Finite Group Databasebeta

← #7652265

Subgroups — #7652265

Order 512.

4296 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42973C211yesmaximal, characteristic, complemented
2#42929C211yesmaximal, characteristic
3#42775C212yesmaximal, complemented
4#42695C211yesmaximal, characteristic, complemented
5#42553C212yesmaximal, complemented
6#42506C211yesmaximal, characteristic
7#41355C214yesmaximal, complemented
8#41192C214yesmaximal, complemented
9#41109C214yesmaximal, complemented
10#41000C214yesmaximal, complemented
11#40437C214yesmaximal
12#40155C212yesmaximal, complemented
13#39867C212yesmaximal, complemented
14#39673C214yesmaximal, complemented
15#39660C212yesmaximal, complemented
16#39604C212yesmaximal, complemented
17#38863C214yesmaximal, complemented
18#38711C214yesmaximal, complemented
19#35599C212yesmaximal, complemented
20#35596C212yesmaximal, complemented
21#35578C212yesmaximal, complemented
22#35324C211yesmaximal, characteristic, complemented
23#35204C212yesmaximal, complemented
24#34950C212yesmaximal, complemented
25#34881C211yesmaximal, characteristic
26#34322C212yesmaximal, complemented
27#34214C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#533C2211yescharacteristic
30#2865C2214yes—
31#2864C2214yes—
32#2864C2211yescharacteristic
33#2862C2211yescharacteristic
34#2855C2212yes—
35#2844C2212yes—
36#2839C2214yes—
37#2838C2214yes—
38#2834C2212yes—
39#2834C2212yes—
40#2823C2212yes—
41#2792C2212yes—
42#2792C2214yes—
43#2791C2214yes—
44#2791C2214yes—
45#2790C2214yes—
46#2789C2212yes—
47#2789C2214yes—
48#2774C2214yes—
49#2774C2214yes—
50#2772C2214yes—
51#2769C2212yes—
52#2766C2214yes—
53#2765C2214yes—
54#2763C2214yes—
55#2763C2212yes—
56#2762C2214yes—
57#2755C2214yes—
58#2755C2214yes—
59#2755C2214yes—
60#2754C2214yes—
61#2729C2214yes—
62#2722C2212yes—
63#2720C2214yes—
64#2720C2214yes—
65#2719C2214yes—
66#2718C2214yes—
67#2716C2214yes—
68#2715C2214yes—
69#2712C2212yes—
70#2700C2214yes—
71#2698C2214yes—
72#2698C2214yes—
73#2689C2214yes—
74#2680C2212yes—
75#2677C2212yes—
76#2674C2214yes—
77#2666C2214yes—
78#2663C2214yes—
79#2660C2214yes—
80#2655C2214yes—
81#2655C2214yes—
82#2654C2214yes—
83#2652C2214yes—
84#2647C2214yes—
85#2645C2212yes—
86#2638C2214yes—
87#2637C2214yes—
88#2637C2214yes—
89#2637C2214yes—
90#2634C2214yes—
91#2628C2211yescharacteristic
92#2627C2214yes—
93#2621C2211yescharacteristic
94#2612C2212yes—
95#2604C2214yes—
96#2597C2214yes—
97#2596C2214yes—
98#2594C2214yes—
99#2593C2212yes—
100#2590C2214yes—
101#2590C2214yes—
102#2590C2214yes—
103#2589C2214yes—
104#2588C2214yes—
105#2588C2214yes—
106#2586C2214yes—
107#2586C2214yes—
108#2586C2214yes—
109#2585C2214yes—
110#2585C2212yes—
111#2582C2212yes—
112#2582C2212yes—
113#2581C2214yes—
114#2575C2214yes—
115#2573C2214yes—
116#2573C2212yes—
117#2570C2212yes—
118#2567C2212yes—
119#2567C2212yes—
120#2560C2214yes—
121#2558C2214yes—
122#2556C2214yes—
123#2554C2212yes—
124#2552C2212yes—
125#2551C2212yes—
126#2551C2212yes—
127#2550C2212yes—
128#2532C2214yes—
129#2530C2214yes—
130#2529C2214yes—
131#2529C2214yes—
132#2528C2214yes—
133#2528C2214yes—
134#2528C2214yes—
135#2527C2214yes—
136#2527C2214yes—
137#2527C2214yes—
138#2525C2212yes—
139#2523C2212yes—
140#2516C2212yes—
141#2514C2212yes—
142#2511C2212yes—
143#2511C2212yes—
144#2508C2212yes—
145#2508C2212yes—
146#2507C2212yes—
147#2507C2214yes—
148#2507C2212yes—
149#2506C2212yes—
150#2502C2212yes—
151#2499C2212yes—
152#2497C2212yes—
153#2496C2212yes—
154#2494C2212yes—
155#2492C2212yes—
156#2492C2212yes—
157#2489C2212yes—
158#2486C2212yes—
159#2485C2212yes—
160#2473C2214yes—
161#2469C2214yes—
162#2469C2214yes—
163#2469C2212yes—
164#2465C2214yes—
165#2465C2214yes—
166#2462C2214yes—
167#2458C2214yes—
168#2458C2212yes—
