Finite Group Databasebeta

← #7717612

Subgroups — #7717612

Order 512.

4666 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51093C212yesmaximal, complemented
2#51091C212yesmaximal, complemented
3#51089C212yesmaximal, complemented
4#51087C212yesmaximal, complemented
5#51049C214yesmaximal, complemented
6#51047C214yesmaximal, complemented
7#44855C214yesmaximal, complemented
8#44624C214yesmaximal, complemented
9#44596C214yesmaximal, complemented
10#44592C214yesmaximal, complemented
11#39729C212yesmaximal, complemented
12#39141C212yesmaximal, complemented
13#38245C214yesmaximal, complemented
14#37779C214yesmaximal, complemented
15#36764C212yesmaximal, complemented
16#36761C212yesmaximal, complemented
17#36359C212yesmaximal, complemented
18#36145C212yesmaximal, complemented
19#35304C211yesmaximal, characteristic, complemented
20#35303C211yesmaximal, characteristic
21#35178C211yesmaximal, characteristic, complemented
22#35103C212yesmaximal, complemented
23#35035C212yesmaximal, complemented
24#34602C211yesmaximal, characteristic, complemented
25#34401C211yesmaximal, characteristic, complemented
26#34388C211yesmaximal, characteristic, complemented
27C2×#2356C211yesmaximal, characteristic, complemented
28C2×#536C2212yes—
29C2×#532C2211yescharacteristic
30C2×#529C2211yescharacteristic
31C2×#529C2214yes—
32C22×C4×Q8C2211yescharacteristic
33#2857C2212yes—
34#2856C2212yes—
35#2854C2212yes—
36#2854C2212yes—
37#2853C2214yes—
38#2851C2212yes—
39#2850C2214yes—
40#2850C2212yes—
41#2800C2214yes—
42#2798C2214yes—
43#2796C2214yes—
44#2796C2214yes—
45#2793C2214yes—
46#2791C2214yes—
47#2789C2214yes—
48#2786C2214yes—
49#2780C2214yes—
50#2777C2214yes—
51#2776C2214yes—
52#2772C2214yes—
53#2770C2214yes—
54#2766C2214yes—
55#2765C2214yes—
56#2762C2214yes—
57#2761C2214yes—
58#2761C2214yes—
59#2757C2214yes—
60#2755C2214yes—
61#2753C2214yes—
62#2749C2214yes—
63#2747C2214yes—
64#2746C2214yes—
65#2744C2214yes—
66#2740C2214yes—
67#2730C2214yes—
68#2729C2214yes—
69#2717C2214yes—
70#2716C2214yes—
71#2715C2214yes—
72#2713C2214yes—
73#2712C2214yes—
74#2709C2214yes—
75#2707C2214yes—
76#2704C2214yes—
77#2702C2214yes—
78#2700C2214yes—
79#2700C2214yes—
80#2698C2214yes—
81#2660C2212yes—
82#2660C2211yescharacteristic
83#2657C2211yescharacteristic
84#2647C2212yes—
85#2643C2214yes—
86#2641C2211yescharacteristic
87#2640C2211yescharacteristic
88#2637C2214yes—
89#2634C2212yes—
90#2632C2212yes—
91#2627C2211yescharacteristic
92#2627C2211yescharacteristic
93#2623C2212yes—
94#2618C2211yescharacteristic
95#2618C2214yes—
96#2618C2212yes—
97#2618C2211yescharacteristic
98#2618C2212yes—
99#2614C2212yes—
100#2612C2214yes—
101#2612C2214yes—
102#2610C2214yes—
103#2610C2214yes—
104#2606C2212yes—
105#2605C2214yes—
106#2605C2212yes—
107#2603C2212yes—
108#2603C2212yes—
109#2601C2214yes—
110#2601C2214yes—
111#2601C2214yes—
112#2601C2214yes—
113#2595C2214yes—
114#2594C2214yes—
115#2589C2214yes—
116#2588C2214yes—
117#2587C2214yes—
118#2578C2214yes—
119#2576C2214yes—
120#2569C2212yes—
121#2566C2214yes—
122#2565C2214yes—
123#2549C2212yes—
124#2548C2212yes—
125#2546C2212yes—
126#2545C2214yes—
127#2545C2212yes—
128#2545C2212yes—
129#2544C2214yes—
130#2543C2212yes—
131#2543C2212yes—
132#2538C2214yes—
133#2536C2214yes—
134#2532C2214yes—
135#2531C2214yes—
136#2531C2214yes—
137#2529C2214yes—
138#2529C2214yes—
139#2529C2214yes—
140#2528C2214yes—
141#2526C2214yes—
142#2525C2214yes—
143#2522C2214yes—
144#2521C2214yes—
145#2519C2214yes—
146#2518C2214yes—
147#2516C2214yes—
148#2515C2214yes—
149#2515C2214yes—
150#2510C2214yes—
151#2510C2214yes—
152#2510C2214yes—
153#2488C2214yes—
154#2479C2214yes—
155#2478C2214yes—
156#2477C2214yes—
157#2475C2214yes—
158#2474C2214yes—
159#2474C2214yes—
160#2471C2214yes—
161#2465C2214yes—
162#2462C2214yes—
163#2461C2214yes—
164#2459C2214yes—
165#2451C2214yes—
166#2450C2214yes—
167#2449C2214yes—
168#2444C2214yes—
169#2443C2214yes—
170#2439C2214yes—
171#2438C2214yes—
172#2438C2214yes—
173#2438C2214yes—
174#2430C2214yes—
175#2425C2214yes—
176#2425C2214yes—
177#2419C2214yes—
