Finite Group Databasebeta

← #7716073

Subgroups — #7716073

Order 512.

4536 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50445C214yesmaximal, complemented
2#50418C214yesmaximal, complemented
3#49263C214yesmaximal, complemented
4#49236C214yesmaximal, complemented
5#44425C214yesmaximal, complemented
6#44301C214yesmaximal, complemented
7#44051C214yesmaximal, complemented
8#43947C214yesmaximal, complemented
9#39755C212yesmaximal, complemented
10#39671C212yesmaximal, complemented
11#37951C212yesmaximal, complemented
12#37896C212yesmaximal, complemented
13#37755C212yesmaximal, complemented
14#37755C212yesmaximal, complemented
15#36968C212yesmaximal, complemented
16#36763C212yesmaximal, complemented
17#36200C212yesmaximal, complemented
18#36116C212yesmaximal, complemented
19#35270C212yesmaximal, complemented
20#35167C211yesmaximal, characteristic, complemented
21#35120C211yesmaximal, characteristic, complemented
22#35119C211yesmaximal, characteristic
23#35013C211yesmaximal, characteristic, complemented
24#35004C211yesmaximal, characteristic
25#34594C211yesmaximal, characteristic
26#34425C212yesmaximal, complemented
27C2×#2371C211yesmaximal, characteristic, complemented
28C2×#544C2212yes—
29C2×#539C2212yes—
30C2×#529C2212yes—
31C2×#529C2212yes—
32C22×#125C2211yescharacteristic
33#2857C2212yes—
34#2857C2212yes—
35#2855C2212yes—
36#2855C2212yes—
37#2855C2212yes—
38#2854C2212yes—
39#2854C2212yes—
40#2854C2212yes—
41#2851C2212yes—
42#2850C2212yes—
43#2800C2214yes—
44#2799C2214yes—
45#2793C2214yes—
46#2793C2214yes—
47#2791C2214yes—
48#2790C2214yes—
49#2790C2214yes—
50#2790C2214yes—
51#2788C2214yes—
52#2784C2214yes—
53#2776C2214yes—
54#2775C2214yes—
55#2772C2214yes—
56#2769C2214yes—
57#2767C2214yes—
58#2766C2214yes—
59#2761C2214yes—
60#2751C2214yes—
61#2744C2214yes—
62#2739C2214yes—
63#2737C2214yes—
64#2731C2214yes—
65#2731C2214yes—
66#2726C2214yes—
67#2726C2214yes—
68#2725C2214yes—
69#2725C2214yes—
70#2725C2214yes—
71#2725C2214yes—
72#2719C2214yes—
73#2719C2214yes—
74#2716C2214yes—
75#2716C2214yes—
76#2716C2214yes—
77#2716C2214yes—
78#2715C2214yes—
79#2707C2214yes—
80#2707C2214yes—
81#2704C2214yes—
82#2704C2214yes—
83#2664C2214yes—
84#2662C2214yes—
85#2659C2211yescharacteristic
86#2659C2211yescharacteristic
87#2659C2211yescharacteristic
88#2659C2212yes—
89#2656C2211yescharacteristic
90#2647C2212yes—
91#2646C2212yes—
92#2645C2212yes—
93#2644C2212yes—
94#2640C2212yes—
95#2639C2212yes—
96#2639C2212yes—
97#2627C2212yes—
98#2618C2212yes—
99#2618C2212yes—
100#2618C2212yes—
101#2612C2214yes—
102#2612C2214yes—
103#2612C2214yes—
104#2611C2214yes—
105#2610C2214yes—
106#2606C2214yes—
107#2605C2214yes—
108#2604C2214yes—
109#2603C2214yes—
110#2597C2214yes—
111#2594C2214yes—
112#2588C2214yes—
113#2586C2214yes—
114#2585C2214yes—
115#2585C2214yes—
116#2579C2214yes—
117#2579C2214yes—
118#2574C2214yes—
119#2574C2214yes—
120#2573C2214yes—
121#2570C2212yes—
122#2566C2212yes—
123#2556C2214yes—
124#2554C2214yes—
125#2552C2214yes—
126#2552C2212yes—
127#2551C2214yes—
128#2550C2214yes—
129#2550C2214yes—
130#2547C2212yes—
131#2533C2214yes—
132#2532C2214yes—
133#2531C2214yes—
134#2530C2214yes—
135#2529C2214yes—
136#2529C2214yes—
137#2529C2214yes—
138#2527C2214yes—
139#2527C2214yes—
140#2525C2214yes—
141#2523C2214yes—
142#2520C2214yes—
143#2519C2214yes—
144#2515C2214yes—
145#2513C2212yes—
146#2512C2212yes—
147#2510C2214yes—
148#2509C2212yes—
149#2507C2212yes—
150#2496C2214yes—
151#2488C2214yes—
152#2488C2214yes—
153#2486C2214yes—
154#2481C2214yes—
155#2478C2214yes—
156#2478C2214yes—
157#2475C2214yes—
158#2475C2214yes—
159#2473C2214yes—
160#2466C2214yes—
161#2462C2214yes—
162#2461C2214yes—
163#2460C2214yes—
164#2460C2214yes—
165#2453C2212yes—
166#2453C2212yes—
