Finite Group Databasebeta

← #8345866

Subgroups — #8345866

Order 512.

4256 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59829C212yesmaximal, complemented
2#59771C212yesmaximal, complemented
3#59134C212yesmaximal, complemented
4#57325C212yesmaximal, complemented
5#57105C214yesmaximal, complemented
6#54969C214yesmaximal, complemented
7#54569C212yesmaximal, complemented
8#54545C214yesmaximal, complemented
9#53126C212yesmaximal, complemented
10#52926C212yesmaximal, complemented
11#52289C211yesmaximal, characteristic, complemented
12#51031C214yesmaximal, complemented
13#48483C214yesmaximal, complemented
14#46346C212yesmaximal, complemented
15#45414C212yesmaximal, complemented
16#43877C212yesmaximal, complemented
17#42961C211yesmaximal, characteristic
18#42817C211yesmaximal, characteristic, complemented
19#42809C212yesmaximal, complemented
20#42700C212yesmaximal, complemented
21#40964C214yesmaximal, complemented
22#40080C212yesmaximal, complemented
23#39219C212yesmaximal, complemented
24#39071C212yesmaximal, complemented
25#39071C212yesmaximal, complemented
26#37523C211yesmaximal, characteristic
27#36041C211yesmaximal, characteristic
28#35711C211yesmaximal, characteristic, complemented
29#35674C211yesmaximal, characteristic, complemented
30C2×#559C2211yescharacteristic
31C2×Q82C2211yescharacteristic
32C2×#556C2212yes—
33C22×C4⋊Q8C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2863C2212yes—
36#2863C2212yes—
37#2841C2212yes—
38#2838C2214yes—
39#2833C2214yes—
40#2832C2212yes—
41#2832C2214yes—
42#2830C2214yes—
43#2827C2214yes—
44#2826C2212yes—
45#2824C2212yes—
46#2821C2214yes—
47#2814C2214yes—
48#2811C2212yes—
49#2807C2211yescharacteristic
50#2804C2214yes—
51#2802C2212yes—
52#2799C2212yes—
53#2799C2214yes—
54#2798C2214yes—
55#2794C2214yes—
56#2792C2212yes—
57#2790C2212yes—
58#2786C2214yes—
59#2783C2214yes—
60#2780C2214yes—
61#2777C2214yes—
62#2775C2214yes—
63#2774C2214yes—
64#2770C2214yes—
65#2769C2214yes—
66#2766C2214yes—
67#2766C2214yes—
68#2764C2214yes—
69#2763C2214yes—
70#2763C2211yescharacteristic
71#2762C2214yes—
72#2760C2212yes—
73#2759C2214yes—
74#2759C2214yes—
75#2759C2214yes—
76#2758C2214yes—
77#2758C2214yes—
78#2758C2214yes—
79#2755C2212yes—
80#2754C2214yes—
81#2754C2214yes—
82#2754C2214yes—
83#2752C2212yes—
84#2751C2214yes—
85#2749C2214yes—
86#2745C2214yes—
87#2744C2214yes—
88#2742C2211yescharacteristic
89#2740C2214yes—
90#2740C2214yes—
91#2737C2214yes—
92#2737C2214yes—
93#2734C2214yes—
94#2718C2214yes—
95#2716C2214yes—
96#2716C2214yes—
97#2716C2214yes—
98#2716C2214yes—
99#2713C2212yes—
100#2704C2212yes—
101#2692C2214yes—
102#2690C2214yes—
103#2687C2214yes—
104#2677C2214yes—
105#2677C2214yes—
106#2677C2211yescharacteristic
107#2674C2214yes—
108#2665C2214yes—
109#2663C2214yes—
110#2653C2214yes—
111#2652C2214yes—
112#2652C2214yes—
113#2652C2214yes—
114#2650C2214yes—
115#2649C2214yes—
116#2640C2212yes—
117#2640C2212yes—
118#2637C2214yes—
119#2632C2212yes—
120#2628C2212yes—
121#2628C2211yescharacteristic
122#2624C2212yes—
123#2621C2214yes—
124#2619C2211yescharacteristic
125#2610C2212yes—
126#2607C2214yes—
127#2607C2212yes—
128#2607C2214yes—
129#2606C2214yes—
130#2599C2214yes—
131#2598C2212yes—
132#2592C2212yes—
133#2589C2214yes—
134#2587C2214yes—
135#2581C2211yescharacteristic
136#2581C2212yes—
137#2581C2212yes—
138#2581C2211yescharacteristic
139#2580C2212yes—
140#2576C2214yes—
141#2576C2214yes—
142#2575C2214yes—
143#2572C2214yes—
144#2572C2214yes—
145#2572C2212yes—
146#2568C2212yes—
147#2568C2212yes—
148#2568C2212yes—
149#2568C2211yescharacteristic
150#2556C2214yes—
151#2553C2214yes—
152#2548C2211yescharacteristic
153#2547C2212yes—
154#2546C2212yes—
155#2545C2212yes—
156#2545C2212yes—
157#2544C2212yes—
158#2528C2214yes—
159#2524C2214yes—
160#2523C2214yes—
161#2523C2214yes—
162#2523C2214yes—
