Finite Group Databasebeta

← #7901053

Subgroups — #7901053

Order 512.

4371 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59764C212yesmaximal, complemented
3#52274C211yesmaximal, characteristic, complemented
4#49521C214yesmaximal, complemented
5#49111C214yesmaximal, complemented
6#47892C214yesmaximal, complemented
7#47300C214yesmaximal, complemented
8#45802C212yesmaximal, complemented
9#45414C212yesmaximal, complemented
10#45213C212yesmaximal, complemented
11#45163C212yesmaximal, complemented
12#43410C214yesmaximal, complemented
13#42612C212yesmaximal
14#42481C212yesmaximal, complemented
15#41743C214yesmaximal, complemented
16#40080C212yesmaximal, complemented
17#39765C211yesmaximal, characteristic, complemented
18#39765C211yesmaximal, characteristic, complemented
19#39760C212yesmaximal, complemented
20#39581C212yesmaximal, complemented
21#38240C212yesmaximal, complemented
22#38240C212yesmaximal, complemented
23#37140C212yesmaximal, complemented
24#36469C211yesmaximal, characteristic
25#35970C212yesmaximal, complemented
26#35615C212yesmaximal, complemented
27#35177C211yesmaximal, characteristic, complemented
28#34500C212yesmaximal, complemented
29#34334C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×D4×Q8C2211yescharacteristic
32#2863C2212yes—
33#2858C2211yescharacteristic
34#2857C2212yes—
35#2855C2212yes—
36#2854C2212yes—
37#2824C2214yes—
38#2814C2214yes—
39#2809C2211yescharacteristic
40#2808C2212yes—
41#2808C2212yes—
42#2808C2212yes—
43#2808C2212yes—
44#2806C2211yescharacteristic
45#2805C2212yes—
46#2805C2211yescharacteristic
47#2805C2212yes—
48#2804C2212yes—
49#2804C2212yes—
50#2802C2212yes—
51#2799C2212yes—
52#2793C2214yes—
53#2793C2214yes—
54#2791C2212yes—
55#2788C2214yes—
56#2788C2214yes—
57#2779C2214yes—
58#2775C2214yes—
59#2775C2214yes—
60#2774C2214yes—
61#2774C2212yes—
62#2770C2214yes—
63#2769C2214yes—
64#2763C2214yes—
65#2762C2214yes—
66#2759C2214yes—
67#2759C2214yes—
68#2759C2214yes—
69#2759C2214yes—
70#2759C2214yes—
71#2759C2214yes—
72#2758C2214yes—
73#2755C2212yes—
74#2751C2214yes—
75#2745C2214yes—
76#2745C2214yes—
77#2745C2214yes—
78#2744C2214yes—
79#2729C2214yes—
80#2726C2211yescharacteristic
81#2724C2212yes—
82#2724C2212yes—
83#2713C2212yes—
84#2708C2214yes—
85#2700C2214yes—
86#2700C2214yes—
87#2696C2214yes—
88#2693C2214yes—
89#2690C2214yes—
90#2681C2214yes—
91#2680C2214yes—
92#2680C2214yes—
93#2665C2214yes—
94#2653C2214yes—
95#2652C2214yes—
96#2644C2212yes—
97#2640C2212yes—
98#2640C2212yes—
99#2639C2214yes—
100#2638C2214yes—
101#2630C2214yes—
102#2614C2214yes—
103#2606C2214yes—
104#2602C2214yes—
105#2599C2214yes—
106#2599C2214yes—
107#2597C2214yes—
108#2597C2214yes—
109#2592C2212yes—
110#2592C2212yes—
111#2592C2212yes—
112#2581C2214yes—
113#2578C2214yes—
114#2578C2214yes—
115#2577C2214yes—
116#2577C2214yes—
117#2576C2214yes—
118#2574C2214yes—
119#2572C2214yes—
120#2571C2212yes—
121#2568C2212yes—
122#2568C2212yes—
123#2567C2211yescharacteristic
124#2567C2212yes—
125#2563C2211yescharacteristic
126#2563C2212yes—
127#2558C2214yes—
128#2557C2214yes—
129#2551C2211yescharacteristic
130#2549C2214yes—
131#2547C2211yescharacteristic
132#2544C2212yes—
133#2541C2211yescharacteristic
134#2538C2211yescharacteristic
135#2532C2214yes—
136#2532C2214yes—
137#2531C2214yes—
138#2528C2214yes—
139#2524C2214yes—
140#2523C2214yes—
141#2523C2214yes—
142#2523C2214yes—
143#2518C2214yes—
144#2518C2214yes—
145#2514C2212yes—
146#2514C2214yes—
147#2514C2212yes—
148#2514C2212yes—
149#2513C2212yes—
150#2513C2212yes—
151#2513C2212yes—
152#2511C2214yes—
153#2510C2214yes—
154#2510C2214yes—
155#2509C2212yes—
156#2509C2212yes—
157#2509C2212yes—
158#2505C2214yes—
159#2499C2214yes—
