Finite Group Databasebeta

← #8810233

Subgroups — #8810233

Order 512.

4702 conjugacy classes of subgroups.

The subgroup lattice has 1301 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60047C211yesmaximal, characteristic, complemented
2#58730C214yesmaximal, complemented
3#57864C214yesmaximal, complemented
4#53183C212yesmaximal, complemented
5#51541C212yesmaximal, complemented
6#51409C212yesmaximal, complemented
7#50953C214yesmaximal, complemented
8#49246C214yesmaximal, complemented
9#48420C214yesmaximal, complemented
10#48128C214yesmaximal, complemented
11#47865C214yesmaximal, complemented
12#47418C212yesmaximal, complemented
13#46427C212yesmaximal, complemented
14#46287C211yesmaximal, characteristic, complemented
15#46091C212yesmaximal, complemented
16#43535C214yesmaximal, complemented
17#43242C214yesmaximal, complemented
18#41244C214yesmaximal, complemented
19#39504C212yesmaximal, complemented
20#38484C212yesmaximal, complemented
21#37154C212yesmaximal, complemented
22#36361C212yesmaximal, complemented
23#35308C211yesmaximal, characteristic, complemented
24C2×#562C2212yes—
25C2×#553C2212yes—
26C2×#551C2212yescomplemented
27C2×#538C2212yescomplemented
28C2×#537C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic, complemented
31C2×C4×#41C2211yescharacteristic, complemented
32#2857C2212yescomplemented
33#2854C2212yes—
34#2854C2212yes—
35#2851C2212yescomplemented
36#2850C2212yes—
37#2836C2214yescomplemented
38#2836C2214yescomplemented
39#2832C2212yes—
40#2826C2212yes—
41#2817C2212yescomplemented
42#2809C2212yescomplemented
43#2809C2211yescharacteristic, complemented
44#2808C2212yes—
45#2808C2212yes—
46#2805C2212yescomplemented
47#2802C2214yescomplemented
48#2798C2214yescomplemented
49#2797C2214yes—
50#2796C2214yes—
51#2793C2214yescomplemented
52#2793C2214yescomplemented
53#2792C2214yescomplemented
54#2786C2214yescomplemented
55#2783C2214yescomplemented
56#2783C2214yescomplemented
57#2783C2214yescomplemented
58#2774C2214yescomplemented
59#2773C2214yescomplemented
60#2761C2214yes—
61#2757C2214yes—
62#2756C2214yes—
63#2750C2214yes—
64#2747C2214yescomplemented
65#2742C2212yescomplemented
66#2741C2214yescomplemented
67#2740C2214yes—
68#2735C2214yescomplemented
69#2734C2211yescharacteristic, complemented
70#2732C2212yes—
71#2729C2214yescomplemented
72#2727C2212yes—
73#2725C2214yescomplemented
74#2725C2214yescomplemented
75#2723C2214yes—
76#2720C2214yescomplemented
77#2717C2212yescomplemented
78#2717C2214yescomplemented
79#2715C2214yes—
80#2715C2214yes—
81#2706C2214yes—
82#2706C2214yescomplemented
83#2703C2214yes—
84#2701C2214yes—
85#2700C2214yescomplemented
86#2698C2214yescomplemented
87#2698C2214yescomplemented
88#2698C2214yescomplemented
89#2697C2212yescomplemented
90#2697C2214yescomplemented
91#2696C2214yes—
92#2693C2212yes—
93#2689C2214yescomplemented
94#2688C2214yes—
95#2687C2214yescomplemented
96#2686C2214yescomplemented
97#2685C2214yes—
98#2683C2211yescharacteristic
99#2683C2214yes—
100#2681C2214yes—
101#2680C2214yescomplemented
102#2679C2211yescharacteristic
103#2678C2214yes—
104#2678C2214yes—
105#2677C2214yescomplemented
106#2674C2214yescomplemented
107#2672C2214yes—
108#2668C2214yes—
109#2668C2214yescomplemented
110#2666C2214yescomplemented
111#2663C2214yescomplemented
112#2660C2212yescomplemented
113#2651C2214yes—
114#2651C2214yes—
115#2650C2214yescomplemented
116#2640C2212yes—
117#2630C2214yes—
118#2621C2212yescomplemented
119#2620C2212yes—
120#2618C2214yes—
121#2611C2212yescomplemented
122#2610C2212yes—
123#2602C2214yes—
124#2597C2214yescomplemented
125#2595C2214yescomplemented
126#2593C2212yes—
127#2589C2214yescomplemented
128#2588C2214yescomplemented
129#2584C2212yescomplemented
130#2580C2212yes—
131#2577C2214yescomplemented
132#2575C2214yescomplemented
133#2574C2214yescomplemented
134#2569C2214yescomplemented
135#2561C2212yescomplemented
136#2560C2214yes—