167#2450C2214yes—
168#2450C2214yes—
169#2447C2212yes—
170#2447C2212yes—
171#2446C2214yes—
172#2446C2214yes—
173#2439C2214yes—
174#2439C2214yes—
175#2419C2214yes—
176#2419C2214yes—
177#2413C2214yes—
178#2413C2214yes—
179#2396C2214yes—
180#2392C2214yes—
181#2383C2214yes—
182#2378C2214yes—
183#2373C2214yes—
184#2373C2214yes—
185#2371C2214yes—
186#2371C2214yes—
187#2371C2214yes—
188#2371C2214yes—
189#2370C2212yes—
190#2365C2212yes—
191#2360C2214yes—
192#2359C2214yes—
193#2359C2214yes—
194#2357C2212yes—
195#2353C2214yes—
196D4×C4⋊C4C2212yes—
197D4×C4⋊C4C2214yes—
198#2344C2214yes—
199#2336C2214yes—
200#2335C2214yes—
201#2331C2212yes—
202#2330C2214yes—
203#2329C2212yes—
204#2329C2212yes—
205#2329C2212yes—
206#2326C2212yes—
207#2325C2212yes—
208#2325C2212yes—
209#2325C2212yes—
210#2322C2214yes—
211#2320C2212yes—
212#2319C2212yes—
213#2316C2212yes—
214#2313C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×#121C2212yes—
217C4×#121C2212yes—
218C4×#121C2212yes—
219C2×#387C2211yescharacteristic
220C2×#387C2211yescharacteristic
221C2×#387C2211yescharacteristic
222C2×#387C2211yescharacteristic
223C2×#387C2211yescharacteristic
224C2×#387C2211yescharacteristic
225C2×#387C2211yescharacteristic
226C2×#387C2211yescharacteristic
227#2285C2212yes—
228#2283C2212yes—
229C2×C4×C4⋊C4C2211yescharacteristic
230C2×C4×C4⋊C4C2211yescharacteristic
231C2×C4×C4⋊C4C2211yescharacteristic
232C2×C4×C4⋊C4C2211yescharacteristic
233C2×#376C2211yescharacteristic
234C2×#376C2211yescharacteristic
235#544—48no—
236#539—216no—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2314yes—
241#529—48no—
242#529—48no—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#125—28no—
248C2×#125C2314yes—
249C2×#125C2314yes—
250C2×#125C2314yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×#121C2312yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×#117C2314yes—
283C2×#117C2314yes—
284C2×#117C2314yes—
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2314yes—
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305#401C2314yes—
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#399C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
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#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
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#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#392C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2312yes—
402#391C2312yes—
403#391C2314yes—
404#391C2314yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2314yes—
411#390C2312yes—
412#390C2312yes—
413#390C2312yes—
414#390C2312yes—
415#390C2312yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
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#388C2314yes—
491#388C2314yes—
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#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
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#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
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#384C2312yes—
574#384C2312yes—
575#384C2312yes—
576#384C2314yes—
577#384C2312yes—
578#383C2314yes—
579#383C2314yes—
580#383C2314yes—
581#382C2312yes—
582#382C2312yes—
583#382C2312yes—
584#382C2314yes—
585#382C2312yes—
586#382C2314yes—
587#382C2314yes—
588#381C2314yes—
589#381C2314yes—
590#381C2314yes—
591#381C2314yes—
592#381C2314yes—
593#380C2312yes—
594#380C2312yes—
595#380C2314yes—
596#380C2312yes—
597#380C2312yes—
598#380C2314yes—
599#380C2314yes—
600#380C2312yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2312yes—
605#380C2314yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639#376C2312yes—
640#376C2312yes—
641#376C2314yes—
642#376C2314yes—
