Finite Group Databasebeta

← #8093817

Subgroups — #8093817

Order 512.

5572 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52409C214yesmaximal, complemented
2#52406C214yesmaximal, complemented
3#52403C214yesmaximal, complemented
4#52401C214yesmaximal, complemented
5#52372C214yesmaximal, complemented
6#52346C214yesmaximal, complemented
7#46335C212yesmaximal, complemented
8#46325C212yesmaximal, complemented
9#46316C212yesmaximal, complemented
10#46310C212yesmaximal, complemented
11#46275C212yesmaximal, complemented
12#46228C212yesmaximal, complemented
13#46205C211yesmaximal, characteristic, complemented
14#46099C211yesmaximal, characteristic, complemented
15#45976C212yesmaximal, complemented
16#45840C214yesmaximal, complemented
17#45760C214yesmaximal, complemented
18#35357C212yesmaximal, complemented
19#35353C214yesmaximal, complemented
20#34999C214yesmaximal, complemented
21#34996C212yesmaximal, complemented
22#34738C212yesmaximal, complemented
23C2×#2432C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C2×#563C2212yescomplemented
26C2×#562C2212yescomplemented
27C2×#532C2212yes—
28C2×#532C2212yes—
29C22×C4⋊Q8C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C2×#525C2212yes—
32C22×C22⋊Q8C2211yescharacteristic
33C2×#520C2212yes—
34#2855C2214yescomplemented
35#2853C2214yescomplemented
36#2852C2214yes—
37#2852C2214yescomplemented
38#2851C2212yes—
39#2851C2214yescomplemented
40#2850C2212yes—
41#2837C2214yescomplemented
42#2837C2214yescomplemented
43#2833C2212yescomplemented
44#2832C2212yescomplemented
45#2830C2214yescomplemented
46#2830C2212yescomplemented
47#2829C2214yescomplemented
48#2829C2214yescomplemented
49#2828C2214yescomplemented
50#2828C2212yescomplemented
51#2827C2214yescomplemented
52#2826C2214yescomplemented
53#2825C2214yescomplemented
54#2824C2214yescomplemented
55#2824C2214yescomplemented
56#2824C2214yescomplemented
57#2821C2214yescomplemented
58#2820C2214yescomplemented
59#2820C2212yescomplemented
60#2819C2212yescomplemented
61#2818C2214yescomplemented
62#2816C2214yescomplemented
63#2813C2214yescomplemented
64#2811C2211yescharacteristic, complemented
65#2809C2211yescharacteristic, complemented
66#2808C2214yescomplemented
67#2805C2212yescomplemented
68#2804C2212yescomplemented
69#2797C2214yescomplemented
70#2797C2214yescomplemented
71#2784C2212yescomplemented
72#2779C2214yescomplemented
73#2778C2214yescomplemented
74#2763C2214yescomplemented
75#2762C2214yescomplemented
76#2761C2214yescomplemented
77#2749C2214yescomplemented
78#2737C2214yescomplemented
79#2737C2214yescomplemented
80#2734C2211yescharacteristic, complemented
81#2734C2212yescomplemented
82#2733C2211yescharacteristic, complemented
83#2731C2212yescomplemented
84#2730C2214yescomplemented
85#2730C2214yescomplemented
86#2729C2214yescomplemented
87#2716C2214yescomplemented
88#2714C2214yescomplemented
89#2713C2214yescomplemented
90#2713C2214yescomplemented
91#2712C2214yescomplemented
92#2711C2214yescomplemented
93#2710C2214yescomplemented
94#2709C2214yescomplemented
95#2709C2214yescomplemented
96#2701C2214yescomplemented
97#2700C2214yescomplemented
98#2700C2214yescomplemented
99#2699C2212yescomplemented
100#2691C2214yescomplemented
101#2691C2214yescomplemented
102#2688C2214yescomplemented
103#2686C2214yescomplemented
104#2677C2214yescomplemented
105#2676C2214yescomplemented
