Finite Group Databasebeta

← #8093816

Subgroups — #8093816

Order 512.

5588 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52373C214yesmaximal, complemented
2#52345C214yesmaximal, complemented
3#52338C214yesmaximal, complemented
4#52334C214yesmaximal, complemented
5#52330C214yesmaximal, complemented
6#52326C214yesmaximal, complemented
7#46334C212yesmaximal, complemented
8#46325C212yesmaximal, complemented
9#46136C211yesmaximal, characteristic, complemented
10#46098C212yesmaximal, complemented
11#45977C211yesmaximal, characteristic, complemented
12#45742C212yesmaximal, complemented
13#45739C214yesmaximal, complemented
14#45731C212yesmaximal, complemented
15#45453C212yesmaximal, complemented
16#45450C214yesmaximal, complemented
17#45442C212yesmaximal, complemented
18#35397C212yesmaximal, complemented
19#35372C214yesmaximal, complemented
20#34996C212yesmaximal, complemented
21#34991C214yesmaximal, complemented
22#34736C212yesmaximal, complemented
23C2×#2432C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C2×#563C2211yescharacteristic, complemented
26C2×#563C2212yescomplemented
27C2×H(3,𝔽4)C2211yescharacteristic, complemented
28C2×#539C2212yes—
29C22×C4⋊Q8C2211yescharacteristic, complemented
30C22×#124C2211yescharacteristic
31C2×#525C2212yes—
32C2×#525C2212yescomplemented
33C22×C22⋊Q8C2211yescharacteristic, complemented
34C22×C4×D4C2212yescomplemented
35#2852C2214yescomplemented
36#2852C2214yescomplemented
37#2851C2212yescomplemented
38#2851C2214yescomplemented
39#2850C2212yes—
40#2849C2214yescomplemented
41#2848C2214yescomplemented
42#2837C2214yescomplemented
43#2832C2214yescomplemented
44#2831C2214yescomplemented
45#2830C2214yescomplemented
46#2829C2214yescomplemented
47#2829C2214yescomplemented
48#2829C2214yescomplemented
49#2829C2214yescomplemented
50#2829C2214yescomplemented
51#2829C2214yescomplemented
52#2828C2214yescomplemented
53#2828C2214yescomplemented
54#2827C2214yescomplemented
55#2826C2214yescomplemented
56#2821C2214yescomplemented
57#2820C2212yescomplemented
58#2819C2212yescomplemented
59#2816C2214yescomplemented
60#2814C2214yescomplemented
61#2813C2214yescomplemented
62#2812C2214yescomplemented
63#2808C2212yescomplemented
64#2806C2212yescomplemented
65#2806C2212yescomplemented
66#2803C2214yescomplemented
67#2803C2214yescomplemented
68#2800C2214yescomplemented
69#2797C2214yescomplemented
70#2796C2214yescomplemented
71#2786C2214yescomplemented
72#2757C2214yescomplemented
73#2756C2214yescomplemented
74#2755C2214yescomplemented
75#2754C2214yescomplemented
76#2748C2212yescomplemented
77#2741C2214yescomplemented
78#2734C2212yescomplemented
79#2733C2212yescomplemented
80#2732C2212yescomplemented
81#2731C2212yescomplemented
82#2731C2212yescomplemented
83#2729C2214yescomplemented
84#2717C2212yescomplemented
85#2716C2214yescomplemented
86#2715C2214yescomplemented
87#2714C2214yescomplemented
88#2713C2214yescomplemented
89#2712C2214yescomplemented
90#2711C2214yescomplemented
91#2710C2214yescomplemented
92#2705C2214yescomplemented
93#2704C2214yescomplemented
94#2700C2214yescomplemented
