Finite Group Databasebeta

← #7848990

Subgroups — #7848990

Order 512.

4806 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59924C211yesmaximal, characteristic, complemented
2#59923C211yesmaximal, characteristic, complemented
3#59727C214yesmaximal, complemented
4#59460C214yesmaximal, complemented
5#52307C211yesmaximal, characteristic, complemented
6#52076C212yesmaximal, complemented
7#51951C212yesmaximal, complemented
8#49896C214yesmaximal, complemented
9#49778C214yesmaximal, complemented
10#47750C212yesmaximal, complemented
11#46969C212yesmaximal, complemented
12#46312C211yesmaximal, characteristic, complemented
13#46099C211yesmaximal, characteristic, complemented
14#44217C214yesmaximal, complemented
15#44181C214yesmaximal, complemented
16#44068C214yesmaximal, complemented
17#43899C214yesmaximal, complemented
18#42043C212yesmaximal, complemented
19#39830C212yesmaximal, complemented
20#39702C212yesmaximal, complemented
21#38820C212yesmaximal, complemented
22#37208C211yesmaximal, characteristic, complemented
23#36513C212yesmaximal, complemented
24#35693C212yesmaximal, complemented
25#35669C212yesmaximal, complemented
26#34523C212yesmaximal, complemented
27#34276C211yesmaximal, characteristic, complemented
28C2×#563C2212yes—
29C2×#547C2212yes—
30C2×#542C2212yes—
31C2×#536C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34#2863C2212yes—
35#2860C2212yes—
36#2850C2212yes—
37#2832C2212yes—
38#2823C2212yes—
39#2811C2211yescharacteristic
40#2811C2211yescharacteristic
41#2811C2212yes—
42#2808C2212yes—
43#2806C2212yes—
44#2804C2212yes—
45#2803C2214yes—
46#2801C2214yes—
47#2800C2214yes—
48#2795C2214yes—
49#2789C2212yes—
50#2785C2214yes—
51#2785C2212yes—
52#2775C2214yes—
53#2767C2214yes—
54#2765C2214yes—
55#2763C2214yes—
56#2763C2214yes—
57#2759C2214yes—
58#2745C2214yes—
59#2734C2211yescharacteristic
60#2733C2211yescharacteristic
61#2733C2214yes—
62#2733C2212yes—
63#2733C2212yes—
64#2732C2212yes—
65#2731C2214yes—
66#2731C2214yes—
67#2731C2212yes—
68#2730C2214yes—
69#2729C2214yes—
70#2729C2214yes—
71#2720C2214yes—
72#2718C2214yes—
73#2718C2214yes—
74#2716C2214yes—
75#2716C2214yes—
76#2712C2214yes—
77#2710C2214yes—
78#2705C2214yes—
79#2704C2214yes—
80#2704C2214yes—
81#2702C2214yes—
82#2686C2214yes—
83#2682C2214yes—
84#2681C2214yes—
85#2674C2214yes—
86#2674C2214yes—
87#2666C2214yes—
88#2662C2214yes—
89#2662C2214yes—
90#2638C2212yes—
91#2638C2212yes—
92#2628C2212yes—
93#2602C2214yes—
94#2601C2214yes—
95#2596C2214yes—
96#2594C2214yes—
97#2593C2214yes—
98#2589C2214yes—
99#2589C2214yes—
100#2587C2214yes—
101#2587C2214yes—
102#2587C2214yes—
103#2587C2214yes—
104#2586C2212yes—
105#2586C2214yes—
106#2583C2212yes—
107#2583C2214yes—
108#2583C2212yes—
109#2574C2214yes—
110#2574C2214yes—
111#2570C2214yes—
112#2570C2212yes—
113#2568C2212yes—
114#2567C2214yes—
115#2567C2212yes—
116#2567C2212yes—
117#2567C2214yes—
118#2566C2214yes—
119#2560C2214yes—
120#2558C2214yes—
121#2558C2214yes—
122#2556C2214yes—
123#2555C2214yes—
124#2554C2214yes—
125#2554C2214yes—
126#2551C2212yes—
127#2551C2214yes—
128#2550C2214yes—
129#2549C2214yes—
130#2545C2212yes—
131#2545C2212yes—
132#2545C2212yes—
133#2536C2212yes—
134#2529C2214yes—
135#2527C2214yes—
136#2525C2214yes—
137#2521C2214yes—
138#2519C2214yes—
139#2519C2214yes—
140#2518C2214yes—
141#2500C2212yes—
142#2499C2212yes—
143#2488C2214yes—
144#2474C2214yes—
145#2474C2214yes—
146#2470C2214yes—
147#2470C2214yes—
148#2470C2214yes—
149#2469C2214yes—
150#2469C2214yes—
151#2466C2214yes—
152#2466C2214yes—
153#2465C2214yes—
154#2465C2214yes—
155#2465C2214yes—
156#2461C2214yes—
157#2461C2214yes—
158#2461C2214yes—
159#2459C2214yes—
160#2458C2214yes—
161#2455C2214yes—
162#2455C2214yes—
163#2453C2214yes—
164#2452C2214yes—
165#2452C2214yes—
166#2451C2214yes—
167#2449C2214yes—
168#2436C2212yes—
169#2434C2212yes—
