Finite Group Databasebeta

← #9058624

Subgroups — #9058624

Order 512.

4138 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60027C211yesmaximal, characteristic, complemented
2#59579C213yesmaximal, complemented
3#58918C211yesmaximal, characteristic
4#58849C211yesmaximal, characteristic, complemented
5#56148C213yesmaximal, complemented
6#54222C213yesmaximal, complemented
7#49372C213yesmaximal, complemented
8#48457C213yesmaximal, complemented
9#47561C213yesmaximal, complemented
10#47466C213yesmaximal, complemented
11#46905C213yesmaximal, complemented
12#46735C213yesmaximal, complemented
13#45283C213yesmaximal, complemented
14#44800C213yesmaximal, complemented
15#44628C213yesmaximal, complemented
16#44610C213yesmaximal, complemented
17#43596C213yesmaximal, complemented
18#43485C213yesmaximal, complemented
19#43468C213yesmaximal, complemented
20#43166C213yesmaximal, complemented
21#36017C213yesmaximal, complemented
22#35742C213yesmaximal, complemented
23#35490C213yesmaximal, complemented
24#2839C2213yescomplemented
25#2836C2213yes—
26#2827C2213yes—
27#2824C2213yes—
28#2803C2213yes—
29#2802C2213yescomplemented
30#2798C2213yes—
31#2798C2213yes—
32#2798C2213yescomplemented
33#2797C2213yes—
34#2795C2213yescomplemented
35#2794C2213yescomplemented
36#2793C2213yes—
37#2791C2213yescomplemented
38#2790C2213yes—
39#2787C2213yes—
40#2787C2213yescomplemented
41#2786C2213yescomplemented
42#2783C2213yes—
43#2781C2213yes—
44#2780C2213yes—
45#2779C2213yes—
46#2777C2213yes—
47#2773C2213yes—
48#2772C2213yes—
49#2769C2213yescomplemented
50#2768C2213yes—
51#2768C2213yescomplemented
52#2764C2213yes—
53#2764C2213yescomplemented
54#2761C2213yescomplemented
55#2756C2213yes—
56#2754C2213yes—
57#2754C2213yescomplemented
58#2749C2213yes—
59#2748C2213yes—
60#2748C2213yescomplemented
61#2747C2213yescomplemented
62#2743C2213yescomplemented
63#2740C2213yes—
64#2740C2213yes—
65#2738C2213yes—
66#2736C2211yescharacteristic
67#2735C2213yes—
68#2735C2213yes—
69#2721C2213yes—
70#2721C2213yes—
71#2721C2213yescomplemented
72#2721C2213yescomplemented
73#2719C2213yescomplemented
74#2718C2213yes—
75#2710C2213yes—
76#2707C2213yes—
77#2706C2213yes—
78#2705C2213yes—
79#2705C2213yes—
80#2695C2213yes—
81#2695C2213yescomplemented
82#2694C2213yes—
83#2694C2213yes—
84#2694C2213yescomplemented
85#2693C2213yes—
86#2685C2213yes—
87#2673C2213yes—
88#2670C2213yes—
89#2668C2213yes—
90#2650C2213yes—
91#2650C2213yescomplemented
92#2648C2213yes—
93#2648C2213yes—
94#2629C2213yescomplemented
95#2618C2213yes—
96#2611C2213yes—
97#2609C2213yes—
98#2606C2213yescomplemented
99#2602C2213yes—
100#2602C2213yes—
101#2601C2213yes—
102#2601C2213yescomplemented
103#2598C2213yes—
104#2597C2213yes—
105#2596C2213yes—
106#2596C2213yes—
107#2594C2213yescomplemented
108#2594C2213yescomplemented
109#2593C2213yes—
110#2593C2213yes—
111#2593C2213yes—
112#2590C2213yescomplemented
113#2590C2213yescomplemented
114#2588C2213yescomplemented
115#2588C2213yescomplemented