160#2499C2214yes—
161#2497C2212yes—
162#2493C2214yes—
163#2492C2214yes—
164#2492C2212yes—
165#2491C2212yes—
166#2488C2214yes—
167#2488C2214yes—
168#2477C2214yes—
169#2477C2214yes—
170#2470C2214yes—
171#2470C2214yes—
172#2465C2214yes—
173#2465C2214yes—
174#2465C2214yes—
175#2458C2214yes—
176#2458C2214yes—
177#2458C2214yes—
178#2452C2212yes—
179#2452C2212yes—
180#2452C2212yes—
181#2452C2212yes—
182#2451C2212yes—
183#2451C2212yes—
184#2451C2212yes—
185#2447C2212yes—
186#2447C2212yes—
187#2446C2212yes—
188#2446C2212yes—
189#2445C2212yes—
190#2445C2212yes—
191#2445C2212yes—
192#2445C2212yes—
193#2425C2214yes—
194#2422C2212yes—
195#2419C2214yes—
196#2415C2214yes—
197#2409C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2399C2212yes—
201#2398C2214yes—
202#2379C2214yes—
203#2376C2214yes—
204#2369C2212yes—
205#2368C2214yes—
206#2367C2212yes—
207#2367C2212yes—
208#2367C2212yes—
209#2367C2212yes—
210#2366C2212yes—
211#2366C2211yescharacteristic
212#2365C2211yescharacteristic
213#2365C2212yes—
214#2365C2211yescharacteristic
215#2360C2212yes—
216#2359C2214yes—
217#2359C2214yes—
218#2357C2212yes—
219#2356C2212yes—
220#2355C2211yescharacteristic
221#2355C2212yes—
222#2352C2214yes—
223#2351C2212yes—
224Q8×C4⋊C4C2212yes—
225#2349C2212yes—
226#2349C2212yes—
227D4×C4⋊C4C2211yescharacteristic
228Q8×C22⋊C4C2212yes—
229#2337C2214yes—
230#2335C2214yes—
231#2331C2212yes—
232#2331C2212yes—
233#2329C2214yes—
234#2329C2214yes—
235#2328C2212yes—
236#2326C2212yes—
237#2326C2212yes—
238#2322C2214yes—
239#2320C2212yes—
240#2320C2212yes—
241#2319C2212yes—
242#2318C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×#125C2212yes—
247C4×#124C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×#121C2212yes—
250#2295C2211yescharacteristic
251#2295C2212yes—
252#2295C2211yescharacteristic
253#2295C2212yes—
254C2×#391C2212yes—
255#2293C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C23×Q8C2312yes—
260#559—216no—
261D4×Q8—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×#127C2312yes—
270C2×#127C2311yescharacteristic
271C2×#125C2312yes—
272C2×#124C2312yes—
273C2×#124C2312yes—
274C2×#124C2314yes—
275C2×#124C2312yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2312yes—
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2314yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2314yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2311yescharacteristic
312C2×#117C2314yes—
313C2×#117C2314yes—
314C22×C4⋊C4C2312yes—
315C22×C42C2312yes—
316#401C2314yes—
317#401C2314yes—
318#401C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#398C2312yes—
343#398C2312yes—
344#398C2312yes—
345#398C2314yes—
346#398C2314yes—
347#398C2312yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2312yes—
353#398C2312yes—
354#398C2312yes—
355#398C2312yes—
356#398C2312yes—
357#398C2312yes—
358#398C2312yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2312yes—
391#395C2314yes—
392#395C2314yes—
393#395C2312yes—
394#395C2312yes—
395#395C2312yes—
396#395C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#392C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2314yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2311yescharacteristic
446#391C2312yes—
447#391C2311yescharacteristic
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2312yes—
455#391C2312yes—
456#391C2311yescharacteristic
457#391C2311yescharacteristic
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2311yescharacteristic
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2311yescharacteristic
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2311yescharacteristic
502#389C2314yes—
503#389C2314yes—
504#389C2311yescharacteristic
