Finite Group Databasebeta

← #9230966

Subgroups — #9230966

Order 512.

5313 conjugacy classes of subgroups.

The subgroup lattice has 1365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59822C211yesmaximal, characteristic, complemented
2#56025C214yesmaximal, complemented
3#53528C212yesmaximal, complemented
4#53190C212yesmaximal, complemented
5#51776C214yesmaximal, complemented
6#50718C212yesmaximal, complemented
7#50652C214yesmaximal, complemented
8#49984C214yesmaximal, complemented
9#47850C214yesmaximal, complemented
10#47678C212yesmaximal, complemented
11#47622C214yesmaximal, complemented
12#45312C212yesmaximal, complemented
13#44693C214yesmaximal, complemented
14#44270C214yesmaximal, complemented
15#44129C214yesmaximal, complemented
16#43032C214yesmaximal, complemented
17#39383C212yesmaximal, complemented
18#38820C212yesmaximal, complemented
19#38466C212yesmaximal, complemented
20#37267C211yesmaximal, characteristic, complemented
21#37250C212yesmaximal, complemented
22#36509C211yesmaximal, characteristic, complemented
23#36362C212yesmaximal, complemented
24C2×#560C2214yes—
25C2×#555C2212yescomplemented
26C2×#553C2212yes—
27C2×#546C2212yes—
28C2×#538C2214yescomplemented
29C2×#538C2214yescomplemented
30#2864C2211yescharacteristic, complemented
31#2861C2212yescomplemented
32#2856C2212yes—
33#2855C2212yescomplemented
34#2850C2212yescomplemented
35#2830C2212yescomplemented
36#2829C2214yescomplemented
37#2823C2212yescomplemented
38#2811C2211yescharacteristic, complemented
39#2808C2212yescomplemented
40#2804C2212yescomplemented
41#2790C2214yescomplemented
42#2790C2214yescomplemented
43#2761C2214yescomplemented
44#2756C2214yescomplemented
45#2753C2214yescomplemented
46#2753C2214yescomplemented
47#2751C2214yescomplemented
48#2749C2214yescomplemented
49#2733C2211yescharacteristic
50#2733C2211yescharacteristic
51#2733C2212yescomplemented
52#2733C2211yescharacteristic, complemented
53#2732C2212yescomplemented
54#2731C2212yescomplemented
55#2730C2214yescomplemented
56#2722C2214yescomplemented
57#2720C2214yescomplemented
58#2715C2214yescomplemented
59#2714C2214yes—
60#2714C2214yescomplemented
61#2714C2214yescomplemented
62#2710C2214yescomplemented
63#2710C2214yescomplemented
64#2709C2214yescomplemented
65#2708C2214yescomplemented
66#2707C2214yescomplemented
67#2706C2214yescomplemented
68#2705C2214yescomplemented
69#2701C2214yescomplemented
70#2701C2214yescomplemented
71#2699C2214yes—
72#2699C2212yescomplemented
73#2699C2212yescomplemented
74#2695C2214yescomplemented
75#2691C2214yes—
76#2691C2214yescomplemented
77#2691C2214yescomplemented
78#2688C2214yescomplemented
79#2688C2214yescomplemented
80#2687C2214yescomplemented
81#2686C2214yescomplemented
82#2682C2212yes—
83#2682C2212yescomplemented
84#2682C2214yescomplemented
85#2681C2214yescomplemented
86#2680C2212yescomplemented
87#2679C2212yes—
88#2679C2212yes—
89#2678C2214yescomplemented
90#2676C2214yescomplemented
91#2676C2214yescomplemented
92#2676C2214yescomplemented
93#2676C2214yescomplemented
94#2675C2214yescomplemented
95#2673C2214yescomplemented
96#2673C2214yescomplemented
97#2673C2214yescomplemented
98#2671C2214yescomplemented
99#2670C2214yescomplemented
100#2669C2214yes—
101#2669C2214yescomplemented
102#2669C2214yescomplemented
103#2668C2214yes—
104#2662C2214yescomplemented
105#2657C2212yes—
106#2648C2214yescomplemented
107#2632C2212yescomplemented
108#2630C2214yescomplemented
109#2617C2214yescomplemented
110#2617C2214yescomplemented
111#2606C2212yescomplemented
112#2603C2214yescomplemented
