Finite Group Databasebeta

← #8115364

Subgroups — #8115364

Order 512.

3751 conjugacy classes of subgroups.

The subgroup lattice has 1235 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58482C214yesmaximal, complemented
2#57938C214yesmaximal, complemented
3#56761C214yesmaximal, complemented
4#56186C214yesmaximal, complemented
5#56153C214yesmaximal, complemented
6#56143C214yesmaximal, complemented
7#56010C214yesmaximal, complemented
8#54658C214yesmaximal
9#53150C211yesmaximal, characteristic, complemented
10#53150C211yesmaximal, characteristic, complemented
11#53075C211yesmaximal, characteristic, complemented
12#53032C211yesmaximal, characteristic, complemented
13#45305C212yesmaximal, complemented
14#45183C212yesmaximal, complemented
15#42867C212yesmaximal
16#42828C212yesmaximal, complemented
17#42779C212yesmaximal, complemented
18#42707C212yesmaximal, complemented
19#39296C212yesmaximal, complemented
20#39067C212yesmaximal, complemented
21#38239C212yesmaximal, complemented
22#38207C212yesmaximal, complemented
23#37408C212yesmaximal, complemented
24#37398C212yesmaximal, complemented
25#35323C211yesmaximal, characteristic, complemented
26#35321C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic
28#2863C2212yes—
29#2863C2212yes—
30#2857C2211yescharacteristic
31#2855C2212yes—
32#2851C2211yescharacteristic
33#2844C2214yes—
34#2839C2214yes—
35#2839C2214yes—
36#2838C2214yes—
37#2838C2214yes—
38#2837C2214yes—
39#2835C2214yes—
40#2833C2214yes—
41#2833C2214yes—
42#2833C2214yes—
43#2832C2214yes—
44#2831C2214yes—
45#2810C2214yes—
46#2806C2214yes—
47#2805C2214yes—
48#2805C2214yes—
49#2800C2214yes—
50#2799C2214yes—
51#2799C2214yes—
52#2799C2214yes—
53#2798C2214yes—
54#2798C2214yes—
55#2796C2214yes—
56#2789C2214yes—
57#2788C2214yes—
58#2788C2214yes—
59#2782C2214yes—
60#2779C2214yes—
61#2777C2214yes—
62#2777C2214yes—
63#2777C2214yes—
64#2776C2214yes—
65#2776C2214yes—
66#2775C2214yes—
67#2775C2214yes—
68#2775C2214yes—
69#2774C2214yes—
70#2771C2214yes—
71#2770C2214yes—
72#2767C2214yes—
73#2766C2214yes—
74#2766C2214yes—
75#2765C2214yes—
76#2764C2214yes—
77#2763C2214yes—
78#2763C2214yes—
79#2762C2214yes—
80#2762C2214yes—
81#2762C2214yes—
82#2762C2214yes—
83#2759C2214yes—
84#2759C2214yes—
85#2759C2214yes—
86#2759C2214yes—
87#2759C2214yes—
88#2759C2214yes—
89#2758C2214yes—
90#2758C2214yes—
91#2758C2214yes—
92#2758C2214yes—
93#2758C2214yes—
94#2758C2214yes—
95#2756C2214yes—
96#2755C2214yes—
97#2755C2214yes—
98#2754C2214yes—
99#2754C2214yes—
100#2751C2214yes—
101#2750C2214yes—
102#2747C2214yes—
103#2745C2214yes—
104#2743C2214yes—
105#2739C2214yes—
106#2738C2214yes—
107#2738C2214yes—
108#2737C2214yes—
109#2666C2214yes—
110#2666C2214yes—
111#2655C2212yes—
112#2654C2212yes—
113#2653C2214yes—
114#2653C2214yes—
115#2653C2212yes—
116#2652C2212yes—
117#2651C2212yes—
118#2651C2214yes—
119#2650C2214yes—
120#2650C2212yes—
121#2650C2214yes—
122#2649C2212yes—
123#2648C2212yes—
124#2647C2211yescharacteristic
125#2647C2211yescharacteristic
126#2645C2212yes—
127#2645C2214yes—
128#2642C2212yes—
129#2642C2211yescharacteristic
130#2642C2211yescharacteristic
131#2629C2211yescharacteristic
132#2628C2212yes—
133#2625C2212yes—
134#2625C2212yes—
135#2621C2211yescharacteristic
136#2605C2214yes—
137#2605C2214yes—
138#2605C2214yes—
139#2597C2214yes—
140#2596C2214yes—
141#2594C2214yes—
142#2590C2214yes—
143#2589C2214yes—
144#2588C2214yes—
145#2588C2214yes—
146#2586C2214yes—
147#2585C2214yes—
148#2584C2212yes—
149#2577C2214yes—
150#2575C2214yes—
151#2574C2214yes—
152#2573C2214yes—
