Finite Group Databasebeta

← #9712244

Subgroups — #9712244

Order 512.

4748 conjugacy classes of subgroups.

The subgroup lattice has 1467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58600C213yesmaximal, complemented
2#56359C213yesmaximal, complemented
3#55606C213yesmaximal, complemented
4#55559C213yesmaximal, complemented
5#55244C211yesmaximal, characteristic, complemented
6#53877C213yesmaximal, complemented
7#53711C213yesmaximal, complemented
8#53304C211yesmaximal, characteristic, complemented
9#53255C211yesmaximal, characteristic, complemented
10#51119C213yesmaximal, complemented
11#48244C213yesmaximal, complemented
12#48144C213yesmaximal, complemented
13#47927C213yesmaximal, complemented
14#47336C213yesmaximal, complemented
15#46616C213yesmaximal, complemented
16#44352C213yesmaximal, complemented
17#43149C213yesmaximal, complemented
18#41310C213yesmaximal, complemented
19#40913C213yesmaximal, complemented
20#40061C213yesmaximal, complemented
21#39464C213yesmaximal, complemented
22#38660C213yesmaximal, complemented
23#38030C213yesmaximal, complemented
24C2×#560C2211yescharacteristic
25C2×#546C2213yes—
26C22×#127C2211yescharacteristic
27C22×#126C2211yescharacteristic
28#2855C2213yes—
29#2853C2213yescomplemented
30#2842C2211yescharacteristic
31#2837C2213yescomplemented
32#2829C2213yescomplemented
33#2829C2213yescomplemented
34#2828C2213yescomplemented
35#2828C2213yescomplemented
36#2827C2213yescomplemented
37#2827C2213yescomplemented
38#2813C2213yescomplemented
39#2810C2211yescharacteristic, complemented
40#2802C2213yescomplemented
41#2799C2213yescomplemented
42#2797C2213yescomplemented
43#2795C2213yescomplemented
44#2794C2213yescomplemented
45#2782C2213yescomplemented
46#2781C2213yescomplemented
47#2780C2213yescomplemented
48#2780C2213yescomplemented
49#2779C2213yescomplemented
50#2779C2213yescomplemented
51#2774C2213yescomplemented
52#2772C2213yescomplemented
53#2770C2213yescomplemented
54#2767C2213yescomplemented
55#2761C2213yescomplemented
56#2757C2213yescomplemented
57#2755C2213yescomplemented
58#2753C2213yescomplemented
59#2752C2213yescomplemented
60#2750C2213yescomplemented
61#2749C2213yescomplemented
62#2744C2213yes—
63#2743C2213yes—
64#2743C2213yescomplemented
65#2743C2213yescomplemented
66#2743C2213yescomplemented
67#2741C2213yescomplemented
68#2740C2213yescomplemented
69#2739C2213yes—
70#2735C2213yes—
71#2735C2213yes—
72#2730C2213yescomplemented
73#2727C2213yescomplemented
74#2727C2213yescomplemented
75#2718C2213yescomplemented
76#2718C2213yescomplemented
77#2717C2213yescomplemented
78#2715C2213yescomplemented
79#2715C2213yescomplemented
80#2715C2213yescomplemented
81#2714C2213yescomplemented
82#2711C2213yescomplemented
83#2710C2213yescomplemented
84#2709C2213yes—
85#2709C2213yes—
86#2709C2213yes—
87#2709C2213yes—
88#2708C2213yescomplemented
89#2707C2213yes—
90#2706C2213yescomplemented
91#2705C2213yescomplemented
92#2705C2213yescomplemented
93#2705C2213yescomplemented
94#2703C2213yescomplemented
95#2701C2213yescomplemented
96#2698C2213yes—
97#2698C2213yes—
98#2695C2213yescomplemented
99#2694C2213yescomplemented
100#2694C2213yescomplemented
101#2693C2213yescomplemented
102#2693C2213yescomplemented
103#2691C2213yescomplemented
104#2691C2213yescomplemented
105#2689C2213yes—
106#2688C2213yescomplemented
107#2688C2213yescomplemented
108#2685C2213yes—
109#2685C2213yes—
110#2685C2213yes—
111#2685C2213yes—
112#2682C2213yescomplemented
113#2682C2213yescomplemented
114#2681C2213yes—
115#2678C2213yes—
116#2673C2213yes—
117#2673C2213yes—
118#2673C2213yes—
119#2673C2213yes—
120#2673C2213yescomplemented
121#2672C2213yescomplemented
122#2672C2213yescomplemented
123#2671C2213yescomplemented
124#2668C2213yes—
125#2661C2213yescomplemented
126#2661C2213yescomplemented