106#2674C2214yescomplemented
107#2673C2214yescomplemented
108#2672C2214yescomplemented
109#2672C2214yescomplemented
110#2653C2214yescomplemented
111#2652C2214yescomplemented
112#2652C2214yescomplemented
113#2649C2214yescomplemented
114#2626C2212yes—
115#2622C2214yes—
116#2617C2212yes—
117#2609C2214yescomplemented
118#2600C2214yescomplemented
119#2599C2214yescomplemented
120#2598C2214yescomplemented
121#2580C2214yescomplemented
122#2579C2214yescomplemented
123#2534C2214yes—
124#2523C2214yescomplemented
125#2523C2214yescomplemented
126#2518C2214yescomplemented
127#2518C2214yescomplemented
128#2517C2214yescomplemented
129#2517C2214yescomplemented
130#2505C2214yescomplemented
131#2493C2214yes—
132#2493C2214yescomplemented
133#2488C2214yes—
134#2484C2212yes—
135#2483C2214yes—
136#2482C2212yes—
137#2481C2214yes—
138#2477C2214yescomplemented
139#2477C2214yescomplemented
140#2476C2214yescomplemented
141#2473C2214yes—
142#2470C2214yescomplemented
143#2467C2214yescomplemented
144#2466C2214yescomplemented
145#2466C2214yescomplemented
146#2465C2214yescomplemented
147#2465C2214yescomplemented
148#2465C2214yescomplemented
149#2463C2214yescomplemented
150#2463C2214yescomplemented
151#2460C2214yescomplemented
152#2460C2214yescomplemented
153#2459C2214yescomplemented
154#2458C2214yescomplemented
155#2456C2214yescomplemented
156#2455C2214yescomplemented
157#2450C2214yescomplemented
158#2449C2214yes—
159#2449C2214yescomplemented
160#2449C2214yescomplemented
161#2449C2214yescomplemented
162#2443C2214yes—
163#2443C2214yescomplemented
164#2438C2214yes—
165#2437C2214yes—
166#2436C2212yes—
167#2435C2212yes—
168#2434C2212yes—
169#2433C2212yes—
170#2432C2214yes—
171#2432C2212yes—
172#2432C2212yes—
173#2432C2212yes—
174#2432C2212yes—
175#2432C2214yes—
176#2432C2212yes—
177#2432C2212yes—
178#2431C2212yes—
179#2431C2212yes—
180#2430C2214yes—
181#2430C2214yes—
182#2430C2214yes—
183#2424C2214yes—
184#2419C2214yescomplemented
185#2418C2214yes—
186#2412C2214yes—
187#2412C2214yes—
188#2411C2214yes—
189#2410C2214yes—
190#2410C2214yes—
191#2409C2214yes—
192#2407C2214yescomplemented
193#2406C2212yes—
194#2406C2214yescomplemented
195#2404C2214yes—
196#2404C2212yes—
197#2388C2214yes—
198#2388C2214yes—
199C2×#394C2214yes—
200#2381C2212yescomplemented
201#2381C2212yescomplemented
202#2379C2212yescomplemented
203#2379C2212yescomplemented
204#2377C2214yescomplemented
205#2329C2212yes—
206#2325C2212yes—
207#2322C2214yes—
208#2318C2214yes—
209#2313C2212yes—
210C4×#120C2214yes—
211C4×#120C2214yes—
212#2297C2212yes—
213#2297C2212yes—
214C2×#391C2211yescharacteristic
215C2×#390C2211yescharacteristic
216C2×#385C2214yes—
217C2×C4×C22⋊C4C2211yescharacteristic
218C2×C4×C22⋊C4C2212yes—
219C22×#41—44no—
220C22×#41—44no—
221C22×#41—44no—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C22×#41C2312yes—
227C22×#41C2312yes—
228C23×Q8C2311yescharacteristic
229C23×Q8C2311yescharacteristic
230C23×D4C2311yescharacteristic
231C23×D4C2312yes—
232C24×C4C2311yescharacteristic
233C24×C4C2312yes—
234#563—48no—
235#562—48no—
236#532—48no—
237#532—48no—
238C2×C4⋊Q8—44no—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2312yes—
244C2×#127C2312yes—
245C2×#127C2312yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#125C2312yes—
249C2×#125C2314yes—
250C2×#124—44no—
