214yescomplemented
167#2455C2214yes—
168#2454C2214yescomplemented
169#2450C2214yescomplemented
170#2444C2214yescomplemented
171#2443C2214yes—
172#2442C2214yescomplemented
173#2438C2214yescomplemented
174#2436C2212yes—
175#2434C2212yescomplemented
176#2430C2214yescomplemented
177#2429C2214yescomplemented
178#2427C2214yescomplemented
179#2425C2214yes—
180#2424C2214yes—
181#2419C2214yescomplemented
182#2419C2214yescomplemented
183#2418C2214yes—
184#2418C2214yes—
185#2418C2214yescomplemented
186#2418C2214yescomplemented
187#2417C2214yescomplemented
188#2415C2214yescomplemented
189#2408C2214yes—
190#2405C2214yes—
191#2398C2212yescomplemented
192#2395C2214yescomplemented
193#2395C2212yescomplemented
194C2×#400C2212yescomplemented
195#2379C2212yescomplemented
196#2379C2212yescomplemented
197#2377C2212yes—
198#2373C2214yescomplemented
199#2369C2212yescomplemented
200#2364C2214yescomplemented
201#2359C2214yescomplemented
202#2359C2214yescomplemented
203#2353C2212yescomplemented
204#2349C2214yescomplemented
205#2347C2212yescomplemented
206#2342C2214yescomplemented
207#2335C2214yes—
208#2329C2212yescomplemented
209#2325C2214yes—
210#2325C2212yescomplemented
211#2316C2211yescharacteristic, complemented
212#2315C2212yescomplemented
213#2313C2211yescharacteristic, complemented
214#2310C2211yescharacteristic, complemented
215#2308C2212yes—
216C2×#386C2212yes—
217#2280C2211yescharacteristic
218#2273C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×D4C2312yes—
222C24×C4C2311yescharacteristic
223#555—48no—
224#553—48no—
225#544—44no—
226#538—48no—
227#536—44no—
228#534—44no—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#125C2312yes—
237C2×#125C2314yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2314yes—
242C2×#124C2312yes—
243#525—44no—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×#123C2312yes—
252C2×#123C2314yes—
253C2×C22⋊Q8—44no—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2312yes—
267C2×#121C2312yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#120C2312yes—
271C2×#120C2314yes—
272C2×#120C2314yes—
273#520—44no—
274C2×C4×Q8C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×#117C2312yes—
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2314yes—
289C2×#117C2312yes—
290C2×#117C2314yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2314yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2312yes—
302#401C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2312yes—
319#400C2312yes—
320#400C2314yes—
321#400C2312yes—
322#400C2314yes—
323#400C2312yes—
324#400C2312yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2312yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2312yes—
334#399C2314yes—
335#399C2314yes—
336#398C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2312yes—
349#398C2314yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2312yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2312yes—
399#394C2312yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2312yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#392C2312yes—
420#392C2314yes—
421#392C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
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#388C2314yes—
485#388C2314yes—
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#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
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#383C2314yes—
562#383C2312yes—
563#382C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2314yes—
567#381C2314yes—
568#381C2314yes—
569#381C2312yes—
570#381C2312yes—
571#381C2312yes—
572#381C2314yes—
573#381C2314yes—
574#381C2312yes—
575#380C2312yes—
576#380C2312yes—
577#380C2312yes—
578#380C2314yes—
579#380C2312yes—
580#380C2312yes—
