Finite Group Databasebeta

← #7715606

Subgroups — #7715606

Order 512.

4368 conjugacy classes of subgroups.

The subgroup lattice has 1329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48978C214yesmaximal, complemented
2#48918C214yesmaximal, complemented
3#48123C214yesmaximal, complemented
4#48053C214yesmaximal, complemented
5#47532C214yesmaximal, complemented
6#47528C214yesmaximal, complemented
7#46960C214yesmaximal, complemented
8#46956C214yesmaximal, complemented
9#39081C212yesmaximal, complemented
10#39080C212yesmaximal, complemented
11#39065C212yesmaximal, complemented
12#39064C212yesmaximal, complemented
13#38069C212yesmaximal, complemented
14#38068C212yesmaximal, complemented
15#38061C212yesmaximal, complemented
16#38060C212yesmaximal, complemented
17#37522C211yesmaximal, characteristic, complemented
18#37520C211yesmaximal, characteristic, complemented
19#37418C211yesmaximal, characteristic
20#37326C212yesmaximal, complemented
21#37307C211yesmaximal, characteristic, complemented
22#35321C211yesmaximal, characteristic, complemented
23#35287C211yesmaximal, characteristic, complemented
24#35270C212yesmaximal, complemented
25#35255C212yesmaximal, complemented
26#34410C212yesmaximal, complemented
27#34056C211yesmaximal, characteristic, complemented
28C2×#537C2212yes—
29C2×C4×#41C2211yescharacteristic
30#2863C2212yes—
31#2860C2212yes—
32#2857C2212yes—
33#2855C2212yes—
34#2855C2212yes—
35#2854C2212yes—
36#2854C2212yes—
37#2850C2212yes—
38#2839C2214yes—
39#2837C2214yes—
40#2807C2214yes—
41#2806C2214yes—
42#2798C2214yes—
43#2794C2214yes—
44#2793C2214yes—
45#2786C2214yes—
46#2783C2214yes—
47#2775C2214yes—
48#2774C2214yes—
49#2773C2214yes—
50#2772C2214yes—
51#2770C2214yes—
52#2767C2214yes—
53#2767C2214yes—
54#2766C2214yes—
55#2758C2214yes—
56#2757C2214yes—
57#2752C2214yes—
58#2750C2214yes—
59#2750C2214yes—
60#2750C2214yes—
61#2749C2214yes—
62#2749C2214yes—
63#2748C2214yes—
64#2746C2214yes—
65#2744C2214yes—
66#2743C2214yes—
67#2743C2214yes—
68#2743C2214yes—
69#2742C2214yes—
70#2740C2214yes—
71#2738C2214yes—
72#2737C2214yes—
73#2732C2214yes—
74#2728C2214yes—
75#2728C2214yes—
76#2723C2214yes—
77#2723C2214yes—
78#2722C2214yes—
79#2706C2214yes—
80#2705C2214yes—
81#2699C2214yes—
82#2698C2214yes—
83#2696C2214yes—
84#2689C2214yes—
85#2688C2214yes—
86#2688C2214yes—
87#2683C2214yes—
88#2652C2214yes—
89#2652C2214yes—
90#2647C2212yes—
91#2647C2211yescharacteristic
92#2647C2211yescharacteristic
93#2645C2212yes—
94#2644C2212yes—
95#2642C2211yescharacteristic
96#2641C2211yescharacteristic
97#2640C2212yes—
98#2636C2214yes—
99#2630C2214yes—
100#2629C2211yescharacteristic
101#2629C2211yescharacteristic
102#2625C2212yes—
103#2625C2212yes—
104#2624C2212yes—
105#2624C2212yes—
106#2621C2211yescharacteristic
107#2619C2211yescharacteristic
108#2601C2214yes—
109#2600C2214yes—
110#2595C2214yes—
111#2593C2214yes—
112#2585C2214yes—
113#2585C2214yes—
114#2578C2214yes—
115#2577C2214yes—
116#2575C2214yes—
117#2575C2214yes—
118#2575C2214yes—
119#2574C2214yes—
120#2573C2214yes—
121#2573C2214yes—
122#2570C2214yes—
123#2564C2214yes—
124#2560C2214yes—
125#2554C2214yes—
126#2553C2214yes—
127#2553C2214yes—
128#2532C2214yes—
129#2530C2214yes—
130#2529C2214yes—
131#2527C2214yes—
132#2524C2214yes—
133#2524C2214yes—
134#2518C2214yes—
135#2518C2214yes—
136#2515C2214yes—
137#2515C2214yes—
138#2512C2212yes—
139#2512C2212yes—
140#2511C2212yes—
141#2511C2212yes—
142#2510C2214yes—
143#2509C2212yes—
144#2509C2212yes—
145#2508C2212yes—
146#2508C2212yes—
147#2505C2214yes—
148#2504C2212yes—
149#2503C2214yes—
150#2503C2212yes—
151#2496C2214yes—
152#2493C2214yes—
153#2493C2214yes—
154#2488C2214yes—
155#2488C2214yes—
156#2484C2214yes—
157#2481C2214yes—
158#2479C2214yes—
159#2468C2214yes—
160#2463C2214yes—
161#2457C2214yes—
162#2454C2212yes—
