Finite Group Databasebeta

← #8115450

Subgroups — #8115450

Order 512.

3850 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58941C214yesmaximal, complemented
2#58932C214yesmaximal, complemented
3#58198C214yesmaximal
4#56258C214yesmaximal, complemented
5#55849C214yesmaximal, complemented
6#55793C214yesmaximal, complemented
7#54681C214yesmaximal, complemented
8#54130C214yesmaximal, complemented
9#53157C211yesmaximal, characteristic, complemented
10#53121C211yesmaximal, characteristic, complemented
11#53075C211yesmaximal, characteristic, complemented
12#52987C211yesmaximal, characteristic, complemented
13#45005C212yesmaximal, complemented
14#44902C212yesmaximal, complemented
15#42934C212yesmaximal
16#42748C212yesmaximal, complemented
17#42587C212yesmaximal, complemented
18#42488C212yesmaximal, complemented
19#39680C212yesmaximal, complemented
20#39545C212yesmaximal, complemented
21#37884C212yesmaximal, complemented
22#37878C212yesmaximal, complemented
23#37433C212yesmaximal, complemented
24#37312C212yesmaximal, complemented
25#35339C211yesmaximal, characteristic, complemented
26#35283C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic
28#2868C2211yescharacteristic
29#2864C2212yes—
30#2864C2212yes—
31#2862C2211yescharacteristic
32#2857C2212yes—
33#2841C2214yes—
34#2839C2214yes—
35#2839C2214yes—
36#2839C2214yes—
37#2838C2214yes—
38#2838C2214yes—
39#2837C2214yes—
40#2836C2214yes—
41#2834C2214yes—
42#2833C2214yes—
43#2833C2214yes—
44#2822C2214yes—
45#2809C2214yes—
46#2802C2214yes—
47#2802C2214yes—
48#2799C2214yes—
49#2798C2214yes—
50#2792C2214yes—
51#2791C2214yes—
52#2791C2214yes—
53#2790C2214yes—
54#2789C2214yes—
55#2789C2214yes—
56#2789C2214yes—
57#2789C2214yes—
58#2783C2214yes—
59#2777C2214yes—
60#2776C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2773C2214yes—
64#2773C2214yes—
65#2773C2214yes—
66#2771C2214yes—
67#2767C2214yes—
68#2767C2214yes—
69#2767C2214yes—
70#2766C2214yes—
71#2766C2214yes—
72#2765C2214yes—
73#2762C2214yes—
74#2762C2214yes—
75#2762C2214yes—
76#2761C2214yes—
77#2755C2214yes—
78#2754C2214yes—
79#2754C2214yes—
80#2754C2214yes—
81#2754C2214yes—
82#2754C2214yes—
83#2751C2214yes—
84#2748C2214yes—
85#2746C2214yes—
86#2745C2214yes—
87#2745C2214yes—
88#2742C2214yes—
89#2734C2214yes—
90#2734C2214yes—
91#2729C2214yes—
92#2728C2214yes—
93#2726C2214yes—
94#2721C2214yes—
95#2720C2214yes—
96#2719C2214yes—
97#2713C2214yes—
98#2713C2214yes—
99#2713C2214yes—
100#2704C2214yes—
101#2698C2214yes—
102#2696C2214yes—
103#2694C2214yes—
104#2692C2214yes—
105#2689C2214yes—
106#2687C2214yes—
107#2677C2214yes—
108#2677C2214yes—
109#2667C2214yes—
110#2666C2214yes—
111#2660C2212yes—
112#2655C2212yes—
113#2655C2214yes—
114#2654C2212yes—
115#2653C2212yes—
116#2652C2212yes—
117#2651C2212yes—
118#2650C2212yes—
119#2650C2214yes—
120#2649C2212yes—
121#2649C2214yes—
122#2648C2212yes—
123#2647C2212yes—
124#2647C2211yescharacteristic
125#2647C2211yescharacteristic
126#2647C2211yescharacteristic
127#2647C2211yescharacteristic
128#2647C2211yescharacteristic
129#2647C2211yescharacteristic
130#2645C2214yes—
131#2628C2212yes—
132#2628C2212yes—
133#2628C2214yes—
134#2628C2212yes—
135#2621C2214yes—
136#2611C2214yes—
137#2604C2214yes—
138#2599C2214yes—
139#2590C2214yes—
140#2590C2214yes—
141#2589C2214yes—
142#2588C2214yes—
143#2586C2214yes—
144#2584C2212yes—
145#2575C2214yes—
146#2570C2214yes—
147#2570C2214yes—
148#2570C2214yes—
149#2570C2212yes—
150#2570C2212yes—
151#2569C2214yes—
152#2569C2214yes—
153#2556C2214yes—
154#2556C2214yes—
155#2552C2212yes—
156#2552C2212yes—
157#2551C2212yes—
