Finite Group Databasebeta

← #8757212

Subgroups — #8757212

Order 512.

4808 conjugacy classes of subgroups.

The subgroup lattice has 1427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58961C212yesmaximal, complemented
2#58335C212yesmaximal, complemented
3#57965C212yesmaximal, complemented
4#57573C212yesmaximal, complemented
5#57394C214yesmaximal, complemented
6#56568C212yesmaximal, complemented
7#56483C212yesmaximal, complemented
8#54886C214yesmaximal, complemented
9#53669C212yesmaximal, complemented
10#53414C212yesmaximal, complemented
11#49661C214yesmaximal, complemented
12#49388C214yesmaximal, complemented
13#48318C214yesmaximal, complemented
14#47122C212yesmaximal, complemented
15#46836C212yesmaximal, complemented
16#46829C212yesmaximal, complemented
17#46710C212yesmaximal, complemented
18#46366C214yesmaximal, complemented
19#46224C212yesmaximal, complemented
20#46141C212yesmaximal, complemented
21#45989C212yesmaximal, complemented
22#45986C212yesmaximal, complemented
23#45978C212yesmaximal, complemented
24#45976C212yesmaximal, complemented
25#35328C211yesmaximal, characteristic, complemented
26#35138C211yesmaximal, characteristic, complemented
27#35129C211yesmaximal, characteristic, complemented
28C2×#562C2212yes—
29C2×#538C2214yes—
30C2×#537C2212yes—
31C2×#532C2211yescharacteristic, complemented
32C22×#125C2211yescharacteristic, complemented
33C22×#124C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2851C2212yes—
36#2851C2212yescomplemented
37#2850C2212yes—
38#2850C2212yes—
39#2850C2212yes—
40#2850C2212yescomplemented
41#2844C2212yescomplemented
42#2835C2212yescomplemented
43#2834C2212yes—
44#2834C2214yescomplemented
45#2827C2214yes—
46#2824C2214yescomplemented
47#2820C2212yes—
48#2820C2212yescomplemented
49#2819C2212yes—
50#2815C2212yes—
51#2814C2214yescomplemented
52#2814C2214yescomplemented
53#2812C2212yes—
54#2806C2214yescomplemented
55#2787C2214yes—
56#2778C2214yescomplemented
57#2778C2214yescomplemented
58#2775C2214yescomplemented
59#2775C2214yescomplemented
60#2773C2214yescomplemented
61#2768C2214yescomplemented
62#2765C2214yescomplemented
63#2764C2212yescomplemented
64#2764C2214yescomplemented
65#2762C2214yescomplemented
66#2760C2212yescomplemented
67#2759C2214yescomplemented
68#2757C2214yescomplemented
69#2756C2214yescomplemented
70#2756C2214yescomplemented
71#2750C2214yes—
72#2749C2214yes—
73#2744C2214yescomplemented
74#2742C2214yescomplemented
75#2741C2214yescomplemented
76#2738C2214yescomplemented
77#2735C2212yes—
78#2730C2214yes—
79#2730C2214yescomplemented
80#2729C2214yescomplemented
81#2723C2214yes—
82#2723C2214yescomplemented
83#2722C2212yes—
84#2715C2214yes—
85#2712C2212yes—
86#2712C2212yes—
87#2711C2214yes—
88#2711C2214yescomplemented
89#2710C2214yes—
90#2710C2214yescomplemented
91#2708C2214yes—
92#2705C2214yes—
93#2704C2214yescomplemented
94#2704C2214yescomplemented
95#2703C2214yescomplemented
96#2700C2214yes—
97#2700C2214yescomplemented
98#2699C2214yes—
99#2699C2214yescomplemented
100#2698C2214yes—
101#2698C2214yescomplemented
102#2694C2214yescomplemented
103#2694C2214yescomplemented
104#2692C2214yescomplemented
105#2692C2214yescomplemented
106#2691C2214yes—
107#2688C2214yes—
108#2688C2214yescomplemented
109#2687C2214yescomplemented
110#2686C2214yes—
111#2686C2214yes—
112#2686C2214yescomplemented
113#2681C2214yescomplemented
114#2676C2214yes—
115#2676C2214yescomplemented
116#2675C2214yes—