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260#525—48no—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×C22⋊Q8—44no—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#120C2314yes—
286C2×#120C2314yes—
287C2×#120C2314yes—
288#520—48no—
289C2×C4×Q8C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×#117C2314yes—
299C2×#117C2312yes—
300C2×#117C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2314yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2314yes—
308C22×C22⋊C4C2314yes—
309C22×C22⋊C4C2314yes—
310C22×C42C2311yescharacteristic
311C22×C42C2312yes—
312C22×C42C2311yescharacteristic
313C22×C42C2312yes—
314#401C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2312yes—
324#400C2314yes—
325#400C2312yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2312yes—
340#398C2312yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2312yes—
377#395C2312yes—
378#395C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
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#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2312yes—
409#394C2314yes—
410#394C2312yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#391C2314yes—
441#391C2312yes—
442#391C2314yes—
443#391C2311yescharacteristic
444#391C2312yes—
445#391C2314yes—
446#391C2312yes—
447#391C2311yescharacteristic
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2314yes—
452#391C2312yes—
453#390C2312yes—
454#390C2314yes—
455#390C2312yes—
456#390C2314yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
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#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
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#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
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#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#383C2314yes—
588#383C2314yes—
589#383C2314yes—
590#382C2312yes—
591#382C2312yes—
592#382C2314yes—
593#382C2314yes—
594#381C2314yes—
595#381C2312yes—
596#381C2312yes—
597#381C2314yes—
598#381C2314yes—
599#381C2314yes—
600#381C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2312yes—
604#380C2312yes—
605#380C2314yes—
606#380C2314yes—
607#380C2314yes—
608#379C2314yes—
609#379C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2312yes—
621C4×C22⋊C4C2312yes—
622C4×C22⋊C4C2312yes—
623C2×#95C2312yes—
624C2×#95C2314yes—
625C2×#95C2314yes—
626C25C2412yes—
627C25C2411yescharacteristic
628C2×#41—28no—
629C2×#41—28no—
630C2×#41—44no—
631C2×#41—44no—
632C2×#41—44no—
633C2×#41—44no—
634C2×#41—44no—
635C2×#41—44no—
636C2×#41—44no—
637C2×#41—44no—
638C2×#41—48no—
639C2×#41—44no—
640C2×#41—44no—
641C2×#41—44no—
642C2×#41—44no—
643C2×#41—44no—
644C2×#41—44no—
645C2×#41—464no—
646C22×Q8—24no—
647C22×Q8—42no—
648C22×Q8—42no—
649C22×Q8—42no—
650C22×Q8—42no—
651C22×Q8—42no—
652C22×Q8C2412yes—
653C22×Q8C2412yes—
654C22×Q8C2412yes—
655C22×Q8C2412yes—
656C22×Q8C2411yescharacteristic
657C22×Q8C2412yes—
658C22×Q8C2412yes—
659C22×Q8C2411yescharacteristic
660C22×D4—24no—
661C22×D4—42no—
662C22×D4—44no—
663C22×D4—42no—
664C22×D4—44no—
665C22×D4—44no—
666C22×D4C2414yes—
667C22×D4C2412yes—
668C22×D4C2412yes—
669C22×D4C2414yes—
670C22×D4C2414yes—
671C22×D4C2412yes—
672C22×D4C2412yes—
673C22×D4C2411yescharacteristic
674C22×D4C2412yes—
675C22×D4C2412yes—
676C22×D4C2414yes—
677C22×D4C2414yes—