169#2455C2212yes—
170#2453C2214yes—
171#2453C2212yes—
172#2453C2214yes—
173#2451C2214yes—
174#2451C2212yes—
175#2451C2212yes—
176#2451C2214yes—
177#2451C2214yes—
178#2449C2214yes—
179#2446C2212yes—
180#2441C2212yes—
181#2440C2212yes—
182#2440C2212yes—
183#2440C2212yes—
184#2439C2212yes—
185#2439C2212yes—
186#2429C2212yes—
187#2429C2214yes—
188#2423C2212yes—
189#2421C2214yes—
190#2417C2212yes—
191#2415C2212yes—
192#2402C2211yescharacteristic
193#2399C2214yes—
194#2399C2214yes—
195#2398C2211yescharacteristic
196#2396C2211yescharacteristic
197#2392C2211yescharacteristic
198#2373C2214yes—
199#2373C2214yes—
200#2367C2214yes—
201#2365C2212yes—
202#2360C2212yes—
203#2360C2212yes—
204#2360C2214yes—
205#2360C2214yes—
206#2355C2212yes—
207#2355C2214yes—
208#2351C2214yes—
209Q8×C4⋊C4C2214yes—
210D4×C4⋊C4C2212yes—
211#2346C2212yes—
212#2346C2212yes—
213#2334C2214yes—
214#2334C2214yes—
215#2334C2214yes—
216#2331C2211yescharacteristic
217#2330C2212yes—
218#2330C2212yes—
219#2327C2214yes—
220#2327C2211yescharacteristic
221#2327C2214yes—
222#2323C2212yes—
223#2323C2212yes—
224#2323C2212yes—
225#2322C2214yes—
226#2317C2211yescharacteristic
227#2317C2211yescharacteristic
228#2314C2212yes—
229C4×C4⋊Q8C2212yes—
230C4×C4⋊Q8C2212yes—
231C4×C4⋊Q8C2212yes—
232C4×C4⋊Q8C2214yes—
233C4×C4⋊Q8C2212yes—
234C4×#126C2212yes—
235C4×#124C2214yes—
236C4×#123C2212yes—
237#2298C2212yes—
238#2295C2212yes—
239#2295C2212yes—
240#2295C2214yes—
241#2295C2214yes—
242#2293C2212yes—
243#2293C2211yescharacteristic
244C2×#384C2211yescharacteristic
245#2274C2211yescharacteristic
246#2274C2212yes—
247#2274C2211yescharacteristic
248C42×Q8C2212yes—
249C42×Q8C2211yescharacteristic
250C4×#117C2211yescharacteristic
251#556—216no—
252#533—28no—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2314yes—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2312yes—
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2314yes—
260C2×#126C2312yes—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#126C2314yes—
264C2×#125C2312yes—
265C2×#125C2314yes—
266C2×#125C2314yes—
267C2×#124C2314yes—
268C2×#123C2312yes—
269C2×#123C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2314yes—
288C2×C4×Q8C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2314yes—
292C2×#117C2312yes—
293C2×#117C2311yescharacteristic
294C2×#117C2311yescharacteristic
295C2×#117C2312yes—
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2314yes—
302C22×C42C2311yescharacteristic
303#401C2314yes—
304#401C2314yes—
305#401C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2312yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2311yescharacteristic
323#400C2314yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#399C2312yes—
331#399C2311yescharacteristic
332#399C2314yes—
333#399C2314yes—
334#398C2314yes—
335#398C2312yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2311yescharacteristic
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2312yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#397C2314yes—
367#397C2311yescharacteristic
368#397C2314yes—
369#397C2312yes—
370#397C2312yes—
371#397C2314yes—
372#397C2312yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2312yes—
383#396C2314yes—
384#396C2314yes—
385#396C2312yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2312yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2311yescharacteristic
401#395C2314yes—
402#394C2314yes—
403#394C2311yescharacteristic
404#394C2314yes—
405#394C2312yes—
406#394C2312yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2312yes—
411#393C2314yes—
412#393C2311yescharacteristic
413#393C2312yes—
414#392C2311yescharacteristic
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#388C2312yes—
489#388C2312yes—
