Finite Group Databasebeta

← #8096696

Subgroups — #8096696

Order 512.

4680 conjugacy classes of subgroups.

The subgroup lattice has 1462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53091C212yesmaximal, complemented
2#53007C212yesmaximal, complemented
3#52993C211yesmaximal, characteristic, complemented
4#52958C211yesmaximal, characteristic, complemented
5#52678C212yesmaximal, complemented
6#52623C212yesmaximal, complemented
7#52554C214yesmaximal, complemented
8#52389C214yesmaximal, complemented
9#52299C211yesmaximal, characteristic
10#52168C212yesmaximal, complemented
11#46261C214yesmaximal, complemented
12#45969C214yesmaximal, complemented
13#45795C214yesmaximal, complemented
14#45759C212yesmaximal, complemented
15#45677C212yesmaximal, complemented
16#45656C212yesmaximal, complemented
17#45631C212yesmaximal, complemented
18#45629C214yesmaximal, complemented
19#45501C212yesmaximal, complemented
20#45488C211yesmaximal, characteristic, complemented
21#36561C212yesmaximal, complemented
22#36544C212yesmaximal, complemented
23#36489C212yesmaximal, complemented
24#36423C211yesmaximal, characteristic, complemented
25#36116C212yesmaximal, complemented
26#35926C211yesmaximal, characteristic, complemented
27#35919C212yesmaximal, complemented
28#35688C212yesmaximal, complemented
29#35686C211yesmaximal, characteristic, complemented
30C2×#563C2212yes—
31C2×#554C2211yescharacteristic
32C2×#554C2212yes—
33C2×#552C2211yescharacteristic
34C2×#529C2214yes—
35C2×#520C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2857C2214yes—
41#2855C2214yes—
42#2855C2211yescharacteristic
43#2855C2212yes—
44#2853C2212yes—
45#2852C2214yes—
46#2851C2214yes—
47#2841C2212yes—
48#2841C2214yes—
49#2841C2214yes—
50#2841C2214yes—
51#2838C2214yes—
52#2838C2214yes—
53#2838C2214yes—
54#2837C2214yes—
55#2837C2214yes—
56#2836C2214yes—
57#2835C2212yes—
58#2834C2212yes—
59#2833C2214yes—
60#2832C2214yes—
61#2832C2212yes—
62#2831C2214yes—
63#2823C2214yes—
64#2821C2214yes—
65#2817C2212yes—
66#2811C2212yes—
67#2806C2214yes—
68#2806C2214yes—
69#2805C2214yes—
70#2802C2214yes—
71#2802C2214yes—
72#2801C2212yes—
73#2796C2214yes—
74#2792C2214yes—
75#2792C2214yes—
76#2788C2214yes—
77#2776C2214yes—
78#2760C2212yes—
79#2760C2211yescharacteristic
80#2752C2214yes—
81#2752C2211yescharacteristic
82#2752C2212yes—
83#2751C2214yes—
84#2747C2214yes—
85#2746C2214yes—
86#2743C2214yes—
87#2742C2211yescharacteristic
88#2742C2212yes—
89#2742C2214yes—
90#2740C2214yes—
91#2737C2214yes—
92#2725C2214yes—
93#2722C2212yes—
94#2717C2212yes—
95#2713C2214yes—
96#2713C2214yes—
97#2712C2214yes—
98#2712C2212yes—
99#2705C2214yes—
100#2705C2214yes—
101#2704C2214yes—
102#2704C2214yes—
103#2704C2214yes—
104#2703C2212yes—
105#2703C2212yes—
106#2703C2212yes—
107#2700C2214yes—
108#2694C2214yes—
109#2693C2214yes—
110#2693C2212yes—
111#2692C2214yes—
112#2691C2214yes—
113#2689C2214yes—
114#2687C2214yes—
115#2681C2214yes—
116#2675C2211yescharacteristic
117#2672C2214yes—
118#2664C2212yes—
119#2660C2211yescharacteristic
120#2655C2214yes—
121#2645C2212yes—
122#2638C2214yes—
123#2633C2212yes—
124#2616C2211yescharacteristic
125#2616C2212yes—
126#2611C2212yes—
127#2603C2212yes—
128#2600C2214yes—
129#2599C2212yes—
130#2594C2214yes—
131#2588C2214yes—
132#2588C2214yes—
133#2584C2214yes—
134#2584C2212yes—
135#2580C2214yes—
136#2575C2214yes—
137#2567C2212yes—
138#2564C2214yes—
139#2564C2214yes—
140#2562C2211yescharacteristic
141#2556C2214yes—
142#2556C2214yes—
143#2556C2214yes—
144#2552C2212yes—
145#2551C2212yes—
146#2547C2212yes—
147#2547C2211yescharacteristic
148#2542C2212yes—
