Finite Group Databasebeta

← #8944566

Subgroups — #8944566

Order 512.

5546 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57972C214yesmaximal, complemented
2#57959C214yesmaximal, complemented
3#57146C212yesmaximal, complemented
4#56342C212yesmaximal, complemented
5#52019C214yesmaximal, complemented
6#51632C214yesmaximal, complemented
7#51041C212yesmaximal, complemented
8#49548C212yesmaximal, complemented
9#48365C214yesmaximal, complemented
10#47885C212yesmaximal, complemented
11#47004C212yesmaximal, complemented
12#46999C212yesmaximal, complemented
13#43076C214yesmaximal, complemented
14#43053C214yesmaximal, complemented
15#40913C214yesmaximal, complemented
16#40652C212yesmaximal, complemented
17#40596C214yesmaximal, complemented
18#38912C214yesmaximal, complemented
19#36711C211yesmaximal, characteristic, complemented
20#35750C212yesmaximal, complemented
21#35693C212yesmaximal, complemented
22#35446C211yesmaximal, characteristic, complemented
23#35356C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25C2×#551C2214yescomplemented
26C2×#547C2212yes—
27C2×#546C2214yes—
28C2×#544C2211yescharacteristic, complemented
29C22×#123C2212yes—
30C22×#123C2211yescharacteristic
31C2×#520C2211yescharacteristic, complemented
32#2848C2212yescomplemented
33#2842C2212yescomplemented
34#2835C2212yescomplemented
35#2831C2214yescomplemented
36#2827C2214yescomplemented
37#2826C2212yescomplemented
38#2813C2214yescomplemented
39#2812C2212yescomplemented
40#2807C2212yescomplemented
41#2807C2214yescomplemented
42#2805C2214yescomplemented
43#2796C2214yescomplemented
44#2790C2214yescomplemented
45#2782C2214yescomplemented
46#2780C2214yescomplemented
47#2779C2214yescomplemented
48#2779C2214yescomplemented
49#2774C2214yescomplemented
50#2771C2212yescomplemented
51#2771C2212yescomplemented
52#2771C2214yescomplemented
53#2764C2212yescomplemented
54#2763C2212yescomplemented
55#2761C2214yescomplemented
56#2752C2214yescomplemented
57#2752C2212yescomplemented
58#2750C2214yescomplemented
59#2750C2214yescomplemented
60#2749C2214yescomplemented
61#2744C2214yescomplemented
62#2743C2214yescomplemented
63#2743C2214yescomplemented
64#2743C2214yescomplemented
65#2743C2214yescomplemented
66#2741C2214yescomplemented
67#2735C2214yescomplemented
68#2735C2212yescomplemented
69#2734C2214yescomplemented
70#2720C2214yescomplemented
71#2718C2214yescomplemented
72#2718C2214yescomplemented
73#2710C2214yescomplemented
74#2708C2214yescomplemented
75#2707C2214yescomplemented
76#2706C2214yescomplemented
77#2706C2214yescomplemented
78#2703C2214yescomplemented
79#2702C2214yescomplemented
80#2701C2214yescomplemented
81#2701C2214yescomplemented
82#2695C2214yescomplemented
83#2695C2214yescomplemented
84#2694C2214yescomplemented
85#2694C2214yescomplemented
86#2689C2214yescomplemented
87#2686C2214yescomplemented
88#2685C2214yescomplemented
89#2685C2214yescomplemented
90#2680C2214yescomplemented
91#2680C2214yescomplemented
92#2674C2214yescomplemented
93#2674C2214yescomplemented
94#2674C2214yescomplemented
95#2672C2214yescomplemented
96#2672C2214yescomplemented
97#2670C2212yescomplemented
98#2667C2212yescomplemented
99#2666C2214yescomplemented
100#2663C2214yescomplemented
101#2648C2214yescomplemented
102#2638C2212yescomplemented
103#2638C2212yescomplemented
104#2636C2214yescomplemented
105#2630C2214yescomplemented
106#2628C2212yescomplemented
107#2626C2212yescomplemented
108#2624C2214yescomplemented
109#2623C2214yescomplemented
110#2622C2214yescomplemented
111#2616C2212yes—
112#2613C2214yes—
