Finite Group Databasebeta

← #8757645

Subgroups — #8757645

Order 512.

5150 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58935C214yesmaximal, complemented
2#58902C214yesmaximal, complemented
3#56303C214yesmaximal, complemented
4#56302C214yesmaximal, complemented
5#54719C214yesmaximal, complemented
6#54011C214yesmaximal, complemented
7#52085C212yesmaximal, complemented
8#51978C211yesmaximal, characteristic, complemented
9#51958C212yesmaximal, complemented
10#51902C211yesmaximal, characteristic, complemented
11#51896C212yesmaximal, complemented
12#51873C212yesmaximal, complemented
13#51783C212yesmaximal, complemented
14#47079C214yesmaximal, complemented
15#47026C212yesmaximal, complemented
16#46997C212yesmaximal, complemented
17#46504C214yesmaximal, complemented
18#46324C212yesmaximal, complemented
19#46279C212yesmaximal, complemented
20#45980C214yesmaximal, complemented
21#45968C214yesmaximal, complemented
22#35272C211yesmaximal, characteristic, complemented
23#35211C212yesmaximal, complemented
24C2×#563C2211yescharacteristic, complemented
25C2×H(3,𝔽4)C2211yescharacteristic, complemented
26C2×#560C2212yescomplemented
27C2×#555C2212yescomplemented
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic, complemented
30C22×#127C2211yescharacteristic
31C2×#529C2212yescomplemented
32C2×C4×#41C2211yescharacteristic, complemented
33#2856C2214yescomplemented
34#2852C2214yescomplemented
35#2852C2214yescomplemented
36#2843C2212yescomplemented
37#2842C2212yescomplemented
38#2828C2214yescomplemented
39#2826C2214yescomplemented
40#2825C2214yescomplemented
41#2825C2214yescomplemented
42#2823C2212yescomplemented
43#2818C2214yes—
44#2813C2214yescomplemented
45#2812C2212yes—
46#2812C2214yescomplemented
47#2803C2214yescomplemented
48#2795C2214yescomplemented
49#2789C2212yescomplemented
50#2788C2214yescomplemented
51#2786C2214yescomplemented
52#2783C2214yescomplemented
53#2782C2212yescomplemented
54#2781C2214yescomplemented
55#2780C2214yescomplemented
56#2778C2214yes—
57#2761C2214yescomplemented
58#2761C2214yescomplemented
59#2753C2214yescomplemented
60#2753C2214yescomplemented
61#2736C2212yescomplemented
62#2733C2212yescomplemented
63#2733C2212yescomplemented
64#2731C2212yescomplemented
65#2731C2212yescomplemented
66#2730C2214yescomplemented
67#2730C2214yescomplemented
68#2723C2214yescomplemented
69#2718C2214yescomplemented
70#2714C2214yescomplemented
71#2714C2214yescomplemented
72#2712C2214yescomplemented
73#2711C2214yescomplemented
74#2711C2214yescomplemented
75#2709C2214yes—
76#2709C2212yescomplemented
77#2709C2212yescomplemented
78#2707C2214yescomplemented
79#2706C2214yescomplemented
80#2706C2214yescomplemented
81#2703C2214yescomplemented
82#2703C2214yescomplemented
83#2701C2214yescomplemented
84#2699C2214yescomplemented
85#2697C2214yes—
86#2697C2214yes—
87#2691C2214yescomplemented
88#2688C2214yescomplemented
89#2688C2214yescomplemented
90#2686C2214yescomplemented
91#2685C2214yescomplemented
92#2685C2214yescomplemented
93#2682C2214yescomplemented
94#2682C2214yescomplemented
95#2681C2214yescomplemented
96#2678C2214yescomplemented
97#2678C2214yescomplemented
98#2676C2214yescomplemented
99#2676C2214yescomplemented
100#2676C2214yescomplemented
101#2675C2214yescomplemented
102#2673C2214yes—
103#2673C2214yescomplemented
104#2673C2214yescomplemented
105#2673C2214yescomplemented
106#2673C2214yescomplemented
107#2673C2214yescomplemented
108#2673C2214yescomplemented
109#2672C2214yescomplemented
110#2671C2214yescomplemented
111#2671C2214yescomplemented
112#2670C2214yes—
113#2670C2214yescomplemented