158#2550C2212yes—
159#2546C2212yes—
160#2533C2214yes—
161#2528C2214yes—
162#2528C2214yes—
163#2515C2214yes—
164#2511C2214yes—
165#2509C2212yes—
166#2509C2212yes—
167#2509C2212yes—
168#2509C2212yes—
169#2508C2212yes—
170#2508C2212yes—
171#2508C2212yes—
172#2508C2212yes—
173#2508C2212yes—
174#2507C2212yes—
175#2507C2212yes—
176#2506C2212yes—
177#2499C2214yes—
178#2498C2214yes—
179#2496C2212yes—
180#2495C2212yes—
181#2495C2212yes—
182#2494C2212yes—
183#2494C2212yes—
184#2494C2212yes—
185#2494C2212yes—
186#2494C2212yes—
187#2493C2214yes—
188#2492C2214yes—
189#2488C2214yes—
190#2487C2212yes—
191#2487C2212yes—
192#2486C2212yes—
193#2485C2212yes—
194#2479C2214yes—
195#2479C2214yes—
196#2475C2214yes—
197#2470C2214yes—
198#2453C2214yes—
199#2451C2214yes—
200#2451C2214yes—
201#2441C2212yes—
202#2441C2212yes—
203#2441C2212yes—
204#2440C2212yes—
205#2440C2212yes—
206#2440C2212yes—
207#2439C2214yes—
208#2439C2212yes—
209#2439C2212yes—
210#2438C2214yes—
211#2423C2214yes—
212#2402C2211yescharacteristic
213#2401C2212yes—
214#2398C2211yescharacteristic
215#2396C2211yescharacteristic
216#2395C2212yes—
217#2392C2211yescharacteristic
218#2370C2212yes—
219#2369C2212yes—
220#2354C2212yes—
221#2352C2212yes—
222#2346C2212yes—
223#2345C2212yes—
224#2344C2212yes—
225#2344C2212yes—
226#2331C2212yes—
227#2331C2212yes—
228#2331C2212yes—
229#2317C2212yes—
230#2317C2212yes—
231#2316C2212yes—
232#2314C2211yescharacteristic
233#2314C2212yes—
234#2314C2211yescharacteristic
235C4×C4⋊Q8C2212yes—
236#2298C2212yes—
237#2295C2211yescharacteristic
238#2293C2211yescharacteristic
239#2290C2212yes—
240#2285C2211yescharacteristic
241C2×#382C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2314yes—
247C2×C4⋊Q8C2314yes—
248C2×C4⋊Q8C2314yes—
249C2×#126C2314yes—
250C2×#125C2312yes—
251C2×#125C2314yes—
252C2×#125C2314yes—
253C2×#125C2314yes—
254C2×#123C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2314yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2312yes—
265C2×#117C2311yescharacteristic
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C42C2311yescharacteristic
273#401C2312yes—
274#401C2314yes—
275#401C2314yes—
276#401C2314yes—
277#401C2314yes—
278#401C2314yes—
279#400C2312yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2312yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2312yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2312yes—
316#400C2312yes—
317#400C2314yes—
318#400C2311yescharacteristic
319#399C2312yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2311yescharacteristic
328#399C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2312yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2311yescharacteristic
364#398C2312yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#397C2314yes—
369#397C2312yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2312yes—
379#397C2312yes—
380#397C2314yes—
381#397C2311yescharacteristic
382#397C2312yes—
383#397C2312yes—
384#397C2312yes—
385#397C2312yes—
386#396C2312yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2312yes—
391#396C2312yes—
392#396C2314yes—
393#396C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2311yescharacteristic
406#395C2314yes—
407#394C2312yes—
408#394C2314yes—
409#394C2311yescharacteristic
410#394C2312yes—
411#394C2312yes—
412#394C2312yes—
413#393C2312yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2311yescharacteristic
419#393C2314yes—
420#392C2311yescharacteristic
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#390C2314yes—
439#390C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2312yes—