127#2650C2213yescomplemented
128#2649C2213yescomplemented
129#2648C2213yescomplemented
130#2648C2213yescomplemented
131#2648C2213yescomplemented
132#2636C2213yescomplemented
133#2636C2213yescomplemented
134#2636C2213yescomplemented
135#2630C2213yescomplemented
136#2622C2213yes—
137#2618C2213yescomplemented
138#2613C2213yes—
139#2613C2213yes—
140#2610C2213yescomplemented
141#2602C2213yescomplemented
142#2601C2213yescomplemented
143#2598C2213yescomplemented
144#2597C2213yescomplemented
145#2591C2213yescomplemented
146#2590C2213yescomplemented
147#2587C2213yescomplemented
148#2578C2213yescomplemented
149#2573C2213yes—
150#2559C2213yescomplemented
151#2559C2213yescomplemented
152#2559C2213yescomplemented
153#2557C2213yescomplemented
154#2556C2213yescomplemented
155#2553C2213yescomplemented
156#2553C2213yescomplemented
157#2553C2213yescomplemented
158#2553C2213yescomplemented
159#2544C2213yes—
160#2544C2213yes—
161#2534C2213yes—
162#2534C2213yes—
163#2526C2213yes—
164#2526C2213yescomplemented
165#2526C2213yescomplemented
166#2523C2213yescomplemented
167#2521C2213yescomplemented
168#2518C2213yescomplemented
169#2518C2213yescomplemented
170#2515C2213yes—
171#2509C2213yescomplemented
172#2504C2213yescomplemented
173#2487C2213yescomplemented
174#2487C2213yescomplemented
175#2481C2213yescomplemented
176#2481C2213yescomplemented
177#2480C2213yes—
178#2480C2213yes—
179#2480C2213yes—
180#2480C2213yes—
181#2480C2213yes—
182#2479C2213yescomplemented
183#2471C2213yescomplemented
184#2471C2213yescomplemented
185#2470C2213yes—
186#2470C2213yescomplemented
187#2467C2213yescomplemented
188#2466C2213yes—
189#2466C2213yes—
190#2466C2213yescomplemented
191#2466C2213yescomplemented
192#2464C2213yescomplemented
193#2464C2213yescomplemented
194#2460C2213yescomplemented
195#2457C2213yescomplemented
196#2456C2213yescomplemented
197#2445C2213yes—
198#2445C2213yes—
199#2444C2213yes—
200#2444C2213yescomplemented
201#2444C2213yescomplemented
202#2443C2213yescomplemented
203#2435C2213yes—
204#2431C2213yes—
205#2431C2213yes—
206#2430C2213yescomplemented
207#2428C2213yes—
208#2428C2213yes—
209#2428C2213yescomplemented
210#2425C2213yescomplemented
211#2424C2213yes—
212#2422C2213yes—
213#2422C2213yescomplemented
214#2420C2213yescomplemented
215#2414C2213yescomplemented
216#2413C2213yescomplemented
217#2412C2213yes—
218#2410C2213yes—
219#2410C2213yes—
220#2408C2213yes—
221#2407C2213yescomplemented
222#2406C2213yescomplemented
223#2405C2213yes—
224#2405C2213yes—
225#2392C2213yescomplemented
226C2×#396C2211yescharacteristic
227#2377C2213yescomplemented
228#2374C2213yescomplemented
229#2364C2213yescomplemented
230#2361C2213yescomplemented
231#2353C2213yescomplemented
232#2343C2213yescomplemented
233#2342C2213yes—
234D4×C22⋊C4C2213yes—
235#2337C2213yescomplemented
236#2335C2213yescomplemented
237#2330C2213yescomplemented
238#2329C2213yescomplemented
239#2322C2213yescomplemented
240#2321C2213yes—
241#2308C2213yes—
242#2308C2213yes—
243C4×#123C2213yes—
244#2297C2213yescomplemented
245C22×#41C2313yes—
246C23×D4C2313yes—
247C23×D4C2313yes—
248#560—44no—
249#546—412no—
250C2×#127—44no—
251C2×#127C2311yescharacteristic
252C2×#127C2311yescharacteristic
253C2×#127C2313yes—
254C2×#127C2313yes—
255C2×#127C2311yescharacteristic
256C2×#126—44no—
257C2×#126C2311yescharacteristic
258C2×#126C2313yes—
259C2×#126C2311yescharacteristic
260C2×#126C2313yes—
261C2×#126C2311yescharacteristic
262C2×#126C2311yescharacteristic
263C2×#126C2313yes—
264C2×#126C2313yes—
265C2×#126C2313yes—
266C2×#126C2313yes—
267C2×#125C2313yes—
268C2×#124C2313yes—
269C2×#124C2313yes—
270C2×#124C2313yes—
271C2×#123C2313yes—
272C2×#123C2313yes—
273C2×#123C2313yes—
274C2×#123C2313yes—
275C2×#123C2313yes—
276C2×#123C2313yes—
277C2×#123C2313yes—