149#2538C2212yes—
150#2538C2212yes—
151#2536C2212yes—
152#2528C2214yes—
153#2527C2214yes—
154#2524C2214yes—
155#2514C2212yes—
156#2509C2212yes—
157#2506C2214yes—
158#2506C2212yes—
159#2502C2211yescharacteristic
160#2499C2212yes—
161#2496C2212yes—
162#2496C2212yes—
163#2496C2212yes—
164#2493C2214yes—
165#2492C2212yes—
166#2492C2212yes—
167#2492C2212yes—
168#2492C2212yes—
169#2488C2214yes—
170#2486C2212yes—
171#2486C2211yescharacteristic
172#2486C2212yes—
173#2485C2212yes—
174#2484C2212yes—
175#2478C2214yes—
176#2478C2214yes—
177#2475C2214yes—
178#2469C2214yes—
179#2469C2214yes—
180#2466C2214yes—
181#2465C2214yes—
182#2465C2214yes—
183#2465C2214yes—
184#2463C2214yes—
185#2462C2214yes—
186#2462C2214yes—
187#2461C2214yes—
188#2460C2214yes—
189#2455C2214yes—
190#2453C2214yes—
191#2453C2212yes—
192#2453C2214yes—
193#2452C2214yes—
194#2451C2212yes—
195#2449C2214yes—
196#2449C2214yes—
197#2447C2214yes—
198#2446C2212yes—
199#2441C2212yes—
200#2440C2212yes—
201#2440C2212yes—
202#2439C2212yes—
203#2434C2211yescharacteristic
204#2429C2212yes—
205#2429C2212yes—
206#2423C2212yes—
207#2423C2212yes—
208#2423C2212yes—
209#2419C2214yes—
210#2419C2214yes—
211#2417C2212yes—
212#2417C2212yes—
213#2417C2212yes—
214#2417C2212yes—
215#2415C2212yes—
216#2415C2214yes—
217#2415C2212yes—
218#2413C2212yes—
219#2409C2211yescharacteristic
220#2409C2212yes—
221#2409C2212yes—
222#2401C2212yes—
223#2397C2211yescharacteristic
224#2396C2214yes—
225#2392C2212yes—
226#2392C2212yes—
227#2392C2214yes—
228#2388C2212yes—
229#2388C2211yescharacteristic
230#2383C2214yes—
231#2378C2214yes—
232#2378C2214yes—
233#2376C2214yes—
234#2365C2212yes—
235#2365C2212yes—
236#2362C2212yes—
237#2360C2212yes—
238#2360C2212yes—
239#2360C2212yes—
240#2355C2212yes—
241#2352C2212yes—
242D4×C4⋊C4C2212yes—
243D4×C4⋊C4C2212yes—
244D4×C4⋊C4C2212yes—
245#2347C2211yescharacteristic
246#2344C2211yescharacteristic
247#2344C2212yes—
248C4×C22⋊Q8C2214yes—
249C4×#123C2211yescharacteristic
250C4×#123C2212yes—
251C4×#121C2212yes—
252C4×#121C2214yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255C4×#121C2214yes—
256#2296C2212yes—
257#2276C2211yescharacteristic
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261#563—48no—
262#554—48no—
263#554—44no—
264#552—44no—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270#529—416no—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2312yes—
275C2×#125C2311yescharacteristic
276C2×#125C2314yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#124C2314yes—
282C2×#124C2312yes—
283C2×#123C2312yes—
284C2×#123C2311yescharacteristic
285C2×#123C2312yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2311yescharacteristic
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308#520—44no—
309C2×C4×Q8—44no—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2314yes—
316C2×C4×Q8C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×#117C2312yes—
332C2×#117C2311yescharacteristic
333C2×#117C2312yes—
334C2×#117C2314yes—
335C2×#117C2312yes—
336C22×C4⋊C4C2311yescharacteristic
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2311yescharacteristic
341C22×C4⋊C4C2312yes—
342C22×C42C2312yes—
343C22×C42C2314yes—
344C22×C42C2311yescharacteristic
345C22×C42C2312yes—
346#401C2312yes—
347#401C2314yes—
348#401C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2312yes—
367#400C2312yes—
368#400C2312yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#399C2311yescharacteristic
375#399C2314yes—
376#399C2311yescharacteristic
377#399C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2312yes—
398#398C2312yes—