95#2697C2212yescomplemented
96#2694C2214yescomplemented
97#2691C2214yescomplemented
98#2686C2214yescomplemented
99#2685C2214yescomplemented
100#2685C2214yescomplemented
101#2685C2214yescomplemented
102#2684C2212yescomplemented
103#2681C2214yescomplemented
104#2678C2214yescomplemented
105#2677C2214yescomplemented
106#2674C2214yescomplemented
107#2674C2214yescomplemented
108#2670C2214yescomplemented
109#2638C2214yescomplemented
110#2636C2214yescomplemented
111#2633C2214yescomplemented
112#2630C2214yescomplemented
113#2626C2212yescomplemented
114#2622C2214yescomplemented
115#2617C2212yes—
116#2597C2214yescomplemented
117#2595C2214yescomplemented
118#2589C2214yescomplemented
119#2587C2214yescomplemented
120#2577C2214yescomplemented
121#2575C2214yescomplemented
122#2574C2214yescomplemented
123#2573C2214yescomplemented
124#2561C2212yescomplemented
125#2560C2214yescomplemented
126#2560C2214yescomplemented
127#2556C2214yescomplemented
128#2556C2214yescomplemented
129#2539C2212yes—
130#2523C2214yescomplemented
131#2518C2214yescomplemented
132#2518C2214yescomplemented
133#2517C2214yescomplemented
134#2498C2214yescomplemented
135#2482C2214yescomplemented
136#2481C2214yescomplemented
137#2480C2214yescomplemented
138#2480C2214yescomplemented
139#2479C2214yescomplemented
140#2478C2214yescomplemented
141#2475C2214yescomplemented
142#2474C2214yescomplemented
143#2473C2214yescomplemented
144#2473C2214yescomplemented
145#2472C2214yes—
146#2468C2214yescomplemented
147#2468C2214yescomplemented
148#2467C2214yescomplemented
149#2466C2214yescomplemented
150#2466C2214yescomplemented
151#2463C2214yescomplemented
152#2461C2214yescomplemented
153#2461C2214yescomplemented
154#2460C2214yescomplemented
155#2460C2214yescomplemented
156#2459C2214yescomplemented
157#2455C2214yescomplemented
158#2454C2214yescomplemented
159#2452C2214yescomplemented
160#2452C2214yescomplemented
161#2449C2214yescomplemented
162#2449C2214yescomplemented
163#2447C2214yescomplemented
164#2443C2214yes—
165#2438C2214yescomplemented
166#2437C2214yescomplemented
167#2436C2212yes—
168#2434C2212yescomplemented
169#2432C2212yes—
170#2432C2212yes—
171#2432C2214yescomplemented
172#2432C2212yescomplemented
173#2432C2212yescomplemented
174#2432C2214yescomplemented
175#2425C2214yes—
176#2419C2214yescomplemented
177#2418C2214yescomplemented
178#2413C2214yescomplemented
179#2412C2214yes—
180#2411C2214yes—
181#2411C2214yescomplemented
182#2410C2214yes—
183#2409C2214yescomplemented
184#2408C2214yes—
185#2407C2214yes—
186#2407C2214yescomplemented
187#2406C2212yes—
188#2406C2212yescomplemented
189#2405C2212yes—
190#2405C2214yescomplemented
191#2405C2212yescomplemented
192#2404C2212yes—
193#2404C2212yescomplemented
194#2403C2212yes—
195#2403C2212yescomplemented
196#2388C2214yes—
197#2388C2214yescomplemented
198C2×#394C2214yescomplemented
199#2381C2212yescomplemented
200#2379C2211yescharacteristic, complemented
201#2379C2211yescharacteristic, complemented
202#2378C2214yescomplemented
203#2376C2212yescomplemented
204#2375C2212yescomplemented
205#2329C2212yescomplemented
206#2325C2212yes—
