Finite Group Databasebeta

← #8115439

Subgroups — #8115439

Order 512.

4002 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58288C214yesmaximal, complemented
2#57689C214yesmaximal, complemented
3#56823C214yesmaximal, complemented
4#56708C214yesmaximal, complemented
5#55768C214yesmaximal, complemented
6#54221C214yesmaximal
7#53890C214yesmaximal, complemented
8#53785C214yesmaximal, complemented
9#53145C212yesmaximal, complemented
10#53034C212yesmaximal, complemented
11#45326C212yesmaximal, complemented
12#45185C212yesmaximal, complemented
13#42980C211yesmaximal, characteristic
14#42929C211yesmaximal, characteristic
15#42901C212yesmaximal, complemented
16#42848C212yesmaximal, complemented
17#42697C211yesmaximal, characteristic, complemented
18#42695C211yesmaximal, characteristic, complemented
19#39673C212yesmaximal, complemented
20#39553C212yesmaximal, complemented
21#37894C212yesmaximal, complemented
22#37868C212yesmaximal, complemented
23#37429C212yesmaximal, complemented
24#37395C212yesmaximal, complemented
25#35339C211yesmaximal, characteristic, complemented
26#35319C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic
28C2×#556C2212yes—
29C2×#552C2212yes—
30C2×#541C2212yes—
31#2868C2211yescharacteristic
32#2864C2212yes—
33#2864C2212yes—
34#2859C2211yescharacteristic
35#2857C2212yes—
36#2843C2214yes—
37#2839C2214yes—
38#2839C2214yes—
39#2839C2214yes—
40#2838C2214yes—
41#2836C2214yes—
42#2835C2212yes—
43#2834C2212yes—
44#2833C2214yes—
45#2833C2214yes—
46#2831C2214yes—
47#2827C2214yes—
48#2823C2212yes—
49#2822C2212yes—
50#2810C2214yes—
51#2805C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2796C2214yes—
56#2794C2212yes—
57#2793C2214yes—
58#2793C2214yes—
59#2793C2214yes—
60#2793C2214yes—
61#2792C2214yes—
62#2792C2212yes—
63#2791C2214yes—
64#2791C2214yes—
65#2791C2214yes—
66#2791C2214yes—
67#2791C2214yes—
68#2791C2214yes—
69#2791C2214yes—
70#2791C2214yes—
71#2791C2214yes—
72#2790C2214yes—
73#2790C2214yes—
74#2789C2212yes—
75#2789C2214yes—
76#2788C2214yes—
77#2788C2214yes—
78#2787C2214yes—
79#2787C2214yes—
80#2783C2214yes—
81#2779C2214yes—
82#2777C2214yes—
83#2776C2214yes—
84#2776C2214yes—
85#2776C2214yes—
86#2775C2214yes—
87#2774C2214yes—
88#2772C2214yes—
89#2772C2214yes—
90#2769C2212yes—
91#2768C2214yes—
92#2767C2214yes—
93#2766C2214yes—
94#2766C2214yes—
95#2758C2214yes—
96#2755C2214yes—
97#2755C2214yes—
98#2747C2214yes—
99#2742C2214yes—
100#2726C2214yes—
101#2725C2214yes—
102#2722C2214yes—
103#2722C2214yes—
104#2722C2214yes—
105#2722C2214yes—
106#2722C2212yes—
107#2722C2212yes—
108#2721C2214yes—
109#2719C2214yes—
110#2717C2214yes—
111#2717C2214yes—
112#2715C2214yes—
113#2715C2214yes—
114#2712C2212yes—
115#2695C2214yes—
116#2695C2214yes—
117#2693C2212yes—
118#2666C2214yes—
119#2660C2212yes—
120#2655C2214yes—
121#2655C2212yes—
122#2654C2212yes—
123#2654C2214yes—
124#2653C2212yes—
125#2652C2212yes—
126#2652C2214yes—
127#2652C2214yes—
128#2652C2214yes—
129#2651C2212yes—
130#2650C2212yes—
131#2649C2212yes—
132#2648C2212yes—
133#2647C2212yes—
134#2647C2212yes—
135#2647C2212yes—
136#2642C2212yes—
137#2637C2214yes—
138#2629C2214yes—
139#2621C2212yes—
140#2621C2212yes—
141#2621C2211yescharacteristic
142#2621C2211yescharacteristic
143#2609C2212yes—
144#2597C2214yes—
145#2594C2214yes—
146#2590C2214yes—
147#2590C2214yes—
148#2590C2214yes—
149#2588C2214yes—
150#2586C2214yes—
151#2585C2214yes—
152#2582C2212yes—
153#2582C2212yes—
154#2581C2212yes—
155#2577C2214yes—
156#2577C2214yes—
157#2571C2212yes—
