Finite Group Databasebeta

← #8757644

Subgroups — #8757644

Order 512.

5150 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58934C214yesmaximal, complemented
2#58901C214yesmaximal, complemented
3#57151C212yesmaximal, complemented
4#57149C212yesmaximal, complemented
5#56348C212yesmaximal, complemented
6#56346C212yesmaximal, complemented
7#54698C214yesmaximal, complemented
8#53988C214yesmaximal, complemented
9#51903C212yesmaximal, complemented
10#51895C212yesmaximal, complemented
11#51869C214yesmaximal, complemented
12#51778C214yesmaximal, complemented
13#47563C211yesmaximal, characteristic, complemented
14#47195C211yesmaximal, characteristic, complemented
15#47026C212yesmaximal, complemented
16#46605C214yesmaximal, complemented
17#46532C214yesmaximal, complemented
18#46324C212yesmaximal, complemented
19#46279C212yesmaximal, complemented
20#45980C214yesmaximal, complemented
21#45968C214yesmaximal, complemented
22#35272C211yesmaximal, characteristic, complemented
23#35210C212yesmaximal, complemented
24C2×#562C2212yescomplemented
25C2×#560C2212yescomplemented
26C2×#551C2212yescomplemented
27C2×#535C2211yescharacteristic
28C2×#535C2211yescharacteristic, complemented
29C22×#127C2211yescharacteristic
30C2×#529C2212yescomplemented
31C2×C4×#41C2211yescharacteristic, complemented
32#2856C2214yescomplemented
33#2852C2214yescomplemented
34#2852C2214yescomplemented
35#2843C2212yescomplemented
36#2842C2211yescharacteristic, complemented
37#2840C2211yescharacteristic
38#2828C2214yescomplemented
39#2828C2214yescomplemented
40#2825C2214yescomplemented
41#2824C2214yescomplemented
42#2823C2212yescomplemented
43#2818C2214yes—
44#2815C2214yescomplemented
45#2813C2214yescomplemented
46#2812C2212yes—
47#2803C2214yescomplemented
48#2801C2214yescomplemented
49#2797C2214yescomplemented
50#2789C2212yescomplemented
51#2788C2214yescomplemented
52#2786C2214yescomplemented
53#2783C2214yescomplemented
54#2782C2212yescomplemented
55#2780C2214yescomplemented
56#2778C2214yes—
57#2778C2214yescomplemented
58#2778C2214yescomplemented
59#2761C2214yescomplemented
60#2753C2214yescomplemented
61#2753C2214yescomplemented
62#2736C2212yescomplemented
63#2735C2212yes—
64#2735C2212yes—
65#2733C2214yescomplemented
66#2730C2214yescomplemented
67#2730C2214yescomplemented
68#2723C2214yescomplemented
69#2723C2214yescomplemented
70#2714C2214yescomplemented
71#2711C2214yescomplemented
72#2710C2214yescomplemented
73#2709C2212yescomplemented
74#2709C2214yescomplemented
75#2709C2212yescomplemented
76#2707C2214yescomplemented
77#2707C2214yescomplemented
78#2706C2214yescomplemented
79#2705C2214yescomplemented
80#2703C2214yescomplemented
81#2703C2214yescomplemented
82#2702C2214yescomplemented
83#2701C2214yescomplemented
84#2699C2214yescomplemented
85#2691C2214yescomplemented
86#2688C2214yescomplemented
87#2686C2214yescomplemented
88#2686C2214yescomplemented
89#2685C2214yes—
90#2685C2214yescomplemented
91#2682C2214yescomplemented
92#2682C2214yescomplemented
93#2681C2214yescomplemented
94#2678C2214yescomplemented
95#2678C2214yescomplemented
96#2678C2214yescomplemented
97#2678C2214yescomplemented
98#2676C2214yescomplemented
99#2676C2214yescomplemented
100#2676C2214yescomplemented
101#2675C2214yescomplemented
102#2673C2214yes—
103#2673C2214yes—
104#2673C2214yes—
105#2673C2214yescomplemented
106#2673C2214yescomplemented
107#2672C2214yescomplemented
108#2671C2214yescomplemented
109#2671C2214yescomplemented
110#2670C2212yes—
111#2670C2212yes—
112#2670C2214yescomplemented
113#2670C2214yescomplemented
114#2669C2214yes—
115#2669C2214yescomplemented
116#2669C2214yescomplemented
117#2669C2212yescomplemented
