Finite Group Databasebeta

← #7891985

Subgroups — #7891985

Order 512.

4723 conjugacy classes of subgroups.

The subgroup lattice has 1464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59832C211yesmaximal, characteristic, complemented
2#59477C212yesmaximal, complemented
3#52272C211yesmaximal, characteristic, complemented
4#50791C214yesmaximal, complemented
5#50156C214yesmaximal, complemented
6#49248C214yesmaximal, complemented
7#47386C214yesmaximal, complemented
8#46290C212yesmaximal, complemented
9#45319C212yesmaximal, complemented
10#45240C212yesmaximal, complemented
11#44998C212yesmaximal, complemented
12#44421C214yesmaximal, complemented
13#42847C212yesmaximal, complemented
14#42457C212yesmaximal, complemented
15#41499C214yesmaximal, complemented
16#40122C212yesmaximal, complemented
17#39765C211yesmaximal, characteristic, complemented
18#39708C212yesmaximal, complemented
19#39356C211yesmaximal, characteristic, complemented
20#39168C212yesmaximal, complemented
21#38823C212yesmaximal, complemented
22#38285C212yesmaximal, complemented
23#37156C212yesmaximal, complemented
24#36469C211yesmaximal, characteristic, complemented
25#35948C212yesmaximal, complemented
26#35658C212yesmaximal, complemented
27#35196C211yesmaximal, characteristic, complemented
28#34439C212yesmaximal, complemented
29#34324C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×Q82C2212yes—
32C2×#556C2211yescharacteristic
33C2×#548C2212yes—
34C2×#536C2212yes—
35#2858C2212yes—
36#2858C2211yescharacteristic
37#2855C2212yes—
38#2854C2212yes—
39#2850C2212yes—
40#2838C2214yes—
41#2831C2214yes—
42#2810C2211yescharacteristic
43#2808C2211yescharacteristic
44#2808C2212yes—
45#2808C2212yes—
46#2805C2211yescharacteristic
47#2804C2212yes—
48#2803C2214yes—
49#2801C2214yes—
50#2800C2212yes—
51#2798C2212yes—
52#2793C2212yes—
53#2786C2214yes—
54#2784C2214yes—
55#2784C2214yes—
56#2777C2214yes—
57#2776C2212yes—
58#2759C2214yes—
59#2759C2212yes—
60#2756C2214yes—
61#2755C2214yes—
62#2752C2214yes—
63#2746C2214yes—
64#2745C2214yes—
65#2742C2214yes—
66#2734C2212yes—
67#2734C2212yes—
68#2733C2214yes—
69#2731C2214yes—
70#2730C2214yes—
71#2729C2214yes—
72#2727C2211yescharacteristic
73#2724C2212yes—
74#2716C2212yes—
75#2714C2214yes—
76#2712C2214yes—
77#2710C2214yes—
78#2706C2214yes—
79#2705C2214yes—
80#2702C2214yes—
81#2696C2214yes—
82#2692C2214yes—
83#2687C2214yes—
84#2686C2214yes—
85#2686C2214yes—
86#2683C2212yes—
87#2683C2212yes—
88#2682C2212yes—
89#2682C2212yes—
90#2674C2214yes—
91#2674C2214yes—
92#2674C2214yes—
93#2674C2214yes—
94#2674C2214yes—
95#2671C2214yes—
96#2665C2214yes—
97#2663C2214yes—
98#2661C2214yes—
99#2653C2214yes—
100#2649C2214yes—
101#2640C2212yes—
102#2640C2212yes—
103#2640C2214yes—
104#2632C2214yes—
105#2620C2212yes—
106#2610C2214yes—
107#2605C2214yes—
108#2602C2214yes—
109#2597C2214yes—
110#2596C2214yes—
111#2594C2214yes—
112#2592C2212yes—
113#2592C2212yes—
114#2592C2214yes—
115#2588C2214yes—
116#2586C2214yes—
117#2582C2212yes—
118#2578C2214yes—
119#2574C2214yes—
120#2571C2211yescharacteristic
121#2567C2212yes—
122#2564C2214yes—
123#2560C2214yes—
124#2557C2214yes—
125#2557C2214yes—
126#2555C2214yes—
127#2554C2214yes—
128#2551C2212yes—
129#2551C2212yes—
130#2548C2212yes—
131#2547C2211yescharacteristic
132#2547C2214yes—
133#2547C2211yescharacteristic
134#2546C2214yes—
135#2545C2212yes—
136#2545C2212yes—
137#2544C2212yes—
138#2542C2211yescharacteristic
139#2542C2212yes—
140#2541C2211yescharacteristic
141#2537C2211yescharacteristic
142#2532C2214yes—
143#2530C2214yes—
144#2529C2214yes—
145#2527C2214yes—
146#2526C2214yes—
147#2522C2214yes—
148#2522C2214yes—
149#2516C2214yes—
150#2516C2214yes—
151#2515C2214yes—
152#2514C2212yes—
153#2513C2212yes—
154#2497C2212yes—
155#2492C2214yes—
156#2492C2214yes—
157#2492C2212yes—
158#2492C2212yes—
159#2491C2214yes—
160#2491C2214yes—
161#2491C2214yes—
162#2491C2212yes—
163#2491C2212yes—
164#2491C2212yes—
165#2488C2214yes—
166#2477C2214yes—
167#2474C2214yes—
168#2471C2214yes—
169#2465C2214yes—
170#2464C2214yes—
171#2461C2214yes—
172#2461C2214yes—
173#2461C2214yes—
174#2459C2214yes—
175#2458C2214yes—