678C22×D4C2414yes—
679C22×D4C2414yes—
680C22×D4C2412yes—
681C22×D4C2412yes—
682C22×D4C2411yescharacteristic
683C23×C4—24no—
684C23×C4—28no—
685C23×C4—42no—
686C23×C4—42no—
687C23×C4—44no—
688C23×C4—44no—
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2414yes—
701C23×C4C2414yes—
702C23×C4C2412yes—
703C23×C4C2414yes—
704C23×C4C2414yes—
705C23×C4C2414yes—
706C23×C4C2411yescharacteristic
707C4⋊Q8—28no—
708C4⋊Q8—28no—
709C4⋊Q8—44no—
710C4⋊Q8—48no—
711C4⋊Q8—44no—
712#127—44no—
713#127—44no—
714#126—48no—
715#126—48no—
716#125—44no—
717#125—48no—
718#124—28no—
719#124—28no—
720#124—44no—
721#124—44no—
722#124—44no—
723#124—44no—
724#124—44no—
725#124—44no—
726#124—44no—
727#123—48no—
728#123—48no—
729#123—48no—
730#123—48no—
731#123—48no—
732C22⋊Q8—44no—
733C22⋊Q8—44no—
734C22⋊Q8—48no—
735C22⋊Q8—48no—
736C22⋊Q8—48no—
737C22⋊Q8—48no—
738C22⋊Q8—44no—
739C22⋊Q8—48no—
740C22⋊Q8—44no—
741C22⋊Q8—44no—
742#121—216no—
743#121—44no—
744#121—48no—
745#121—48no—
746#121—48no—
747#121—44no—
748#121—44no—
749#121—48no—
750#120—48no—
751#120—48no—
752#120—48no—
753C4×Q8—48no—
754C4×D4—216no—
755C4×D4—48no—
756C4×D4—48no—
757C4×D4—48no—
758C4×D4—48no—
759C4×D4—48no—
760C4×D4—48no—
761C4×D4—48no—
762#117—44no—
763#117—48no—
764#117—44no—
765C2×C4⋊C4—28no—
766C2×C4⋊C4—48no—
767C2×C4⋊C4—48no—
768C2×C4⋊C4—42no—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C22⋊C4—48no—
809C2×C22⋊C4—48no—
810C2×C22⋊C4—48no—
811C2×C22⋊C4—44no—
812C2×C22⋊C4—44no—
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⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C42—42no—
863C2×C42—42no—
864C2×C42—44no—
865C2×C42—44no—
866C2×C42C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2411yescharacteristic
876C2×C42C2412yes—
877C2×C42C2411yescharacteristic
878C2×C42C2412yes—
879C2×C42C2412yes—
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#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928C24—22no—
929C24—24no—
930C24—24no—
931C24—28no—
932C24—24no—
933C24—42no—
934C24—41no—
935C24—41no—
936C24—44no—
937C24—42no—
938C24C2512yes—
939C24C2512yes—
940C24C2514yes—
941C24C2512yes—
942C24C2511yescharacteristic
943#41—432no—
944#41—432no—
945#41—432no—
946#41—432no—
947#41—432no—
948#41—816no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—22no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—42no—
956C2×Q8—41no—
957C2×Q8—41no—
958C2×Q8—41no—
959C2×Q8—42no—
960C2×Q8—41no—
961C2×Q8—44no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—42no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—416no—
972C2×Q8—88no—
973C2×Q8H(5,𝔽2)14yes—
974C2×D4—28no—
975C2×D4—24no—
976C2×D4—24no—
977C2×D4—24no—
978C2×D4—28no—
979C2×D4—28no—
980C2×D4—28no—
981C2×D4—28no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—22no—
985C2×D4—24no—
986C2×D4—24no—
987C2×D4—42no—
988C2×D4—42no—
989C2×D4—41no—
990C2×D4—41no—
991C2×D4—42no—
992C2×D4—42no—
993C2×D4—41no—
994C2×D4—42no—
995C2×D4—41no—
996C2×D4—42no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—42no—
1000C2×D4—42no—
1001C2×D4—44no—
1002C2×D4—416no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—42no—
1013C2×D4—44no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—42no—
1022C2×D4—42no—
1023C2×D4—42no—
1024C2×D4—432no—
1025C2×D4H(5,𝔽2)14yes—
1026C22×C4—24no—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—22no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—28no—
