Finite Group Databasebeta

← #7714767

Subgroups — #7714767

Order 512.

4834 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51996C214yesmaximal, complemented
2#51960C214yesmaximal, complemented
3#51953C214yesmaximal, complemented
4#51952C214yesmaximal, complemented
5#47380C214yesmaximal, complemented
6#47376C214yesmaximal, complemented
7#47373C214yesmaximal, complemented
8#47369C214yesmaximal, complemented
9#38126C214yesmaximal, complemented
10#38114C214yesmaximal, complemented
11#37941C212yesmaximal, complemented
12#37933C212yesmaximal, complemented
13#37753C212yesmaximal, complemented
14#37745C212yesmaximal, complemented
15#37517C212yesmaximal, complemented
16#37236C212yesmaximal, complemented
17#37187C212yesmaximal, complemented
18#35154C211yesmaximal, characteristic, complemented
19#35153C211yesmaximal, characteristic, complemented
20#35099C212yesmaximal, complemented
21#35031C212yesmaximal, complemented
22#34409C212yesmaximal, complemented
23C2×#2326C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#536C2212yes—
27C22×#124C2211yescharacteristic
28C2×#525C2212yes—
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31#2855C2212yes—
32#2855C2212yes—
33#2854C2212yes—
34#2854C2212yes—
35#2853C2214yes—
36#2848C2212yes—
37#2847C2212yes—
38#2830C2212yes—
39#2829C2214yes—
40#2828C2212yes—
41#2803C2214yescomplemented
42#2801C2214yescomplemented
43#2800C2214yescomplemented
44#2798C2214yescomplemented
45#2798C2214yescomplemented
46#2797C2214yescomplemented
47#2795C2212yescomplemented
48#2794C2212yescomplemented
49#2793C2214yescomplemented
50#2792C2212yescomplemented
51#2791C2214yescomplemented
52#2790C2214yescomplemented
53#2783C2214yescomplemented
54#2780C2214yescomplemented
55#2779C2214yescomplemented
56#2779C2214yescomplemented
57#2770C2214yescomplemented
58#2768C2214yescomplemented
59#2759C2214yescomplemented
60#2757C2214yescomplemented
61#2754C2214yescomplemented
62#2752C2214yescomplemented
63#2739C2214yescomplemented
64#2738C2214yescomplemented
65#2733C2212yes—
66#2733C2212yes—
67#2733C2214yes—
68#2731C2212yes—
69#2731C2212yes—
70#2731C2214yes—
71#2730C2214yes—
72#2730C2214yes—
73#2730C2214yes—
74#2730C2214yes—
75#2730C2214yescomplemented
76#2729C2214yescomplemented
77#2725C2214yescomplemented
78#2721C2214yescomplemented
79#2720C2214yescomplemented
80#2718C2214yescomplemented
81#2711C2214yescomplemented
82#2707C2214yescomplemented
83#2705C2214yescomplemented
84#2701C2214yescomplemented
85#2701C2214yescomplemented
86#2698C2214yescomplemented
87#2692C2214yescomplemented
88#2688C2214yescomplemented
89#2687C2214yescomplemented
90#2680C2212yescomplemented
91#2674C2214yescomplemented
92#2671C2214yescomplemented
93#2662C2214yes—
94#2661C2214yes—
95#2651C2214yes—
96#2648C2214yes—
97#2646C2212yes—
98#2643C2214yes—
99#2639C2212yes—
100#2627C2212yes—
101#2627C2212yes—
102#2622C2214yes—
103#2618C2212yes—
104#2618C2212yes—
105#2613C2214yes—
106#2611C2214yescomplemented
107#2602C2214yes—
108#2602C2214yes—
109#2601C2214yescomplemented
110#2600C2214yes—
111#2600C2214yes—
112#2597C2214yescomplemented
113#2594C2214yescomplemented
114#2593C2212yes—
115#2593C2214yescomplemented
116#2559C2214yescomplemented
117#2556C2214yescomplemented
118#2555C2212yes—
119#2554C2214yes—
120#2554C2214yescomplemented
121#2533C2214yescomplemented
122#2532C2214yescomplemented
123#2531C2214yescomplemented
124#2531C2214yescomplemented
125#2530C2214yescomplemented
126#2530C2214yescomplemented
127#2529C2214yescomplemented
128#2528C2214yescomplemented
129#2527C2214yescomplemented
130#2526C2214yescomplemented
131#2526C2214yescomplemented
132#2525C2214yescomplemented