118#2669C2214yescomplemented
119#2669C2212yescomplemented
120#2668C2212yes—
121#2663C2214yescomplemented
122#2657C2212yescomplemented
123#2649C2214yescomplemented
124#2641C2212yescomplemented
125#2638C2212yescomplemented
126#2638C2212yescomplemented
127#2635C2212yes—
128#2635C2212yescomplemented
129#2630C2214yescomplemented
130#2619C2214yescomplemented
131#2619C2214yescomplemented
132#2617C2214yescomplemented
133#2611C2212yescomplemented
134#2611C2212yescomplemented
135#2611C2212yescomplemented
136#2610C2212yes—
137#2610C2212yes—
138#2610C2214yescomplemented
139#2610C2212yescomplemented
140#2610C2214yescomplemented
141#2609C2214yescomplemented
142#2603C2214yescomplemented
143#2602C2214yescomplemented
144#2602C2214yescomplemented
145#2597C2214yescomplemented
146#2581C2212yescomplemented
147#2580C2212yescomplemented
148#2559C2214yescomplemented
149#2559C2214yescomplemented
150#2555C2214yescomplemented
151#2554C2214yescomplemented
152#2548C2214yescomplemented
153#2541C2214yescomplemented
154#2539C2214yescomplemented
155#2536C2212yescomplemented
156#2535C2212yes—
157#2531C2214yescomplemented
158#2529C2214yescomplemented
159#2528C2214yescomplemented
160#2526C2214yescomplemented
161#2526C2214yescomplemented
162#2485C2214yescomplemented
163#2483C2211yescharacteristic, complemented
164#2479C2214yescomplemented
165#2476C2214yescomplemented
166#2476C2214yescomplemented
167#2476C2214yescomplemented
168#2475C2214yescomplemented
169#2474C2214yescomplemented
170#2472C2214yescomplemented
171#2471C2214yescomplemented
172#2471C2214yescomplemented
173#2470C2214yescomplemented
174#2464C2214yescomplemented
175#2464C2214yescomplemented
176#2461C2214yescomplemented
177#2458C2214yescomplemented
178#2456C2214yescomplemented
179#2456C2214yescomplemented
180#2437C2212yescomplemented
181#2428C2214yescomplemented
182#2428C2214yescomplemented
183#2427C2214yescomplemented
184#2426C2214yescomplemented
185#2424C2214yescomplemented
186#2424C2214yescomplemented
187#2424C2214yescomplemented
188#2418C2214yescomplemented
189#2414C2214yescomplemented
190#2414C2214yescomplemented
191#2411C2214yescomplemented
192#2410C2214yes—
193#2410C2214yescomplemented
194#2410C2214yescomplemented
195#2410C2214yescomplemented
196#2408C2212yes—
197#2408C2212yes—
198#2408C2212yescomplemented
199#2408C2212yescomplemented
200#2407C2214yescomplemented
201#2405C2214yes—
202#2405C2212yes—
203#2403C2214yes—
204#2403C2211yescharacteristic
205#2403C2212yes—
206#2383C2214yescomplemented
207#2380C2212yescomplemented
208#2379C2212yescomplemented
209#2372C2212yescomplemented
210#2324C2214yescomplemented
211#2323C2214yescomplemented
212#2321C2214yescomplemented
213#2312C2212yescomplemented
214#2309C2212yes—
215#2309C2211yescharacteristic
216#2309C2211yescharacteristic, complemented
217#2285C2211yescharacteristic, complemented
218#2283C2212yescomplemented
219C22×#41C2311yescharacteristic
220C23×D4C2311yescharacteristic
221C23×D4C2311yescharacteristic
222C23×D4C2312yes—
223C23×D4C2312yes—
224C23×D4C2312yes—
225#562—48no—
226#560—48no—
227#551—48no—
228#535—44no—
229#535—44no—
230C2×#127—44no—
231C2×#127C2312yes—
232C2×#127C2312yes—
233C2×#127C2312yes—
234C2×#127C2312yes—
235C2×#127C2314yes—
236C2×#127C2314yes—
237#529—48no—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#125C2312yes—
242C2×#125C2312yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2312yes—
247C2×#124C2314yes—
248C2×#124C2314yes—
249C2×#124C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2312yes—
253C2×#123C2314yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2312yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#120C2314yes—