399#398C2312yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#397C2312yes—
404#397C2312yes—
405#397C2314yes—
406#397C2312yes—
407#397C2314yes—
408#397C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2312yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2312yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2312yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2312yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2311yescharacteristic
447#395C2312yes—
448#395C2314yes—
449#395C2312yes—
450#394C2312yes—
451#394C2312yes—
452#394C2314yes—
453#394C2314yes—
454#394C2311yescharacteristic
455#394C2312yes—
456#394C2314yes—
457#394C2314yes—
458#394C2312yes—
459#394C2312yes—
460#394C2312yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#393C2314yes—
466#393C2314yes—
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2312yes—
471#393C2314yes—
472#393C2311yescharacteristic
473#393C2314yes—
474#393C2312yes—
475#392C2312yes—
476#392C2311yescharacteristic
477#392C2312yes—
478#392C2311yescharacteristic
479#392C2312yes—
480#392C2312yes—
481#392C2311yescharacteristic
482#392C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2314yes—
486#391C2314yes—
487#391C2312yes—
488#391C2314yes—
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2314yes—
497#391C2314yes—
498#391C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2314yes—
502#390C2312yes—
503#390C2314yes—
504#390C2314yes—
505#390C2314yes—
506#390C2312yes—
507#390C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2314yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2312yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2312yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2312yes—
568#388C2312yes—
569#388C2314yes—
570#388C2312yes—
571#388C2312yes—
572#388C2312yes—
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#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2312yes—
610#387C2312yes—
611#386C2312yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2312yes—
616#386C2314yes—
617#386C2314yes—
618#386C2311yescharacteristic
619#386C2312yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2312yes—
624#386C2312yes—
625#386C2312yes—
626#386C2312yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2312yes—
643#385C2314yes—
644#385C2314yes—
645#385C2312yes—
646#385C2312yes—
647#385C2311yescharacteristic
648#384C2312yes—
649#384C2312yes—
650#384C2314yes—
651#384C2312yes—
652#384C2312yes—
653#383C2314yes—
654#383C2312yes—
655#382C2314yes—
656#382C2312yes—
657#381C2311yescharacteristic
658#381C2314yes—
659#381C2312yes—
660#381C2314yes—
661#381C2314yes—
662#381C2312yes—
663#381C2312yes—
664#381C2312yes—
665#381C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2312yes—
675#380C2314yes—
676#380C2312yes—
677#380C2311yescharacteristic
678#380C2312yes—
679#380C2314yes—
680#380C2312yes—
681#380C2312yes—
682#380C2312yes—
683#380C2312yes—
684#380C2311yescharacteristic
685#380C2312yes—
686#380C2312yes—
687#380C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716#376C2312yes—
717#376C2311yescharacteristic
718C2×#95C2314yes—
719C2×#41—42no—
720C2×#41—44no—
721C22×Q8—42no—
722C22×Q8—44no—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2414yes—
729C22×Q8C2412yes—
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C4⋊Q8—44no—
754C4⋊Q8—44no—
755C4⋊Q8—42no—
756C4⋊Q8—48no—
757C4⋊Q8—44no—
758#126—216no—
759#126—48no—
760#126—44no—
761#126—48no—
762#125—44no—
763#125—42no—
764#125—48no—
765#125—44no—
766#125—48no—
767#125—48no—
768#124—48no—
769#124—44no—
770#123—24no—
771#123—28no—
772#123—48no—
773#123—44no—
