Finite Group Databasebeta

← #10086334

Subgroups — #10086334

Order 512.

4907 conjugacy classes of subgroups.

The subgroup lattice has 1311 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59419C211yesmaximal, characteristic, complemented
2#58382C212yesmaximal, complemented
3#57203C214yesmaximal, complemented
4#54853C212yesmaximal, complemented
5#54811C214yesmaximal, complemented
6#53666C214yesmaximal, complemented
7#52325C214yesmaximal, complemented
8#51016C214yesmaximal, complemented
9#49690C214yesmaximal, complemented
10#47678C212yesmaximal, complemented
11#46812C212yesmaximal, complemented
12#46378C214yesmaximal, complemented
13#46162C212yesmaximal, complemented
14#45378C212yesmaximal, complemented
15#43972C214yesmaximal, complemented
16#43895C212yesmaximal, complemented
17#43012C214yesmaximal, complemented
18#42410C212yesmaximal, complemented
19#42158C212yesmaximal, complemented
20#40842C214yesmaximal, complemented
21#39167C211yesmaximal, characteristic, complemented
22#38769C212yesmaximal, complemented
23#37249C211yesmaximal, characteristic, complemented
24C2×#556C2211yescharacteristic, complemented
25C2×#550C2212yes—
26C2×D4×Q8C2211yescharacteristic
27C2×#540C2212yes—
28C2×#538C2214yes—
29C2×#538C2212yescomplemented
30#2862C2211yescharacteristic, complemented
31#2861C2212yes—
32#2832C2214yes—
33#2824C2214yescomplemented
34#2824C2214yescomplemented
35#2823C2212yes—
36#2820C2212yescomplemented
37#2819C2212yes—
38#2819C2214yescomplemented
39#2818C2212yes—
40#2816C2212yescomplemented
41#2815C2214yes—
42#2813C2214yescomplemented
43#2812C2212yescomplemented
44#2806C2212yescomplemented
45#2804C2212yes—
46#2804C2211yescharacteristic
47#2804C2212yescomplemented
48#2795C2212yes—
49#2795C2212yescomplemented
50#2794C2212yescomplemented
51#2788C2214yescomplemented
52#2784C2214yescomplemented
53#2775C2214yescomplemented
54#2774C2214yescomplemented
55#2765C2214yescomplemented
56#2760C2214yes—
57#2759C2214yescomplemented
58#2759C2214yescomplemented
59#2755C2214yescomplemented
60#2751C2214yescomplemented
61#2748C2214yescomplemented
62#2746C2214yescomplemented
63#2740C2214yescomplemented
64#2733C2212yes—
65#2731C2214yescomplemented
66#2730C2214yes—
67#2725C2214yescomplemented
68#2723C2214yescomplemented
69#2723C2214yescomplemented
70#2722C2212yescomplemented
71#2716C2214yescomplemented
72#2714C2214yes—
73#2714C2214yescomplemented
74#2712C2214yescomplemented
75#2711C2214yes—
76#2710C2214yescomplemented
77#2710C2214yescomplemented
78#2709C2214yescomplemented
79#2706C2214yes—
80#2701C2214yes—
81#2699C2212yes—
82#2699C2212yescomplemented
83#2698C2214yescomplemented
84#2696C2214yes—
85#2696C2214yescomplemented
86#2693C2212yescomplemented
87#2691C2214yes—
88#2691C2214yescomplemented
89#2691C2214yescomplemented
90#2688C2214yes—
91#2688C2214yescomplemented
92#2687C2214yescomplemented
93#2686C2214yes—
94#2686C2214yes—
95#2686C2214yescomplemented
96#2686C2214yescomplemented
97#2682C2212yes—
98#2679C2211yescharacteristic
99#2676C2214yes—
100#2676C2214yes—
101#2676C2214yescomplemented
102#2676C2214yescomplemented
103#2674C2214yescomplemented
104#2673C2214yes—
105#2671C2214yes—
106#2671C2214yes—
107#2670C2214yes—
108#2669C2212yes—
109#2669C2214yes—
110#2669C2214yescomplemented
111#2665C2214yescomplemented
112#2664C2212yescomplemented
113#2653C2214yescomplemented
114#2653C2214yescomplemented
115#2653C2214yescomplemented
116#2643C2214yescomplemented
117#2640C2212yescomplemented
118#2639C2212yes—
119#2636C2212yescomplemented
120#2635C2214yes—
121#2635C2212yes—
122#2634C2212yescomplemented
123#2631C2214yes—
124#2607C2214yescomplemented
125#2603C2212yes—
126#2603C2214yes—
127#2602C2214yes—
128#2600C2214yescomplemented
129#2582C2211yescharacteristic, complemented
130#2576C2214yescomplemented
131#2572C2214yescomplemented
132#2567C2212yescomplemented
133#2560C2214yes—
134#2559C2214yescomplemented