113#2603C2214yescomplemented
114#2601C2214yescomplemented
115#2601C2214yescomplemented
116#2595C2214yescomplemented
117#2590C2214yescomplemented
118#2574C2214yescomplemented
119#2566C2212yescomplemented
120#2560C2214yescomplemented
121#2559C2214yescomplemented
122#2559C2214yescomplemented
123#2557C2214yescomplemented
124#2555C2212yes—
125#2555C2214yescomplemented
126#2554C2214yescomplemented
127#2554C2214yescomplemented
128#2554C2214yescomplemented
129#2548C2212yescomplemented
130#2548C2214yescomplemented
131#2548C2212yescomplemented
132#2544C2212yescomplemented
133#2543C2214yescomplemented
134#2543C2214yescomplemented
135#2541C2212yes—
136#2541C2214yes—
137#2541C2214yescomplemented
138#2537C2212yes—
139#2537C2212yescomplemented
140#2536C2211yescharacteristic
141#2536C2211yescharacteristic
142#2532C2214yescomplemented
143#2521C2214yescomplemented
144#2515C2214yescomplemented
145#2512C2214yescomplemented
146#2512C2214yescomplemented
147#2502C2212yescomplemented
148#2500C2212yes—
149#2496C2212yescomplemented
150#2481C2214yescomplemented
151#2478C2214yescomplemented
152#2476C2214yescomplemented
153#2474C2214yescomplemented
154#2472C2214yescomplemented
155#2468C2214yescomplemented
156#2467C2214yescomplemented
157#2466C2214yes—
158#2464C2214yes—
159#2464C2214yes—
160#2461C2214yescomplemented
161#2459C2214yescomplemented
162#2457C2214yescomplemented
163#2456C2214yescomplemented
164#2456C2214yescomplemented
165#2455C2214yescomplemented
166#2450C2214yescomplemented
167#2445C2214yescomplemented
168#2445C2214yescomplemented
169#2433C2212yescomplemented
170#2433C2214yescomplemented
171#2431C2212yes—
172#2429C2212yescomplemented
173#2428C2214yescomplemented
174#2427C2214yescomplemented
175#2425C2214yescomplemented
176#2424C2214yes—
177#2424C2214yes—
178#2424C2214yes—
179#2424C2214yes—
180#2424C2214yescomplemented
181#2424C2214yescomplemented
182#2424C2214yescomplemented
183#2419C2214yescomplemented
184#2414C2214yescomplemented
185#2414C2214yescomplemented
186#2412C2214yescomplemented
187#2412C2214yescomplemented
188#2411C2214yescomplemented
189#2410C2214yescomplemented
190#2407C2214yes—
191#2404C2214yes—
192#2402C2212yescomplemented
193#2392C2214yescomplemented
194#2380C2212yescomplemented
195#2373C2214yescomplemented
196#2367C2214yescomplemented
197#2361C2214yescomplemented
198#2359C2214yescomplemented
199#2358C2214yescomplemented
200#2358C2214yescomplemented
201#2357C2212yescomplemented
202#2356C2211yescharacteristic, complemented
203#2354C2214yescomplemented
204#2351C2211yescharacteristic, complemented
205#2342C2214yescomplemented
206#2337C2212yescomplemented
207#2333C2214yescomplemented
208#2332C2214yescomplemented
209#2328C2212yescomplemented
210#2326C2212yescomplemented
211#2325C2214yescomplemented
212#2324C2214yes—
213C4×C4⋊Q8C2211yescharacteristic, complemented
214C4×#127C2212yescomplemented
215C4×C22⋊Q8C2212yescomplemented
216#2297C2212yes—
217C2×#390C2212yescomplemented
218C42×D4C2211yescharacteristic
219C22×#41C2312yes—
220C23×D4C2312yes—
221#560—416no—
222#555—48no—
223#553—48no—
224#546—48no—
225#538—416no—
226#538—416no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×#127C2312yes—
229C2×#127C2312yes—
230C2×#127C2312yes—
231C2×#127C2314yes—
232C2×#127C2312yes—
233C2×#127C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#125C2312yes—
241C2×#124C2312yes—
242C2×#124C2314yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#124C2312yes—
248C2×#124C2312yes—
249C2×#124C2312yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2312yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#120C2314yes—