163#2453C2212yes—
164#2452C2212yes—
165#2451C2212yes—
166#2450C2214yes—
167#2448C2212yes—
168#2447C2212yes—
169#2446C2212yes—
170#2445C2212yes—
171#2444C2214yes—
172#2444C2214yes—
173#2443C2214yes—
174#2443C2214yes—
175#2441C2212yes—
176#2441C2212yes—
177#2440C2212yes—
178#2440C2212yes—
179#2438C2214yes—
180#2432C2212yes—
181#2431C2212yes—
182#2423C2214yes—
183#2422C2214yes—
184#2421C2214yes—
185#2420C2214yes—
186#2419C2214yes—
187#2419C2214yes—
188#2419C2214yes—
189#2417C2214yes—
190#2377C2214yes—
191#2377C2214yes—
192#2364C2214yes—
193#2363C2214yes—
194#2363C2212yes—
195#2362C2212yes—
196#2361C2212yes—
197#2360C2212yes—
198#2345C2212yes—
199#2344C2212yes—
200#2341C2212yes—
201#2339C2212yes—
202#2333C2214yes—
203#2332C2214yes—
204#2331C2212yes—
205#2329C2214yes—
206#2326C2212yes—
207#2324C2214yes—
208#2324C2212yes—
209#2323C2212yes—
210#2320C2212yes—
211#2320C2212yes—
212#2320C2212yes—
213#2320C2212yes—
214#2319C2212yes—
215#2319C2212yes—
216#2319C2212yes—
217#2319C2212yes—
218#2318C2212yes—
219#2318C2212yes—
220#2318C2212yes—
221#2318C2212yes—
222#2317C2212yes—
223#2311C2212yes—
224#2311C2212yes—
225C4×C4⋊Q8C2211yescharacteristic
226C4×#127C2211yescharacteristic
227C4×#125C2211yescharacteristic
228C4×#125C2211yescharacteristic
229C4×C22⋊Q8C2212yes—
230C4×#121C2212yes—
231#2298C2212yes—
232#2298C2212yes—
233#2297C2211yescharacteristic
234#2297C2211yescharacteristic
235#2297C2212yes—
236#2296C2211yescharacteristic
237#2296C2211yescharacteristic
238C2×#389C2212yes—
239#2283C2212yes—
240#2283C2212yes—
241C4×#117C2211yescharacteristic
242C2×#376C2211yescharacteristic
243C22×#41C2312yes—
244C22×#41C2311yescharacteristic
245#537—216no—
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2312yes—
248C2×#127C2311yescharacteristic
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#125C2311yescharacteristic
253C2×#125C2311yescharacteristic
254C2×#124C2312yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×#121C2314yes—
266C2×#121C2312yes—
267C2×#121C2312yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C4×#41—28no—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×#117C2312yes—
283C2×#117C2311yescharacteristic
284C2×#117C2312yes—
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2314yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2314yes—
291C22×C42C2311yescharacteristic
292C22×C42C2312yes—
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295#401C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#392C2314yes—
389#392C2314yes—
390#392C2314yes—
391#391C2314yes—
392#391C2312yes—
393#391C2314yes—
394#391C2312yes—
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2312yes—
405#391C2314yes—
406#391C2312yes—
407#390C2314yes—
408#390C2312yes—
409#390C2314yes—
410#390C2312yes—
411#390C2314yes—
412#390C2311yescharacteristic
413#390C2311yescharacteristic
414#390C2312yes—
415#390C2312yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#390C2312yes—
423#390C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2312yes—
430#389C2312yes—
431#389C2314yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2312yes—
444#389C2312yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#388C2312yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2312yes—
462#388C2312yes—
463#388C2312yes—
464#388C2312yes—
465#388C2312yes—
466#388C2312yes—
467#388C2312yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2312yes—
494#387C2314yes—
495#387C2312yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2312yes—
504#387C2312yes—
505#387C2312yes—
506#387C2312yes—
507#387C2312yes—
508#387C2312yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
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#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2312yes—
542#386C2312yes—
543#386C2312yes—