284C2×#120C2314yes—
285C2×#120C2312yes—
286C2×#120C2312yes—
287C2×#120C2312yes—
288C2×#120C2312yes—
289C2×#120C2312yes—
290C2×#120C2312yes—
291C2×#120C2314yes—
292C2×#120C2314yes—
293C2×#120C2314yes—
294C2×#120C2314yes—
295C2×#120C2314yes—
296C4×#41—44no—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2314yes—
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2311yescharacteristic
309C2×#117C2314yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C2×#117C2314yes—
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2314yes—
316C22×C42C2311yescharacteristic
317C22×C42C2312yes—
318#401C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2312yes—
326#399C2312yes—
327#399C2312yes—
328#399C2312yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#398C2312yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2312yes—
338#398C2312yes—
339#397C2314yes—
340#397C2314yes—
341#397C2312yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2312yes—
351#397C2312yes—
352#397C2314yes—
353#397C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#395C2312yes—
366#395C2312yes—
367#395C2312yes—
368#395C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2312yes—
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#394C2312yes—
398#394C2312yes—
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#394C2314yes—
412#393C2312yes—
413#393C2314yes—
414#393C2314yes—
415#393C2312yes—
416#393C2312yes—
417#393C2314yes—
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#392C2314yes—
437#392C2312yes—
438#392C2312yes—
439#392C2314yes—
440#392C2312yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#392C2314yes—
450#391C2314yes—
451#391C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
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#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
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#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
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#386C2312yes—
552#386C2312yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2312yes—
557#386C2314yes—
558#386C2312yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
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#384C2312yes—
585#383C2314yes—
586#382C2312yes—
587#382C2312yes—
588#382C2314yes—
589#382C2312yes—
590#381C2312yes—
591#381C2312yes—
592#381C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2312yes—
598#380C2312yes—
599#380C2314yes—
600#379C2311yescharacteristic
601#379C2311yescharacteristic
602#379C2312yes—
603#379C2311yescharacteristic
604#379C2311yescharacteristic
605#379C2314yes—
606#379C2312yes—
607#379C2312yes—
608#379C2312yes—
609#379C2314yes—
610#379C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618#376C2312yes—
619#376C2312yes—
620#376C2312yes—
621#376C2312yes—
622C25C2411yescharacteristic
623C25C2412yes—
624C25C2411yescharacteristic
625C25C2412yes—
626C2×#41—24no—
627C2×#41—42no—
628C2×#41—42no—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×Q8C2411yescharacteristic
632C22×D4—42no—
633C22×D4—42no—
634C22×D4—44no—
635C22×D4—44no—
636C22×D4—42no—
637C22×D4—42no—
638C22×D4—42no—
639C22×D4—42no—
640C22×D4—44no—
641C22×D4—84no—
642C22×D4—84no—
643C22×D4—84no—
644C22×D4C2412yes—
645C22×D4C2411yescharacteristic
646C22×D4C2414yes—
647C22×D4C2412yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2412yes—
651C22×D4C2414yes—
652C22×D4C2412yes—
653C22×D4C2412yes—
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×C4C2414yes—
673C23×C4C2412yes—
674C23×C4C2412yes—
675C23×C4C2412yes—
676C23×C4C2414yes—
677C23×C4C2412yes—
678C23×C4C2414yes—
679C23×C4C2412yes—