643#376C2314yes—
644#376C2314yes—
645#376C2312yes—
646#376C2312yes—
647C2×#95C2311yescharacteristic
648C2×#95C2311yescharacteristic
649C2×#95C2311yescharacteristic
650C2×#95C2311yescharacteristic
651C2×#95C2311yescharacteristic
652C2×#95C2311yescharacteristic
653C2×#95C2311yescharacteristic
654C2×#95C2311yescharacteristic
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2311yescharacteristic
660C2×#95C2311yescharacteristic
661C2×#95C2311yescharacteristic
662C2×#95C2311yescharacteristic
663C22×Q8C2412yes—
664C22×Q8C2412yes—
665C22×Q8C2412yes—
666C22×Q8C2414yes—
667C22×D4C2414yes—
668C22×D4C2412yes—
669C22×D4C2412yes—
670C22×D4C2412yes—
671C23×C4C2411yescharacteristic
672C23×C4C2411yescharacteristic
673C23×C4C2411yescharacteristic
674C23×C4C2411yescharacteristic
675C23×C4C2411yescharacteristic
676C23×C4C2411yescharacteristic
677C23×C4C2411yescharacteristic
678C23×C4C2414yes—
679C23×C4C2411yescharacteristic
680C23×C4C2414yes—
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2414yes—
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C4⋊Q8—44no—
690C4⋊Q8—44no—
691C4⋊Q8—48no—
692C4⋊Q8—48no—
693#126—216no—
694#126—48no—
695#126—48no—
696#126—48no—
697#125—216no—
698#125—216no—
699#125—216no—
700#125—44no—
701#125—44no—
702#125—44no—
703#125—48no—
704#125—48no—
705#124—44no—
706#124—44no—
707#124—44no—
708#123—216no—
709#123—216no—
710#123—48no—
711#123—48no—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—216no—
716C22⋊Q8—48no—
717#121—28no—
718#121—28no—
719#121—28no—
720C4×Q8—44no—
721C4×Q8—44no—
722C4×Q8—44no—
723C4×D4—216no—
724C4×D4—44no—
725C4×D4—44no—
726C4×D4—44no—
727C4×D4—44no—
728C4×D4—44no—
729C4×D4—48no—
730C4×D4—48no—
731#117—48no—
732#117—48no—
733#117—48no—
734C2×C4⋊C4—24no—
735C2×C4⋊C4—24no—
736C2×C4⋊C4—24no—
737C2×C4⋊C4—24no—
738C2×C4⋊C4—24no—
739C2×C4⋊C4—24no—
740C2×C4⋊C4—24no—
741C2×C4⋊C4—42no—
742C2×C4⋊C4—48no—
743C2×C4⋊C4—42no—
744C2×C4⋊C4#4118yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
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×C42—24no—
834C2×C42—24no—
835C2×C42—24no—
836C2×C42—24no—
837C2×C42—24no—
838C2×C42—42no—
839C2×C42—42no—
840C2×C42—42no—
841C2×C42—42no—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2414yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2414yes—
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2412yes—
880#95C2414yes—
881#95C2412yes—
882#95C2412yes—
883#95C2414yes—
884#95C2412yes—
885#95C2414yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2412yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
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#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—
935C24C2514yes—
936C24C2511yescharacteristic
937C2×Q8—24no—
938C2×Q8—24no—
939C2×Q8—24no—
940C2×Q8—42no—
941C2×Q8—42no—
942C2×Q8—42no—
943C2×Q8—42no—
944C2×Q8—42no—
945C2×Q8—42no—
946C2×Q8—44no—
947C2×Q8—44no—
948C2×Q8—44no—
949C2×D4—28no—
950C2×D4—28no—
951C2×D4—28no—
952C2×D4—24no—
953C2×D4—24no—
954C2×D4—24no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—42no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—22no—
966C22×C4—22no—
967C22×C4—22no—
968C22×C4—22no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—22no—
972C22×C4—22no—
973C22×C4—22no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—28no—
980C22×C4—28no—
981C22×C4—41no—
982C22×C4—41no—
983C22×C4—41no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—41no—
988C22×C4—41no—
989C22×C4—41no—
990C22×C4—41no—
991C22×C4—41no—
992C22×C4—41no—
993C22×C4—41no—
994C22×C4—41no—
995C22×C4—41no—
996C22×C4—41no—
997C22×C4—44no—
998C22×C4—41no—
999C22×C4—44no—
1000C22×C4—41no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—41no—
1006C22×C4—41no—
1007C22×C4—44no—