178#2399C2212yes—
179#2398C2212yes—
180#2396C2214yes—
181#2383C2214yes—
182#2381C2212yes—
183#2380C2212yes—
184#2372C2214yes—
185#2364C2212yes—
186#2364C2212yes—
187#2362C2214yes—
188#2359C2214yes—
189#2359C2214yes—
190#2356C2214yes—
191#2356C2214yes—
192#2356C2212yes—
193#2356C2212yes—
194#2356C2212yes—
195#2356C2212yes—
196#2353C2212yes—
197#2353C2214yes—
198#2349C2212yes—
199#2347C2212yes—
200#2346C2214yes—
201#2343C2212yes—
202#2339C2214yes—
203#2337C2214yes—
204#2337C2212yes—
205#2336C2212yes—
206#2331C2212yes—
207#2330C2212yes—
208#2329C2212yes—
209#2328C2212yes—
210#2326C2212yes—
211#2325C2212yes—
212#2325C2212yes—
213#2325C2214yes—
214#2325C2212yes—
215#2322C2214yes—
216#2320C2212yes—
217#2318C2212yes—
218#2318C2214yes—
219#2311C2212yes—
220C4×#123C2212yes—
221C4×#123C2212yes—
222C2×#391C2212yes—
223#2290C2214yes—
224C2×#387C2212yes—
225C2×#387C2212yes—
226#2285C2211yescharacteristic
227#2283C2211yescharacteristic
228C2×#383C2211yescharacteristic
229C2×#383C2211yescharacteristic
230C2×#382C2211yescharacteristic
231C2×C4×C4⋊C4C2212yes—
232C2×C4×C4⋊C4C2211yescharacteristic
233C2×#376C2211yescharacteristic
234C2×#376C2211yescharacteristic
235C22×#41C2312yes—
236C23×Q8C2311yescharacteristic
237#536—48no—
238#532—28no—
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×#127C2311yescharacteristic
244C2×#127C2312yes—
245#529—28no—
246#529—416no—
247C2×#126C2312yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#125C2311yescharacteristic
251C2×#125C2314yes—
252C2×#125C2312yes—
253C2×#124C2312yes—
254C2×#124C2311yescharacteristic
255C2×#124C2312yes—
256C2×#124C2314yes—
257C2×#124C2314yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#123C2314yes—
261C2×#123C2312yes—
262C2×#123C2312yes—
263C2×#123C2314yes—
264C2×#123C2312yes—
265C2×#123C2314yes—
266C2×C22⋊Q8C2311yescharacteristic
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×#121C2312yes—
272C2×#121C2311yescharacteristic
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×C4×Q8—28no—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2314yes—
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2314yes—
294C2×#117C2314yes—
295C2×#117C2314yes—
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C42C2312yes—
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2312yes—
305C22×C42C2312yes—
306C22×C42C2311yescharacteristic
307#401C2314yes—
308#401C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2312yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#398C2312yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2312yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2312yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2312yes—
351#397C2312yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#395C2312yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2312yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2312yes—
387#394C2314yes—
388#394C2312yes—
389#394C2312yes—
390#394C2314yes—
391#394C2314yes—
392#394C2312yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#392C2312yes—
401#392C2312yes—
402#392C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2312yes—
406#391C2312yes—
407#391C2314yes—
408#391C2312yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#390C2314yes—
419#390C2314yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#390C2312yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
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#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#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2312yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2312yes—
551#386C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
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#384C2312yes—
572#384C2312yes—
573#384C2312yes—
574#383C2312yes—
575#383C2312yes—
576#383C2312yes—
577#383C2314yes—
578#383C2312yes—
579#383C2312yes—
580#383C2312yes—
581#383C2314yes—
582#383C2312yes—
583#383C2312yes—
584#382C2314yes—
585#382C2312yes—
586#382C2312yes—
587#382C2312yes—
588#382C2314yes—
589#382C2312yes—