680C23×C4C2414yes—
681C23×C4C2412yes—
682#127—28no—
683#127—44no—
684#127—48no—
685#127—44no—
686#127—44no—
687#127—84no—
688#126—216no—
689#126—48no—
690#126—84no—
691#125—44no—
692#125—44no—
693#124—28no—
694#124—28no—
695#124—44no—
696#124—44no—
697#124—84no—
698#124—84no—
699#124—84no—
700#123—48no—
701#123—48no—
702#123—48no—
703#123—48no—
704#123—44no—
705#123—48no—
706#123—44no—
707#123—84no—
708#123—84no—
709C22⋊Q8—216no—
710C22⋊Q8—48no—
711C22⋊Q8—44no—
712C22⋊Q8—84no—
713#121—44no—
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—84no—
723#121—84no—
724#121—84no—
725#121—84no—
726#121—84no—
727#121—84no—
728#121—84no—
729#121—84no—
730#121—84no—
731#121—84no—
732#121—84no—
733#120—44no—
734#120—44no—
735#120—44no—
736#120—44no—
737#120—44no—
738#120—48no—
739#120—44no—
740#120—48no—
741#120—84no—
742#120—84no—
743#120—84no—
744#120—84no—
745#120—84no—
746C4×Q8—44no—
747C4×Q8—44no—
748C4×D4—44no—
749C4×D4—44no—
750C4×D4—44no—
751C4×D4—44no—
752C4×D4—48no—
753C4×D4—48no—
754C4×D4—84no—
755#117—42no—
756#117—44no—
757#117—42no—
758#117—42no—
759#117—48no—
760#117—48no—
761#117—84no—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C22⋊C4—48no—
794C2×C22⋊C4—44no—
795C2×C22⋊C4—84no—
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⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
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⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C42—28no—
864C2×C42—24no—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2411yescharacteristic
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2411yescharacteristic
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
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—
917C24—22no—
918C24—24no—
919C24—22no—
920C24—41no—
921C24—41no—
922C24—42no—
923C24—42no—
924C24—44no—
925C24—44no—
926C24—44no—
927C24—44no—
928C24—44no—
929C24—41no—
930C24—42no—
931C24—41no—
932C24—44no—
933C24—42no—
934C24—42no—
935C24C2512yes—
936C24C2514yes—
937C24C2512yes—
938C24C2514yes—
939C24C2512yes—
940C24C2511yescharacteristic
941#41—416no—
942C2×Q8—41no—
943C2×Q8—41no—
944C2×Q8—42no—
945C2×Q8—44no—
946C2×Q8—42no—
947C2×Q8—44no—
948C2×Q8H(5,𝔽2)14yes—
949C2×D4—24no—
950C2×D4—28no—
951C2×D4—24no—
952C2×D4—22no—
953C2×D4—24no—
954C2×D4—24no—
955C2×D4—28no—
956C2×D4—24no—
957C2×D4—24no—
958C2×D4—28no—
959C2×D4—42no—
960C2×D4—41no—
961C2×D4—41no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—42no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—42no—
975C2×D4—42no—
976C2×D4—44no—
977C2×D4—44no—
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—42no—
988C2×D4—42no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—42no—
992C2×D4—42no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
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—42no—
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—88no—
1026C2×D4—88no—
1027C2×D4—816no—
1028C2×D4—816no—
1029C2×D4—816no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—28no—
1039C22×C4—44no—
1040C22×C4—42no—
1041C22×C4—44no—
1042C22×C4—42no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4C2514yes—
1062C22×C4C2514yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
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—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—41no—
1127C22⋊C4—42no—
1128C22⋊C4—41no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
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—42no—
1142C22⋊C4—44no—
1143C22⋊C4—42no—
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⋊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—44no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C42—24no—
