Finite Group Databasebeta

← #8701604

Subgroups — #8701604

Order 512.

4371 conjugacy classes of subgroups.

The subgroup lattice has 1427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59921C212yesmaximal, complemented
2#59866C212yesmaximal, complemented
3#59293C212yesmaximal, complemented
4#59217C212yesmaximal, complemented
5#57167C214yesmaximal, complemented
6#54738C214yesmaximal, complemented
7#54234C214yesmaximal, complemented
8#52303C211yesmaximal, characteristic, complemented
9#51885C214yesmaximal, complemented
10#51026C214yesmaximal, complemented
11#50877C214yesmaximal, complemented
12#46158C211yesmaximal, characteristic, complemented
13#46152C211yesmaximal, characteristic, complemented
14C4⋊#564C211yesmaximal, characteristic, complemented
15#45128C212yesmaximal, complemented
16#45035C212yesmaximal, complemented
17#44943C212yesmaximal, complemented
18#42935C212yesmaximal, complemented
19#42577C212yesmaximal, complemented
20#42455C212yesmaximal, complemented
21#40005C212yesmaximal, complemented
22#39607C212yesmaximal, complemented
23#39400C212yesmaximal, complemented
24#37220C212yesmaximal, complemented
25#37157C212yesmaximal, complemented
26#37130C212yesmaximal, complemented
27#36464C211yesmaximal, characteristic, complemented
28#36464C211yesmaximal, characteristic, complemented
29#36290C211yesmaximal, characteristic, complemented
30C2×#564C2212yes—
31C2×#539C2214yes—
32#2859C2211yescharacteristic
33#2859C2211yescharacteristic
34#2859C2211yescharacteristic
35#2857C2212yes—
36#2854C2212yes—
37#2854C2212yes—
38#2851C2212yes—
39#2844C2212yes—
40#2839C2214yes—
41#2837C2214yes—
42#2827C2214yes—
43#2822C2212yes—
44#2820C2212yes—
45#2809C2212yes—
46#2808C2211yescharacteristic
47#2806C2211yescharacteristic
48#2805C2212yes—
49#2802C2214yes—
50#2788C2214yes—
51#2786C2214yes—
52#2784C2214yes—
53#2783C2212yes—
54#2781C2214yes—
55#2781C2212yes—
56#2781C2214yes—
57#2780C2214yes—
58#2779C2214yes—
59#2779C2214yes—
60#2775C2214yes—
61#2773C2214yes—
62#2758C2214yes—
63#2755C2214yes—
64#2755C2214yes—
65#2750C2214yes—
66#2747C2214yes—
67#2744C2212yes—
68#2741C2214yes—
69#2740C2214yes—
70#2739C2214yes—
71#2738C2214yes—
72#2732C2214yes—
73#2732C2211yescharacteristic
74#2730C2212yes—
75#2727C2212yes—
76#2726C2212yes—
77#2726C2212yes—
78#2725C2214yes—
79#2725C2214yes—
80#2725C2214yes—
81#2720C2214yes—
82#2720C2214yes—
83#2719C2214yes—
84#2719C2214yes—
85#2719C2214yes—
86#2711C2214yes—
87#2711C2214yes—
88#2708C2214yes—
89#2707C2214yes—
90#2707C2214yes—
91#2707C2214yes—
92#2705C2214yes—
93#2704C2214yes—
94#2704C2214yes—
95#2704C2214yes—
96#2702C2214yes—
97#2695C2214yes—
98#2694C2212yes—
99#2694C2214yes—
100#2692C2214yes—
101#2691C2214yes—
102#2690C2214yes—
103#2690C2214yes—
104#2687C2214yes—
105#2686C2212yes—
106#2683C2212yes—
107#2682C2211yescharacteristic
108#2681C2214yes—
109#2664C2214yes—
110#2664C2214yes—
111#2654C2214yes—
112#2650C2214yes—
113#2649C2214yes—
114#2638C2214yes—
115#2637C2214yes—
116#2629C2214yes—
117#2629C2212yes—
118#2618C2214yes—
119#2590C2214yes—
120#2585C2214yes—
121#2585C2214yes—
122#2584C2212yes—
123#2583C2214yes—
124#2577C2214yes—
125#2574C2214yes—
126#2571C2211yescharacteristic
127#2569C2214yes—
128#2567C2212yes—
129#2566C2214yes—
130#2564C2214yes—
131#2562C2214yes—
132#2559C2214yes—
133#2558C2214yes—
134#2558C2214yes—
135#2558C2214yes—
136#2556C2214yes—
137#2552C2212yes—
138#2552C2212yes—
139#2552C2212yes—
140#2552C2211yescharacteristic
141#2552C2212yes—
142#2543C2214yes—
143#2538C2211yescharacteristic
144#2538C2211yescharacteristic
145#2537C2212yes—
146#2537C2211yescharacteristic
147#2537C2212yes—
148#2537C2211yescharacteristic
149#2525C2214yes—
150#2524C2214yes—
151#2522C2214yes—
