Finite Group Databasebeta

← #7642645

Subgroups — #7642645

Order 512.

4554 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39254C214yesmaximal, complemented
2#39083C212yesmaximal, complemented
3#39082C212yesmaximal, complemented
4#39069C212yesmaximal, complemented
5#39068C212yesmaximal, complemented
6#39050C214yesmaximal, complemented
7#38267C212yesmaximal, complemented
8#38266C212yesmaximal, complemented
9#38253C212yesmaximal, complemented
10#38252C212yesmaximal, complemented
11#38223C214yesmaximal, complemented
12#38210C214yesmaximal, complemented
13#37018C214yesmaximal, complemented
14#37012C214yesmaximal, complemented
15#36638C212yesmaximal, complemented
16#35502C214yesmaximal, complemented
17#35487C214yesmaximal, complemented
18#35315C211yesmaximal, characteristic, complemented
19#35271C211yesmaximal, characteristic, complemented
20#35263C212yesmaximal, complemented
21#35087C211yesmaximal, characteristic, complemented
22#35082C211yesmaximal, characteristic, complemented
23#35032C211yesmaximal, characteristic
24#35024C212yesmaximal, complemented
25#35020C211yesmaximal, characteristic, complemented
26#34233C212yesmaximal, complemented
27C2×#2298C211yesmaximal, characteristic, complemented
28C2×#525C2212yes—
29C22×#117C2211yescharacteristic
30#2866C2214yescomplemented
31#2865C2214yescomplemented
32#2864C2212yescomplemented
33#2863C2212yescomplemented
34#2861C2212yescomplemented
35#2860C2212yescomplemented
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2855C2212yes—
39#2855C2212yes—
40#2854C2212yes—
41#2854C2212yes—
42#2853C2214yes—
43#2852C2214yes—
44#2851C2211yescharacteristic
45#2851C2211yescharacteristic
46#2851C2212yes—
47#2850C2212yes—
48#2796C2214yes—
49#2787C2214yes—
50#2786C2214yes—
51#2781C2214yes—
52#2779C2214yes—
53#2778C2214yes—
54#2778C2214yes—
55#2776C2214yescomplemented
56#2773C2214yescomplemented
57#2772C2214yescomplemented
58#2770C2214yes—
59#2770C2214yescomplemented
60#2767C2214yescomplemented
61#2766C2214yescomplemented
62#2766C2214yescomplemented
63#2756C2214yes—
64#2753C2214yes—
65#2750C2214yes—
66#2747C2214yes—
67#2747C2214yes—
68#2747C2214yescomplemented
69#2747C2214yescomplemented
70#2746C2214yes—
71#2746C2214yescomplemented
72#2743C2214yescomplemented
73#2741C2214yes—
74#2741C2214yes—
75#2741C2214yescomplemented
76#2741C2214yescomplemented
77#2739C2214yescomplemented
78#2738C2214yescomplemented
79#2738C2214yescomplemented
80#2655C2214yescomplemented
81#2651C2214yescomplemented
82#2647C2211yescharacteristic, complemented
83#2647C2211yescharacteristic, complemented
84#2646C2214yes—
85#2645C2212yescomplemented
86#2644C2212yescomplemented
87#2643C2214yes—
88#2642C2211yescharacteristic, complemented
89#2641C2211yescharacteristic, complemented
90#2625C2212yes—
91#2625C2212yes—
92#2624C2212yes—
93#2624C2212yes—
94#2623C2214yes—
95#2617C2214yes—
96#2611C2214yescomplemented
97#2606C2214yescomplemented
98#2602C2214yes—
99#2602C2214yes—
100#2602C2214yes—
101#2598C2214yes—
102#2597C2214yes—
103#2596C2214yescomplemented
104#2596C2214yescomplemented
105#2594C2214yescomplemented
106#2585C2214yescomplemented
107#2578C2214yes—
108#2578C2214yes—
109#2578C2214yescomplemented
110#2577C2214yes—
111#2577C2214yescomplemented
112#2575C2214yescomplemented
113#2569C2214yes—
114#2569C2214yes—
115#2569C2214yescomplemented
116#2562C2214yes—
117#2553C2214yescomplemented
118#2533C2214yescomplemented
119#2533C2214yescomplemented
120#2533C2214yescomplemented
121#2531C2214yes—
122#2531C2214yescomplemented
123#2530C2214yes—
124#2530C2214yescomplemented
125#2530C2214yescomplemented
126#2528C2214yescomplemented
