Finite Group Databasebeta

← #8634703

Subgroups — #8634703

Order 512.

4416 conjugacy classes of subgroups.

The subgroup lattice has 1425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59432C212yesmaximal, complemented
2#58390C212yesmaximal, complemented
3#55132C214yesmaximal, complemented
4#54044C214yesmaximal, complemented
5#53017C211yesmaximal, characteristic, complemented
6#51020C214yesmaximal, complemented
7#49958C214yesmaximal, complemented
8#48609C214yesmaximal, complemented
9#46912C212yesmaximal, complemented
10#46608C214yesmaximal, complemented
11#45696C211yesmaximal, characteristic, complemented
12#45668C212yesmaximal, complemented
13#45375C211yesmaximal, characteristic, complemented
14#45330C212yesmaximal, complemented
15#45165C212yesmaximal, complemented
16#42944C211yesmaximal, characteristic, complemented
17#42514C212yesmaximal, complemented
18#40974C212yesmaximal, complemented
19#39622C212yesmaximal, complemented
20#39193C212yesmaximal, complemented
21#39134C211yesmaximal, characteristic, complemented
22#38907C212yesmaximal, complemented
23#37687C212yesmaximal, complemented
24#37373C212yesmaximal, complemented
25D4×#125C212yesmaximal, complemented
26#35923C211yesmaximal, characteristic
27#35612C212yesmaximal, complemented
28#35107C212yesmaximal, complemented
29#34921C211yesmaximal, characteristic, complemented
30C2×#553C2211yescharacteristic
31C2×#547C2211yescharacteristic
32C2×#544C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C22×#125C2212yes—
35#2859C2212yes—
36#2857C2212yes—
37#2854C2211yescharacteristic
38#2854C2212yes—
39#2851C2212yes—
40#2851C2212yes—
41#2841C2212yes—
42#2839C2214yes—
43#2838C2214yes—
44#2835C2212yes—
45#2831C2214yes—
46#2822C2212yes—
47#2821C2212yes—
48#2810C2214yes—
49#2807C2214yes—
50#2806C2214yes—
51#2806C2214yes—
52#2800C2214yes—
53#2795C2214yes—
54#2792C2214yes—
55#2792C2214yes—
56#2788C2214yes—
57#2779C2214yes—
58#2779C2214yes—
59#2776C2214yes—
60#2771C2212yes—
61#2771C2212yes—
62#2769C2212yes—
63#2766C2214yes—
64#2764C2212yes—
65#2764C2212yes—
66#2758C2214yes—
67#2758C2214yes—
68#2757C2214yes—
69#2757C2214yes—
70#2757C2214yes—
71#2747C2214yes—
72#2746C2214yes—
73#2745C2214yes—
74#2745C2214yes—
75#2740C2214yes—
76#2738C2214yes—
77#2738C2214yes—
78#2728C2214yes—
79#2726C2214yes—
80#2724C2212yes—
81#2721C2214yes—
82#2720C2214yes—
83#2720C2214yes—
84#2718C2214yes—
85#2717C2214yes—
86#2713C2214yes—
87#2707C2214yes—
88#2704C2214yes—
89#2701C2214yes—
90#2695C2214yes—
91#2694C2214yes—
92#2694C2214yes—
93#2694C2214yes—
94#2692C2214yes—
95#2691C2214yes—
96#2690C2214yes—
97#2690C2214yes—
98#2690C2214yes—
99#2687C2214yes—
100#2687C2214yes—
101#2672C2214yes—
102#2664C2212yes—
103#2663C2212yes—
104#2660C2212yes—
105#2660C2211yescharacteristic
106#2654C2214yes—
107#2650C2214yes—
108#2633C2212yes—
109#2630C2214yes—
110#2630C2214yes—
111#2629C2212yes—
112#2625C2214yes—
113#2624C2211yescharacteristic
114#2623C2214yes—
115#2618C2212yes—
116#2608C2214yes—
117#2607C2211yescharacteristic
118#2602C2212yes—
119#2600C2212yes—
120#2600C2212yes—
121#2600C2211yescharacteristic
122#2596C2212yes—
123#2596C2214yes—
124#2589C2212yes—
125#2587C2214yes—
126#2586C2214yes—
127#2586C2214yes—
128#2584C2212yes—
129#2577C2214yes—
130#2575C2212yes—
131#2573C2214yes—
132#2569C2214yes—
133#2566C2212yes—
134#2564C2212yes—
135#2563C2211yescharacteristic
136#2562C2212yes—
137#2562C2212yes—
138#2562C2211yescharacteristic
139#2557C2212yes—
140#2556C2214yes—
141#2553C2214yes—
142#2552C2212yes—
143#2552C2212yes—
144#2552C2212yes—
145#2550C2212yes—
146#2550C2212yes—
147#2550C2212yes—
148#2550C2212yes—
149#2547C2212yes—
150#2538C2212yes—
151#2537C2212yes—
152#2535C2212yes—
153#2525C2214yes—
154#2525C2214yes—
155#2524C2214yes—
156#2522C2214yes—
157#2517C2211yescharacteristic
158#2509C2212yes—
159#2507C2214yes—
160#2507C2214yes—
161#2506C2214yes—
162#2506C2214yes—
163#2506C2212yes—
164#2504C2212yes—
165#2504C2211yescharacteristic
166#2501C2211yescharacteristic
167#2501C2212yes—
168#2497C2212yes—
169#2497C2214yes—