158#2570C2214yes—
159#2570C2214yes—
160#2570C2212yes—
161#2569C2214yes—
162#2569C2214yes—
163#2569C2214yes—
164#2569C2214yes—
165#2567C2212yes—
166#2565C2212yes—
167#2553C2214yes—
168#2552C2212yes—
169#2550C2212yes—
170#2523C2212yes—
171#2521C2214yes—
172#2517C2212yes—
173#2514C2212yes—
174#2514C2212yes—
175#2514C2212yes—
176#2511C2212yes—
177#2510C2214yes—
178#2510C2214yes—
179#2506C2214yes—
180#2506C2214yes—
181#2502C2212yes—
182#2499C2212yes—
183#2499C2212yes—
184#2499C2212yes—
185#2496C2214yes—
186#2496C2214yes—
187#2496C2214yes—
188#2496C2214yes—
189#2478C2214yes—
190#2478C2214yes—
191#2475C2214yes—
192#2462C2214yes—
193#2462C2214yes—
194#2462C2214yes—
195#2453C2214yes—
196#2453C2212yes—
197#2453C2212yes—
198#2451C2212yes—
199#2451C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2446C2212yes—
203#2446C2212yes—
204#2442C2212yes—
205#2442C2212yes—
206#2441C2212yes—
207#2441C2214yes—
208#2439C2212yes—
209#2429C2212yes—
210#2429C2212yes—
211#2429C2212yes—
212#2429C2212yes—
213#2423C2212yes—
214#2421C2212yes—
215#2421C2212yes—
216#2421C2212yes—
217#2417C2212yes—
218#2417C2212yes—
219#2417C2212yes—
220#2415C2212yes—
221#2402C2211yescharacteristic
222#2401C2212yes—
223#2398C2211yescharacteristic
224#2396C2211yescharacteristic
225#2395C2212yes—
226#2392C2211yescharacteristic
227#2362C2212yes—
228#2360C2212yes—
229#2360C2212yes—
230#2360C2212yes—
231#2351C2212yes—
232Q8×C4⋊C4C2212yes—
233#2327C2212yes—
234#2327C2212yes—
235#2327C2211yescharacteristic
236#2327C2211yescharacteristic
237#2317C2211yescharacteristic
238#2317C2211yescharacteristic
239#2317C2212yes—
240#2316C2211yescharacteristic
241#2316C2211yescharacteristic
242#2314C2212yes—
243C4×C4⋊Q8C2212yes—
244#2298C2212yes—
245#2295C2211yescharacteristic
246#2293C2211yescharacteristic
247#2290C2212yes—
248#2285C2211yescharacteristic
249C2×#382C2211yescharacteristic
250C4×#117C2211yescharacteristic
251#556—48no—
252#552—48no—
253#541—48no—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2312yes—
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#126C2314yes—
264C2×#125C2312yes—
265C2×#125C2314yes—
266C2×#125C2312yes—
267C2×#125C2314yes—
268C2×#125C2314yes—
269C2×#124C2314yes—
270C2×#123C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2311yescharacteristic
287C2×#117C2312yes—
288C2×#117C2311yescharacteristic
289C2×#117C2311yescharacteristic
290C2×#117C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C2×#117C2312yes—
293C2×#117C2314yes—
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2312yes—
297C22×C42C2311yescharacteristic
298#401C2314yes—
299#401C2314yes—
300#401C2314yes—
301#401C2312yes—
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#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2312yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2311yescharacteristic
339#400C2312yes—
340#399C2314yes—
341#399C2311yescharacteristic
342#399C2314yes—
343#399C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2311yescharacteristic
347#398C2314yes—
348#398C2312yes—
349#398C2314yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
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#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2312yes—
398#397C2314yes—
399#397C2314yes—
400#397C2312yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2312yes—
410#397C2312yes—
411#397C2311yescharacteristic
412#397C2312yes—
413#397C2312yes—
414#397C2312yes—
415#397C2312yes—
416#397C2312yes—
417#397C2314yes—