127#2526C2214yescomplemented
128#2522C2214yescomplemented
129#2519C2214yescomplemented
130#2514C2212yescomplemented
131#2514C2212yescomplemented
132#2513C2212yescomplemented
133#2513C2212yescomplemented
134#2510C2214yescomplemented
135#2509C2212yescomplemented
136#2508C2212yescomplemented
137#2507C2212yescomplemented
138#2506C2212yescomplemented
139#2505C2214yes—
140#2500C2212yes—
141#2499C2212yes—
142#2498C2214yes—
143#2498C2214yes—
144#2498C2214yescomplemented
145#2495C2214yes—
146#2494C2214yes—
147#2493C2214yes—
148#2493C2214yes—
149#2493C2214yescomplemented
150#2487C2214yes—
151#2486C2214yes—
152#2485C2214yes—
153#2485C2214yes—
154#2485C2214yes—
155#2473C2214yes—
156#2468C2214yes—
157#2467C2214yes—
158#2460C2214yes—
159#2457C2214yes—
160#2454C2212yescomplemented
161#2454C2212yescomplemented
162#2453C2212yescomplemented
163#2453C2212yescomplemented
164#2448C2212yescomplemented
165#2447C2212yescomplemented
166#2446C2212yescomplemented
167#2445C2212yescomplemented
168#2444C2214yes—
169#2443C2214yes—
170#2442C2212yes—
171#2442C2212yes—
172#2442C2212yes—
173#2442C2212yes—
174#2432C2212yes—
175#2431C2212yes—
176#2425C2214yes—
177#2425C2214yes—
178#2412C2214yes—
179#2412C2214yes—
180#2361C2212yes—
181#2361C2212yes—
182#2360C2212yes—
183#2360C2212yes—
184#2358C2214yes—
185#2358C2214yes—
186#2353C2214yes—
187#2349C2214yes—
188#2347C2212yes—
189#2346C2212yes—
190#2341C2212yes—
191#2339C2212yes—
192#2336C2214yescomplemented
193#2335C2214yes—
194#2335C2214yes—
195#2335C2214yescomplemented
196#2330C2211yescharacteristic, complemented
197#2330C2211yescharacteristic, complemented
198#2328C2211yescharacteristic, complemented
199#2327C2211yescharacteristic, complemented
200#2325C2214yes—
201#2322C2214yes—
202#2320C2212yescomplemented
203#2319C2212yescomplemented
204#2318C2214yes—
205#2318C2214yes—
206#2316C2212yes—
207#2316C2212yes—
208#2315C2214yes—
209#2311C2212yes—
210#2311C2212yes—
211C4×#125C2212yescomplemented
212C4×#126C2214yescomplemented
213C4×#124C2212yescomplemented
214C4×C22⋊Q8C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×#123C2214yes—
217C4×#121C2212yes—
218C4×#121C2212yes—
219#2298C2212yes—
220#2298C2212yes—
221#2298C2212yes—
222#2298C2212yes—
223#2298C2212yes—
224#2298C2212yes—
225#2298C2212yes—
226#2298C2212yes—
227#2298C2214yescomplemented
228#2295C2212yescomplemented
229#2293C2212yescomplemented
230#2290C2214yes—
231C2×#388C2212yes—
232C2×#388C2212yes—
233C2×#387C2212yes—
234C2×#387C2212yes—
235C2×#380C2212yes—
236#2275C2214yes—
237C2×C4×C4⋊C4C2211yescharacteristic
238C2×C4×C4⋊C4C2211yescharacteristic
239C2×C4×C22⋊C4C2211yescharacteristic
240C2×C4×C22⋊C4C2211yescharacteristic
241C2×#376C2211yescharacteristic
242C2×C43C2211yescharacteristic
243C22×#41C2312yes—
244C24×C4C2311yescharacteristic
245C2×C4⋊Q8C2311yescharacteristic
246C2×#127C2311yescharacteristic
247C2×#126C2314yes—
248C2×#125C2312yes—
249C2×#125C2314yes—
250C2×#125C2311yescharacteristic
251C2×#125C2311yescharacteristic
252C2×#124C2312yes—
253#525—216no—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2314yes—
263C2×#120C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×#117—28no—
275C2×#117C2312yes—
276C2×#117C2312yes—
277C2×#117C2312yes—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2314yes—
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C22⋊C4C2311yescharacteristic
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2312yes—
297C22×C42C2312yes—
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300#401C2314yes—
301#401C2314yes—
302#401C2314yes—
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#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