153#2573C2214yes—
154#2568C2212yes—
155#2568C2212yes—
156#2568C2212yes—
157#2563C2212yes—
158#2550C2212yes—
159#2550C2212yes—
160#2536C2212yes—
161#2533C2214yes—
162#2533C2214yes—
163#2532C2214yes—
164#2532C2214yes—
165#2530C2214yes—
166#2530C2214yes—
167#2529C2214yes—
168#2527C2214yes—
169#2524C2214yes—
170#2524C2214yes—
171#2524C2214yes—
172#2523C2214yes—
173#2516C2214yes—
174#2515C2214yes—
175#2514C2212yes—
176#2514C2212yes—
177#2514C2214yes—
178#2514C2214yes—
179#2514C2212yes—
180#2514C2214yes—
181#2511C2212yes—
182#2511C2212yes—
183#2509C2214yes—
184#2508C2214yes—
185#2495C2212yes—
186#2495C2212yes—
187#2494C2212yes—
188#2494C2212yes—
189#2492C2212yes—
190#2492C2212yes—
191#2492C2212yes—
192#2489C2212yes—
193#2489C2212yes—
194#2489C2212yes—
195#2485C2212yes—
196#2453C2212yes—
197#2451C2212yes—
198#2451C2212yes—
199#2451C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2446C2212yes—
203#2441C2212yes—
204#2441C2212yes—
205#2434C2212yes—
206#2434C2212yes—
207#2429C2212yes—
208#2421C2212yes—
209#2415C2212yes—
210#2409C2212yes—
211#2409C2212yes—
212#2402C2211yescharacteristic
213#2401C2212yes—
214#2398C2211yescharacteristic
215#2396C2211yescharacteristic
216#2395C2212yes—
217#2392C2211yescharacteristic
218#2370C2212yes—
219#2369C2212yes—
220#2365C2212yes—
221#2362C2212yes—
222#2356C2212yes—
223#2347C2212yes—
224Q8×C22⋊C4C2212yes—
225Q8×C22⋊C4C2212yes—
226#2331C2212yes—
227#2330C2211yescharacteristic
228#2327C2211yescharacteristic
229#2323C2212yes—
230#2323C2212yes—
231#2323C2212yes—
232#2320C2212yes—
233#2320C2212yes—
234#2310C2212yes—
235C4×C4⋊Q8C2211yescharacteristic
236C4×#125C2211yescharacteristic
237#2298C2212yes—
238#2295C2212yes—
239#2295C2211yescharacteristic
240#2293C2211yescharacteristic
241#2290C2212yes—
242C4×#117C2211yescharacteristic
243C23×Q8C2312yes—
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2311yescharacteristic
249C2×#125C2311yescharacteristic
250C2×#125C2312yes—
251C2×#125C2311yescharacteristic
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C22×C42C2311yescharacteristic
268#401C2314yes—
269#401C2314yes—
270#401C2314yes—
271#401C2314yes—
272#401C2314yes—
273#401C2314yes—
274#401C2312yes—
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#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#400C2314yes—
305#400C2312yes—
306#400C2312yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2312yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2312yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2311yescharacteristic
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2312yes—
328#399C2314yes—
329#399C2311yescharacteristic
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2312yes—
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#398C2311yescharacteristic
349#398C2312yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2312yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2312yes—
369#397C2314yes—
370#397C2311yescharacteristic
371#397C2312yes—
372#397C2312yes—
373#397C2312yes—
374#397C2312yes—
375#397C2312yes—
376#396C2314yes—
377#396C2314yes—
378#396C2312yes—
379#396C2312yes—
380#396C2314yes—
381#396C2314yes—
382#396C2312yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2311yescharacteristic
397#394C2312yes—
398#394C2314yes—
399#394C2314yes—
400#394C2312yes—
401#394C2314yes—
402#394C2311yescharacteristic
403#394C2312yes—
404#394C2312yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2312yes—
412#393C2314yes—
413#393C2314yes—
414#393C2311yescharacteristic
415#392C2311yescharacteristic