113#2602C2214yescomplemented
114#2601C2214yescomplemented
115#2598C2214yescomplemented
116#2583C2214yescomplemented
117#2583C2212yescomplemented
118#2583C2212yescomplemented
119#2579C2214yescomplemented
120#2579C2212yescomplemented
121#2569C2214yescomplemented
122#2567C2212yescomplemented
123#2553C2214yescomplemented
124#2553C2214yescomplemented
125#2536C2212yescomplemented
126#2534C2214yescomplemented
127#2518C2214yescomplemented
128#2515C2214yescomplemented
129#2505C2214yescomplemented
130#2485C2214yescomplemented
131#2483C2212yescomplemented
132#2482C2214yescomplemented
133#2482C2211yescharacteristic, complemented
134#2482C2211yescharacteristic, complemented
135#2482C2212yescomplemented
136#2482C2212yescomplemented
137#2480C2214yescomplemented
138#2480C2214yescomplemented
139#2479C2214yescomplemented
140#2477C2214yescomplemented
141#2476C2214yescomplemented
142#2476C2214yescomplemented
143#2474C2214yescomplemented
144#2473C2214yescomplemented
145#2471C2214yescomplemented
146#2470C2214yescomplemented
147#2470C2214yescomplemented
148#2470C2214yescomplemented
149#2470C2214yescomplemented
150#2470C2214yescomplemented
151#2470C2214yescomplemented
152#2470C2214yescomplemented
153#2468C2214yescomplemented
154#2466C2214yescomplemented
155#2466C2214yescomplemented
156#2460C2214yescomplemented
157#2458C2214yescomplemented
158#2456C2214yescomplemented
159#2455C2214yescomplemented
160#2455C2214yescomplemented
161#2455C2214yescomplemented
162#2443C2214yescomplemented
163#2440C2214yescomplemented
164#2438C2214yescomplemented
165#2437C2212yescomplemented
166#2437C2212yescomplemented
167#2437C2212yescomplemented
168#2435C2212yes—
169#2432C2214yes—
170#2432C2214yescomplemented
171#2430C2214yes—
172#2422C2214yescomplemented
173#2422C2214yescomplemented
174#2419C2214yescomplemented
175#2418C2214yescomplemented
176#2411C2214yescomplemented
177#2410C2214yes—
178#2410C2214yes—
179#2408C2212yes—
180#2407C2214yes—
181#2407C2214yescomplemented
182#2406C2212yes—
183#2406C2214yes—
184#2406C2214yes—
185#2406C2214yes—
186#2406C2212yes—
187#2406C2212yescomplemented
188#2405C2214yes—
189#2405C2212yes—
190#2405C2214yes—
191#2405C2214yes—
192#2405C2214yes—
193#2405C2212yes—
194#2404C2211yescharacteristic, complemented
195#2404C2211yescharacteristic, complemented
196#2392C2212yescomplemented
197#2388C2212yes—
198#2388C2212yescomplemented
199C2×#394C2214yes—
200#2383C2214yescomplemented
201#2378C2212yescomplemented
202#2360C2214yescomplemented
203#2357C2212yescomplemented
204D4×C4⋊C4C2214yescomplemented
205#2342C2214yescomplemented
206#2342C2214yescomplemented
207#2339C2212yes—
208D4×C22⋊C4C2214yes—
209#2321C2212yescomplemented
210#2321C2214yescomplemented
211#2317C2214yescomplemented
212#2315C2214yescomplemented
213#2313C2211yescharacteristic, complemented
214#2313C2211yescharacteristic, complemented
215#2312C2214yescomplemented
216#2308C2211yescharacteristic
217#2308C2212yes—
218C4×#120C2212yescomplemented
219C2×H(5,𝔽2)—48no—
220C2×H(5,𝔽2)—44no—
221C22×#41C2312yes—
222C22×#41C2314yes—
223C22×#41C2312yes—
224C22×#41C2311yescharacteristic
225C23×D4C2312yes—
226C23×D4C2311yescharacteristic
227C23×D4C2314yes—
228C23×D4C2312yes—
229C24×C4C2311yescharacteristic
230#551—416no—
231#547—48no—
232#546—416no—
233#544—44no—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#125C2314yes—
240C2×#124C2314yes—
241C2×#124C2314yes—
242C2×#123—48no—
243C2×#123—44no—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#120C2314yes—
269C2×#120C2312yes—
270C2×#120C2314yes—