117#2675C2212yes—
118#2673C2214yescomplemented
119#2672C2214yes—
120#2671C2214yescomplemented
121#2671C2214yescomplemented
122#2670C2214yes—
123#2668C2214yes—
124#2668C2214yes—
125#2668C2212yes—
126#2667C2214yescomplemented
127#2654C2214yescomplemented
128#2653C2214yescomplemented
129#2648C2214yescomplemented
130#2635C2214yes—
131#2634C2212yescomplemented
132#2633C2212yes—
133#2632C2212yes—
134#2631C2212yes—
135#2624C2214yescomplemented
136#2621C2211yescharacteristic
137#2621C2211yescharacteristic, complemented
138#2619C2211yescharacteristic
139#2619C2211yescharacteristic, complemented
140#2611C2212yes—
141#2611C2212yescomplemented
142#2610C2212yes—
143#2610C2212yes—
144#2610C2214yescomplemented
145#2605C2214yescomplemented
146#2600C2212yes—
147#2598C2214yes—
148#2595C2214yescomplemented
149#2592C2212yes—
150#2584C2212yescomplemented
151#2578C2214yes—
152#2574C2214yescomplemented
153#2564C2214yescomplemented
154#2564C2214yescomplemented
155#2562C2212yes—
156#2555C2214yes—
157#2549C2214yescomplemented
158#2543C2212yes—
159#2543C2212yes—
160#2543C2212yescomplemented
161#2543C2212yescomplemented
162#2540C2212yes—
163#2536C2212yescomplemented
164#2536C2212yescomplemented
165#2535C2212yes—
166#2535C2212yes—
167#2535C2214yescomplemented
168#2527C2214yescomplemented
169#2526C2214yescomplemented
170#2525C2214yescomplemented
171#2521C2214yes—
172#2510C2214yescomplemented
173#2510C2214yescomplemented
174#2487C2211yescharacteristic
175#2487C2211yescharacteristic, complemented
176#2486C2211yescharacteristic
177#2486C2211yescharacteristic, complemented
178#2484C2212yescomplemented
179#2483C2212yes—
180#2482C2212yes—
181#2481C2214yescomplemented
182#2480C2214yes—
183#2477C2214yescomplemented
184#2474C2214yescomplemented
185#2468C2214yescomplemented
186#2464C2214yescomplemented
187#2464C2214yescomplemented
188#2463C2212yescomplemented
189#2456C2214yes—
190#2455C2212yes—
191#2455C2214yescomplemented
192#2450C2214yescomplemented
193#2449C2214yescomplemented
194#2449C2214yescomplemented
195#2449C2214yescomplemented
196#2447C2214yescomplemented
197#2444C2214yes—
198#2443C2214yescomplemented
199#2443C2214yescomplemented
200#2438C2214yescomplemented
201#2437C2214yes—
202#2430C2214yescomplemented
203#2427C2214yes—
204#2427C2214yes—
205#2425C2214yescomplemented
206#2424C2214yes—
207#2424C2214yes—
208#2418C2214yes—
209#2416C2214yes—
210#2416C2214yescomplemented
211#2412C2214yes—
212#2410C2214yes—
213#2409C2211yescharacteristic
214#2409C2214yes—
215#2409C2211yescharacteristic
216#2408C2211yescharacteristic
217#2408C2211yescharacteristic
218#2407C2214yescomplemented
219#2406C2212yes—
220#2404C2212yes—
221#2382C2212yescomplemented
222#2379C2212yes—
223#2379C2212yescomplemented
224#2377C2214yescomplemented
225#2363C2214yescomplemented
226#2325C2214yes—
227#2322C2212yes—
228#2322C2212yescomplemented
229#2321C2212yes—
230#2321C2212yes—
231#2311C2212yescomplemented
232#2283C2211yescharacteristic
233#2283C2211yescharacteristic, complemented
234C2×#382C2211yescharacteristic, complemented
235C22×#41C2311yescharacteristic
236C22×#41C2312yes—
237C23×Q8C2311yescharacteristic
238C23×D4C2311yescharacteristic
239#562—48no—
240#538—416no—
241#537—48no—
242#532—44no—
243C2×C4⋊Q8C2311yescharacteristic
244C2×#127C2311yescharacteristic
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#125—44no—