544#386C2312yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2312yes—
567#385C2312yes—
568#385C2311yescharacteristic
569#385C2311yescharacteristic
570#385C2311yescharacteristic
571#385C2311yescharacteristic
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#384C2311yescharacteristic
584#384C2311yescharacteristic
585#384C2314yes—
586#384C2312yes—
587#383C2312yes—
588#383C2314yes—
589#383C2312yes—
590#383C2312yes—
591#383C2312yes—
592#383C2314yes—
593#383C2314yes—
594#382C2311yescharacteristic
595#382C2311yescharacteristic
596#382C2314yes—
597#382C2314yes—
598#382C2314yes—
599#382C2312yes—
600#382C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2314yes—
604#382C2314yes—
605#382C2312yes—
606#381C2314yes—
607#381C2314yes—
608#381C2312yes—
609#381C2312yes—
610#381C2312yes—
611#381C2312yes—
612#381C2314yes—
613#381C2314yes—
614#381C2314yes—
615#381C2314yes—
616#381C2314yes—
617#381C2314yes—
618#381C2314yes—
619#380C2314yes—
620#380C2314yes—
621#380C2314yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2314yes—
631#380C2314yes—
632#380C2314yes—
633#380C2314yes—
634#380C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664#376C2311yescharacteristic
665#376C2312yes—
666#376C2312yes—
667#376C2312yes—
668#376C2311yescharacteristic
669#376C2312yes—
670C2×#95C2314yes—
671C2×#95C2312yes—
672C2×#95C2312yes—
673C2×#95C2314yes—
674C43C2311yescharacteristic
675C43C2311yescharacteristic
676C2×#41—28no—
677C2×#41—42no—
678C2×#41—42no—
679C2×#41—44no—
680C2×#41—44no—
681C2×#41#4118yes—
682C22×Q8C2412yes—
683C22×Q8C2414yes—
684C22×Q8C2411yescharacteristic
685C22×D4C2412yes—
686C22×D4C2414yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2414yes—
690C22×D4C2412yes—
691C22×D4C2411yescharacteristic
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2414yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2414yes—
701C23×C4C2414yes—
702C23×C4C2412yes—
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C4⋊Q8—44no—
706C4⋊Q8—42no—
707#127—42no—
708#126—84no—
709#126—84no—
710#126—84no—
711#125—42no—
712#125—42no—
713#124—44no—
714#123—84no—
715#123—84no—
716#123—84no—
717C22⋊Q8—216no—
718C22⋊Q8—28no—
719C22⋊Q8—28no—
720C22⋊Q8—84no—
721C22⋊Q8—84no—
722C22⋊Q8—84no—
723C22⋊Q8—84no—
724#121—216no—
725#121—216no—
726#121—216no—
727#121—28no—
728#121—28no—
729C4×Q8—28no—
730C4×Q8—44no—
731C4×Q8—44no—
732C4×D4—28no—
733C4×D4—28no—
734C4×D4—28no—
735C4×D4—44no—
736C4×D4—44no—
737C4×D4—84no—
738C4×D4—84no—
739C4×D4—84no—
740#117—28no—
741#117—24no—
742#117—42no—
743#117—42no—
744#117—44no—
745#117—84no—
746C2×C4⋊C4—28no—
747C2×C4⋊C4—44no—
748C2×C4⋊C4—84no—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C42—28no—
844C2×C42—24no—
845C2×C42—42no—
846C2×C42—42no—
847C2×C42C2411yescharacteristic
848C2×C42C2412yes—
849C2×C42C2411yescharacteristic
850C2×C42C2411yescharacteristic
851C2×C42C2411yescharacteristic
852C2×C42C2411yescharacteristic
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2411yescharacteristic
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2412yes—
872C2×C42C2414yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945C24C2514yes—
946C24C2511yescharacteristic
947C24C2512yes—
948#41—416no—
949#41—816no—
950C2×Q8—24no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—41no—
954C2×Q8—41no—
955C2×Q8—44no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×Q8C2×#4114yes—
959C2×D4—28no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—24no—
963C2×D4—24no—
964C2×D4—24no—
965C2×D4—41no—
966C2×D4—41no—
967C2×D4—42no—
968C2×D4—42no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4C2×#4114yes—
979C2×D4C2×#4118yes—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—28no—
988C22×C4—28no—
989C22×C4—42no—
990C22×C4—41no—
991C22×C4—41no—