774#123—44no—
775#123—48no—
776C22⋊Q8—216no—
777C22⋊Q8—48no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—48no—
782C22⋊Q8—48no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787C22⋊Q8—42no—
788C22⋊Q8—42no—
789C22⋊Q8—44no—
790C22⋊Q8—44no—
791C22⋊Q8—44no—
792#121—28no—
793#121—28no—
794#121—28no—
795C4×Q8—28no—
796C4×Q8—24no—
797C4×Q8—48no—
798C4×Q8—44no—
799C4×Q8—48no—
800C4×Q8—44no—
801C4×Q8—44no—
802C4×D4—48no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—44no—
808C4×D4—42no—
809C4×D4—48no—
810C4×D4—44no—
811C4×D4—44no—
812C4×D4—42no—
813C4×D4—48no—
814C4×D4—48no—
815C4×D4—48no—
816#117—24no—
817#117—28no—
818#117—44no—
819#117—48no—
820#117—44no—
821C2×C4⋊C4—24no—
822C2×C4⋊C4—28no—
823C2×C4⋊C4—28no—
824C2×C4⋊C4—44no—
825C2×C4⋊C4—44no—
826C2×C4⋊C4—42no—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2411yescharacteristic
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2411yescharacteristic
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2411yescharacteristic
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2411yescharacteristic
938C2×C22⋊C4C2412yes—
939C2×C42—44no—
940C2×C42—42no—
941C2×C42—48no—
942C2×C42—44no—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2414yes—
959C2×C42C2412yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2411yescharacteristic
968#95C2414yes—
969#95C2412yes—
970#95C2411yescharacteristic
971#95C2412yes—
972#95C2412yes—
973#95C2411yescharacteristic
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2411yescharacteristic
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030C24C2511yescharacteristic
1031C24C2512yes—
1032C24C2511yescharacteristic
1033C24C2512yes—
1034#41—416no—
1035C2×Q8—24no—
1036C2×Q8—22no—
1037C2×Q8—28no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—24no—
1041C2×Q8—42no—
1042C2×Q8—41no—
1043C2×Q8—44no—
1044C2×Q8—42no—
1045C2×Q8—44no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×Q8—44no—
1049C2×Q8—42no—
1050C2×Q8—42no—
1051C2×Q8—44no—
1052C2×Q8—42no—
1053C2×Q8—416no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—22no—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—24no—
1065C2×D4—42no—
1066C2×D4—41no—
1067C2×D4—41no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—41no—
1076C2×D4—42no—
1077C2×D4—42no—
1078C2×D4—41no—
1079C22×C4—24no—
1080C22×C4—22no—
1081C22×C4—28no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—22no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—22no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—28no—
1098C22×C4—28no—
1099C22×C4—41no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—44no—
1104C22×C4—41no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—42no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—42no—
1113C22×C4—41no—
1114C22×C4—42no—
1115C22×C4—42no—
1116C22×C4—42no—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2514yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2514yes—
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2512yes—
1130C22×C4C2511yescharacteristic
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2511yescharacteristic
1142C4⋊C4—24no—
1143C4⋊C4—28no—
1144C4⋊C4—22no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—22no—
1150C4⋊C4—28no—
1151C4⋊C4—28no—
1152C4⋊C4—28no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—28no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—28no—
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—41no—
1183C4⋊C4—41no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4H(5,𝔽2)14yes—
1206C22⋊C4—24no—
1207C22⋊C4—28no—
1208C22⋊C4—28no—
