Finite Group Databasebeta

← #8891525

Subgroups — #8891525

Order 512.

5090 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58048C214yesmaximal, complemented
2#54848C212yesmaximal, complemented
3#53991C214yesmaximal, complemented
4#53488C212yesmaximal, complemented
5#49379C214yesmaximal, complemented
6#49186C214yesmaximal, complemented
7#48114C214yesmaximal, complemented
8#47223C212yesmaximal, complemented
9#47217C212yesmaximal, complemented
10#46816C214yesmaximal, complemented
11#46813C212yesmaximal, complemented
12#46717C214yesmaximal, complemented
13#46418C214yesmaximal, complemented
14#40072C214yesmaximal, complemented
15#39443C214yesmaximal, complemented
16#37761C212yesmaximal, complemented
17#37752C212yesmaximal, complemented
18#37304C212yesmaximal, complemented
19#36708C211yesmaximal, characteristic, complemented
20#35634C211yesmaximal, characteristic, complemented
21#35501C212yesmaximal, complemented
22#35474C212yesmaximal, complemented
23#35377C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic, complemented
25C2×#543C2212yescomplemented
26C2×#542C2214yescomplemented
27C2×#540C2212yes—
28C2×#538C2212yescomplemented
29C2×#537C2211yescharacteristic, complemented
30C2×#536C2212yescomplemented
31C2×#534C2211yescharacteristic
32C2×#525C2212yes—
33C22×C22⋊Q8C2211yescharacteristic
34#2859C2212yescomplemented
35#2858C2212yescomplemented
36#2848C2211yescharacteristic
37#2848C2211yescharacteristic
38#2843C2212yescomplemented
39#2836C2214yescomplemented
40#2828C2212yescomplemented
41#2816C2214yescomplemented
42#2815C2212yes—
43#2814C2214yescomplemented
44#2804C2212yescomplemented
45#2797C2214yescomplemented
46#2795C2212yescomplemented
47#2793C2214yescomplemented
48#2790C2214yescomplemented
49#2784C2212yescomplemented
50#2756C2214yes—
51#2756C2214yescomplemented
52#2754C2214yescomplemented
53#2743C2214yescomplemented
54#2738C2214yescomplemented
55#2738C2214yescomplemented
56#2737C2214yescomplemented
57#2730C2214yes—
58#2730C2214yescomplemented
59#2730C2214yescomplemented
60#2729C2214yescomplemented
61#2728C2214yes—
62#2723C2214yes—
63#2723C2214yescomplemented
64#2723C2214yescomplemented
65#2715C2214yescomplemented
66#2712C2214yescomplemented
67#2706C2214yes—
68#2706C2214yescomplemented
69#2706C2214yescomplemented
70#2703C2214yescomplemented
71#2699C2214yescomplemented
72#2697C2214yescomplemented
73#2696C2214yescomplemented
74#2694C2214yes—
75#2694C2214yescomplemented
76#2694C2214yescomplemented
77#2692C2214yes—
78#2692C2214yescomplemented
79#2690C2214yescomplemented
80#2690C2214yescomplemented
81#2690C2214yescomplemented
82#2688C2214yes—
83#2688C2214yescomplemented
84#2682C2214yes—
85#2681C2214yescomplemented
86#2681C2214yescomplemented
87#2680C2214yescomplemented
88#2680C2212yescomplemented
89#2678C2214yes—
90#2677C2214yescomplemented
91#2677C2214yescomplemented
92#2677C2214yescomplemented
93#2676C2214yes—
94#2674C2214yescomplemented
95#2674C2214yescomplemented
96#2674C2214yescomplemented
97#2673C2214yescomplemented
98#2672C2214yescomplemented
99#2672C2214yescomplemented
100#2671C2214yes—
101#2671C2214yes—
102#2670C2214yescomplemented
103#2669C2214yes—
104#2660C2212yescomplemented
105#2659C2212yescomplemented
106#2649C2214yes—
107#2649C2214yescomplemented
108#2641C2212yescomplemented
109#2639C2212yescomplemented
110#2632C2214yescomplemented
111#2631C2214yes—
112#2627C2211yescharacteristic, complemented
113#2627C2211yescharacteristic, complemented
114#2626C2212yescomplemented
115#2617C2212yescomplemented
116#2607C2212yescomplemented
117#2596C2214yescomplemented
118#2591C2212yes—
119#2591C2212yes—
120#2572C2214yescomplemented
121#2571C2212yescomplemented
122#2566C2212yescomplemented
123#2566C2212yescomplemented
124#2564C2214yescomplemented
125#2563C2212yescomplemented
126#2561C2212yes—
127#2560C2214yescomplemented
128#2560C2214yescomplemented
129#2557C2214yescomplemented
130#2557C2214yescomplemented
131#2557C2214yescomplemented