137#2556C2214yescomplemented
138#2555C2214yes—
139#2549C2214yescomplemented
140#2534C2214yescomplemented
141#2533C2214yescomplemented
142#2530C2214yescomplemented
143#2526C2214yes—
144#2523C2212yescomplemented
145#2518C2214yes—
146#2516C2214yescomplemented
147#2512C2214yes—
148#2508C2214yescomplemented
149#2498C2214yescomplemented
150#2497C2214yescomplemented
151#2488C2214yescomplemented
152#2488C2214yescomplemented
153#2487C2212yescomplemented
154#2486C2214yescomplemented
155#2485C2214yes—
156#2485C2212yescomplemented
157#2481C2214yescomplemented
158#2481C2214yescomplemented
159#2481C2214yescomplemented
160#2480C2214yescomplemented
161#2479C2214yes—
162#2479C2214yescomplemented
163#2479C2214yescomplemented
164#2477C2214yes—
165#2474C2214yescomplemented
166#2472C2214yes—
167#2472C2214yes—
168#2470C2214yescomplemented
169#2469C2214yescomplemented
170#2467C2214yes—
171#2467C2214yes—
172#2464C2214yes—
173#2457C2214yes—
174#2455C2214yescomplemented
175#2449C2214yescomplemented
176#2444C2214yes—
177#2444C2214yes—
178#2443C2214yescomplemented
179#2439C2214yescomplemented
180#2437C2214yescomplemented
181#2432C2212yes—
182#2430C2214yescomplemented
183#2429C2214yescomplemented
184#2427C2214yes—
185#2427C2214yescomplemented
186#2425C2214yescomplemented
187#2425C2214yescomplemented
188#2424C2214yes—
189#2422C2214yescomplemented
190#2420C2214yescomplemented
191#2417C2214yescomplemented
192#2416C2212yes—
193#2414C2212yes—
194#2409C2214yescomplemented
195#2404C2212yes—
196#2395C2214yescomplemented
197#2378C2214yescomplemented
198#2376C2212yescomplemented
199#2375C2212yes—
200#2373C2214yescomplemented
201#2372C2212yescomplemented
202#2369C2212yescomplemented
203#2361C2214yescomplemented
204#2359C2214yescomplemented
205#2359C2214yescomplemented
206#2352C2212yescomplemented
207#2352C2214yescomplemented
208#2335C2214yescomplemented
209#2333C2212yescomplemented
210#2332C2214yescomplemented
211#2321C2214yes—
212#2317C2211yescharacteristic, complemented
213#2313C2214yescomplemented
214C4×#121C2212yes—
215#2297C2211yescharacteristic
216#2296C2212yescomplemented
217C2×#391C2211yescharacteristic, complemented
218C2×#389C2212yescomplemented
219C22×#41C2311yescharacteristic
220C22×#41C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222#562—48no—
223#553—48no—
224#551—48no—
225#538—48no—
226#537—44no—
227#536—44no—
228#536—44no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×#126C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#125C2312yes—
237C2×#125C2312yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2314yes—
242C2×#124C2312yes—
243C2×#123C2314yes—
244C2×#123C2312yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2312yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×#121C2312yes—
264C2×#121C2314yes—
265C2×#121C2312yes—
266C2×#121C2312yes—
267C2×#121C2312yes—
268C2×#121C2312yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#120C2314yes—
273C2×#120C2312yes—
274C2×#120C2312yes—
275C2×#120C2314yes—
276C4×#41—44no—
277C2×C4×Q8C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2314yes—
289C2×#117C2312yes—
290C2×#117C2312yes—
291C2×#117C2312yes—
292C22×C4⋊C4C2314yes—
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2314yes—
298C22×C42C2312yes—
299C22×C42C2311yescharacteristic
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2312yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#399C2312yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2312yes—
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#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2312yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2312yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2312yes—
406#393C2314yes—
407#392C2312yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#392C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2311yescharacteristic