116#2578C2213yes—
117#2578C2213yes—
118#2578C2213yescomplemented
119#2577C2213yes—
120#2577C2213yes—
121#2574C2213yes—
122#2574C2213yescomplemented
123#2573C2213yescomplemented
124#2571C2213yescomplemented
125#2570C2213yescomplemented
126#2569C2213yescomplemented
127#2565C2213yescomplemented
128#2562C2213yes—
129#2559C2213yes—
130#2557C2213yes—
131#2554C2213yes—
132#2554C2213yes—
133#2553C2213yescomplemented
134#2553C2213yescomplemented
135#2533C2213yescomplemented
136#2531C2213yes—
137#2531C2213yes—
138#2531C2213yes—
139#2531C2213yescomplemented
140#2531C2213yescomplemented
141#2529C2213yes—
142#2529C2213yes—
143#2527C2213yes—
144#2527C2213yescomplemented
145#2525C2213yes—
146#2525C2213yes—
147#2525C2213yes—
148#2524C2213yescomplemented
149#2524C2213yescomplemented
150#2524C2213yescomplemented
151#2524C2213yescomplemented
152#2522C2213yes—
153#2521C2213yes—
154#2521C2213yes—
155#2520C2213yescomplemented
156#2520C2213yescomplemented
157#2519C2213yes—
158#2518C2213yes—
159#2518C2213yes—
160#2518C2213yes—
161#2518C2213yes—
162#2518C2213yescomplemented
163#2518C2213yescomplemented
164#2517C2213yes—
165#2516C2213yes—
166#2515C2213yes—
167#2515C2213yescomplemented
168#2512C2213yes—
169#2507C2213yescomplemented
170#2498C2213yes—
171#2498C2213yescomplemented
172#2497C2213yescomplemented
173#2495C2213yescomplemented
174#2494C2213yes—
175#2490C2213yes—
176#2485C2213yes—
177#2485C2213yescomplemented
178#2481C2213yes—
179#2481C2213yescomplemented
180#2481C2213yescomplemented
181#2480C2213yes—
182#2479C2213yes—
183#2478C2213yes—
184#2478C2213yescomplemented
185#2476C2213yes—
186#2474C2213yes—
187#2474C2213yes—
188#2473C2213yescomplemented
189#2469C2213yes—
190#2469C2213yescomplemented
191#2467C2213yes—
192#2453C2213yescomplemented
193#2448C2213yes—
194#2448C2213yes—
195#2445C2213yescomplemented
196#2443C2213yes—
197#2436C2213yes—
198#2422C2213yes—
199#2420C2213yes—
200#2418C2213yes—
201#2418C2213yes—
202#2413C2213yescomplemented
203#2411C2213yes—
204#2401C2213yescomplemented
205#2401C2211yescharacteristic, complemented
206#2396C2213yes—
207#2396C2213yescomplemented
208#2392C2213yes—
209C2×#395C2211yescharacteristic, complemented
210#2380C2211yescharacteristic, complemented
211#2375C2211yescharacteristic
212#2374C2213yescomplemented
213#2373C2213yes—
214#2373C2213yescomplemented
215#2370C2213yescomplemented
216#2367C2213yes—
217#2364C2213yes—
218#2359C2213yes—
219#2359C2213yescomplemented
220#2356C2213yescomplemented
221#2354C2213yes—
222#2352C2213yes—
223#2352C2213yes—
224#2352C2213yescomplemented
225#2347C2213yes—
226#2346C2213yescomplemented
227#2345C2213yescomplemented
228#2342C2213yes—
229Q8×C22⋊C4C2213yescomplemented
230#2336C2213yescomplemented
231#2335C2213yes—
232#2335C2213yescomplemented
233#2334C2213yes—
234#2334C2213yescomplemented
235#2333C2213yes—
236#2330C2213yescomplemented
237#2326C2213yes—
238#2322C2213yes—
239#2321C2213yes—
240#2320C2213yescomplemented
241C4×#126C2211yescharacteristic, complemented
