Finite Group Databasebeta

← #7648462

Subgroups — #7648462

Order 512.

4488 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41734C214yesmaximal, complemented
2#41608C214yesmaximal, complemented
3#41095C214yesmaximal, complemented
4#40921C214yesmaximal, complemented
5#40326C214yesmaximal, complemented
6#40245C214yesmaximal, complemented
7#38727C214yesmaximal, complemented
8#38629C214yesmaximal, complemented
9#37573C212yesmaximal, complemented
10#37567C211yesmaximal, characteristic, complemented
11#37539C211yesmaximal, characteristic, complemented
12#37366C212yesmaximal, complemented
13#37335C212yesmaximal, complemented
14#37295C212yesmaximal, complemented
15#37292C212yesmaximal, complemented
16#35614C212yesmaximal, complemented
17#35598C212yesmaximal, complemented
18#35295C212yesmaximal, complemented
19#35292C211yesmaximal, characteristic
20#35282C212yesmaximal, complemented
21#35218C212yesmaximal, complemented
22#35138C211yesmaximal, characteristic, complemented
23#35116C212yesmaximal, complemented
24#34893C212yesmaximal, complemented
25#34217C211yesmaximal, characteristic, complemented
26#34125C211yesmaximal, characteristic, complemented
27#34086C211yesmaximal, characteristic, complemented
28C2×#532C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31#2864C2212yes—
32#2860C2212yes—
33#2860C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2856C2212yes—
37#2853C2214yes—
38#2852C2214yes—
39#2851C2212yes—
40#2851C2212yes—
41#2841C2214yes—
42#2838C2214yes—
43#2829C2214yes—
44#2820C2214yes—
45#2808C2214yes—
46#2807C2214yes—
47#2796C2214yes—
48#2777C2214yes—
49#2776C2214yes—
50#2773C2214yes—
51#2769C2214yes—
52#2762C2214yes—
53#2761C2214yes—
54#2757C2214yes—
55#2755C2214yes—
56#2747C2214yes—
57#2743C2214yes—
58#2737C2214yes—
59#2737C2214yes—
60#2727C2214yes—
61#2723C2214yes—
62#2722C2214yes—
63#2706C2214yes—
64#2705C2214yes—
65#2705C2214yes—
66#2701C2214yes—
67#2698C2214yes—
68#2696C2214yes—
69#2695C2214yes—
70#2694C2214yes—
71#2694C2214yes—
72#2691C2214yes—
73#2689C2214yes—
74#2689C2214yes—
75#2686C2214yes—
76#2672C2214yes—
77#2667C2212yes—
78#2666C2214yes—
79#2665C2212yes—
80#2662C2214yes—
81#2660C2212yes—
82#2660C2212yes—
83#2654C2214yes—
84#2654C2214yes—
85#2653C2214yes—
86#2652C2214yes—
87#2649C2214yes—
88#2648C2214yes—
89#2647C2212yes—
90#2641C2212yes—
91#2637C2214yes—
92#2634C2212yes—
93#2633C2212yes—
94#2633C2212yes—
95#2633C2212yes—
96#2629C2212yes—
97#2628C2212yes—
98#2624C2212yes—
99#2624C2212yes—
100#2624C2212yes—
101#2618C2214yes—
102#2615C2212yes—
103#2611C2214yes—
104#2606C2212yes—
105#2605C2212yes—
106#2597C2214yes—
107#2597C2214yes—
108#2597C2214yes—
109#2597C2214yes—
110#2596C2214yes—
111#2595C2214yes—
112#2594C2214yes—
113#2592C2212yes—
114#2589C2214yes—
115#2589C2214yes—
116#2587C2214yes—
117#2586C2214yes—
118#2585C2214yes—
119#2584C2212yes—
120#2580C2212yes—
121#2576C2214yes—
122#2574C2214yes—
123#2573C2214yes—
124#2570C2212yes—
125#2566C2212yes—
126#2566C2212yes—
127#2562C2212yes—
128#2559C2214yes—
129#2559C2214yes—
130#2557C2214yes—
131#2556C2214yes—
132#2554C2214yes—
133#2554C2214yes—
134#2554C2214yes—
135#2550C2212yes—
136#2540C2212yes—
137#2535C2212yes—
138#2522C2214yes—
139#2522C2214yes—
140#2520C2214yes—
141#2519C2214yes—
142#2516C2214yes—
143#2513C2214yes—
144#2513C2212yes—
145#2512C2212yes—
146#2509C2212yes—
147#2508C2212yes—
148#2507C2212yes—
149#2507C2212yes—
150#2504C2212yes—
151#2501C2212yes—
152#2496C2212yes—
153#2496C2212yes—
154#2495C2212yes—
155#2494C2212yes—
156#2491C2212yes—