415#391C2312yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2311yescharacteristic
421#391C2314yes—
422#391C2312yes—
423#390C2312yes—
424#390C2314yes—
425#390C2314yes—
426#390C2312yes—
427#390C2314yes—
428#390C2314yes—
429#390C2311yescharacteristic
430#390C2311yescharacteristic
431#390C2314yes—
432#390C2312yes—
433#390C2314yes—
434#390C2314yes—
435#390C2312yes—
436#389C2314yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2314yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#388C2314yes—
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#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
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#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2312yes—
548#386C2312yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2312yes—
557#385C2312yes—
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#384C2312yes—
572#384C2314yes—
573#383C2314yes—
574#382C2312yes—
575#382C2314yes—
576#382C2314yes—
577#382C2312yes—
578#382C2314yes—
579#381C2314yes—
580#381C2312yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#380C2312yes—
585#380C2314yes—
586#380C2312yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2312yes—
593#380C2312yes—
594#380C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#379C2314yes—
599#379C2314yes—
600#379C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618#376C2312yes—
619#376C2312yes—
620C2×#95C2314yes—
621C2×#95C2314yes—
622C25C2412yes—
623C2×#41—24no—
624C2×#41—42no—
625C2×#41—42no—
626C2×#41—42no—
627C2×#41—42no—
628C2×#41—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8—42no—
632C22×Q8C2411yescharacteristic
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2411yescharacteristic
636C22×Q8C2412yes—
637C22×Q8C2412yes—
638C22×D4C2412yes—
639C22×D4C2412yes—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2411yescharacteristic
645C22×D4C2412yes—
646C22×D4C2412yes—
647C22×D4C2414yes—
648C22×D4C2411yescharacteristic
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2414yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2412yes—
662C4⋊Q8—44no—
663C4⋊Q8—44no—
664C4⋊Q8—44no—
665#126—48no—
666#126—48no—
667#126—48no—
668#126—48no—
669#125—44no—
670#125—44no—
671#124—28no—
672#124—44no—
673#124—44no—
674#124—48no—
675#124—44no—
676#123—28no—
677#123—216no—
678#123—48no—
679#123—48no—
680#123—48no—
681#123—48no—
682#123—44no—
683#123—48no—
684#123—48no—
685C22⋊Q8—44no—
686C22⋊Q8—44no—
687C22⋊Q8—44no—
688C22⋊Q8—48no—
689C22⋊Q8—48no—
690C22⋊Q8—48no—
691C22⋊Q8—48no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—44no—
695C22⋊Q8—44no—
696#121—28no—
697#121—216no—
698#121—44no—
699#121—48no—
700#121—48no—
701#121—48no—
702#121—44no—
703#121—44no—
704#121—44no—
705#120—48no—
706#120—44no—
707#120—48no—
708#120—44no—
709C4×Q8—44no—
710C4×D4—28no—
711C4×D4—44no—
712C4×D4—48no—
713C4×D4—44no—
714C4×D4—48no—
715C4×D4—44no—
716C4×D4—48no—
717C4×D4—48no—
718#117—24no—
719#117—42no—
720#117—44no—
721#117—44no—
722#117—44no—
723#117—48no—
724C2×C4⋊C4—44no—
725C2×C4⋊C4—48no—
726C2×C4⋊C4—42no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C22⋊C4—44no—
777C2×C22⋊C4—48no—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
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⋊C4C2411yescharacteristic
827C2×C42—44no—
828C2×C42—42no—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2411yescharacteristic
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2411yescharacteristic
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2412yes—
855#95C2412yes—
856#95C2414yes—
857#95C2414yes—
858#95C2412yes—
859#95C2412yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896C24—42no—
897C24—44no—
898C24—42no—
899C24—44no—
900C24—42no—
901C24C2512yes—
902C24C2514yes—
903C24C2512yes—
904C24C2511yescharacteristic
905#41—416no—
906#41—88no—
907C2×Q8—22no—
908C2×Q8—24no—
909C2×Q8—24no—
910C2×Q8—22no—
911C2×Q8—41no—
912C2×Q8—41no—