1037C22×C4—28no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—28no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—416no—
1079C22×C4—432no—
1080C22×C4H(5,𝔽2)14yes—
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2514yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2512yes—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—41no—
1110C4⋊C4—42no—
1111C4⋊C4—41no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
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—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C42—24no—
1188C42—24no—
1189C42—24no—
1190C42—24no—
1191C42—28no—
1192C42—44no—
1193C42—44no—
1194C42—41no—
1195C42—41no—
1196C42—42no—
1197C42—42no—
1198C42—42no—
1199C42—44no—
1200C42—44no—
1201C23—21no—
1202C23—21no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—24no—
1223C23—24no—
1224C23—24no—
1225C23—48no—
1226C23—416no—
1227C23—44no—
1228C23—44no—
1229C23—48no—
1230C23—44no—
1231C23—84no—
1232C23—88no—
1233C23—84no—
1234C23—84no—
1235C23C2×H(5,𝔽2)14yes—
1236C23C2×H(5,𝔽2)12yes—
1237C23#58514yes—
1238C23C2611yescharacteristic
1239Q8—44no—
1240Q8—48no—
1241Q8—44no—
1242Q8—48no—
1243Q8—84no—
1244Q8—84no—
1245Q8—84no—
1246Q8—162no—
1247D4—44no—
1248D4—48no—
1249D4—48no—
1250D4—48no—
1251D4—44no—
1252D4—48no—
1253D4—48no—
1254D4—48no—
1255D4—416no—
1256D4—84no—
1257D4—88no—
1258D4—88no—
1259D4—88no—
1260D4—88no—
1261D4—88no—
1262D4—88no—
1263D4—162no—
1264C2×C4—28no—
1265C2×C4—216no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—44no—
1315C2×C4—48no—
1316C2×C4—48no—
1317C2×C4—48no—
1318C2×C4—48no—
1319C2×C4—48no—
1320C2×C4—48no—
1321C2×C4—48no—
1322C2×C4—416no—
1323C2×C4—48no—
1324C2×C4—88no—
1325C2×C4—84no—
1326C2×C4—88no—
1327C2×C4—84no—
1328C2×C4—88no—
1329C2×C4—164no—
1330C2×C4C2×H(5,𝔽2)12yes—
1331C2×C4C2×H(5,𝔽2)12yes—
1332C2×C4C2×H(5,𝔽2)14yes—
1333C2×C4C2×H(5,𝔽2)14yes—
1334C22—22no—
1335C22—22no—
1336C22—24no—
1337C22—24no—
1338C22—24no—
1339C22—28no—
1340C22—42no—
1341C22—44no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—44no—
1346C22—42no—
1347C22—44no—
1348C22—42no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—42no—
1359C22—42no—
1360C22—816no—
1361C22—88no—
1362C22#352914yes—
1363C22C22×H(5,𝔽2)11yescharacteristic
1364C22C22×H(5,𝔽2)11yescharacteristic
1365C22C22×H(5,𝔽2)11yescharacteristic
1366C22C2×#58512yes—
1367C222−1+612yes—
1368C4—24no—
1369C4—24no—
1370C4—22no—
1371C4—22no—
1372C4—42no—
1373C4—44no—
1374C4—44no—
1375C4—44no—
1376C4—44no—
1377C4—44no—
1378C4—44no—
1379C4—42no—
1380C4—44no—
1381C4—42no—
1382C4—44no—
1383C4—42no—
1384C4—44no—
1385C4—42no—
1386C2—24no—
1387C2—44no—
1388C2—84no—
1389C2—82no—
1390C2—82no—
1391C2C2×#352911yescharacteristic
1392C2#6281711yescharacteristic
1393C2#6288611yescharacteristic
1394C2#6289712yes—
1395C2#6289812yes—
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. #52409C2semidirect
2. #52406C2semidirect
3. #52403C2semidirect
4. #52401C2semidirect
5. #52372C2semidirect
6. #52346C2semidirect
7. #46335C2semidirect
8. #46325C2semidirect
9. #46316C2semidirect
10. #46310C2semidirect
11. #46275C2semidirect
12. #46228C2semidirect
13. #46205C2semidirect
14. #46099C2semidirect
15. #45976C2semidirect
16. #45840C2semidirect
17. #45760C2semidirect
18. #35357C2semidirect