271C2×#120C2312yes—
272#520—44no—
273C2×C4×Q8C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×#117C2314yes—
284C2×#117C2314yes—
285C2×#117C2314yes—
286C2×#117C2312yes—
287C2×#117C2311yescharacteristic
288C2×#117C2312yes—
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2314yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2314yes—
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2314yes—
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2314yes—
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2314yes—
302C22×C22⋊C4C2311yescharacteristic
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#399C2312yes—
318#399C2314yes—
319#399C2312yes—
320#399C2314yes—
321#399C2312yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2312yes—
326#399C2314yes—
327#399C2312yes—
328#399C2312yes—
329#398C2312yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#397C2314yes—
343#397C2312yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2312yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2312yes—
358#397C2312yes—
359#397C2314yes—
360#397C2312yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#395C2312yes—
375#395C2312yes—
376#395C2312yes—
377#395C2312yes—
378#395C2314yes—
379#395C2314yes—
380#395C2312yes—
381#395C2312yes—
382#395C2314yes—
383#395C2314yes—
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#394C2312yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2312yes—
412#394C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#393C2312yes—
418#393C2312yes—
419#393C2312yes—
420#393C2312yes—
421#393C2312yes—
422#393C2312yes—
423#392C2312yes—
424#392C2314yes—
425#392C2314yes—
426#392C2312yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2312yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2312yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2312yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2312yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2312yes—
550#385C2312yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#384C2314yes—
570#384C2314yes—
571#383C2314yes—
572#382C2314yes—
573#382C2314yes—
574#382C2312yes—
575#381C2312yes—
576#381C2312yes—
577#381C2312yes—
578#381C2311yescharacteristic
579#381C2311yescharacteristic
580#381C2312yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2312yes—
585#381C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2312yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#379C2312yes—
599#379C2312yes—
600#379C2312yes—
601#379C2314yes—
602#379C2312yes—
603#379C2314yes—
604#379C2314yes—
605#379C2314yes—
606#379C2314yes—
607#379C2312yes—
608#379C2312yes—
609#379C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622C2×#95C2314yes—
623C25C2411yescharacteristic
624C25C2412yes—
625C25C2411yescharacteristic
626C25C2412yes—
627H(5,𝔽2)—464no—
628C2×#41—28no—
629C2×#41—42no—
630C2×#41—48no—
631C2×#41—48no—
632C2×#41—48no—
633C2×#41—48no—
634C2×#41—44no—
635C2×#41—48no—
636C2×#41—44no—
637C22×Q8C2411yescharacteristic
638C22×Q8C2412yes—
639C22×Q8C2412yes—
640C22×Q8C2412yes—
641C22×D4—28no—
642C22×D4—216no—
643C22×D4—24no—
644C22×D4—48no—
645C22×D4—48no—
646C22×D4—44no—
647C22×D4—48no—
648C22×D4—44no—
649C22×D4—44no—
650C22×D4—44no—
651C22×D4C2412yes—
652C22×D4C2412yes—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C22×D4C2411yescharacteristic
661C22×D4C2414yes—
662C23×C4—44no—
663C23×C4—42no—
664C23×C4C2414yes—
665C23×C4C2414yes—
666C23×C4C2411yescharacteristic
667C23×C4C2411yescharacteristic
668C23×C4C2414yes—
669C23×C4C2414yes—
670C23×C4C2414yes—