242C4×#126C2213yescomplemented
243#2298C2213yes—
244#2274C2213yescomplemented
245C23×Q8C2311yescharacteristic
246C2×#127C2311yescharacteristic
247C2×#126C2313yes—
248C2×#126C2311yescharacteristic
249C2×#126C2313yes—
250C2×#126C2313yes—
251C2×#126C2313yes—
252C2×#126C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#124C2313yes—
257C2×#124C2313yes—
258C2×#123C2313yes—
259C2×#123C2313yes—
260C2×#123C2313yes—
261C2×#123C2313yes—
262C2×#123C2313yes—
263C2×#123C2313yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266C2×#120C2313yes—
267C2×#120C2311yescharacteristic
268C2×C4×Q8C2313yes—
269C2×C4×Q8C2313yes—
270C2×C4×D4C2313yes—
271C2×C4×D4C2313yes—
272C2×C4×D4C2313yes—
273C2×C4×D4C2313yes—
274C2×#117C2313yes—
275C2×#117C2313yes—
276C2×#117C2313yes—
277C2×#117C2313yes—
278C2×#117C2313yes—
279C22×C4⋊C4C2313yes—
280C22×C4⋊C4C2313yes—
281C22×C22⋊C4C2313yes—
282#401C2311yescharacteristic
283#401C2313yes—
284#400C2313yes—
285#400C2313yes—
286#400C2313yes—
287#400C2313yes—
288#400C2313yes—
289#400C2313yes—
290#400C2313yes—
291#400C2313yes—
292#400C2313yes—
293#400C2313yes—
294#400C2313yes—
295#400C2313yes—
296#400C2313yes—
297#400C2313yes—
298#400C2313yes—
299#400C2313yes—
300#400C2313yes—
301#400C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#399C2313yes—
307#399C2313yes—
308#399C2313yes—
309#399C2313yes—
310#399C2313yes—
311#399C2313yes—
312#399C2313yes—
313#399C2313yes—
314#399C2313yes—
315#399C2313yes—
316#398C2313yes—
317#398C2313yes—
318#398C2313yes—
319#398C2313yes—
320#398C2313yes—
321#398C2313yes—
322#398C2313yes—
323#398C2313yes—
324#398C2313yes—
325#398C2313yes—
326#398C2313yes—
327#398C2313yes—
328#398C2313yes—
329#398C2313yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#397C2313yes—
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2313yes—
348#397C2313yes—
349#397C2313yes—
350#397C2313yes—
351#397C2313yes—
352#397C2313yes—
353#397C2313yes—
354#397C2313yes—
355#397C2313yes—
356#397C2313yes—
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#396C2313yes—
369#396C2313yes—
370#396C2313yes—
371#396C2313yes—
372#396C2313yes—
373#396C2313yes—
374#396C2313yes—
375#396C2313yes—
376#396C2313yes—
377#396C2313yes—
378#396C2313yes—
379#396C2313yes—
380#396C2313yes—
381#396C2311yescharacteristic
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#395C2311yescharacteristic
387#395C2313yes—
388#395C2311yescharacteristic
389#395C2313yes—
390#394C2313yes—
391#394C2313yes—
392#394C2313yes—
393#394C2313yes—
394#394C2313yes—
395#394C2313yes—
396#394C2313yes—
397#394C2313yes—
398#394C2313yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#393C2313yes—
411#393C2313yes—
412#393C2313yes—
413#393C2313yes—
414#392C2313yes—
415#392C2313yes—
416#392C2313yes—
417#392C2313yes—
418#391C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2313yes—
423#391C2313yes—
424#391C2313yes—
425#391C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2313yes—
