Finite Group Databasebeta

← #8755546

Subgroups — #8755546

Order 512.

4826 conjugacy classes of subgroups.

The subgroup lattice has 1335 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58800C214yesmaximal, complemented
2#58248C212yesmaximal, complemented
3#58003C214yesmaximal, complemented
4#57591C214yesmaximal, complemented
5#56384C212yesmaximal, complemented
6#54569C212yesmaximal, complemented
7#54375C214yesmaximal, complemented
8#54333C212yesmaximal, complemented
9#50103C214yesmaximal, complemented
10#49921C214yesmaximal, complemented
11#48088C212yesmaximal, complemented
12#47881C212yesmaximal, complemented
13#47666C214yesmaximal, complemented
14#47654C214yesmaximal, complemented
15#47031C211yesmaximal, characteristic, complemented
16#46507C212yesmaximal, complemented
17#46387C211yesmaximal, characteristic, complemented
18#45779C214yesmaximal, complemented
19#45761C214yesmaximal, complemented
20#45473C212yesmaximal, complemented
21#45455C212yesmaximal, complemented
22#35301C212yesmaximal, complemented
23#35097C211yesmaximal, characteristic, complemented
24C2×#560C2212yescomplemented
25C2×#532C2212yescomplemented
26C22×#123C2211yescharacteristic
27C22×#117C2211yescharacteristic, complemented
28#2854C2214yescomplemented
29#2853C2214yescomplemented
30#2847C2214yescomplemented
31#2842C2211yescharacteristic
32#2841C2212yescomplemented
33#2838C2214yescomplemented
34#2838C2214yescomplemented
35#2832C2214yescomplemented
36#2828C2214yescomplemented
37#2828C2214yescomplemented
38#2826C2212yes—
39#2826C2214yescomplemented
40#2815C2211yescharacteristic, complemented
41#2815C2212yescomplemented
42#2813C2214yes—
43#2807C2212yescomplemented
44#2804C2214yescomplemented
45#2804C2212yescomplemented
46#2783C2214yescomplemented
47#2782C2214yescomplemented
48#2781C2214yescomplemented
49#2780C2214yescomplemented
50#2779C2214yescomplemented
51#2777C2214yescomplemented
52#2775C2214yescomplemented
53#2764C2214yescomplemented
54#2760C2212yescomplemented
55#2758C2214yescomplemented
56#2758C2214yescomplemented
57#2757C2214yescomplemented
58#2756C2214yescomplemented
59#2752C2212yes—
60#2752C2212yes—
61#2752C2214yescomplemented
62#2752C2212yescomplemented
63#2751C2214yescomplemented
64#2750C2214yescomplemented
65#2750C2214yescomplemented
66#2750C2214yescomplemented
67#2749C2214yes—
68#2749C2214yescomplemented
69#2749C2214yescomplemented
70#2749C2214yescomplemented
71#2746C2214yescomplemented
72#2743C2214yescomplemented
73#2737C2214yescomplemented
74#2737C2214yescomplemented
75#2716C2214yescomplemented
76#2715C2214yescomplemented
77#2711C2214yescomplemented
78#2711C2214yescomplemented
79#2710C2214yescomplemented
80#2710C2214yescomplemented
81#2709C2212yescomplemented
82#2705C2214yes—
83#2703C2214yes—
84#2703C2214yescomplemented
85#2701C2214yescomplemented
86#2699C2214yescomplemented
87#2697C2212yescomplemented
88#2696C2214yescomplemented
89#2693C2214yescomplemented
90#2693C2214yescomplemented
91#2690C2214yescomplemented
92#2688C2214yes—
93#2688C2214yes—
94#2688C2214yes—
95#2688C2214yescomplemented
96#2688C2214yescomplemented
97#2684C2214yes—
98#2684C2214yescomplemented
99#2682C2214yescomplemented
100#2678C2214yes—
101#2678C2214yes—
102#2678C2214yescomplemented
103#2676C2214yescomplemented
104#2675C2212yes—
105#2674C2214yescomplemented
106#2673C2214yes—
107#2673C2214yescomplemented
108#2673C2214yescomplemented
109#2672C2214yescomplemented
110#2671C2214yescomplemented
111#2670C2212yes—
112#2670C2214yescomplemented
113#2669C2214yescomplemented