418#397C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2312yes—
429#396C2312yes—
430#396C2312yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2311yescharacteristic
440#394C2311yescharacteristic
441#394C2314yes—
442#394C2312yes—
443#394C2312yes—
444#394C2312yes—
445#394C2312yes—
446#393C2312yes—
447#393C2311yescharacteristic
448#393C2314yes—
449#392C2311yescharacteristic
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#390C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2312yes—
528#388C2312yes—
529#388C2312yes—
530#388C2312yes—
531#388C2312yes—
532#388C2312yes—
533#388C2314yes—
534#388C2314yes—
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#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#386C2314yes—
605#386C2312yes—
606#386C2312yes—
607#386C2314yes—
608#386C2314yes—
609#385C2312yes—
610#385C2312yes—
611#385C2312yes—
612#385C2312yes—
613#385C2312yes—
614#385C2312yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#384C2312yes—
625#384C2312yes—
626#384C2312yes—
627#384C2312yes—
628#384C2312yes—
629#384C2312yes—
630#384C2314yes—
631#384C2314yes—
632#384C2314yes—
633#384C2314yes—
634#383C2314yes—
635#383C2314yes—
636#383C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2311yescharacteristic
642#382C2314yes—
643#382C2311yescharacteristic
644#382C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2314yes—
648#382C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687#376C2311yescharacteristic
688#376C2312yes—
689#376C2311yescharacteristic
690C2×#95C2314yes—
691C43C2311yescharacteristic
692C43C2311yescharacteristic
693C22×Q8C2412yes—
694C22×Q8C2412yes—
695C22×Q8C2414yes—
696C22×Q8C2411yescharacteristic
697C22×D4C2412yes—
698C22×D4C2411yescharacteristic
699C23×C4C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2412yes—
702C23×C4C2414yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C4⋊Q8—28no—
706C4⋊Q8—44no—
707C4⋊Q8—42no—
708C4⋊Q8—42no—
709C4⋊Q8—44no—
710#126—48no—
711#126—48no—
712#126—48no—
713#126—48no—
714#126—48no—
715#125—44no—
716#125—48no—
717#125—44no—
718#125—48no—
719#125—48no—
720#124—48no—
721#123—48no—
722C22⋊Q8—28no—
723C22⋊Q8—28no—
724C22⋊Q8—44no—
725C22⋊Q8—44no—
726C22⋊Q8—44no—
727C22⋊Q8—44no—
728C4×Q8—42no—
729C4×Q8—48no—
730C4×Q8—44no—
731C4×Q8—44no—
732C4×Q8—44no—
733C4×Q8—44no—
734C4×Q8—44no—
735C4×Q8—44no—
736C4×D4—28no—
737C4×D4—42no—
738#117—24no—
739#117—24no—
740#117—24no—
741#117—28no—
742#117—42no—
743#117—48no—
744#117—44no—
745C2×C4⋊C4—42no—
746C2×C4⋊C4—42no—
747C2×C4⋊C4—44no—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C42—24no—
851C2×C42C2412yes—
852C2×C42C2411yescharacteristic
853C2×C42C2411yescharacteristic
854C2×C42C2412yes—
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2411yescharacteristic
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2411yescharacteristic
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2412yes—
893#95C2412yes—
894#95C2414yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2412yes—
912#95C2411yescharacteristic
913#95C2412yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2411yescharacteristic
919#95C2412yes—
920#95C2412yes—
921#95C2411yescharacteristic
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2414yes—
927#95C2411yescharacteristic
928#95C2414yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960C24C2512yes—
961C24C2511yescharacteristic
962C2×Q8—24no—
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—24no—
968C2×Q8—44no—
969C2×Q8—41no—
970C2×Q8—42no—
971C2×Q8—44no—