437#390C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#388C2313yes—
463#388C2313yes—
464#388C2313yes—
465#388C2313yes—
466#388C2313yes—
467#388C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2313yes—
471#388C2313yes—
472#388C2313yes—
473#388C2313yes—
474#388C2313yes—
475#388C2313yes—
476#388C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2313yes—
480#388C2313yes—
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2313yes—
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#387C2313yes—
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2313yes—
537#387C2313yes—
538#387C2313yes—
539#387C2313yes—
540#387C2313yes—
541#387C2313yes—
542#387C2313yes—
543#387C2313yes—
544#387C2313yes—
545#387C2313yes—
546#387C2313yes—
547#387C2313yes—
548#387C2313yes—
549#387C2313yes—
550#387C2313yes—
551#387C2313yes—
552#387C2313yes—
553#387C2313yes—
554#387C2313yes—
555#387C2313yes—
556#387C2313yes—
557#387C2313yes—
558#387C2313yes—
559#387C2313yes—
560#387C2313yes—
561#387C2313yes—
562#387C2313yes—
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#386C2313yes—
591#386C2313yes—
592#386C2313yes—
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#385C2313yes—
613#385C2313yes—
614#385C2313yes—
615#385C2313yes—
616#385C2313yes—
617#385C2313yes—
618#385C2313yes—
619#385C2313yes—
620#385C2313yes—
621#385C2313yes—
622#385C2313yes—
623#385C2313yes—
624#385C2313yes—
625#385C2313yes—
626#385C2313yes—
627#385C2313yes—
628#385C2313yes—
629#385C2313yes—
630#384C2313yes—
631#384C2313yes—
632#384C2313yes—
633#383C2311yescharacteristic
634#383C2313yes—
635#383C2313yes—
636#383C2313yes—
637#383C2313yes—
638#383C2313yes—
639#383C2313yes—
640#383C2311yescharacteristic
641#383C2311yescharacteristic
642#382C2313yes—
643#382C2313yes—
644#382C2313yes—
645#382C2313yes—
646#382C2313yes—
647#382C2313yes—
648#382C2313yes—
649#382C2313yes—
650#381C2313yes—
651#381C2313yes—
652#381C2313yes—
653#380C2313yes—
654#380C2313yes—
655#380C2313yes—
656#380C2313yes—
657#380C2313yes—
658#380C2313yes—
659#380C2313yes—
660#380C2313yes—
661#380C2313yes—
662#380C2313yes—
663#380C2313yes—
664#380C2313yes—
665#380C2313yes—
666#380C2313yes—
667#380C2313yes—
668#379C2313yes—
669#379C2313yes—
670#379C2311yescharacteristic
671#379C2311yescharacteristic
672C4×C4⋊C4C2313yes—
673C4×C4⋊C4C2313yes—
674C4×C4⋊C4C2313yes—
675C4×C4⋊C4C2313yes—
676C4×C4⋊C4C2313yes—
677C4×C4⋊C4C2313yes—
678C4×C4⋊C4C2313yes—
679C4×C4⋊C4C2313yes—
680C4×C4⋊C4C2313yes—
681C4×C4⋊C4C2313yes—
682C4×C4⋊C4C2313yes—
683C4×C4⋊C4C2313yes—
684C4×C4⋊C4C2313yes—
685C4×C4⋊C4C2313yes—
686C4×C4⋊C4C2313yes—
687C4×C4⋊C4C2313yes—
688C4×C4⋊C4C2313yes—
689C4×C4⋊C4C2313yes—
690C4×C4⋊C4C2313yes—
691C4×C4⋊C4C2313yes—
692C4×C4⋊C4C2313yes—
693C4×C4⋊C4C2313yes—
694C4×C4⋊C4C2313yes—
695C4×C22⋊C4C2313yes—
696C4×C22⋊C4C2313yes—
697C4×C22⋊C4C2313yes—
698C4×C22⋊C4C2313yes—
699C4×C22⋊C4C2313yes—
700C4×C22⋊C4C2313yes—
701C4×C22⋊C4C2313yes—
702C4×C22⋊C4C2313yes—
703C4×C22⋊C4C2313yes—
704C4×C22⋊C4C2313yes—