170#2497C2212yes—
171#2496C2212yes—
172#2495C2212yes—
173#2495C2214yes—
174#2495C2212yes—
175#2495C2212yes—
176#2495C2212yes—
177#2494C2212yes—
178#2491C2212yes—
179#2490C2212yes—
180#2490C2212yes—
181#2490C2212yes—
182#2487C2212yes—
183#2486C2212yes—
184#2486C2211yescharacteristic
185#2486C2211yescharacteristic
186#2485C2214yes—
187#2478C2214yes—
188#2477C2214yes—
189#2474C2214yes—
190#2473C2214yes—
191#2473C2214yes—
192#2473C2214yes—
193#2473C2214yes—
194#2473C2214yes—
195#2470C2214yes—
196#2466C2214yes—
197#2464C2214yes—
198#2461C2214yes—
199#2461C2214yes—
200#2459C2212yes—
201#2455C2211yescharacteristic
202#2455C2214yes—
203#2454C2212yes—
204#2454C2212yes—
205#2449C2214yes—
206#2442C2212yes—
207#2442C2212yes—
208#2442C2212yes—
209#2442C2212yes—
210#2442C2212yes—
211#2442C2212yes—
212#2441C2214yes—
213#2441C2212yes—
214#2440C2212yes—
215#2440C2214yes—
216#2438C2214yes—
217#2430C2212yes—
218#2427C2214yes—
219#2417C2214yes—
220#2413C2214yes—
221#2406C2214yes—
222#2398C2212yes—
223#2397C2211yescharacteristic
224#2395C2211yescharacteristic
225#2388C2212yes—
226#2383C2214yes—
227#2376C2212yes—
228#2355C2212yes—
229#2355C2212yes—
230#2352C2212yes—
231D4×C4⋊C4C2214yes—
232D4×C4⋊C4C2212yes—
233D4×C4⋊C4C2214yes—
234D4×C4⋊C4C2212yes—
235D4×C4⋊C4C2212yes—
236#2347C2214yes—
237#2347C2211yescharacteristic
238#2345C2211yescharacteristic
239#2344C2212yes—
240#2337C2214yes—
241#2335C2214yes—
242#2330C2212yes—
243#2330C2212yes—
244#2330C2212yes—
245#2324C2214yes—
246#2322C2212yes—
247#2319C2212yes—
248#2311C2214yes—
249C4×#125C2212yes—
250C4×#125C2212yes—
251C4×#124C2212yes—
252C4×#123C2212yes—
253C4×#123C2211yescharacteristic
254#2295C2212yes—
255#2293C2212yes—
256#2290C2212yes—
257#2275C2211yescharacteristic
258C42×D4C2212yes—
259C22×#41C2312yes—
260#553—44no—
261#547—44no—
262#544—44no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×#126C2312yes—
267C2×#126C2314yes—
268C2×#125—48no—
269C2×#125—44no—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2311yescharacteristic
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#124C2314yes—
283C2×#124C2312yes—
284C2×#123C2312yes—
285C2×#123C2314yes—
286C2×#123C2311yescharacteristic
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×#123C2312yes—
290C2×#123C2312yes—
291C2×#123C2312yes—
292C2×#123C2312yes—
293C2×#123C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2311yescharacteristic
302C2×#121C2312yes—
303C2×#121C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×#117C2311yescharacteristic
318C2×#117C2314yes—
319C2×#117C2311yescharacteristic
320C2×#117C2314yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2314yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2314yes—
330C22×C42C2311yescharacteristic
331C22×C42C2312yes—
332#401C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2311yescharacteristic
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#399C2311yescharacteristic
357#399C2314yes—
358#399C2312yes—
359#399C2314yes—
360#399C2311yescharacteristic
361#399C2311yescharacteristic
362#399C2314yes—
363#399C2314yes—
364#399C2312yes—
365#399C2314yes—
366#398C2311yescharacteristic
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#397C2312yes—
394#397C2312yes—
395#397C2314yes—
396#397C2312yes—
397#397C2312yes—
398#397C2312yes—
399#397C2314yes—
400#397C2312yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2311yescharacteristic
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2312yes—
412#397C2314yes—
413#397C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#395C2312yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2312yes—
433#395C2314yes—
434#395C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2312yes—
438#394C2312yes—
439#394C2312yes—
440#394C2312yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#393C2312yes—
449#393C2312yes—
450#393C2314yes—
451#393C2312yes—
452#393C2312yes—
453#392C2311yescharacteristic
454#392C2311yescharacteristic
455#392C2312yes—
456#392C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2312yes—
462#391C2312yes—