135#2559C2214yescomplemented
136#2557C2214yes—
137#2557C2214yescomplemented
138#2555C2214yescomplemented
139#2555C2214yescomplemented
140#2553C2214yescomplemented
141#2548C2212yes—
142#2547C2211yescharacteristic
143#2544C2212yes—
144#2543C2212yes—
145#2543C2212yescomplemented
146#2542C2211yescharacteristic, complemented
147#2537C2212yes—
148#2537C2211yescharacteristic, complemented
149#2536C2212yes—
150#2527C2214yescomplemented
151#2527C2214yescomplemented
152#2518C2214yescomplemented
153#2515C2214yescomplemented
154#2493C2214yescomplemented
155#2491C2214yescomplemented
156#2483C2212yescomplemented
157#2473C2214yescomplemented
158#2472C2214yescomplemented
159#2471C2214yescomplemented
160#2469C2214yescomplemented
161#2468C2214yes—
162#2468C2214yescomplemented
163#2466C2214yes—
164#2466C2214yescomplemented
165#2465C2214yescomplemented
166#2460C2214yescomplemented
167#2459C2214yes—
168#2459C2214yes—
169#2459C2214yescomplemented
170#2459C2214yescomplemented
171#2458C2214yescomplemented
172#2456C2214yescomplemented
173#2450C2214yescomplemented
174#2450C2214yescomplemented
175#2447C2214yescomplemented
176#2436C2214yes—
177#2436C2212yescomplemented
178#2431C2214yescomplemented
179#2430C2214yes—
180#2428C2214yes—
181#2428C2214yes—
182#2428C2214yescomplemented
183#2424C2214yes—
184#2424C2214yes—
185#2424C2214yes—
186#2424C2214yes—
187#2424C2214yescomplemented
188#2420C2214yes—
189#2420C2214yescomplemented
190#2419C2214yes—
191#2416C2214yes—
192#2416C2214yescomplemented
193#2415C2214yescomplemented
194#2412C2214yes—
195#2412C2214yescomplemented
196#2409C2214yescomplemented
197#2406C2214yescomplemented
198#2404C2214yescomplemented
199#2398C2212yescomplemented
200#2388C2214yes—
201C2×#393C2212yescomplemented
202#2382C2212yescomplemented
203#2379C2212yes—
204#2368C2212yescomplemented
205#2364C2214yes—
206#2361C2214yescomplemented
207#2358C2214yescomplemented
208#2345C2214yescomplemented
209#2343C2212yescomplemented
210#2339C2214yescomplemented
211#2326C2212yes—
212#2325C2214yes—
213#2322C2214yescomplemented
214#2321C2212yes—
215#2319C2214yescomplemented
216C4×#127C2211yescharacteristic
217C4×#124C2212yescomplemented
218#2295C2211yescharacteristic, complemented
219C22×#41C2314yes—
220C23×Q8C2312yes—
221#556—44no—
222#550—48no—
223D4×Q8—44no—
224#540—48no—
225#538—416no—
226#538—48no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×#127C2311yescharacteristic
231C2×#127C2312yes—
232C2×#127C2314yes—
233C2×#126C2314yes—
234C2×#126C2312yes—
235C2×#126C2314yes—
236C2×#126C2312yes—
237C2×#126C2314yes—
238C2×#125C2312yes—
239C2×#125C2312yes—
240C2×#124C2312yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#124C2314yes—
248C2×#124C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×#121C2314yes—
260C2×#121C2312yes—
261C2×#121C2314yes—
262C2×#121C2314yes—
263C2×#121C2312yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2312yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#120C2312yes—
277C2×#120C2314yes—
278C2×#120C2314yes—
279C2×#120C2314yes—
280C2×#120C2314yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×#117C2312yes—
298C22×C4⋊C4C2314yes—
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2314yes—
302#401C2314yes—
303#401C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2312yes—
311#400C2312yes—
312#400C2314yes—
313#400C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2312yes—
317#399C2314yes—
318#398C2314yes—
319#398C2312yes—
320#398C2312yes—
321#398C2312yes—
322#398C2314yes—
323#398C2312yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#397C2312yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2312yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2312yes—
344#397C2312yes—
345#397C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#394C2314yes—
361#394C2312yes—
362#394C2314yes—
363#394C2312yes—
364#394C2314yes—
365#394C2314yes—