157#2490C2212yes—
158#2487C2212yes—
159#2486C2212yes—
160#2484C2212yes—
161#2479C2214yes—
162#2479C2214yes—
163#2479C2214yes—
164#2479C2214yes—
165#2478C2214yes—
166#2478C2214yes—
167#2476C2214yes—
168#2476C2214yes—
169#2475C2214yes—
170#2474C2214yes—
171#2471C2214yes—
172#2470C2214yes—
173#2469C2214yes—
174#2465C2214yes—
175#2465C2214yes—
176#2462C2214yes—
177#2458C2214yes—
178#2454C2212yes—
179#2452C2212yes—
180#2448C2214yes—
181#2441C2212yes—
182#2439C2212yes—
183#2422C2212yes—
184#2420C2212yes—
185#2414C2212yes—
186#2414C2212yes—
187#2407C2214yes—
188#2406C2212yes—
189#2406C2212yes—
190#2406C2212yes—
191#2396C2214yes—
192#2396C2214yes—
193#2370C2214yes—
194#2370C2214yes—
195#2357C2212yes—
196#2357C2212yes—
197#2357C2212yes—
198#2351C2212yes—
199#2347C2212yes—
200#2347C2212yes—
201#2347C2212yes—
202#2345C2214yes—
203#2345C2214yes—
204#2341C2212yes—
205#2337C2214yes—
206#2334C2214yes—
207#2334C2214yes—
208#2333C2214yes—
209#2331C2211yescharacteristic
210#2331C2211yescharacteristic
211#2330C2212yes—
212#2330C2212yes—
213#2328C2211yescharacteristic
214#2328C2211yescharacteristic
215#2324C2212yes—
216#2324C2212yes—
217#2324C2212yes—
218#2324C2212yes—
219#2324C2214yes—
220#2322C2214yes—
221#2316C2211yescharacteristic
222#2316C2211yescharacteristic
223#2314C2212yes—
224#2314C2212yes—
225C4×C4⋊Q8C2212yes—
226C4×#125C2212yes—
227C4×#125C2212yes—
228C4×#125C2212yes—
229C4×C22⋊Q8C2214yes—
230#2297C2214yes—
231#2296C2214yes—
232#2293C2212yes—
233#2293C2212yes—
234#2293C2212yes—
235#2293C2212yes—
236#2293C2211yescharacteristic
237#2293C2211yescharacteristic
238#2293C2212yes—
239#2290C2214yes—
240#2285C2211yescharacteristic
241#2283C2211yescharacteristic
242#2283C2211yescharacteristic
243#2283C2212yes—
244#2274C2211yescharacteristic
245#2274C2211yescharacteristic
246C42×Q8C2211yescharacteristic
247C42×Q8C2211yescharacteristic
248C42×D4C2212yes—
249C4×#117C2211yescharacteristic
250C4×#117C2212yes—
251C22×#41C2311yescharacteristic
252C22×#41C2312yes—
253#532—28no—
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2312yes—
256C2×#127C2311yescharacteristic
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#125—28no—
263C2×#125C2312yes—
264C2×#125C2312yes—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#125C2314yes—
269C2×#124C2312yes—
270C2×#124C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C4×#41—28no—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2314yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×#117C2312yes—
298C2×#117C2312yes—
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2311yescharacteristic
302C2×#117C2311yescharacteristic
303C2×#117C2311yescharacteristic
304C2×#117C2312yes—
305C2×#117C2314yes—
306C2×#117C2314yes—
307C2×#117C2314yes—
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C42C2312yes—
313C22×C42C2314yes—
314C22×C42C2311yescharacteristic
315#401C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2312yes—
432#390C2312yes—
433#390C2314yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2312yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2314yes—
507#388C2312yes—
508#388C2312yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2312yes—
518#388C2312yes—
519#388C2312yes—
520#388C2312yes—
521#388C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#384C2312yes—
590#384C2312yes—
591#384C2312yes—
592#384C2312yes—
593#383C2314yes—
594#383C2312yes—
595#383C2311yescharacteristic
596#383C2311yescharacteristic
597#383C2312yes—
598#383C2312yes—
599#382C2312yes—