581#380C2312yes—
582#380C2314yes—
583#380C2312yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#379C2314yes—
596#379C2314yes—
597#379C2314yes—
598#379C2314yes—
599#379C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617#376C2312yes—
618C2×#95C2314yes—
619C2×#95C2312yes—
620C2×#95C2312yes—
621C2×#95C2314yes—
622C2×#95C2312yes—
623C25C2411yescharacteristic
624C25C2412yes—
625C2×#41—24no—
626C2×#41—42no—
627C2×#41—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8C2411yescharacteristic
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×D4—44no—
637C22×D4—44no—
638C22×D4—44no—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2412yes—
647C22×D4C2411yescharacteristic
648C23×C4—42no—
649C23×C4—42no—
650C23×C4—42no—
651C23×C4C2411yescharacteristic
652C23×C4C2412yes—
653C23×C4C2411yescharacteristic
654C23×C4C2411yescharacteristic
655C23×C4C2411yescharacteristic
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2411yescharacteristic
660C23×C4C2414yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2414yes—
665C23×C4C2414yes—
666C23×C4C2414yes—
667C23×C4C2412yes—
668C23×C4C2411yescharacteristic
669C4⋊Q8—48no—
670C4⋊Q8—44no—
671C4⋊Q8—44no—
672C4⋊Q8—44no—
673#126—48no—
674#126—48no—
675#126—48no—
676#125—48no—
677#125—44no—
678#124—28no—
679#124—48no—
680#124—48no—
681#124—44no—
682#124—44no—
683#123—48no—
684#123—48no—
685#123—48no—
686#123—44no—
687#123—44no—
688#123—44no—
689#123—48no—
690#123—48no—
691#123—48no—
692C22⋊Q8—48no—
693C22⋊Q8—44no—
694C22⋊Q8—44no—
695C22⋊Q8—48no—
696C22⋊Q8—48no—
697C22⋊Q8—44no—
698C22⋊Q8—44no—
699C22⋊Q8—44no—
700#121—28no—
701#121—216no—
702#121—28no—
703#121—48no—
704#121—48no—
705#121—48no—
706#121—44no—
707#121—44no—
708#120—48no—
709#120—44no—
710#120—48no—
711C4×Q8—44no—
712C4×D4—28no—
713C4×D4—48no—
714C4×D4—44no—
715C4×D4—44no—
716C4×D4—48no—
717C4×D4—44no—
718C4×D4—48no—
719C4×D4—48no—
720C4×D4—48no—
721#117—28no—
722#117—42no—
723#117—44no—
724#117—48no—
725#117—42no—
726#117—48no—
727#117—42no—
728C2×C4⋊C4—24no—
729C2×C4⋊C4—24no—
730C2×C4⋊C4—44no—
731C2×C4⋊C4—44no—
732C2×C4⋊C4—42no—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C22⋊C4—24no—
781C2×C22⋊C4—44no—
782C2×C22⋊C4—44no—
783C2×C22⋊C4—48no—
784C2×C22⋊C4—44no—
785C2×C22⋊C4—42no—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
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×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2412yes—
845C2×C42C2414yes—
846C2×C42C2412yes—
847C2×C42C2414yes—
848#95C2414yes—
849#95C2412yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2412yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2412yes—
863#95C2414yes—
864#95C2412yes—
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—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900C24—22no—
901C24—24no—
902C24—24no—
903C24—42no—
904C24—42no—
905C24—41no—
906C24—41no—
907C24—42no—
908C24—42no—
909C24—42no—
910C24—42no—
911C24—42no—
912C24C2514yes—
913C24C2511yescharacteristic
914C24C2512yes—
915C24C2512yes—
916#41—416no—
917C2×Q8—22no—
918C2×Q8—24no—
919C2×Q8—24no—
920C2×Q8—41no—
921C2×Q8—41no—
922C2×Q8—42no—
923C2×Q8—42no—
924C2×Q8—42no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8—42no—
932C2×Q8—88no—
933C2×D4—24no—
934C2×D4—28no—
935C2×D4—24no—
936C2×D4—28no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—28no—
940C2×D4—28no—
941C2×D4—24no—
942C2×D4—41no—
943C2×D4—44no—
944C2×D4—41no—
945C2×D4—42no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—816no—
959C2×D4H(5,𝔽2)14yes—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—24no—
964C22×C4—22no—
965C22×C4—22no—
966C22×C4—22no—
967C22×C4—22no—
968C22×C4—28no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—41no—
982C22×C4—42no—