176#2452C2214yes—
177#2452C2214yes—
178#2451C2214yes—
179#2451C2212yes—
180#2451C2212yes—
181#2450C2214yes—
182#2448C2214yes—
183#2448C2214yes—
184#2448C2212yes—
185#2446C2212yes—
186#2446C2212yes—
187#2445C2212yes—
188#2436C2212yes—
189#2434C2212yes—
190#2431C2212yes—
191#2431C2212yes—
192#2428C2212yes—
193#2426C2212yes—
194#2426C2212yes—
195#2425C2214yes—
196#2423C2212yes—
197#2422C2212yes—
198#2422C2212yes—
199#2421C2212yes—
200#2420C2212yes—
201#2401C2212yes—
202#2398C2212yes—
203#2398C2214yes—
204#2396C2212yes—
205#2378C2214yes—
206#2376C2214yes—
207#2374C2214yes—
208#2373C2214yes—
209#2373C2214yes—
210#2368C2214yes—
211#2367C2212yes—
212#2367C2212yes—
213#2367C2212yes—
214#2366C2211yescharacteristic
215#2365C2211yescharacteristic
216#2365C2211yescharacteristic
217#2365C2212yes—
218#2365C2212yes—
219#2362C2212yes—
220#2355C2212yes—
221#2354C2211yescharacteristic
222Q8×C4⋊C4C2211yescharacteristic
223#2346C2212yes—
224#2341C2212yes—
225#2341C2212yes—
226Q8×C22⋊C4C2212yes—
227Q8×C22⋊C4C2212yes—
228Q8×C22⋊C4C2212yes—
229#2339C2212yes—
230#2335C2214yes—
231#2335C2214yes—
232#2334C2214yes—
233#2333C2214yes—
234#2332C2214yes—
235#2329C2214yes—
236#2327C2212yes—
237#2326C2212yes—
238#2326C2212yes—
239#2326C2212yes—
240#2324C2212yes—
241#2319C2212yes—
242#2314C2212yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×#126C2212yes—
248C4×#124C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×#121C2212yes—
251#2298C2212yes—
252#2296C2212yes—
253#2295C2212yes—
254#2295C2211yescharacteristic
255#2295C2212yes—
256#2293C2211yescharacteristic
257#2276C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261#559—48no—
262Q82—48no—
263#556—28no—
264#548—48no—
265#536—216no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×#127C2311yescharacteristic
278C2×#127C2312yes—
279C2×#126C2312yes—
280C2×#126C2314yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2312yes—
287C2×#124C2314yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#124C2314yes—
291C2×#124C2314yes—
292C2×#124C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2312yes—
314C2×#121C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2314yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C22×C42C2312yes—
340#401C2314yes—
341#401C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2312yes—
354#400C2312yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2312yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2312yes—
383#397C2314yes—
384#397C2312yes—
385#397C2312yes—
386#397C2312yes—
387#397C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2312yes—
395#396C2312yes—
396#396C2312yes—
397#396C2314yes—
398#396C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2312yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2314yes—
420#394C2312yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2312yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2312yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2312yes—
439#393C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2314yes—
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2314yes—
460#391C2312yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2311yescharacteristic
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2311yescharacteristic
474#390C2314yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2314yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2314yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2314yes—
489#390C2311yescharacteristic
490#390C2314yes—
491#390C2312yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2314yes—
496#390C2312yes—
497#390C2314yes—
498#390C2311yescharacteristic
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2311yescharacteristic
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2311yescharacteristic
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2312yes—
520#389C2311yescharacteristic
521#389C2311yescharacteristic
522#389C2314yes—
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2312yes—
526#389C2311yescharacteristic
527#388C2312yes—
528#388C2312yes—
529#388C2312yes—
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#388C2314yes—