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2311yescharacteristic
509#389C2311yescharacteristic
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#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#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2312yes—
577#387C2312yes—
578#387C2314yes—
579#387C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2312yes—
587#387C2314yes—
588#387C2312yes—
589#387C2314yes—
590#387C2312yes—
591#387C2314yes—
592#387C2312yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#384C2311yescharacteristic
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#384C2312yes—
629#384C2314yes—
630#383C2314yes—
631#383C2314yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#383C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2314yes—
642#382C2312yes—
643#382C2314yes—
644#382C2314yes—
645#382C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#381C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2314yes—
659#380C2314yes—
660#380C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
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⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2312yes—
708#376C2314yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C22×Q8—28no—
715C22×Q8—82no—
716C22×Q8—82no—
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2414yes—
724C22×Q8C2414yes—
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2414yes—
729C22×D4C2414yes—
730C22×D4C2412yes—
731C23×C4C2414yes—
732C23×C4C2412yes—
733C23×C4C2414yes—
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2412yes—
739C4⋊Q8—28no—
740C4⋊Q8—24no—
741C4⋊Q8—24no—
742C4⋊Q8—44no—
743C4⋊Q8—42no—
744C4⋊Q8—42no—
745C4⋊Q8—82no—
746#127—28no—
747#127—42no—
748#125—44no—
749#124—28no—
750#124—216no—
751#124—28no—
752#124—28no—
753#123—216no—
754#123—216no—
755#123—48no—
756#123—84no—
757#123—84no—
758#123—84no—
759C22⋊Q8—28no—
760C22⋊Q8—216no—
761C22⋊Q8—48no—
762C22⋊Q8—84no—
763C22⋊Q8—84no—
764C22⋊Q8—82no—
765C22⋊Q8—84no—
766#121—44no—
767#121—82no—
768C4×Q8—28no—
769C4×Q8—24no—
770C4×Q8—28no—
771C4×Q8—24no—
772C4×Q8—44no—
773C4×Q8—44no—
774C4×Q8—44no—
775C4×Q8—82no—
776C4×Q8—84no—
777C4×Q8—82no—
778C4×D4—28no—
779C4×D4—216no—
780C4×D4—28no—
781C4×D4—24no—
782C4×D4—44no—
783C4×D4—44no—
784C4×D4—44no—
785C4×D4—42no—
786C4×D4—82no—
787C4×D4—84no—
788C4×D4#4118yes—
789#117—84no—
790#117—84no—
791C2×C4⋊C4—82no—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
891C2×C42—82no—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916C2×C42C2412yes—
917C2×C42C2411yescharacteristic
918C2×C42C2414yes—
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000C24C2514yes—
1001C24C2512yes—
1002C2×Q8—24no—
1003C2×Q8—22no—
1004C2×Q8—24no—
1005C2×Q8—24no—
1006C2×Q8—28no—
1007C2×Q8—24no—
1008C2×Q8—24no—
1009C2×Q8—22no—
1010C2×Q8—24no—
1011C2×Q8—42no—
1012C2×Q8—42no—
1013C2×Q8—42no—
1014C2×Q8—42no—
1015C2×Q8—41no—
1016C2×Q8—41no—
1017C2×Q8—41no—
1018C2×Q8—44no—
1019C2×Q8—44no—
1020C2×Q8—42no—
1021C2×Q8—42no—
1022C2×Q8—41no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—816no—
1027C2×D4—28no—
1028C2×D4—28no—
1029C2×D4—24no—
1030C2×D4—22no—
1031C2×D4—24no—
1032C2×D4—22no—
1033C2×D4—24no—
1034C2×D4—24no—
1035C2×D4—42no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—42no—
1040C2×D4—44no—
1041C2×D4—42no—
1042C2×D4—42no—
1043C2×D4—42no—
1044C2×D4C2×#4114yes—
1045C22×C4—28no—
1046C22×C4—28no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—42no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4C2×#4118yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2514yes—
1086C22×C4C2514yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2512yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—22no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—28no—
