Finite Group Databasebeta

← #7657439

Subgroups — #7657439

Order 512.

4472 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#41966C214yesmaximal, complemented
2#41680C214yesmaximal, complemented
3#41673C214yesmaximal, complemented
4#41019C214yesmaximal, complemented
5#41004C214yesmaximal, complemented
6#40551C214yesmaximal, complemented
7#39810C212yesmaximal, complemented
8#39758C211yesmaximal, characteristic, complemented
9#39680C212yesmaximal, complemented
10#39628C211yesmaximal, characteristic, complemented
11#38971C211yesmaximal, characteristic, complemented
12#38969C211yesmaximal, characteristic, complemented
13#38241C212yesmaximal, complemented
14#38238C212yesmaximal, complemented
15#37619C211yesmaximal, characteristic, complemented
16#37551C211yesmaximal, characteristic, complemented
17#37523C212yesmaximal, complemented
18#37521C212yesmaximal, complemented
19#36609C211yesmaximal, characteristic, complemented
20#36566C211yesmaximal, characteristic, complemented
21#36403C211yesmaximal, characteristic, complemented
22#36370C211yesmaximal, characteristic, complemented
23#35790C214yesmaximal, complemented
24#35718C214yesmaximal, complemented
25#35344C211yesmaximal, characteristic, complemented
26#35268C212yesmaximal, complemented
27#34624C211yesmaximal, characteristic
28#34619C212yesmaximal, complemented
29#34236C211yesmaximal, characteristic, complemented
30#34224C211yesmaximal, characteristic, complemented
31#34145C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#2864C2212yes—
36#2864C2211yescharacteristic
37#2864C2211yescharacteristic
38#2862C2211yescharacteristic
39#2862C2211yescharacteristic
40#2860C2212yes—
41#2860C2212yes—
42#2858C2212yes—
43#2838C2214yes—
44#2836C2214yes—
45#2826C2214yes—
46#2824C2214yes—
47#2821C2212yes—
48#2821C2212yes—
49#2816C2212yes—
50#2816C2212yes—
51#2809C2214yes—
52#2808C2214yes—
53#2804C2214yes—
54#2802C2214yes—
55#2800C2214yes—
56#2799C2214yes—
57#2798C2214yes—
58#2797C2214yes—
59#2787C2214yes—
60#2786C2214yes—
61#2771C2214yes—
62#2759C2214yes—
63#2759C2214yes—
64#2752C2214yes—
65#2751C2214yes—
66#2745C2214yes—
67#2732C2214yes—
68#2716C2214yes—
69#2713C2214yes—
70#2712C2214yes—
71#2710C2214yes—
72#2700C2214yes—
73#2694C2214yes—
74#2689C2214yes—
75#2663C2212yes—
76#2663C2212yes—
77#2663C2214yes—
78#2663C2214yes—
79#2662C2214yes—
80#2661C2214yes—
81#2660C2211yescharacteristic
82#2658C2212yes—
83#2657C2211yescharacteristic
84#2654C2214yes—
85#2653C2214yes—
86#2653C2214yes—
87#2650C2214yes—
88#2649C2214yes—
89#2649C2214yes—
90#2649C2214yes—
91#2649C2214yes—
92#2647C2212yes—
93#2645C2212yes—
94#2644C2212yes—
95#2641C2211yescharacteristic
96#2640C2212yes—
97#2640C2211yescharacteristic
98#2640C2212yes—
99#2638C2214yes—
100#2638C2214yes—
101#2633C2214yes—
102#2633C2214yes—
103#2628C2212yes—
104#2628C2212yes—
105#2625C2212yes—
106#2624C2212yes—
107#2624C2212yes—
108#2624C2212yes—
109#2620C2211yescharacteristic
110#2620C2211yescharacteristic
111#2619C2211yescharacteristic
112#2619C2211yescharacteristic
113#2611C2214yes—
114#2607C2214yes—
115#2607C2214yes—
116#2605C2214yes—
117#2605C2214yes—
118#2604C2214yes—
119#2602C2214yes—
120#2596C2214yes—
121#2594C2214yes—
122#2592C2214yes—
123#2592C2212yes—
124#2590C2214yes—
125#2589C2214yes—
126#2588C2214yes—
127#2584C2212yes—
128#2581C2211yescharacteristic
129#2581C2211yescharacteristic
130#2580C2211yescharacteristic
131#2580C2211yescharacteristic
