Finite Group Databasebeta

← #8726315

Subgroups — #8726315

Order 512.

4379 conjugacy classes of subgroups.

The subgroup lattice has 1407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59935C211yesmaximal, characteristic, complemented
2#59874C212yesmaximal, complemented
3#59547C212yesmaximal, complemented
4#59096C212yesmaximal, complemented
5#59042C212yesmaximal, complemented
6#58628C214yesmaximal, complemented
7#57898C214yesmaximal, complemented
8#55616C212yesmaximal, complemented
9#54491C214yesmaximal, complemented
10#53041C212yesmaximal, complemented
11#53033C211yesmaximal, characteristic, complemented
12#52304C211yesmaximal, characteristic, complemented
13#47814C212yesmaximal, complemented
14#47266C214yesmaximal, complemented
15#45436C211yesmaximal, characteristic, complemented
16#45308C212yesmaximal, complemented
17#45194C212yesmaximal, complemented
18#44592C214yesmaximal, complemented
19#42847C212yesmaximal, complemented
20#42481C211yesmaximal, characteristic, complemented
21#42252C212yesmaximal, complemented
22#40938C214yesmaximal, complemented
23#40146C212yesmaximal
24#40025C212yesmaximal, complemented
25#39879C212yesmaximal, complemented
26#39171C211yesmaximal, characteristic
27#38983C212yesmaximal, complemented
28#35959C211yesmaximal, characteristic, complemented
29#35885C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×D4×Q8C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#533C2212yes—
35#2858C2211yescharacteristic
36#2850C2212yes—
37#2844C2212yes—
38#2843C2212yes—
39#2841C2214yes—
40#2838C2214yes—
41#2838C2214yes—
42#2833C2214yes—
43#2831C2214yes—
44#2827C2214yes—
45#2814C2212yes—
46#2809C2212yes—
47#2805C2212yes—
48#2800C2214yes—
49#2798C2214yes—
50#2796C2214yes—
51#2794C2212yes—
52#2789C2212yes—
53#2789C2211yescharacteristic
54#2789C2211yescharacteristic
55#2788C2214yes—
56#2786C2214yes—
57#2784C2212yes—
58#2784C2214yes—
59#2780C2214yes—
60#2780C2214yes—
61#2780C2214yes—
62#2777C2214yes—
63#2775C2214yes—
64#2772C2214yes—
65#2769C2214yes—
66#2769C2212yes—
67#2769C2212yes—
68#2766C2214yes—
69#2765C2212yes—
70#2765C2212yes—
71#2762C2214yes—
72#2762C2214yes—
73#2761C2214yes—
74#2761C2214yes—
75#2759C2214yes—
76#2759C2214yes—
77#2759C2214yes—
78#2756C2214yes—
79#2749C2214yes—
80#2746C2214yes—
81#2745C2214yes—
82#2745C2214yes—
83#2742C2214yes—
84#2739C2214yes—
85#2725C2214yes—
86#2724C2211yescharacteristic
87#2717C2212yes—
88#2713C2214yes—
89#2709C2214yes—
90#2707C2214yes—
91#2704C2214yes—
92#2704C2214yes—
93#2702C2214yes—
94#2700C2214yes—
95#2696C2214yes—
96#2696C2214yes—
97#2690C2212yes—
98#2690C2214yes—
99#2690C2214yes—
100#2690C2212yes—
101#2683C2214yes—
102#2683C2211yescharacteristic
103#2680C2214yes—
104#2665C2214yes—
105#2663C2212yes—
106#2658C2211yescharacteristic
107#2653C2214yes—
108#2652C2214yes—
109#2651C2214yes—
110#2645C2212yes—
111#2643C2214yes—
112#2640C2212yes—
113#2640C2211yescharacteristic
114#2638C2212yes—
115#2637C2214yes—
116#2630C2214yes—
117#2614C2212yes—
118#2612C2212yes—
119#2612C2214yes—
120#2612C2214yes—
121#2612C2212yes—
122#2612C2212yes—
123#2609C2214yes—
124#2601C2214yes—
125#2595C2214yes—
126#2592C2211yescharacteristic
127#2592C2211yescharacteristic
128#2581C2212yes—
129#2578C2214yes—
130#2578C2214yes—
131#2576C2214yes—
132#2576C2214yes—
133#2574C2214yes—
134#2568C2211yescharacteristic
135#2568C2211yescharacteristic
136#2568C2212yes—
137#2567C2211yescharacteristic
138#2564C2214yes—
139#2564C2212yes—
140#2563C2212yes—
141#2553C2214yes—
142#2549C2214yes—
143#2547C2212yes—
144#2547C2212yes—
145#2546C2212yes—
146#2546C2212yes—
147#2545C2212yes—
148#2545C2212yes—
149#2545C2212yes—
150#2544C2212yes—
151#2544C2212yes—
152#2541C2211yescharacteristic
153#2536C2214yes—
154#2531C2214yes—
155#2531C2214yes—
156#2528C2214yes—
157#2528C2214yes—