705C4×C22⋊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—
714#376C2313yes—
715#376C2313yes—
716#376C2311yescharacteristic
717#376C2313yes—
718C2×#95C2313yes—
719C43C2311yescharacteristic
720C25C2411yescharacteristic
721C22×Q8—46no—
722C22×Q8C2413yes—
723C22×Q8C2411yescharacteristic
724C22×D4C2413yes—
725C22×D4C2413yes—
726C22×D4C2413yes—
727C22×D4C2413yes—
728C22×D4C2413yes—
729C22×D4C2413yes—
730C23×C4C2413yes—
731C23×C4C2413yes—
732C23×C4C2413yes—
733C23×C4C2413yes—
734C23×C4C2413yes—
735C23×C4C2411yescharacteristic
736C23×C4C2413yes—
737C23×C4C2413yes—
738#127—42no—
739#126—46no—
740#126—42no—
741#126—46no—
742#126—46no—
743#126—46no—
744#126—46no—
745#125—46no—
746#125—46no—
747#125—46no—
748#124—46no—
749#124—46no—
750#123—46no—
751#123—46no—
752#123—46no—
753#123—46no—
754#123—46no—
755#123—46no—
756#121—46no—
757#121—46no—
758#120—46no—
759#120—42no—
760C4×Q8—46no—
761C4×Q8—46no—
762C4×D4—46no—
763C4×D4—46no—
764C4×D4—46no—
765C4×D4—46no—
766#117—46no—
767#117—46no—
768#117—46no—
769#117—46no—
770#117—46no—
771C2×C4⋊C4—46no—
772C2×C4⋊C4—46no—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2413yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C22⋊C4—46no—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2413yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C42C2413yes—
881C2×C42C2413yes—
882C2×C42C2413yes—
883C2×C42C2413yes—
884C2×C42C2413yes—
885C2×C42C2413yes—
886C2×C42C2413yes—
887C2×C42C2413yes—
888C2×C42C2413yes—
889C2×C42C2413yes—
890C2×C42C2413yes—
891C2×C42C2413yes—
892C2×C42C2413yes—
893C2×C42C2413yes—
894C2×C42C2413yes—
895C2×C42C2413yes—
896C2×C42C2413yes—
897C2×C42C2413yes—
898C2×C42C2413yes—
899C2×C42C2411yescharacteristic
900C2×C42C2413yes—
901C2×C42C2413yes—
902C2×C42C2413yes—
903C2×C42C2411yescharacteristic
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2411yescharacteristic
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2413yes—
933#95C2413yes—
934#95C2413yes—
935#95C2413yes—
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2413yes—
941#95C2413yes—
942#95C2413yes—
943#95C2413yes—
944#95C2413yes—
945#95C2413yes—
946#95C2413yes—
947#95C2413yes—
948#95C2413yes—
949#95C2413yes—
950#95C2413yes—
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2413yes—
960#95C2413yes—
961#95C2413yes—
962#95C2413yes—
963#95C2413yes—
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978C24—43no—
979C24—43no—
980C24—41no—
981C24C2513yes—
982C24C2513yes—
983C24C2511yescharacteristic
984C2×Q8—26no—
985C2×Q8—26no—
986C2×Q8—43no—
987C2×Q8—43no—
988C2×Q8—88no—
989C2×D4—26no—
990C2×D4—26no—
991C2×D4—26no—
992C2×D4—43no—
993C2×D4—43no—
994C2×D4—43no—
995C2×D4—43no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—43no—
999C2×D4—43no—
1000C2×D4—43no—
1001C2×D4—43no—
1002C2×D4—43no—
1003C2×D4—43no—
1004C2×D4—43no—
1005C2×D4—43no—
1006C2×D4—43no—
1007C22×C4—26no—
1008C22×C4—26no—
1009C22×C4—26no—
1010C22×C4—26no—
1011C22×C4—26no—
1012C22×C4—43no—