600#382C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2312yes—
604#382C2314yes—
605#382C2314yes—
606#382C2311yescharacteristic
607#382C2311yescharacteristic
608#382C2312yes—
609#382C2312yes—
610#381C2314yes—
611#381C2314yes—
612#381C2312yes—
613#381C2311yescharacteristic
614#381C2311yescharacteristic
615#381C2312yes—
616#381C2312yes—
617#380C2312yes—
618#380C2312yes—
619#380C2312yes—
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2311yescharacteristic
647C4×C4⋊C4C2311yescharacteristic
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685#376C2311yescharacteristic
686#376C2311yescharacteristic
687#376C2312yes—
688#376C2312yes—
689C43C2311yescharacteristic
690C43C2311yescharacteristic
691C43C2312yes—
692C43C2312yes—
693C2×#41—24no—
694C2×#41—28no—
695C2×#41—44no—
696C2×#41—84no—
697C22×Q8C2411yescharacteristic
698C22×Q8C2412yes—
699C22×Q8C2414yes—
700C22×D4C2412yes—
701C22×D4C2412yes—
702C22×D4C2411yescharacteristic
703C22×D4C2412yes—
704C22×D4C2414yes—
705C22×D4C2412yes—
706C22×D4C2414yes—
707C22×D4C2414yes—
708C23×C4C2412yes—
709C23×C4C2412yes—
710C23×C4C2411yescharacteristic
711C23×C4C2412yes—
712C23×C4C2412yes—
713C23×C4C2414yes—
714C23×C4C2414yes—
715C23×C4C2412yes—
716C23×C4C2414yes—
717C23×C4C2411yescharacteristic
718C23×C4C2411yescharacteristic
719C4⋊Q8—24no—
720C4⋊Q8—44no—
721#127—24no—
722#126—48no—
723#126—48no—
724#126—84no—
725#126—84no—
726#126—84no—
727#125—28no—
728#125—28no—
729#125—28no—
730#125—28no—
731#125—44no—
732#125—84no—
733#124—28no—
734#124—84no—
735#123—48no—
736#123—84no—
737#123—84no—
738#123—84no—
739C22⋊Q8—48no—
740C22⋊Q8—84no—
741#121—28no—
742#121—28no—
743#121—48no—
744#121—44no—
745#121—44no—
746#121—84no—
747C4×Q8—24no—
748C4×Q8—24no—
749C4×Q8—44no—
750C4×Q8—44no—
751C4×Q8—84no—
752C4×D4—28no—
753C4×D4—28no—
754C4×D4—24no—
755C4×D4—24no—
756C4×D4—28no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—44no—
760#117—24no—
761#117—28no—
762#117—24no—
763#117—28no—
764#117—42no—
765#117—44no—
766#117—48no—
767#117—42no—
768#117—42no—
769#117—84no—
770#117—84no—
771C2×C4⋊C4—24no—
772C2×C4⋊C4—24no—
773C2×C4⋊C4—28no—
774C2×C4⋊C4—28no—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C42—28no—
879C2×C42—84no—
880C2×C42#4118yes—
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2411yescharacteristic
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2414yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2411yescharacteristic
952#95C2411yescharacteristic
953#95C2411yescharacteristic
954#95C2411yescharacteristic
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979C24C2512yes—
980C24C2514yes—
981C24C2511yescharacteristic
982#41—416no—
983#41—816no—
984C2×Q8—22no—
985C2×Q8—24no—
986C2×Q8—24no—
987C2×Q8—44no—
988C2×Q8—44no—
989C2×Q8—44no—
990C2×Q8—44no—
991C2×D4—24no—
992C2×D4—28no—
993C2×D4—22no—
994C2×D4—24no—
995C2×D4—24no—
996C2×D4—24no—
997C2×D4—24no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—42no—
1001C2×D4—42no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—28no—
1019C22×C4—24no—
1020C22×C4—28no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—42no—
1034C22×C4—44no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4C2×#4114yes—
1039C22×C4C2×#4114yes—
1040C22×C4C2×#4114yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2511yescharacteristic
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—24no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—42no—
1154C22⋊C4—42no—
1155C22⋊C4—44no—
