Finite Group Databasebeta

← #8115375

Subgroups — #8115375

Order 512.

3715 conjugacy classes of subgroups.

The subgroup lattice has 1231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58495C214yesmaximal, complemented
2#57115C214yesmaximal, complemented
3#57090C214yesmaximal
4#56160C214yesmaximal, complemented
5#56160C214yesmaximal, complemented
6#56154C214yesmaximal, complemented
7#55996C214yesmaximal, complemented
8#54689C214yesmaximal, complemented
9#53156C211yesmaximal, characteristic, complemented
10#53146C211yesmaximal, characteristic, complemented
11#53077C211yesmaximal, characteristic, complemented
12#53030C211yesmaximal, characteristic, complemented
13#45317C212yesmaximal, complemented
14#45184C212yesmaximal, complemented
15#42861C212yesmaximal, complemented
16#42827C212yesmaximal, complemented
17#42771C212yesmaximal
18#42708C212yesmaximal, complemented
19#39283C212yesmaximal, complemented
20#39082C212yesmaximal, complemented
21#38229C212yesmaximal, complemented
22#38215C212yesmaximal, complemented
23#37415C212yesmaximal, complemented
24#37399C212yesmaximal, complemented
25#35323C211yesmaximal, characteristic, complemented
26#35321C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic
28#2863C2212yes—
29#2863C2212yes—
30#2857C2211yescharacteristic
31#2855C2212yes—
32#2851C2211yescharacteristic
33#2841C2214yes—
34#2839C2214yes—
35#2839C2214yes—
36#2839C2214yes—
37#2839C2214yes—
38#2839C2214yes—
39#2839C2214yes—
40#2837C2214yes—
41#2837C2214yes—
42#2836C2214yes—
43#2836C2214yes—
44#2836C2214yes—
45#2810C2214yes—
46#2807C2214yes—
47#2807C2214yes—
48#2802C2214yes—
49#2802C2214yes—
50#2802C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2800C2214yes—
56#2798C2214yes—
57#2793C2214yes—
58#2791C2214yes—
59#2791C2214yes—
60#2791C2214yes—
61#2787C2214yes—
62#2786C2214yes—
63#2786C2214yes—
64#2781C2214yes—
65#2777C2214yes—
66#2777C2214yes—
67#2777C2214yes—
68#2776C2214yes—
69#2776C2214yes—
70#2775C2214yes—
71#2773C2214yes—
72#2773C2214yes—
73#2773C2214yes—
74#2773C2214yes—
75#2773C2214yes—
76#2773C2214yes—
77#2773C2214yes—
78#2772C2214yes—
79#2772C2214yes—
80#2772C2214yes—
81#2771C2214yes—
82#2769C2214yes—
83#2769C2214yes—
84#2769C2214yes—
85#2769C2214yes—
86#2768C2214yes—
87#2768C2214yes—
88#2767C2214yes—
89#2767C2214yes—
90#2767C2214yes—
91#2767C2214yes—
92#2767C2214yes—
93#2766C2214yes—
94#2766C2214yes—
95#2766C2214yes—
96#2765C2214yes—
97#2762C2214yes—
98#2753C2214yes—
99#2747C2214yes—
100#2747C2214yes—
101#2746C2214yes—
102#2743C2214yes—
103#2743C2214yes—
104#2740C2214yes—
105#2739C2214yes—
106#2739C2214yes—
107#2738C2214yes—
108#2738C2214yes—
109#2666C2214yes—
110#2655C2212yes—
111#2655C2214yes—
112#2654C2214yes—
113#2654C2214yes—
114#2654C2212yes—
115#2653C2212yes—
116#2652C2212yes—
117#2651C2214yes—
118#2651C2212yes—
119#2650C2212yes—
120#2649C2214yes—
121#2649C2214yes—
122#2649C2212yes—
123#2648C2212yes—
124#2647C2214yes—
125#2647C2211yescharacteristic
126#2647C2212yes—
127#2647C2211yescharacteristic
128#2645C2212yes—
129#2642C2211yescharacteristic
130#2642C2211yescharacteristic
131#2629C2211yescharacteristic
132#2625C2212yes—
133#2625C2212yes—
134#2621C2212yes—
135#2621C2211yescharacteristic
136#2608C2214yes—
137#2606C2214yes—
138#2606C2214yes—
139#2596C2214yes—
140#2594C2214yes—
141#2594C2214yes—
142#2590C2214yes—
143#2590C2214yes—
144#2585C2214yes—
145#2585C2214yes—
146#2585C2214yes—
147#2582C2212yes—
148#2581C2212yes—
149#2577C2214yes—
150#2577C2214yes—
151#2577C2214yes—
152#2573C2214yes—
153#2573C2214yes—