114#2669C2212yescomplemented
115#2668C2212yes—
116#2668C2214yescomplemented
117#2665C2212yescomplemented
118#2652C2214yescomplemented
119#2643C2214yescomplemented
120#2631C2214yes—
121#2630C2214yescomplemented
122#2628C2212yescomplemented
123#2628C2212yescomplemented
124#2623C2214yescomplemented
125#2622C2214yescomplemented
126#2619C2212yes—
127#2619C2212yescomplemented
128#2615C2212yescomplemented
129#2611C2214yescomplemented
130#2610C2214yescomplemented
131#2610C2214yescomplemented
132#2610C2214yescomplemented
133#2607C2211yescharacteristic, complemented
134#2598C2212yes—
135#2598C2212yescomplemented
136#2598C2214yescomplemented
137#2598C2212yescomplemented
138#2598C2212yescomplemented
139#2597C2214yescomplemented
140#2593C2214yescomplemented
141#2591C2212yescomplemented
142#2591C2212yescomplemented
143#2573C2214yescomplemented
144#2572C2214yescomplemented
145#2564C2214yescomplemented
146#2558C2214yescomplemented
147#2557C2214yescomplemented
148#2543C2214yescomplemented
149#2539C2212yes—
150#2539C2212yes—
151#2539C2212yescomplemented
152#2533C2214yescomplemented
153#2531C2214yescomplemented
154#2510C2214yescomplemented
155#2510C2214yescomplemented
156#2498C2214yescomplemented
157#2498C2214yescomplemented
158#2484C2212yescomplemented
159#2484C2212yescomplemented
160#2482C2212yes—
161#2482C2212yes—
162#2482C2214yescomplemented
163#2481C2214yescomplemented
164#2476C2214yescomplemented
165#2475C2214yescomplemented
166#2474C2214yescomplemented
167#2474C2214yescomplemented
168#2471C2214yes—
169#2471C2214yes—
170#2470C2214yescomplemented
171#2467C2214yescomplemented
172#2466C2214yescomplemented
173#2456C2214yescomplemented
174#2456C2214yescomplemented
175#2456C2214yescomplemented
176#2455C2212yescomplemented
177#2454C2214yescomplemented
178#2444C2214yescomplemented
179#2433C2212yes—
180#2431C2214yes—
181#2431C2214yescomplemented
182#2430C2214yescomplemented
183#2430C2214yescomplemented
184#2425C2214yescomplemented
185#2424C2214yescomplemented
186#2424C2214yescomplemented
187#2424C2214yescomplemented
188#2419C2214yescomplemented
189#2418C2214yes—
190#2418C2214yescomplemented
191#2416C2214yescomplemented
192#2414C2214yescomplemented
193#2410C2214yes—
194#2410C2214yes—
195#2407C2214yescomplemented
196#2406C2214yescomplemented
197#2404C2212yescomplemented
198#2404C2214yescomplemented
199#2404C2214yescomplemented
200#2403C2211yescharacteristic
201#2403C2212yes—
202#2380C2212yescomplemented
203#2377C2212yescomplemented
204#2377C2214yescomplemented
205#2376C2212yescomplemented
206#2358C2212yescomplemented
207#2339C2212yescomplemented
208#2333C2212yescomplemented
209#2324C2214yescomplemented
210#2324C2214yescomplemented
211#2324C2214yescomplemented
212#2315C2211yescharacteristic, complemented
213#2315C2211yescharacteristic, complemented
214#2309C2212yes—
215#2308C2211yescharacteristic
216#2308C2211yescharacteristic
217#2283C2212yescomplemented
218C2×#381C2211yescharacteristic, complemented
219C22×#41C2312yes—
220C22×#41C2314yes—
221C23×D4C2311yescharacteristic
222C23×D4C2312yes—
223C24×C4C2311yescharacteristic
224#560—48no—
225#532—48no—
226C2×C4⋊Q8C2312yes—
227C2×#127C2312yes—
228C2×#127C2312yes—
229C2×#127C2312yes—
230C2×#126C2314yes—
231C2×#125C2314yes—
232C2×#124C2314yes—
233C2×#124C2314yes—
234C2×#124C2314yes—
235C2×#123—44no—
236C2×#123C2312yes—
237C2×#123C2312yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2314yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2314yes—
258C2×#121C2314yes—