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#398C2314yes—
344#398C2314yes—
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#397C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#392C2314yes—
379#392C2314yes—
380#391C2312yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#391C2312yes—
387#391C2312yes—
388#390C2312yes—
389#390C2312yes—
390#390C2312yes—
391#390C2312yes—
392#390C2312yes—
393#390C2314yes—
394#390C2314yes—
395#390C2314yes—
396#390C2312yes—
397#390C2312yes—
398#390C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2314yes—
402#389C2312yes—
403#389C2312yes—
404#389C2314yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2314yes—
410#389C2314yes—
411#389C2312yes—
412#389C2312yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2312yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2312yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2312yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2312yes—
460#388C2314yes—
461#388C2314yes—
462#388C2312yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2312yes—
469#388C2312yes—
470#388C2312yes—
471#388C2312yes—
472#388C2312yes—
473#388C2312yes—
474#388C2312yes—
475#388C2312yes—
476#388C2312yes—
477#388C2312yes—
478#388C2312yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2312yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2312yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2312yes—
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#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#384C2311yescharacteristic
577#384C2311yescharacteristic
578#383C2314yes—
579#383C2314yes—
580#383C2314yes—
581#383C2314yes—
582#383C2314yes—
583#382C2312yes—
584#382C2314yes—
585#382C2314yes—
586#382C2314yes—
587#382C2311yescharacteristic
588#382C2311yescharacteristic
589#382C2312yes—
590#381C2314yes—
591#381C2314yes—
592#381C2314yes—
593#381C2314yes—
594#381C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610#380C2314yes—
611#380C2314yes—
612#380C2314yes—
613#380C2312yes—
614#380C2312yes—
615#380C2312yes—
616#380C2312yes—
617#380C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2312yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2312yes—
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2312yes—
654#376C2311yescharacteristic
655#376C2311yescharacteristic
656#376C2311yescharacteristic
657#376C2311yescharacteristic
658#376C2314yes—
659#376C2312yes—
660#376C2312yes—
661#376C2314yes—
662C2×#95C2314yes—
663C2×#95C2314yes—
664C2×#95C2312yes—
665C2×#95C2312yes—
666C2×#95C2312yes—
667C2×#95C2312yes—
668C2×#95C2312yes—
669C2×#95C2312yes—
670C43C2311yescharacteristic
671C43C2312yes—
672C43C2312yes—
673C43C2311yescharacteristic
674C43C2311yescharacteristic
675C43C2311yescharacteristic
676C25C2411yescharacteristic
677C2×#41—28no—
678C2×#41—44no—
679C2×#41—44no—
680C22×Q8C2412yes—
681C22×D4C2414yes—
682C22×D4C2412yes—
683C22×D4C2414yes—
684C22×D4C2414yes—
685C22×D4C2414yes—
686C23×C4—42no—
687C23×C4—42no—
688C23×C4#4118yes—
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2411yescharacteristic
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2411yescharacteristic
698C23×C4C2412yes—
699C23×C4C2414yes—
700C23×C4C2414yes—
701C23×C4C2414yes—
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2411yescharacteristic
705C23×C4C2412yes—
706C4⋊Q8—42no—
707#127—42no—
708#126—48no—
709#125—44no—
710#125—42no—
711#125—42no—
712#125—48no—
713#124—44no—
714#123—216no—
715#123—48no—
716#123—48no—
717#123—48no—
718C22⋊Q8—28no—
719C22⋊Q8—28no—
720#121—28no—
721#121—28no—
722#121—48no—
723#120—216no—
724C4×Q8—44no—
725C4×Q8—44no—