1013C22×C4—43no—
1014C22×C4—43no—
1015C22×C4—43no—
1016C22×C4—43no—
1017C22×C4—43no—
1018C22×C4—43no—
1019C22×C4—43no—
1020C22×C4—43no—
1021C22×C4—43no—
1022C22×C4—43no—
1023C22×C4—43no—
1024C22×C4—43no—
1025C22×C4—43no—
1026C22×C4—43no—
1027C22×C4—43no—
1028C22×C4—43no—
1029C22×C4C2513yes—
1030C22×C4C2513yes—
1031C22×C4C2513yes—
1032C22×C4C2513yes—
1033C22×C4C2513yes—
1034C22×C4C2513yes—
1035C22×C4C2513yes—
1036C22×C4C2513yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2513yes—
1040C22×C4C2513yes—
1041C22×C4C2513yes—
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2513yes—
1045C22×C4C2513yes—
1046C22×C4C2513yes—
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—26no—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—26no—
1059C4⋊C4—26no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—43no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—43no—
1097C4⋊C4—43no—
1098C4⋊C4—43no—
1099C4⋊C4—43no—
1100C4⋊C4—43no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C22⋊C4—26no—
1104C22⋊C4—26no—
1105C22⋊C4—26no—
1106C22⋊C4—26no—
1107C22⋊C4—26no—
1108C22⋊C4—26no—
1109C22⋊C4—26no—
1110C22⋊C4—26no—
1111C22⋊C4—26no—
1112C22⋊C4—26no—
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⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—43no—
1154C22⋊C4—43no—
1155C42—26no—
1156C42—26no—
1157C42—26no—
1158C42—26no—
1159C42—43no—
1160C42—43no—
1161C42—43no—
1162C42—43no—
1163C42—43no—
1164C42—43no—
1165C42—43no—
1166C42—43no—
1167C42—43no—
1168C42—43no—
1169C42—43no—
1170C42—43no—
1171C42—43no—
1172C42—43no—
1173C42—43no—
1174C42—41no—
1175C42—43no—
1176C42—43no—
1177C42—43no—
1178C42—41no—
1179C23—23no—
1180C23—23no—
1181C23—23no—
1182C23—23no—
1183C23—23no—
1184C23—23no—
1185C23—23no—
1186C23—23no—
1187C23—23no—
1188C23—23no—
1189C23—23no—
1190C23—23no—
1191C23—23no—
1192C23—23no—
1193C23—23no—
1194C23—23no—
1195C23—86no—
1196C23—161no—
1197C23—163no—
1198C23#58512yes—
1199C23C2611yescharacteristic
1200Q8—412no—
1201Q8—82no—
1202D4—86no—
1203D4—86no—
1204D4—86no—
1205D4—86no—
1206D4—163no—
1207D4—163no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—412no—
1263C2×C4—86no—
1264C2×C4—86no—
1265C2×C4—86no—
1266C2×C4—86no—
1267C2×C4—86no—
1268C2×C4—161no—
1269C2×C4—163no—
1270C2×C4#58516yes—
1271C2×C4#58516yes—
1272C22—26no—
1273C22—41no—
1274C22—43no—
1275C22—43no—
1276C22—43no—
1277C22—43no—
1278C22—43no—
1279C22—43no—
1280C22—43no—
1281C22—43no—
1282C22—43no—
1283C22—43no—
1284C22—43no—
1285C22—43no—
1286C22—43no—
1287C22—43no—
1288C22—43no—
1289C22—164no—
1290C22C2×#58513yes—
1291C22C2×#58513yes—
1292C22C2×#58511yescharacteristic
1293C4—26no—
1294C4—26no—
1295C4—43no—
1296C4—41no—
1297C4—41no—
1298C4—43no—
1299C4—43no—
1300C4—43no—
1301C4—43no—
1302C4—43no—
1303C4—43no—
1304C4—43no—
1305C4—43no—
1306C4—43no—
1307C4—43no—
1308C4—43no—
1309C4—43no—
1310C4—43no—
1311C4—43no—
1312C4—43no—
1313C2—42no—
1314C2—83no—
1315C2—83no—
1316C2#6282813yes—
1317C2#6302611yescharacteristic