154#2570C2212yes—
155#2570C2212yes—
156#2546C2212yes—
157#2546C2212yes—
158#2542C2212yes—
159#2536C2212yes—
160#2533C2214yes—
161#2533C2214yes—
162#2533C2214yes—
163#2533C2214yes—
164#2531C2214yes—
165#2531C2214yes—
166#2530C2214yes—
167#2528C2214yes—
168#2528C2214yes—
169#2525C2214yes—
170#2525C2214yes—
171#2524C2214yes—
172#2520C2214yes—
173#2515C2214yes—
174#2515C2214yes—
175#2514C2212yes—
176#2509C2212yes—
177#2509C2214yes—
178#2509C2212yes—
179#2509C2212yes—
180#2508C2214yes—
181#2508C2212yes—
182#2508C2212yes—
183#2507C2212yes—
184#2507C2214yes—
185#2503C2212yes—
186#2499C2212yes—
187#2495C2212yes—
188#2495C2212yes—
189#2495C2214yes—
190#2495C2214yes—
191#2487C2212yes—
192#2453C2212yes—
193#2453C2212yes—
194#2446C2212yes—
195#2446C2212yes—
196#2446C2212yes—
197#2442C2212yes—
198#2441C2212yes—
199#2429C2212yes—
200#2429C2212yes—
201#2429C2212yes—
202#2429C2212yes—
203#2429C2212yes—
204#2423C2212yes—
205#2423C2212yes—
206#2423C2212yes—
207#2421C2212yes—
208#2421C2212yes—
209#2417C2212yes—
210#2415C2212yes—
211#2415C2212yes—
212#2402C2211yescharacteristic
213#2401C2212yes—
214#2398C2211yescharacteristic
215#2396C2211yescharacteristic
216#2395C2212yes—
217#2392C2211yescharacteristic
218#2365C2212yes—
219#2362C2212yes—
220#2360C2212yes—
221#2360C2212yes—
222#2355C2212yes—
223#2351C2212yes—
224#2351C2212yes—
225#2346C2212yes—
226#2330C2211yescharacteristic
227#2327C2212yes—
228#2327C2211yescharacteristic
229#2323C2212yes—
230#2323C2212yes—
231#2323C2212yes—
232#2320C2212yes—
233#2320C2212yes—
234#2316C2212yes—
235C4×C4⋊Q8C2211yescharacteristic
236C4×#125C2211yescharacteristic
237#2298C2212yes—
238#2295C2212yes—
239#2295C2211yescharacteristic
240#2293C2211yescharacteristic
241#2290C2212yes—
242C4×#117C2211yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×#125C2311yescharacteristic
248C2×#125C2311yescharacteristic
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2311yescharacteristic
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C22×C4⋊C4C2312yes—
269C22×C42C2311yescharacteristic
270#401C2314yes—
271#401C2314yes—
272#401C2312yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2312yes—
290#400C2312yes—
291#400C2314yes—
292#400C2314yes—
293#400C2312yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2312yes—
315#400C2312yes—
316#400C2312yes—
317#400C2311yescharacteristic
318#400C2312yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2311yescharacteristic
327#399C2312yes—
328#398C2314yes—
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#398C2312yes—
351#398C2312yes—
352#398C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2311yescharacteristic
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#397C2312yes—
372#397C2314yes—
373#397C2312yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2311yescharacteristic
389#397C2312yes—
390#397C2312yes—
391#397C2312yes—
392#397C2314yes—
393#397C2312yes—
394#396C2314yes—
395#396C2314yes—
396#396C2312yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2312yes—
404#396C2312yes—
405#395C2314yes—
406#395C2311yescharacteristic
407#394C2312yes—
408#394C2312yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2311yescharacteristic
413#394C2312yes—
414#394C2312yes—
415#393C2312yes—
416#393C2311yescharacteristic
417#392C2311yescharacteristic
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#390C2312yes—
433#390C2314yes—
434#389C2312yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2312yes—
444#389C2312yes—