114#2670C2214yescomplemented
115#2669C2214yes—
116#2669C2214yes—
117#2669C2212yescomplemented
118#2669C2214yescomplemented
119#2669C2212yescomplemented
120#2668C2212yes—
121#2661C2214yescomplemented
122#2657C2212yescomplemented
123#2653C2214yescomplemented
124#2641C2212yescomplemented
125#2636C2214yescomplemented
126#2630C2214yescomplemented
127#2630C2214yescomplemented
128#2620C2214yescomplemented
129#2619C2214yescomplemented
130#2619C2214yescomplemented
131#2611C2212yescomplemented
132#2610C2212yes—
133#2610C2214yescomplemented
134#2609C2214yescomplemented
135#2609C2214yescomplemented
136#2609C2214yescomplemented
137#2603C2214yescomplemented
138#2603C2214yescomplemented
139#2600C2214yescomplemented
140#2600C2214yescomplemented
141#2597C2214yescomplemented
142#2576C2214yescomplemented
143#2566C2212yescomplemented
144#2565C2212yescomplemented
145#2559C2214yescomplemented
146#2557C2214yescomplemented
147#2555C2214yescomplemented
148#2554C2214yescomplemented
149#2548C2212yes—
150#2548C2212yescomplemented
151#2545C2212yescomplemented
152#2544C2212yes—
153#2541C2212yes—
154#2541C2212yescomplemented
155#2531C2214yescomplemented
156#2531C2214yescomplemented
157#2529C2214yescomplemented
158#2528C2214yescomplemented
159#2526C2214yescomplemented
160#2500C2212yescomplemented
161#2499C2212yescomplemented
162#2479C2214yescomplemented
163#2477C2214yescomplemented
164#2476C2214yescomplemented
165#2476C2214yescomplemented
166#2475C2214yescomplemented
167#2474C2214yescomplemented
168#2472C2214yescomplemented
169#2471C2214yescomplemented
170#2471C2214yescomplemented
171#2464C2214yescomplemented
172#2464C2214yescomplemented
173#2461C2214yescomplemented
174#2458C2214yescomplemented
175#2456C2214yescomplemented
176#2456C2214yescomplemented
177#2437C2212yescomplemented
178#2433C2214yes—
179#2432C2212yescomplemented
180#2431C2212yes—
181#2428C2214yescomplemented
182#2426C2214yescomplemented
183#2424C2214yescomplemented
184#2424C2214yescomplemented
185#2424C2214yescomplemented
186#2424C2214yescomplemented
187#2424C2214yescomplemented
188#2422C2214yescomplemented
189#2414C2214yescomplemented
190#2411C2214yescomplemented
191#2411C2214yescomplemented
192#2411C2214yescomplemented
193#2410C2214yes—
194#2410C2214yes—
195#2410C2214yescomplemented
196#2408C2214yescomplemented
197#2408C2214yescomplemented
198#2405C2212yes—
199#2405C2212yescomplemented
200#2405C2214yescomplemented
201#2403C2212yes—
202#2403C2214yescomplemented
203#2383C2214yescomplemented
204#2380C2212yescomplemented
205#2379C2212yescomplemented
206#2372C2211yescharacteristic, complemented
207#2372C2211yescharacteristic, complemented
208#2328C2212yes—
209#2327C2212yescomplemented
210#2326C2212yescomplemented
211#2326C2212yescomplemented
212#2321C2214yescomplemented
213#2312C2212yescomplemented
214#2309C2211yescharacteristic
215#2309C2211yescharacteristic, complemented
216#2308C2212yescomplemented
217#2285C2211yescharacteristic, complemented
218#2283C2212yescomplemented
219C22×#41C2311yescharacteristic
220C23×D4C2311yescharacteristic
221C23×D4C2311yescharacteristic
222C23×D4C2312yes—
223C23×D4C2314yes—
224#563—44no—
225H(3,𝔽4)—44no—
226#560—48no—
227#555—48no—
228#535—44no—
229#535—44no—
230C2×C4⋊Q8C2312yes—
231C2×#127—44no—
232C2×#127C2312yes—
233C2×#127C2312yes—
234C2×#127C2312yes—
235C2×#127C2312yes—
236C2×#127C2311yescharacteristic
237C2×#127C2311yescharacteristic
238C2×#127C2312yes—
239C2×#127C2312yes—
240C2×#127C2314yes—
241#529—48no—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#125C2312yes—
246C2×#125C2312yes—
247C2×#124C2312yes—