416#391C2312yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#390C2314yes—
457#390C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#388C2314yes—
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2312yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2312yes—
516#388C2312yes—
517#388C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2312yes—
521#388C2314yes—
522#388C2312yes—
523#388C2314yes—
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#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#386C2314yes—
587#386C2312yes—
588#386C2312yes—
589#386C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2312yes—
598#385C2312yes—
599#385C2314yes—
600#384C2311yescharacteristic
601#384C2311yescharacteristic
602#383C2314yes—
603#383C2314yes—
604#383C2314yes—
605#383C2314yes—
606#383C2314yes—
607#383C2314yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#382C2311yescharacteristic
614#382C2314yes—
615#382C2311yescharacteristic
616#382C2312yes—
617#382C2314yes—
618#382C2312yes—
619#382C2314yes—
620#382C2314yes—
621#382C2314yes—
622#382C2314yes—
623#382C2314yes—
624#381C2314yes—
625#381C2314yes—
626#381C2314yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
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×Q8—44no—
675C22×Q8—44no—
676C22×Q8—44no—
677C22×Q8C2412yes—
678C22×Q8C2412yes—
679C22×Q8C2411yescharacteristic
680C22×Q8C2414yes—
681C22×Q8C2414yes—
682C22×Q8C2414yes—
683C22×D4C2412yes—
684C22×D4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2412yes—
687C23×C4C2414yes—
688C23×C4C2412yes—
689C4⋊Q8—44no—
690C4⋊Q8—44no—
691C4⋊Q8—42no—
692C4⋊Q8—42no—
693C4⋊Q8—44no—
694#125—42no—
695#125—42no—
696#125—44no—
697C22⋊Q8—44no—
698C22⋊Q8—44no—
699C22⋊Q8—44no—
700C22⋊Q8—44no—
701C4×Q8—42no—
702C4×Q8—44no—
703C4×Q8—44no—
704C4×Q8—44no—
705C4×Q8—44no—
706C4×D4—42no—
707C4×D4—44no—
708#117—44no—
709#117—42no—
710#117—42no—
711#117—44no—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2411yescharacteristic
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⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C42—42no—
799C2×C42C2411yescharacteristic
800C2×C42C2411yescharacteristic
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2412yes—
804C2×C42C2411yescharacteristic
805C2×C42C2412yes—
806C2×C42C2412yes—
807C2×C42C2411yescharacteristic
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2412yes—
824#95C2412yes—
825#95C2412yes—
826#95C2412yes—
827#95C2412yes—
828#95C2412yes—
829#95C2414yes—
830#95C2414yes—
831#95C2412yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2412yes—
836#95C2414yes—
837#95C2414yes—
838#95C2412yes—
839#95C2412yes—
840#95C2412yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2412yes—
845#95C2412yes—
846#95C2412yes—
847#95C2412yes—
848#95C2414yes—
849#95C2414yes—
850#95C2412yes—
851#95C2414yes—
852#95C2414yes—
853#95C2412yes—
854#95C2412yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2414yes—
868#95C2412yes—
869#95C2412yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2414yes—
882#95C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2414yes—
885#95C2414yes—
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—
916C24C2511yescharacteristic
917C24C2512yes—
918C2×Q8—24no—
919C2×Q8—24no—
920C2×Q8—24no—
921C2×Q8—24no—
922C2×Q8—24no—
923C2×Q8—24no—
924C2×Q8—41no—
925C2×Q8—44no—
926C2×Q8—44no—
927C2×Q8—44no—
928C2×Q8—42no—
929C2×Q8—44no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—44no—
935C2×Q8—816no—