726C4×D4—216no—
727C4×D4—216no—
728C4×D4—48no—
729C4×D4—44no—
730C4×D4—44no—
731C4×D4—48no—
732C4×D4—48no—
733C4×D4—48no—
734#117—28no—
735#117—28no—
736#117—28no—
737#117—28no—
738#117—28no—
739#117—48no—
740C2×C4⋊C4—24no—
741C2×C4⋊C4—24no—
742C2×C4⋊C4—44no—
743C2×C4⋊C4—44no—
744C2×C4⋊C4—44no—
745C2×C4⋊C4—44no—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C22⋊C4—24no—
794C2×C22⋊C4—24no—
795C2×C22⋊C4—44no—
796C2×C22⋊C4—48no—
797C2×C22⋊C4—44no—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C42—24no—
840C2×C42—24no—
841C2×C42—44no—
842C2×C42—42no—
843C2×C42—42no—
844C2×C42—42no—
845C2×C42—42no—
846C2×C42—44no—
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849C2×C42C2412yes—
850C2×C42C2411yescharacteristic
851C2×C42C2411yescharacteristic
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2411yescharacteristic
857C2×C42C2412yes—
858C2×C42C2411yescharacteristic
859C2×C42C2412yes—
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880#95C2412yes—
881#95C2414yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
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—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950C24—24no—
951C24—42no—
952C24—41no—
953C24—41no—
954C24C2×#4114yes—
955C24C2514yes—
956C24C2512yes—
957C24C2511yescharacteristic
958#41—816no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×D4—28no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—28no—
993C22×C4—28no—
994C22×C4—416no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4C2×#4114yes—
1022C22×C4C2×#4118yes—
1023C22×C4C2×#4114yes—
1024C22×C4C2×#4118yes—
1025C22×C4C2512yes—
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2511yescharacteristic
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
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—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C22⋊C4—24no—
1097C22⋊C4—24no—
1098C22⋊C4—24no—
1099C22⋊C4—24no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—24no—
1108C22⋊C4—24no—
1109C22⋊C4—28no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
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—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C42—22no—
1138C42—22no—
1139C42—24no—
1140C42—22no—
1141C42—22no—
1142C42—24no—
1143C42—28no—
1144C42—24no—
1145C42—22no—
1146C42—24no—
1147C42—22no—
1148C42—24no—
1149C42—22no—
1150C42—22no—
1151C42—24no—
1152C42—28no—
1153C42—41no—
1154C42—42no—
1155C42—41no—
1156C42—41no—
1157C42—41no—
1158C42—42no—
1159C42—42no—
1160C42—42no—
1161C42—42no—
1162C42—42no—
1163C42—42no—
1164C42—42no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C23—21no—
1171C23—21no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—28no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—24no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—44no—
1188C23—44no—
1189C23—84no—
1190C23—84no—
1191C23C22×#4114yes—
1192C23C22×#4112yes—
1193C23#58514yes—
1194C23C2611yescharacteristic
1195Q8—48no—
1196D4—416no—
1197D4—416no—
1198D4—48no—
1199D4—88no—
1200D4—164no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—28no—
1208C2×C4—216no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—44no—
1266C2×C4—48no—
1267C2×C4—48no—
1268C2×C4—48no—
1269C2×C4—44no—
1270C2×C4—44no—
1271C2×C4—44no—
1272C2×C4—44no—
1273C2×C4—88no—
1274C2×C4—88no—
1275C2×C4—84no—
1276C2×C4—84no—
1277C2×C4—164no—
1278C2×C4—164no—
1279C2×C4—164no—
1280C2×C4C22×#4112yes—
1281C2×C4C22×#4114yes—
1282C2×C4C22×#4112yes—
1283C2×C4#58514yes—
1284C2×C4#58512yes—
1285C2×C4#58512yes—
1286C22—22no—
1287C22—24no—
1288C22—24no—
1289C22—22no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22—88no—