1318C2#6303113yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#58918C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #60027C2semidirect
2. #59579C2semidirect
4. #58849C2semidirect
5. #56148C2semidirect
6. #54222C2semidirect
7. #49372C2semidirect
8. #48457C2semidirect
9. #47561C2semidirect
10. #47466C2semidirect
11. #46905C2semidirect
12. #46735C2semidirect
13. #45283C2semidirect
14. #44800C2semidirect
15. #44628C2semidirect
16. #44610C2semidirect
17. #43596C2semidirect
18. #43485C2semidirect
19. #43468C2semidirect
20. #43166C2semidirect
21. #36017C2semidirect
22. #35742C2semidirect
23. #35490C2semidirect
24. #2839C22semidirect
29. #2802C22semidirect
32. #2798C22semidirect
34. #2795C22semidirect
35. #2794C22semidirect
37. #2791C22semidirect
40. #2787C22semidirect
41. #2786C22semidirect
49. #2769C22semidirect
51. #2768C22semidirect
53. #2764C22semidirect
54. #2761C22semidirect
57. #2754C22semidirect
60. #2748C22semidirect
61. #2747C22semidirect
62. #2743C22semidirect
71. #2721C22semidirect
72. #2721C22semidirect
73. #2719C22semidirect
81. #2695C22semidirect
84. #2694C22semidirect
91. #2650C22semidirect
94. #2629C22semidirect
98. #2606C22semidirect
102. #2601C22semidirect
107. #2594C22semidirect
108. #2594C22semidirect
112. #2590C22semidirect
113. #2590C22semidirect
114. #2588C22semidirect
115. #2588C22semidirect
118. #2578C22semidirect
122. #2574C22semidirect
123. #2573C22semidirect
124. #2571C22semidirect
125. #2570C22semidirect
126. #2569C22semidirect
127. #2565C22semidirect
133. #2553C22semidirect
134. #2553C22semidirect
135. #2533C22semidirect
139. #2531C22semidirect
140. #2531C22semidirect
144. #2527C22semidirect
148. #2524C22semidirect
149. #2524C22semidirect
150. #2524C22semidirect
151. #2524C22semidirect
155. #2520C22semidirect
156. #2520C22semidirect
162. #2518C22semidirect
163. #2518C22semidirect
167. #2515C22semidirect
169. #2507C22semidirect
171. #2498C22semidirect
172. #2497C22semidirect
173. #2495C22semidirect
177. #2485C22semidirect
179. #2481C22semidirect
180. #2481C22semidirect
184. #2478C22semidirect
188. #2473C22semidirect
190. #2469C22semidirect
192. #2453C22semidirect
195. #2445C22semidirect
202. #2413C22semidirect
204. #2401C22semidirect
205. #2401C22semidirect
207. #2396C22semidirect
209. C2×#395C22semidirect
210. #2380C22semidirect
212. #2374C22semidirect
214. #2373C22semidirect
215. #2370C22semidirect
219. #2359C22semidirect
220. #2356C22semidirect
224. #2352C22semidirect
226. #2346C22semidirect
227. #2345C22semidirect
229. Q8×C22⋊C4C22semidirect
230. #2336C22semidirect
232. #2335C22semidirect
234. #2334C22semidirect
236. #2330C22semidirect
240. #2320C22semidirect
241. C4×#126C22semidirect
242. C4×#126C22semidirect
244. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#600272
#595792
#589182
#588492
#561482
#542222
#493722
#484572
#475612
#474662
#469052
#467352
#452832
#448002
#446282
#446102
#435962
#434852
#434682
#431662
#360172
#357422
#354902