170#2432C2214yes—
171#2432C2214yes—
172#2430C2214yes—
173#2429C2212yes—
174#2426C2212yes—
175#2422C2214yes—
176#2422C2212yes—
177#2421C2212yes—
178#2407C2214yes—
179#2406C2212yes—
180#2406C2212yes—
181#2392C2212yes—
182#2388C2212yes—
183#2388C2214yes—
184#2388C2212yes—
185#2382C2214yes—
186#2379C2212yes—
187#2374C2214yes—
188#2374C2214yes—
189#2373C2214yes—
190#2373C2214yes—
191#2369C2212yes—
192#2369C2214yes—
193#2369C2212yes—
194#2368C2214yes—
195#2367C2214yes—
196#2367C2214yes—
197#2367C2212yes—
198#2362C2214yes—
199#2360C2214yes—
200#2360C2214yes—
201#2360C2214yes—
202#2359C2214yes—
203#2359C2214yes—
204#2357C2212yes—
205#2351C2212yes—
206D4×C4⋊C4C2214yes—
207#2337C2214yes—
208#2334C2214yes—
209#2334C2214yes—
210#2332C2214yes—
211#2332C2214yes—
212#2327C2212yes—
213#2327C2211yescharacteristic
214#2327C2211yescharacteristic
215#2326C2211yescharacteristic
216#2326C2212yes—
217#2326C2211yescharacteristic
218#2322C2214yes—
219#2317C2211yescharacteristic
220C4×C4⋊Q8C2212yes—
221C4×C4⋊Q8C2211yescharacteristic
222C4×C4⋊Q8C2211yescharacteristic
223C4×C4⋊Q8C2212yes—
224C4×#125C2214yes—
225C4×#124C2212yes—
226C4×#124C2214yes—
227C4×#124C2212yes—
228C4×#124C2211yescharacteristic
229C4×#124C2211yescharacteristic
230C4×C22⋊Q8C2212yes—
231#2298C2212yes—
232#2297C2211yescharacteristic
233C2×#391C2211yescharacteristic
234C4×#117C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C22×#41C2312yes—
237C22×#41C2312yes—
238C23×Q8C2311yescharacteristic
239#563—216no—
240#547—48no—
241#542—48no—
242#536—28no—
243C2×C4⋊Q8C2311yescharacteristic
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2314yes—
251C2×C4⋊Q8C2311yescharacteristic
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2312yes—
267C2×#124C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×#121C2314yes—
285C2×#121C2312yes—
286C2×#121C2312yes—
287#520—44no—
288#519—44no—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×#117C2311yescharacteristic
313C2×#117C2312yes—
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2312yes—
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2314yes—
320C22×C4⋊C4C2312yes—
321C22×C42C2311yescharacteristic
322#401C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#398C2314yes—
335#398C2312yes—
336#398C2314yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2312yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2312yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#395C2312yes—
368#395C2312yes—
369#395C2314yes—
370#395C2314yes—
371#395C2312yes—
372#395C2312yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2312yes—
378#395C2312yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#394C2314yes—
384#394C2312yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2312yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2312yes—
400#394C2314yes—
401#394C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2312yes—
408#393C2312yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#392C2314yes—
413#392C2312yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#391C2314yes—
419#391C2311yescharacteristic
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2311yescharacteristic
424#391C2312yes—
425#391C2311yescharacteristic
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2311yescharacteristic
450#390C2312yes—
451#390C2312yes—
452#390C2314yes—
453#390C2312yes—
454#390C2312yes—
455#390C2314yes—
456#390C2312yes—
457#390C2314yes—
458#390C2311yescharacteristic
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
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#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#384C2312yes—
596#384C2311yescharacteristic
597#384C2312yes—
598#384C2311yescharacteristic
599#384C2314yes—
600#384C2312yes—
601#383C2314yes—
602#382C2314yes—
603#382C2314yes—
604#382C2312yes—