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#388C2312yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
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#387C2312yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2312yes—
602#387C2312yes—
603#387C2314yes—
604#387C2312yes—
605#387C2314yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#384C2312yes—
640#384C2311yescharacteristic
641#384C2311yescharacteristic
642#384C2311yescharacteristic
643#384C2312yes—
644#383C2312yes—
645#383C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#381C2314yes—
650#381C2314yes—
651#381C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
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⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2312yes—
711#376C2312yes—
712#376C2314yes—
713#376C2314yes—
714C2×#95C2314yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C2×#41—28no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8—28no—
721C22×Q8—44no—
722C22×Q8—44no—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×Q8C2414yes—
730C22×Q8C2414yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2412yes—
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C4⋊Q8—28no—
750C4⋊Q8—24no—
751C4⋊Q8—24no—
752C4⋊Q8—44no—
753C4⋊Q8—48no—
754C4⋊Q8—44no—
755C4⋊Q8—42no—
756C4⋊Q8—48no—
757C4⋊Q8—48no—
758C4⋊Q8—84no—
759C4⋊Q8#4118yes—
760#127—42no—
761#127—44no—
762#126—216no—
763#126—28no—
764#124—28no—
765#124—28no—
766#124—28no—
767#124—28no—
768#124—48no—
769#124—44no—
770#124—48no—
771#124—82no—
772#124—84no—
773#124—84no—
774#124—84no—
775#124—84no—
776#123—216no—
777#123—216no—
778#123—48no—
779#123—48no—
780#123—84no—
781#123—84no—
782C22⋊Q8—216no—
783C22⋊Q8—216no—
784C22⋊Q8—28no—
785C22⋊Q8—48no—
786C22⋊Q8—44no—
787C22⋊Q8—84no—
788C22⋊Q8—84no—
789C22⋊Q8—82no—
790C22⋊Q8—82no—
791#121—28no—
792#121—48no—
793#121—44no—
794#121—44no—
795#121—84no—
796#121—82no—
797#121—82no—
798C4×Q8—28no—
799C4×Q8—24no—
800C4×Q8—28no—
801C4×Q8—28no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×Q8—48no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—82no—
809C4×Q8—82no—
810C4×D4—24no—
811C4×D4—24no—
812C4×D4—24no—
813C4×D4—48no—
814C4×D4—44no—
815C4×D4—42no—
816C4×D4—44no—
817C4×D4—48no—
818C4×D4—82no—
819#117—28no—
820#117—28no—
821#117—82no—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C42—82no—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2411yescharacteristic
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026C24C2512yes—
1027C24C2514yes—
1028C24C2512yes—
1029#41—816no—
1030C2×Q8—22no—
1031C2×Q8—24no—
1032C2×Q8—28no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—41no—
1041C2×Q8—42no—
1042C2×Q8—41no—
1043C2×Q8—42no—
1044C2×Q8—44no—
1045C2×Q8—42no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8—44no—
1052C2×Q8—44no—
1053C2×Q8—816no—
1054C2×Q8C2×#4118yes—
1055C2×D4—22no—
1056C2×D4—24no—
1057C2×D4—28no—
1058C2×D4—22no—
1059C2×D4—24no—
1060C2×D4—22no—
1061C2×D4—28no—
1062C2×D4—24no—
1063C2×D4—22no—
1064C2×D4—24no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—41no—
1070C2×D4—44no—
1071C2×D4—41no—
1072C2×D4—44no—
1073C2×D4—42no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—42no—
1082C2×D4—42no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—28no—
1090C22×C4—28no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—42no—
1100C22×C4—42no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2514yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2514yes—
1127C22×C4C2511yescharacteristic
1128C22×C4C2514yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C22×C4C2512yes—
1134C22×C4C2511yescharacteristic
1135C4⋊C4—22no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—22no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—28no—
1142C4⋊C4—28no—
1143C4⋊C4—22no—
1144C4⋊C4—22no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—22no—
1156C4⋊C4—22no—
1157C4⋊C4—24no—
1158C4⋊C4—42no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—41no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—41no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—41no—