286C2×#120C2314yes—
287C2×#120C2314yes—
288C2×#120C2314yes—
289C2×#120C2314yes—
290C2×#120C2314yes—
291C2×#120C2314yes—
292C2×#120C2314yes—
293C2×#120C2314yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2314yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C2×#117C2314yes—
313C22×C4⋊C4C2312yes—
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2314yes—
316C22×C22⋊C4C2314yes—
317C22×C22⋊C4C2314yes—
318C22×C42C2312yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#399C2314yes—
324#399C2314yes—
325#398C2314yes—
326#398C2312yes—
327#398C2314yes—
328#398C2312yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#395C2314yes—
361#395C2312yes—
362#395C2312yes—
363#394C2314yes—
364#394C2314yes—
365#394C2312yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2312yes—
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#394C2312yes—
394#394C2312yes—
395#394C2312yes—
396#394C2314yes—
397#394C2314yes—
398#394C2312yes—
399#394C2314yes—
400#394C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
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#391C2314yes—
428#391C2311yescharacteristic
429#391C2311yescharacteristic
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#390C2314yes—
437#390C2312yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2314yes—
444#390C2312yes—
445#390C2314yes—
446#390C2314yes—
447#390C2312yes—
448#390C2314yes—
449#390C2312yes—
450#390C2312yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2312yes—
462#390C2314yes—
463#390C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
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#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#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#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#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#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#384C2312yes—
573#384C2311yescharacteristic
574#384C2312yes—
575#384C2312yes—
576#383C2312yes—
577#383C2312yes—
578#382C2312yes—
579#382C2312yes—
580#382C2311yescharacteristic
581#382C2311yescharacteristic
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2312yes—
591#380C2314yes—
592#380C2314yes—
593#380C2312yes—
594#379C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2311yescharacteristic
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616#376C2312yes—
617#376C2312yes—
618C2×#95C2314yes—
619C43C2311yescharacteristic
620C25C2414yes—
621C2×#41—44no—
622C2×#41—44no—
623C2×#41—82no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×Q8C2411yescharacteristic
628C22×D4—44no—
629C22×D4—44no—
630C22×D4—82no—
631C22×D4C2411yescharacteristic
632C22×D4C2414yes—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2412yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2412yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2412yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2414yes—
654C22×D4C2412yes—
655C22×D4C2412yes—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2414yes—
662C23×C4C2414yes—
663C23×C4C2414yes—
664C23×C4C2414yes—
665C23×C4C2414yes—
666C23×C4C2414yes—
667C4⋊Q8—24no—
668#127—44no—
669#127—44no—
670#127—44no—
671#127—48no—
672#127—82no—
673#127—84no—
674#126—216no—
675#126—48no—
676#126—48no—
677#126—48no—
678#126—48no—
679#126—48no—
680#125—44no—
681#124—28no—
682#124—216no—
683#124—44no—
684#124—48no—
685#124—44no—
686#124—48no—
687#124—44no—
688#124—44no—
689#124—82no—
690#123—216no—
691#123—48no—
692#123—48no—
693#123—48no—
694#123—48no—
695#123—48no—