152#2519C2214yes—
153#2519C2214yes—
154#2518C2214yes—
155#2518C2214yes—
156#2509C2212yes—
157#2508C2212yes—
158#2507C2212yes—
159#2507C2212yes—
160#2506C2212yes—
161#2506C2212yes—
162#2506C2212yes—
163#2506C2212yes—
164#2506C2214yes—
165#2505C2214yes—
166#2497C2214yes—
167#2497C2212yes—
168#2497C2212yes—
169#2497C2212yes—
170#2497C2212yes—
171#2497C2212yes—
172#2497C2212yes—
173#2497C2212yes—
174#2496C2212yes—
175#2496C2212yes—
176#2496C2212yes—
177#2495C2212yes—
178#2495C2212yes—
179#2490C2214yes—
180#2489C2214yes—
181#2487C2212yes—
182#2486C2212yes—
183#2485C2212yes—
184#2485C2212yes—
185#2485C2212yes—
186#2485C2212yes—
187#2479C2214yes—
188#2476C2214yes—
189#2476C2214yes—
190#2475C2214yes—
191#2473C2214yes—
192#2473C2214yes—
193#2473C2214yes—
194#2466C2214yes—
195#2462C2214yes—
196#2460C2214yes—
197#2454C2212yes—
198#2454C2214yes—
199#2453C2214yes—
200#2452C2212yes—
201#2442C2212yes—
202#2442C2212yes—
203#2441C2212yes—
204#2441C2212yes—
205#2441C2212yes—
206#2440C2212yes—
207#2440C2212yes—
208#2439C2212yes—
209#2426C2212yes—
210#2426C2212yes—
211#2422C2212yes—
212#2422C2212yes—
213#2417C2214yes—
214#2416C2214yes—
215#2396C2212yes—
216#2395C2212yes—
217#2392C2212yes—
218#2382C2212yes—
219#2379C2212yes—
220#2370C2212yes—
221#2370C2214yes—
222#2369C2212yes—
223#2368C2214yes—
224#2363C2212yes—
225#2363C2212yes—
226#2363C2212yes—
227#2361C2212yes—
228#2354C2211yescharacteristic
229#2354C2212yes—
230#2354C2211yescharacteristic
231#2352C2212yes—
232Q8×C4⋊C4C2211yescharacteristic
233Q8×C4⋊C4C2211yescharacteristic
234#2349C2212yes—
235D4×C4⋊C4C2211yescharacteristic
236D4×C4⋊C4C2212yes—
237D4×C4⋊C4C2211yescharacteristic
238#2347C2212yes—
239#2347C2212yes—
240#2345C2214yes—
241#2332C2214yes—
242#2324C2212yes—
243#2323C2214yes—
244#2316C2212yes—
245#2314C2212yes—
246C4×#125C2211yescharacteristic
247C4×#124C2211yescharacteristic
248C4×#124C2211yescharacteristic
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×#123C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255#2296C2212yes—
256C2×#389C2212yes—
257#2285C2212yes—
258C42×D4C2211yescharacteristic
259#564—48no—
260#539—416no—
261C2×C4⋊Q8C2312yes—
262C2×#126C2314yes—
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#125C2311yescharacteristic
266C2×#125C2314yes—
267C2×#125C2314yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2314yes—
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#125C2314yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#124C2311yescharacteristic
280C2×#124C2311yescharacteristic
281C2×#123C2312yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2314yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2314yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2312yes—
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2312yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2314yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2314yes—
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2312yes—
323C22×C42C2312yes—
324C22×C42C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2312yes—
352#399C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2312yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2312yes—
409#396C2312yes—
410#396C2312yes—
411#396C2312yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2312yes—
420#395C2314yes—
421#395C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2312yes—
427#394C2314yes—
428#394C2314yes—
429#394C2312yes—
430#394C2314yes—
431#394C2312yes—
432#394C2312yes—
433#394C2314yes—
434#394C2314yes—
435#394C2312yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2312yes—
442#392C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2314yes—
448#391C2314yes—
449#391C2311yescharacteristic