132#2580C2211yescharacteristic
133#2580C2211yescharacteristic
134#2580C2211yescharacteristic
135#2580C2211yescharacteristic
136#2575C2214yes—
137#2574C2214yes—
138#2573C2214yes—
139#2560C2214yes—
140#2557C2214yes—
141#2557C2214yes—
142#2556C2214yes—
143#2548C2212yes—
144#2546C2212yes—
145#2532C2214yes—
146#2530C2214yes—
147#2527C2214yes—
148#2527C2214yes—
149#2523C2214yes—
150#2521C2214yes—
151#2521C2214yes—
152#2516C2214yes—
153#2516C2214yes—
154#2514C2212yes—
155#2513C2212yes—
156#2513C2212yes—
157#2513C2212yes—
158#2509C2212yes—
159#2509C2212yes—
160#2507C2212yes—
161#2506C2212yes—
162#2493C2214yes—
163#2492C2214yes—
164#2479C2214yes—
165#2474C2214yes—
166#2468C2214yes—
167#2467C2214yes—
168#2467C2214yes—
169#2466C2214yes—
170#2465C2214yes—
171#2463C2214yes—
172#2460C2214yes—
173#2459C2214yes—
174#2459C2214yes—
175#2459C2214yes—
176#2458C2214yes—
177#2455C2214yes—
178#2453C2214yes—
179#2452C2212yes—
180#2452C2212yes—
181#2452C2212yes—
182#2451C2214yes—
183#2451C2212yes—
184#2450C2214yes—
185#2450C2214yes—
186#2448C2214yes—
187#2448C2212yes—
188#2447C2214yes—
189#2447C2212yes—
190#2445C2212yes—
191#2445C2212yes—
192#2432C2214yes—
193#2419C2214yes—
194#2415C2214yes—
195#2401C2214yes—
196#2398C2214yes—
197#2396C2214yes—
198#2395C2214yes—
199#2392C2214yes—
200#2388C2214yes—
201#2373C2214yes—
202#2373C2214yes—
203#2370C2212yes—
204#2370C2212yes—
205#2370C2212yes—
206#2369C2212yes—
207#2369C2212yes—
208#2368C2212yes—
209#2368C2212yes—
210#2368C2214yes—
211#2367C2214yes—
212#2367C2212yes—
213#2366C2212yes—
214#2365C2212yes—
215#2361C2214yes—
216#2360C2212yes—
217#2360C2212yes—
218#2359C2214yes—
219#2357C2211yescharacteristic
220#2357C2211yescharacteristic
221#2357C2211yescharacteristic
222#2356C2211yescharacteristic
223#2351C2211yescharacteristic
224#2349C2211yescharacteristic
225#2349C2211yescharacteristic
226#2349C2211yescharacteristic
227#2347C2212yes—
228#2343C2212yes—
229#2339C2212yes—
230#2339C2212yes—
231#2337C2214yes—
232#2331C2212yes—
233#2331C2212yes—
234#2331C2212yes—
235#2328C2212yes—
236#2322C2214yes—
237#2319C2212yes—
238#2319C2212yes—
239#2319C2212yes—
240#2318C2212yes—
241C4×C4⋊Q8C2212yes—
242C4×#127C2211yescharacteristic
243C4×#127C2211yescharacteristic
244C4×#124C2211yescharacteristic
245C4×#124C2212yes—
246C4×#124C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×#121C2212yes—
249C4×#121C2212yes—
250C4×#121C2212yes—
251#2296C2212yes—
252#2295C2212yes—
253#2295C2212yes—
254#2295C2211yescharacteristic
255#2295C2211yescharacteristic
256#2295C2212yes—
257#2293C2212yes—
258#2283C2211yescharacteristic
259#2283C2211yescharacteristic
260#2275C2212yes—
261#2275C2212yes—
262C42×Q8C2211yescharacteristic
263C42×Q8C2211yescharacteristic
264C4×#117C2211yescharacteristic
265C4×#117C2212yes—
266C2×C4×C4⋊C4C2211yescharacteristic
267C22×#41C2312yes—
268#533—28no—
269#532—28no—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×#127C2311yescharacteristic
277C2×#127C2311yescharacteristic
278C2×#127C2311yescharacteristic
279#529—28no—
280C2×#126C2312yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#125C2311yescharacteristic
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#124C2311yescharacteristic
287C2×#124C2312yes—
288C2×#124C2311yescharacteristic
289C2×#124C2314yes—
290C2×#124C2311yescharacteristic
291C2×#124C2314yes—
292C2×#124C2314yes—
293C2×#123C2312yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×C22⋊Q8C2311yescharacteristic