163#2521C2214yes—
164#2515C2214yes—
165#2514C2212yes—
166#2514C2212yes—
167#2514C2214yes—
168#2514C2212yes—
169#2513C2212yes—
170#2509C2212yes—
171#2509C2212yes—
172#2509C2212yes—
173#2493C2214yes—
174#2492C2214yes—
175#2492C2214yes—
176#2488C2214yes—
177#2484C2212yes—
178#2484C2212yes—
179#2484C2212yes—
180#2484C2212yes—
181#2481C2214yes—
182#2481C2214yes—
183#2471C2214yes—
184#2470C2214yes—
185#2466C2214yes—
186#2463C2212yes—
187#2458C2214yes—
188#2455C2212yes—
189#2452C2212yes—
190#2452C2212yes—
191#2452C2212yes—
192#2452C2214yes—
193#2451C2214yes—
194#2451C2212yes—
195#2451C2212yes—
196#2451C2212yes—
197#2451C2212yes—
198#2451C2212yes—
199#2450C2214yes—
200#2448C2212yes—
201#2448C2212yes—
202#2448C2212yes—
203#2447C2212yes—
204#2447C2212yes—
205#2447C2212yes—
206#2446C2214yes—
207#2446C2212yes—
208#2446C2212yes—
209#2446C2214yes—
210#2446C2212yes—
211#2446C2212yes—
212#2446C2212yes—
213#2446C2212yes—
214#2445C2212yes—
215#2439C2214yes—
216#2439C2214yes—
217#2439C2212yes—
218#2439C2212yes—
219#2436C2212yes—
220#2436C2212yes—
221#2417C2214yes—
222#2402C2212yes—
223#2399C2212yes—
224#2398C2212yes—
225#2396C2211yescharacteristic
226#2396C2211yescharacteristic
227#2396C2212yes—
228#2381C2214yes—
229#2369C2212yes—
230#2368C2214yes—
231#2367C2212yes—
232#2365C2212yes—
233#2363C2212yes—
234#2363C2212yes—
235#2359C2214yes—
236#2356C2211yescharacteristic
237#2352C2214yes—
238#2351C2211yescharacteristic
239#2351C2212yes—
240#2349C2212yes—
241Q8×C22⋊C4C2212yes—
242Q8×C22⋊C4C2212yes—
243#2332C2214yes—
244#2329C2214yes—
245#2320C2212yes—
246#2320C2212yes—
247#2310C2211yescharacteristic
248#2310C2211yescharacteristic
249#2310C2211yescharacteristic
250C4×C4⋊Q8C2212yes—
251C4×#125C2212yes—
252C4×#124C2212yes—
253C4×#124C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#121C2212yes—
256#2298C2212yes—
257#2296C2211yescharacteristic
258#2296C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261#559—44no—
262Q82—44no—
263#556—48no—
264C2×C4⋊Q8—44no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2314yes—
275C2×#127C2311yescharacteristic
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2312yes—
292#519—44no—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2314yes—
312C2×#117C2311yescharacteristic
313C2×#117C2311yescharacteristic
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2314yes—
318C2×#117C2312yes—
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C42C2311yescharacteristic
322#401C2314yes—
323#401C2314yes—
324#401C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2311yescharacteristic
328#400C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2312yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2311yescharacteristic
352#400C2312yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2312yes—
359#399C2314yes—
360#399C2314yes—
361#399C2311yescharacteristic
362#399C2314yes—
363#399C2311yescharacteristic
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2312yes—
414#396C2312yes—
415#396C2314yes—
416#396C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2311yescharacteristic
421#395C2314yes—
422#395C2312yes—
423#395C2314yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#395C2312yes—
428#395C2311yescharacteristic
429#395C2312yes—
430#395C2312yes—
431#395C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2312yes—
437#394C2312yes—
438#394C2314yes—
439#394C2312yes—
440#394C2314yes—
441#394C2312yes—
442#393C2314yes—
443#393C2314yes—
444#393C2312yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2311yescharacteristic
456#393C2314yes—
457#393C2314yes—
458#393C2311yescharacteristic
459#393C2314yes—
460#392C2312yes—
461#392C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2314yes—
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2312yes—
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2314yes—