366#394C2312yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2312yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2312yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2312yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2312yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#392C2314yes—
413#392C2312yes—
414#392C2312yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2314yes—
445#390C2314yes—
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2312yes—
453#390C2314yes—
454#390C2312yes—
455#390C2314yes—
456#390C2312yes—
457#390C2314yes—
458#390C2314yes—
459#390C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2312yes—
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#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2312yes—
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#384C2311yescharacteristic
573#384C2312yes—
574#383C2312yes—
575#383C2314yes—
576#382C2312yes—
577#382C2314yes—
578#382C2312yes—
579#382C2312yes—
580#382C2312yes—
581#381C2312yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2314yes—
587#381C2314yes—
588#381C2314yes—
589#381C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#379C2312yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2312yes—
602C4×C4⋊C4C2311yescharacteristic
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614#376C2312yes—
615#376C2312yes—
616C2×#95C2314yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C43C2311yescharacteristic
620C25C2412yes—
621C2×#41—48no—
622C2×#41—48no—
623C2×#41—84no—
624C22×Q8—44no—
625C22×Q8—84no—
626C22×Q8C2412yes—
627C22×Q8C2411yescharacteristic
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2414yes—
631C22×Q8C2412yes—
632C22×D4C2414yes—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2414yes—
636C22×D4C2411yescharacteristic
637C22×D4C2412yes—
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2412yes—
648C22×D4C2414yes—
649C22×D4C2414yes—
650C22×D4C2411yescharacteristic
651C23×C4C2412yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2412yes—
658C23×C4C2414yes—
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2414yes—
662C4⋊Q8—44no—
663C4⋊Q8—42no—
664C4⋊Q8—42no—
665#127—24no—
666#127—44no—
667#127—48no—
668#126—48no—
669#126—44no—
670#126—44no—
671#126—48no—
672#126—48no—
673#125—44no—
674#125—44no—
675#124—28no—
676#124—44no—
677#124—44no—
678#124—44no—
679#124—48no—
680#124—48no—
681#124—84no—
682#124—84no—
683#124—84no—
684#123—216no—
685#123—48no—
686#123—48no—
687#123—48no—
688#123—84no—
689C22⋊Q8—28no—
690C22⋊Q8—48no—
691C22⋊Q8—48no—
692C22⋊Q8—44no—
693C22⋊Q8—84no—
694#121—216no—
695#121—44no—
696#121—44no—
697#121—48no—
698#121—44no—
699#121—48no—
700#121—48no—
701#121—48no—
702#121—48no—
703#121—48no—
704#121—48no—
705#121—48no—
706#121—48no—
707#121—84no—
708#121—84no—
709#121—84no—
710#121—84no—
711#120—28no—
712#120—48no—
713#120—48no—
714#120—48no—
715#120—84no—
716C4×Q8—24no—
717C4×Q8—44no—
718C4×Q8—44no—
719C4×D4—48no—
720C4×D4—44no—
721C4×D4—44no—
722C4×D4—44no—
723C4×D4—44no—
724C4×D4—42no—
725C4×D4—42no—
726C4×D4—48no—
727C4×D4—48no—
728C4×D4—48no—
729C4×D4—48no—
730C4×D4—84no—
731C4×D4—84no—
732#117—28no—
733C2×C4⋊C4—48no—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C22⋊C4—44no—
774C2×C22⋊C4—48no—
775C2×C22⋊C4—84no—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2411yescharacteristic
835C2×C42C2411yescharacteristic
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2411yescharacteristic
847#95C2414yes—
848#95C2412yes—
849#95C2414yes—
850#95C2412yes—
851#95C2414yes—
852#95C2412yes—
853#95C2414yes—
854#95C2414yes—
855#95C2412yes—
856#95C2414yes—
857#95C2412yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2412yes—
879#95C2412yes—
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—
895C24—24no—
896C24—42no—
897C24—44no—
898C24—44no—
899C24—42no—
900C24C2514yes—
901C24C2512yes—
902C24C2514yes—