278C2×#123C2313yes—
279C2×#123C2313yes—
280C2×#123C2313yes—
281C2×#123C2313yes—
282C2×#123C2313yes—
283C2×#123C2313yes—
284C2×C22⋊Q8C2313yes—
285C2×C22⋊Q8C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2313yes—
290C2×#121C2313yes—
291C2×#121C2313yes—
292C2×#121C2313yes—
293C2×#121C2313yes—
294C2×#121C2313yes—
295C2×#121C2313yes—
296C2×#121C2313yes—
297C2×#121C2313yes—
298C2×#121C2313yes—
299C2×#120C2313yes—
300C2×#120C2313yes—
301C2×#120C2313yes—
302C2×#120C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×#117C2313yes—
312C2×#117C2313yes—
313C22×C4⋊C4C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C22⋊C4C2313yes—
316C22×C22⋊C4C2313yes—
317C22×C22⋊C4C2313yes—
318C22×C22⋊C4C2313yes—
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#400C2313yes—
329#400C2313yes—
330#400C2313yes—
331#400C2313yes—
332#400C2313yes—
333#400C2313yes—
334#400C2313yes—
335#400C2313yes—
336#400C2313yes—
337#400C2313yes—
338#400C2313yes—
339#399C2313yes—
340#399C2313yes—
341#399C2313yes—
342#399C2313yes—
343#399C2313yes—
344#399C2311yescharacteristic
345#399C2313yes—
346#399C2313yes—
347#399C2313yes—
348#399C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#397C2313yes—
381#397C2313yes—
382#397C2313yes—
383#397C2313yes—
384#397C2313yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#396C2313yes—
395#396C2313yes—
396#396C2311yescharacteristic
397#396C2313yes—
398#396C2311yescharacteristic
399#396C2313yes—
400#396C2313yes—
401#396C2313yes—
402#396C2313yes—
403#396C2313yes—
404#396C2313yes—
405#396C2311yescharacteristic
406#396C2311yescharacteristic
407#396C2313yes—
408#396C2313yes—
409#395C2313yes—
410#395C2313yes—
411#395C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2313yes—
417#394C2313yes—
418#394C2313yes—
419#394C2313yes—
420#394C2313yes—
421#394C2313yes—
422#394C2313yes—
423#394C2313yes—
424#394C2313yes—
425#394C2313yes—
426#394C2313yes—
427#394C2313yes—
428#394C2313yes—
429#394C2313yes—
430#394C2313yes—
431#394C2313yes—
432#394C2313yes—
433#394C2313yes—
434#394C2313yes—
435#394C2313yes—
436#394C2313yes—
437#394C2313yes—
438#394C2313yes—
439#394C2313yes—
440#394C2313yes—
441#394C2313yes—
442#394C2313yes—
443#394C2313yes—
444#394C2313yes—
445#394C2313yes—
446#394C2313yes—
447#394C2313yes—
448#394C2313yes—
449#394C2313yes—
450#394C2313yes—
451#394C2313yes—
452#394C2313yes—
453#394C2313yes—
454#394C2313yes—
455#394C2313yes—
456#394C2313yes—
457#394C2313yes—
458#394C2313yes—
459#394C2313yes—
460#393C2313yes—
461#392C2313yes—
462#392C2313yes—
463#392C2313yes—
464#392C2313yes—
465#392C2313yes—
466#392C2313yes—
467#392C2313yes—
468#392C2313yes—
469#392C2313yes—
470#392C2313yes—
471#392C2313yes—
472#392C2313yes—
473#392C2313yes—
474#392C2313yes—
475#392C2313yes—
476#392C2313yes—
477#392C2313yes—
478#392C2313yes—
479#391C2313yes—
480#391C2313yes—
481#391C2313yes—
482#391C2313yes—
483#391C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2313yes—
490#390C2313yes—
491#390C2313yes—
492#390C2313yes—
493#390C2313yes—
494#390C2313yes—
495#390C2313yes—
496#390C2313yes—
497#390C2313yes—
498#390C2313yes—
499#390C2313yes—
500#390C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2313yes—
517#389C2313yes—
518#389C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2313yes—
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2313yes—
533#388C2313yes—
534#388C2313yes—
535#388C2313yes—
536#388C2313yes—
537#388C2313yes—
538#388C2313yes—
539#388C2313yes—
540#388C2313yes—
541#388C2313yes—
542#388C2313yes—
543#388C2313yes—
544#388C2313yes—
545#388C2313yes—
546#388C2313yes—
547#388C2313yes—
548#388C2313yes—
549#388C2313yes—
550#388C2313yes—
551#388C2313yes—
552#388C2313yes—
553#388C2313yes—
554#388C2313yes—
555#388C2313yes—
556#388C2313yes—
557#388C2313yes—
558#388C2313yes—