671C23×C4C2411yescharacteristic
672C23×C4C2414yes—
673C23×C4C2411yescharacteristic
674C23×C4C2412yes—
675C23×C4C2412yes—
676C23×C4C2412yes—
677C23×C4C2414yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2411yescharacteristic
681C4⋊Q8—44no—
682C4⋊Q8—48no—
683#126—48no—
684#126—48no—
685#126—48no—
686#125—48no—
687#124—48no—
688#124—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—
698#123—48no—
699#123—48no—
700#123—48no—
701#123—48no—
702C22⋊Q8—28no—
703C22⋊Q8—44no—
704C22⋊Q8—48no—
705C22⋊Q8—48no—
706C22⋊Q8—48no—
707C22⋊Q8—48no—
708C22⋊Q8—44no—
709#121—48no—
710#121—48no—
711#121—48no—
712#121—48no—
713#120—216no—
714#120—44no—
715#120—44no—
716#120—48no—
717C4×Q8—44no—
718C4×D4—28no—
719C4×D4—44no—
720C4×D4—48no—
721C4×D4—44no—
722C4×D4—44no—
723C4×D4—48no—
724C4×D4—48no—
725C4×D4—48no—
726C4×D4—48no—
727#117—48no—
728#117—44no—
729#117—42no—
730#117—44no—
731#117—48no—
732#117—48no—
733C2×C4⋊C4—24no—
734C2×C4⋊C4—24no—
735C2×C4⋊C4—44no—
736C2×C4⋊C4—48no—
737C2×C4⋊C4—48no—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
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×C22⋊C4—216no—
782C2×C22⋊C4—216no—
783C2×C22⋊C4—48no—
784C2×C22⋊C4—48no—
785C2×C22⋊C4—48no—
786C2×C22⋊C4—44no—
787C2×C22⋊C4—42no—
788C2×C22⋊C4—42no—
789C2×C22⋊C4—42no—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858#95C2412yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2412yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2412yes—
881#95C2414yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2414yes—
901#95C2412yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906C24—24no—
907C24—22no—
908C24—22no—
909C24—28no—
910C24—44no—
911C24—42no—
912C24—42no—
913C24—42no—
914C24—42no—
915C24—44no—
916C24—42no—
917C24—42no—
918C24—44no—
919C24—42no—
920C24—42no—
921C24—42no—
922C24—42no—
923C24H(5,𝔽2)18yes—
924C24C2512yes—
925C24C2512yes—
926C24C2512yes—
927C24C2511yescharacteristic
928C24C2514yes—
929#41—432no—
930#41—416no—
931#41—464no—
932#41—816no—
933C2×Q8—24no—
934C2×Q8—24no—
935C2×Q8—24no—
936C2×Q8—41no—
937C2×Q8—44no—
938C2×Q8—44no—
939C2×Q8—44no—
940C2×Q8—42no—
941C2×D4—28no—
942C2×D4—24no—
943C2×D4—28no—
944C2×D4—28no—
945C2×D4—28no—
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—28no—
949C2×D4—28no—
950C2×D4—28no—
951C2×D4—28no—
952C2×D4—24no—
953C2×D4—28no—
954C2×D4—24no—
955C2×D4—41no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—464no—
973C2×D4—416no—
974C2×D4—432no—
975C2×D4—432no—
976C22×C4—28no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—24no—
980C22×C4—28no—
981C22×C4—28no—
982C22×C4—28no—
983C22×C4—28no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—28no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—28no—
990C22×C4—42no—
991C22×C4—44no—
992C22×C4—42no—
993C22×C4—44no—
994C22×C4—42no—
995C22×C4—44no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—88no—
1019C22×C4H(5,𝔽2)14yes—
1020C22×C4C2512yes—
1021C22×C4C2514yes—
1022C22×C4C2514yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2514yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—41no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—41no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—24no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—24no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—42no—
1105C22⋊C4—44no—
1106C22⋊C4—42no—
1107C22⋊C4—44no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—42no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
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—42no—