696#123—48no—
697#123—48no—
698C22⋊Q8—28no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701C22⋊Q8—44no—
702C22⋊Q8—82no—
703#121—216no—
704#121—48no—
705#121—48no—
706#121—44no—
707#121—48no—
708#121—48no—
709#121—48no—
710#121—48no—
711#121—48no—
712#121—48no—
713#121—48no—
714#121—48no—
715#121—48no—
716#121—48no—
717#121—48no—
718#121—48no—
719#121—48no—
720#121—48no—
721#121—48no—
722#121—44no—
723#121—44no—
724#121—84no—
725#120—216no—
726#120—48no—
727#120—48no—
728#120—48no—
729#120—48no—
730#120—48no—
731#120—48no—
732#120—48no—
733#120—84no—
734C4×Q8—42no—
735C4×Q8—42no—
736C4×Q8—82no—
737C4×D4—28no—
738C4×D4—48no—
739C4×D4—42no—
740C4×D4—44no—
741C4×D4—48no—
742C4×D4—48no—
743C4×D4—48no—
744C4×D4—48no—
745C4×D4—44no—
746C4×D4—44no—
747C4×D4—48no—
748C4×D4—48no—
749C4×D4—84no—
750#117—48no—
751#117—48no—
752#117—44no—
753C2×C4⋊C4—44no—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C22⋊C4—48no—
791C2×C22⋊C4—48no—
792C2×C22⋊C4—48no—
793C2×C22⋊C4—48no—
794C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C42—82no—
853C2×C42C2414yes—
854C2×C42C2411yescharacteristic
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2411yescharacteristic
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2414yes—
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2411yescharacteristic
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2411yescharacteristic
877#95C2412yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2411yescharacteristic
883#95C2412yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2414yes—
906#95C2412yes—
907#95C2414yes—
908#95C2412yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2412yes—
913C24—28no—
914C24—44no—
915C24—44no—
916C24—44no—
917C24—44no—
918C24—44no—
919C24—44no—
920C24C2514yes—
921C24C2514yes—
922C24C2514yes—
923C24C2512yes—
924#41—816no—
925C2×Q8—22no—
926C2×Q8—24no—
927C2×Q8—41no—
928C2×Q8—41no—
929C2×Q8—41no—
930C2×Q8—42no—
931C2×Q8—41no—
932C2×Q8—42no—
933C2×Q8—44no—
934C2×Q8—42no—
935C2×Q8H(5,𝔽2)14yes—
936C2×D4—24no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—28no—
940C2×D4—28no—
941C2×D4—28no—
942C2×D4—28no—
943C2×D4—24no—
944C2×D4—28no—
945C2×D4—28no—
946C2×D4—24no—
947C2×D4—28no—
948C2×D4—24no—
949C2×D4—24no—
950C2×D4—42no—
951C2×D4—41no—
952C2×D4—42no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—42no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—42no—
961C2×D4—44no—
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—42no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—42no—
976C2×D4—44no—
977C2×D4—42no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—42no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—42no—
993C2×D4—42no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—42no—
1000C2×D4—44no—
1001C2×D4—42no—
1002C2×D4—42no—
1003C2×D4—42no—
1004C2×D4—42no—
1005C2×D4—42no—
1006C2×D4—44no—
1007C2×D4—816no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—24no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—28no—
1014C22×C4—28no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4C2514yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2514yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2512yes—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—24no—
1070C4⋊C4—28no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—42no—
1077C4⋊C4—41no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—24no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—24no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