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—41no—
916C2×Q8—42no—
917C2×Q8—41no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—42no—
922C2×Q8—44no—
923C2×Q8—42no—
924C2×Q8—88no—
925C2×D4—24no—
926C2×D4—24no—
927C2×D4—28no—
928C2×D4—28no—
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—24no—
932C2×D4—24no—
933C2×D4—22no—
934C2×D4—41no—
935C2×D4—41no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—41no—
941C2×D4—42no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—41no—
946C2×D4—42no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—42no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—42no—
955C2×D4—44no—
956C2×D4H(5,𝔽2)14yes—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—28no—
964C22×C4—24no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—28no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—44no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—42no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2514yes—
998C22×C4C2514yes—
999C22×C4C2514yes—
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2514yes—
1005C22×C4C2512yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2514yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2511yescharacteristic
1013C4⋊C4—28no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—28no—
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—24no—
1025C4⋊C4—28no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—44no—
1033C4⋊C4—42no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C22⋊C4—22no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—24no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
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—42no—
1085C22⋊C4—44no—
1086C22⋊C4—42no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—42no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—42no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4H(5,𝔽2)14yes—
1110C42—24no—
1111C42—24no—
1112C42—24no—
1113C42—41no—
1114C42—41no—
1115C42—42no—
1116C42—42no—
1117C42—44no—
1118C42—44no—
1119C42—44no—
1120C42—42no—
1121C42—44no—
1122C42—44no—
1123C42—44no—
1124C42—44no—
1125C42—44no—
1126C42—42no—
1127C23—22no—
1128C23—21no—
1129C23—22no—
1130C23—22no—
1131C23—22no—
1132C23—22no—
1133C23—21no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—24no—
1139C23—24no—
1140C23—22no—
1141C23—24no—
1142C23—24no—
1143C23—24no—
1144C23—24no—
1145C23—22no—
1146C23—24no—
1147C23—24no—
1148C23—24no—
1149C23—84no—
1150C23—88no—
1151C23—162no—
1152C23—162no—
1153C23—164no—
1154C23C2×H(5,𝔽2)14yes—
1155C23C2×H(5,𝔽2)12yes—
1156C23C2611yescharacteristic
1157Q8—44no—
1158Q8—84no—
1159Q8—84no—
1160Q8—82no—
1161Q8—162no—
1162Q8—162no—
1163D4—44no—
1164D4—48no—
1165D4—84no—
1166D4—82no—
1167D4—88no—
1168D4—88no—
1169D4—88no—
1170D4—88no—
1171D4—84no—
1172D4—162no—
1173D4—164no—
1174C2×C4—28no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—48no—
1227C2×C4—48no—
1228C2×C4—48no—
1229C2×C4—84no—
1230C2×C4—88no—
1231C2×C4—84no—
1232C2×C4—88no—
1233C2×C4—84no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—164no—
1237C2×C4—164no—
1238C2×C4C2×H(5,𝔽2)14yes—
1239C2×C4C2×H(5,𝔽2)12yes—
1240C2×C4#58514yes—
1241C2×C4#58512yes—
1242C22—24no—
1243C22—24no—
1244C22—22no—
1245C22—24no—
1246C22—24no—
1247C22—41no—
1248C22—41no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—44no—
1256C22—42no—
1257C22—44no—
1258C22—42no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—168no—
1267C22C22×H(5,𝔽2)11yescharacteristic
1268C22C22×H(5,𝔽2)11yescharacteristic
1269C22C2×#58512yes—
1270C22C2×#58511yescharacteristic
1271C222−1+612yes—
1272C4—22no—
1273C4—22no—
1274C4—24no—
1275C4—24no—
1276C4—44no—
1277C4—44no—
1278C4—42no—
1279C4—42no—
1280C4—44no—
1281C4—42no—
1282C4—44no—
1283C4—42no—
1284C4—44no—
1285C4—42no—
1286C4—42no—
1287C4—44no—
1288C4—44no—
1289C4—44no—
1290C4—44no—
1291C2—44no—
1292C2—42no—
1293C2—82no—
1294C2—84no—