559#388C2313yes—
560#388C2313yes—
561#388C2313yes—
562#388C2313yes—
563#387C2313yes—
564#387C2313yes—
565#387C2313yes—
566#387C2313yes—
567#387C2313yes—
568#387C2313yes—
569#387C2313yes—
570#387C2313yes—
571#387C2313yes—
572#387C2313yes—
573#387C2313yes—
574#387C2313yes—
575#387C2313yes—
576#387C2313yes—
577#387C2313yes—
578#387C2313yes—
579#387C2313yes—
580#387C2313yes—
581#387C2313yes—
582#387C2313yes—
583#387C2313yes—
584#387C2313yes—
585#387C2313yes—
586#387C2313yes—
587#387C2313yes—
588#387C2313yes—
589#387C2313yes—
590#387C2313yes—
591#387C2313yes—
592#387C2313yes—
593#386C2313yes—
594#386C2313yes—
595#386C2313yes—
596#386C2313yes—
597#386C2313yes—
598#386C2313yes—
599#386C2313yes—
600#386C2313yes—
601#386C2313yes—
602#386C2313yes—
603#386C2313yes—
604#386C2313yes—
605#386C2313yes—
606#386C2313yes—
607#386C2313yes—
608#386C2313yes—
609#386C2313yes—
610#386C2313yes—
611#386C2313yes—
612#386C2313yes—
613#386C2313yes—
614#386C2313yes—
615#386C2313yes—
616#386C2313yes—
617#386C2313yes—
618#386C2313yes—
619#386C2313yes—
620#386C2313yes—
621#386C2313yes—
622#386C2313yes—
623#386C2313yes—
624#386C2313yes—
625#386C2313yes—
626#386C2313yes—
627#386C2313yes—
628#386C2313yes—
629#386C2313yes—
630#386C2313yes—
631#386C2313yes—
632#386C2313yes—
633#386C2313yes—
634#386C2313yes—
635#386C2313yes—
636#386C2313yes—
637#386C2313yes—
638#386C2313yes—
639#386C2313yes—
640#385C2313yes—
641#385C2313yes—
642#385C2313yes—
643#385C2313yes—
644#385C2313yes—
645#385C2313yes—
646#385C2313yes—
647#385C2313yes—
648#385C2313yes—
649#385C2313yes—
650#385C2313yes—
651#385C2313yes—
652#385C2313yes—
653#385C2313yes—
654#385C2313yes—
655#385C2313yes—
656#385C2313yes—
657#385C2313yes—
658#385C2313yes—
659#385C2313yes—
660#385C2313yes—
661#385C2313yes—
662#385C2313yes—
663#385C2313yes—
664#385C2313yes—
665#385C2313yes—
666#385C2313yes—
667#384C2313yes—
668#383C2313yes—
669#383C2313yes—
670#382C2313yes—
671#382C2313yes—
672#382C2313yes—
673#382C2313yes—
674#381C2313yes—
675#381C2313yes—
676#381C2313yes—
677#381C2313yes—
678#381C2313yes—
679#381C2313yes—
680#381C2313yes—
681#381C2313yes—
682#380C2313yes—
683#380C2313yes—
684#380C2313yes—
685#380C2313yes—
686#380C2313yes—
687#380C2313yes—
688#380C2313yes—
689#380C2313yes—
690#380C2313yes—
691#380C2313yes—
692#380C2313yes—
693#380C2313yes—
694#379C2313yes—
695#379C2313yes—
696#379C2313yes—
697#379C2313yes—
698#379C2313yes—
699#379C2313yes—
700#379C2313yes—
701#379C2313yes—
702C4×C4⋊C4C2313yes—
703C4×C4⋊C4C2313yes—
704C4×C4⋊C4C2313yes—
705C4×C4⋊C4C2313yes—
706C4×C22⋊C4C2313yes—
707C4×C22⋊C4C2313yes—
708C4×C22⋊C4C2313yes—
709C4×C22⋊C4C2313yes—
710C4×C22⋊C4C2313yes—
711C4×C22⋊C4C2313yes—
712C4×C22⋊C4C2313yes—
713C4×C22⋊C4C2313yes—
714C4×C22⋊C4C2313yes—
715C4×C22⋊C4C2313yes—
716C4×C22⋊C4C2313yes—
717C4×C22⋊C4C2313yes—
718C4×C22⋊C4C2313yes—
719C4×C22⋊C4C2313yes—
720C4×C22⋊C4C2313yes—
721#376C2313yes—
722C2×#95C2313yes—
723C2×#95C2311yescharacteristic
724C25C2413yes—
725C25C2411yescharacteristic
726C2×#41—46no—
727C2×#41—46no—
728C2×#41—83no—
729C22×Q8C2413yes—
730C22×D4—212no—
731C22×D4—46no—
732C22×D4—46no—
733C22×D4—46no—
734C22×D4—83no—
735C22×D4—83no—
736C22×D4C2413yes—
737C22×D4C2413yes—
738C22×D4C2413yes—
739C22×D4C2413yes—
740C22×D4C2413yes—
741C22×D4C2413yes—
742C22×D4C2413yes—
743C22×D4C2413yes—
744C22×D4C2413yes—
745C22×D4C2413yes—
746C22×D4C2413yes—
747C22×D4C2413yes—
748C22×D4C2413yes—
749C22×D4C2413yes—
750C22×D4C2413yes—
751C22×D4C2413yes—
752C22×D4C2413yes—
753C22×D4C2413yes—
754C23×C4C2413yes—
755C23×C4C2413yes—
756C23×C4C2413yes—
757C23×C4C2413yes—
758C23×C4C2413yes—
759C23×C4C2413yes—
760C23×C4C2413yes—
761C23×C4C2413yes—
762C23×C4C2413yes—
763C23×C4C2413yes—
764C23×C4C2413yes—
765C23×C4C2413yes—
766#127—46no—
767#127—46no—