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—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4H(5,𝔽2)18yes—
1154C42—28no—
1155C42—24no—
1156C42—22no—
1157C42—24no—
1158C42—28no—
1159C42—24no—
1160C42—22no—
1161C42—24no—
1162C42—24no—
1163C42—41no—
1164C42—42no—
1165C42—42no—
1166C42—42no—
1167C42—42no—
1168C42—42no—
1169C42—44no—
1170C42—44no—
1171C42—42no—
1172C42—44no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—24no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—24no—
1188C23—24no—
1189C23—24no—
1190C23—24no—
1191C23—24no—
1192C23—24no—
1193C23—24no—
1194C23—24no—
1195C23—24no—
1196C23—24no—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23—88no—
1201C23—88no—
1202C23—88no—
1203C23—88no—
1204C23—88no—
1205C23—164no—
1206C23—164no—
1207C23C2×H(5,𝔽2)14yes—
1208C23C2611yescharacteristic
1209Q8—44no—
1210Q8—82no—
1211Q8—84no—
1212Q8—162no—
1213D4—48no—
1214D4—44no—
1215D4—88no—
1216D4—88no—
1217D4—84no—
1218D4—88no—
1219D4—88no—
1220D4—84no—
1221D4—84no—
1222D4—88no—
1223D4—88no—
1224D4—88no—
1225D4—88no—
1226D4—88no—
1227D4—88no—
1228D4—164no—
1229D4—164no—
1230D4—162no—
1231D4—162no—
1232D4—162no—
1233D4—164no—
1234D4—164no—
1235D4—164no—
1236D4—162no—
1237D4—162no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—48no—
1286C2×C4—48no—
1287C2×C4—88no—
1288C2×C4—88no—
1289C2×C4—84no—
1290C2×C4—88no—
1291C2×C4—164no—
1292C2×C4—164no—
1293C2×C4—164no—
1294C2×C4—164no—
1295C2×C4—164no—
1296C2×C4C2×H(5,𝔽2)14yes—
1297C2×C4C2×H(5,𝔽2)14yes—
1298C2×C4C2×H(5,𝔽2)12yes—
1299C2×C4C2×H(5,𝔽2)14yes—
1300C2×C4#58512yes—
1301C2×C4#58514yes—
1302C22—24no—
1303C22—24no—
1304C22—24no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—44no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—44no—
1322C22—44no—
1323C22—44no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—1616no—
1331C22C22×H(5,𝔽2)11yescharacteristic
1332C22C22×H(5,𝔽2)12yes—
1333C22C2×#58512yes—
1334C22C2×#58511yescharacteristic
1335C22H(7,𝔽2)11yescharacteristic
1336C4—24no—
1337C4—22no—
1338C4—24no—
1339C4—24no—
1340C4—22no—
1341C4—24no—
1342C4—44no—
1343C4—44no—
1344C4—44no—
1345C4—44no—
1346C4—42no—
1347C4—44no—
1348C4—41no—
1349C4—42no—
1350C4—42no—
1351C4—44no—
1352C4—44no—
1353C4—42no—
1354C4—42no—
1355C2—44no—
1356C2—84no—
1357C2—84no—
1358C2—84no—
1359C2#6283411yescharacteristic
1360C2#6289612yes—
1361C2#6290511yescharacteristic
1362C2#6301412yes—
1363C2#6302811yescharacteristic
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. #59822C2semidirect
2. #56025C2semidirect
3. #53528C2semidirect
4. #53190C2semidirect
5. #51776C2semidirect
6. #50718C2semidirect
7. #50652C2semidirect
8. #49984C2semidirect
9. #47850C2semidirect
10. #47678C2semidirect
11. #47622C2semidirect
12. #45312C2semidirect
13. #44693C2semidirect
14. #44270C2semidirect
15. #44129C2semidirect
16. #43032C2semidirect
17. #39383C2semidirect
18. #38820C2semidirect
19. #38466C2semidirect
20. #37267C2semidirect
21. #37250C2semidirect
22. #36509C2semidirect
23. #36362C2semidirect
25. C2×#555C22semidirect
28. C2×#538C22semidirect
29. C2×#538C22semidirect
30. #2864C22semidirect
31. #2861C22semidirect
33. #2855C22semidirect
34. #2850C22semidirect
35. #2830C22semidirect
36. #2829C22semidirect
37. #2823C22semidirect
38. #2811C22semidirect
39. #2808C22semidirect
40. #2804C22semidirect
41. #2790C22semidirect
42. #2790C22semidirect
43. #2761C22semidirect
44. #2756C22semidirect
45. #2753C22semidirect
46. #2753C22semidirect
47. #2751C22semidirect
48. #2749C22semidirect
51. #2733C22semidirect
52. #2733C22semidirect
53. #2732C22semidirect