1177C42—24no—
1178C42—22no—
1179C42—24no—
1180C42—24no—
1181C42—24no—
1182C42—24no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42H(5,𝔽2)14yes—
1190C23—21no—
1191C23—21no—
1192C23—24no—
1193C23—24no—
1194C23—22no—
1195C23—24no—
1196C23—24no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—24no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—24no—
1206C23—24no—
1207C23—22no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—84no—
1223C23—82no—
1224C23—84no—
1225C23—82no—
1226C23—84no—
1227C23—88no—
1228C23—84no—
1229C23—84no—
1230C23—84no—
1231C23—84no—
1232C23—84no—
1233C23—88no—
1234C23—164no—
1235C23—162no—
1236C23—162no—
1237C23—162no—
1238C23—162no—
1239C23—164no—
1240C23#58512yes—
1241C23C2611yescharacteristic
1242Q8—44no—
1243Q8—84no—
1244Q8—162no—
1245D4—48no—
1246D4—44no—
1247D4—84no—
1248D4—84no—
1249D4—84no—
1250D4—84no—
1251D4—88no—
1252D4—88no—
1253D4—88no—
1254D4—88no—
1255D4—88no—
1256D4—84no—
1257D4—88no—
1258D4—88no—
1259D4—88no—
1260D4—88no—
1261D4—164no—
1262D4—164no—
1263D4—164no—
1264D4—164no—
1265D4—164no—
1266D4—164no—
1267D4—162no—
1268D4—164no—
1269D4—164no—
1270D4—164no—
1271C2×C4—28no—
1272C2×C4—22no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
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—48no—
1314C2×C4—48no—
1315C2×C4—48no—
1316C2×C4—88no—
1317C2×C4—84no—
1318C2×C4—84no—
1319C2×C4—88no—
1320C2×C4—162no—
1321C2×C4—164no—
1322C2×C4—162no—
1323C2×C4—164no—
1324C2×C4C2×H(5,𝔽2)12yes—
1325C2×C4C2×H(5,𝔽2)12yes—
1326C2×C4C2×H(5,𝔽2)14yes—
1327C2×C4C2×H(5,𝔽2)14yes—
1328C22—24no—
1329C22—22no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—44no—
1335C22—42no—
1336C22—44no—
1337C22—44no—
1338C22—44no—
1339C22—42no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22—44no—
1348C22—42no—
1349C22—44no—
1350C22—42no—
1351C22—44no—
1352C22—42no—
1353C22—42no—
1354C22—42no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—164no—
1362C22—168no—
1363C22—164no—
1364C22—168no—
1365C22C22×H(5,𝔽2)11yescharacteristic
1366C22C22×H(5,𝔽2)11yescharacteristic
1367C22C2×#58511yescharacteristic
1368C22H(7,𝔽2)14yes—
1369C4—22no—
1370C4—22no—
1371C4—24no—
1372C4—24no—
1373C4—44no—
1374C4—44no—
1375C4—44no—
1376C4—44no—
1377C4—44no—
1378C4—42no—
1379C4—42no—
1380C4—44no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—44no—
1386C2—42no—
1387C2—82no—
1388C2—82no—
1389C2—84no—
1390C2—84no—
1391C2—82no—
1392C2#6281811yescharacteristic
1393C2#6287412yes—
1394C2#6304212yes—
1395C2#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. #58934C2semidirect
2. #58901C2semidirect
3. #57151C2semidirect
4. #57149C2semidirect
5. #56348C2semidirect
6. #56346C2semidirect
7. #54698C2semidirect
8. #53988C2semidirect
9. #51903C2semidirect
10. #51895C2semidirect
11. #51869C2semidirect
12. #51778C2semidirect
13. #47563C2semidirect
14. #47195C2semidirect
15. #47026C2semidirect
16. #46605C2semidirect
17. #46532C2semidirect
18. #46324C2semidirect
19. #46279C2semidirect
20. #45980C2semidirect
21. #45968C2semidirect
22. #35272C2semidirect
23. #35210C2semidirect
24. C2×#562C22semidirect
25. C2×#560C22semidirect
26. C2×#551C22semidirect
28. C2×#535C22semidirect
30. C2×#529C22semidirect
31. C2×C4×#41C22semidirect
32. #2856C22semidirect
33. #2852C22semidirect
34. #2852C22semidirect
35. #2843C22semidirect
36. #2842C22semidirect
38. #2828C22semidirect
39. #2828C22semidirect
40. #2825C22semidirect
41. #2824C22semidirect
42. #2823C22semidirect
44. #2815C22semidirect
45. #2813C22semidirect
47. #2803C22semidirect
48. #2801C22semidirect
49. #2797C22semidirect
50. #2789C22semidirect