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#124—44no—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2314yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#123C2312yes—
262C2×#123C2312yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2314yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2312yes—
289C2×#121C2314yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#120C2312yes—
296C2×#120C2312yes—
297C2×#120C2314yes—
298C2×#120C2314yes—
299C4×#41—44no—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2314yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2314yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×#117C2311yescharacteristic
316C2×#117C2311yescharacteristic
317C2×#117C2311yescharacteristic
318C2×#117C2314yes—
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2311yescharacteristic
324C22×C22⋊C4C2312yes—
325C22×C22⋊C4C2312yes—
326C22×C22⋊C4C2314yes—
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330#401C2314yes—
331#401C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2312yes—
348#399C2314yes—
349#399C2314yes—
350#399C2312yes—
351#399C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2312yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2312yes—
382#397C2314yes—
383#397C2314yes—
384#397C2312yes—
385#397C2312yes—
386#397C2312yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#395C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2312yes—
428#394C2312yes—
429#394C2312yes—
430#394C2312yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2312yes—
448#393C2312yes—
449#393C2314yes—
450#392C2314yes—
451#392C2314yes—
452#392C2314yes—
453#392C2312yes—
454#392C2312yes—
455#392C2312yes—
456#392C2312yes—
457#392C2312yes—
458#392C2312yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2314yes—
464#392C2314yes—
465#392C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#390C2312yes—
478#390C2312yes—
479#390C2314yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#390C2314yes—
487#390C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2312yes—
559#386C2314yes—
560#386C2312yes—
561#386C2312yes—
562#386C2312yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2312yes—
594#385C2312yes—
595#385C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2312yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#383C2314yes—
613#383C2314yes—
614#383C2312yes—
615#383C2312yes—
616#382C2312yes—
617#382C2312yes—
618#382C2312yes—
619#382C2314yes—
620#382C2311yescharacteristic
621#382C2311yescharacteristic
622#382C2312yes—
623#382C2312yes—
624#381C2312yes—
625#381C2312yes—
626#381C2314yes—
627#381C2314yes—
628#381C2312yes—
629#381C2312yes—
630#381C2314yes—
631#381C2314yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2311yescharacteristic
644#380C2311yescharacteristic
645#380C2314yes—
646#380C2314yes—
647#380C2311yescharacteristic
648#380C2311yescharacteristic
649#379C2312yes—
650#379C2312yes—
651#379C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660#376C2312yes—
661#376C2312yes—
662C2×#95C2312yes—
663C2×#95C2314yes—
664C2×#95C2312yes—
665C25C2412yes—
666C2×#41—24no—
667C2×#41—42no—
668C2×#41—44no—
669C2×#41—42no—
670C2×#41—44no—
671C2×#41—44no—
672C22×Q8—42no—
673C22×Q8—82no—
674C22×Q8C2411yescharacteristic
675C22×Q8C2412yes—
676C22×Q8C2412yes—
677C22×Q8C2414yes—
678C22×Q8C2412yes—
679C22×D4—42no—
680C22×D4—82no—
681C22×D4C2411yescharacteristic
682C22×D4C2411yescharacteristic
683C22×D4C2414yes—
684C22×D4C2414yes—