158#2527C2214yes—
159#2527C2214yes—
160#2526C2214yes—
161#2524C2214yes—
162#2523C2214yes—
163#2521C2214yes—
164#2518C2214yes—
165#2514C2212yes—
166#2514C2212yes—
167#2514C2212yes—
168#2510C2214yes—
169#2510C2214yes—
170#2510C2214yes—
171#2508C2212yes—
172#2508C2212yes—
173#2504C2212yes—
174#2498C2212yes—
175#2497C2214yes—
176#2494C2214yes—
177#2493C2214yes—
178#2492C2212yes—
179#2492C2212yes—
180#2477C2214yes—
181#2477C2214yes—
182#2465C2214yes—
183#2462C2214yes—
184#2457C2214yes—
185#2452C2212yes—
186#2451C2212yes—
187#2451C2214yes—
188#2451C2212yes—
189#2451C2212yes—
190#2450C2214yes—
191#2450C2214yes—
192#2450C2214yes—
193#2448C2212yes—
194#2447C2212yes—
195#2447C2212yes—
196#2446C2212yes—
197#2446C2212yes—
198#2446C2212yes—
199#2445C2212yes—
200#2438C2214yes—
201#2436C2212yes—
202#2436C2212yes—
203#2434C2212yes—
204#2434C2212yes—
205#2429C2212yes—
206#2429C2212yes—
207#2427C2212yes—
208#2427C2212yes—
209#2427C2212yes—
210#2426C2212yes—
211#2426C2212yes—
212#2421C2214yes—
213#2421C2214yes—
214#2420C2212yes—
215#2417C2212yes—
216#2409C2214yes—
217#2409C2212yes—
218#2401C2212yes—
219#2401C2212yes—
220#2399C2211yescharacteristic
221#2399C2211yescharacteristic
222#2398C2214yes—
223#2395C2212yes—
224#2372C2212yes—
225#2367C2212yes—
226#2367C2212yes—
227#2367C2212yes—
228#2365C2212yes—
229#2365C2212yes—
230#2361C2212yes—
231#2360C2212yes—
232#2360C2212yes—
233#2359C2214yes—
234#2356C2212yes—
235#2356C2214yes—
236#2356C2212yes—
237#2353C2214yes—
238#2351C2212yes—
239#2345C2212yes—
240Q8×C22⋊C4C2212yes—
241Q8×C22⋊C4C2214yes—
242#2335C2214yes—
243#2328C2212yes—
244#2328C2214yes—
245#2327C2212yes—
246#2323C2214yes—
247#2319C2211yescharacteristic
248#2318C2214yes—
249C4×#125C2212yes—
250C4×#124C2211yescharacteristic
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×#123C2212yes—
254C4×#121C2212yes—
255#2295C2211yescharacteristic
256#2295C2212yes—
257C2×#391C2212yes—
258#2275C2211yescharacteristic
259C23×Q8C2312yes—
260C23×Q8C2312yes—
261#559—44no—
262#556—44no—
263D4×Q8—44no—
264D4×Q8—44no—
265#533—48no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×#127C2312yes—
275C2×#127C2311yescharacteristic
276C2×#126C2314yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#124C2311yescharacteristic
280C2×#124C2311yescharacteristic
281C2×#124C2311yescharacteristic
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#123C2312yes—
288C2×#123C2314yes—
289C2×#123C2312yes—
290C2×#123C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×#117C2312yes—
325C2×#117C2314yes—
326C22×C4⋊C4C2312yes—
327C22×C42C2312yes—
328#401C2314yes—
329#401C2314yes—
330#401C2312yes—
331#401C2314yes—
332#401C2312yes—
333#401C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#400C2314yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2312yes—
359#400C2312yes—
360#399C2312yes—
361#399C2314yes—
362#399C2312yes—
363#399C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2311yescharacteristic
379#398C2311yescharacteristic
380#398C2314yes—
381#398C2312yes—
382#398C2311yescharacteristic
383#398C2311yescharacteristic
384#398C2314yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2312yes—
399#397C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2312yes—
408#397C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2312yes—
421#396C2312yes—
422#396C2314yes—
423#395C2311yescharacteristic
424#395C2314yes—
425#395C2312yes—
426#395C2312yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2311yescharacteristic
433#395C2311yescharacteristic
434#395C2311yescharacteristic
435#395C2312yes—
436#395C2314yes—
437#395C2314yes—
438#395C2312yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2312yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2312yes—
456#393C2314yes—
457#393C2312yes—
458#393C2312yes—
459#393C2314yes—