133#2522C2214yescomplemented
134#2521C2214yescomplemented
135#2518C2214yescomplemented
136#2518C2214yescomplemented
137#2516C2214yescomplemented
138#2516C2214yescomplemented
139#2513C2214yescomplemented
140#2510C2214yescomplemented
141#2490C2214yescomplemented
142#2488C2214yescomplemented
143#2485C2212yes—
144#2485C2212yes—
145#2482C2214yes—
146#2481C2214yes—
147#2480C2214yes—
148#2478C2214yescomplemented
149#2477C2214yescomplemented
150#2475C2214yescomplemented
151#2473C2214yes—
152#2472C2214yes—
153#2470C2214yescomplemented
154#2464C2214yescomplemented
155#2460C2214yescomplemented
156#2453C2214yescomplemented
157#2453C2214yescomplemented
158#2452C2214yescomplemented
159#2451C2214yescomplemented
160#2451C2214yescomplemented
161#2450C2214yescomplemented
162#2449C2214yes—
163#2443C2214yes—
164#2432C2214yescomplemented
165#2430C2214yescomplemented
166#2429C2214yescomplemented
167#2429C2214yescomplemented
168#2426C2214yescomplemented
169#2426C2214yescomplemented
170#2424C2214yes—
171#2418C2214yes—
172#2415C2212yes—
173#2415C2212yes—
174#2414C2212yes—
175#2414C2212yes—
176#2411C2214yes—
177#2411C2214yes—
178#2407C2212yes—
179#2407C2212yes—
180#2404C2214yes—
181#2381C2212yescomplemented
182#2379C2212yescomplemented
183#2378C2214yescomplemented
184#2372C2212yescomplemented
185#2369C2212yescomplemented
186#2368C2214yescomplemented
187#2359C2214yes—
188#2359C2214yes—
189#2343C2214yes—
190#2339C2214yes—
191#2337C2214yescomplemented
192#2332C2214yescomplemented
193#2331C2214yescomplemented
194#2329C2212yes—
195#2329C2214yescomplemented
196#2326C2214yes—
197#2326C2214yes—
198#2326C2214yes—
199#2326C2214yes—
200#2325C2212yes—
201#2322C2214yes—
202#2321C2214yes—
203#2318C2214yes—
204#2316C2211yescharacteristic
205#2316C2211yescharacteristic
206#2310C2212yes—
207C4×#123C2214yes—
208#2297C2212yes—
209#2296C2212yes—
210C2×#391C2211yescharacteristic
211C2×#390C2211yescharacteristic
212C2×#388C2212yes—
213C2×#388C2212yes—
214C2×#385C2212yes—
215C2×#385C2212yes—
216C2×#384C2211yescharacteristic
217#2280C2212yes—
218C2×#376C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2312yes—
221C23×Q8C2311yescharacteristic
222C23×D4C2311yescharacteristic
223C24×C4C2312yes—
224#544—44no—
225#537—44no—
226#536—216no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#125C2314yes—
233C2×#125C2314yes—
234C2×#124—28no—
235C2×#124C2312yes—
236C2×#124C2312yes—
237C2×#124C2314yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2314yes—
241#525—48no—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2314yes—
256C2×#121C2312yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2314yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2314yes—
263C2×#120C2314yes—
264C2×#120C2314yes—
265C2×C4×Q8—44no—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2314yes—
268C2×C4×D4—44no—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×#117C2312yes—
277C2×#117C2312yes—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2312yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298#401C2314yes—
299#400C2312yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2312yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#398C2314yes—
317#398C2312yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2312yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#395C2312yes—
361#395C2312yes—
362#395C2314yes—
363#395C2314yes—
364#394C2314yes—
365#394C2312yes—
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#394C2314yes—
379#394C2312yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#392C2314yes—
392#392C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2314yes—
396#392C2314yes—