685C22×D4C2414yes—
686C22×D4C2414yes—
687C22×D4C2414yes—
688C22×D4C2412yes—
689C22×D4C2412yes—
690C22×D4C2414yes—
691C22×D4C2412yes—
692C22×D4C2412yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2412yes—
697C22×D4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2412yes—
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C23×C4C2414yes—
706C23×C4C2411yescharacteristic
707C23×C4C2411yescharacteristic
708C23×C4C2411yescharacteristic
709C23×C4C2412yes—
710C23×C4C2414yes—
711C23×C4C2414yes—
712C23×C4C2412yes—
713C23×C4C2414yes—
714C23×C4C2414yes—
715C23×C4C2414yes—
716C4⋊Q8—42no—
717#127—42no—
718#126—48no—
719#126—48no—
720#125—28no—
721#125—44no—
722#125—44no—
723#125—44no—
724#124—28no—
725#124—28no—
726#124—44no—
727#124—44no—
728#124—44no—
729#124—48no—
730#124—48no—
731#124—84no—
732#123—28no—
733#123—48no—
734#123—48no—
735#123—44no—
736#123—48no—
737#123—84no—
738C22⋊Q8—44no—
739C22⋊Q8—44no—
740C22⋊Q8—48no—
741C22⋊Q8—48no—
742C22⋊Q8—48no—
743C22⋊Q8—48no—
744C22⋊Q8—84no—
745C22⋊Q8—82no—
746C22⋊Q8—84no—
747C22⋊Q8—82no—
748#121—216no—
749#121—44no—
750#121—44no—
751#121—48no—
752#121—48no—
753#121—48no—
754#121—48no—
755#121—48no—
756#121—48no—
757#121—48no—
758#121—44no—
759#121—44no—
760#121—48no—
761#121—84no—
762#121—82no—
763#121—84no—
764#121—84no—
765#121—82no—
766#120—28no—
767#120—48no—
768#120—44no—
769#120—84no—
770C4×Q8—42no—
771C4×Q8—42no—
772C4×D4—44no—
773C4×D4—44no—
774C4×D4—42no—
775C4×D4—42no—
776C4×D4—42no—
777C4×D4—42no—
778C4×D4—42no—
779C4×D4—42no—
780C4×D4—48no—
781C4×D4—48no—
782C4×D4—84no—
783C4×D4—84no—
784C4×D4—84no—
785#117—42no—
786#117—42no—
787#117—42no—
788#117—84no—
789C2×C4⋊C4—44no—
790C2×C4⋊C4—44no—
791C2×C4⋊C4—42no—
792C2×C4⋊C4—42no—
793C2×C4⋊C4—44no—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C22⋊C4—44no—
839C2×C22⋊C4—44no—
840C2×C22⋊C4—48no—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2411yescharacteristic
858C2×C22⋊C4C2411yescharacteristic
859C2×C22⋊C4C2411yescharacteristic
860C2×C22⋊C4C2411yescharacteristic
861C2×C22⋊C4C2411yescharacteristic
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C42—24no—
898C2×C42—24no—
899C2×C42—24no—
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2411yescharacteristic
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
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—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966C24—24no—
967C24—42no—
968C24—44no—
969C24—44no—
970C24—42no—
971C24C2514yes—
972C24C2514yes—
973C24C2511yescharacteristic
974C24C2511yescharacteristic
975C24C2511yescharacteristic
976#41—416no—
977#41—816no—
978C2×Q8—22no—
979C2×Q8—24no—
980C2×Q8—24no—
981C2×Q8—41no—
982C2×Q8—41no—
983C2×Q8—42no—
984C2×Q8—42no—
985C2×Q8—42no—
986C2×Q8—44no—
987C2×Q8—42no—
988C2×Q8—42no—
989C2×Q8—44no—
990C2×Q8—44no—
991C2×Q8—44no—
992C2×Q8—88no—
993C2×D4—22no—
994C2×D4—22no—
995C2×D4—22no—
996C2×D4—22no—
997C2×D4—28no—
998C2×D4—28no—
999C2×D4—28no—
1000C2×D4—28no—
1001C2×D4—28no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—41no—
1005C2×D4—41no—
1006C2×D4—41no—
1007C2×D4—41no—
1008C2×D4—44no—
1009C2×D4—42no—
1010C2×D4—42no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—42no—
1021C2×D4—42no—
1022C2×D4—44no—
1023C2×D4—42no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—42no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—88no—