132#2555C2212yescomplemented
133#2555C2214yescomplemented
134#2554C2214yescomplemented
135#2553C2214yescomplemented
136#2542C2214yescomplemented
137#2542C2214yescomplemented
138#2542C2212yescomplemented
139#2540C2214yescomplemented
140#2540C2214yescomplemented
141#2539C2214yes—
142#2539C2212yes—
143#2539C2212yes—
144#2532C2214yescomplemented
145#2531C2214yescomplemented
146#2524C2214yescomplemented
147#2517C2214yescomplemented
148#2517C2214yescomplemented
149#2516C2214yescomplemented
150#2516C2214yescomplemented
151#2511C2214yescomplemented
152#2504C2212yes—
153#2501C2212yescomplemented
154#2501C2212yescomplemented
155#2500C2212yes—
156#2500C2212yescomplemented
157#2499C2214yescomplemented
158#2491C2214yescomplemented
159#2488C2214yes—
160#2488C2214yes—
161#2488C2214yescomplemented
162#2484C2212yescomplemented
163#2482C2212yes—
164#2482C2214yescomplemented
165#2479C2214yescomplemented
166#2477C2214yescomplemented
167#2472C2214yes—
168#2472C2214yes—
169#2472C2214yes—
170#2472C2214yescomplemented
171#2471C2214yescomplemented
172#2471C2214yescomplemented
173#2467C2214yescomplemented
174#2464C2214yescomplemented
175#2463C2214yes—
176#2463C2214yescomplemented
177#2461C2214yes—
178#2458C2214yescomplemented
179#2457C2214yescomplemented
180#2456C2214yes—
181#2451C2214yescomplemented
182#2450C2214yescomplemented
183#2447C2214yescomplemented
184#2444C2214yescomplemented
185#2439C2214yescomplemented
186#2436C2212yes—
187#2434C2212yescomplemented
188#2430C2214yescomplemented
189#2427C2214yes—
190#2425C2214yes—
191#2423C2214yescomplemented
192#2423C2214yescomplemented
193#2422C2214yes—
194#2418C2214yes—
195#2418C2214yes—
196#2418C2214yescomplemented
197#2410C2214yes—
198#2408C2214yes—
199#2407C2214yescomplemented
200#2377C2214yes—
201#2363C2214yes—
202#2358C2214yescomplemented
203#2349C2214yescomplemented
204#2335C2214yescomplemented
205#2333C2212yes—
206#2333C2212yescomplemented
207#2332C2214yescomplemented
208#2329C2214yescomplemented
209#2329C2212yescomplemented
210#2325C2212yescomplemented
211#2313C2211yescharacteristic, complemented
212#2308C2212yes—
213C4×#126C2214yescomplemented
214C4×#124C2214yescomplemented
215#2298C2212yescomplemented
216C2×#386C2212yes—
217#2274C2211yescharacteristic, complemented
218#2273C2211yescharacteristic
219C22×#41C2312yes—
220C23×Q8C2311yescharacteristic
221C23×D4C2312yes—
222C24×C4C2311yescharacteristic
223#544—44no—
224#543—48no—
225#542—416no—
226#540—48no—
227#538—48no—
228#537—44no—
229#536—48no—
230#534—44no—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2314yes—
235C2×#127C2312yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#125C2312yes—
239C2×#125C2312yes—
240C2×#125C2312yes—
241C2×#124C2314yes—
242C2×#124C2314yes—
243C2×#124C2314yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247#525—48no—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8—44no—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2311yescharacteristic
267C2×C22⋊Q8C2311yescharacteristic
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2312yes—
290C2×#120C2314yes—
291C2×#120C2314yes—
292C2×#120C2314yes—
293C2×#120C2314yes—
294C2×C4×Q8C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2314yes—
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2312yes—
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2314yes—
313C22×C22⋊C4C2312yes—
314#400C2314yes—
315#400C2312yes—
316#400C2312yes—
317#400C2314yes—
318#400C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2312yes—
324#400C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#395C2314yes—
375#395C2312yes—
376#395C2314yes—
377#395C2312yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2312yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2312yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#390C2312yes—
435#390C2314yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2312yes—
453#390C2314yes—
454#390C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