605#382C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2314yes—
609#382C2311yescharacteristic
610#382C2311yescharacteristic
611#382C2312yes—
612#381C2314yes—
613#381C2312yes—
614#381C2312yes—
615#380C2314yes—
616#380C2314yes—
617#380C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657#376C2311yescharacteristic
658#376C2312yes—
659#376C2311yescharacteristic
660C2×#95C2314yes—
661C43C2312yes—
662C43C2311yescharacteristic
663C43C2311yescharacteristic
664C2×#41—24no—
665C2×#41—42no—
666C2×#41—44no—
667C2×#41—42no—
668C2×#41—44no—
669C2×#41—84no—
670C2×#41—84no—
671C22×Q8—24no—
672C22×Q8—42no—
673C22×Q8—42no—
674C22×Q8C2412yes—
675C22×Q8C2411yescharacteristic
676C22×Q8C2412yes—
677C22×Q8C2412yes—
678C22×Q8C2414yes—
679C22×Q8C2412yes—
680C22×Q8C2412yes—
681C22×Q8C2411yescharacteristic
682C22×Q8C2411yescharacteristic
683C22×Q8C2412yes—
684C22×D4C2412yes—
685C22×D4C2414yes—
686C22×D4C2411yescharacteristic
687C22×D4C2412yes—
688C22×D4C2412yes—
689C22×D4C2414yes—
690C22×D4C2412yes—
691C22×D4C2414yes—
692C23×C4C2411yescharacteristic
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2412yes—
701C23×C4C2414yes—
702C4⋊Q8—24no—
703C4⋊Q8—28no—
704C4⋊Q8—28no—
705C4⋊Q8—44no—
706C4⋊Q8—44no—
707C4⋊Q8—44no—
708C4⋊Q8—84no—
709C4⋊Q8—84no—
710C4⋊Q8#4118yescomplemented
711#126—216no—
712#126—216no—
713#126—48no—
714#126—84no—
715#125—216no—
716#125—84no—
717#124—24no—
718#124—28no—
719#124—216no—
720#124—28no—
721#124—24no—
722#124—44no—
723#124—44no—
724#124—48no—
725#124—44no—
726#124—84no—
727#123—216no—
728#123—216no—
729#123—216no—
730#123—48no—
731#123—84no—
732#123—84no—
733C22⋊Q8—216no—
734C22⋊Q8—28no—
735C22⋊Q8—216no—
736C22⋊Q8—216no—
737C22⋊Q8—44no—
738C22⋊Q8—44no—
739C22⋊Q8—48no—
740C22⋊Q8—44no—
741C22⋊Q8—84no—
742C22⋊Q8—82no—
743#121—48no—
744#121—44no—
745#121—82no—
746C4×Q8—42no—
747C4×Q8—42no—
748C4×Q8—42no—
749C4×Q8—44no—
750C4×Q8—44no—
751C4×Q8—42no—
752C4×Q8—42no—
753C4×Q8—44no—
754C4×Q8—42no—
755C4×Q8—44no—
756C4×Q8—82no—
757C4×Q8—82no—
758C4×Q8—82no—
759C4×D4—28no—
760C4×D4—42no—
761C4×D4—44no—
762C4×D4—42no—
763C4×D4—44no—
764C4×D4—48no—
765C4×D4—44no—
766C4×D4—82no—
767C4×D4—84no—
768C4×D4—84no—
769#117—24no—
770#117—28no—
771#117—24no—
772#117—44no—
773#117—44no—
774#117—42no—
775C2×C4⋊C4—44no—
776C2×C4⋊C4—48no—
777C2×C4⋊C4—42no—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2411yescharacteristic
874C2×C42—42no—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879C2×C42C2412yes—
880C2×C42C2411yescharacteristic
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
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#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958C24C2514yes—
959C24C2512yes—
960C24C2511yescharacteristic
961#41—416no—
962#41—816no—
963#41—816no—
964C2×Q8—24no—
965C2×Q8—22no—
966C2×Q8—24no—
967C2×Q8—24no—
968C2×Q8—24no—
969C2×Q8—41no—
970C2×Q8—42no—
971C2×Q8—41no—
972C2×Q8—41no—
973C2×Q8—42no—
974C2×Q8—42no—
975C2×Q8—41no—
976C2×Q8—41no—
977C2×Q8—41no—
978C2×Q8—42no—
979C2×Q8—42no—
980C2×Q8—42no—
981C2×Q8—42no—
982C2×Q8—42no—
983C2×Q8—42no—
984C2×Q8—44no—
985C2×Q8—44no—
986C2×Q8—44no—
987C2×Q8—44no—
988C2×Q8—44no—
989C2×Q8—416no—
990C2×Q8C2×#4114yes—
991C2×Q8C2×#4114yes—
992C2×Q82−1+418yes—
993C2×D4—24no—
994C2×D4—28no—
995C2×D4—24no—
996C2×D4—22no—
997C2×D4—24no—
998C2×D4—28no—
999C2×D4—24no—
1000C2×D4—41no—
1001C2×D4—44no—
1002C2×D4—42no—
1003C2×D4—44no—
1004C2×D4—42no—
1005C2×D4—41no—
1006C2×D4—44no—
1007C2×D4—42no—
1008C2×D4—42no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—42no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—22no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—28no—
1025C22×C4—24no—
1026C22×C4—28no—
1027C22×C4—24no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—42no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4C2511yescharacteristic