972C2×Q8—44no—
973C2×D4—24no—
974C2×D4—41no—
975C2×D4—42no—
976C2×D4—42no—
977C2×D4—42no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—44no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4H(5,𝔽2)14yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2514yes—
1007C22×C4C2514yes—
1008C22×C4C2514yes—
1009C22×C4C2514yes—
1010C22×C4C2514yes—
1011C22×C4C2512yes—
1012C22×C4C2514yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2512yes—
1018C22×C4C2511yescharacteristic
1019C4⋊C4—24no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—28no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—44no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C22⋊C4—24no—
1093C22⋊C4—24no—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—24no—
1099C22⋊C4—24no—
1100C22⋊C4—24no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—42no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C42—24no—
1122C42—22no—
1123C42—24no—
1124C42—22no—
1125C42—24no—
1126C42—24no—
1127C42—22no—
1128C42—24no—
1129C42—22no—
1130C42—22no—
1131C42—24no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—44no—
1137C42—44no—
1138C42—44no—
1139C42—44no—
1140C42—44no—
1141C42—44no—
1142C42—44no—
1143C42—44no—
1144C42—44no—
1145C422−1+414yes—
1146C23—21no—
1147C23—21no—
1148C23—22no—
1149C23—22no—
1150C23—22no—
1151C23—22no—
1152C23—22no—
1153C23—22no—
1154C23—22no—
1155C23—22no—
1156C23—22no—
1157C23C2×H(5,𝔽2)12yes—
1158C23C2611yescharacteristic
1159Q8—48no—
1160Q8—48no—
1161Q8—88no—
1162Q8—82no—
1163D4—84no—
1164D4—82no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—28no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—48no—
1233C2×C4—84no—
1234C2×C4—88no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4C2×H(5,𝔽2)12yes—
1238C2×C4C2×H(5,𝔽2)12yes—
1239C2×C4C2×2−1+414yes—
1240C2×C4C2×2−1+412yes—
1241C2×C4#58512yes—
1242C22—22no—
1243C22—24no—
1244C22—42no—
1245C22—41no—
1246C22—41no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22C22×H(5,𝔽2)11yescharacteristic
1255C22C22×2−1+411yescharacteristic
1256C22C2×#58511yescharacteristic
1257C222−1+612yes—
1258C222−1+612yes—
1259C4—22no—
1260C4—24no—
1261C4—42no—
1262C4—44no—
1263C4—44no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—44no—
1268C4—44no—
1269C4—42no—
1270C4—44no—
1271C4—44no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—41no—
1277C4—41no—
1278C4—44no—
1279C4—44no—
1280C4—41no—
1281C4—42no—
1282C4—41no—
1283C4#355914yes—
1284C2—42no—
1285C2—82no—
1286C2C2×#355911yescharacteristic
1287C2#6288812yes—
1288C2#6288912yes—
1289C2#6289111yescharacteristic
1290C2#6289111yescharacteristic
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. #58288C2semidirect
2. #57689C2semidirect
3. #56823C2semidirect
4. #56708C2semidirect
5. #55768C2semidirect
7. #53890C2semidirect
8. #53785C2semidirect
9. #53145C2semidirect
10. #53034C2semidirect
11. #45326C2semidirect
12. #45185C2semidirect
15. #42901C2semidirect
16. #42848C2semidirect
17. #42697C2semidirect
18. #42695C2semidirect
19. #39673C2semidirect
20. #39553C2semidirect
21. #37894C2semidirect
22. #37868C2semidirect
23. #37429C2semidirect
24. #37395C2semidirect
25. #35339C2semidirect
26. #35319C2semidirect

Maximal subgroups

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

subgroupindex
#582882
#576892
#568232
#567082
#557682
#542212
#538902
#537852
#531452
#530342
#453262
#451852
#429802
#429292
#429012
#428482
#426972
#426952
#396732
#395532
#378942
#378682
#374292
#373952
#353392
#353192
#346402