259C2×#121C2314yes—
260C2×#121C2314yes—
261C2×#121C2314yes—
262C2×#120C2312yes—
263C2×#120C2312yes—
264C2×#120C2314yes—
265C2×#120C2314yes—
266C2×#120C2314yes—
267C2×#120C2314yes—
268C2×#120C2314yes—
269C2×#120C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×#117—44no—
277C2×#117C2312yes—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2314yes—
282C2×#117C2314yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C22⋊C4C2311yescharacteristic
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2311yescharacteristic
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2311yescharacteristic
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2314yes—
292C22×C42C2312yes—
293#401C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2312yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2312yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2312yes—
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#399C2312yes—
313#399C2312yes—
314#399C2314yes—
315#399C2314yes—
316#399C2312yes—
317#399C2312yes—
318#399C2314yes—
319#399C2312yes—
320#399C2312yes—
321#399C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2312yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2312yes—
377#394C2314yes—
378#394C2312yes—
379#394C2312yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2312yes—
397#393C2312yes—
398#393C2314yes—
399#392C2312yes—
400#392C2314yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2312yes—
408#392C2312yes—
409#392C2312yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2312yes—
418#392C2312yes—
419#392C2312yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
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#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
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#386C2314yes—
503#386C2314yes—
504#386C2312yes—
505#386C2312yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2312yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2312yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#385C2312yes—
550#385C2314yes—
551#385C2312yes—
552#385C2314yes—
553#385C2312yes—
554#385C2314yes—
555#385C2314yes—
556#385C2312yes—
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#383C2314yes—
573#383C2314yes—
574#383C2312yes—
575#383C2312yes—
576#383C2314yes—
577#382C2312yes—
578#382C2312yes—
579#381C2312yes—
580#381C2311yescharacteristic
581#381C2311yescharacteristic
582#381C2314yes—
583#381C2314yes—
584#381C2312yes—
585#381C2312yes—
586#381C2312yes—
587#381C2314yes—
588#381C2314yes—
589#381C2312yes—
590#381C2312yes—
591#380C2314yes—
592#380C2314yes—
593#380C2312yes—
594#380C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#379C2311yescharacteristic
602#379C2311yescharacteristic
603#379C2312yes—
604#379C2312yes—
605#379C2314yes—
606#379C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2312yes—
615#376C2314yes—
616C2×#95C2314yes—
617C2×#95C2314yes—
618C25C2411yescharacteristic
619C25C2411yescharacteristic
620C25C2412yes—
621C2×#41—48no—
622C2×#41—44no—
623C2×#41—84no—
624C2×#41—84no—
625C2×#41—84no—
626C22×Q8C2414yes—
627C22×Q8C2412yes—
628C22×D4—42no—
629C22×D4—42no—
630C22×D4—44no—
631C22×D4—42no—
632C22×D4—84no—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2414yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2412yes—
653C23×C4—24no—
654C23×C4—42no—
655C23×C4—42no—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2411yescharacteristic
662C23×C4C2411yescharacteristic
663C23×C4C2412yes—
664C23×C4C2414yes—
