Finite Group Databasebeta

← #7656596

Subgroups — #7656596

Order 512.

4600 conjugacy classes of subgroups.

The subgroup lattice has 1473 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42672C212yesmaximal, complemented
2#42669C212yesmaximal, complemented
3#42668C212yesmaximal, complemented
4#42665C212yesmaximal, complemented
5#41684C214yesmaximal, complemented
6#41680C214yesmaximal, complemented
7#41678C214yesmaximal, complemented
8#41674C214yesmaximal, complemented
9#39806C212yesmaximal
10#39760C211yesmaximal, characteristic, complemented
11#39678C212yesmaximal, complemented
12#39632C211yesmaximal, characteristic, complemented
13#38974C212yesmaximal, complemented
14#38235C214yesmaximal, complemented
15#37615C212yesmaximal, complemented
16#37525C214yesmaximal, complemented
17#36579C211yesmaximal, characteristic, complemented
18#36544C211yesmaximal, characteristic, complemented
19#36232C212yesmaximal, complemented
20#35834C212yesmaximal, complemented
21#35818C212yesmaximal, complemented
22#35789C212yesmaximal, complemented
23#35773C212yesmaximal, complemented
24#35104C211yesmaximal, characteristic, complemented
25#35098C212yesmaximal, complemented
26#34594C211yesmaximal, characteristic
27#34584C212yesmaximal, complemented
28#34241C212yesmaximal, complemented
29C2×#2365C211yesmaximal, characteristic, complemented
30C2×#556C2211yescharacteristic
31C2×#554C2211yescharacteristic
32C2×#552C2212yes—
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2212yes—
35C22×C4×Q8C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2852C2214yes—
40#2851C2212yes—
41#2851C2212yes—
42#2850C2212yes—
43#2839C2214yes—
44#2838C2214yes—
45#2837C2214yes—
46#2836C2214yes—
47#2821C2214yes—
48#2821C2214yes—
49#2808C2212yes—
50#2806C2212yes—
51#2805C2212yes—
52#2804C2212yes—
53#2799C2214yes—
54#2798C2214yes—
55#2797C2214yes—
56#2793C2214yes—
57#2793C2214yes—
58#2791C2214yes—
59#2791C2214yes—
60#2788C2214yes—
61#2786C2214yes—
62#2775C2214yes—
63#2774C2214yes—
64#2773C2214yes—
65#2767C2214yes—
66#2762C2214yes—
67#2759C2214yes—
68#2759C2214yes—
69#2755C2214yes—
70#2754C2214yes—
71#2752C2214yes—
72#2751C2214yes—
73#2745C2214yes—
74#2740C2214yes—
75#2667C2214yes—
76#2666C2214yes—
77#2664C2212yes—
78#2664C2212yes—
79#2664C2214yes—
80#2663C2214yes—
81#2662C2212yes—
82#2662C2212yes—
83#2660C2214yes—
84#2659C2211yescharacteristic
85#2656C2211yescharacteristic
86#2655C2214yes—
87#2655C2214yes—
88#2654C2214yes—
89#2654C2214yes—
90#2652C2214yes—
91#2651C2214yes—
92#2650C2214yes—
93#2649C2214yes—
94#2646C2212yes—
95#2643C2214yes—
96#2640C2214yes—
97#2639C2212yes—
98#2639C2212yes—
99#2627C2212yes—
100#2627C2212yes—
101#2623C2214yes—
102#2623C2214yes—
103#2621C2212yes—
104#2621C2212yes—
105#2621C2212yes—
106#2621C2212yes—
107#2618C2211yescharacteristic
108#2618C2211yescharacteristic
109#2618C2212yes—
110#2606C2214yes—
111#2605C2214yes—
112#2604C2214yes—
113#2602C2214yes—
114#2601C2214yes—
115#2599C2214yes—
116#2592C2212yes—
117#2588C2214yes—
118#2585C2214yes—
119#2584C2212yes—
120#2581C2212yes—
121#2580C2212yes—
122#2575C2214yes—
123#2573C2214yes—
124#2570C2212yes—
125#2570C2212yes—
126#2568C2211yescharacteristic
127#2568C2212yes—
128#2568C2212yes—
129#2567C2211yescharacteristic
130#2565C2212yes—
131#2565C2214yes—
132#2560C2214yes—
133#2557C2214yes—
134#2556C2214yes—
135#2553C2214yes—
136#2550C2212yes—
137#2550C2212yes—
138#2542C2212yes—
139#2542C2212yes—
140#2538C2211yescharacteristic
141#2538C2211yescharacteristic
142#2536C2212yes—
143#2528C2214yes—
144#2527C2214yes—
145#2525C2214yes—
146#2524C2214yes—
147#2524C2214yes—
148#2523C2214yes—
149#2522C2214yes—
150#2521C2214yes—
151#2520C2214yes—
152#2520C2214yes—
153#2519C2214yes—
154#2517C2214yes—
155#2516C2214yes—
156#2515C2214yes—
157#2514C2212yes—
158#2514C2212yes—
159#2511C2212yes—
160#2511C2212yes—
161#2510C2214yes—
162#2506C2214yes—
163#2505C2214yes—
164#2504C2214yes—
165#2503C2212yes—
166#2502C2214yes—
167#2502C2212yes—
168#2499C2212yes—
169#2499C2212yes—
170#2499C2214yes—
171#2496C2214yes—
172#2492C2212yes—
173#2492C2212yes—