1008C22×C4—41no—
1009C22×C4—41no—
1010C22×C4C2×#4114yes—
1011C22×C4C2×#4114yes—
1012C22×C4C2×#4114yes—
1013C22×C4H(5,𝔽2)14yes—
1014C22×C42−1+414yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2514yes—
1022C22×C4C2512yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2511yescharacteristic
1025C22×C4C2514yes—
1026C22×C4C2514yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—24no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—24no—
1064C4⋊C4—28no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
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—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4C2×#41116yes—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
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—
1128C42—24no—
1129C42—24no—
1130C42—28no—
1131C42—24no—
1132C42—24no—
1133C42—24no—
1134C42—24no—
1135C42—24no—
1136C42—24no—
1137C42—24no—
1138C42—24no—
1139C42—24no—
1140C42—24no—
1141C42—24no—
1142C42—24no—
1143C42—42no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—44no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—24no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23C22×#4112yes—
1167C23C2×H(5,𝔽2)12yes—
1168C23C2×2−1+412yes—
1169C23C2611yescharacteristic
1170Q8—84no—
1171Q8—84no—
1172Q8—84no—
1173Q8—164no—
1174D4—48no—
1175D4—416no—
1176D4—84no—
1177D4—84no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—28no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—44no—
1248C2×C4—44no—
1249C2×C4—44no—
1250C2×C4—44no—
1251C2×C4—44no—
1252C2×C4—44no—
1253C2×C4—44no—
1254C2×C4—44no—
1255C2×C4—44no—
1256C2×C4—44no—
1257C2×C4—88no—
1258C2×C4—88no—
1259C2×C4—82no—
1260C2×C4—82no—
1261C2×C4—82no—
1262C2×C4—82no—
1263C2×C4—88no—
1264C2×C4C22×#4114yes—
1265C2×C4C22×#4114yes—
1266C2×C4C22×#4114yes—
1267C2×C4C2×H(5,𝔽2)14yes—
1268C2×C4C2×2−1+414yes—
1269C2×C4#58512yes—
1270C2×C4#58512yes—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22#351114yes—
1285C22C23×#4111yescharacteristic
1286C22C22×H(5,𝔽2)11yescharacteristic
1287C22C22×2−1+411yescharacteristic
1288C22C2×#58511yescharacteristic
1289C22C2×#58511yescharacteristic
1290C222−1+611yescharacteristic
1291C222−1+611yescharacteristic
1292C4—24no—
1293C4—24no—
1294C4—24no—
1295C4—24no—
1296C4—24no—
1297C4—22no—
1298C4—22no—
1299C4—42no—
1300C4—44no—
1301C4—41no—
1302C4—41no—
1303C4—42no—
1304C4—44no—
1305C4—44no—
1306C4—42no—
1307C4—42no—
1308C4—44no—
1309C4—44no—
1310C4—42no—
1311C4—41no—
1312C4—44no—
1313C4—44no—
1314C4—42no—
1315C4—41no—
1316C4—42no—
1317C2—24no—
1318C2—84no—
1319C2#6278111yescharacteristic
1320C2C2×#351111yescharacteristic
1321C2#6285011yescharacteristic
1322C2#6290111yescharacteristic
1323C2#6290411yescharacteristic
1324C2#6292711yescharacteristic
1325C2#6292811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2656C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50445C2semidirect
2. #50418C2semidirect
3. #49263C2semidirect
4. #49236C2semidirect
5. #44425C2semidirect
6. #44301C2semidirect
7. #44051C2semidirect
8. #43947C2semidirect
9. #39755C2semidirect
10. #39671C2semidirect
11. #37951C2semidirect
12. #37896C2semidirect
13. #37755C2semidirect
14. #37755C2semidirect
15. #36968C2semidirect
16. #36763C2semidirect
17. #36200C2semidirect
18. #36116C2semidirect
19. #35270C2semidirect
20. #35167C2semidirect
21. #35120C2semidirect
23. #35013C2semidirect
26. #34425C2semidirect
27. C2×#2371C2semidirect

Maximal subgroups

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

subgroupindex
#504452
#504182
#492632
#492362
#444252
#443012
#440512
#439472
#397552
#396712
#379512
#378962
#377552
#369682
#367632
#362002
#361162
#352702
#351672
#351202
#351192
#350132
#350042
#345942
#344252
C2×#23712