207#2322C2214yescomplemented
208#2318C2214yescomplemented
209C4×#120C2214yes—
210C4×#120C2214yescomplemented
211#2297C2212yes—
212#2297C2212yescomplemented
213C2×#391C2211yescharacteristic, complemented
214C2×#390C2211yescharacteristic
215C2×#385C2214yescomplemented
216#2280C2212yescomplemented
217#2274C2212yescomplemented
218C2×C4×C22⋊C4C2211yescharacteristic, complemented
219C22×#41—44no—
220C22×#41—44no—
221C22×#41—44no—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C23×Q8C2311yescharacteristic
227C23×Q8C2311yescharacteristic
228C23×D4C2311yescharacteristic
229C23×D4C2312yes—
230C23×D4C2312yes—
231C24×C4C2312yes—
232C24×C4C2311yescharacteristic
233C24×C4C2312yes—
234#563—48no—
235#563—44no—
236H(3,𝔽4)—44no—
237#539—48no—
238C2×C4⋊Q8—44no—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125C2312yes—
250C2×#125C2314yes—
251C2×#125C2314yes—
252C2×#124—44no—
253C2×#124C2311yescharacteristic
254C2×#124C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2312yes—
257C2×#124C2311yescharacteristic
258C2×#124C2314yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262#525—48no—
263#525—48no—
264C2×#123C2312yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2312yes—
269C2×#123C2312yes—
270C2×#123C2312yes—
271C2×#123C2314yes—
272C2×C22⋊Q8—44no—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×#121C2314yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2312yes—
287C2×#120C2312yes—
288C2×#120C2314yes—
289C2×#120C2314yes—
290C2×#120C2312yes—
291C2×#120C2314yes—
292C2×#120C2312yes—
293C2×#120C2312yes—
294C2×C4×D4—48no—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×#117C2314yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2314yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C22⋊C4C2312yes—
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2314yes—
313C22×C22⋊C4C2314yes—
314C22×C22⋊C4C2312yes—
315C22×C22⋊C4C2312yes—
316C22×C42C2311yescharacteristic
317C22×C42C2312yes—
318C22×C42C2311yescharacteristic
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
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#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
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#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#391C2312yes—
443#391C2314yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
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#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
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#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2312yes—
535#386C2314yes—
536#386C2312yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2312yes—
549#386C2312yes—
550#386C2312yes—
551#386C2312yes—
552#386C2314yes—
553#386C2312yes—
554#386C2312yes—
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#383C2314yes—
585#383C2314yes—
586#382C2312yes—
587#382C2312yes—
588#382C2314yes—
589#381C2314yes—
590#381C2314yes—
591#381C2312yes—
592#381C2314yes—
593#381C2312yes—
594#380C2314yes—
595#380C2314yes—
596#380C2312yes—
597#380C2312yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#379C2314yes—