397#392C2314yes—
398#391C2312yes—
399#391C2314yes—
400#391C2312yes—
401#391C2314yes—
402#391C2312yes—
403#391C2312yes—
404#391C2314yes—
405#391C2312yes—
406#391C2312yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2314yes—
413#391C2314yes—
414#390C2312yes—
415#390C2312yes—
416#390C2314yes—
417#390C2314yes—
418#390C2314yes—
419#390C2314yes—
420#390C2314yes—
421#390C2312yes—
422#390C2312yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
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#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#386C2314yes—
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#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
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#384C2312yes—
571#384C2314yes—
572#384C2312yes—
573#383C2314yes—
574#383C2314yes—
575#382C2314yes—
576#382C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#380C2312yes—
583#380C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2312yes—
594#379C2314yes—
595#379C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613#376C2314yes—
614#376C2314yes—
615#376C2314yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2314yes—
619C2×#95C2312yes—
620C2×#95C2312yes—
621C25C2412yes—
622C2×#41—28no—
623C2×#41—44no—
624C2×#41—44no—
625C2×#41—44no—
626C2×#41—82no—
627C2×#41—82no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8#4118yescomplemented
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×D4—24no—
637C22×D4—42no—
638C22×D4—42no—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2411yescharacteristic
642C22×D4C2411yescharacteristic
643C22×D4C2412yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C23×C4—28no—
651C23×C4—82no—
652C23×C4—82no—
653C23×C4C2411yescharacteristic
654C23×C4C2411yescharacteristic
655C23×C4C2411yescharacteristic
656C23×C4C2411yescharacteristic
657C23×C4C2411yescharacteristic
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2411yescharacteristic
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2412yes—
666C23×C4C2414yes—
667C23×C4C2414yes—
668C23×C4C2414yes—
669C23×C4C2411yescharacteristic
670C4⋊Q8—28no—
671C4⋊Q8—28no—
672C4⋊Q8—48no—
673#126—84no—
674#126—84no—
675#125—48no—
676#125—84no—
677#124—28no—
678#124—28no—
679#124—216no—
680#124—28no—
681#124—28no—
682#124—84no—
683#123—216no—
684#123—216no—
685#123—48no—
686#123—84no—
687#123—84no—
688C22⋊Q8—216no—
689C22⋊Q8—216no—
690C22⋊Q8—28no—
691C22⋊Q8—44no—
692C22⋊Q8—48no—
693C22⋊Q8—44no—
694C22⋊Q8—84no—
695C22⋊Q8—82no—
696C22⋊Q8—82no—
697#121—28no—
698#121—48no—
699#121—44no—
700#121—44no—
701#121—84no—
702#121—82no—
703#121—82no—
704#120—48no—
705#120—48no—
706C4×Q8—48no—
707C4×Q8—48no—
708C4×D4—44no—
709C4×D4—44no—
710C4×D4—44no—
711C4×D4—44no—
712C4×D4—48no—
713C4×D4—48no—
714C4×D4—48no—
715#117—28no—
716#117—44no—
717#117—44no—
718#117—44no—
719#117—82no—
720#117—82no—
721C2×C4⋊C4—24no—
722C2×C4⋊C4—24no—
723C2×C4⋊C4—42no—
724C2×C4⋊C4—42no—
725C2×C4⋊C4—82no—
726C2×C4⋊C4—82no—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C22⋊C4—28no—
773C2×C22⋊C4—28no—
774C2×C22⋊C4—44no—
775C2×C22⋊C4—82no—
776C2×C22⋊C4—82no—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
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⋊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×C42—24no—
825C2×C42—24no—
826C2×C42—42no—
827C2×C42—42no—
828C2×C42—42no—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2414yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
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#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898C24—24no—
899C24—24no—
900C24—24no—
901C24—42no—