450#391C2311yescharacteristic
451#390C2314yes—
452#390C2314yes—
453#390C2312yes—
454#390C2314yes—
455#390C2311yescharacteristic
456#390C2311yescharacteristic
457#390C2312yes—
458#390C2312yes—
459#390C2314yes—
460#390C2312yes—
461#390C2314yes—
462#390C2312yes—
463#389C2311yescharacteristic
464#389C2311yescharacteristic
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
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#388C2312yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2312yes—
546#388C2312yes—
547#388C2312yes—
548#388C2312yes—
549#388C2312yes—
550#388C2312yes—
551#388C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2312yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2312yes—
597#386C2312yes—
598#386C2314yes—
599#386C2312yes—
600#385C2312yes—
601#385C2314yes—
602#385C2312yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2312yes—
619#385C2314yes—
620#384C2314yes—
621#384C2312yes—
622#384C2311yescharacteristic
623#384C2312yes—
624#384C2311yescharacteristic
625#384C2311yescharacteristic
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#384C2311yescharacteristic
629#384C2312yes—
630#384C2312yes—
631#384C2312yes—
632#383C2314yes—
633#383C2314yes—
634#382C2311yescharacteristic
635#382C2312yes—
636#382C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2311yescharacteristic
640#382C2312yes—
641#382C2312yes—
642#382C2311yescharacteristic
643#382C2314yes—
644#381C2314yes—
645#381C2312yes—
646#380C2312yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2312yes—
651#380C2314yes—
652#380C2312yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C2×#95C2314yes—
713C43C2311yescharacteristic
714C22×Q8C2411yescharacteristic
715C22×Q8C2414yes—
716C22×Q8C2411yescharacteristic
717C22×D4C2411yescharacteristic
718C22×D4C2414yes—
719C22×D4C2414yes—
720C22×D4C2411yescharacteristic
721C22×D4C2412yes—
722C22×D4C2411yescharacteristic
723C22×D4C2412yes—
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2414yes—
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2412yes—
732C23×C4C2414yes—
733C23×C4C2414yes—
734C4⋊Q8—44no—
735#126—48no—
736#126—48no—
737#126—84no—
738#125—216no—
739#125—24no—
740#125—44no—
741#125—44no—
742#125—48no—
743#125—48no—
744#125—44no—
745#125—44no—
746#125—48no—
747#125—48no—
748#125—48no—
749#125—48no—
750#125—82no—
751#125—84no—
752#124—24no—
753#124—42no—
754#123—28no—
755#123—48no—
756#123—48no—
757#123—48no—
758C22⋊Q8—28no—
759C22⋊Q8—28no—
760C22⋊Q8—48no—
761C22⋊Q8—48no—
762C22⋊Q8—48no—
763C22⋊Q8—48no—
764C22⋊Q8—44no—
765#121—28no—
766#121—28no—
767#121—44no—
768#121—48no—
769#121—82no—
770#121—84no—
771#121—82no—
772C4×Q8—42no—
773C4×Q8—42no—
774C4×Q8—82no—
775C4×Q8—82no—
776C4×D4—24no—
777C4×D4—44no—
778C4×D4—44no—
779C4×D4—42no—
780C4×D4—42no—
781C4×D4—44no—
782C4×D4—44no—
783C4×D4—42no—
784C4×D4—42no—
785C4×D4—48no—
786C4×D4—48no—
787#117—44no—
788#117—44no—
789#117—44no—
790#117—44no—
791#117—84no—
792C2×C4⋊C4—28no—
793C2×C4⋊C4—48no—
794C2×C4⋊C4—44no—
795C2×C4⋊C4—82no—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C42—44no—
918C2×C42—82no—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2412yes—
943C2×C42C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
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—
1007C24C2512yes—
1008C24C2512yes—
1009C24C2512yes—
1010C2×Q8—22no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—41no—
1014C2×Q8—41no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×Q8—44no—
1018C2×Q82−1+414yes—
1019C2×D4—28no—
1020C2×D4—28no—
1021C2×D4—24no—
1022C2×D4—22no—
1023C2×D4—22no—
1024C2×D4—22no—
1025C2×D4—22no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—42no—
1029C2×D4—41no—
1030C2×D4—41no—