1177C4⋊C4—44no—
1178C4⋊C4—41no—
1179C4⋊C4—41no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4C2×#4118yes—
1192C4⋊C4C2×#4118yes—
1193C4⋊C42−1+414yes—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—28no—
1197C22⋊C4—24no—
1198C22⋊C4—28no—
1199C22⋊C4—28no—
1200C22⋊C4—28no—
1201C22⋊C4—28no—
1202C22⋊C4—28no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—28no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—24no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C42—28no—
1245C42—24no—
1246C42—24no—
1247C42—28no—
1248C42—24no—
1249C42—24no—
1250C42—24no—
1251C42—22no—
1252C42—24no—
1253C42—22no—
1254C42—41no—
1255C42—42no—
1256C42—42no—
1257C42—42no—
1258C42—41no—
1259C42—42no—
1260C42—44no—
1261C42—44no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—41no—
1267C42—44no—
1268C42—44no—
1269C42—42no—
1270C42—42no—
1271C42C2×#4114yes—
1272C42H(5,𝔽2)14yes—
1273C23—22no—
1274C23—24no—
1275C23—22no—
1276C23—24no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—24no—
1281C23—22no—
1282C23—22no—
1283C23—24no—
1284C23—22no—
1285C23—22no—
1286C23—24no—
1287C23—22no—
1288C23—24no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—24no—
1293C23—22no—
1294C23C2611yescharacteristic
1295Q8—216no—
1296Q8—48no—
1297Q8—44no—
1298Q8—48no—
1299Q8—84no—
1300Q8—88no—
1301Q8—164no—
1302Q8—164no—
1303D4—44no—
1304D4—48no—
1305D4—82no—
1306D4—88no—
1307D4—84no—
1308D4—88no—
1309D4—88no—
1310D4—164no—
1311D4—162no—
1312D4—164no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—24no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—48no—
1382C2×C4—48no—
1383C2×C4—84no—
1384C2×C4—84no—
1385C2×C4—88no—
1386C2×C4—88no—
1387C2×C4—164no—
1388C2×C4—164no—
1389C2×C4C22×#4118yes—
1390C2×C4C22×#4112yes—
1391C2×C4C22×#4112yes—
1392C2×C4C22×#4112yes—
1393C2×C4C2×H(5,𝔽2)12yes—
1394C2×C4C2×H(5,𝔽2)12yes—
1395C2×C4C2×H(5,𝔽2)12yes—
1396C2×C4C2×2−1+414yes—
1397C2×C4C2×2−1+412yes—
1398C2×C4#58512yes—
1399C22—42no—
1400C22—44no—
1401C22—42no—
1402C22—42no—
1403C22—44no—
1404C22—42no—
1405C22—44no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—44no—
1410C22—42no—
1411C22—42no—
1412C22—44no—
1413C22—42no—
1414C22—42no—
1415C22—44no—
1416C22—42no—
1417C22—42no—
1418C22—44no—
1419C22—42no—
1420C22C23×#4111yescharacteristic
1421C22C22×H(5,𝔽2)11yescharacteristic
1422C22C22×2−1+411yescharacteristic
1423C22C2×#58511yescharacteristic
1424C22H(7,𝔽2)11yescharacteristic
1425C22H(7,𝔽2)11yescharacteristic
1426C222−1+611yescharacteristic
1427C4—22no—
1428C4—28no—
1429C4—22no—
1430C4—22no—
1431C4—22no—
1432C4—24no—
1433C4—22no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—44no—
1438C4—42no—
1439C4—44no—
1440C4—41no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—44no—
1447C4—42no—
1448C4—44no—
1449C4—42no—
1450C4—42no—
1451C4—42no—
1452C4#351414yes—
1453C2—82no—
1454C2—84no—
1455C2—82no—
1456C2C2×#351411yescharacteristic
1457C2#6285111yescharacteristic
1458C2#6288011yescharacteristic
1459C2#6294211yescharacteristic
1460C2#6296211yescharacteristic
1461C2#6299911yescharacteristic
1462C2#6306911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59832C2semidirect
2. #59477C2semidirect
3. #52272C2semidirect
4. #50791C2semidirect
5. #50156C2semidirect
6. #49248C2semidirect
7. #47386C2semidirect
8. #46290C2semidirect
9. #45319C2semidirect
10. #45240C2semidirect
11. #44998C2semidirect
12. #44421C2semidirect
13. #42847C2semidirect
14. #42457C2semidirect
15. #41499C2semidirect
16. #40122C2semidirect
17. #39765C2semidirect
18. #39708C2semidirect
19. #39356C2semidirect
20. #39168C2semidirect
21. #38823C2semidirect
22. #38285C2semidirect
23. #37156C2semidirect
24. #36469C2semidirect
25. #35948C2semidirect
26. #35658C2semidirect
27. #35196C2semidirect
28. #34439C2semidirect
29. #34324C2semidirect

Maximal subgroups

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

subgroupindex
#598322
#594772
#522722
#507912
#501562
#492482
#473862
#462902
#453192
#452402
#449982
#444212
#428472
#424572
#414992
#401222
#397652
#397082
#393562
#391682
#388232
#382852
#371562
#364692
#359482
#356582
#351962
#344392
#343242