54. #2731C22semidirect
55. #2730C22semidirect
56. #2722C22semidirect
57. #2720C22semidirect
58. #2715C22semidirect
60. #2714C22semidirect
61. #2714C22semidirect
62. #2710C22semidirect
63. #2710C22semidirect
64. #2709C22semidirect
65. #2708C22semidirect
66. #2707C22semidirect
67. #2706C22semidirect
68. #2705C22semidirect
69. #2701C22semidirect
70. #2701C22semidirect
72. #2699C22semidirect
73. #2699C22semidirect
74. #2695C22semidirect
76. #2691C22semidirect
77. #2691C22semidirect
78. #2688C22semidirect
79. #2688C22semidirect
80. #2687C22semidirect
81. #2686C22semidirect
83. #2682C22semidirect
84. #2682C22semidirect
85. #2681C22semidirect
86. #2680C22semidirect
89. #2678C22semidirect
90. #2676C22semidirect
91. #2676C22semidirect
92. #2676C22semidirect
93. #2676C22semidirect
94. #2675C22semidirect
95. #2673C22semidirect
96. #2673C22semidirect
97. #2673C22semidirect
98. #2671C22semidirect
99. #2670C22semidirect
101. #2669C22semidirect
102. #2669C22semidirect
104. #2662C22semidirect
106. #2648C22semidirect
107. #2632C22semidirect
108. #2630C22semidirect
109. #2617C22semidirect
110. #2617C22semidirect
111. #2606C22semidirect
112. #2603C22semidirect
113. #2603C22semidirect
114. #2601C22semidirect
115. #2601C22semidirect
116. #2595C22semidirect
117. #2590C22semidirect
118. #2574C22semidirect
119. #2566C22semidirect
120. #2560C22semidirect
121. #2559C22semidirect
122. #2559C22semidirect
123. #2557C22semidirect
125. #2555C22semidirect
126. #2554C22semidirect
127. #2554C22semidirect
128. #2554C22semidirect
129. #2548C22semidirect
130. #2548C22semidirect
131. #2548C22semidirect
132. #2544C22semidirect
133. #2543C22semidirect
134. #2543C22semidirect
137. #2541C22semidirect
139. #2537C22semidirect
142. #2532C22semidirect
143. #2521C22semidirect
144. #2515C22semidirect
145. #2512C22semidirect
146. #2512C22semidirect
147. #2502C22semidirect
149. #2496C22semidirect
150. #2481C22semidirect
151. #2478C22semidirect
152. #2476C22semidirect
153. #2474C22semidirect
154. #2472C22semidirect
155. #2468C22semidirect
156. #2467C22semidirect
160. #2461C22semidirect
161. #2459C22semidirect
162. #2457C22semidirect
163. #2456C22semidirect
164. #2456C22semidirect
165. #2455C22semidirect
166. #2450C22semidirect
167. #2445C22semidirect
168. #2445C22semidirect
169. #2433C22semidirect
170. #2433C22semidirect
172. #2429C22semidirect
173. #2428C22semidirect
174. #2427C22semidirect
175. #2425C22semidirect
180. #2424C22semidirect
181. #2424C22semidirect
182. #2424C22semidirect
183. #2419C22semidirect
184. #2414C22semidirect
185. #2414C22semidirect
186. #2412C22semidirect
187. #2412C22semidirect
188. #2411C22semidirect
189. #2410C22semidirect
192. #2402C22semidirect
193. #2392C22semidirect
194. #2380C22semidirect
195. #2373C22semidirect
196. #2367C22semidirect
197. #2361C22semidirect
198. #2359C22semidirect
199. #2358C22semidirect
200. #2358C22semidirect
201. #2357C22semidirect
202. #2356C22semidirect
203. #2354C22semidirect
204. #2351C22semidirect
205. #2342C22semidirect
206. #2337C22semidirect
207. #2333C22semidirect
208. #2332C22semidirect
209. #2328C22semidirect
210. #2326C22semidirect
211. #2325C22semidirect
213. C4×C4⋊Q8C22semidirect
214. C4×#127C22semidirect
215. C4×C22⋊Q8C22semidirect
217. C2×#390C22semidirect

Maximal subgroups

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

subgroupindex
#598222
#560252
#535282
#531902
#517762
#507182
#506522
#499842
#478502
#476782
#476222
#453122
#446932
#442702
#441292
#430322
#393832
#388202
#384662
#372672
#372502
#365092
#363622