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#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#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
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#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2312yes—
557#385C2312yes—
558#385C2314yes—
559#385C2314yes—
560#385C2312yes—
561#385C2312yes—
562#385C2314yes—
563#385C2314yes—
564#384C2312yes—
565#384C2312yes—
566#384C2312yes—
567#384C2312yes—
568#384C2312yes—
569#384C2312yes—
570#383C2314yes—
571#383C2314yes—
572#382C2312yes—
573#382C2312yes—
574#382C2312yes—
575#382C2312yes—
576#382C2314yes—
577#382C2314yes—
578#381C2314yes—
579#381C2312yes—
580#381C2312yes—
581#381C2314yes—
582#381C2312yes—
583#381C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2311yescharacteristic
588#380C2311yescharacteristic
589#380C2312yes—
590#380C2312yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#379C2312yes—
596#379C2312yes—
597#379C2314yes—
598#379C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619#376C2312yes—
620C2×#95C2314yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C43C2312yes—
624C25C2411yescharacteristic
625C25C2412yes—
626C2×#41—44no—
627C2×#41—44no—
628C2×#41—44no—
629C22×Q8—42no—
630C22×Q8—44no—
631C22×Q8C2414yes—
632C22×Q8C2412yes—
633C22×Q8C2414yes—
634C22×Q8C2411yescharacteristic
635C22×Q8C2411yescharacteristic
636C22×Q8C2412yes—
637C22×D4—44no—
638C22×D4—44no—
639C22×D4—44no—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2412yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2412yes—
654C23×C4—44no—
655C23×C4—42no—
656C23×C4C2411yescharacteristic
657C23×C4C2411yescharacteristic
658C23×C4C2411yescharacteristic
659C23×C4C2411yescharacteristic
660C23×C4C2414yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2411yescharacteristic
664C23×C4C2414yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2414yes—
669C23×C4C2414yes—
670C23×C4C2414yes—
671C23×C4C2411yescharacteristic
672C4⋊Q8—48no—
673C4⋊Q8—44no—
674C4⋊Q8—44no—
675C4⋊Q8—48no—
676#127—44no—
677#126—216no—
678#126—48no—
679#125—44no—
680#125—44no—
681#125—44no—
682#124—48no—
683#124—48no—
684#124—48no—
685#124—48no—
686#124—48no—
687#124—48no—
688#123—48no—
689#123—48no—
690#123—48no—
691#123—48no—
692#123—48no—
693#123—48no—
694#123—48no—
695#123—48no—
696#123—48no—
697#123—48no—
698C22⋊Q8—28no—
699C22⋊Q8—216no—
700C22⋊Q8—216no—
701C22⋊Q8—44no—
702C22⋊Q8—42no—
703C22⋊Q8—42no—
704C22⋊Q8—48no—
705C22⋊Q8—48no—
706C22⋊Q8—48no—
707C22⋊Q8—48no—
708C22⋊Q8—48no—
709C22⋊Q8—48no—
710C22⋊Q8—48no—
711C22⋊Q8—44no—
712C22⋊Q8—44no—
713C22⋊Q8—44no—
714C22⋊Q8—48no—
715C22⋊Q8—48no—
716#121—28no—
717#121—28no—
718#121—28no—
719#121—48no—
720#121—48no—
721#121—48no—
722#121—48no—
723#121—48no—
724#121—48no—
725#121—48no—
726#121—44no—
727#121—44no—
728#121—44no—
729#120—48no—
730#120—48no—
731#120—48no—
732#120—48no—
733C4×Q8—48no—
734C4×D4—48no—
735C4×D4—48no—
736C4×D4—48no—
737C4×D4—44no—
738C4×D4—44no—
739C4×D4—48no—
740C4×D4—48no—
741#117—28no—
742#117—28no—
743#117—48no—
744C2×C4⋊C4—24no—
745C2×C4⋊C4—24no—
746C2×C4⋊C4—42no—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C22⋊C4—24no—
793C2×C22⋊C4—44no—
794C2×C22⋊C4—48no—
795C2×C22⋊C4—44no—
796C2×C22⋊C4—44no—
797C2×C22⋊C4—42no—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C42C2414yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2412yes—
876#95C2414yes—
877#95C2414yes—
878#95C2412yes—
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—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2414yes—
901#95C2412yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910C24—22no—
911C24—24no—
912C24—24no—
913C24—42no—
914C24—42no—
915C24—42no—
916C24—41no—
917C24—41no—
918C24—42no—
919C24—42no—
920C24—42no—
921C24—42no—
922C24C2514yes—
923C24C2514yes—
924C24C2511yescharacteristic
925C24C2512yes—
926#41—816no—
927C2×Q8—28no—
928C2×Q8—24no—
929C2×Q8—28no—