463#391C2314yes—
464#391C2312yes—
465#391C2314yes—
466#391C2314yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2314yes—
471#390C2314yes—
472#390C2312yes—
473#390C2312yes—
474#390C2314yes—
475#390C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2312yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2312yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#386C2314yes—
590#386C2312yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2312yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2312yes—
599#386C2314yes—
600#386C2311yescharacteristic
601#386C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2312yes—
608#385C2311yescharacteristic
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2312yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#384C2312yes—
629#384C2312yes—
630#384C2312yes—
631#384C2314yes—
632#384C2314yes—
633#384C2312yes—
634#384C2314yes—
635#383C2312yes—
636#383C2314yes—
637#383C2314yes—
638#383C2314yes—
639#383C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#381C2314yes—
648#381C2314yes—
649#381C2312yes—
650#381C2312yes—
651#381C2311yescharacteristic
652#381C2312yes—
653#380C2312yes—
654#380C2311yescharacteristic
655#380C2311yescharacteristic
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2311yescharacteristic
715C2×#95C2312yes—
716C43C2312yes—
717C2×#41—44no—
718C2×#41—48no—
719C22×Q8C2412yes—
720C22×Q8C2414yes—
721C22×Q8C2412yes—
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C22×D4C2412yes—
725C22×D4C2411yescharacteristic
726C22×D4C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2414yes—
729C22×D4C2412yes—
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2414yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2411yescharacteristic
742C23×C4C2412yes—
743C23×C4C2412yes—
744C4⋊Q8—44no—
745C4⋊Q8—44no—
746C4⋊Q8—42no—
747#126—44no—
748#126—48no—
749#125—28no—
750#125—28no—
751#125—28no—
752#125—44no—
753#125—44no—
754#125—44no—
755#125—44no—
756#125—42no—
757#125—48no—
758#125—48no—
759#125—48no—
760#125—84no—
761#124—44no—
762#124—48no—
763#123—44no—
764#123—44no—
765#123—48no—
766#123—44no—
767#123—48no—
768#123—42no—
769#123—44no—
770#123—82no—
771#123—82no—
772#123—82no—
773C22⋊Q8—48no—
774C22⋊Q8—44no—
775C22⋊Q8—84no—
776C22⋊Q8—84no—
777C22⋊Q8—84no—
778#121—44no—
779#121—48no—
780#121—44no—
781#121—42no—
782#121—42no—
783C4×Q8—28no—
784C4×D4—24no—
785C4×D4—28no—
786C4×D4—28no—
787C4×D4—28no—
788C4×D4—42no—
789C4×D4—44no—
790C4×D4—42no—
791C4×D4—48no—
792C4×D4—48no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—84no—
796#117—24no—
797#117—42no—
798#117—48no—
799#117—84no—
800C2×C4⋊C4—28no—
801C2×C4⋊C4—24no—
802C2×C4⋊C4—42no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4—44no—
805C2×C4⋊C4—44no—
806C2×C4⋊C4—48no—
807C2×C4⋊C4—48no—
808C2×C4⋊C4—42no—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2411yescharacteristic
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2411yescharacteristic
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C42—42no—
923C2×C42—44no—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2412yes—
946#95C2411yescharacteristic
947#95C2414yes—
948#95C2412yes—
949#95C2411yescharacteristic
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2411yescharacteristic
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2411yescharacteristic
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2414yes—
1015C24C2511yescharacteristic
1016C24C2512yes—
1017C24C2511yescharacteristic
1018C24C2512yes—
1019#41—816no—
1020C2×Q8—24no—
1021C2×Q8—42no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×D4—24no—
1029C2×D4—24no—
1030C2×D4—24no—
1031C2×D4—24no—
1032C2×D4—28no—
1033C2×D4—22no—
1034C2×D4—24no—
1035C2×D4—22no—
1036C2×D4—24no—
1037C2×D4—24no—
1038C2×D4—24no—
1039C2×D4—41no—
1040C2×D4—42no—
1041C2×D4—41no—
1042C2×D4—42no—
1043C2×D4—44no—
1044C2×D4—41no—
1045C2×D4—42no—
1046C2×D4—44no—
1047C2×D4—42no—
1048C2×D4—44no—
1049C22×C4—28no—
1050C22×C4—24no—
1051C22×C4—22no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—22no—