460#392C2314yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2314yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2312yes—
486#391C2311yescharacteristic
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2314yes—
491#391C2314yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2311yescharacteristic
496#390C2314yes—
497#390C2314yes—
498#390C2312yes—
499#390C2314yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2312yes—
525#389C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2312yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
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#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#387C2312yes—
558#387C2312yes—
559#387C2312yes—
560#387C2312yes—
561#387C2314yes—
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#387C2312yes—
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#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2314yes—
600#387C2312yes—
601#387C2312yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2312yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#385C2312yes—
639#384C2312yes—
640#383C2314yes—
641#383C2314yes—
642#383C2314yes—
643#383C2314yes—
644#383C2314yes—
645#382C2312yes—
646#382C2311yescharacteristic
647#382C2312yes—
648#382C2314yes—
649#382C2312yes—
650#382C2314yes—
651#382C2314yes—
652#382C2312yes—
653#382C2312yes—
654#382C2314yes—
655#381C2314yes—
656#381C2312yes—
657#381C2314yes—
658#381C2314yes—
659#381C2312yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2312yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2314yes—
672#380C2312yes—
673#380C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707#376C2311yescharacteristic
708#376C2314yes—
709#376C2312yes—
710#376C2314yes—
711#376C2314yes—
712#376C2311yescharacteristic
713C2×#95C2314yes—
714C2×#95C2312yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C22×Q8—44no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8—44no—
721C22×Q8—48no—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2414yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×Q8C2414yes—
731C22×D4C2411yescharacteristic
732C22×D4C2411yescharacteristic
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2411yescharacteristic
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C4⋊Q8—28no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750C4⋊Q8—44no—
751C4⋊Q8—44no—
752C4⋊Q8—44no—
753C4⋊Q8—42no—
754C4⋊Q8—42no—
755#127—28no—
756#127—42no—
757#126—48no—
758#125—44no—
759#125—48no—
760#124—24no—
761#124—44no—
762#124—44no—
763#124—44no—
764#124—44no—
765#124—44no—
766#124—42no—
767#124—42no—
768#123—28no—
769#123—48no—
770#123—44no—
771#123—44no—
772C22⋊Q8—28no—
773C22⋊Q8—48no—
774C22⋊Q8—44no—
775C22⋊Q8—48no—
776C22⋊Q8—48no—
777C22⋊Q8—48no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783#121—44no—
784#121—44no—
785C4×Q8—28no—
786C4×Q8—24no—
787C4×Q8—42no—
788C4×Q8—42no—
789C4×Q8—42no—
790C4×Q8—48no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—48no—
796C4×D4—24no—
797C4×D4—24no—
798C4×D4—48no—
799C4×D4—44no—
800C4×D4—44no—
801C4×D4—44no—
802C4×D4—48no—
803C4×D4—42no—
804C4×D4—44no—
805#117—44no—
806#117—48no—
807C2×C4⋊C4—44no—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C42—44no—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2412yes—
934#95C2411yescharacteristic
935#95C2414yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2411yescharacteristic
950#95C2412yes—
951#95C2411yescharacteristic
952#95C2414yes—
953#95C2414yes—
954#95C2411yescharacteristic
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013C24C2512yes—
1014C24C2512yes—
1015C24C2512yes—
1016C2×Q8—24no—
1017C2×Q8—22no—
1018C2×Q8—24no—
1019C2×Q8—28no—
1020C2×Q8—22no—
1021C2×Q8—24no—
1022C2×Q8—28no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—41no—