174#2489C2212yes—
175#2489C2212yes—
176#2481C2214yes—
177#2473C2214yes—
178#2469C2214yes—
179#2465C2214yes—
180#2462C2214yes—
181#2458C2214yes—
182#2450C2214yes—
183#2449C2214yes—
184#2444C2214yes—
185#2443C2214yes—
186#2423C2212yes—
187#2423C2212yes—
188#2421C2212yes—
189#2421C2212yes—
190#2417C2212yes—
191#2417C2212yes—
192#2415C2212yes—
193#2415C2212yes—
194#2409C2212yes—
195#2409C2212yes—
196#2409C2212yes—
197#2409C2212yes—
198#2402C2214yes—
199#2401C2214yes—
200#2396C2214yes—
201#2396C2212yes—
202#2396C2212yes—
203#2395C2214yes—
204#2392C2212yes—
205#2392C2212yes—
206#2373C2214yes—
207#2373C2214yes—
208#2368C2214yes—
209#2365C2212yes—
210#2365C2212yes—
211#2365C2212yes—
212#2365C2214yes—
213#2365C2212yes—
214#2365C2214yes—
215#2364C2214yes—
216#2362C2212yes—
217#2362C2212yes—
218#2360C2212yes—
219#2360C2212yes—
220#2356C2212yes—
221#2355C2212yes—
222#2355C2211yescharacteristic
223#2355C2212yes—
224#2355C2211yescharacteristic
225#2352C2212yes—
226#2352C2212yes—
227#2352C2212yes—
228#2352C2212yes—
229D4×C4⋊C4C2212yes—
230D4×C4⋊C4C2212yes—
231#2337C2214yes—
232#2336C2214yes—
233#2329C2212yes—
234#2329C2212yes—
235#2329C2212yes—
236#2325C2212yes—
237#2318C2214yes—
238#2314C2212yes—
239#2314C2212yes—
240C4×C22⋊Q8C2212yes—
241C4×#123C2214yes—
242C4×#123C2214yes—
243C4×#121C2212yes—
244C4×#121C2212yes—
245C4×#121C2211yescharacteristic
246C4×#121C2211yescharacteristic
247C2×#391C2211yescharacteristic
248C2×#391C2211yescharacteristic
249C2×#389C2212yes—
250#2290C2214yes—
251C2×#387C2212yes—
252C2×#387C2212yes—
253#2283C2212yes—
254#2274C2212yes—
255#2274C2212yes—
256C2×C4×C4⋊C4C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261#556—44no—
262#554—44no—
263#552—48no—
264C2×C4⋊Q8—28no—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270#529—216no—
271C2×#126C2312yes—
272C2×#126C2312yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#123C2312yes—
282C2×#123C2312yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×#121C2311yescharacteristic
297C2×#121C2311yescharacteristic
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×C4×Q8—44no—
301C2×C4×Q8—44no—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C2×#117C2314yes—
326C2×#117C2312yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2311yescharacteristic
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2312yes—
337C22×C42C2312yes—
338C22×C42C2311yescharacteristic
339C22×C42C2312yes—
340C22×C42C2311yescharacteristic
341C22×C42C2312yes—
342C22×C42C2311yescharacteristic
343#401C2314yes—
344#401C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2312yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2312yes—
373#399C2314yes—
374#399C2314yes—
375#399C2312yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2312yes—
398#398C2312yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2312yes—
419#397C2312yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#396C2312yes—
424#396C2312yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2312yes—
430#396C2312yes—
431#396C2312yes—
432#396C2312yes—
433#396C2312yes—
434#396C2312yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2312yes—
442#395C2314yes—
443#395C2312yes—
444#394C2312yes—
445#394C2312yes—
446#394C2314yes—
447#394C2314yes—
448#394C2312yes—
449#394C2314yes—
450#394C2312yes—
451#394C2312yes—
452#394C2312yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#393C2314yes—
458#393C2314yes—
459#393C2312yes—
460#393C2312yes—
461#392C2312yes—
462#392C2312yes—
463#391C2314yes—
464#391C2312yes—
465#391C2312yes—
466#391C2314yes—
467#391C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2314yes—
487#391C2312yes—
488#391C2312yes—
489#391C2314yes—
490#390C2314yes—
491#390C2311yescharacteristic
492#390C2312yes—
493#390C2311yescharacteristic
494#390C2312yes—
495#390C2314yes—
496#390C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2311yescharacteristic
507#389C2312yes—
508#389C2314yes—
509#389C2311yescharacteristic
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