1305C22#351214yes—
1306C22C23×#4111yescharacteristic
1307C22C2×#58511yescharacteristic
1308C22C2×#58511yescharacteristic
1309C22C2×#58512yes—
1310C22C2×#58512yes—
1311C4—24no—
1312C4—22no—
1313C4—24no—
1314C4—44no—
1315C4—41no—
1316C4—41no—
1317C4—42no—
1318C4—44no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—44no—
1324C4—44no—
1325C4—42no—
1326C4—42no—
1327C4—44no—
1328C4—42no—
1329C4—44no—
1330C4—41no—
1331C4—41no—
1332C4—42no—
1333C4—44no—
1334C4#349114yes—
1335C2—24no—
1336C2—44no—
1337C2—84no—
1338C2#6268611yescharacteristic
1339C2C2×#349111yescharacteristic
1340C2C2×#351211yescharacteristic
1341C2#6282712yes—
1342C2#6282812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35032C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39254C2semidirect
2. #39083C2semidirect
3. #39082C2semidirect
4. #39069C2semidirect
5. #39068C2semidirect
6. #39050C2semidirect
7. #38267C2semidirect
8. #38266C2semidirect
9. #38253C2semidirect
10. #38252C2semidirect
11. #38223C2semidirect
12. #38210C2semidirect
13. #37018C2semidirect
14. #37012C2semidirect
15. #36638C2semidirect
16. #35502C2semidirect
17. #35487C2semidirect
18. #35315C2semidirect
19. #35271C2semidirect
20. #35263C2semidirect
21. #35087C2semidirect
22. #35082C2semidirect
24. #35024C2semidirect
25. #35020C2semidirect
26. #34233C2semidirect
27. C2×#2298C2semidirect
30. #2866C22semidirect
31. #2865C22semidirect
32. #2864C22semidirect
33. #2863C22semidirect
34. #2861C22semidirect
35. #2860C22semidirect
55. #2776C22semidirect
56. #2773C22semidirect
57. #2772C22semidirect
59. #2770C22semidirect
60. #2767C22semidirect
61. #2766C22semidirect
62. #2766C22semidirect
68. #2747C22semidirect
69. #2747C22semidirect
71. #2746C22semidirect
72. #2743C22semidirect
75. #2741C22semidirect
76. #2741C22semidirect
77. #2739C22semidirect
78. #2738C22semidirect
79. #2738C22semidirect
80. #2655C22semidirect
81. #2651C22semidirect
82. #2647C22semidirect
83. #2647C22semidirect
85. #2645C22semidirect
86. #2644C22semidirect
88. #2642C22semidirect
89. #2641C22semidirect
96. #2611C22semidirect
97. #2606C22semidirect
103. #2596C22semidirect
104. #2596C22semidirect
105. #2594C22semidirect
106. #2585C22semidirect
109. #2578C22semidirect
111. #2577C22semidirect
112. #2575C22semidirect
115. #2569C22semidirect
117. #2553C22semidirect
118. #2533C22semidirect
119. #2533C22semidirect
120. #2533C22semidirect
122. #2531C22semidirect
124. #2530C22semidirect
125. #2530C22semidirect
126. #2528C22semidirect
127. #2526C22semidirect
128. #2522C22semidirect
129. #2519C22semidirect
130. #2514C22semidirect
131. #2514C22semidirect
132. #2513C22semidirect
133. #2513C22semidirect
134. #2510C22semidirect
135. #2509C22semidirect
136. #2508C22semidirect
137. #2507C22semidirect
138. #2506C22semidirect
144. #2498C22semidirect
149. #2493C22semidirect
160. #2454C22semidirect
161. #2454C22semidirect
162. #2453C22semidirect
163. #2453C22semidirect
164. #2448C22semidirect
165. #2447C22semidirect
166. #2446C22semidirect
167. #2445C22semidirect
192. #2336C22semidirect
195. #2335C22semidirect
196. #2330C22semidirect
197. #2330C22semidirect
198. #2328C22semidirect
199. #2327C22semidirect
202. #2320C22semidirect
203. #2319C22semidirect
211. C4×#125C22semidirect
212. C4×#126C22semidirect
213. C4×#124C22semidirect
227. #2298C22semidirect
228. #2295C22semidirect
229. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#392542
#390832
#390822
#390692
#390682
#390502
#382672
#382662
#382532
#382522
#382232
#382102
#370182
#370122
#366382
#355022
#354872
#353152
#352712
#352632
#350872
#350822
#350322
#350242
#350202
#342332
C2×#22982