1132C22⋊C4—42no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C42—24no—
1140C42—28no—
1141C42—44no—
1142C42—44no—
1143C42—42no—
1144C42—42no—
1145C42—44no—
1146C42—44no—
1147C42—44no—
1148C42—44no—
1149C23—28no—
1150C23—22no—
1151C23—22no—
1152C23—22no—
1153C23—24no—
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—22no—
1158C23—24no—
1159C23—22no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—22no—
1164C23—24no—
1165C23—22no—
1166C23—24no—
1167C23—24no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—24no—
1172C23—22no—
1173C23—48no—
1174C23—416no—
1175C23—48no—
1176C23—44no—
1177C23—82no—
1178C23—82no—
1179C23—88no—
1180C23—82no—
1181C23—82no—
1182C23—88no—
1183C23—88no—
1184C23—162no—
1185C23—162no—
1186C23—162no—
1187C23—162no—
1188C23—164no—
1189C23—164no—
1190C23C2×H(5,𝔽2)18yes—
1191C23C2×H(5,𝔽2)14yes—
1192C23C2×H(5,𝔽2)12yes—
1193C23C2611yescharacteristic
1194Q8—44no—
1195Q8—48no—
1196Q8—84no—
1197Q8—162no—
1198D4—216no—
1199D4—416no—
1200D4—48no—
1201D4—416no—
1202D4—416no—
1203D4—416no—
1204D4—416no—
1205D4—44no—
1206D4—88no—
1207D4—88no—
1208D4—164no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—44no—
1254C2×C4—416no—
1255C2×C4—48no—
1256C2×C4—44no—
1257C2×C4—416no—
1258C2×C4—48no—
1259C2×C4—44no—
1260C2×C4—48no—
1261C2×C4—88no—
1262C2×C4—84no—
1263C2×C4—88no—
1264C2×C4—82no—
1265C2×C4—88no—
1266C2×C4—82no—
1267C2×C4—88no—
1268C2×C4—162no—
1269C2×C4—164no—
1270C2×C4C2×H(5,𝔽2)14yes—
1271C2×C4#58514yes—
1272C22—22no—
1273C22—24no—
1274C22—28no—
1275C22—22no—
1276C22—22no—
1277C22—28no—
1278C22—28no—
1279C22—28no—
1280C22—44no—
1281C22—42no—
1282C22—42no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—88no—
1299C22—168no—
1300C22—168no—
1301C22—164no—
1302C22C22×H(5,𝔽2)11yescharacteristic
1303C22C22×H(5,𝔽2)12yes—
1304C22C2×#58512yes—
1305C222−1+612yes—
1306C4—24no—
1307C4—24no—
1308C4—44no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—44no—
1313C4—41no—
1314C4—41no—
1315C4—44no—
1316C4—42no—
1317C4—42no—
1318C4—44no—
1319C4—44no—
1320C4—44no—
1321C4—44no—
1322C4—44no—
1323C4—44no—
1324C2—42no—
1325C2—44no—
1326C2—48no—
1327C2—82no—
1328C2—82no—
1329C2#6281711yescharacteristic
1330C2#6282111yescharacteristic
1331C2#6288711yescharacteristic
1332C2#6290114yes—
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. #57972C2semidirect
2. #57959C2semidirect
3. #57146C2semidirect
4. #56342C2semidirect
5. #52019C2semidirect
6. #51632C2semidirect
7. #51041C2semidirect
8. #49548C2semidirect
9. #48365C2semidirect
10. #47885C2semidirect
11. #47004C2semidirect
12. #46999C2semidirect
13. #43076C2semidirect
14. #43053C2semidirect
15. #40913C2semidirect
16. #40652C2semidirect
17. #40596C2semidirect
18. #38912C2semidirect
19. #36711C2semidirect
20. #35750C2semidirect
21. #35693C2semidirect
22. #35446C2semidirect
23. #35356C2semidirect
25. C2×#551C22semidirect
28. C2×#544C22semidirect
31. C2×#520C22semidirect
32. #2848C22semidirect
33. #2842C22semidirect
34. #2835C22semidirect
35. #2831C22semidirect
36. #2827C22semidirect
37. #2826C22semidirect
38. #2813C22semidirect
39. #2812C22semidirect
40. #2807C22semidirect
41. #2807C22semidirect
42. #2805C22semidirect
43. #2796C22semidirect
44. #2790C22semidirect
45. #2782C22semidirect
46. #2780C22semidirect
47. #2779C22semidirect
48. #2779C22semidirect
49. #2774C22semidirect
50. #2771C22semidirect
51. #2771C22semidirect
52. #2771C22semidirect
53. #2764C22semidirect
54. #2763C22semidirect
55. #2761C22semidirect
56. #2752C22semidirect