768#127—42no—
769#127—42no—
770#127—42no—
771#126—46no—
772#126—42no—
773#126—46no—
774#126—42no—
775#126—42no—
776#126—42no—
777#126—83no—
778#126—83no—
779#126—83no—
780#126—83no—
781#125—46no—
782#124—46no—
783#124—46no—
784#124—83no—
785#123—46no—
786#123—46no—
787#123—46no—
788#123—46no—
789#123—46no—
790#123—46no—
791#123—46no—
792#123—83no—
793#123—83no—
794#123—83no—
795#123—83no—
796#123—83no—
797#123—83no—
798C22⋊Q8—46no—
799C22⋊Q8—46no—
800#121—46no—
801#121—46no—
802#121—46no—
803#121—46no—
804#121—46no—
805#121—46no—
806#121—46no—
807#121—46no—
808#121—83no—
809#121—83no—
810#121—83no—
811#121—83no—
812#121—83no—
813#120—212no—
814#120—46no—
815#120—83no—
816#120—83no—
817C4×D4—46no—
818C4×D4—46no—
819C4×D4—46no—
820C4×D4—83no—
821C4×D4—83no—
822C4×D4—83no—
823C4×D4—83no—
824C4×D4—83no—
825#117—46no—
826#117—83no—
827C2×C4⋊C4—46no—
828C2×C4⋊C4—83no—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2413yes—
831C2×C4⋊C4C2413yes—
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2413yes—
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2413yes—
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2413yes—
870C2×C4⋊C4C2413yes—
871C2×C4⋊C4C2413yes—
872C2×C22⋊C4—212no—
873C2×C22⋊C4—46no—
874C2×C22⋊C4—83no—
875C2×C22⋊C4—83no—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2413yes—
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2413yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2413yes—
912C2×C22⋊C4C2413yes—
913C2×C22⋊C4C2413yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2413yes—
917C2×C22⋊C4C2413yes—
918C2×C22⋊C4C2413yes—
919C2×C22⋊C4C2413yes—
920C2×C22⋊C4C2413yes—
921C2×C22⋊C4C2413yes—
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2413yes—
924C2×C22⋊C4C2413yes—
925C2×C22⋊C4C2413yes—
926C2×C22⋊C4C2413yes—
927C2×C22⋊C4C2413yes—
928C2×C22⋊C4C2413yes—
929C2×C22⋊C4C2413yes—
930C2×C22⋊C4C2413yes—
931C2×C22⋊C4C2413yes—
932C2×C22⋊C4C2413yes—
933C2×C22⋊C4C2413yes—
934C2×C22⋊C4C2413yes—
935C2×C22⋊C4C2413yes—
936C2×C22⋊C4C2413yes—
937C2×C22⋊C4C2413yes—
938C2×C22⋊C4C2413yes—
939C2×C22⋊C4C2413yes—
940C2×C22⋊C4C2413yes—
941C2×C22⋊C4C2413yes—
942C2×C22⋊C4C2413yes—
943C2×C22⋊C4C2413yes—
944C2×C22⋊C4C2413yes—
945C2×C22⋊C4C2413yes—
946C2×C22⋊C4C2413yes—
947C2×C22⋊C4C2413yes—
948C2×C42—42no—
949C2×C42—42no—
950C2×C42C2413yes—
951C2×C42C2413yes—
952C2×C42C2413yes—
953C2×C42C2413yes—
954C2×C42C2413yes—
955C2×C42C2413yes—
956C2×C42C2413yes—
957C2×C42C2413yes—
958C2×C42C2413yes—
959C2×C42C2413yes—
960C2×C42C2411yescharacteristic
961C2×C42C2413yes—
962C2×C42C2411yescharacteristic
963C2×C42C2413yes—
964C2×C42C2411yescharacteristic
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2411yescharacteristic
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2413yes—
979#95C2413yes—
980#95C2413yes—
981#95C2413yes—
982#95C2413yes—
983#95C2413yes—
984#95C2413yes—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2413yes—
993#95C2413yes—
994#95C2413yes—
995#95C2413yes—
996#95C2413yes—
997#95C2413yes—
998#95C2413yes—
999#95C2413yes—
1000#95C2413yes—
1001#95C2413yes—
1002#95C2413yes—
1003#95C2413yes—
1004#95C2413yes—
1005#95C2413yes—
1006#95C2413yes—
1007#95C2413yes—
1008#95C2413yes—
1009#95C2413yes—
1010#95C2413yes—
1011#95C2413yes—
1012#95C2413yes—
1013#95C2411yescharacteristic
1014#95C2413yes—
1015#95C2413yes—
1016#95C2413yes—
1017#95C2413yes—
1018#95C2413yes—
1019#95C2413yes—
1020#95C2413yes—
1021#95C2413yes—
1022#95C2413yes—
1023C24—26no—
1024C24—43no—
1025C24—43no—
1026C24—43no—
1027C24—43no—
1028C24—43no—
1029C24—43no—
1030C24—43no—
1031C24—43no—
1032C24H(5,𝔽2)14yes—
1033C24C2513yes—
1034C24C2513yes—
1035C24C2513yes—
1036C24C2511yescharacteristic
1037C24C2511yescharacteristic
1038C24C2511yescharacteristic
1039#41—824no—
1040C2×Q8—26no—