936C2×D4—41no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—24no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2511yescharacteristic
957C22×C4C2512yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2511yescharacteristic
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2511yescharacteristic
969C22×C4C2512yes—
970C22×C4C2511yescharacteristic
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2514yes—
975C22×C4C2514yes—
976C22×C4C2511yescharacteristic
977C22×C4C2511yescharacteristic
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—44no—
989C4⋊C4—42no—
990C4⋊C4—44no—
991C4⋊C4—42no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—41no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—42no—
1015C4⋊C4—44no—
1016C4⋊C4—41no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—42no—
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—
1034C4⋊C4—44no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—44no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—44no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—42no—
1051C22⋊C4—41no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—41no—
1056C22⋊C4—44no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C42—22no—
1065C42—22no—
1066C42—22no—
1067C42—22no—
1068C42—22no—
1069C42—24no—
1070C42—22no—
1071C42—24no—
1072C42—24no—
1073C42—42no—
1074C42—44no—
1075C42—42no—
1076C42—44no—
1077C42—42no—
1078C42—44no—
1079C42—44no—
1080C42—44no—
1081C42—44no—
1082C42—42no—
1083C42—42no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23C2611yescharacteristic
1102Q8—48no—
1103Q8—48no—
1104Q8—82no—
1105Q8—88no—
1106Q8—164no—
1107Q8—164no—
1108D4—82no—
1109D4—84no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—21no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—21no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—44no—
1179C2×C4—48no—
1180C2×C4—84no—
1181C2×C4—88no—
1182C2×C4#58512yes—
1183C2×C4#58512yes—
1184C2×C4#58512yes—
1185C22—42no—
1186C22—41no—
1187C22—42no—
1188C22—41no—
1189C22—41no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22C2×#58511yescharacteristic
1198C22C2×#58511yescharacteristic
1199C22C2×#58511yescharacteristic
1200C222−1+612yes—
1201C222−1+612yes—
1202C4—41no—
1203C4—42no—
1204C4—44no—
1205C4—44no—
1206C4—41no—
1207C4—41no—
1208C4—42no—
1209C4—44no—
1210C4—44no—
1211C4—41no—
1212C4—41no—
1213C4—42no—
1214C4—42no—
1215C4—42no—
1216C4—42no—
1217C4—42no—
1218C4—42no—
1219C4—42no—
1220C4—44no—
1221C4—44no—
1222C4—44no—
1223C4—44no—
1224C4—42no—
1225C4—42no—
1226C4#356814yes—
1227C2—82no—
1228C2—81no—
1229C2C2×#356811yescharacteristic
1230C2#6289011yescharacteristic
1231C2#6289011yescharacteristic
1232C2#6289112yes—
1233C2#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. #58482C2semidirect
2. #57938C2semidirect
3. #56761C2semidirect
4. #56186C2semidirect
5. #56153C2semidirect
6. #56143C2semidirect
7. #56010C2semidirect
9. #53150C2semidirect
10. #53150C2semidirect
11. #53075C2semidirect
12. #53032C2semidirect
13. #45305C2semidirect
14. #45183C2semidirect
16. #42828C2semidirect
17. #42779C2semidirect
18. #42707C2semidirect
19. #39296C2semidirect
20. #39067C2semidirect
21. #38239C2semidirect
22. #38207C2semidirect
23. #37408C2semidirect
24. #37398C2semidirect
25. #35323C2semidirect
26. #35321C2semidirect

Maximal subgroups

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

subgroupindex
#584822
#579382
#567612
#561862
#561532
#561432
#560102
#546582
#531502
#530752
#530322
#453052
#451832
#428672
#428282
#427792
#427072
#392962
#390672
#382392
#382072
#374082
#373982
#353232
#353212
#346402