930C2×Q8—44no—
931C2×Q8—42no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—42no—
935C2×Q8—44no—
936C2×Q8—42no—
937C2×Q8—42no—
938C2×Q8—44no—
939C2×Q8—41no—
940C2×Q8—42no—
941C2×Q8—41no—
942C2×Q8—88no—
943C2×D4—28no—
944C2×D4—28no—
945C2×D4—28no—
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—28no—
949C2×D4—24no—
950C2×D4—24no—
951C2×D4—24no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—42no—
959C2×D4—44no—
960C2×D4—42no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—42no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—42no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—42no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—42no—
982C2×D4—42no—
983C2×D4—44no—
984C2×D4—816no—
985C22×C4—22no—
986C22×C4—24no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—24no—
992C22×C4—28no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—28no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—41no—
1011C22×C4—41no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—44no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—44no—
1028C22×C4—88no—
1029C22×C4H(5,𝔽2)14yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C4⋊C4—28no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—41no—
1084C4⋊C4—42no—
1085C4⋊C4—41no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4H(5,𝔽2)18yes—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
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—28no—
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—42no—
1123C22⋊C4—42no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C42—28no—
1148C42—24no—
1149C42—24no—
1150C42—28no—
1151C42—42no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—42no—
1156C42—42no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—44no—
1161C42—44no—
1162C23—28no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—21no—
1170C23—21no—
1171C23—22no—
1172C23—22no—
1173C23—24no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—24no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—24no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—48no—
1188C23—82no—
1189C23—82no—
1190C23—84no—
1191C23—84no—
1192C23—84no—
1193C23—84no—
1194C23—162no—
1195C23—162no—
1196C23—162no—
1197C23—162no—
1198C23C2×H(5,𝔽2)12yes—
1199C23#58514yes—
1200C23C2611yescharacteristic
1201Q8—88no—
1202Q8—88no—
1203Q8—84no—
1204Q8—161no—
1205Q8—161no—
1206Q8—162no—
1207D4—416no—
1208D4—84no—
1209D4—84no—
1210D4—84no—
1211D4—88no—
1212D4—88no—
1213D4—88no—
1214D4—88no—
1215D4—88no—
1216D4—164no—
1217D4—162no—
1218D4—164no—
1219D4—162no—
1220D4—164no—
1221C2×C4—28no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—44no—
1269C2×C4—88no—
1270C2×C4—84no—
1271C2×C4—84no—
1272C2×C4—88no—
1273C2×C4—82no—
1274C2×C4—82no—
1275C2×C4—84no—
1276C2×C4—82no—
1277C2×C4—82no—
1278C2×C4—164no—
1279C2×C4—164no—
1280C2×C4—162no—
1281C2×C4—162no—
1282C2×C4—164no—
1283C2×C4C2×H(5,𝔽2)18yes—
1284C2×C4C2×H(5,𝔽2)14yes—
1285C2×C4C2×H(5,𝔽2)14yes—
1286C22—24no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—24no—
1291C22—24no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—88no—
1313C22—168no—
1314C22C22×H(5,𝔽2)11yescharacteristic
1315C22C22×H(5,𝔽2)12yes—
1316C22C2×#58512yes—
1317C222−1+611yescharacteristic
1318C222−1+611yescharacteristic
1319C4—24no—
1320C4—24no—
1321C4—28no—
1322C4—44no—
1323C4—42no—
1324C4—42no—
1325C4—41no—
1326C4—41no—
1327C4—44no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4—44no—
1335C4—44no—
1336C4—44no—
1337C4—44no—
1338C2—42no—
1339C2—44no—
1340C2—84no—
1341C2—84no—
1342C2#6282411yescharacteristic
1343C2#6283211yescharacteristic
1344C2#6287111yescharacteristic
1345C2#6289812yes—
1346C2#6291912yes—
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. #58048C2semidirect
2. #54848C2semidirect
3. #53991C2semidirect
4. #53488C2semidirect
5. #49379C2semidirect
6. #49186C2semidirect
7. #48114C2semidirect
8. #47223C2semidirect