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#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#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#386C2314yes—
601#386C2312yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2312yes—
609#386C2312yes—
610#386C2312yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#384C2312yes—
629#384C2314yes—
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2314yes—
634#383C2314yes—
635#383C2314yes—
636#383C2314yes—
637#383C2314yes—
638#382C2312yes—
639#382C2314yes—
640#382C2314yes—
641#382C2314yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#381C2314yes—
650#381C2314yes—
651#381C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2312yes—
658#380C2311yescharacteristic
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2311yescharacteristic
663#380C2312yes—
664#380C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2314yes—
711#376C2314yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2311yescharacteristic
715C2×#95C2311yescharacteristic
716C2×#95C2312yes—
717C2×#95C2312yes—
718C2×#95C2312yes—
719C22×Q8—24no—
720C22×Q8—24no—
721C22×Q8—42no—
722C22×Q8—42no—
723C22×Q8—42no—
724C22×Q8—42no—
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×Q8C2412yes—
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×Q8C2412yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2412yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2414yes—
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C4⋊Q8—28no—
755C4⋊Q8—28no—
756C4⋊Q8—216no—
757C4⋊Q8—42no—
758C4⋊Q8—42no—
759#126—28no—
760#126—28no—
761#126—48no—
762#126—48no—
763#125—28no—
764#125—44no—
765#125—48no—
766#125—44no—
767#124—28no—
768#124—44no—
769#123—28no—
770#123—28no—
771#123—48no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—44no—
775C22⋊Q8—48no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784#121—28no—
785#121—24no—
786#121—24no—
787#121—44no—
788C4×Q8—28no—
789C4×Q8—24no—
790C4×Q8—24no—
791C4×Q8—28no—
792C4×Q8—44no—
793C4×Q8—48no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—42no—
798C4×Q8—42no—
799C4×D4—28no—
800C4×D4—28no—
801C4×D4—28no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—42no—
805C4×D4—42no—
806C4×D4—48no—
807C4×D4—48no—
808#117—28no—
809#117—28no—
810#117—28no—
811#117—48no—
812#117—44no—
813C2×C4⋊C4—28no—
814C2×C4⋊C4—28no—
815C2×C4⋊C4—24no—
816C2×C4⋊C4—24no—
817C2×C4⋊C4—28no—
818C2×C4⋊C4—42no—
819C2×C4⋊C4—44no—
820C2×C4⋊C4—44no—
821C2×C4⋊C4—44no—
822C2×C4⋊C4—42no—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C42—44no—
930C2×C42—42no—
931C2×C42—44no—
932C2×C42—42no—
933C2×C42—44no—
934C2×C42#4118yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029C24C2512yes—
1030C24C2512yes—
1031C24C2511yescharacteristic
1032C2×Q8—24no—
1033C2×Q8—24no—
1034C2×Q8—22no—
1035C2×Q8—22no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—22no—
1040C2×Q8—22no—
1041C2×Q8—24no—
1042C2×Q8—24no—
1043C2×Q8—22no—
1044C2×Q8—22no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—42no—
1050C2×Q8—42no—
1051C2×Q8—42no—
1052C2×Q8—42no—
1053C2×Q8—42no—
1054C2×Q8—42no—
1055C2×Q8—42no—
1056C2×Q8—416no—
1057C2×Q8—416no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—24no—
1065C2×D4—22no—
1066C2×D4—22no—
1067C2×D4—41no—
1068C2×D4—41no—
1069C2×D4—42no—
1070C2×D4—41no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—41no—
1075C2×D4—42no—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—22no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—22no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—22no—
1086C22×C4—22no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—28no—
1095C22×C4—41no—
1096C22×C4—41no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—41no—
1101C22×C4—41no—
1102C22×C4—41no—
1103C22×C4—41no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—41no—
1107C22×C4—41no—
1108C22×C4—42no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—42no—
1112C22×C4—41no—
1113C22×C4—41no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4C2×#4114yes—
1118C22×C4C2×#4114yes—
1119C22×C4C2×#4114yes—
1120C22×C42−1+414yes—