1295C2#6281811yescharacteristic
1296C2#6289812yes—
1297C2#6296812yes—
1298C2#6302411yescharacteristic
1299C2#6306311yescharacteristic
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. #60047C2semidirect
2. #58730C2semidirect
3. #57864C2semidirect
4. #53183C2semidirect
5. #51541C2semidirect
6. #51409C2semidirect
7. #50953C2semidirect
8. #49246C2semidirect
9. #48420C2semidirect
10. #48128C2semidirect
11. #47865C2semidirect
12. #47418C2semidirect
13. #46427C2semidirect
14. #46287C2semidirect
15. #46091C2semidirect
16. #43535C2semidirect
17. #43242C2semidirect
18. #41244C2semidirect
19. #39504C2semidirect
20. #38484C2semidirect
21. #37154C2semidirect
22. #36361C2semidirect
23. #35308C2semidirect
26. C2×#551C22semidirect
27. C2×#538C22semidirect
30. C2×#536C22semidirect
31. C2×C4×#41C22semidirect
32. #2857C22semidirect
35. #2851C22semidirect
37. #2836C22semidirect
38. #2836C22semidirect
41. #2817C22semidirect
42. #2809C22semidirect
43. #2809C22semidirect
46. #2805C22semidirect
47. #2802C22semidirect
48. #2798C22semidirect
51. #2793C22semidirect
52. #2793C22semidirect
53. #2792C22semidirect
54. #2786C22semidirect
55. #2783C22semidirect
56. #2783C22semidirect
57. #2783C22semidirect
58. #2774C22semidirect
59. #2773C22semidirect
64. #2747C22semidirect
65. #2742C22semidirect
66. #2741C22semidirect
68. #2735C22semidirect
69. #2734C22semidirect
71. #2729C22semidirect
73. #2725C22semidirect
74. #2725C22semidirect
76. #2720C22semidirect
77. #2717C22semidirect
78. #2717C22semidirect
82. #2706C22semidirect
85. #2700C22semidirect
86. #2698C22semidirect
87. #2698C22semidirect
88. #2698C22semidirect
89. #2697C22semidirect
90. #2697C22semidirect
93. #2689C22semidirect
95. #2687C22semidirect
96. #2686C22semidirect
101. #2680C22semidirect
105. #2677C22semidirect
106. #2674C22semidirect
109. #2668C22semidirect
110. #2666C22semidirect
111. #2663C22semidirect
112. #2660C22semidirect
115. #2650C22semidirect
118. #2621C22semidirect
121. #2611C22semidirect
124. #2597C22semidirect
125. #2595C22semidirect
127. #2589C22semidirect
128. #2588C22semidirect
129. #2584C22semidirect
131. #2577C22semidirect
132. #2575C22semidirect
133. #2574C22semidirect
134. #2569C22semidirect
135. #2561C22semidirect
137. #2556C22semidirect
139. #2549C22semidirect
140. #2534C22semidirect
141. #2533C22semidirect
142. #2530C22semidirect
144. #2523C22semidirect
146. #2516C22semidirect
148. #2508C22semidirect
149. #2498C22semidirect
150. #2497C22semidirect
151. #2488C22semidirect
152. #2488C22semidirect
153. #2487C22semidirect
154. #2486C22semidirect
156. #2485C22semidirect
157. #2481C22semidirect
158. #2481C22semidirect
159. #2481C22semidirect
160. #2480C22semidirect
162. #2479C22semidirect
163. #2479C22semidirect
165. #2474C22semidirect
168. #2470C22semidirect
169. #2469C22semidirect
174. #2455C22semidirect
175. #2449C22semidirect
178. #2443C22semidirect
179. #2439C22semidirect
180. #2437C22semidirect
182. #2430C22semidirect
183. #2429C22semidirect
185. #2427C22semidirect
186. #2425C22semidirect
187. #2425C22semidirect
189. #2422C22semidirect
190. #2420C22semidirect
191. #2417C22semidirect
194. #2409C22semidirect
196. #2395C22semidirect
197. #2378C22semidirect
198. #2376C22semidirect
200. #2373C22semidirect
201. #2372C22semidirect
202. #2369C22semidirect
203. #2361C22semidirect
204. #2359C22semidirect
205. #2359C22semidirect
206. #2352C22semidirect
207. #2352C22semidirect
208. #2335C22semidirect
209. #2333C22semidirect
210. #2332C22semidirect
212. #2317C22semidirect
213. #2313C22semidirect
216. #2296C22semidirect
217. C2×#391C22semidirect
218. C2×#389C22semidirect

Maximal subgroups

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

subgroupindex
#600472
#587302
#578642
#531832
#515412
#514092
#509532
#492462
#484202
#481282
#478652
#474182
#464272
#462872
#460912
#435352
#432422
#412442
#395042
#384842
#371542
#363612
#353082