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#124C2314yes—
254C2×#124C2312yes—
255C2×#124C2314yes—
256C2×#124C2314yes—
257C2×#123C2314yes—
258C2×#123C2312yes—
259C2×#123C2312yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2312yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#120C2314yes—
289C2×#120C2312yes—
290C2×#120C2312yes—
291C2×#120C2314yes—
292C2×#120C2314yes—
293C2×#120C2314yes—
294C2×#120C2314yes—
295C2×#120C2314yes—
296C2×#120C2314yes—
297C2×#120C2314yes—
298C2×#120C2314yes—
299C4×#41—44no—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×#117C2311yescharacteristic
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2312yes—
313C2×#117C2314yes—
314C2×#117C2314yes—
315C2×#117C2314yes—
316C22×C22⋊C4C2312yes—
317C22×C22⋊C4C2314yes—
318C22×C22⋊C4C2314yes—
319C22×C42C2311yescharacteristic
320C22×C42C2312yes—
321#401C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2312yes—
331#398C2314yes—
332#398C2314yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2312yes—
349#397C2314yes—
350#397C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#395C2312yes—
367#395C2314yes—
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#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#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#393C2312yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
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#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2312yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#390C2314yes—
451#390C2312yes—
452#390C2312yes—
453#390C2314yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#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#386C2314yes—
554#386C2314yes—
555#386C2312yes—
556#386C2312yes—
557#386C2312yes—
558#386C2312yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#384C2312yes—
586#384C2312yes—
587#384C2312yes—
588#383C2314yes—
589#382C2312yes—
590#382C2312yes—
591#382C2314yes—
592#382C2314yes—
593#382C2312yes—
594#381C2314yes—
595#381C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#379C2312yes—
601#379C2312yes—
602#379C2312yes—
603#379C2312yes—
604#379C2312yes—
605#379C2312yes—
606#379C2314yes—
607#379C2314yes—
608#379C2314yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2312yes—
619#376C2312yes—
620#376C2312yes—
621#376C2312yes—
622#376C2312yes—
623C25C2412yes—
624C25C2412yes—
625C25C2412yes—
626C2×#41—24no—
627C2×#41—42no—
628C2×#41—42no—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×Q8C2411yescharacteristic
632C22×D4—42no—
633C22×D4—42no—
634C22×D4—48no—
635C22×D4—42no—
636C22×D4—42no—
637C22×D4—42no—
638C22×D4—42no—
639C22×D4—44no—
640C22×D4—84no—
641C22×D4—84no—
642C22×D4—84no—
643C22×D4C2412yes—
644C22×D4C2411yescharacteristic
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2411yescharacteristic
648C22×D4C2412yes—
649C22×D4C2414yes—
650C22×D4C2412yes—
651C22×D4C2414yes—
652C22×D4C2412yes—
653C22×D4C2411yescharacteristic
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C22×D4C2414yes—
661C22×D4C2414yes—
662C22×D4C2412yes—
663C22×D4C2414yes—
664C22×D4C2414yes—
665C22×D4C2414yes—
666C22×D4C2414yes—
667C22×D4C2414yes—
668C22×D4C2414yes—
669C22×D4C2414yes—
670C23×C4C2411yescharacteristic
671C23×C4C2412yes—
672C23×C4C2412yes—
673C23×C4C2412yes—
674C23×C4C2412yes—
675C23×C4C2414yes—
676C23×C4C2414yes—
677C23×C4C2414yes—
678C23×C4C2414yes—
679C23×C4C2412yes—
680C23×C4C2412yes—
681C23×C4C2412yes—
682C4⋊Q8—28no—
683#127—28no—
684#127—44no—
685#127—44no—
686#127—44no—
687#127—44no—
688#127—42no—
689#127—42no—
690#127—44no—
691#127—84no—
692#126—216no—