445#389C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2312yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2312yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2312yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2312yes—
512#388C2312yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
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#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2312yes—
577#387C2312yes—
578#387C2314yes—
579#387C2312yes—
580#387C2312yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#386C2312yes—
591#386C2312yes—
592#386C2314yes—
593#386C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2312yes—
602#384C2311yescharacteristic
603#384C2311yescharacteristic
604#384C2312yes—
605#384C2314yes—
606#383C2314yes—
607#383C2314yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#382C2311yescharacteristic
614#382C2312yes—
615#382C2312yes—
616#382C2314yes—
617#382C2314yes—
618#382C2312yes—
619#382C2311yescharacteristic
620#382C2314yes—
621#382C2314yes—
622#382C2314yes—
623#382C2314yes—
624#382C2314yes—
625#382C2314yes—
626#381C2314yes—
627#381C2314yes—
628#381C2314yes—
629#380C2314yes—
630#380C2314yes—
631#380C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637#380C2312yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2311yescharacteristic
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667#376C2311yescharacteristic
668#376C2312yes—
669#376C2314yes—
670#376C2314yes—
671#376C2311yescharacteristic
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×Q8C2411yescharacteristic
677C22×D4C2412yes—
678C22×D4C2411yescharacteristic
679C23×C4C2412yes—
680C23×C4C2411yescharacteristic
681C23×C4C2414yes—
682C23×C4C2412yes—
683C4⋊Q8—42no—
684C4⋊Q8—44no—
685C4⋊Q8—42no—
686C4⋊Q8—44no—
687#125—42no—
688#125—42no—
689C22⋊Q8—44no—
690C22⋊Q8—44no—
691C22⋊Q8—44no—
692C22⋊Q8—44no—
693C22⋊Q8—44no—
694C22⋊Q8—44no—
695C4×Q8—42no—
696C4×Q8—44no—
697C4×Q8—44no—
698C4×Q8—44no—
699C4×Q8—44no—
700C4×Q8—44no—
701C4×Q8—44no—
702C4×D4—42no—
703C4×D4—44no—
704#117—44no—
705#117—42no—
706#117—42no—
707#117—44no—
708C2×C4⋊C4—44no—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C22⋊C4C2411yescharacteristic
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C42—42no—
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2412yes—
810C2×C42C2411yescharacteristic
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2411yescharacteristic
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830#95C2412yes—
831#95C2412yes—
832#95C2412yes—
833#95C2412yes—
834#95C2412yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2412yes—
839#95C2414yes—
840#95C2414yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2414yes—
845#95C2414yes—
846#95C2412yes—
847#95C2412yes—
848#95C2414yes—
849#95C2414yes—
850#95C2412yes—
851#95C2412yes—
852#95C2412yes—
853#95C2412yes—
854#95C2412yes—
855#95C2412yes—
856#95C2414yes—
857#95C2412yes—
858#95C2414yes—
859#95C2412yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2414yes—
869#95C2412yes—
870#95C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2412yes—
881#95C2412yes—
882#95C2411yescharacteristic
883#95C2412yes—
884#95C2412yes—
885#95C2411yescharacteristic
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
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—
916C24C2512yes—
917C24C2511yescharacteristic
918C2×Q8—24no—
919C2×Q8—24no—
920C2×Q8—24no—
921C2×Q8—24no—
922C2×Q8—24no—
923C2×Q8—24no—
924C2×Q8—41no—
925C2×Q8—42no—
926C2×D4—41no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C22×C4—22no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—24no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4C2512yes—