903C24C2512yes—
904#41—832no—
905C2×Q8—22no—
906C2×Q8—24no—
907C2×Q8—24no—
908C2×Q8—24no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—44no—
914C2×Q8—44no—
915C2×Q8—44no—
916C2×Q8—44no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—816no—
922C2×D4—28no—
923C2×D4—28no—
924C2×D4—28no—
925C2×D4—28no—
926C2×D4—28no—
927C2×D4—22no—
928C2×D4—28no—
929C2×D4—24no—
930C2×D4—41no—
931C2×D4—44no—
932C2×D4—41no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—41no—
938C2×D4—42no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—42no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—41no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—42no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—42no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—42no—
972C2×D4—42no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4H(5,𝔽2)14yes—
976C22×C4—28no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—28no—
980C22×C4—28no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4C2512yes—
1007C22×C4C2514yes—
1008C22×C4C2514yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2514yes—
1012C22×C4C2512yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2514yes—
1016C22×C4C2512yes—
1017C22×C4C2514yes—
1018C22×C4C2514yes—
1019C22×C4C2512yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C22×C4C2512yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2512yes—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—42no—
1036C4⋊C4—41no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—42no—
1042C4⋊C4—41no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4H(5,𝔽2)14yes—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—24no—
1068C22⋊C4—28no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—42no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C42—24no—
1121C42—24no—
1122C42—22no—
1123C42—22no—
1124C42—24no—
1125C42—24no—
1126C42—24no—
1127C42—41no—
1128C42—44no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—42no—
1133C42—44no—
1134C42—44no—
1135C23—22no—
1136C23—24no—
1137C23—24no—
1138C23—22no—
1139C23—22no—
1140C23—24no—
1141C23—24no—
1142C23—24no—
1143C23—24no—
1144C23—22no—
1145C23—24no—
1146C23—24no—
1147C23—24no—
1148C23—24no—
1149C23—24no—
1150C23—24no—
1151C23—24no—
1152C23—24no—
1153C23—24no—
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—22no—
1158C23—84no—
1159C23—88no—
1160C23—88no—
1161C23—162no—
1162C23—162no—
1163C23C2×H(5,𝔽2)14yes—
1164C23C2611yescharacteristic
1165Q8—44no—
1166Q8—48no—
1167Q8—84no—
1168Q8—84no—
1169Q8—88no—
1170Q8—162no—
1171D4—44no—
1172D4—416no—
1173D4—88no—
1174D4—82no—
1175D4—84no—
1176D4—88no—
1177D4—88no—
1178D4—88no—
1179D4—88no—
1180D4—84no—
1181D4—84no—
1182D4—88no—
1183D4—88no—
1184D4—164no—
1185D4—162no—
1186D4—162no—
1187D4—164no—
1188D4—164no—
1189D4—164no—
1190C2×C4—21no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—88no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4—88no—
1241C2×C4—88no—
1242C2×C4—88no—
1243C2×C4—88no—
1244C2×C4—162no—
1245C2×C4—164no—
1246C2×C4—164no—
1247C2×C4—164no—
1248C2×C4C2×H(5,𝔽2)12yes—
1249C2×C4C2×H(5,𝔽2)14yes—
1250C2×C4C2×H(5,𝔽2)12yes—
1251C2×C4#58514yes—
1252C22—24no—
1253C22—28no—
1254C22—42no—
1255C22—44no—
1256C22—42no—
1257C22—44no—
1258C22—44no—
1259C22—42no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—42no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—42no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—168no—
1277C22C22×H(5,𝔽2)11yescharacteristic
1278C22C22×H(5,𝔽2)11yescharacteristic
1279C22C2×#58512yes—
1280C22H(7,𝔽2)12yes—
1281C222−1+611yescharacteristic
1282C4—24no—
1283C4—22no—
1284C4—22no—
1285C4—24no—
1286C4—41no—
1287C4—44no—
1288C4—44no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—44no—
1293C4—42no—
1294C4—42no—
1295C4—44no—
1296C4—42no—
1297C4—44no—
1298C4—44no—
1299C4—44no—
1300C4—44no—