693#126—48no—
694#126—84no—
695#125—44no—
696#125—44no—
697#124—28no—
698#124—24no—
699#124—24no—
700#124—28no—
701#124—44no—
702#124—48no—
703#124—44no—
704#124—44no—
705#124—48no—
706#124—84no—
707#123—48no—
708#123—44no—
709#123—48no—
710#123—44no—
711#123—84no—
712#123—84no—
713#123—84no—
714#123—84no—
715#123—84no—
716C22⋊Q8—48no—
717C22⋊Q8—44no—
718C22⋊Q8—84no—
719#121—44no—
720#121—48no—
721#121—48no—
722#121—48no—
723#121—48no—
724#121—48no—
725#121—48no—
726#121—48no—
727#121—84no—
728#121—84no—
729#121—84no—
730#121—84no—
731#121—84no—
732#121—84no—
733#121—84no—
734#121—84no—
735#121—84no—
736#121—84no—
737#121—84no—
738#120—48no—
739#120—48no—
740#120—44no—
741#120—48no—
742#120—44no—
743#120—48no—
744#120—48no—
745#120—84no—
746#120—84no—
747#120—84no—
748#120—84no—
749C4×Q8—44no—
750C4×Q8—44no—
751C4×D4—44no—
752C4×D4—48no—
753C4×D4—44no—
754C4×D4—44no—
755C4×D4—44no—
756C4×D4—48no—
757C4×D4—84no—
758#117—42no—
759#117—44no—
760#117—42no—
761#117—42no—
762#117—48no—
763#117—48no—
764#117—48no—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C22⋊C4—44no—
797C2×C22⋊C4—84no—
798C2×C22⋊C4—84no—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
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⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C42—28no—
866C2×C42—24no—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2411yescharacteristic
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2411yescharacteristic
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2412yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920C24—24no—
921C24—24no—
922C24—44no—
923C24—42no—
924C24—42no—
925C24—42no—
926C24—44no—
927C24—44no—
928C24—44no—
929C24—44no—
930C24—42no—
931C24—42no—
932C24—42no—
933C24—42no—
934C24—44no—
935C24C2512yes—
936C24C2514yes—
937C24C2512yes—
938C24C2514yes—
939C24C2512yes—
940C24C2511yescharacteristic
941#41—416no—
942C2×Q8—24no—
943C2×Q8—41no—
944C2×Q8—41no—
945C2×Q8—42no—
946C2×Q8—42no—
947C2×Q8—44no—
948C2×Q8—42no—
949C2×Q8H(5,𝔽2)14yes—
950C2×D4—24no—
951C2×D4—28no—
952C2×D4—24no—
953C2×D4—22no—
954C2×D4—24no—
955C2×D4—22no—
956C2×D4—24no—
957C2×D4—28no—
958C2×D4—24no—
959C2×D4—24no—
960C2×D4—28no—
961C2×D4—22no—
962C2×D4—42no—
963C2×D4—41no—
964C2×D4—41no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—42no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—42no—
978C2×D4—42no—
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—41no—
989C2×D4—42no—
990C2×D4—41no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—42no—
994C2×D4—44no—
995C2×D4—42no—
996C2×D4—42no—
997C2×D4—41no—
998C2×D4—42no—
999C2×D4—41no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—42no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—88no—
1031C2×D4—88no—
1032C2×D4—832no—
1033C2×D4—816no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—44no—
1043C22×C4—42no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—44no—
1060C22×C4—42no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2514yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
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—41no—
1133C22⋊C4—42no—
1134C22⋊C4—41no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
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—42no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C42—24no—
1180C42—22no—
1181C42—24no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—22no—
1187C42—22no—
1188C42—24no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—42no—
1193C42—44no—
1194C42—42no—
1195C42H(5,𝔽2)14yes—
1196C23—21no—
1197C23—21no—