1041C2×Q8—43no—
1042C2×Q8—43no—
1043C2×D4—26no—
1044C2×D4—26no—
1045C2×D4—26no—
1046C2×D4—26no—
1047C2×D4—26no—
1048C2×D4—26no—
1049C2×D4—26no—
1050C2×D4—26no—
1051C2×D4—26no—
1052C2×D4—26no—
1053C2×D4—26no—
1054C2×D4—43no—
1055C2×D4—43no—
1056C2×D4—43no—
1057C2×D4—43no—
1058C2×D4—43no—
1059C2×D4—43no—
1060C2×D4—43no—
1061C2×D4—43no—
1062C2×D4—43no—
1063C2×D4—43no—
1064C2×D4—43no—
1065C2×D4—43no—
1066C2×D4—43no—
1067C2×D4—43no—
1068C2×D4—43no—
1069C2×D4—43no—
1070C2×D4—43no—
1071C2×D4—43no—
1072C2×D4—43no—
1073C2×D4—43no—
1074C2×D4—43no—
1075C2×D4—43no—
1076C2×D4—43no—
1077C2×D4—43no—
1078C2×D4—43no—
1079C2×D4—43no—
1080C2×D4—43no—
1081C2×D4—43no—
1082C2×D4—43no—
1083C2×D4—43no—
1084C2×D4—43no—
1085C2×D4—43no—
1086C2×D4—43no—
1087C2×D4—43no—
1088C2×D4—43no—
1089C2×D4—43no—
1090C2×D4—43no—
1091C2×D4—43no—
1092C2×D4—43no—
1093C2×D4—43no—
1094C2×D4—43no—
1095C2×D4—43no—
1096C2×D4—43no—
1097C2×D4—824no—
1098C2×D4—824no—
1099C22×C4—26no—
1100C22×C4—26no—
1101C22×C4—26no—
1102C22×C4—26no—
1103C22×C4—26no—
1104C22×C4—43no—
1105C22×C4—43no—
1106C22×C4—43no—
1107C22×C4—43no—
1108C22×C4—43no—
1109C22×C4—43no—
1110C22×C4—43no—
1111C22×C4—43no—
1112C22×C4—43no—
1113C22×C4—43no—
1114C22×C4—43no—
1115C22×C4—43no—
1116C22×C4—43no—
1117C22×C4—43no—
1118C22×C4—43no—
1119C22×C4—43no—
1120C22×C4—43no—
1121C22×C4—43no—
1122C22×C4—43no—
1123C22×C4—43no—
1124C22×C4—43no—
1125C22×C4—43no—
1126C22×C4—43no—
1127C22×C4—43no—
1128C22×C4—43no—
1129C22×C4—43no—
1130C22×C4—43no—
1131C22×C4—43no—
1132C22×C4—43no—
1133C22×C4—43no—
1134C22×C4—43no—
1135C22×C4C2513yes—
1136C22×C4C2513yes—
1137C22×C4C2513yes—
1138C22×C4C2513yes—
1139C22×C4C2513yes—
1140C22×C4C2513yes—
1141C22×C4C2513yes—
1142C22×C4C2513yes—
1143C22×C4C2513yes—
1144C22×C4C2513yes—
1145C22×C4C2513yes—
1146C22×C4C2513yes—
1147C22×C4C2513yes—
1148C22×C4C2513yes—
1149C22×C4C2513yes—
1150C22×C4C2513yes—
1151C22×C4C2513yes—
1152C4⋊C4—26no—
1153C4⋊C4—26no—
1154C4⋊C4—26no—
1155C4⋊C4—26no—
1156C4⋊C4—26no—
1157C4⋊C4—43no—
1158C4⋊C4—43no—
1159C4⋊C4—43no—
1160C4⋊C4—43no—
1161C4⋊C4—43no—
1162C4⋊C4—43no—
1163C4⋊C4—43no—
1164C4⋊C4—43no—
1165C4⋊C4—43no—
1166C4⋊C4—43no—
1167C4⋊C4—43no—
1168C4⋊C4—43no—
1169C4⋊C4—43no—
1170C4⋊C4—43no—
1171C4⋊C4—43no—
1172C4⋊C4—43no—
1173C4⋊C4—43no—
1174C4⋊C4—43no—
1175C4⋊C4—43no—
1176C4⋊C4—43no—
1177C4⋊C4—43no—
1178C4⋊C4—43no—
1179C4⋊C4—43no—
1180C4⋊C4—43no—
1181C4⋊C4—43no—
1182C4⋊C4—43no—
1183C4⋊C4—43no—
1184C4⋊C4—43no—
1185C4⋊C4—43no—
1186C4⋊C4—43no—
1187C4⋊C4—43no—
1188C4⋊C4—43no—
1189C4⋊C4—43no—
1190C4⋊C4—43no—
1191C4⋊C4—43no—
1192C4⋊C4—43no—
1193C4⋊C4—43no—
1194C4⋊C4—43no—
1195C22⋊C4—26no—
1196C22⋊C4—26no—
1197C22⋊C4—26no—
1198C22⋊C4—26no—
1199C22⋊C4—26no—
1200C22⋊C4—26no—
1201C22⋊C4—26no—
1202C22⋊C4—26no—
1203C22⋊C4—26no—
1204C22⋊C4—43no—
1205C22⋊C4—43no—
1206C22⋊C4—43no—
1207C22⋊C4—43no—
1208C22⋊C4—43no—
1209C22⋊C4—43no—
1210C22⋊C4—43no—
1211C22⋊C4—43no—
1212C22⋊C4—43no—
1213C22⋊C4—43no—
1214C22⋊C4—43no—
1215C22⋊C4—43no—
1216C22⋊C4—43no—
1217C22⋊C4—43no—
1218C22⋊C4—43no—
1219C22⋊C4—43no—
1220C22⋊C4—43no—
1221C22⋊C4—43no—
1222C22⋊C4—43no—
1223C22⋊C4—43no—
1224C22⋊C4—43no—
1225C22⋊C4—43no—
1226C22⋊C4—43no—
1227C22⋊C4—43no—
1228C22⋊C4—43no—
1229C22⋊C4—43no—
1230C22⋊C4—43no—
1231C22⋊C4—43no—
1232C22⋊C4—43no—
1233C22⋊C4—43no—
1234C22⋊C4—43no—
1235C22⋊C4—43no—
1236C22⋊C4—43no—
1237C22⋊C4—43no—
1238C22⋊C4—43no—
1239C22⋊C4—43no—
1240C22⋊C4—43no—
1241C22⋊C4—43no—
1242C22⋊C4—43no—
1243C22⋊C4—43no—
1244C22⋊C4—43no—
1245C22⋊C4—43no—
1246C22⋊C4—43no—
1247C22⋊C4—43no—
1248C22⋊C4—43no—
1249C22⋊C4—43no—
1250C22⋊C4—43no—
1251C22⋊C4—43no—
1252C22⋊C4—43no—
1253C22⋊C4—43no—
1254C22⋊C4—43no—
1255C22⋊C4—43no—
1256C22⋊C4—43no—
1257C22⋊C4—43no—
1258C22⋊C4—43no—
1259C22⋊C4—43no—
1260C22⋊C4—43no—
1261C22⋊C4—43no—
1262C22⋊C4—43no—
1263C22⋊C4—43no—