665C23×C4C2412yes—
666C23×C4C2414yes—
667C23×C4C2412yes—
668C23×C4C2414yes—
669C23×C4C2414yes—
670C23×C4C2414yes—
671C23×C4C2411yescharacteristic
672C4⋊Q8—44no—
673#127—44no—
674#127—44no—
675#127—44no—
676#126—48no—
677#125—84no—
678#124—48no—
679#124—84no—
680#124—84no—
681#123—28no—
682#123—48no—
683#123—48no—
684#123—44no—
685#123—84no—
686#123—84no—
687#123—84no—
688#123—84no—
689#123—84no—
690C22⋊Q8—84no—
691#121—216no—
692#121—48no—
693#121—48no—
694#121—48no—
695#121—48no—
696#121—48no—
697#121—44no—
698#121—44no—
699#121—44no—
700#121—44no—
701#121—84no—
702#121—84no—
703#121—84no—
704#121—84no—
705#121—84no—
706#121—84no—
707#120—48no—
708#120—44no—
709#120—44no—
710#120—84no—
711#120—84no—
712#120—84no—
713#120—84no—
714#120—84no—
715C4×D4—44no—
716C4×D4—44no—
717C4×D4—48no—
718C4×D4—84no—
719C4×D4—84no—
720C4×D4—84no—
721#117—44no—
722#117—44no—
723#117—44no—
724#117—44no—
725#117—84no—
726#117—84no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4—44no—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C22⋊C4—44no—
761C2×C22⋊C4—42no—
762C2×C22⋊C4—42no—
763C2×C22⋊C4—42no—
764C2×C22⋊C4—42no—
765C2×C22⋊C4—42no—
766C2×C22⋊C4—84no—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2411yescharacteristic
775C2×C22⋊C4C2411yescharacteristic
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
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⋊C4C2412yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C42—28no—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843#95C2412yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2412yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2412yes—
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#95C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891C24—22no—
892C24—22no—
893C24—22no—
894C24—22no—
895C24—41no—
896C24—44no—
897C24—42no—
898C24—44no—
899C24—44no—
900C24—44no—
901C24—41no—
902C24—42no—
903C24—42no—
904C24C2512yes—
905C24C2514yes—
906C24C2514yes—
907C24C2511yescharacteristic
908C24C2511yescharacteristic
909C24C2511yescharacteristic
910#41—832no—
911#41—816no—
912C2×Q8—44no—
913C2×Q8—44no—
914C2×Q8—44no—
915C2×Q8—44no—
916C2×Q8—42no—
917C2×D4—28no—
918C2×D4—24no—
919C2×D4—28no—
920C2×D4—28no—
921C2×D4—24no—
922C2×D4—28no—
923C2×D4—28no—
924C2×D4—28no—
925C2×D4—28no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—44no—
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—42no—
953C2×D4—44no—
954C2×D4—42no—
955C2×D4—42no—
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—44no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—816no—
974C2×D4—88no—
975C22×C4—24no—
976C22×C4—22no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—22no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—44no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—41no—
990C22×C4—41no—
991C22×C4—42no—
992C22×C4—44no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—41no—
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×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—41no—
1010C22×C4—44no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—416no—
1017C22×C4H(5,𝔽2)14yes—
1018C22×C4C2514yes—
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2512yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—42no—
1072C22⋊C4—41no—
1073C22⋊C4—42no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—42no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—42no—
1080C22⋊C4—41no—