1031C2×D4—42no—
1032C2×D4—42no—
1033C2×D4—42no—
1034C2×D4—41no—
1035C2×D4—41no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—42no—
1039C2×D42−1+414yes—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—28no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—24no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—22no—
1107C4⋊C4—22no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—41no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—41no—
1136C4⋊C4—41no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—41no—
1141C4⋊C4—41no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—41no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4H(5,𝔽2)14yes—
1173C22⋊C4—24no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—28no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C42—28no—
1218C42—22no—
1219C42—22no—
1220C42—22no—
1221C42—24no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—22no—
1226C42—22no—
1227C42—22no—
1228C42—42no—
1229C42—42no—
1230C42—41no—
1231C42—42no—
1232C42—42no—
1233C42—42no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—44no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23C2×2−1+414yes—
1263C23C2611yescharacteristic
1264Q8—44no—
1265Q8—44no—
1266Q8—164no—
1267D4—28no—
1268D4—84no—
1269D4—82no—
1270D4—82no—
1271D4—88no—
1272D4—88no—
1273D4—84no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—48no—
1345C2×C4—48no—
1346C2×C4—48no—
1347C2×C4—48no—
1348C2×C4—88no—
1349C2×C4—84no—
1350C2×C4—84no—
1351C2×C4—84no—
1352C2×C4—164no—
1353C2×C4—164no—
1354C2×C4C2×H(5,𝔽2)14yes—
1355C2×C4C2×H(5,𝔽2)12yes—
1356C2×C4C2×2−1+412yes—
1357C2×C4C2×2−1+414yes—
1358C2×C4C2×2−1+412yes—
1359C2×C4#58512yes—
1360C2×C4#58512yes—
1361C2×C4#58512yes—
1362C22—24no—
1363C22—24no—
1364C22—24no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22C22×H(5,𝔽2)11yescharacteristic
1384C22C22×2−1+411yescharacteristic
1385C22C22×2−1+411yescharacteristic
1386C22C2×#58511yescharacteristic
1387C22C2×#58511yescharacteristic
1388C22C2×#58511yescharacteristic
1389C22H(7,𝔽2)11yescharacteristic
1390C4—24no—
1391C4—24no—
1392C4—22no—
1393C4—22no—
1394C4—22no—
1395C4—42no—
1396C4—42no—
1397C4—41no—
1398C4—44no—
1399C4—42no—
1400C4—44no—
1401C4—41no—
1402C4—44no—
1403C4—41no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—44no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—44no—
1414C4—44no—
1415C4#355314yes—
1416C2—44no—
1417C2—82no—
1418C2—82no—
1419C2C2×#355311yescharacteristic
1420C2#6290211yescharacteristic
1421C2#6290811yescharacteristic
1422C2#6294411yescharacteristic
1423C2#6302411yescharacteristic
1424C2#6303211yescharacteristic
1425C2#6303911yescharacteristic
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. #59921C2semidirect
2. #59866C2semidirect
3. #59293C2semidirect
4. #59217C2semidirect
5. #57167C2semidirect
6. #54738C2semidirect
7. #54234C2semidirect
8. #52303C2semidirect
9. #51885C2semidirect
10. #51026C2semidirect
11. #50877C2semidirect
12. #46158C2semidirect
13. #46152C2semidirect
14. C4⋊#564C2semidirect
15. #45128C2semidirect
16. #45035C2semidirect
17. #44943C2semidirect
18. #42935C2semidirect
19. #42577C2semidirect
20. #42455C2semidirect
21. #40005C2semidirect
22. #39607C2semidirect
23. #39400C2semidirect
24. #37220C2semidirect
25. #37157C2semidirect
26. #37130C2semidirect
27. #36464C2semidirect
28. #36464C2semidirect
29. #36290C2semidirect

Maximal subgroups

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

subgroupindex
#599212
#598662
#592932
#592172
#571672
#547382
#542342
#523032
#518852
#510262
#508772
#461582
#461522
C4⋊#5642
#451282
#450352
#449432
#429352
#425772
#424552
#400052
#396072
#394002
#372202
#371572
#371302
#364642
#362902