1301C2—44no—
1302C2—84no—
1303C2—82no—
1304C2—84no—
1305C2#6287411yescharacteristic
1306C2#6289511yescharacteristic
1307C2#6289612yes—
1308C2#6302411yescharacteristic
1309C2#6305612yes—
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. #59419C2semidirect
2. #58382C2semidirect
3. #57203C2semidirect
4. #54853C2semidirect
5. #54811C2semidirect
6. #53666C2semidirect
7. #52325C2semidirect
8. #51016C2semidirect
9. #49690C2semidirect
10. #47678C2semidirect
11. #46812C2semidirect
12. #46378C2semidirect
13. #46162C2semidirect
14. #45378C2semidirect
15. #43972C2semidirect
16. #43895C2semidirect
17. #43012C2semidirect
18. #42410C2semidirect
19. #42158C2semidirect
20. #40842C2semidirect
21. #39167C2semidirect
22. #38769C2semidirect
23. #37249C2semidirect
24. C2×#556C22semidirect
29. C2×#538C22semidirect
30. #2862C22semidirect
33. #2824C22semidirect
34. #2824C22semidirect
36. #2820C22semidirect
38. #2819C22semidirect
40. #2816C22semidirect
42. #2813C22semidirect
43. #2812C22semidirect
44. #2806C22semidirect
47. #2804C22semidirect
49. #2795C22semidirect
50. #2794C22semidirect
51. #2788C22semidirect
52. #2784C22semidirect
53. #2775C22semidirect
54. #2774C22semidirect
55. #2765C22semidirect
57. #2759C22semidirect
58. #2759C22semidirect
59. #2755C22semidirect
60. #2751C22semidirect
61. #2748C22semidirect
62. #2746C22semidirect
63. #2740C22semidirect
65. #2731C22semidirect
67. #2725C22semidirect
68. #2723C22semidirect
69. #2723C22semidirect
70. #2722C22semidirect
71. #2716C22semidirect
73. #2714C22semidirect
74. #2712C22semidirect
76. #2710C22semidirect
77. #2710C22semidirect
78. #2709C22semidirect
82. #2699C22semidirect
83. #2698C22semidirect
85. #2696C22semidirect
86. #2693C22semidirect
88. #2691C22semidirect
89. #2691C22semidirect
91. #2688C22semidirect
92. #2687C22semidirect
95. #2686C22semidirect
96. #2686C22semidirect
101. #2676C22semidirect
102. #2676C22semidirect
103. #2674C22semidirect
110. #2669C22semidirect
111. #2665C22semidirect
112. #2664C22semidirect
113. #2653C22semidirect
114. #2653C22semidirect
115. #2653C22semidirect
116. #2643C22semidirect
117. #2640C22semidirect
119. #2636C22semidirect
122. #2634C22semidirect
124. #2607C22semidirect
128. #2600C22semidirect
129. #2582C22semidirect
130. #2576C22semidirect
131. #2572C22semidirect
132. #2567C22semidirect
134. #2559C22semidirect
135. #2559C22semidirect
137. #2557C22semidirect
138. #2555C22semidirect
139. #2555C22semidirect
140. #2553C22semidirect
145. #2543C22semidirect
146. #2542C22semidirect
148. #2537C22semidirect
150. #2527C22semidirect
151. #2527C22semidirect
152. #2518C22semidirect
153. #2515C22semidirect
154. #2493C22semidirect
155. #2491C22semidirect
156. #2483C22semidirect
157. #2473C22semidirect
158. #2472C22semidirect
159. #2471C22semidirect
160. #2469C22semidirect
162. #2468C22semidirect
164. #2466C22semidirect
165. #2465C22semidirect
166. #2460C22semidirect
169. #2459C22semidirect
170. #2459C22semidirect
171. #2458C22semidirect
172. #2456C22semidirect
173. #2450C22semidirect
174. #2450C22semidirect
175. #2447C22semidirect
177. #2436C22semidirect
178. #2431C22semidirect
182. #2428C22semidirect
187. #2424C22semidirect
189. #2420C22semidirect
192. #2416C22semidirect
193. #2415C22semidirect
195. #2412C22semidirect
196. #2409C22semidirect
197. #2406C22semidirect
198. #2404C22semidirect
199. #2398C22semidirect
201. C2×#393C22semidirect
202. #2382C22semidirect
204. #2368C22semidirect
206. #2361C22semidirect
207. #2358C22semidirect
208. #2345C22semidirect
209. #2343C22semidirect
210. #2339C22semidirect
213. #2322C22semidirect
215. #2319C22semidirect
217. C4×#124C22semidirect
218. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#594192
#583822
#572032
#548532
#548112
#536662
#523252
#510162
#496902
#476782
#468122
#463782
#461622
#453782
#439722
#438952
#430122
#424102
#421582
#408422
#391672
#387692
#372492