57. #2752C22semidirect
58. #2750C22semidirect
59. #2750C22semidirect
60. #2749C22semidirect
61. #2744C22semidirect
62. #2743C22semidirect
63. #2743C22semidirect
64. #2743C22semidirect
65. #2743C22semidirect
66. #2741C22semidirect
67. #2735C22semidirect
68. #2735C22semidirect
69. #2734C22semidirect
70. #2720C22semidirect
71. #2718C22semidirect
72. #2718C22semidirect
73. #2710C22semidirect
74. #2708C22semidirect
75. #2707C22semidirect
76. #2706C22semidirect
77. #2706C22semidirect
78. #2703C22semidirect
79. #2702C22semidirect
80. #2701C22semidirect
81. #2701C22semidirect
82. #2695C22semidirect
83. #2695C22semidirect
84. #2694C22semidirect
85. #2694C22semidirect
86. #2689C22semidirect
87. #2686C22semidirect
88. #2685C22semidirect
89. #2685C22semidirect
90. #2680C22semidirect
91. #2680C22semidirect
92. #2674C22semidirect
93. #2674C22semidirect
94. #2674C22semidirect
95. #2672C22semidirect
96. #2672C22semidirect
97. #2670C22semidirect
98. #2667C22semidirect
99. #2666C22semidirect
100. #2663C22semidirect
101. #2648C22semidirect
102. #2638C22semidirect
103. #2638C22semidirect
104. #2636C22semidirect
105. #2630C22semidirect
106. #2628C22semidirect
107. #2626C22semidirect
108. #2624C22semidirect
109. #2623C22semidirect
110. #2622C22semidirect
113. #2602C22semidirect
114. #2601C22semidirect
115. #2598C22semidirect
116. #2583C22semidirect
117. #2583C22semidirect
118. #2583C22semidirect
119. #2579C22semidirect
120. #2579C22semidirect
121. #2569C22semidirect
122. #2567C22semidirect
123. #2553C22semidirect
124. #2553C22semidirect
125. #2536C22semidirect
126. #2534C22semidirect
127. #2518C22semidirect
128. #2515C22semidirect
129. #2505C22semidirect
130. #2485C22semidirect
131. #2483C22semidirect
132. #2482C22semidirect
133. #2482C22semidirect
134. #2482C22semidirect
135. #2482C22semidirect
136. #2482C22semidirect
137. #2480C22semidirect
138. #2480C22semidirect
139. #2479C22semidirect
140. #2477C22semidirect
141. #2476C22semidirect
142. #2476C22semidirect
143. #2474C22semidirect
144. #2473C22semidirect
145. #2471C22semidirect
146. #2470C22semidirect
147. #2470C22semidirect
148. #2470C22semidirect
149. #2470C22semidirect
150. #2470C22semidirect
151. #2470C22semidirect
152. #2470C22semidirect
153. #2468C22semidirect
154. #2466C22semidirect
155. #2466C22semidirect
156. #2460C22semidirect
157. #2458C22semidirect
158. #2456C22semidirect
159. #2455C22semidirect
160. #2455C22semidirect
161. #2455C22semidirect
162. #2443C22semidirect
163. #2440C22semidirect
164. #2438C22semidirect
165. #2437C22semidirect
166. #2437C22semidirect
167. #2437C22semidirect
170. #2432C22semidirect
172. #2422C22semidirect
173. #2422C22semidirect
174. #2419C22semidirect
175. #2418C22semidirect
176. #2411C22semidirect
181. #2407C22semidirect
187. #2406C22semidirect
194. #2404C22semidirect
195. #2404C22semidirect
196. #2392C22semidirect
198. #2388C22semidirect
200. #2383C22semidirect
201. #2378C22semidirect
202. #2360C22semidirect
203. #2357C22semidirect
204. D4×C4⋊C4C22semidirect
205. #2342C22semidirect
206. #2342C22semidirect
209. #2321C22semidirect
210. #2321C22semidirect
211. #2317C22semidirect
212. #2315C22semidirect
213. #2313C22semidirect
214. #2313C22semidirect
215. #2312C22semidirect
218. C4×#120C22semidirect

Maximal subgroups

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

subgroupindex
#579722
#579592
#571462
#563422
#520192
#516322
#510412
#495482
#483652
#478852
#470042
#469992
#430762
#430532
#409132
#406522
#405962
#389122
#367112
#357502
#356932
#354462
#353562