1029C2×Q8—44no—
1030C2×Q8—41no—
1031C2×Q8—41no—
1032C2×Q8—44no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—41no—
1039C2×Q8—816no—
1040C2×Q8—816no—
1041C2×D4—28no—
1042C2×D4—28no—
1043C2×D4—22no—
1044C2×D4—22no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—41no—
1049C2×D4—41no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—44no—
1058C2×D42−1+414yes—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—28no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—28no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—41no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—41no—
1136C4⋊C4—41no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—41no—
1149C4⋊C4—41no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4H(5,𝔽2)14yes—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—28no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—42no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C42—24no—
1211C42—24no—
1212C42—28no—
1213C42—22no—
1214C42—22no—
1215C42—24no—
1216C42—22no—
1217C42—22no—
1218C42—24no—
1219C42—28no—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—42no—
1224C42—42no—
1225C42—41no—
1226C42—42no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—42no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—24no—
1249C23—22no—
1250C23—22no—
1251C23C2×2−1+414yes—
1252C23C2611yescharacteristic
1253Q8—416no—
1254Q8—44no—
1255Q8—48no—
1256Q8—48no—
1257Q8—44no—
1258Q8—82no—
1259Q8—82no—
1260Q8—88no—
1261Q8—84no—
1262D4—44no—
1263D4—44no—
1264D4—44no—
1265D4—84no—
1266D4—88no—
1267D4—88no—
1268D4—162no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—21no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—48no—
1337C2×C4—48no—
1338C2×C4—84no—
1339C2×C4—84no—
1340C2×C4—88no—
1341C2×C4—84no—
1342C2×C4—88no—
1343C2×C4—164no—
1344C2×C4—164no—
1345C2×C4C2×H(5,𝔽2)14yes—
1346C2×C4C2×H(5,𝔽2)12yes—
1347C2×C4C2×2−1+412yes—
1348C2×C4#58514yes—
1349C2×C4#58514yes—
1350C22—24no—
1351C22—24no—
1352C22—24no—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—44no—
1362C22—44no—
1363C22—42no—
1364C22—42no—
1365C22—44no—
1366C22—44no—
1367C22C22×H(5,𝔽2)11yescharacteristic
1368C22C22×2−1+411yescharacteristic
1369C22C2×#58512yes—
1370C22C2×#58512yes—
1371C222−1+611yescharacteristic
1372C4—24no—
1373C4—24no—
1374C4—22no—
1375C4—42no—
1376C4—42no—
1377C4—44no—
1378C4—44no—
1379C4—41no—
1380C4—41no—
1381C4—44no—
1382C4—42no—
1383C4—41no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—44no—
1388C4—42no—
1389C4—42no—
1390C4—41no—
1391C4—41no—
1392C4—42no—
1393C4—42no—
1394C4—44no—
1395C4—44no—
1396C4—42no—
1397C4#355114yes—
1398C2—44no—
1399C2—82no—
1400C2—82no—
1401C2C2×#355111yescharacteristic
1402C2#6289311yescharacteristic
1403C2#6296812yes—
1404C2#6301711yescharacteristic
1405C2#6302512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59935C2semidirect
2. #59874C2semidirect
3. #59547C2semidirect
4. #59096C2semidirect
5. #59042C2semidirect
6. #58628C2semidirect
7. #57898C2semidirect
8. #55616C2semidirect
9. #54491C2semidirect
10. #53041C2semidirect
11. #53033C2semidirect
12. #52304C2semidirect
13. #47814C2semidirect
14. #47266C2semidirect
15. #45436C2semidirect
16. #45308C2semidirect
17. #45194C2semidirect
18. #44592C2semidirect
19. #42847C2semidirect
20. #42481C2semidirect
21. #42252C2semidirect
22. #40938C2semidirect
24. #40025C2semidirect
25. #39879C2semidirect
27. #38983C2semidirect
28. #35959C2semidirect
29. #35885C2semidirect

Maximal subgroups

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

subgroupindex
#599352
#598742
#595472
#590962
#590422
#586282
#578982
#556162
#544912
#530412
#530332
#523042
#478142
#472662
#454362
#453082
#451942
#445922
#428472
#424812
#422522
#409382
#401462
#400252
#398792
#391712
#389832
#359592
#358852