944C22×C4C2512yes—
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2514yes—
950C22×C4C2514yes—
951C22×C4C2511yescharacteristic
952C22×C4C2512yes—
953C22×C4C2511yescharacteristic
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2514yes—
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2511yescharacteristic
966C22×C4C2512yes—
967C22×C4C2511yescharacteristic
968C4⋊C4—24no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—44no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—44no—
991C4⋊C4—42no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—42no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—42no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—41no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—42no—
1012C4⋊C4—44no—
1013C4⋊C4—41no—
1014C4⋊C4—42no—
1015C4⋊C4—44no—
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—44no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—44no—
1047C22⋊C4—42no—
1048C22⋊C4—41no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—41no—
1053C22⋊C4—44no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C42—22no—
1064C42—22no—
1065C42—22no—
1066C42—22no—
1067C42—22no—
1068C42—24no—
1069C42—22no—
1070C42—24no—
1071C42—24no—
1072C42—42no—
1073C42—44no—
1074C42—42no—
1075C42—42no—
1076C42—44no—
1077C42—44no—
1078C42—44no—
1079C42—42no—
1080C42—42no—
1081C42—44no—
1082C42—44no—
1083C42—44no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C23—22no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23C2611yescharacteristic
1101Q8—48no—
1102Q8—48no—
1103Q8—82no—
1104D4—82no—
1105D4—84no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—44no—
1175C2×C4—48no—
1176C2×C4—84no—
1177C2×C4—164no—
1178C2×C4#58512yes—
1179C2×C4#58512yes—
1180C2×C4#58512yes—
1181C22—42no—
1182C22—41no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—41no—
1188C22—41no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22C2×#58511yescharacteristic
1194C22C2×#58511yescharacteristic
1195C22C2×#58511yescharacteristic
1196C222−1+612yes—
1197C222−1+612yes—
1198C4—41no—
1199C4—42no—
1200C4—44no—
1201C4—44no—
1202C4—41no—
1203C4—42no—
1204C4—42no—
1205C4—41no—
1206C4—42no—
1207C4—44no—
1208C4—44no—
1209C4—44no—
1210C4—44no—
1211C4—42no—
1212C4—42no—
1213C4—41no—
1214C4—42no—
1215C4—41no—
1216C4—42no—
1217C4—42no—
1218C4—42no—
1219C4—44no—
1220C4—44no—
1221C4—42no—
1222C4#356714yes—
1223C2—81no—
1224C2—82no—
1225C2C2×#356711yescharacteristic
1226C2#6289011yescharacteristic
1227C2#6289012yes—
1228C2#6289011yescharacteristic
1229C2#6289112yes—
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. #58495C2semidirect
2. #57115C2semidirect
4. #56160C2semidirect
5. #56160C2semidirect
6. #56154C2semidirect
7. #55996C2semidirect
8. #54689C2semidirect
9. #53156C2semidirect
10. #53146C2semidirect
11. #53077C2semidirect
12. #53030C2semidirect
13. #45317C2semidirect
14. #45184C2semidirect
15. #42861C2semidirect
16. #42827C2semidirect
18. #42708C2semidirect
19. #39283C2semidirect
20. #39082C2semidirect
21. #38229C2semidirect
22. #38215C2semidirect
23. #37415C2semidirect
24. #37399C2semidirect
25. #35323C2semidirect
26. #35321C2semidirect

Maximal subgroups

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

subgroupindex
#584952
#571152
#570902
#561602
#561542
#559962
#546892
#531562
#531462
#530772
#530302
#453172
#451842
#428612
#428272
#427712
#427082
#392832
#390822
#382292
#382152
#374152
#373992
#353232
#353212
#346402