500#388C2312yes—
501#388C2314yes—
502#388C2312yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2312yes—
507#388C2312yes—
508#388C2314yes—
509#388C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2312yes—
513#388C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2312yes—
567#387C2314yes—
568#387C2312yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#386C2314yes—
578#386C2312yes—
579#386C2312yes—
580#386C2314yes—
581#386C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2312yes—
591#385C2314yes—
592#385C2312yes—
593#384C2312yes—
594#384C2311yescharacteristic
595#384C2311yescharacteristic
596#384C2314yes—
597#384C2311yescharacteristic
598#384C2312yes—
599#384C2312yes—
600#384C2314yes—
601#384C2311yescharacteristic
602#383C2314yes—
603#383C2314yes—
604#382C2314yes—
605#382C2312yes—
606#382C2311yescharacteristic
607#382C2311yescharacteristic
608#382C2314yes—
609#382C2312yes—
610#382C2312yes—
611#382C2314yes—
612#382C2314yes—
613#382C2314yes—
614#382C2312yes—
615#382C2312yes—
616#382C2314yes—
617#382C2314yes—
618#382C2311yescharacteristic
619#382C2311yescharacteristic
620#382C2314yes—
621#381C2314yes—
622#381C2314yes—
623#381C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2314yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2312yes—
633#380C2314yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667#376C2311yescharacteristic
668#376C2312yes—
669#376C2314yes—
670#376C2311yescharacteristic
671C2×#95C2314yes—
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C22×Q8C2414yes—
675C22×Q8C2411yescharacteristic
676C22×Q8C2414yes—
677C22×Q8C2414yes—
678C22×D4C2412yes—
679C22×D4C2411yescharacteristic
680C23×C4C2412yes—
681C23×C4C2411yescharacteristic
682C23×C4C2414yes—
683C23×C4C2412yes—
684C23×C4C2414yes—
685C4⋊Q8—28no—
686C4⋊Q8—44no—
687C4⋊Q8—44no—
688C4⋊Q8—84no—
689C4⋊Q8—84no—
690C4⋊Q8—84no—
691#126—84no—
692#125—44no—
693#125—84no—
694#125—84no—
695#125—84no—
696#123—84no—
697C22⋊Q8—84no—
698C22⋊Q8—84no—
699C22⋊Q8—84no—
700C22⋊Q8—84no—
701C4×Q8—42no—
702C4×Q8—84no—
703C4×D4—28no—
704C4×D4—42no—
705#117—24no—
706#117—28no—
707#117—42no—
708#117—44no—
709#117—44no—
710#117—84no—
711#117—84no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—44no—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C42—24no—
811C2×C42C2411yescharacteristic
812C2×C42C2411yescharacteristic
813C2×C42C2411yescharacteristic
814C2×C42C2411yescharacteristic
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2411yescharacteristic
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2411yescharacteristic
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2412yes—
840#95C2412yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2412yes—
848#95C2412yes—
849#95C2412yes—
850#95C2412yes—
851#95C2414yes—
852#95C2412yes—
853#95C2414yes—
854#95C2414yes—
855#95C2412yes—
856#95C2412yes—
857#95C2414yes—
858#95C2412yes—
859#95C2412yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2412yes—
864#95C2412yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2414yes—
882#95C2412yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2412yes—
889#95C2411yescharacteristic
890#95C2414yes—
891#95C2414yes—
892#95C2411yescharacteristic
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—
917#95C2414yes—
918#95C2414yes—
919C24C2512yes—
920C24C2511yescharacteristic
921C2×Q8—28no—
922C2×Q8—41no—
923C2×Q8—44no—
924C2×Q8—42no—
925C2×Q8—44no—
926C2×Q8—44no—
927C2×Q8—44no—
928C2×Q8—44no—
929C2×Q8—44no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×D4—24no—