51. #2788C22semidirect
52. #2786C22semidirect
53. #2783C22semidirect
54. #2782C22semidirect
55. #2780C22semidirect
57. #2778C22semidirect
58. #2778C22semidirect
59. #2761C22semidirect
60. #2753C22semidirect
61. #2753C22semidirect
62. #2736C22semidirect
65. #2733C22semidirect
66. #2730C22semidirect
67. #2730C22semidirect
68. #2723C22semidirect
69. #2723C22semidirect
70. #2714C22semidirect
71. #2711C22semidirect
72. #2710C22semidirect
73. #2709C22semidirect
74. #2709C22semidirect
75. #2709C22semidirect
76. #2707C22semidirect
77. #2707C22semidirect
78. #2706C22semidirect
79. #2705C22semidirect
80. #2703C22semidirect
81. #2703C22semidirect
82. #2702C22semidirect
83. #2701C22semidirect
84. #2699C22semidirect
85. #2691C22semidirect
86. #2688C22semidirect
87. #2686C22semidirect
88. #2686C22semidirect
90. #2685C22semidirect
91. #2682C22semidirect
92. #2682C22semidirect
93. #2681C22semidirect
94. #2678C22semidirect
95. #2678C22semidirect
96. #2678C22semidirect
97. #2678C22semidirect
98. #2676C22semidirect
99. #2676C22semidirect
100. #2676C22semidirect
101. #2675C22semidirect
105. #2673C22semidirect
106. #2673C22semidirect
107. #2672C22semidirect
108. #2671C22semidirect
109. #2671C22semidirect
112. #2670C22semidirect
113. #2670C22semidirect
115. #2669C22semidirect
116. #2669C22semidirect
117. #2669C22semidirect
118. #2669C22semidirect
119. #2669C22semidirect
121. #2663C22semidirect
122. #2657C22semidirect
123. #2649C22semidirect
124. #2641C22semidirect
125. #2638C22semidirect
126. #2638C22semidirect
128. #2635C22semidirect
129. #2630C22semidirect
130. #2619C22semidirect
131. #2619C22semidirect
132. #2617C22semidirect
133. #2611C22semidirect
134. #2611C22semidirect
135. #2611C22semidirect
138. #2610C22semidirect
139. #2610C22semidirect
140. #2610C22semidirect
141. #2609C22semidirect
142. #2603C22semidirect
143. #2602C22semidirect
144. #2602C22semidirect
145. #2597C22semidirect
146. #2581C22semidirect
147. #2580C22semidirect
148. #2559C22semidirect
149. #2559C22semidirect
150. #2555C22semidirect
151. #2554C22semidirect
152. #2548C22semidirect
153. #2541C22semidirect
154. #2539C22semidirect
155. #2536C22semidirect
157. #2531C22semidirect
158. #2529C22semidirect
159. #2528C22semidirect
160. #2526C22semidirect
161. #2526C22semidirect
162. #2485C22semidirect
163. #2483C22semidirect
164. #2479C22semidirect
165. #2476C22semidirect
166. #2476C22semidirect
167. #2476C22semidirect
168. #2475C22semidirect
169. #2474C22semidirect
170. #2472C22semidirect
171. #2471C22semidirect
172. #2471C22semidirect
173. #2470C22semidirect
174. #2464C22semidirect
175. #2464C22semidirect
176. #2461C22semidirect
177. #2458C22semidirect
178. #2456C22semidirect
179. #2456C22semidirect
180. #2437C22semidirect
181. #2428C22semidirect
182. #2428C22semidirect
183. #2427C22semidirect
184. #2426C22semidirect
185. #2424C22semidirect
186. #2424C22semidirect
187. #2424C22semidirect
188. #2418C22semidirect
189. #2414C22semidirect
190. #2414C22semidirect
191. #2411C22semidirect
193. #2410C22semidirect
194. #2410C22semidirect
195. #2410C22semidirect
198. #2408C22semidirect
199. #2408C22semidirect
200. #2407C22semidirect
206. #2383C22semidirect
207. #2380C22semidirect
208. #2379C22semidirect
209. #2372C22semidirect
210. #2324C22semidirect
211. #2323C22semidirect
212. #2321C22semidirect
213. #2312C22semidirect
216. #2309C22semidirect
217. #2285C22semidirect
218. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#589342
#589012
#571512
#571492
#563482
#563462
#546982
#539882
#519032
#518952
#518692
#517782
#475632
#471952
#470262
#466052
#465322
#463242
#462792
#459802
#459682
#352722
#352102