1156C22⋊C4—42no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—42no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—42no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C42—24no—
1169C42—24no—
1170C42—24no—
1171C42—22no—
1172C42—24no—
1173C42—22no—
1174C42—24no—
1175C42—22no—
1176C42—24no—
1177C42—24no—
1178C42—42no—
1179C42—44no—
1180C42—44no—
1181C42—44no—
1182C42—44no—
1183C42—42no—
1184C42—42no—
1185C42—42no—
1186C42—42no—
1187C42—44no—
1188C42—42no—
1189C42—42no—
1190C42—42no—
1191C42—42no—
1192C42—42no—
1193C42—44no—
1194C42—42no—
1195C42—44no—
1196C42—42no—
1197C42C2×#4114yes—
1198C42C2×#4114yes—
1199C42C2×#4114yes—
1200C42C2×#4114yes—
1201C422−1+414yes—
1202C23—21no—
1203C23—21no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—24no—
1208C23—22no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—22no—
1213C23—24no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—22no—
1219C23—24no—
1220C23C22×#4112yes—
1221C23C2611yescharacteristic
1222Q8—28no—
1223Q8—84no—
1224Q8—88no—
1225D4—48no—
1226D4—44no—
1227D4—48no—
1228D4—84no—
1229D4—84no—
1230D4—88no—
1231D4—164no—
1232D4—164no—
1233C2×C4—22no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—28no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—44no—
1293C2×C4—44no—
1294C2×C4—48no—
1295C2×C4—416no—
1296C2×C4—416no—
1297C2×C4—48no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—88no—
1302C2×C4C22×#4112yes—
1303C2×C4C22×#4112yes—
1304C2×C4C22×#4112yes—
1305C2×C4C22×#4112yes—
1306C2×C4C22×#4112yes—
1307C2×C4C22×#4112yes—
1308C2×C4C2×2−1+414yes—
1309C2×C4C2×2−1+412yes—
1310C2×C4#58514yes—
1311C2×C4#58512yes—
1312C22—22no—
1313C22—22no—
1314C22—22no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—44no—
1319C22—44no—
1320C22—42no—
1321C22—44no—
1322C22—42no—
1323C22—42no—
1324C22—44no—
1325C22—42no—
1326C22—44no—
1327C22—44no—
1328C22—42no—
1329C22—44no—
1330C22—42no—
1331C22C23×#4111yescharacteristic
1332C22C22×2−1+411yescharacteristic
1333C22C2×#58512yes—
1334C22C2×#58511yescharacteristic
1335C22H(7,𝔽2)12yes—
1336C4—22no—
1337C4—22no—
1338C4—24no—
1339C4—22no—
1340C4—22no—
1341C4—24no—
1342C4—22no—
1343C4—44no—
1344C4—44no—
1345C4—42no—
1346C4—44no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—44no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—44no—
1356C4—44no—
1357C4—44no—
1358C4—42no—
1359C4#346114yes—
1360C2—42no—
1361C2—82no—
1362C2—84no—
1363C2C2×#346111yescharacteristic
1364C2#6281411yescharacteristic
1365C2#6285511yescharacteristic
1366C2#6292612yes—
1367C2#6296912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35292C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41734C2semidirect
2. #41608C2semidirect
3. #41095C2semidirect
4. #40921C2semidirect
5. #40326C2semidirect
6. #40245C2semidirect
7. #38727C2semidirect
8. #38629C2semidirect
9. #37573C2semidirect
10. #37567C2semidirect
11. #37539C2semidirect
12. #37366C2semidirect
13. #37335C2semidirect
14. #37295C2semidirect
15. #37292C2semidirect
16. #35614C2semidirect
17. #35598C2semidirect
18. #35295C2semidirect
20. #35282C2semidirect
21. #35218C2semidirect
22. #35138C2semidirect
23. #35116C2semidirect
24. #34893C2semidirect
25. #34217C2semidirect
26. #34125C2semidirect
27. #34086C2semidirect

Maximal subgroups

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

subgroupindex
#417342
#416082
#410952
#409212
#403262
#402452
#387272
#386292
#375732
#375672
#375392
#373662
#373352
#372952
#372922
#356142
#355982
#352952
#352922
#352822
#352182
#351382
#351162
#348932
#342172
#341252
#340862