1081C22⋊C4—42no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—42no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—42no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C42—24no—
1131C42—24no—
1132C42—24no—
1133C42—24no—
1134C42—44no—
1135C42—44no—
1136C42—44no—
1137C42—44no—
1138C42—44no—
1139C42—42no—
1140C42—42no—
1141C23—28no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—24no—
1149C23—24no—
1150C23—24no—
1151C23—22no—
1152C23—24no—
1153C23—24no—
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—24no—
1158C23—22no—
1159C23—22no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—24no—
1168C23—24no—
1169C23—24no—
1170C23—84no—
1171C23—84no—
1172C23—84no—
1173C23—84no—
1174C23—82no—
1175C23—84no—
1176C23—84no—
1177C23—88no—
1178C23—162no—
1179C23—162no—
1180C23—162no—
1181C23—164no—
1182C23C2×H(5,𝔽2)12yes—
1183C23#58512yes—
1184C23#58512yes—
1185C23C2611yescharacteristic
1186Q8—84no—
1187Q8—88no—
1188D4—48no—
1189D4—88no—
1190D4—88no—
1191D4—88no—
1192D4—88no—
1193D4—84no—
1194D4—84no—
1195D4—88no—
1196D4—88no—
1197D4—88no—
1198D4—84no—
1199D4—84no—
1200D4—88no—
1201D4—88no—
1202D4—162no—
1203D4—164no—
1204D4—164no—
1205D4—162no—
1206D4—164no—
1207D4—164no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
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—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—44no—
1253C2×C4—48no—
1254C2×C4—48no—
1255C2×C4—44no—
1256C2×C4—48no—
1257C2×C4—48no—
1258C2×C4—84no—
1259C2×C4—82no—
1260C2×C4—84no—
1261C2×C4—88no—
1262C2×C4—84no—
1263C2×C4—88no—
1264C2×C4—88no—
1265C2×C4—88no—
1266C2×C4—162no—
1267C2×C4—164no—
1268C2×C4C2×H(5,𝔽2)14yes—
1269C22—24no—
1270C22—24no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—24no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—42no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—44no—
1291C22—44no—
1292C22—42no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—88no—
1301C22—164no—
1302C22—168no—
1303C22C22×H(5,𝔽2)11yescharacteristic
1304C22C2×#58511yescharacteristic
1305C22C2×#58511yescharacteristic
1306C22H(7,𝔽2)14yes—
1307C4—24no—
1308C4—44no—
1309C4—42no—
1310C4—44no—
1311C4—42no—
1312C4—44no—
1313C4—44no—
1314C4—44no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—44no—
1321C4—44no—
1322C4—42no—
1323C4—44no—
1324C2—42no—
1325C2—42no—
1326C2—42no—
1327C2—84no—
1328C2—84no—
1329C2—82no—
1330C2#6282011yescharacteristic
1331C2#6287412yes—
1332C2#6304212yes—
1333C2#6304212yes—
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. #58800C2semidirect
2. #58248C2semidirect
3. #58003C2semidirect
4. #57591C2semidirect
5. #56384C2semidirect
6. #54569C2semidirect
7. #54375C2semidirect
8. #54333C2semidirect
9. #50103C2semidirect
10. #49921C2semidirect
11. #48088C2semidirect
12. #47881C2semidirect
13. #47666C2semidirect
14. #47654C2semidirect
15. #47031C2semidirect
16. #46507C2semidirect
17. #46387C2semidirect
18. #45779C2semidirect
19. #45761C2semidirect
20. #45473C2semidirect
21. #45455C2semidirect
22. #35301C2semidirect
23. #35097C2semidirect
24. C2×#560C22semidirect
25. C2×#532C22semidirect
27. C22×#117C22semidirect
28. #2854C22semidirect
29. #2853C22semidirect
30. #2847C22semidirect
32. #2841C22semidirect
33. #2838C22semidirect
34. #2838C22semidirect
35. #2832C22semidirect
36. #2828C22semidirect
37. #2828C22semidirect
39. #2826C22semidirect
40. #2815C22semidirect
41. #2815C22semidirect
43. #2807C22semidirect
44. #2804C22semidirect
45. #2804C22semidirect
46. #2783C22semidirect
47. #2782C22semidirect
48. #2781C22semidirect
49. #2780C22semidirect