604#379C2314yes—
605#379C2314yes—
606#379C2314yes—
607#379C2312yes—
608#379C2312yes—
609#379C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2312yes—
622C4×C22⋊C4C2312yes—
623C4×C22⋊C4C2314yes—
624C4×C22⋊C4C2312yes—
625C2×#95C2312yes—
626C2×#95C2314yes—
627C25C2412yes—
628C25C2411yescharacteristic
629C25C2412yes—
630C2×#41—28no—
631C2×#41—28no—
632C2×#41—44no—
633C2×#41—44no—
634C2×#41—44no—
635C2×#41—44no—
636C2×#41—44no—
637C2×#41—44no—
638C2×#41—44no—
639C2×#41—44no—
640C2×#41—44no—
641C2×#41—44no—
642C2×#41—464no—
643C22×Q8—24no—
644C22×Q8—42no—
645C22×Q8—42no—
646C22×Q8—42no—
647C22×Q8—42no—
648C22×Q8—42no—
649C22×Q8C2412yes—
650C22×Q8C2411yescharacteristic
651C22×Q8C2412yes—
652C22×Q8C2411yescharacteristic
653C22×Q8C2411yescharacteristic
654C22×Q8C2412yes—
655C22×Q8C2412yes—
656C22×Q8C2411yescharacteristic
657C22×D4—24no—
658C22×D4—42no—
659C22×D4—44no—
660C22×D4—42no—
661C22×D4—44no—
662C22×D4—44no—
663C22×D4—48no—
664C22×D4—44no—
665C22×D4C2414yes—
666C22×D4C2412yes—
667C22×D4C2412yes—
668C22×D4C2414yes—
669C22×D4C2412yes—
670C22×D4C2412yes—
671C22×D4C2411yescharacteristic
672C22×D4C2414yes—
673C22×D4C2414yes—
674C22×D4C2414yes—
675C22×D4C2414yes—
676C22×D4C2412yes—
677C22×D4C2412yes—
678C22×D4C2412yes—
679C22×D4C2411yescharacteristic
680C23×C4—28no—
681C23×C4—24no—
682C23×C4—42no—
683C23×C4—42no—
684C23×C4—44no—
685C23×C4—44no—
686C23×C4—44no—
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×C4C2412yes—
701C23×C4C2414yes—
702C23×C4C2414yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2412yes—
706C23×C4C2411yescharacteristic
707C4⋊Q8—28no—
708C4⋊Q8—44no—
709C4⋊Q8—44no—
710C4⋊Q8—44no—
711C4⋊Q8—44no—
712C4⋊Q8—44no—
713#126—48no—
714#126—48no—
715#126—48no—
716#126—48no—
717#125—48no—
718#125—44no—
719#125—48no—
720#124—24no—
721#124—24no—
722#124—44no—
723#124—42no—
724#124—42no—
725#124—48no—
726#124—48no—
727#124—44no—
728#124—44no—
729#123—28no—
730#123—48no—
731#123—48no—
732#123—48no—
733#123—44no—
734#123—48no—
735#123—44no—
736#123—44no—
737C22⋊Q8—216no—
738C22⋊Q8—44no—
739C22⋊Q8—44no—
740C22⋊Q8—48no—
741C22⋊Q8—48no—
742C22⋊Q8—44no—
743C22⋊Q8—48no—
744C22⋊Q8—44no—
745C22⋊Q8—48no—
746C22⋊Q8—48no—
747#121—48no—
748#121—48no—
749#121—44no—
750#121—44no—
751#120—28no—
752#120—44no—
753#120—44no—
754#120—48no—
755#120—48no—
756#120—44no—
757#120—48no—
758C4×D4—216no—
759C4×D4—48no—
760C4×D4—48no—
761C4×D4—48no—
762C4×D4—48no—
763C4×D4—48no—
764C4×D4—48no—
765C4×D4—48no—
766#117—48no—
767#117—44no—
768#117—44no—
769C2×C4⋊C4—28no—
770C2×C4⋊C4—44no—
771C2×C4⋊C4—48no—
772C2×C4⋊C4—42no—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C22⋊C4—44no—
814C2×C22⋊C4—44no—
815C2×C22⋊C4—48no—
816C2×C22⋊C4—48no—
817C2×C22⋊C4—44no—
818C2×C22⋊C4—44no—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C42—44no—
874C2×C42—42no—
875C2×C42—42no—
876C2×C42C2414yes—
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879C2×C42C2412yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933C24—22no—
934C24—24no—
935C24—24no—
936C24—28no—
937C24—24no—
938C24—24no—