19. #35353C2semidirect
20. #34999C2semidirect
21. #34996C2semidirect
22. #34738C2semidirect
23. C2×#2432C2semidirect
25. C2×#563C22semidirect
26. C2×#562C22semidirect
34. #2855C22semidirect
35. #2853C22semidirect
37. #2852C22semidirect
39. #2851C22semidirect
41. #2837C22semidirect
42. #2837C22semidirect
43. #2833C22semidirect
44. #2832C22semidirect
45. #2830C22semidirect
46. #2830C22semidirect
47. #2829C22semidirect
48. #2829C22semidirect
49. #2828C22semidirect
50. #2828C22semidirect
51. #2827C22semidirect
52. #2826C22semidirect
53. #2825C22semidirect
54. #2824C22semidirect
55. #2824C22semidirect
56. #2824C22semidirect
57. #2821C22semidirect
58. #2820C22semidirect
59. #2820C22semidirect
60. #2819C22semidirect
61. #2818C22semidirect
62. #2816C22semidirect
63. #2813C22semidirect
64. #2811C22semidirect
65. #2809C22semidirect
66. #2808C22semidirect
67. #2805C22semidirect
68. #2804C22semidirect
69. #2797C22semidirect
70. #2797C22semidirect
71. #2784C22semidirect
72. #2779C22semidirect
73. #2778C22semidirect
74. #2763C22semidirect
75. #2762C22semidirect
76. #2761C22semidirect
77. #2749C22semidirect
78. #2737C22semidirect
79. #2737C22semidirect
80. #2734C22semidirect
81. #2734C22semidirect
82. #2733C22semidirect
83. #2731C22semidirect
84. #2730C22semidirect
85. #2730C22semidirect
86. #2729C22semidirect
87. #2716C22semidirect
88. #2714C22semidirect
89. #2713C22semidirect
90. #2713C22semidirect
91. #2712C22semidirect
92. #2711C22semidirect
93. #2710C22semidirect
94. #2709C22semidirect
95. #2709C22semidirect
96. #2701C22semidirect
97. #2700C22semidirect
98. #2700C22semidirect
99. #2699C22semidirect
100. #2691C22semidirect
101. #2691C22semidirect
102. #2688C22semidirect
103. #2686C22semidirect
104. #2677C22semidirect
105. #2676C22semidirect
106. #2674C22semidirect
107. #2673C22semidirect
108. #2672C22semidirect
109. #2672C22semidirect
110. #2653C22semidirect
111. #2652C22semidirect
112. #2652C22semidirect
113. #2649C22semidirect
117. #2609C22semidirect
118. #2600C22semidirect
119. #2599C22semidirect
120. #2598C22semidirect
121. #2580C22semidirect
122. #2579C22semidirect
124. #2523C22semidirect
125. #2523C22semidirect
126. #2518C22semidirect
127. #2518C22semidirect
128. #2517C22semidirect
129. #2517C22semidirect
130. #2505C22semidirect
132. #2493C22semidirect
138. #2477C22semidirect
139. #2477C22semidirect
140. #2476C22semidirect
142. #2470C22semidirect
143. #2467C22semidirect
144. #2466C22semidirect
145. #2466C22semidirect
146. #2465C22semidirect
147. #2465C22semidirect
148. #2465C22semidirect
149. #2463C22semidirect
150. #2463C22semidirect
151. #2460C22semidirect
152. #2460C22semidirect
153. #2459C22semidirect
154. #2458C22semidirect
155. #2456C22semidirect
156. #2455C22semidirect
157. #2450C22semidirect
159. #2449C22semidirect
160. #2449C22semidirect
161. #2449C22semidirect
163. #2443C22semidirect
184. #2419C22semidirect
192. #2407C22semidirect
194. #2406C22semidirect
200. #2381C22semidirect
201. #2381C22semidirect
202. #2379C22semidirect
203. #2379C22semidirect
204. #2377C22semidirect

Maximal subgroups

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

subgroupindex
#524092
#524062
#524032
#524012
#523722
#523462
#463352
#463252
#463162
#463102
#462752
#462282
#462052
#460992
#459762
#458402
#457602
#353572
#353532
#349992
#349962
#347382
C2×#24322