Finite Group Databasebeta

← #8095326

Subgroups — #8095326

Order 512.

4209 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53150C211yesmaximal, characteristic, complemented
2#53146C211yesmaximal, characteristic, complemented
3#53140C212yesmaximal, complemented
4#53032C211yesmaximal, characteristic, complemented
5#53030C211yesmaximal, characteristic, complemented
6#53011C212yesmaximal
7#52954C214yesmaximal, complemented
8#52947C214yesmaximal, complemented
9#52933C214yesmaximal, complemented
10#52929C214yesmaximal, complemented
11#46069C212yesmaximal, complemented
12#46002C212yesmaximal, complemented
13#45666C214yesmaximal, complemented
14#45626C212yesmaximal, complemented
15#45585C214yesmaximal, complemented
16#45575C214yesmaximal
17#45503C212yesmaximal, complemented
18#45496C214yesmaximal, complemented
19#35656C212yesmaximal, complemented
20#35645C212yesmaximal, complemented
21#35637C212yesmaximal, complemented
22#35323C211yesmaximal, characteristic, complemented
23#35319C211yesmaximal, characteristic, complemented
24#35248C212yesmaximal, complemented
25#35244C212yesmaximal, complemented
26#34879C211yesmaximal, characteristic
27#34691C212yesmaximal, complemented
28C2×#541C2211yescharacteristic
29C2×#541C2211yescharacteristic
30C2×#533C2212yes—
31C22×C4×Q8C2212yes—
32#2868C2211yescharacteristic
33#2863C2212yes—
34#2859C2211yescharacteristic
35#2857C2212yes—
36#2857C2211yescharacteristic
37#2855C2214yes—
38#2855C2214yes—
39#2852C2214yes—
40#2851C2214yes—
41#2851C2211yescharacteristic
42#2844C2214yes—
43#2843C2214yes—
44#2843C2214yes—
45#2841C2214yes—
46#2841C2214yes—
47#2841C2214yes—
48#2839C2214yes—
49#2839C2214yes—
50#2839C2214yes—
51#2839C2214yes—
52#2839C2214yes—
53#2839C2214yes—
54#2839C2214yes—
55#2839C2214yes—
56#2838C2214yes—
57#2835C2214yes—
58#2833C2214yes—
59#2831C2214yes—
60#2831C2214yes—
61#2827C2214yes—
62#2807C2214yes—
63#2807C2214yes—
64#2806C2214yes—
65#2802C2214yes—
66#2802C2214yes—
67#2799C2214yes—
68#2798C2214yes—
69#2792C2214yes—
70#2792C2214yes—
71#2792C2214yes—
72#2792C2214yes—
73#2792C2214yes—
74#2790C2214yes—
75#2790C2214yes—
76#2790C2214yes—
77#2790C2214yes—
78#2788C2214yes—
79#2782C2214yes—
80#2774C2214yes—
81#2772C2214yes—
82#2771C2214yes—
83#2769C2214yes—
84#2763C2214yes—
85#2758C2214yes—
86#2758C2214yes—
87#2755C2214yes—
88#2755C2214yes—
89#2750C2214yes—
90#2749C2214yes—
91#2748C2214yes—
92#2746C2214yes—
93#2744C2214yes—
94#2743C2214yes—
95#2742C2214yes—
96#2739C2214yes—
97#2739C2214yes—
98#2738C2214yes—
99#2737C2214yes—
100#2689C2214yes—
101#2687C2214yes—
102#2647C2211yescharacteristic
103#2642C2211yescharacteristic
104#2642C2211yescharacteristic
105#2642C2211yescharacteristic
106#2637C2214yes—
107#2634C2214yes—
108#2634C2214yes—
109#2634C2214yes—
110#2625C2212yes—
111#2621C2212yes—
112#2611C2214yes—
113#2604C2214yes—
114#2601C2214yes—
115#2590C2214yes—
116#2590C2214yes—
117#2588C2214yes—
118#2581C2212yes—
119#2581C2214yes—
120#2581C2214yes—
121#2577C2214yes—
122#2575C2214yes—
123#2574C2212yes—
124#2573C2214yes—
125#2573C2212yes—
126#2572C2212yes—
127#2570C2212yes—
128#2568C2212yes—
129#2568C2212yes—
130#2568C2212yes—
131#2565C2214yes—
132#2560C2214yes—
133#2556C2214yes—
134#2553C2212yes—
135#2550C2212yes—
136#2546C2212yes—
137#2546C2212yes—
138#2546C2212yes—
139#2546C2212yes—
140#2542C2212yes—
141#2536C2212yes—
142#2533C2214yes—
143#2533C2214yes—
144#2533C2214yes—
145#2533C2214yes—
146#2530C2214yes—
147#2530C2214yes—
148#2528C2214yes—
149#2528C2214yes—
150#2524C2214yes—
151#2524C2214yes—
152#2524C2214yes—
153#2524C2212yes—
154#2522C2214yes—
155#2520C2214yes—
156#2519C2214yes—
157#2515C2212yes—
158#2514C2212yes—
159#2511C2212yes—