939C24—42no—
940C24—42no—
941C24—41no—
942C24—41no—
943C24—44no—
944C24—44no—
945C24—42no—
946C24—42no—
947C24—44no—
948C24C2514yes—
949C24C2512yes—
950C24C2512yes—
951C24C2512yes—
952C24C2511yescharacteristic
953#41—432no—
954#41—432no—
955#41—432no—
956#41—432no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—22no—
960C2×Q8—22no—
961C2×Q8—22no—
962C2×Q8—24no—
963C2×Q8—41no—
964C2×Q8—42no—
965C2×Q8—41no—
966C2×Q8—41no—
967C2×Q8—41no—
968C2×Q8—41no—
969C2×Q8—42no—
970C2×Q8—41no—
971C2×Q8—42no—
972C2×Q8—41no—
973C2×Q8—41no—
974C2×Q8—42no—
975C2×Q8—42no—
976C2×Q8—42no—
977C2×Q8—42no—
978C2×Q8—42no—
979C2×Q8—42no—
980C2×Q8—416no—
981C2×Q8—88no—
982C2×Q8H(5,𝔽2)14yes—
983C2×D4—28no—
984C2×D4—24no—
985C2×D4—24no—
986C2×D4—24no—
987C2×D4—28no—
988C2×D4—28no—
989C2×D4—28no—
990C2×D4—24no—
991C2×D4—24no—
992C2×D4—24no—
993C2×D4—22no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—41no—
1000C2×D4—41no—
1001C2×D4—41no—
1002C2×D4—42no—
1003C2×D4—41no—
1004C2×D4—42no—
1005C2×D4—42no—
1006C2×D4—42no—
1007C2×D4—42no—
1008C2×D4—42no—
1009C2×D4—42no—
1010C2×D4—416no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—42no—
1023C2×D4—42no—
1024C2×D4—42no—
1025C2×D4—42no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4—432no—
1029C2×D4—432no—
1030C2×D4H(5,𝔽2)14yes—
1031C22×C4—22no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—28no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—28no—
1055C22×C4—28no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—41no—
1059C22×C4—41no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—42no—
1081C22×C4—432no—
1082C22×C4—416no—
1083C22×C4—816no—
1084C22×C4H(5,𝔽2)14yes—
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—24no—
1147C22⋊C4—24no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
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—42no—
1177C22⋊C4—42no—
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—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C42—28no—
1198C42—22no—
1199C42—22no—
1200C42—24no—
1201C42—44no—
1202C42—42no—
1203C42—42no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—42no—
1209C42—42no—
1210C42—42no—
1211C42—42no—
1212C23—21no—
1213C23—21no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—24no—
1229C23—24no—
1230C23—24no—
1231C23—24no—
1232C23—24no—
1233C23—24no—
1234C23—24no—
1235C23—24no—
1236C23—48no—
1237C23—416no—
1238C23—44no—
1239C23—44no—
1240C23—48no—
1241C23—48no—
1242C23—44no—
1243C23—84no—
1244C23—84no—
1245C23—88no—
1246C23—84no—
1247C23—84no—
1248C23—88no—
1249C23—84no—
1250C23—88no—
1251C23C2×H(5,𝔽2)14yes—
1252C23C2×H(5,𝔽2)12yes—
1253C23#58514yes—
1254C23C2611yescharacteristic
1255Q8—44no—
1256Q8—48no—
1257Q8—44no—
1258Q8—82no—
1259Q8—84no—
1260Q8—82no—
1261Q8—162no—
1262Q8—162no—
1263D4—44no—
1264D4—48no—
1265D4—48no—
1266D4—48no—
1267D4—44no—
1268D4—48no—
1269D4—416no—
1270D4—48no—
1271D4—416no—
1272D4—88no—
1273D4—88no—
1274D4—88no—
1275D4—88no—
1276D4—162no—
1277D4—162no—
1278C2×C4—216no—
1279C2×C4—28no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—44no—
1331C2×C4—48no—