1104C4⋊C4—24no—
1105C4⋊C4—22no—
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—22no—
1113C4⋊C4—28no—
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—22no—
1118C4⋊C4—41no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—41no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—41no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—41no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—41no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—41no—
1160C4⋊C4C2×#4114yes—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4C2×#4118yes—
1195C42—28no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—24no—
1202C42—22no—
1203C42—22no—
1204C42—41no—
1205C42—42no—
1206C42—42no—
1207C42—42no—
1208C42—41no—
1209C42—44no—
1210C42—42no—
1211C42—42no—
1212C42—42no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—41no—
1220C42—44no—
1221C42—42no—
1222C42C2×#4114yes—
1223C422−1+414yes—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—24no—
1231C23—24no—
1232C23—24no—
1233C23—24no—
1234C23—24no—
1235C23—24no—
1236C23—24no—
1237C23C22×#4114yes—
1238C23C2611yescharacteristic
1239Q8—48no—
1240Q8—48no—
1241Q8—44no—
1242Q8—48no—
1243Q8—84no—
1244Q8—82no—
1245Q8—88no—
1246Q8—164no—
1247D4—28no—
1248D4—48no—
1249D4—84no—
1250D4—88no—
1251D4—88no—
1252D4—162no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—21no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—48no—
1326C2×C4—88no—
1327C2×C4—84no—
1328C2×C4—84no—
1329C2×C4—88no—
1330C2×C4—88no—
1331C2×C4—164no—
1332C2×C4—164no—
1333C2×C4C22×#4114yes—
1334C2×C4C22×#4112yes—
1335C2×C4C22×#4112yes—
1336C2×C4C22×#4112yes—
1337C2×C4C2×2−1+412yes—
1338C2×C4C2×2−1+412yes—
1339C2×C4C2×2−1+412yes—
1340C2×C4#58512yes—
1341C2×C4#58512yes—
1342C22—24no—
1343C22—24no—
1344C22—24no—
1345C22—42no—
1346C22—42no—
1347C22—42no—
1348C22—42no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22C23×#4111yescharacteristic
1357C22C22×2−1+411yescharacteristic
1358C22C2×#58511yescharacteristic
1359C22C2×#58511yescharacteristic
1360C22H(7,𝔽2)11yescharacteristic
1361C22H(7,𝔽2)11yescharacteristic
1362C222−1+611yescharacteristic
1363C4—22no—
1364C4—22no—
1365C4—24no—
1366C4—22no—
1367C4—22no—
1368C4—22no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—44no—
1376C4—41no—
1377C4—42no—
1378C4—42no—
1379C4—44no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—42no—
1386C4—44no—
1387C4—42no—
1388C4—42no—
1389C4#350714yes—
1390C2—44no—
1391C2—84no—
1392C2C2×#350711yescharacteristic
1393C2#6284611yescharacteristic
1394C2#6287911yescharacteristic
1395C2#6292611yescharacteristic
1396C2#6296511yescharacteristic
1397C2#6300911yescharacteristic
1398C2#6306911yescharacteristic
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. #59870C2semidirect
2. #59764C2semidirect
3. #52274C2semidirect
4. #49521C2semidirect
5. #49111C2semidirect
6. #47892C2semidirect
7. #47300C2semidirect
8. #45802C2semidirect
9. #45414C2semidirect
10. #45213C2semidirect
11. #45163C2semidirect
12. #43410C2semidirect
14. #42481C2semidirect
15. #41743C2semidirect
16. #40080C2semidirect
17. #39765C2semidirect
18. #39765C2semidirect
19. #39760C2semidirect
20. #39581C2semidirect
21. #38240C2semidirect
22. #38240C2semidirect
23. #37140C2semidirect
25. #35970C2semidirect
26. #35615C2semidirect
27. #35177C2semidirect
28. #34500C2semidirect
29. #34334C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#597642
#522742
#495212
#491112
#478922
#473002
#458022
#454142
#452132
#451632
#434102
#426122
#424812
#417432
#400802
#397652
#397602
#395812
#382402
#371402
#364692
#359702
#356152
#351772
#345002
#343342