493#391C2314yes—
494#391C2314yes—
495#391C2312yes—
496#391C2314yes—
497#391C2312yes—
498#391C2314yes—
499#391C2314yes—
500#391C2312yes—
501#390C2314yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2314yes—
506#390C2312yes—
507#390C2314yes—
508#390C2312yes—
509#390C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#388C2312yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2312yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
564#388C2314yes—
565#388C2314yes—
566#387C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2312yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2312yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2312yes—
617#387C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#385C2311yescharacteristic
629#385C2311yescharacteristic
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2311yescharacteristic
642#385C2311yescharacteristic
643#385C2312yes—
644#385C2312yes—
645#385C2312yes—
646#385C2312yes—
647#384C2312yes—
648#383C2314yes—
649#383C2314yes—
650#383C2314yes—
651#383C2314yes—
652#383C2314yes—
653#383C2312yes—
654#383C2314yes—
655#383C2314yes—
656#382C2312yes—
657#382C2311yescharacteristic
658#382C2312yes—
659#382C2312yes—
660#382C2314yes—
661#382C2314yes—
662#382C2314yes—
663#382C2314yes—
664#382C2312yes—
665#382C2311yescharacteristic
666#381C2312yes—
667#381C2312yes—
668#381C2312yes—
669#381C2312yes—
670#381C2312yes—
671#381C2312yes—
672#381C2314yes—
673#381C2314yes—
674#381C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2312yes—
678#380C2314yes—
679#380C2314yes—
680#380C2312yes—
681#380C2314yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2312yes—
715C2×#95C2314yes—
716C43C2312yes—
717C22×Q8—24no—
718C22×Q8—24no—
719C22×Q8—24no—
720C22×Q8—42no—
721C22×Q8—42no—
722C22×Q8—42no—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2411yescharacteristic
731C22×Q8C2412yes—
732C22×Q8C2414yes—
733C22×Q8C2414yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2411yescharacteristic
744C23×C4C2414yes—
745C23×C4C2414yes—
746C4⋊Q8—28no—
747C4⋊Q8—44no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750C4⋊Q8—48no—
751C4⋊Q8—44no—
752C4⋊Q8—44no—
753C4⋊Q8—48no—
754C4⋊Q8—48no—
755C4⋊Q8—44no—
756#127—42no—
757#126—48no—
758#126—48no—
759#125—44no—
760#124—28no—
761#124—44no—
762#124—44no—
763#124—44no—
764#124—44no—
765#123—48no—
766#123—48no—
767C22⋊Q8—48no—
768C22⋊Q8—48no—
769C22⋊Q8—48no—
770C22⋊Q8—48no—
771C22⋊Q8—44no—
772#121—28no—
773C4×Q8—24no—
774C4×Q8—24no—
775C4×Q8—28no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—42no—
779C4×Q8—42no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—42no—
784C4×Q8—42no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×D4—44no—
788C4×D4—44no—
789C4×D4—44no—
790C4×D4—44no—
791C4×D4—48no—
792#117—24no—
793#117—44no—
794#117—42no—
795#117—48no—
796#117—42no—
797#117—42no—
798#117—44no—
799C2×C4⋊C4—44no—
800C2×C4⋊C4—44no—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2411yescharacteristic
866C2×C22⋊C4C2411yescharacteristic
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C42—42no—
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2414yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2411yescharacteristic
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
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#95C2412yes—
957#95C2412yes—
958#95C2411yescharacteristic
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2411yescharacteristic
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2411yescharacteristic
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24C2514yes—
1009C24C2511yescharacteristic
1010C2×Q8—24no—
1011C2×Q8—22no—
1012C2×Q8—24no—
1013C2×Q8—22no—
1014C2×Q8—24no—
1015C2×Q8—22no—
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—22no—