590#382C2312yes—
591#382C2314yes—
592#382C2312yes—
593#382C2312yes—
594#381C2312yes—
595#381C2314yes—
596#381C2312yes—
597#381C2312yes—
598#381C2312yes—
599#381C2314yes—
600#381C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2312yes—
605#380C2312yes—
606#380C2314yes—
607#380C2311yescharacteristic
608#380C2311yescharacteristic
609#380C2312yes—
610#380C2314yes—
611#380C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2311yescharacteristic
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2311yescharacteristic
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C22⋊C4C2312yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2312yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638#376C2312yes—
639#376C2312yes—
640#376C2312yes—
641#376C2314yes—
642#376C2311yescharacteristic
643#376C2311yescharacteristic
644#376C2311yescharacteristic
645#376C2314yes—
646#376C2311yescharacteristic
647#376C2312yes—
648#376C2312yes—
649#376C2312yes—
650C2×#95C2311yescharacteristic
651C2×#95C2314yes—
652C2×#95C2312yes—
653C2×#95C2312yes—
654C2×#95C2312yes—
655C2×#95C2312yes—
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2312yes—
659C2×#95C2312yes—
660C2×#95C2312yes—
661C2×#95C2312yes—
662C2×#95C2311yescharacteristic
663C2×#41—28no—
664C2×#41—44no—
665C2×#41—44no—
666C22×Q8—24no—
667C22×Q8—24no—
668C22×Q8—42no—
669C22×Q8C2412yes—
670C22×Q8C2412yes—
671C22×Q8C2414yes—
672C22×Q8C2411yescharacteristic
673C22×Q8C2412yes—
674C22×D4C2412yes—
675C22×D4C2414yes—
676C22×D4C2414yes—
677C22×D4C2411yescharacteristic
678C22×D4C2412yes—
679C22×D4C2412yes—
680C22×D4C2412yes—
681C22×D4C2414yes—
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2412yes—
692C23×C4C2414yes—
693C23×C4C2414yes—
694C23×C4C2414yes—
695C23×C4C2414yes—
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C4⋊Q8—24no—
699C4⋊Q8—44no—
700C4⋊Q8—44no—
701C4⋊Q8—44no—
702#127—24no—
703#127—44no—
704#126—28no—
705#126—48no—
706#126—48no—
707#125—24no—
708#125—44no—
709#125—48no—
710#124—24no—
711#124—28no—
712#124—44no—
713#124—48no—
714#124—48no—
715#124—44no—
716#124—44no—
717#123—28no—
718#123—28no—
719#123—216no—
720#123—44no—
721#123—48no—
722#123—48no—
723C22⋊Q8—24no—
724C22⋊Q8—48no—
725C22⋊Q8—48no—
726C22⋊Q8—48no—
727C22⋊Q8—48no—
728#121—24no—
729#121—28no—
730#121—28no—
731#121—48no—
732#121—48no—
733C4×Q8—28no—
734C4×Q8—28no—
735C4×Q8—28no—
736C4×Q8—28no—
737C4×Q8—24no—
738C4×Q8—48no—
739C4×D4—28no—
740C4×D4—24no—
741C4×D4—28no—
742C4×D4—28no—
743C4×D4—48no—
744C4×D4—48no—
745C4×D4—48no—
746C4×D4—48no—
747#117—28no—
748#117—48no—
749#117—48no—
750#117—48no—
751#117—44no—
752C2×C4⋊C4—24no—
753C2×C4⋊C4—24no—
754C2×C4⋊C4—24no—
755C2×C4⋊C4—44no—
756C2×C4⋊C4—44no—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C42—24no—
845C2×C42—24no—
846C2×C42—28no—
847C2×C42—44no—
848C2×C42—44no—
849C2×C42#4118yes—
850C2×C42C2414yes—
851C2×C42C2412yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2411yescharacteristic
872C2×C42C2411yescharacteristic
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875#95C2412yes—
876#95C2414yes—
877#95C2412yes—
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2412yes—
881#95C2414yes—
882#95C2412yes—
883#95C2412yes—
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2412yes—
890#95C2412yes—
891#95C2414yes—
892#95C2412yes—
893#95C2414yes—
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941C24C2512yes—
942C24C2514yes—
943C24C2511yescharacteristic
944#41—816no—
945C2×Q8—24no—
946C2×Q8—24no—
947C2×Q8—22no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—28no—
952C2×Q8—42no—
953C2×Q8—42no—
954C2×Q8—44no—
955C2×Q8—42no—
956C2×Q8—42no—
957C2×Q8—44no—
958C2×Q8—42no—
959C2×Q8—416no—
960C2×D4—24no—
961C2×D4—28no—
962C2×D4—24no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—24no—
966C2×D4—22no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—28no—
971C2×D4—44no—
972C2×D4—42no—
973C2×D4—42no—
974C2×D4—42no—