490#388C2312yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2312yes—
496#388C2314yes—
497#388C2312yes—
498#388C2312yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2312yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2312yes—
512#388C2312yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2314yes—
518#388C2312yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2312yes—
535#387C2312yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2312yes—
565#387C2314yes—
566#387C2312yes—
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#386C2314yes—
587#386C2312yes—
588#385C2312yes—
589#385C2312yes—
590#385C2312yes—
591#385C2312yes—
592#385C2314yes—
593#385C2312yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#384C2312yes—
604#384C2312yes—
605#384C2314yes—
606#384C2312yes—
607#384C2312yes—
608#384C2312yes—
609#384C2312yes—
610#384C2312yes—
611#384C2314yes—
612#383C2312yes—
613#383C2314yes—
614#382C2312yes—
615#382C2311yescharacteristic
616#382C2312yes—
617#382C2312yes—
618#382C2314yes—
619#382C2314yes—
620#382C2311yescharacteristic
621#382C2314yes—
622#382C2314yes—
623#382C2314yes—
624#382C2314yes—
625#382C2314yes—
626#381C2312yes—
627#381C2314yes—
628#381C2314yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682#376C2311yescharacteristic
683#376C2314yes—
684#376C2314yes—
685#376C2311yescharacteristic
686#376C2314yes—
687#376C2314yes—
688C43C2311yescharacteristic
689C43C2311yescharacteristic
690C43C2312yes—
691C43C2314yes—
692C22×Q8C2412yes—
693C22×Q8C2414yes—
694C22×Q8C2414yes—
695C22×Q8C2411yescharacteristic
696C22×Q8C2414yes—
697C22×Q8C2412yes—
698C22×D4C2412yes—
699C22×D4C2411yescharacteristic
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2414yes—
706C4⋊Q8—28no—
707C4⋊Q8—28no—
708C4⋊Q8—216no—
709C4⋊Q8—42no—
710C4⋊Q8—44no—
711C4⋊Q8—42no—
712C4⋊Q8—84no—
713#126—28no—
714#126—216no—
715#126—216no—
716#126—84no—
717#125—28no—
718#125—84no—
719#125—84no—
720#124—216no—
721#123—28no—
722#123—84no—
723C22⋊Q8—28no—
724C22⋊Q8—28no—
725C22⋊Q8—216no—
726C22⋊Q8—44no—
727C22⋊Q8—84no—
728C22⋊Q8—84no—
729C22⋊Q8—84no—
730C4×Q8—28no—
731C4×Q8—28no—
732C4×Q8—216no—
733C4×Q8—216no—
734C4×Q8—28no—
735C4×Q8—42no—
736C4×Q8—44no—
737C4×Q8—84no—
738C4×Q8—84no—
739C4×Q8—84no—
740C4×Q8—84no—
741C4×Q8—84no—
742C4×D4—28no—
743C4×D4—42no—
744C4×D4—84no—
745#117—24no—
746#117—28no—
747#117—24no—
748#117—28no—
749#117—42no—
750#117#4118yes—
751C2×C4⋊C4—42no—
752C2×C4⋊C4—44no—
753C2×C4⋊C4—42no—
754C2×C4⋊C4—84no—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2411yescharacteristic
840C2×C22⋊C4C2411yescharacteristic
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C42—24no—
854C2×C42C2411yescharacteristic
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2411yescharacteristic
858C2×C42C2411yescharacteristic
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2411yescharacteristic
869C2×C42C2412yes—
870C2×C42C2411yescharacteristic
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887#95C2412yes—
888#95C2412yes—
889#95C2414yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2414yes—
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2411yescharacteristic
929#95C2411yescharacteristic
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2411yescharacteristic
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2411yescharacteristic
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965C24C2512yes—
966C24C2511yescharacteristic
967C2×Q8—24no—
968C2×Q8—28no—
969C2×Q8—28no—
970C2×Q8—24no—
971C2×Q8—24no—
972C2×Q8—28no—
973C2×Q8—28no—
974C2×Q8—24no—
975C2×Q8—41no—
976C2×Q8—44no—
977C2×Q8—44no—
978C2×Q8—44no—
979C2×Q8—44no—
980C2×Q8—44no—
981C2×Q8—44no—
982C2×Q8—42no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—42no—