160#2511C2212yes—
161#2509C2212yes—
162#2508C2214yes—
163#2506C2214yes—
164#2506C2214yes—
165#2506C2214yes—
166#2503C2212yes—
167#2503C2212yes—
168#2496C2214yes—
169#2496C2214yes—
170#2495C2212yes—
171#2492C2212yes—
172#2489C2212yes—
173#2489C2212yes—
174#2484C2214yes—
175#2484C2214yes—
176#2481C2214yes—
177#2473C2214yes—
178#2473C2214yes—
179#2469C2214yes—
180#2468C2212yes—
181#2465C2214yes—
182#2462C2214yes—
183#2462C2214yes—
184#2457C2212yes—
185#2453C2212yes—
186#2453C2212yes—
187#2451C2212yes—
188#2449C2214yes—
189#2446C2212yes—
190#2446C2212yes—
191#2446C2212yes—
192#2446C2212yes—
193#2446C2212yes—
194#2442C2212yes—
195#2440C2212yes—
196#2434C2212yes—
197#2434C2212yes—
198#2434C2212yes—
199#2434C2212yes—
200#2429C2212yes—
201#2429C2212yes—
202#2429C2212yes—
203#2429C2212yes—
204#2429C2212yes—
205#2423C2212yes—
206#2423C2212yes—
207#2421C2212yes—
208#2417C2212yes—
209#2417C2212yes—
210#2409C2212yes—
211#2409C2212yes—
212#2402C2211yescharacteristic
213#2399C2214yes—
214#2398C2211yescharacteristic
215#2396C2211yescharacteristic
216#2396C2214yes—
217#2392C2211yescharacteristic
218#2383C2214yes—
219#2378C2214yes—
220#2378C2214yes—
221#2376C2214yes—
222#2330C2211yescharacteristic
223#2327C2212yes—
224#2327C2212yes—
225#2327C2212yes—
226#2327C2211yescharacteristic
227#2323C2212yes—
228#2320C2212yes—
229C4×C4⋊Q8C2212yes—
230C4×#126C2212yes—
231C4×C22⋊Q8C2212yes—
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2214yes—
234C4×#123C2212yes—
235#2295C2211yescharacteristic
236#2295C2212yes—
237#2290C2214yes—
238#2290C2212yes—
239#2283C2212yes—
240#2276C2212yes—
241C42×D4C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C23×Q8C2312yes—
244#541—44no—
245#541—44no—
246#533—48no—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2312yes—
256C2×#126C2312yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#125C2314yes—
260C2×#125C2311yescharacteristic
261C2×#125C2314yes—
262C2×#125C2311yescharacteristic
263C2×#125C2311yescharacteristic
264C2×#125C2314yes—
265C2×#123C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C4×Q8—48no—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2312yes—
290C2×#117C2311yescharacteristic
291C2×#117C2314yes—
292C2×#117C2311yescharacteristic
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2314yes—
295C22×C42C2312yes—
296C22×C42C2314yes—
297C22×C42C2311yescharacteristic
298#401C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2312yes—
309#400C2311yescharacteristic
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2311yescharacteristic
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2312yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2311yescharacteristic
385#398C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2311yescharacteristic
396#396C2314yes—
397#396C2314yes—
398#396C2312yes—
399#396C2314yes—
400#396C2314yes—
401#396C2312yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#395C2311yescharacteristic
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2311yescharacteristic
423#394C2312yes—
424#393C2314yes—
425#393C2311yescharacteristic
426#393C2312yes—
427#393C2314yes—
428#393C2314yes—
429#392C2311yescharacteristic
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2314yes—
455#390C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#388C2312yes—
492#388C2312yes—
493#388C2312yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2312yes—
501#388C2312yes—
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#387C2312yes—
515#387C2312yes—
516#387C2312yes—
517#387C2314yes—
518#387C2312yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2312yes—
529#387C2312yes—