1041C2×D4H(5,𝔽2)14yes—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—24no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—22no—
1056C22×C4—28no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4C2511yescharacteristic
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2514yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2514yes—
1104C22×C4C2514yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—28no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—41no—
1126C4⋊C4—41no—
1127C4⋊C4—41no—
1128C4⋊C4—41no—
1129C4⋊C4—41no—
1130C4⋊C4—41no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—41no—
1176C22⋊C4—41no—
1177C22⋊C4—41no—
1178C22⋊C4—41no—
1179C22⋊C4—41no—
1180C22⋊C4—41no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—22no—
1216C42—22no—
1217C42—22no—
1218C42—22no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42H(5,𝔽2)14yes—
1226C23—21no—
1227C23—21no—
1228C23—21no—
1229C23—21no—
1230C23—21no—
1231C23—21no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—24no—
1239C23—24no—
1240C23—24no—
1241C23—24no—
1242C23—24no—
1243C23—24no—
1244C23—24no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—24no—
1249C23—24no—
1250C23—24no—
1251C23—24no—
1252C23—88no—
1253C23—84no—
1254C23—84no—
1255C23—84no—
1256C23—164no—
1257C23C2×H(5,𝔽2)12yes—
1258C23C2×H(5,𝔽2)12yes—
1259C23#58512yes—
1260C23C2611yescharacteristic
1261Q8—44no—
1262Q8—84no—
1263Q8—84no—
1264Q8—84no—
1265Q8—164no—
1266D4—44no—
1267D4—44no—
1268D4—44no—
1269D4—84no—
1270D4—84no—
1271D4—88no—
1272D4—88no—
1273D4—88no—
1274D4—88no—
1275D4—88no—
1276D4—88no—
1277D4—84no—
1278D4—84no—
1279D4—84no—
1280D4—164no—
1281D4—164no—
1282D4—164no—
1283C2×C4—28no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—21no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—21no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—44no—
1339C2×C4—44no—
1340C2×C4—44no—
1341C2×C4—44no—
1342C2×C4—82no—
1343C2×C4—82no—
1344C2×C4—82no—
1345C2×C4—82no—
1346C2×C4—88no—
1347C2×C4—84no—
1348C2×C4—88no—
1349C2×C4—84no—
1350C2×C4—84no—
1351C2×C4—164no—
1352C2×C4—164no—
1353C2×C4—164no—
1354C2×C4—164no—
1355C2×C4C2×H(5,𝔽2)12yes—
1356C2×C4C2×H(5,𝔽2)12yes—
1357C2×C4C2×H(5,𝔽2)12yes—
1358C2×C4C2×H(5,𝔽2)12yes—
1359C22—24no—
1360C22—24no—
1361C22—24no—
1362C22—22no—
1363C22—22no—
1364C22—22no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—41no—
1369C22—41no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—41no—
1374C22—44no—
1375C22—44no—
1376C22—44no—
1377C22—44no—
1378C22—44no—
1379C22—44no—
1380C22—44no—
1381C22—44no—
1382C22—44no—
1383C22—44no—
1384C22—44no—
1385C22—44no—
1386C22—44no—
1387C22—44no—
1388C22—168no—
1389C22C22×H(5,𝔽2)11yescharacteristic
1390C22C22×H(5,𝔽2)11yescharacteristic
1391C22C2×#58511yescharacteristic
1392C22H(7,𝔽2)12yes—
1393C222−1+612yes—
1394C4—22no—
1395C4—22no—
1396C4—22no—
1397C4—22no—
1398C4—44no—
1399C4—44no—
1400C4—44no—
1401C4—44no—
1402C4—44no—
1403C4—44no—
1404C4—41no—
1405C4—41no—
1406C4—44no—
1407C4—44no—
1408C4—41no—
1409C4—41no—
1410C4—44no—
1411C4—44no—
1412C4—41no—
1413C4—41no—
1414C4—41no—
1415C4—41no—
1416C2—42no—
1417C2—42no—
1418C2—42no—
1419C2—84no—
1420C2—84no—
1421C2#6281811yescharacteristic
1422C2#6287411yescharacteristic
1423C2#6288611yescharacteristic
1424C2#6304912yes—
1425C2#6305912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58961C2semidirect
2. #58335C2semidirect
3. #57965C2semidirect
4. #57573C2semidirect
5. #57394C2semidirect
6. #56568C2semidirect