1332C2×C4—48no—
1333C2×C4—48no—
1334C2×C4—48no—
1335C2×C4—48no—
1336C2×C4—48no—
1337C2×C4—48no—
1338C2×C4—48no—
1339C2×C4—48no—
1340C2×C4—88no—
1341C2×C4—88no—
1342C2×C4—84no—
1343C2×C4—84no—
1344C2×C4—84no—
1345C2×C4—84no—
1346C2×C4C2×H(5,𝔽2)12yes—
1347C2×C4C2×H(5,𝔽2)12yes—
1348C2×C4C2×H(5,𝔽2)14yes—
1349C2×C4C2×H(5,𝔽2)14yes—
1350C22—22no—
1351C22—22no—
1352C22—24no—
1353C22—24no—
1354C22—24no—
1355C22—28no—
1356C22—42no—
1357C22—44no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—44no—
1362C22—42no—
1363C22—44no—
1364C22—42no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—44no—
1369C22—44no—
1370C22—44no—
1371C22—44no—
1372C22—44no—
1373C22—42no—
1374C22—44no—
1375C22—42no—
1376C22—816no—
1377C22—88no—
1378C22—816no—
1379C22#352914yes—
1380C22C22×H(5,𝔽2)11yescharacteristic
1381C22C22×H(5,𝔽2)11yescharacteristic
1382C22C22×H(5,𝔽2)11yescharacteristic
1383C22C2×#58512yes—
1384C222−1+612yes—
1385C4—24no—
1386C4—24no—
1387C4—22no—
1388C4—22no—
1389C4—42no—
1390C4—44no—
1391C4—42no—
1392C4—42no—
1393C4—44no—
1394C4—44no—
1395C4—44no—
1396C4—44no—
1397C4—42no—
1398C4—42no—
1399C4—44no—
1400C4—44no—
1401C4—44no—
1402C4—44no—
1403C2—24no—
1404C2—44no—
1405C2—82no—
1406C2—82no—
1407C2—84no—
1408C2C2×#352911yescharacteristic
1409C2#6281711yescharacteristic
1410C2#6288611yescharacteristic
1411C2#6289712yes—
1412C2#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. #52373C2semidirect
2. #52345C2semidirect
3. #52338C2semidirect
4. #52334C2semidirect
5. #52330C2semidirect
6. #52326C2semidirect
7. #46334C2semidirect
8. #46325C2semidirect
9. #46136C2semidirect
10. #46098C2semidirect
11. #45977C2semidirect
12. #45742C2semidirect
13. #45739C2semidirect
14. #45731C2semidirect
15. #45453C2semidirect
16. #45450C2semidirect
17. #45442C2semidirect
18. #35397C2semidirect
19. #35372C2semidirect
20. #34996C2semidirect
21. #34991C2semidirect
22. #34736C2semidirect
23. C2×#2432C2semidirect
25. C2×#563C22semidirect
26. C2×#563C22semidirect
27. C2×H(3,𝔽4)C22semidirect
29. C22×C4⋊Q8C22semidirect
32. C2×#525C22semidirect
33. C22×C22⋊Q8C22semidirect
34. C22×C4×D4C22semidirect
35. #2852C22semidirect
36. #2852C22semidirect
37. #2851C22semidirect
38. #2851C22semidirect
40. #2849C22semidirect
41. #2848C22semidirect
42. #2837C22semidirect
43. #2832C22semidirect
44. #2831C22semidirect
45. #2830C22semidirect
46. #2829C22semidirect
47. #2829C22semidirect
48. #2829C22semidirect
49. #2829C22semidirect
50. #2829C22semidirect
51. #2829C22semidirect
52. #2828C22semidirect
53. #2828C22semidirect
54. #2827C22semidirect
55. #2826C22semidirect
56. #2821C22semidirect
57. #2820C22semidirect
58. #2819C22semidirect
59. #2816C22semidirect
60. #2814C22semidirect
61. #2813C22semidirect
62. #2812C22semidirect
63. #2808C22semidirect
64. #2806C22semidirect
65. #2806C22semidirect
66. #2803C22semidirect
67. #2803C22semidirect
68. #2800C22semidirect
69. #2797C22semidirect
70. #2796C22semidirect
71. #2786C22semidirect
72. #2757C22semidirect
73. #2756C22semidirect
74. #2755C22semidirect
75. #2754C22semidirect
76. #2748C22semidirect
77. #2741C22semidirect