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#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2312yes—
575#386C2312yes—
576#386C2314yes—
577#386C2312yes—
578#386C2312yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2312yes—
586#385C2312yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2312yes—
600#384C2312yes—
601#384C2314yes—
602#384C2311yescharacteristic
603#384C2314yes—
604#384C2314yes—
605#383C2312yes—
606#383C2312yes—
607#383C2314yes—
608#383C2312yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#382C2314yes—
613#382C2311yescharacteristic
614#382C2312yes—
615#382C2312yes—
616#382C2312yes—
617#382C2314yes—
618#382C2312yes—
619#382C2314yes—
620#382C2312yes—
621#382C2314yes—
622#381C2312yes—
623#381C2312yes—
624#381C2312yes—
625#381C2314yes—
626#381C2314yes—
627#381C2314yes—
628#381C2314yes—
629#380C2312yes—
630#380C2314yes—
631#380C2312yes—
632#380C2314yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2312yes—
637#380C2314yes—
638#380C2312yes—
639#380C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671#376C2312yes—
672#376C2311yescharacteristic
673#376C2314yes—
674#376C2311yescharacteristic
675#376C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C22×Q8—44no—
679C22×Q8—44no—
680C22×Q8—44no—
681C22×Q8C2412yes—
682C22×Q8C2412yes—
683C22×Q8C2412yes—
684C22×Q8C2414yes—
685C22×Q8C2414yes—
686C22×Q8C2411yescharacteristic
687C22×D4C2411yescharacteristic
688C22×D4C2412yes—
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2414yes—
694C23×C4C2412yes—
695C23×C4C2414yes—
696C4⋊Q8—44no—
697C4⋊Q8—42no—
698C4⋊Q8—44no—
699C4⋊Q8—44no—
700C4⋊Q8—44no—
701C4⋊Q8—44no—
702C4⋊Q8—44no—
703C4⋊Q8—42no—
704C4⋊Q8—42no—
705#126—28no—
706#126—48no—
707#126—48no—
708#125—42no—
709#125—48no—
710#125—48no—
711#125—42no—
712#125—42no—
713#125—48no—
714#123—28no—
715C22⋊Q8—216no—
716C22⋊Q8—48no—
717C22⋊Q8—44no—
718C22⋊Q8—44no—
719C22⋊Q8—44no—
720C22⋊Q8—44no—
721C22⋊Q8—44no—
722C22⋊Q8—44no—
723C22⋊Q8—44no—
724C4×Q8—28no—
725C4×Q8—28no—
726C4×Q8—28no—
727C4×Q8—48no—
728C4×Q8—42no—
729C4×Q8—48no—
730C4×Q8—48no—
731C4×Q8—44no—
732C4×Q8—44no—
733C4×Q8—44no—
734C4×Q8—44no—
735C4×D4—28no—
736C4×D4—42no—
737C4×D4—44no—
738#117—24no—
739#117—42no—
740#117—48no—
741C2×C4⋊C4—44no—
742C2×C4⋊C4—48no—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C42—28no—
835C2×C42—48no—
836C2×C42—42no—
837C2×C42C2411yescharacteristic
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2414yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2411yescharacteristic
850C2×C42C2412yes—
851C2×C42C2411yescharacteristic
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863#95C2412yes—
864#95C2412yes—
865#95C2412yes—
866#95C2412yes—
867#95C2412yes—
868#95C2412yes—
869#95C2412yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2412yes—
879#95C2412yes—
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2412yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2411yescharacteristic
905#95C2412yes—
906#95C2412yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2412yes—
912#95C2414yes—
913#95C2411yescharacteristic
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946C24C2511yescharacteristic
947C24C2512yes—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—28no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—44no—
959C2×Q8—44no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—41no—
963C2×Q8—44no—
964C2×Q8—42no—
965C2×Q8—432no—
966C2×D4—24no—
967C2×D4—24no—
968C2×D4—41no—
969C2×D4—42no—
970C2×D4—42no—
971C22×C4—24no—
972C22×C4—28no—
973C22×C4—24no—
974C22×C4—24no—
975C22×C4—24no—
976C22×C4—22no—
977C22×C4—24no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—44no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—44no—