1264C22⋊C4—43no—
1265C22⋊C4—43no—
1266C22⋊C4—43no—
1267C42—26no—
1268C42—43no—
1269C42—41no—
1270C42—43no—
1271C42—41no—
1272C42—43no—
1273C42—43no—
1274C42—43no—
1275C42—43no—
1276C42—43no—
1277C42—43no—
1278C42—43no—
1279C42—43no—
1280C42—43no—
1281C42—41no—
1282C23—23no—
1283C23—23no—
1284C23—23no—
1285C23—23no—
1286C23—23no—
1287C23—23no—
1288C23—23no—
1289C23—23no—
1290C23—23no—
1291C23—23no—
1292C23—23no—
1293C23—23no—
1294C23—23no—
1295C23—23no—
1296C23—23no—
1297C23—23no—
1298C23—23no—
1299C23—23no—
1300C23—23no—
1301C23—23no—
1302C23—23no—
1303C23—23no—
1304C23—23no—
1305C23—23no—
1306C23—23no—
1307C23—23no—
1308C23—23no—
1309C23—412no—
1310C23—412no—
1311C23—86no—
1312C23—86no—
1313C23—161no—
1314C23—163no—
1315C23—163no—
1316C23—163no—
1317C23—163no—
1318C23—163no—
1319C23C2×H(5,𝔽2)12yes—
1320C23C2×H(5,𝔽2)12yes—
1321C23C2×H(5,𝔽2)12yes—
1322C23C2611yescharacteristic
1323Q8—86no—
1324D4—412no—
1325D4—412no—
1326D4—86no—
1327D4—86no—
1328D4—86no—
1329D4—86no—
1330D4—86no—
1331D4—86no—
1332D4—86no—
1333D4—86no—
1334D4—86no—
1335D4—86no—
1336D4—86no—
1337D4—86no—
1338D4—86no—
1339D4—163no—
1340D4—163no—
1341D4—163no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—23no—
1345C2×C4—23no—
1346C2×C4—23no—
1347C2×C4—23no—
1348C2×C4—23no—
1349C2×C4—23no—
1350C2×C4—23no—
1351C2×C4—23no—
1352C2×C4—23no—
1353C2×C4—23no—
1354C2×C4—23no—
1355C2×C4—23no—
1356C2×C4—23no—
1357C2×C4—23no—
1358C2×C4—23no—
1359C2×C4—23no—
1360C2×C4—23no—
1361C2×C4—23no—
1362C2×C4—23no—
1363C2×C4—23no—
1364C2×C4—23no—
1365C2×C4—23no—
1366C2×C4—23no—
1367C2×C4—23no—
1368C2×C4—23no—
1369C2×C4—23no—
1370C2×C4—23no—
1371C2×C4—23no—
1372C2×C4—23no—
1373C2×C4—23no—
1374C2×C4—23no—
1375C2×C4—23no—
1376C2×C4—23no—
1377C2×C4—23no—
1378C2×C4—23no—
1379C2×C4—23no—
1380C2×C4—23no—
1381C2×C4—23no—
1382C2×C4—23no—
1383C2×C4—23no—
1384C2×C4—23no—
1385C2×C4—23no—
1386C2×C4—23no—
1387C2×C4—23no—
1388C2×C4—23no—
1389C2×C4—23no—
1390C2×C4—23no—
1391C2×C4—23no—
1392C2×C4—412no—
1393C2×C4—412no—
1394C2×C4—86no—
1395C2×C4—86no—
1396C2×C4—86no—
1397C2×C4—86no—
1398C2×C4—86no—
1399C2×C4—163no—
1400C2×C4—163no—
1401C2×C4—163no—
1402C2×C4—163no—
1403C2×C4—163no—
1404C2×C4#58516yes—
1405C22—26no—
1406C22—26no—
1407C22—26no—
1408C22—41no—
1409C22—41no—
1410C22—41no—
1411C22—43no—
1412C22—43no—
1413C22—43no—
1414C22—43no—
1415C22—43no—
1416C22—43no—
1417C22—43no—
1418C22—43no—
1419C22—43no—
1420C22—43no—
1421C22—43no—
1422C22—43no—
1423C22—43no—
1424C22—43no—
1425C22—43no—
1426C22—43no—
1427C22—43no—
1428C22—43no—
1429C22—43no—
1430C22—43no—
1431C22—43no—
1432C22—43no—
1433C22—43no—
1434C22—43no—
1435C22—164no—
1436C22—1612no—
1437C22C22×H(5,𝔽2)11yescharacteristic
1438C22C2×#58513yes—
1439C22H(7,𝔽2)13yes—
1440C4—26no—
1441C4—43no—
1442C4—43no—
1443C4—43no—
1444C4—43no—
1445C4—43no—
1446C4—43no—
1447C4—43no—
1448C4—43no—
1449C4—43no—
1450C4—43no—
1451C4—43no—
1452C4—43no—
1453C4—43no—
1454C4—43no—
1455C4—43no—
1456C4—43no—
1457C2—42no—
1458C2—42no—
1459C2—42no—
1460C2—83no—
1461C2—83no—
1462C2—83no—
1463C2#6288313yes—
1464C2#6290013yes—
1465C2#6303611yescharacteristic
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. #58600C2semidirect
2. #56359C2semidirect
3. #55606C2semidirect
4. #55559C2semidirect
5. #55244C2semidirect
6. #53877C2semidirect
7. #53711C2semidirect
8. #53304C2semidirect
9. #53255C2semidirect
10. #51119C2semidirect
11. #48244C2semidirect
12. #48144C2semidirect
13. #47927C2semidirect
14. #47336C2semidirect
15. #46616C2semidirect
16. #44352C2semidirect
17. #43149C2semidirect
18. #41310C2semidirect
19. #40913C2semidirect
20. #40061C2semidirect
21. #39464C2semidirect
22. #38660C2semidirect
23. #38030C2semidirect
29. #2853C22semidirect
31. #2837C22semidirect
32. #2829C22semidirect
33. #2829C22semidirect