933C2×D4—41no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—28no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—42no—
948C22×C4—44no—
949C22×C4—42no—
950C22×C4—44no—
951C22×C42−1+414yes—
952C22×C4C2512yes—
953C22×C4C2514yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2511yescharacteristic
957C22×C4C2512yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2511yescharacteristic
966C22×C4C2512yes—
967C22×C4C2514yes—
968C22×C4C2511yescharacteristic
969C22×C4C2512yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2511yescharacteristic
973C22×C4C2514yes—
974C22×C4C2511yescharacteristic
975C22×C4C2512yes—
976C22×C4C2511yescharacteristic
977C4⋊C4—28no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—28no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—44no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—42no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—42no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—42no—
1045C22⋊C4—24no—
1046C22⋊C4—24no—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—24no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—42no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—42no—
1073C42—24no—
1074C42—22no—
1075C42—22no—
1076C42—22no—
1077C42—24no—
1078C42—24no—
1079C42—22no—
1080C42—22no—
1081C42—24no—
1082C42—42no—
1083C42—42no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C42—42no—
1093C42—44no—
1094C42—44no—
1095C42—42no—
1096C422−1+414yes—
1097C23—21no—
1098C23—21no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23C2×2−1+412yes—
1109C23C2611yescharacteristic
1110Q8—88no—
1111Q8—82no—
1112Q8—164no—
1113Q8—164no—
1114D4—84no—
1115D4—82no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—28no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—48no—
1184C2×C4—84no—
1185C2×C4—88no—
1186C2×C4—88no—
1187C2×C4C2×2−1+414yes—
1188C2×C4C2×2−1+412yes—
1189C2×C4C2×2−1+412yes—
1190C2×C4C2×2−1+412yes—
1191C2×C4#58512yes—
1192C22—22no—
1193C22—24no—
1194C22—42no—
1195C22—41no—
1196C22—41no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22C22×2−1+411yescharacteristic
1205C22C22×2−1+411yescharacteristic
1206C22C2×#58511yescharacteristic
1207C22H(7,𝔽2)12yes—
1208C222−1+612yes—
1209C4—22no—
1210C4—24no—
1211C4—42no—
1212C4—42no—
1213C4—42no—
1214C4—42no—
1215C4—42no—
1216C4—42no—
1217C4—42no—
1218C4—44no—
1219C4—44no—
1220C4—42no—
1221C4—44no—
1222C4—44no—
1223C4—44no—
1224C4—44no—
1225C4—41no—
1226C4—42no—
1227C4—44no—
1228C4—41no—
1229C4—41no—
1230C4—42no—
1231C4—44no—
1232C4—41no—
1233C4#356314yes—
1234C2—42no—
1235C2—82no—
1236C2C2×#356311yescharacteristic
1237C2#6287912yes—
1238C2#6287912yes—
1239C2#6288311yescharacteristic
1240C2#6289011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58941C2semidirect
2. #58932C2semidirect
4. #56258C2semidirect
5. #55849C2semidirect
6. #55793C2semidirect
7. #54681C2semidirect
8. #54130C2semidirect
9. #53157C2semidirect
10. #53121C2semidirect
11. #53075C2semidirect
12. #52987C2semidirect
13. #45005C2semidirect
14. #44902C2semidirect
16. #42748C2semidirect
17. #42587C2semidirect
18. #42488C2semidirect
19. #39680C2semidirect
20. #39545C2semidirect
21. #37884C2semidirect
22. #37878C2semidirect
23. #37433C2semidirect
24. #37312C2semidirect
25. #35339C2semidirect
26. #35283C2semidirect

Maximal subgroups

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

subgroupindex
#589412
#589322
#581982
#562582
#558492
#557932
#546812
#541302
#531572
#531212
#530752
#529872
#450052
#449022
#429342
#427482
#425872
#424882
#396802
#395452
#378842
#378782
#374332
#373122
#353392
#352832
#346402