297C2×C22⋊Q8C2311yescharacteristic
298C2×C22⋊Q8C2311yescharacteristic
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×#121C2312yes—
304C2×#121C2311yescharacteristic
305C2×#121C2311yescharacteristic
306C2×#121C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×#117C2312yes—
330C2×#117C2311yescharacteristic
331C2×#117C2312yes—
332C2×#117C2311yescharacteristic
333C2×#117C2314yes—
334C22×C4⋊C4C2312yes—
335C22×C42C2312yes—
336C22×C42C2311yescharacteristic
337#401C2314yes—
338#401C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#399C2312yes—
356#399C2312yes—
357#399C2312yes—
358#399C2312yes—
359#399C2312yes—
360#399C2312yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#395C2312yes—
406#395C2312yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#393C2314yes—
431#393C2312yes—
432#393C2312yes—
433#393C2312yes—
434#393C2312yes—
435#393C2312yes—
436#393C2312yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2311yescharacteristic
470#391C2311yescharacteristic
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#390C2314yes—
476#390C2311yescharacteristic
477#390C2314yes—
478#390C2311yescharacteristic
479#390C2311yescharacteristic
480#390C2311yescharacteristic
481#390C2314yes—
482#390C2311yescharacteristic
483#390C2312yes—
484#390C2312yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2314yes—
491#390C2314yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2311yescharacteristic
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2314yes—
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#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#387C2312yes—
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#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2312yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#385C2312yes—
617#385C2312yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2312yes—
634#385C2314yes—
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#383C2312yes—
638#383C2314yes—
639#383C2312yes—
640#383C2312yes—
641#382C2312yes—
642#382C2311yescharacteristic
643#382C2311yescharacteristic
644#382C2311yescharacteristic
645#382C2311yescharacteristic
646#382C2312yes—
647#382C2311yescharacteristic
648#382C2312yes—
649#382C2311yescharacteristic
650#381C2312yes—
651#381C2314yes—
652#381C2312yes—
653#381C2312yes—
654#381C2312yes—
655#381C2314yes—
656#381C2314yes—
657#381C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720#376C2312yes—
721#376C2312yes—
722#376C2312yes—
723#376C2311yescharacteristic
724#376C2311yescharacteristic
725#376C2312yes—
726#376C2314yes—
727#376C2312yes—
728C2×#95C2311yescharacteristic
729C2×#95C2311yescharacteristic
730C2×#95C2312yes—
731C2×#95C2312yes—
732C2×#95C2312yes—
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2312yes—
736C43C2312yes—
737C2×#41—28no—
738C2×#41—84no—
739C22×Q8C2411yescharacteristic
740C22×Q8C2411yescharacteristic
741C22×Q8C2411yescharacteristic
742C22×Q8C2412yes—
743C22×Q8C2414yes—
744C22×Q8C2412yes—
745C22×Q8C2414yes—
746C22×D4C2411yescharacteristic
747C22×D4C2411yescharacteristic
748C22×D4C2411yescharacteristic
749C22×D4C2412yes—
750C22×D4C2412yes—
751C22×D4C2412yes—
752C22×D4C2412yes—
753C22×D4C2414yes—
754C22×D4C2412yes—
755C22×D4C2414yes—
756C23×C4C2411yescharacteristic
757C23×C4C2412yes—
758C23×C4C2412yes—
759C23×C4C2414yes—
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2412yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C23×C4C2411yescharacteristic