1198C23—24no—
1199C23—24no—
1200C23—22no—
1201C23—24no—
1202C23—24no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—24no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—24no—
1212C23—22no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—24no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23—24no—
1228C23—48no—
1229C23—84no—
1230C23—84no—
1231C23—84no—
1232C23—88no—
1233C23—84no—
1234C23—88no—
1235C23—88no—
1236C23—162no—
1237C23—162no—
1238C23—164no—
1239C23—162no—
1240C23—164no—
1241C23—162no—
1242C23—164no—
1243C23#58512yes—
1244C23C2611yescharacteristic
1245Q8—44no—
1246Q8—84no—
1247Q8—162no—
1248D4—48no—
1249D4—44no—
1250D4—84no—
1251D4—84no—
1252D4—84no—
1253D4—82no—
1254D4—84no—
1255D4—82no—
1256D4—88no—
1257D4—88no—
1258D4—88no—
1259D4—88no—
1260D4—88no—
1261D4—88no—
1262D4—88no—
1263D4—88no—
1264D4—88no—
1265D4—164no—
1266D4—164no—
1267D4—164no—
1268D4—164no—
1269D4—164no—
1270D4—162no—
1271D4—164no—
1272D4—164no—
1273D4—164no—
1274D4—164no—
1275C2×C4—28no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—48no—
1318C2×C4—48no—
1319C2×C4—84no—
1320C2×C4—84no—
1321C2×C4—88no—
1322C2×C4—88no—
1323C2×C4—88no—
1324C2×C4—84no—
1325C2×C4—162no—
1326C2×C4—162no—
1327C2×C4—164no—
1328C2×C4C2×H(5,𝔽2)12yes—
1329C2×C4C2×H(5,𝔽2)12yes—
1330C2×C4C2×H(5,𝔽2)14yes—
1331C2×C4C2×H(5,𝔽2)14yes—
1332C22—24no—
1333C22—22no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—44no—
1339C22—44no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—42no—
1344C22—42no—
1345C22—44no—
1346C22—44no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—42no—
1353C22—42no—
1354C22—44no—
1355C22—42no—
1356C22—44no—
1357C22—42no—
1358C22—44no—
1359C22—42no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—168no—
1366C22—168no—
1367C22—168no—
1368C22C22×H(5,𝔽2)11yescharacteristic
1369C22C22×H(5,𝔽2)11yescharacteristic
1370C22C2×#58511yescharacteristic
1371C22H(7,𝔽2)14yes—
1372C4—22no—
1373C4—22no—
1374C4—24no—
1375C4—24no—
1376C4—44no—
1377C4—44no—
1378C4—44no—
1379C4—44no—
1380C4—44no—
1381C4—42no—
1382C4—42no—
1383C4—44no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—44no—
1388C4—44no—
1389C2—42no—
1390C2—82no—
1391C2—82no—
1392C2—84no—
1393C2—84no—
1394C2—82no—
1395C2#6281811yescharacteristic
1396C2#6287412yes—
1397C2#6304212yes—
1398C2#6306612yes—
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. #58935C2semidirect
2. #58902C2semidirect
3. #56303C2semidirect
4. #56302C2semidirect
5. #54719C2semidirect
6. #54011C2semidirect
7. #52085C2semidirect
8. #51978C2semidirect
9. #51958C2semidirect
10. #51902C2semidirect
11. #51896C2semidirect
12. #51873C2semidirect
13. #51783C2semidirect
14. #47079C2semidirect
15. #47026C2semidirect
16. #46997C2semidirect
17. #46504C2semidirect
18. #46324C2semidirect
19. #46279C2semidirect
20. #45980C2semidirect
21. #45968C2semidirect
22. #35272C2semidirect
23. #35211C2semidirect
24. C2×#563C22semidirect
25. C2×H(3,𝔽4)C22semidirect
26. C2×#560C22semidirect
27. C2×#555C22semidirect
29. C2×#535C22semidirect
31. C2×#529C22semidirect
32. C2×C4×#41C22semidirect
33. #2856C22semidirect
34. #2852C22semidirect
35. #2852C22semidirect
36. #2843C22semidirect
37. #2842C22semidirect
38. #2828C22semidirect
39. #2826C22semidirect
40. #2825C22semidirect
41. #2825C22semidirect
42. #2823C22semidirect
44. #2813C22semidirect
46. #2812C22semidirect
47. #2803C22semidirect
48. #2795C22semidirect
49. #2789C22semidirect
50. #2788C22semidirect
51. #2786C22semidirect
52. #2783C22semidirect
53. #2782C22semidirect
54. #2781C22semidirect
55. #2780C22semidirect
57. #2761C22semidirect