34. #2828C22semidirect
35. #2828C22semidirect
36. #2827C22semidirect
37. #2827C22semidirect
38. #2813C22semidirect
39. #2810C22semidirect
40. #2802C22semidirect
41. #2799C22semidirect
42. #2797C22semidirect
43. #2795C22semidirect
44. #2794C22semidirect
45. #2782C22semidirect
46. #2781C22semidirect
47. #2780C22semidirect
48. #2780C22semidirect
49. #2779C22semidirect
50. #2779C22semidirect
51. #2774C22semidirect
52. #2772C22semidirect
53. #2770C22semidirect
54. #2767C22semidirect
55. #2761C22semidirect
56. #2757C22semidirect
57. #2755C22semidirect
58. #2753C22semidirect
59. #2752C22semidirect
60. #2750C22semidirect
61. #2749C22semidirect
64. #2743C22semidirect
65. #2743C22semidirect
66. #2743C22semidirect
67. #2741C22semidirect
68. #2740C22semidirect
72. #2730C22semidirect
73. #2727C22semidirect
74. #2727C22semidirect
75. #2718C22semidirect
76. #2718C22semidirect
77. #2717C22semidirect
78. #2715C22semidirect
79. #2715C22semidirect
80. #2715C22semidirect
81. #2714C22semidirect
82. #2711C22semidirect
83. #2710C22semidirect
88. #2708C22semidirect
90. #2706C22semidirect
91. #2705C22semidirect
92. #2705C22semidirect
93. #2705C22semidirect
94. #2703C22semidirect
95. #2701C22semidirect
98. #2695C22semidirect
99. #2694C22semidirect
100. #2694C22semidirect
101. #2693C22semidirect
102. #2693C22semidirect
103. #2691C22semidirect
104. #2691C22semidirect
106. #2688C22semidirect
107. #2688C22semidirect
112. #2682C22semidirect
113. #2682C22semidirect
120. #2673C22semidirect
121. #2672C22semidirect
122. #2672C22semidirect
123. #2671C22semidirect
125. #2661C22semidirect
126. #2661C22semidirect
127. #2650C22semidirect
128. #2649C22semidirect
129. #2648C22semidirect
130. #2648C22semidirect
131. #2648C22semidirect
132. #2636C22semidirect
133. #2636C22semidirect
134. #2636C22semidirect
135. #2630C22semidirect
137. #2618C22semidirect
140. #2610C22semidirect
141. #2602C22semidirect
142. #2601C22semidirect
143. #2598C22semidirect
144. #2597C22semidirect
145. #2591C22semidirect
146. #2590C22semidirect
147. #2587C22semidirect
148. #2578C22semidirect
150. #2559C22semidirect
151. #2559C22semidirect
152. #2559C22semidirect
153. #2557C22semidirect
154. #2556C22semidirect
155. #2553C22semidirect
156. #2553C22semidirect
157. #2553C22semidirect
158. #2553C22semidirect
164. #2526C22semidirect
165. #2526C22semidirect
166. #2523C22semidirect
167. #2521C22semidirect
168. #2518C22semidirect
169. #2518C22semidirect
171. #2509C22semidirect
172. #2504C22semidirect
173. #2487C22semidirect
174. #2487C22semidirect
175. #2481C22semidirect
176. #2481C22semidirect
182. #2479C22semidirect
183. #2471C22semidirect
184. #2471C22semidirect
186. #2470C22semidirect
187. #2467C22semidirect
190. #2466C22semidirect
191. #2466C22semidirect
192. #2464C22semidirect
193. #2464C22semidirect
194. #2460C22semidirect
195. #2457C22semidirect
196. #2456C22semidirect
200. #2444C22semidirect
201. #2444C22semidirect
202. #2443C22semidirect
206. #2430C22semidirect
209. #2428C22semidirect
210. #2425C22semidirect
213. #2422C22semidirect
214. #2420C22semidirect
215. #2414C22semidirect
216. #2413C22semidirect
221. #2407C22semidirect
222. #2406C22semidirect
225. #2392C22semidirect
227. #2377C22semidirect
228. #2374C22semidirect
229. #2364C22semidirect
230. #2361C22semidirect
231. #2353C22semidirect
232. #2343C22semidirect
235. #2337C22semidirect
236. #2335C22semidirect
237. #2330C22semidirect
238. #2329C22semidirect
239. #2322C22semidirect
244. #2297C22semidirect

Maximal subgroups

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

subgroupindex
#586002
#563592
#556062
#555592
#552442
#538772
#537112
#533042
#532552
#511192
#482442
#481442
#479272
#473362
#466162
#443522
#431492
#413102
#409132
#400612
#394642
#386602
#380302