50. #2779C22semidirect
51. #2777C22semidirect
52. #2775C22semidirect
53. #2764C22semidirect
54. #2760C22semidirect
55. #2758C22semidirect
56. #2758C22semidirect
57. #2757C22semidirect
58. #2756C22semidirect
61. #2752C22semidirect
62. #2752C22semidirect
63. #2751C22semidirect
64. #2750C22semidirect
65. #2750C22semidirect
66. #2750C22semidirect
68. #2749C22semidirect
69. #2749C22semidirect
70. #2749C22semidirect
71. #2746C22semidirect
72. #2743C22semidirect
73. #2737C22semidirect
74. #2737C22semidirect
75. #2716C22semidirect
76. #2715C22semidirect
77. #2711C22semidirect
78. #2711C22semidirect
79. #2710C22semidirect
80. #2710C22semidirect
81. #2709C22semidirect
84. #2703C22semidirect
85. #2701C22semidirect
86. #2699C22semidirect
87. #2697C22semidirect
88. #2696C22semidirect
89. #2693C22semidirect
90. #2693C22semidirect
91. #2690C22semidirect
95. #2688C22semidirect
96. #2688C22semidirect
98. #2684C22semidirect
99. #2682C22semidirect
102. #2678C22semidirect
103. #2676C22semidirect
105. #2674C22semidirect
107. #2673C22semidirect
108. #2673C22semidirect
109. #2672C22semidirect
110. #2671C22semidirect
112. #2670C22semidirect
113. #2669C22semidirect
114. #2669C22semidirect
116. #2668C22semidirect
117. #2665C22semidirect
118. #2652C22semidirect
119. #2643C22semidirect
121. #2630C22semidirect
122. #2628C22semidirect
123. #2628C22semidirect
124. #2623C22semidirect
125. #2622C22semidirect
127. #2619C22semidirect
128. #2615C22semidirect
129. #2611C22semidirect
130. #2610C22semidirect
131. #2610C22semidirect
132. #2610C22semidirect
133. #2607C22semidirect
135. #2598C22semidirect
136. #2598C22semidirect
137. #2598C22semidirect
138. #2598C22semidirect
139. #2597C22semidirect
140. #2593C22semidirect
141. #2591C22semidirect
142. #2591C22semidirect
143. #2573C22semidirect
144. #2572C22semidirect
145. #2564C22semidirect
146. #2558C22semidirect
147. #2557C22semidirect
148. #2543C22semidirect
151. #2539C22semidirect
152. #2533C22semidirect
153. #2531C22semidirect
154. #2510C22semidirect
155. #2510C22semidirect
156. #2498C22semidirect
157. #2498C22semidirect
158. #2484C22semidirect
159. #2484C22semidirect
162. #2482C22semidirect
163. #2481C22semidirect
164. #2476C22semidirect
165. #2475C22semidirect
166. #2474C22semidirect
167. #2474C22semidirect
170. #2470C22semidirect
171. #2467C22semidirect
172. #2466C22semidirect
173. #2456C22semidirect
174. #2456C22semidirect
175. #2456C22semidirect
176. #2455C22semidirect
177. #2454C22semidirect
178. #2444C22semidirect
181. #2431C22semidirect
182. #2430C22semidirect
183. #2430C22semidirect
184. #2425C22semidirect
185. #2424C22semidirect
186. #2424C22semidirect
187. #2424C22semidirect
188. #2419C22semidirect
190. #2418C22semidirect
191. #2416C22semidirect
192. #2414C22semidirect
195. #2407C22semidirect
196. #2406C22semidirect
197. #2404C22semidirect
198. #2404C22semidirect
199. #2404C22semidirect
202. #2380C22semidirect
203. #2377C22semidirect
204. #2377C22semidirect
205. #2376C22semidirect
206. #2358C22semidirect
207. #2339C22semidirect
208. #2333C22semidirect
209. #2324C22semidirect
210. #2324C22semidirect
211. #2324C22semidirect
212. #2315C22semidirect
213. #2315C22semidirect
217. #2283C22semidirect
218. C2×#381C22semidirect

Maximal subgroups

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

subgroupindex
#588002
#582482
#580032
#575912
#563842
#545692
#543752
#543332
#501032
#499212
#480882
#478812
#476662
#476542
#470312
#465072
#463872
#457792
#457612
#454732
#454552
#353012
#350972