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2512yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2511yescharacteristic
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2511yescharacteristic
1017C4⋊C4—24no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—28no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—24no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—42no—
1049C4⋊C4—44no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—41no—
1055C4⋊C4—42no—
1056C4⋊C4—41no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
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—
1082C22⋊C4—28no—
1083C22⋊C4—24no—
1084C22⋊C4—24no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—24no—
1088C22⋊C4—24no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—44no—
1092C22⋊C4—42no—
1093C22⋊C4—44no—
1094C22⋊C4—42no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C42−1+418yes—
1108C42—24no—
1109C42—24no—
1110C42—24no—
1111C42—28no—
1112C42—28no—
1113C42—22no—
1114C42—28no—
1115C42—24no—
1116C42—24no—
1117C42—22no—
1118C42—22no—
1119C42—22no—
1120C42—22no—
1121C42—24no—
1122C42—24no—
1123C42—42no—
1124C42—44no—
1125C42—44no—
1126C42—42no—
1127C42—44no—
1128C42—42no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—44no—
1133C42H(5,𝔽2)14yes—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—21no—
1141C23—22no—
1142C23—21no—
1143C23—21no—
1144C23—22no—
1145C23C2×2−1+414yes—
1146C23C2611yescharacteristic
1147Q8—416no—
1148Q8—48no—
1149Q8—48no—
1150Q8—48no—
1151Q8—88no—
1152Q8—82no—
1153D4—44no—
1154D4—84no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—21no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—21no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—48no—
1221C2×C4—48no—
1222C2×C4—416no—
1223C2×C4—44no—
1224C2×C4—48no—
1225C2×C4—84no—
1226C2×C4—88no—
1227C2×C4C2×H(5,𝔽2)14yes—
1228C2×C4C2×H(5,𝔽2)12yes—
1229C2×C4C2×2−1+414yes—
1230C2×C4C2×2−1+414yes—
1231C2×C4#58512yes—
1232C2×C4#58512yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—41no—
1241C22—41no—
1242C22—42no—
1243C22—41no—
1244C22—42no—
1245C22C22×H(5,𝔽2)11yescharacteristic
1246C22C22×2−1+412yes—
1247C22C2×#58511yescharacteristic
1248C22C2×#58511yescharacteristic
1249C222−1+612yes—
1250C4—24no—
1251C4—24no—
1252C4—24no—
1253C4—41no—
1254C4—42no—
1255C4—41no—
1256C4—41no—
1257C4—44no—
1258C4—41no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—44no—
1263C4—44no—
1264C4—44no—
1265C4—41no—
1266C4—42no—
1267C4—44no—
1268C4—44no—
1269C4—44no—
1270C4—42no—
1271C4—44no—
1272C4—42no—
1273C4—42no—
1274C4#352914yes—
1275C2—44no—
1276C2—81no—
1277C2C2×#352911yescharacteristic
1278C2#6283711yescharacteristic
1279C2#6289011yescharacteristic
1280C2#6294212yes—
1281C2#6295012yes—
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. #53150C2semidirect
2. #53146C2semidirect
3. #53140C2semidirect
4. #53032C2semidirect
5. #53030C2semidirect
7. #52954C2semidirect
8. #52947C2semidirect
9. #52933C2semidirect
10. #52929C2semidirect
11. #46069C2semidirect
12. #46002C2semidirect
13. #45666C2semidirect
14. #45626C2semidirect
15. #45585C2semidirect
17. #45503C2semidirect
18. #45496C2semidirect
19. #35656C2semidirect
20. #35645C2semidirect
21. #35637C2semidirect
22. #35323C2semidirect
23. #35319C2semidirect
24. #35248C2semidirect
25. #35244C2semidirect
27. #34691C2semidirect

Maximal subgroups

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

subgroupindex
#531502
#531462
#531402
#530322
#530302
#530112
#529542
#529472
#529332
#529292
#460692
#460022
#456662
#456262
#455852
#455752
#455032
#454962
#356562
#356452
#356372
#353232
#353192
#352482
#352442
#348792
#346912