992C22×C4—44no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—44no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4C2×#4118yes—
1016C22×C4C2×#4114yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2511yescharacteristic
1023C22×C4C2512yes—
1024C22×C4C2511yescharacteristic
1025C22×C4C2514yes—
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C4⋊C4—28no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—42no—
1066C4⋊C4—41no—
1067C4⋊C4—42no—
1068C4⋊C4—41no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—24no—
1094C22⋊C4—24no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—42no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—44no—
1105C22⋊C4—42no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—41no—
1109C22⋊C4—41no—
1110C22⋊C4—42no—
1111C22⋊C4—44no—
1112C22⋊C4—42no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—42no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C42—22no—
1136C42—22no—
1137C42—24no—
1138C42—24no—
1139C42—24no—
1140C42—24no—
1141C42—24no—
1142C42—24no—
1143C42—22no—
1144C42—22no—
1145C42—22no—
1146C42—22no—
1147C42—41no—
1148C42—42no—
1149C42—41no—
1150C42—42no—
1151C42—44no—
1152C42—42no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—42no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—42no—
1161C23—21no—
1162C23—21no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23C22×#4112yes—
1179C23C22×#4114yes—
1180C23C2611yescharacteristic
1181Q8—44no—
1182Q8—48no—
1183Q8—164no—
1184D4—48no—
1185D4—44no—
1186D4—48no—
1187D4—88no—
1188D4—88no—
1189D4—88no—
1190D4—88no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—28no—
1196C2×C4—216no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—88no—
1257C2×C4—84no—
1258C2×C4—84no—
1259C2×C4—84no—
1260C2×C4—88no—
1261C2×C4—88no—
1262C2×C4—82no—
1263C2×C4—84no—
1264C2×C4—82no—
1265C2×C4—164no—
1266C2×C4—164no—
1267C2×C4C22×#4112yes—
1268C2×C4C22×#4114yes—
1269C2×C4C22×#4112yes—
1270C2×C4#58512yes—
1271C2×C4#58512yes—
1272C22—24no—
1273C22—22no—
1274C22—24no—
1275C22—24no—
1276C22—24no—
1277C22—42no—
1278C22—41no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—41no—
1283C22—42no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—44no—
1291C22C23×#4111yescharacteristic
1292C22C2×#58511yescharacteristic
1293C22C2×#58511yescharacteristic
1294C22H(7,𝔽2)12yes—
1295C222−1+612yes—
1296C4—24no—
1297C4—22no—
1298C4—44no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—44no—
1304C4—44no—
1305C4—41no—
1306C4—44no—
1307C4—44no—
1308C4—42no—
1309C4—41no—
1310C4—42no—
1311C4—44no—
1312C4—42no—
1313C4—42no—
1314C4—44no—
1315C4—42no—
1316C4—41no—
1317C4—41no—
1318C4—42no—
1319C4#349114yes—
1320C2—44no—
1321C2—42no—
1322C2—84no—
1323C2C2×#349111yescharacteristic
1324C2#6285712yes—
1325C2#6288311yescharacteristic
1326C2#6288412yes—
1327C2#6289011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37418C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48978C2semidirect
2. #48918C2semidirect
3. #48123C2semidirect
4. #48053C2semidirect
5. #47532C2semidirect
6. #47528C2semidirect
7. #46960C2semidirect
8. #46956C2semidirect
9. #39081C2semidirect
10. #39080C2semidirect
11. #39065C2semidirect
12. #39064C2semidirect
13. #38069C2semidirect
14. #38068C2semidirect
15. #38061C2semidirect
16. #38060C2semidirect
17. #37522C2semidirect
18. #37520C2semidirect
20. #37326C2semidirect
21. #37307C2semidirect
22. #35321C2semidirect
23. #35287C2semidirect
24. #35270C2semidirect
25. #35255C2semidirect
26. #34410C2semidirect
27. #34056C2semidirect

Maximal subgroups

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

subgroupindex
#489782
#489182
#481232
#480532
#475322
#475282
#469602
#469562
#390812
#390802
#390652
#390642
#380692
#380682
#380612
#380602
#375222
#375202
#374182
#373262
#373072
#353212
#352872
#352702
#352552
#344102
#340562