983C22×C4—41no—
984C22×C4—41no—
985C22×C4—44no—
986C22×C4—42no—
987C22×C4—41no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—42no—
991C22×C4—44no—
992C22×C4—42no—
993C22×C4—41no—
994C22×C4—41no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—44no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—44no—
1009C22×C4—88no—
1010C22×C4H(5,𝔽2)14yes—
1011C22×C4C2514yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2514yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—41no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—41no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C22⋊C4—28no—
1078C22⋊C4—24no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
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—24no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
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—42no—
1106C22⋊C4—44no—
1107C22⋊C4—42no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
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—
1124C42—28no—
1125C42—24no—
1126C42—24no—
1127C42—44no—
1128C42—44no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—44no—
1134C42—42no—
1135C42—44no—
1136C42—42no—
1137C42—44no—
1138C42—42no—
1139C23—28no—
1140C23—22no—
1141C23—22no—
1142C23—21no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—24no—
1147C23—22no—
1148C23—21no—
1149C23—22no—
1150C23—22no—
1151C23—22no—
1152C23—24no—
1153C23—22no—
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—24no—
1158C23—24no—
1159C23—24no—
1160C23—24no—
1161C23—48no—
1162C23—82no—
1163C23—82no—
1164C23—84no—
1165C23—84no—
1166C23—84no—
1167C23—84no—
1168C23—162no—
1169C23—162no—
1170C23—162no—
1171C23—162no—
1172C23C2×H(5,𝔽2)14yes—
1173C23C2×H(5,𝔽2)12yes—
1174C23#58514yes—
1175C23C2611yescharacteristic
1176Q8—44no—
1177Q8—84no—
1178Q8—84no—
1179Q8—162no—
1180Q8—162no—
1181D4—44no—
1182D4—416no—
1183D4—48no—
1184D4—84no—
1185D4—88no—
1186D4—88no—
1187D4—88no—
1188D4—88no—
1189D4—162no—
1190C2×C4—28no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—44no—
1242C2×C4—48no—
1243C2×C4—84no—
1244C2×C4—84no—
1245C2×C4—84no—
1246C2×C4—82no—
1247C2×C4—88no—
1248C2×C4—82no—
1249C2×C4—84no—
1250C2×C4—82no—
1251C2×C4—82no—
1252C2×C4—88no—
1253C2×C4—164no—
1254C2×C4—164no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4—162no—
1258C2×C4C2×H(5,𝔽2)14yes—
1259C2×C4C2×H(5,𝔽2)12yes—
1260C2×C4#58512yes—
1261C22—22no—
1262C22—24no—
1263C22—24no—
1264C22—22no—
1265C22—22no—
1266C22—28no—
1267C22—24no—
1268C22—24no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—44no—
1277C22—42no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—88no—
1286C22—168no—
1287C22C22×H(5,𝔽2)11yescharacteristic
1288C22C22×H(5,𝔽2)11yescharacteristic
1289C22C2×#58511yescharacteristic
1290C22C2×#58512yes—
1291C222−1+612yes—
1292C4—22no—
1293C4—22no—
1294C4—24no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—44no—
1300C4—44no—
1301C4—42no—
1302C4—44no—
1303C4—42no—
1304C4—42no—
1305C4—44no—
1306C4—44no—
1307C4—44no—
1308C4—44no—
1309C4—44no—
1310C4—44no—
1311C2—44no—
1312C2—42no—
1313C2—44no—
1314C2—84no—
1315C2#6281811yescharacteristic
1316C2#6282411yescharacteristic
1317C2#6287111yescharacteristic
1318C2#6289812yes—
1319C2#6293412yes—
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. #57650C2semidirect
2. #54899C2semidirect
3. #54891C2semidirect
4. #51840C2semidirect
5. #51531C2semidirect
6. #51042C2semidirect
7. #50182C2semidirect
8. #48776C2semidirect
9. #48716C2semidirect
10. #48090C2semidirect
11. #46480C2semidirect
12. #43810C2semidirect
13. #43504C2semidirect
14. #42944C2semidirect
15. #41456C2semidirect
16. #41450C2semidirect
17. #37932C2semidirect
18. #37761C2semidirect
19. #36708C2semidirect
20. #36032C2semidirect