1121C22×C4C2514yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2514yes—
1130C22×C4C2511yescharacteristic
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2512yes—
1144C22×C4C2511yescharacteristic
1145C22×C4C2511yescharacteristic
1146C22×C4C2511yescharacteristic
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—22no—
1163C4⋊C4—24no—
1164C4⋊C4—28no—
1165C4⋊C4—24no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—22no—
1173C4⋊C4—24no—
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—41no—
1186C4⋊C4—42no—
1187C4⋊C4—41no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—42no—
1214C4⋊C4H(5,𝔽2)14yes—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—28no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—42no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C42—24no—
1254C42—24no—
1255C42—28no—
1256C42—24no—
1257C42—24no—
1258C42—22no—
1259C42—22no—
1260C42—24no—
1261C42—28no—
1262C42—44no—
1263C42—44no—
1264C42—41no—
1265C42—42no—
1266C42—41no—
1267C42—42no—
1268C42—42no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42—44no—
1274C42—44no—
1275C42—44no—
1276C42—44no—
1277C42C2×#4118yes—
1278C42C2×#4118yes—
1279C23—21no—
1280C23—21no—
1281C23—21no—
1282C23—21no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23C22×#4112yes—
1298C23C2×2−1+412yes—
1299C23#58512yes—
1300C23C2611yescharacteristic
1301Q8—48no—
1302Q8—48no—
1303Q8—48no—
1304Q8—44no—
1305Q8—44no—
1306Q8—84no—
1307Q8—84no—
1308Q8—162no—
1309D4—44no—
1310D4—48no—
1311D4—48no—
1312D4—84no—
1313D4—82no—
1314D4—84no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—28no—
1328C2×C4—28no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—44no—
1387C2×C4—44no—
1388C2×C4—48no—
1389C2×C4—44no—
1390C2×C4—48no—
1391C2×C4—48no—
1392C2×C4—48no—
1393C2×C4—48no—
1394C2×C4—88no—
1395C2×C4—82no—
1396C2×C4—82no—
1397C2×C4—84no—
1398C2×C4—164no—
1399C2×C4C22×#4114yes—
1400C2×C4C22×#4112yes—
1401C2×C4C22×#4114yes—
1402C2×C4C22×#4112yes—
1403C2×C4C2×H(5,𝔽2)14yes—
1404C2×C4C2×H(5,𝔽2)12yes—
1405C2×C4C2×2−1+412yes—
1406C2×C4C2×2−1+412yes—
1407C2×C4#58512yes—
1408C22—22no—
1409C22—22no—
1410C22—22no—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22#350714yes—
1429C22C23×#4111yescharacteristic
1430C22C22×H(5,𝔽2)11yescharacteristic
1431C22C22×2−1+411yescharacteristic
1432C22C2×#58511yescharacteristic
1433C22C2×#58511yescharacteristic
1434C222−1+611yescharacteristic
1435C222−1+611yescharacteristic
1436C4—24no—
1437C4—24no—
1438C4—22no—
1439C4—22no—
1440C4—24no—
1441C4—22no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—42no—
1447C4—44no—
1448C4—42no—
1449C4—41no—
1450C4—42no—
1451C4—44no—
1452C4—41no—
1453C4—42no—
1454C4—42no—
1455C4—44no—
1456C4—42no—
1457C4—42no—
1458C4—44no—
1459C4—44no—
1460C4—44no—
1461C4#346014yes—
1462C2—24no—
1463C2—82no—
1464C2—82no—
1465C2C2×#346011yescharacteristic
1466C2C2×#350711yescharacteristic
1467C2#6286011yescharacteristic
1468C2#6289311yescharacteristic
1469C2#6289811yescharacteristic
1470C2#6295611yescharacteristic
1471C2#6296411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2656C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42672C2semidirect
2. #42669C2semidirect
3. #42668C2semidirect
4. #42665C2semidirect
5. #41684C2semidirect
6. #41680C2semidirect
7. #41678C2semidirect
8. #41674C2semidirect
10. #39760C2semidirect
11. #39678C2semidirect
12. #39632C2semidirect
13. #38974C2semidirect
14. #38235C2semidirect
15. #37615C2semidirect
16. #37525C2semidirect
17. #36579C2semidirect
18. #36544C2semidirect
19. #36232C2semidirect
20. #35834C2semidirect
21. #35818C2semidirect
22. #35789C2semidirect
23. #35773C2semidirect
24. #35104C2semidirect
25. #35098C2semidirect
27. #34584C2semidirect
28. #34241C2semidirect
29. C2×#2365C2semidirect

Maximal subgroups

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

subgroupindex
#426722
#426692
#426682
#426652
#416842
#416802
#416782
#416742
#398062
#397602
#396782
#396322
#389742
#382352
#376152
#375252
#365792
#365442
#362322
#358342
#358182
#357892
#357732
#351042
#350982
#345942
#345842
#342412
C2×#23652