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2511yescharacteristic
1067C4⋊C4—24no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—22no—
1077C4⋊C4—28no—
1078C4⋊C4—22no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—42no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—41no—
1094C4⋊C4—42no—
1095C4⋊C4—41no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4C2×#41116yes—
1122C22⋊C4—22no—
1123C22⋊C4—24no—
1124C22⋊C4—28no—
1125C22⋊C4—24no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—42no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4H(5,𝔽2)14yes—
1163C42—22no—
1164C42—24no—
1165C42—24no—
1166C42—22no—
1167C42—24no—
1168C42—22no—
1169C42—24no—
1170C42—24no—
1171C42—24no—
1172C42—28no—
1173C42—24no—
1174C42—24no—
1175C42—41no—
1176C42—41no—
1177C42—42no—
1178C42—42no—
1179C42—42no—
1180C42—42no—
1181C42—44no—
1182C42—44no—
1183C42—42no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—42no—
1188C42—44no—
1189C42—44no—
1190C42—42no—
1191C42—44no—
1192C42—42no—
1193C42C2×#4114yes—
1194C23—21no—
1195C23—22no—
1196C23—21no—
1197C23—22no—
1198C23—24no—
1199C23—22no—
1200C23—22no—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—22no—
1207C23—24no—
1208C23—24no—
1209C23—24no—
1210C23C2×H(5,𝔽2)12yes—
1211C23C2611yescharacteristic
1212Q8—44no—
1213Q8—44no—
1214Q8—48no—
1215Q8—48no—
1216Q8—44no—
1217Q8—84no—
1218Q8—84no—
1219Q8—84no—
1220Q8—84no—
1221Q8—164no—
1222D4—48no—
1223D4—416no—
1224D4—44no—
1225D4—48no—
1226D4—84no—
1227D4—84no—
1228D4—88no—
1229D4—88no—
1230C2×C4—28no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—21no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—48no—
1287C2×C4—48no—
1288C2×C4—88no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4—88no—
1292C2×C4—84no—
1293C2×C4—88no—
1294C2×C4—162no—
1295C2×C4C22×#4114yes—
1296C2×C4C22×#4112yes—
1297C2×C4C22×#4114yes—
1298C2×C4C22×#4114yes—
1299C2×C4C2×H(5,𝔽2)12yes—
1300C2×C4C2×H(5,𝔽2)12yes—
1301C2×C4C2×2−1+414yes—
1302C2×C4C2×2−1+418yes—
1303C2×C4#58512yes—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—42no—
1308C22—42no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—42no—
1313C22—44no—
1314C22—42no—
1315C22—44no—
1316C22—44no—
1317C22—42no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22C23×#4111yescharacteristic
1322C22C22×H(5,𝔽2)11yescharacteristic
1323C22C22×2−1+412yes—
1324C22C2×#58511yescharacteristic
1325C22H(7,𝔽2)12yes—
1326C4—24no—
1327C4—22no—
1328C4—22no—
1329C4—24no—
1330C4—24no—
1331C4—22no—
1332C4—22no—
1333C4—24no—
1334C4—28no—
1335C4—42no—
1336C4—44no—
1337C4—44no—
1338C4—42no—
1339C4—44no—
1340C4—41no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4—44no—
1346C4—41no—
1347C4—42no—
1348C4—42no—
1349C4—44no—
1350C2—42no—
1351C2—82no—
1352C2—84no—
1353C2#6277311yescharacteristic
1354C2#6290212yes—
1355C2#6299912yes—
1356C2#6303711yescharacteristic
1357C2#6304511yescharacteristic
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. #59924C2semidirect
2. #59923C2semidirect
3. #59727C2semidirect
4. #59460C2semidirect
5. #52307C2semidirect
6. #52076C2semidirect
7. #51951C2semidirect
8. #49896C2semidirect
9. #49778C2semidirect
10. #47750C2semidirect
11. #46969C2semidirect
12. #46312C2semidirect
13. #46099C2semidirect
14. #44217C2semidirect
15. #44181C2semidirect
16. #44068C2semidirect
17. #43899C2semidirect
18. #42043C2semidirect
19. #39830C2semidirect
20. #39702C2semidirect
21. #38820C2semidirect
22. #37208C2semidirect
23. #36513C2semidirect
24. #35693C2semidirect
25. #35669C2semidirect
26. #34523C2semidirect
27. #34276C2semidirect
710. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599242
#599232
#597272
#594602
#523072
#520762
#519512
#498962
#497782
#477502
#469692
#463122
#460992
#442172
#441812
#440682
#438992
#420432
#398302
#397022
#388202
#372082
#365132
#356932
#356692
#345232
#342762