902C24—42no—
903C24—42no—
904C24—42no—
905C24C2512yes—
906C24C2512yes—
907C24C2514yes—
908C24C2511yescharacteristic
909#41—816no—
910#41—816no—
911C2×Q8—24no—
912C2×Q8—24no—
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—416no—
916C2×Q8—42no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—42no—
922C2×Q8—42no—
923C2×Q8—44no—
924C2×Q8C2×#4118yes—
925C2×Q8C2×#4118yes—
926C2×D4—28no—
927C2×D4—28no—
928C2×D4—28no—
929C2×D4—24no—
930C2×D4—22no—
931C2×D4—22no—
932C2×D4—24no—
933C2×D4—24no—
934C2×D4—41no—
935C2×D4—42no—
936C2×D4—41no—
937C2×D4—42no—
938C2×D4—41no—
939C2×D4—41no—
940C2×D4—416no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—42no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—42no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—24no—
966C22×C4—22no—
967C22×C4—22no—
968C22×C4—22no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—28no—
974C22×C4—24no—
975C22×C4—24no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—42no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—816no—
1003C22×C4C2×#4114yes—
1004C22×C4C2×#4114yes—
1005C22×C4C2×#4114yes—
1006C22×C4H(5,𝔽2)14yes—
1007C22×C4C2514yes—
1008C22×C4C2514yes—
1009C22×C4C2512yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2511yescharacteristic
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—41no—
1037C4⋊C4—42no—
1038C4⋊C4—41no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
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—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
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⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C42—24no—
1119C42—24no—
1120C42—24no—
1121C42—24no—
1122C42—24no—
1123C42—24no—
1124C42—42no—
1125C42—42no—
1126C42—44no—
1127C42—44no—
1128C42—44no—
1129C42—42no—
1130C42—42no—
1131C42—44no—
1132C42—44no—
1133C42—44no—
1134C42—44no—
1135C42—44no—
1136C42—44no—
1137C23—22no—
1138C23—22no—
1139C23—24no—
1140C23—22no—
1141C23—22no—
1142C23—24no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—22no—
1147C23—24no—
1148C23—22no—
1149C23—22no—
1150C23—22no—
1151C23—24no—
1152C23—24no—
1153C23—22no—
1154C23—22no—
1155C23—24no—
1156C23—24no—
1157C23—22no—
1158C23—22no—
1159C23—22no—
1160C23—48no—
1161C23—48no—
1162C23—48no—
1163C23—84no—
1164C23—84no—
1165C23—84no—
1166C23—84no—
1167C23C22×#4112yes—
1168C23C2×H(5,𝔽2)12yes—
1169C23#58512yes—
1170C23C2611yescharacteristic
1171Q8—48no—
1172Q8—48no—
1173Q8—84no—
1174Q8—84no—
1175Q8—162no—
1176D4—44no—
1177D4—48no—
1178D4—44no—
1179D4—416no—
1180D4—84no—
1181D4—84no—
1182D4—88no—
1183D4—88no—
1184D4—162no—
1185D4—164no—
1186D4—164no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—28no—
1198C2×C4—28no—
1199C2×C4—28no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—44no—
1241C2×C4—48no—
1242C2×C4—48no—
1243C2×C4—48no—
1244C2×C4—44no—
1245C2×C4—84no—
1246C2×C4—84no—
1247C2×C4—88no—
1248C2×C4—82no—
1249C2×C4—82no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4—88no—
1253C2×C4—164no—
1254C2×C4C22×#4112yes—
1255C2×C4C22×#4112yes—
1256C2×C4C22×#4114yes—
1257C2×C4C22×#4114yes—
1258C2×C4C2×H(5,𝔽2)14yes—
1259C22—24no—
1260C22—22no—
1261C22—24no—
1262C22—22no—
1263C22—44no—
1264C22—42no—
1265C22—42no—
1266C22—44no—
1267C22—44no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—44no—
1275C22—44no—
1276C22—42no—
1277C22—42no—
1278C22—44no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—44no—
1283C22—42no—
1284C22—816no—
1285C22#350514yes—
1286C22C23×#4111yescharacteristic
1287C22C22×H(5,𝔽2)11yescharacteristic
1288C22C2×#58511yescharacteristic
1289C22H(7,𝔽2)12yes—
1290C222−1+612yes—
1291C4—24no—