7. #56483C2semidirect
8. #54886C2semidirect
9. #53669C2semidirect
10. #53414C2semidirect
11. #49661C2semidirect
12. #49388C2semidirect
13. #48318C2semidirect
14. #47122C2semidirect
15. #46836C2semidirect
16. #46829C2semidirect
17. #46710C2semidirect
18. #46366C2semidirect
19. #46224C2semidirect
20. #46141C2semidirect
21. #45989C2semidirect
22. #45986C2semidirect
23. #45978C2semidirect
24. #45976C2semidirect
25. #35328C2semidirect
26. #35138C2semidirect
27. #35129C2semidirect
31. C2×#532C22semidirect
32. C22×#125C22semidirect
36. #2851C22semidirect
40. #2850C22semidirect
41. #2844C22semidirect
42. #2835C22semidirect
44. #2834C22semidirect
46. #2824C22semidirect
48. #2820C22semidirect
51. #2814C22semidirect
52. #2814C22semidirect
54. #2806C22semidirect
56. #2778C22semidirect
57. #2778C22semidirect
58. #2775C22semidirect
59. #2775C22semidirect
60. #2773C22semidirect
61. #2768C22semidirect
62. #2765C22semidirect
63. #2764C22semidirect
64. #2764C22semidirect
65. #2762C22semidirect
66. #2760C22semidirect
67. #2759C22semidirect
68. #2757C22semidirect
69. #2756C22semidirect
70. #2756C22semidirect
73. #2744C22semidirect
74. #2742C22semidirect
75. #2741C22semidirect
76. #2738C22semidirect
79. #2730C22semidirect
80. #2729C22semidirect
82. #2723C22semidirect
88. #2711C22semidirect
90. #2710C22semidirect
93. #2704C22semidirect
94. #2704C22semidirect
95. #2703C22semidirect
97. #2700C22semidirect
99. #2699C22semidirect
101. #2698C22semidirect
102. #2694C22semidirect
103. #2694C22semidirect
104. #2692C22semidirect
105. #2692C22semidirect
108. #2688C22semidirect
109. #2687C22semidirect
112. #2686C22semidirect
113. #2681C22semidirect
115. #2676C22semidirect
118. #2673C22semidirect
120. #2671C22semidirect
121. #2671C22semidirect
126. #2667C22semidirect
127. #2654C22semidirect
128. #2653C22semidirect
129. #2648C22semidirect
131. #2634C22semidirect
135. #2624C22semidirect
137. #2621C22semidirect
139. #2619C22semidirect
141. #2611C22semidirect
144. #2610C22semidirect
145. #2605C22semidirect
148. #2595C22semidirect
150. #2584C22semidirect
152. #2574C22semidirect
153. #2564C22semidirect
154. #2564C22semidirect
157. #2549C22semidirect
160. #2543C22semidirect
161. #2543C22semidirect
163. #2536C22semidirect
164. #2536C22semidirect
167. #2535C22semidirect
168. #2527C22semidirect
169. #2526C22semidirect
170. #2525C22semidirect
172. #2510C22semidirect
173. #2510C22semidirect
175. #2487C22semidirect
177. #2486C22semidirect
178. #2484C22semidirect
181. #2481C22semidirect
183. #2477C22semidirect
184. #2474C22semidirect
185. #2468C22semidirect
186. #2464C22semidirect
187. #2464C22semidirect
188. #2463C22semidirect
191. #2455C22semidirect
192. #2450C22semidirect
193. #2449C22semidirect
194. #2449C22semidirect
195. #2449C22semidirect
196. #2447C22semidirect
198. #2443C22semidirect
199. #2443C22semidirect
200. #2438C22semidirect
202. #2430C22semidirect
205. #2425C22semidirect
210. #2416C22semidirect
218. #2407C22semidirect
221. #2382C22semidirect
223. #2379C22semidirect
224. #2377C22semidirect
225. #2363C22semidirect
228. #2322C22semidirect
231. #2311C22semidirect
233. #2283C22semidirect
234. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#589612
#583352
#579652
#575732
#573942
#565682
#564832
#548862
#536692
#534142
#496612
#493882
#483182
#471222
#468362
#468292
#467102
#463662
#462242
#461412
#459892
#459862
#459782
#459762
#353282
#351382
#351292