1019C2×Q8—24no—
1020C2×Q8—22no—
1021C2×Q8—24no—
1022C2×Q8—41no—
1023C2×Q8—42no—
1024C2×Q8—42no—
1025C2×Q8—42no—
1026C2×Q8—41no—
1027C2×Q8—42no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—416no—
1040C2×Q8—88no—
1041C2×Q8H(5,𝔽2)14yes—
1042C2×D4—28no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—42no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—28no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C42−1+414yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—22no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—41no—
1137C4⋊C4—41no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—41no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—41no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C22⋊C4—22no—
1165C22⋊C4—22no—
1166C22⋊C4—28no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—41no—
1178C22⋊C4—42no—
1179C22⋊C4—41no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C42—24no—
1200C42—24no—
1201C42—22no—
1202C42—24no—
1203C42—22no—
1204C42—28no—
1205C42—24no—
1206C42—24no—
1207C42—24no—
1208C42—24no—
1209C42—24no—
1210C42—42no—
1211C42—44no—
1212C42—42no—
1213C42—42no—
1214C42—42no—
1215C42—42no—
1216C42—42no—
1217C42—42no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—42no—
1223C42—44no—
1224C42—42no—
1225C23—21no—
1226C23—22no—
1227C23—21no—
1228C23—22no—
1229C23—24no—
1230C23—24no—
1231C23—24no—
1232C23—24no—
1233C23—24no—
1234C23—24no—
1235C23—24no—
1236C23C2×2−1+412yes—
1237C23C2611yescharacteristic
1238Q8—28no—
1239Q8—48no—
1240Q8—44no—
1241Q8—44no—
1242Q8—48no—
1243Q8—84no—
1244Q8—84no—
1245Q8—82no—
1246Q8—162no—
1247Q8—164no—
1248Q8—164no—
1249D4—48no—
1250D4—88no—
1251D4—84no—
1252D4—162no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—28no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—44no—
1324C2×C4—48no—
1325C2×C4—44no—
1326C2×C4—88no—
1327C2×C4—84no—
1328C2×C4—164no—
1329C2×C4—164no—
1330C2×C4C2×H(5,𝔽2)14yes—
1331C2×C4C2×H(5,𝔽2)12yes—
1332C2×C4C2×2−1+412yes—
1333C2×C4C2×2−1+412yes—
1334C2×C4#58514yes—
1335C2×C4#58512yes—
1336C22—22no—
1337C22—24no—
1338C22—41no—
1339C22—41no—
1340C22—42no—
1341C22—44no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22—44no—
1348C22C22×H(5,𝔽2)11yescharacteristic
1349C22C22×2−1+411yescharacteristic
1350C22C2×#58511yescharacteristic
1351C22C2×#58512yes—
1352C222−1+612yes—
1353C4—22no—
1354C4—24no—
1355C4—24no—
1356C4—42no—
1357C4—44no—
1358C4—44no—
1359C4—41no—
1360C4—42no—
1361C4—42no—
1362C4—41no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—41no—
1368C4—42no—
1369C4—41no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—44no—
1378C4—42no—
1379C4#353514yes—
1380C2—42no—
1381C2—84no—
1382C2C2×#353511yescharacteristic
1383C2#6293212yes—
1384C2#6296812yes—
1385C2#6302011yescharacteristic
1386C2#6304811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2619C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59829C2semidirect
2. #59771C2semidirect
3. #59134C2semidirect
4. #57325C2semidirect
5. #57105C2semidirect
6. #54969C2semidirect
7. #54569C2semidirect
8. #54545C2semidirect
9. #53126C2semidirect
10. #52926C2semidirect
11. #52289C2semidirect
12. #51031C2semidirect
13. #48483C2semidirect
14. #46346C2semidirect
15. #45414C2semidirect
16. #43877C2semidirect
18. #42817C2semidirect
19. #42809C2semidirect
20. #42700C2semidirect
21. #40964C2semidirect
22. #40080C2semidirect
23. #39219C2semidirect
24. #39071C2semidirect
25. #39071C2semidirect
28. #35711C2semidirect
29. #35674C2semidirect

Maximal subgroups

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

subgroupindex
#598292
#597712
#591342
#573252
#571052
#549692
#545692
#545452
#531262
#529262
#522892
#510312
#484832
#463462
#454142
#438772
#429612
#428172
#428092
#427002
#409642
#400802
#392192
#390712
#375232
#360412
#357112
#356742