766C23×C4C2411yescharacteristic
767C4⋊Q8—24no—
768C4⋊Q8—24no—
769C4⋊Q8—24no—
770C4⋊Q8—28no—
771C4⋊Q8—44no—
772C4⋊Q8—84no—
773#127—24no—
774#127—24no—
775#127—42no—
776#126—28no—
777#126—48no—
778#126—84no—
779#125—24no—
780#125—28no—
781#125—84no—
782#124—24no—
783#124—28no—
784#124—24no—
785#124—48no—
786#124—42no—
787#124—84no—
788#124—84no—
789#123—28no—
790#123—48no—
791#123—84no—
792C22⋊Q8—24no—
793C22⋊Q8—28no—
794C22⋊Q8—24no—
795C22⋊Q8—24no—
796C22⋊Q8—48no—
797C22⋊Q8—84no—
798C22⋊Q8—84no—
799#121—24no—
800#121—24no—
801#121—24no—
802#121—28no—
803C4×Q8—24no—
804C4×Q8—24no—
805C4×Q8—24no—
806C4×Q8—28no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—44no—
810C4×Q8—84no—
811C4×D4—28no—
812C4×D4—24no—
813C4×D4—28no—
814C4×D4—24no—
815C4×D4—24no—
816C4×D4—44no—
817C4×D4—44no—
818C4×D4—44no—
819C4×D4—48no—
820C4×D4—48no—
821C4×D4—84no—
822C4×D4—84no—
823C4×D4—84no—
824C4×D4—84no—
825#117—28no—
826#117—28no—
827#117—24no—
828#117—42no—
829#117—84no—
830C2×C4⋊C4—44no—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
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×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C42—44no—
933C2×C42#4118yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968#95C2411yescharacteristic
969#95C2411yescharacteristic
970#95C2411yescharacteristic
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2411yescharacteristic
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040C24C2512yes—
1041C24C2512yes—
1042C24C2512yes—
1043C24C2511yescharacteristic
1044#41—816no—
1045C2×Q8—22no—
1046C2×Q8—22no—
1047C2×Q8—22no—
1048C2×Q8—24no—
1049C2×Q8—24no—
1050C2×Q8—22no—
1051C2×Q8—28no—
1052C2×Q8—22no—
1053C2×Q8—42no—
1054C2×Q8—42no—
1055C2×Q8—44no—
1056C2×Q8—44no—
1057C2×Q8—42no—
1058C2×Q8—42no—
1059C2×Q8—44no—
1060C2×Q8—44no—
1061C2×Q8—44no—
1062C2×Q8—44no—
1063C2×D4—24no—
1064C2×D4—24no—
1065C2×D4—24no—
1066C2×D4—22no—
1067C2×D4—24no—
1068C2×D4—22no—
1069C2×D4—22no—
1070C2×D4—24no—
1071C2×D4—22no—
1072C2×D4—22no—
1073C2×D4—22no—
1074C2×D4—28no—
1075C2×D4—22no—
1076C2×D4—22no—
1077C2×D4—22no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C22×C4—22no—
1089C22×C4—22no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—28no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—42no—
1103C22×C4—44no—
1104C22×C4—42no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4C2×#4114yes—
1114C22×C4C2×#4114yes—
1115C22×C4C2×#4114yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2514yes—
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C22×C4C2511yescharacteristic
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2511yescharacteristic
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—22no—
1149C4⋊C4—22no—
1150C4⋊C4—22no—
1151C4⋊C4—24no—
1152C4⋊C4—22no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—22no—
1158C4⋊C4—22no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—28no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—28no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
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—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C42—24no—
1245C42—24no—
1246C42—24no—
1247C42—22no—
1248C42—24no—
1249C42—24no—
1250C42—22no—
1251C42—22no—
1252C42—24no—
1253C42—24no—
1254C42—42no—
1255C42—42no—
1256C42—42no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—42no—