9. #47217C2semidirect
10. #46816C2semidirect
11. #46813C2semidirect
12. #46717C2semidirect
13. #46418C2semidirect
14. #40072C2semidirect
15. #39443C2semidirect
16. #37761C2semidirect
17. #37752C2semidirect
18. #37304C2semidirect
19. #36708C2semidirect
20. #35634C2semidirect
21. #35501C2semidirect
22. #35474C2semidirect
23. #35377C2semidirect
24. C2×#544C22semidirect
25. C2×#543C22semidirect
26. C2×#542C22semidirect
28. C2×#538C22semidirect
29. C2×#537C22semidirect
30. C2×#536C22semidirect
34. #2859C22semidirect
35. #2858C22semidirect
38. #2843C22semidirect
39. #2836C22semidirect
40. #2828C22semidirect
41. #2816C22semidirect
43. #2814C22semidirect
44. #2804C22semidirect
45. #2797C22semidirect
46. #2795C22semidirect
47. #2793C22semidirect
48. #2790C22semidirect
49. #2784C22semidirect
51. #2756C22semidirect
52. #2754C22semidirect
53. #2743C22semidirect
54. #2738C22semidirect
55. #2738C22semidirect
56. #2737C22semidirect
58. #2730C22semidirect
59. #2730C22semidirect
60. #2729C22semidirect
63. #2723C22semidirect
64. #2723C22semidirect
65. #2715C22semidirect
66. #2712C22semidirect
68. #2706C22semidirect
69. #2706C22semidirect
70. #2703C22semidirect
71. #2699C22semidirect
72. #2697C22semidirect
73. #2696C22semidirect
75. #2694C22semidirect
76. #2694C22semidirect
78. #2692C22semidirect
79. #2690C22semidirect
80. #2690C22semidirect
81. #2690C22semidirect
83. #2688C22semidirect
85. #2681C22semidirect
86. #2681C22semidirect
87. #2680C22semidirect
88. #2680C22semidirect
90. #2677C22semidirect
91. #2677C22semidirect
92. #2677C22semidirect
94. #2674C22semidirect
95. #2674C22semidirect
96. #2674C22semidirect
97. #2673C22semidirect
98. #2672C22semidirect
99. #2672C22semidirect
102. #2670C22semidirect
104. #2660C22semidirect
105. #2659C22semidirect
107. #2649C22semidirect
108. #2641C22semidirect
109. #2639C22semidirect
110. #2632C22semidirect
112. #2627C22semidirect
113. #2627C22semidirect
114. #2626C22semidirect
115. #2617C22semidirect
116. #2607C22semidirect
117. #2596C22semidirect
120. #2572C22semidirect
121. #2571C22semidirect
122. #2566C22semidirect
123. #2566C22semidirect
124. #2564C22semidirect
125. #2563C22semidirect
127. #2560C22semidirect
128. #2560C22semidirect
129. #2557C22semidirect
130. #2557C22semidirect
131. #2557C22semidirect
132. #2555C22semidirect
133. #2555C22semidirect
134. #2554C22semidirect
135. #2553C22semidirect
136. #2542C22semidirect
137. #2542C22semidirect
138. #2542C22semidirect
139. #2540C22semidirect
140. #2540C22semidirect
144. #2532C22semidirect
145. #2531C22semidirect
146. #2524C22semidirect
147. #2517C22semidirect
148. #2517C22semidirect
149. #2516C22semidirect
150. #2516C22semidirect
151. #2511C22semidirect
153. #2501C22semidirect
154. #2501C22semidirect
156. #2500C22semidirect
157. #2499C22semidirect
158. #2491C22semidirect
161. #2488C22semidirect
162. #2484C22semidirect
164. #2482C22semidirect
165. #2479C22semidirect
166. #2477C22semidirect
170. #2472C22semidirect
171. #2471C22semidirect
172. #2471C22semidirect
173. #2467C22semidirect
174. #2464C22semidirect
176. #2463C22semidirect
178. #2458C22semidirect
179. #2457C22semidirect
181. #2451C22semidirect
182. #2450C22semidirect
183. #2447C22semidirect
184. #2444C22semidirect
185. #2439C22semidirect
187. #2434C22semidirect
188. #2430C22semidirect
191. #2423C22semidirect
192. #2423C22semidirect
196. #2418C22semidirect
199. #2407C22semidirect
202. #2358C22semidirect
203. #2349C22semidirect
204. #2335C22semidirect
206. #2333C22semidirect
207. #2332C22semidirect
208. #2329C22semidirect
209. #2329C22semidirect
210. #2325C22semidirect
211. #2313C22semidirect
213. C4×#126C22semidirect
214. C4×#124C22semidirect
215. #2298C22semidirect
217. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#580482
#548482
#539912
#534882
#493792
#491862
#481142
#472232
#472172
#468162
#468132
#467172
#464182
#400722
#394432
#377612
#377522
#373042
#367082
#356342
#355012
#354742
#353772