1209C22⋊C4—28no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—41no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—41no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—41no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—42no—
1252C22⋊C4H(5,𝔽2)14yes—
1253C22⋊C42−1+418yes—
1254C42—28no—
1255C42—28no—
1256C42—24no—
1257C42—28no—
1258C42—24no—
1259C42—24no—
1260C42—22no—
1261C42—24no—
1262C42—24no—
1263C42—24no—
1264C42—42no—
1265C42—42no—
1266C42—44no—
1267C42—42no—
1268C42—44no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42—42no—
1274C23—22no—
1275C23—22no—
1276C23—21no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—21no—
1283C23—22no—
1284C23—21no—
1285C23—21no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—21no—
1296C23C2×H(5,𝔽2)12yes—
1297C23C2×2−1+414yes—
1298C23C2611yescharacteristic
1299Q8—48no—
1300Q8—44no—
1301Q8—44no—
1302Q8—48no—
1303Q8—88no—
1304Q8—164no—
1305Q8—162no—
1306D4—48no—
1307D4—48no—
1308D4—48no—
1309D4—48no—
1310D4—44no—
1311D4—44no—
1312D4—48no—
1313D4—82no—
1314D4—84no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—21no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—48no—
1379C2×C4—44no—
1380C2×C4—48no—
1381C2×C4—48no—
1382C2×C4—48no—
1383C2×C4—44no—
1384C2×C4—48no—
1385C2×C4—44no—
1386C2×C4—88no—
1387C2×C4—88no—
1388C2×C4—88no—
1389C2×C4—82no—
1390C2×C4—84no—
1391C2×C4—162no—
1392C2×C4C2×H(5,𝔽2)14yes—
1393C2×C4C2×H(5,𝔽2)14yes—
1394C2×C4C2×H(5,𝔽2)12yes—
1395C2×C4C2×2−1+414yes—
1396C2×C4C2×2−1+414yes—
1397C2×C4#58514yes—
1398C22—24no—
1399C22—24no—
1400C22—24no—
1401C22—22no—
1402C22—24no—
1403C22—42no—
1404C22—41no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—41no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—41no—
1415C22—42no—
1416C22—41no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—41no—
1421C22—42no—
1422C22C22×H(5,𝔽2)11yescharacteristic
1423C22C22×H(5,𝔽2)11yescharacteristic
1424C22C22×2−1+412yes—
1425C22C2×#58512yes—
1426C222−1+611yescharacteristic
1427C4—24no—
1428C4—24no—
1429C4—24no—
1430C4—24no—
1431C4—44no—
1432C4—44no—
1433C4—42no—
1434C4—44no—
1435C4—42no—
1436C4—41no—
1437C4—42no—
1438C4—44no—
1439C4—44no—
1440C4—42no—
1441C4—41no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—41no—
1447C4—42no—
1448C4—44no—
1449C4—41no—
1450C4—42no—
1451C4#352914yes—
1452C2—44no—
1453C2—42no—
1454C2—82no—
1455C2—81no—
1456C2C2×#352911yescharacteristic
1457C2#6291411yescharacteristic
1458C2#6293212yes—
1459C2#6301312yes—
1460C2#6301611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52299C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53091C2semidirect
2. #53007C2semidirect
3. #52993C2semidirect
4. #52958C2semidirect
5. #52678C2semidirect
6. #52623C2semidirect
7. #52554C2semidirect
8. #52389C2semidirect
10. #52168C2semidirect
11. #46261C2semidirect
12. #45969C2semidirect
13. #45795C2semidirect
14. #45759C2semidirect
15. #45677C2semidirect
16. #45656C2semidirect
17. #45631C2semidirect
18. #45629C2semidirect
19. #45501C2semidirect
20. #45488C2semidirect
21. #36561C2semidirect
22. #36544C2semidirect
23. #36489C2semidirect
24. #36423C2semidirect
25. #36116C2semidirect
26. #35926C2semidirect
27. #35919C2semidirect
28. #35688C2semidirect
29. #35686C2semidirect

Maximal subgroups

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

subgroupindex
#530912
#530072
#529932
#529582
#526782
#526232
#525542
#523892
#522992
#521682
#462612
#459692
#457952
#457592
#456772
#456562
#456312
#456292
#455012
#454882
#365612
#365442
#364892
#364232
#361162
#359262
#359192
#356882
#356862