1261C42—42no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—42no—
1266C42—42no—
1267C42—42no—
1268C42—42no—
1269C42—42no—
1270C42—42no—
1271C42—44no—
1272C42—42no—
1273C42C2×#4114yes—
1274C42C2×#4114yes—
1275C42C2×#4114yes—
1276C42C2×#4114yes—
1277C422−1+414yes—
1278C23—21no—
1279C23—21no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—24no—
1289C23—24no—
1290C23—24no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—24no—
1295C23—24no—
1296C23—24no—
1297C23C22×#4112yes—
1298C23C2611yescharacteristic
1299Q8—44no—
1300Q8—44no—
1301Q8—44no—
1302Q8—84no—
1303Q8—88no—
1304Q8—84no—
1305Q8—164no—
1306D4—48no—
1307D4—48no—
1308D4—48no—
1309D4—48no—
1310D4—44no—
1311D4—44no—
1312D4—44no—
1313D4—88no—
1314D4—84no—
1315D4—88no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—28no—
1327C2×C4—22no—
1328C2×C4—22no—
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—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
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—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—44no—
1381C2×C4—44no—
1382C2×C4—84no—
1383C2×C4—84no—
1384C2×C4—88no—
1385C2×C4—84no—
1386C2×C4—84no—
1387C2×C4—84no—
1388C2×C4—164no—
1389C2×C4—164no—
1390C2×C4C22×#4112yes—
1391C2×C4C22×#4112yes—
1392C2×C4C22×#4112yes—
1393C2×C4C22×#4112yes—
1394C2×C4C22×#4112yes—
1395C2×C4C22×#4112yes—
1396C2×C4C2×2−1+414yes—
1397C2×C4C2×2−1+412yes—
1398C2×C4#58514yes—
1399C2×C4#58512yes—
1400C22—22no—
1401C22—22no—
1402C22—22no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—44no—
1415C22—44no—
1416C22—44no—
1417C22—44no—
1418C22—44no—
1419C22—44no—
1420C22C23×#4111yescharacteristic
1421C22C22×2−1+411yescharacteristic
1422C22C2×#58511yescharacteristic
1423C22C2×#58512yes—
1424C22H(7,𝔽2)12yes—
1425C4—22no—
1426C4—22no—
1427C4—22no—
1428C4—22no—
1429C4—22no—
1430C4—24no—
1431C4—24no—
1432C4—42no—
1433C4—42no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—42no—
1438C4—42no—
1439C4—42no—
1440C4—42no—
1441C4—42no—
1442C4—44no—
1443C4—44no—
1444C4—42no—
1445C4—42no—
1446C4—42no—
1447C4—44no—
1448C4—44no—
1449C4—42no—
1450C4—42no—
1451C4#350714yes—
1452C2—42no—
1453C2—82no—
1454C2—82no—
1455C2—82no—
1456C2#6268611yescharacteristic
1457C2C2×#350711yescharacteristic
1458C2#6285511yescharacteristic
1459C2#6296212yes—
1460C2#6297012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34624C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41966C2semidirect
2. #41680C2semidirect
3. #41673C2semidirect
4. #41019C2semidirect
5. #41004C2semidirect
6. #40551C2semidirect
7. #39810C2semidirect
8. #39758C2semidirect
9. #39680C2semidirect
10. #39628C2semidirect
11. #38971C2semidirect
12. #38969C2semidirect
13. #38241C2semidirect
14. #38238C2semidirect
15. #37619C2semidirect
16. #37551C2semidirect
17. #37523C2semidirect
18. #37521C2semidirect
19. #36609C2semidirect
20. #36566C2semidirect
21. #36403C2semidirect
22. #36370C2semidirect
23. #35790C2semidirect
24. #35718C2semidirect
25. #35344C2semidirect
26. #35268C2semidirect
28. #34619C2semidirect
29. #34236C2semidirect
30. #34224C2semidirect
31. #34145C2semidirect

Maximal subgroups

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

subgroupindex
#419662
#416802
#416732
#410192
#410042
#405512
#398102
#397582
#396802
#396282
#389712
#389692
#382412
#382382
#376192
#375512
#375232
#375212
#366092
#365662
#364032
#363702
#357902
#357182
#353442
#352682
#346242
#346192
#342362
#342242
#341452