975C2×D4—42no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—42no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—24no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—28no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
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—42no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—42no—
1018C22×C4—44no—
1019C22×C4—42no—
1020C22×C4—44no—
1021C22×C4C2×#4114yes—
1022C22×C4C2×#4114yes—
1023C22×C4C2×#4114yes—
1024C22×C4H(5,𝔽2)14yes—
1025C22×C4C2512yes—
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—22no—
1060C4⋊C4—24no—
1061C4⋊C4—22no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
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—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C22⋊C4—24no—
1098C22⋊C4—28no—
1099C22⋊C4—24no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—24no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
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⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C42—24no—
1137C42—24no—
1138C42—24no—
1139C42—24no—
1140C42—24no—
1141C42—28no—
1142C42—28no—
1143C42—28no—
1144C42—24no—
1145C42—24no—
1146C42—42no—
1147C42—42no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—42no—
1155C42—42no—
1156C42—44no—
1157C42C2×#4114yes—
1158C42C2×#4114yes—
1159C42C2×#4114yes—
1160C42C2×#4114yes—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—24no—
1165C23—24no—
1166C23—22no—
1167C23—24no—
1168C23—22no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23—24no—
1175C23C22×#4112yes—
1176C23C2×H(5,𝔽2)12yes—
1177C23#58512yes—
1178C23C2611yescharacteristic
1179Q8—48no—
1180Q8—48no—
1181Q8—82no—
1182Q8—88no—
1183Q8—84no—
1184D4—48no—
1185D4—416no—
1186D4—82no—
1187D4—84no—
1188D4—84no—
1189D4—88no—
1190D4—84no—
1191D4—164no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—28no—
1205C2×C4—28no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—44no—
1251C2×C4—44no—
1252C2×C4—48no—
1253C2×C4—44no—
1254C2×C4—44no—
1255C2×C4—44no—
1256C2×C4—84no—
1257C2×C4—88no—
1258C2×C4—84no—
1259C2×C4—84no—
1260C2×C4—84no—
1261C2×C4—88no—
1262C2×C4—88no—
1263C2×C4—88no—
1264C2×C4C22×#4112yes—
1265C2×C4C22×#4112yes—
1266C2×C4C22×#4112yes—
1267C2×C4C22×#4112yes—
1268C2×C4C22×#4112yes—
1269C2×C4C22×#4112yes—
1270C2×C4C2×H(5,𝔽2)14yes—
1271C2×C4#58514yes—
1272C22—22no—
1273C22—22no—
1274C22—24no—
1275C22—24no—
1276C22—44no—
1277C22—42no—
1278C22—42no—
1279C22—44no—
1280C22—42no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22#349414yes—
1289C22C23×#4111yescharacteristic
1290C22C22×H(5,𝔽2)11yescharacteristic
1291C22C2×#58511yescharacteristic
1292C22C2×#58512yes—
1293C222−1+612yes—
1294C4—22no—
1295C4—22no—
1296C4—24no—
1297C4—22no—
1298C4—22no—
1299C4—22no—
1300C4—22no—
1301C4—24no—
1302C4—42no—
1303C4—44no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—44no—
1311C4—44no—
1312C4—42no—
1313C4—42no—
1314C4—44no—
1315C4—44no—
1316C4—44no—
1317C4—44no—
1318C2—24no—
1319C2—84no—
1320C2—82no—
1321C2C2×#349411yescharacteristic
1322C2#6281511yescharacteristic
1323C2#6286011yescharacteristic
1324C2#6291112yes—
1325C2#6292712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35303C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51093C2semidirect
2. #51091C2semidirect
3. #51089C2semidirect
4. #51087C2semidirect
5. #51049C2semidirect
6. #51047C2semidirect
7. #44855C2semidirect
8. #44624C2semidirect
9. #44596C2semidirect
10. #44592C2semidirect
11. #39729C2semidirect
12. #39141C2semidirect
13. #38245C2semidirect
14. #37779C2semidirect
15. #36764C2semidirect
16. #36761C2semidirect
17. #36359C2semidirect
18. #36145C2semidirect
19. #35304C2semidirect
21. #35178C2semidirect
22. #35103C2semidirect
23. #35035C2semidirect
24. #34602C2semidirect
25. #34401C2semidirect
26. #34388C2semidirect
27. C2×#2356C2semidirect

Maximal subgroups

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

subgroupindex
#510932
#510912
#510892
#510872
#510492
#510472
#448552
#446242
#445962
#445922
#397292
#391412
#382452
#377792
#367642
#367612
#363592
#361452
#353042
#353032
#351782
#351032
#350352
#346022
#344012
#343882
C2×#23562