21. #35851C2semidirect
22. #35633C2semidirect
23. #35377C2semidirect
24. C2×#555C22semidirect
26. C2×#544C22semidirect
27. C2×#538C22semidirect
28. C2×#536C22semidirect
32. C2×#520C22semidirect
34. #2839C22semidirect
35. #2838C22semidirect
36. #2837C22semidirect
38. #2821C22semidirect
39. #2809C22semidirect
40. #2807C22semidirect
41. #2788C22semidirect
42. #2787C22semidirect
44. #2782C22semidirect
46. #2774C22semidirect
47. #2773C22semidirect
48. #2770C22semidirect
49. #2768C22semidirect
50. #2767C22semidirect
51. #2766C22semidirect
52. #2757C22semidirect
53. #2755C22semidirect
55. #2746C22semidirect
56. #2745C22semidirect
57. #2744C22semidirect
58. #2743C22semidirect
60. #2741C22semidirect
61. #2741C22semidirect
62. #2740C22semidirect
63. #2740C22semidirect
64. #2739C22semidirect
65. #2735C22semidirect
66. #2734C22semidirect
67. #2731C22semidirect
68. #2731C22semidirect
70. #2716C22semidirect
72. #2708C22semidirect
73. #2706C22semidirect
78. #2690C22semidirect
79. #2690C22semidirect
80. #2687C22semidirect
81. #2687C22semidirect
82. #2686C22semidirect
83. #2686C22semidirect
85. #2684C22semidirect
86. #2677C22semidirect
87. #2677C22semidirect
88. #2674C22semidirect
89. #2672C22semidirect
90. #2672C22semidirect
91. #2672C22semidirect
95. #2667C22semidirect
96. #2664C22semidirect
97. #2659C22semidirect
98. #2652C22semidirect
99. #2650C22semidirect
100. #2649C22semidirect
101. #2646C22semidirect
102. #2646C22semidirect
104. #2634C22semidirect
105. #2633C22semidirect
106. #2628C22semidirect
107. #2627C22semidirect
108. #2626C22semidirect
109. #2626C22semidirect
111. #2618C22semidirect
112. #2611C22semidirect
113. #2609C22semidirect
114. #2602C22semidirect
115. #2598C22semidirect
116. #2594C22semidirect
119. #2590C22semidirect
120. #2589C22semidirect
121. #2578C22semidirect
122. #2575C22semidirect
123. #2575C22semidirect
126. #2553C22semidirect
127. #2550C22semidirect
128. #2547C22semidirect
129. #2543C22semidirect
132. #2529C22semidirect
133. #2522C22semidirect
134. #2522C22semidirect
135. #2521C22semidirect
136. #2516C22semidirect
137. #2505C22semidirect
139. #2498C22semidirect
140. #2495C22semidirect
141. #2491C22semidirect
144. #2487C22semidirect
145. #2486C22semidirect
146. #2486C22semidirect
147. #2484C22semidirect
149. #2481C22semidirect
151. #2480C22semidirect
152. #2479C22semidirect
153. #2479C22semidirect
154. #2478C22semidirect
156. #2474C22semidirect
159. #2470C22semidirect
160. #2470C22semidirect
161. #2469C22semidirect
162. #2468C22semidirect
165. #2457C22semidirect
166. #2457C22semidirect
168. #2454C22semidirect
169. #2450C22semidirect
170. #2444C22semidirect
172. #2442C22semidirect
173. #2438C22semidirect
175. #2434C22semidirect
176. #2430C22semidirect
177. #2429C22semidirect
178. #2427C22semidirect
181. #2419C22semidirect
182. #2419C22semidirect
185. #2418C22semidirect
186. #2418C22semidirect
187. #2417C22semidirect
188. #2415C22semidirect
191. #2398C22semidirect
192. #2395C22semidirect
193. #2395C22semidirect
194. C2×#400C22semidirect
195. #2379C22semidirect
196. #2379C22semidirect
198. #2373C22semidirect
199. #2369C22semidirect
200. #2364C22semidirect
201. #2359C22semidirect
202. #2359C22semidirect
203. #2353C22semidirect
204. #2349C22semidirect
205. #2347C22semidirect
206. #2342C22semidirect
208. #2329C22semidirect
210. #2325C22semidirect
211. #2316C22semidirect
212. #2315C22semidirect
213. #2313C22semidirect
214. #2310C22semidirect

Maximal subgroups

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

subgroupindex
#576502
#548992
#548912
#518402
#515312
#510422
#501822
#487762
#487162
#480902
#464802
#438102
#435042
#429442
#414562
#414502
#379322
#377612
#367082
#360322
#358512
#356332
#353772