78. #2734C22semidirect
79. #2733C22semidirect
80. #2732C22semidirect
81. #2731C22semidirect
82. #2731C22semidirect
83. #2729C22semidirect
84. #2717C22semidirect
85. #2716C22semidirect
86. #2715C22semidirect
87. #2714C22semidirect
88. #2713C22semidirect
89. #2712C22semidirect
90. #2711C22semidirect
91. #2710C22semidirect
92. #2705C22semidirect
93. #2704C22semidirect
94. #2700C22semidirect
95. #2697C22semidirect
96. #2694C22semidirect
97. #2691C22semidirect
98. #2686C22semidirect
99. #2685C22semidirect
100. #2685C22semidirect
101. #2685C22semidirect
102. #2684C22semidirect
103. #2681C22semidirect
104. #2678C22semidirect
105. #2677C22semidirect
106. #2674C22semidirect
107. #2674C22semidirect
108. #2670C22semidirect
109. #2638C22semidirect
110. #2636C22semidirect
111. #2633C22semidirect
112. #2630C22semidirect
113. #2626C22semidirect
114. #2622C22semidirect
116. #2597C22semidirect
117. #2595C22semidirect
118. #2589C22semidirect
119. #2587C22semidirect
120. #2577C22semidirect
121. #2575C22semidirect
122. #2574C22semidirect
123. #2573C22semidirect
124. #2561C22semidirect
125. #2560C22semidirect
126. #2560C22semidirect
127. #2556C22semidirect
128. #2556C22semidirect
130. #2523C22semidirect
131. #2518C22semidirect
132. #2518C22semidirect
133. #2517C22semidirect
134. #2498C22semidirect
135. #2482C22semidirect
136. #2481C22semidirect
137. #2480C22semidirect
138. #2480C22semidirect
139. #2479C22semidirect
140. #2478C22semidirect
141. #2475C22semidirect
142. #2474C22semidirect
143. #2473C22semidirect
144. #2473C22semidirect
146. #2468C22semidirect
147. #2468C22semidirect
148. #2467C22semidirect
149. #2466C22semidirect
150. #2466C22semidirect
151. #2463C22semidirect
152. #2461C22semidirect
153. #2461C22semidirect
154. #2460C22semidirect
155. #2460C22semidirect
156. #2459C22semidirect
157. #2455C22semidirect
158. #2454C22semidirect
159. #2452C22semidirect
160. #2452C22semidirect
161. #2449C22semidirect
162. #2449C22semidirect
163. #2447C22semidirect
165. #2438C22semidirect
166. #2437C22semidirect
168. #2434C22semidirect
171. #2432C22semidirect
172. #2432C22semidirect
173. #2432C22semidirect
174. #2432C22semidirect
176. #2419C22semidirect
177. #2418C22semidirect
178. #2413C22semidirect
181. #2411C22semidirect
183. #2409C22semidirect
186. #2407C22semidirect
188. #2406C22semidirect
190. #2405C22semidirect
191. #2405C22semidirect
193. #2404C22semidirect
195. #2403C22semidirect
197. #2388C22semidirect
198. C2×#394C22semidirect
199. #2381C22semidirect
200. #2379C22semidirect
201. #2379C22semidirect
202. #2378C22semidirect
203. #2376C22semidirect
204. #2375C22semidirect
205. #2329C22semidirect
207. #2322C22semidirect
208. #2318C22semidirect
210. C4×#120C22semidirect
212. #2297C22semidirect
213. C2×#391C22semidirect
215. C2×#385C22semidirect
216. #2280C22semidirect
217. #2274C22semidirect
218. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#523732
#523452
#523382
#523342
#523302
#523262
#463342
#463252
#461362
#460982
#459772
#457422
#457392
#457312
#454532
#454502
#454422
#353972
#353722
#349962
#349912
#347362
C2×#24322