986C2×D4—41no—
987C2×D4—42no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4C2×#4114yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2514yes—
1011C22×C4C2512yes—
1012C22×C4C2514yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2514yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2511yescharacteristic
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—41no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4C2×#4118yes—
1097C4⋊C42−1+418yes—
1098C22⋊C4—24no—
1099C22⋊C4—24no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—24no—
1103C22⋊C4—28no—
1104C22⋊C4—24no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—24no—
1108C22⋊C4—24no—
1109C22⋊C4—24no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—24no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—42no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—42no—
1126C22⋊C4C2×#4118yes—
1127C42—24no—
1128C42—22no—
1129C42—22no—
1130C42—24no—
1131C42—28no—
1132C42—24no—
1133C42—28no—
1134C42—22no—
1135C42—24no—
1136C42—24no—
1137C42—24no—
1138C42—24no—
1139C42—28no—
1140C42—24no—
1141C42—28no—
1142C42—22no—
1143C42—22no—
1144C42—24no—
1145C42—44no—
1146C42—44no—
1147C42—44no—
1148C42—42no—
1149C42—42no—
1150C42—44no—
1151C42—44no—
1152C42—42no—
1153C42—44no—
1154C42—42no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42C2×#4118yes—
1159C422−1+414yes—
1160C23—21no—
1161C23—22no—
1162C23—21no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23C22×#4112yes—
1172C23C2611yescharacteristic
1173Q8—416no—
1174Q8—416no—
1175Q8—44no—
1176Q8—48no—
1177Q8—88no—
1178Q8—162no—
1179D4—48no—
1180D4—82no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—21no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—28no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—48no—
1245C2×C4—48no—
1246C2×C4—162no—
1247C2×C4—164no—
1248C2×C4—162no—
1249C2×C4C22×#4112yes—
1250C2×C4C22×#4118yes—
1251C2×C4C22×#4112yes—
1252C2×C4C2×2−1+414yes—
1253C2×C4C2×2−1+414yes—
1254C2×C4C2×2−1+414yes—
1255C2×C4C2×2−1+414yes—
1256C2×C4C2×2−1+412yes—
1257C2×C4#58512yes—
1258C22—24no—
1259C22—22no—
1260C22—41no—
1261C22—41no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22C23×#4111yescharacteristic
1271C22C22×2−1+412yes—
1272C22C22×2−1+411yescharacteristic
1273C22C2×#58511yescharacteristic
1274C22H(7,𝔽2)12yes—
1275C4—24no—
1276C4—28no—
1277C4—24no—
1278C4—24no—
1279C4—22no—
1280C4—24no—
1281C4—42no—
1282C4—42no—
1283C4—44no—
1284C4—44no—
1285C4—41no—
1286C4—41no—
1287C4—44no—
1288C4—44no—
1289C4—44no—
1290C4—41no—
1291C4—42no—
1292C4—41no—
1293C4—42no—
1294C4—44no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—44no—
1299C4#346114yes—
1300C2—42no—
1301C2—82no—
1302C2C2×#346111yescharacteristic
1303C2#6283711yescharacteristic
1304C2#6288511yescharacteristic
1305C2#6294312yes—
1306C2#6300012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42973C2semidirect
3. #42775C2semidirect
4. #42695C2semidirect
5. #42553C2semidirect
7. #41355C2semidirect
8. #41192C2semidirect
9. #41109C2semidirect
10. #41000C2semidirect
12. #40155C2semidirect
13. #39867C2semidirect
14. #39673C2semidirect
15. #39660C2semidirect
16. #39604C2semidirect
17. #38863C2semidirect
18. #38711C2semidirect
19. #35599C2semidirect
20. #35596C2semidirect
21. #35578C2semidirect
22. #35324C2semidirect
23. #35204C2semidirect
24. #34950C2semidirect
26. #34322C2semidirect
27. #34214C2semidirect

Maximal subgroups

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

subgroupindex
#429732
#429292
#427752
#426952
#425532
#425062
#413552
#411922
#411092
#410002
#404372
#401552
#398672
#396732
#396602
#396042
#388632
#387112
#355992
#355962
#355782
#353242
#352042
#349502
#348812
#343222
#342142