58. #2761C22semidirect
59. #2753C22semidirect
60. #2753C22semidirect
61. #2736C22semidirect
62. #2733C22semidirect
63. #2733C22semidirect
64. #2731C22semidirect
65. #2731C22semidirect
66. #2730C22semidirect
67. #2730C22semidirect
68. #2723C22semidirect
69. #2718C22semidirect
70. #2714C22semidirect
71. #2714C22semidirect
72. #2712C22semidirect
73. #2711C22semidirect
74. #2711C22semidirect
76. #2709C22semidirect
77. #2709C22semidirect
78. #2707C22semidirect
79. #2706C22semidirect
80. #2706C22semidirect
81. #2703C22semidirect
82. #2703C22semidirect
83. #2701C22semidirect
84. #2699C22semidirect
87. #2691C22semidirect
88. #2688C22semidirect
89. #2688C22semidirect
90. #2686C22semidirect
91. #2685C22semidirect
92. #2685C22semidirect
93. #2682C22semidirect
94. #2682C22semidirect
95. #2681C22semidirect
96. #2678C22semidirect
97. #2678C22semidirect
98. #2676C22semidirect
99. #2676C22semidirect
100. #2676C22semidirect
101. #2675C22semidirect
103. #2673C22semidirect
104. #2673C22semidirect
105. #2673C22semidirect
106. #2673C22semidirect
107. #2673C22semidirect
108. #2673C22semidirect
109. #2672C22semidirect
110. #2671C22semidirect
111. #2671C22semidirect
113. #2670C22semidirect
114. #2670C22semidirect
117. #2669C22semidirect
118. #2669C22semidirect
119. #2669C22semidirect
121. #2661C22semidirect
122. #2657C22semidirect
123. #2653C22semidirect
124. #2641C22semidirect
125. #2636C22semidirect
126. #2630C22semidirect
127. #2630C22semidirect
128. #2620C22semidirect
129. #2619C22semidirect
130. #2619C22semidirect
131. #2611C22semidirect
133. #2610C22semidirect
134. #2609C22semidirect
135. #2609C22semidirect
136. #2609C22semidirect
137. #2603C22semidirect
138. #2603C22semidirect
139. #2600C22semidirect
140. #2600C22semidirect
141. #2597C22semidirect
142. #2576C22semidirect
143. #2566C22semidirect
144. #2565C22semidirect
145. #2559C22semidirect
146. #2557C22semidirect
147. #2555C22semidirect
148. #2554C22semidirect
150. #2548C22semidirect
151. #2545C22semidirect
154. #2541C22semidirect
155. #2531C22semidirect
156. #2531C22semidirect
157. #2529C22semidirect
158. #2528C22semidirect
159. #2526C22semidirect
160. #2500C22semidirect
161. #2499C22semidirect
162. #2479C22semidirect
163. #2477C22semidirect
164. #2476C22semidirect
165. #2476C22semidirect
166. #2475C22semidirect
167. #2474C22semidirect
168. #2472C22semidirect
169. #2471C22semidirect
170. #2471C22semidirect
171. #2464C22semidirect
172. #2464C22semidirect
173. #2461C22semidirect
174. #2458C22semidirect
175. #2456C22semidirect
176. #2456C22semidirect
177. #2437C22semidirect
179. #2432C22semidirect
181. #2428C22semidirect
182. #2426C22semidirect
183. #2424C22semidirect
184. #2424C22semidirect
185. #2424C22semidirect
186. #2424C22semidirect
187. #2424C22semidirect
188. #2422C22semidirect
189. #2414C22semidirect
190. #2411C22semidirect
191. #2411C22semidirect
192. #2411C22semidirect
195. #2410C22semidirect
196. #2408C22semidirect
197. #2408C22semidirect
199. #2405C22semidirect
200. #2405C22semidirect
202. #2403C22semidirect
203. #2383C22semidirect
204. #2380C22semidirect
205. #2379C22semidirect
206. #2372C22semidirect
207. #2372C22semidirect
209. #2327C22semidirect
210. #2326C22semidirect
211. #2326C22semidirect
212. #2321C22semidirect
213. #2312C22semidirect
215. #2309C22semidirect
216. #2308C22semidirect
217. #2285C22semidirect
218. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#589352
#589022
#563032
#563022
#547192
#540112
#520852
#519782
#519582
#519022
#518962
#518732
#517832
#470792
#470262
#469972
#465042
#463242
#462792
#459802
#459682
#352722
#352112