1292C4—22no—
1293C4—22no—
1294C4—24no—
1295C4—24no—
1296C4—44no—
1297C4—44no—
1298C4—44no—
1299C4—44no—
1300C4—42no—
1301C4—42no—
1302C4—44no—
1303C4—42no—
1304C4—42no—
1305C4—44no—
1306C4—44no—
1307C4—44no—
1308C4—42no—
1309C4—44no—
1310C2—24no—
1311C2—84no—
1312C2—82no—
1313C2—82no—
1314C2C2×#350511yescharacteristic
1315C2#6285112yes—
1316C2#6286211yescharacteristic
1317C2#6287212yes—
1318C2#6288611yescharacteristic
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. #51996C2semidirect
2. #51960C2semidirect
3. #51953C2semidirect
4. #51952C2semidirect
5. #47380C2semidirect
6. #47376C2semidirect
7. #47373C2semidirect
8. #47369C2semidirect
9. #38126C2semidirect
10. #38114C2semidirect
11. #37941C2semidirect
12. #37933C2semidirect
13. #37753C2semidirect
14. #37745C2semidirect
15. #37517C2semidirect
16. #37236C2semidirect
17. #37187C2semidirect
18. #35154C2semidirect
19. #35153C2semidirect
20. #35099C2semidirect
21. #35031C2semidirect
22. #34409C2semidirect
23. C2×#2326C2semidirect
41. #2803C22semidirect
42. #2801C22semidirect
43. #2800C22semidirect
44. #2798C22semidirect
45. #2798C22semidirect
46. #2797C22semidirect
47. #2795C22semidirect
48. #2794C22semidirect
49. #2793C22semidirect
50. #2792C22semidirect
51. #2791C22semidirect
52. #2790C22semidirect
53. #2783C22semidirect
54. #2780C22semidirect
55. #2779C22semidirect
56. #2779C22semidirect
57. #2770C22semidirect
58. #2768C22semidirect
59. #2759C22semidirect
60. #2757C22semidirect
61. #2754C22semidirect
62. #2752C22semidirect
63. #2739C22semidirect
64. #2738C22semidirect
75. #2730C22semidirect
76. #2729C22semidirect
77. #2725C22semidirect
78. #2721C22semidirect
79. #2720C22semidirect
80. #2718C22semidirect
81. #2711C22semidirect
82. #2707C22semidirect
83. #2705C22semidirect
84. #2701C22semidirect
85. #2701C22semidirect
86. #2698C22semidirect
87. #2692C22semidirect
88. #2688C22semidirect
89. #2687C22semidirect
90. #2680C22semidirect
91. #2674C22semidirect
92. #2671C22semidirect
106. #2611C22semidirect
109. #2601C22semidirect
112. #2597C22semidirect
113. #2594C22semidirect
115. #2593C22semidirect
116. #2559C22semidirect
117. #2556C22semidirect
120. #2554C22semidirect
121. #2533C22semidirect
122. #2532C22semidirect
123. #2531C22semidirect
124. #2531C22semidirect
125. #2530C22semidirect
126. #2530C22semidirect
127. #2529C22semidirect
128. #2528C22semidirect
129. #2527C22semidirect
130. #2526C22semidirect
131. #2526C22semidirect
132. #2525C22semidirect
133. #2522C22semidirect
134. #2521C22semidirect
135. #2518C22semidirect
136. #2518C22semidirect
137. #2516C22semidirect
138. #2516C22semidirect
139. #2513C22semidirect
140. #2510C22semidirect
141. #2490C22semidirect
142. #2488C22semidirect
148. #2478C22semidirect
149. #2477C22semidirect
150. #2475C22semidirect
153. #2470C22semidirect
154. #2464C22semidirect
155. #2460C22semidirect
156. #2453C22semidirect
157. #2453C22semidirect
158. #2452C22semidirect
159. #2451C22semidirect
160. #2451C22semidirect
161. #2450C22semidirect
164. #2432C22semidirect
165. #2430C22semidirect
166. #2429C22semidirect
167. #2429C22semidirect
168. #2426C22semidirect
169. #2426C22semidirect
181. #2381C22semidirect
182. #2379C22semidirect
183. #2378C22semidirect
184. #2372C22semidirect
185. #2369C22semidirect
186. #2368C22semidirect
191. #2337C22semidirect
192. #2332C22semidirect
193. #2331C22semidirect
195. #2329C22semidirect
630. C22×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#519962
#519602
#519532
#519522
#473802
#473762
#473732
#473692
#381262
#381142
#379412
#379332
#377532
#377452
#375172
#372362
#371872
#351542
#351532
#350992
#350312
#344092
C2×#23262