1055C22×C4—28no—
1056C22×C4—22no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—28no—
1064C22×C4—44no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—41no—
1081C22×C4—42no—
1082C22×C4—44no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C4⋊C4—22no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—22no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—41no—
1152C4⋊C4—42no—
1153C4⋊C4—41no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4H(5,𝔽2)14yes—
1178C22⋊C4—24no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—22no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—41no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—41no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—41no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C42—24no—
1225C42—24no—
1226C42—24no—
1227C42—22no—
1228C42—24no—
1229C42—24no—
1230C42—42no—
1231C42—42no—
1232C42—42no—
1233C42—44no—
1234C42—44no—
1235C42—42no—
1236C42—44no—
1237C42—44no—
1238C42—42no—
1239C42—44no—
1240C42—42no—
1241C42—42no—
1242C42—44no—
1243C42—42no—
1244C42—44no—
1245C422−1+418yes—
1246C23—22no—
1247C23—21no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—21no—
1256C23—21no—
1257C23—22no—
1258C23—22no—
1259C23—24no—
1260C23—22no—
1261C23—21no—
1262C23—22no—
1263C23—24no—
1264C23—22no—
1265C23—21no—
1266C23#58514yes—
1267C23#58512yes—
1268C23C2611yescharacteristic
1269Q8—84no—
1270Q8—84no—
1271Q8—164no—
1272D4—216no—
1273D4—48no—
1274D4—44no—
1275D4—44no—
1276D4—82no—
1277D4—84no—
1278D4—88no—
1279D4—162no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—21no—
1333C2×C4—22no—
1334C2×C4—21no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—416no—
1345C2×C4—48no—
1346C2×C4—44no—
1347C2×C4—44no—
1348C2×C4—84no—
1349C2×C4—88no—
1350C2×C4—84no—
1351C2×C4—84no—
1352C2×C4—82no—
1353C2×C4—84no—
1354C2×C4—82no—
1355C2×C4—88no—
1356C2×C4—84no—
1357C2×C4—162no—
1358C2×C4C2×H(5,𝔽2)14yes—
1359C2×C4C2×H(5,𝔽2)12yes—
1360C2×C4C2×2−1+414yes—
1361C2×C4C2×2−1+414yes—
1362C2×C4C2×2−1+414yes—
1363C22—24no—
1364C22—24no—
1365C22—24no—
1366C22—22no—
1367C22—24no—
1368C22—42no—
1369C22—41no—
1370C22—41no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—41no—
1376C22—42no—
1377C22—42no—
1378C22—41no—
1379C22—44no—
1380C22—42no—
1381C22—41no—
1382C22—42no—
1383C22—44no—
1384C22—42no—
1385C22C22×H(5,𝔽2)11yescharacteristic
1386C22C22×2−1+412yes—
1387C22C2×#58512yes—
1388C22C2×#58511yescharacteristic
1389C22H(7,𝔽2)11yescharacteristic
1390C4—24no—
1391C4—24no—
1392C4—24no—
1393C4—41no—
1394C4—42no—
1395C4—41no—
1396C4—44no—
1397C4—42no—
1398C4—42no—
1399C4—41no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—42no—
1405C4—44no—
1406C4—44no—
1407C4—42no—
1408C4—41no—
1409C4—42no—
1410C4—44no—
1411C4—44no—
1412C4—42no—
1413C4—42no—
1414C4#355014yes—
1415C2—44no—
1416C2—42no—
1417C2—81no—
1418C2—82no—
1419C2C2×#355011yescharacteristic
1420C2#6282512yes—
1421C2#6289911yescharacteristic
1422C2#6295812yes—
1423C2#6301711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35923C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59432C2semidirect
2. #58390C2semidirect
3. #55132C2semidirect
4. #54044C2semidirect
5. #53017C2semidirect
6. #51020C2semidirect
7. #49958C2semidirect
8. #48609C2semidirect
9. #46912C2semidirect
10. #46608C2semidirect
11. #45696C2semidirect
12. #45668C2semidirect
13. #45375C2semidirect
14. #45330C2semidirect
15. #45165C2semidirect
16. #42944C2semidirect
17. #42514C2semidirect
18. #40974C2semidirect
19. #39622C2semidirect
20. #39193C2semidirect
21. #39134C2semidirect
22. #38907C2semidirect
23. #37687C2semidirect
24. #37373C2semidirect
25. D4×#125C2semidirect
27. #35612C2semidirect
28. #35107C2semidirect
29. #34921C2semidirect

Maximal subgroups

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

subgroupindex
#594322
#583902
#551322
#540442
#530172
#510202
#499582
#486092
#469122
#466082
#456962
#456682
#453752
#453302
#451652
#429442
#425142
#409742
#396222
#391932
#391342
#389072
#376872
#373732
D4×#1252
#359232
#356122
#351072
#349212