Finite Group Databasebeta

← #7715655

Subgroups — #7715655

Order 512.

4342 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#49616C214yesmaximal, complemented
2#49614C214yesmaximal, complemented
3#47909C214yesmaximal, complemented
4#47907C214yesmaximal, complemented
5#47806C214yesmaximal, complemented
6#47805C214yesmaximal, complemented
7#47784C214yesmaximal, complemented
8#47751C214yesmaximal, complemented
9#39295C212yesmaximal, complemented
10#39294C212yesmaximal, complemented
11#39285C212yesmaximal, complemented
12#39284C212yesmaximal, complemented
13#38285C212yesmaximal, complemented
14#38284C212yesmaximal, complemented
15#38279C212yesmaximal, complemented
16#38278C212yesmaximal, complemented
17#37642C211yesmaximal, characteristic, complemented
18#37542C211yesmaximal, characteristic, complemented
19#37381C211yesmaximal, characteristic, complemented
20#37284C211yesmaximal, characteristic
21#37282C212yesmaximal, complemented
22#35324C211yesmaximal, characteristic, complemented
23#35302C212yesmaximal, complemented
24#35296C211yesmaximal, characteristic, complemented
25#35290C212yesmaximal, complemented
26#34383C212yesmaximal, complemented
27#34048C211yesmaximal, characteristic, complemented
28C2×#529C2212yes—
29C22×#117C2211yescharacteristic
30#2864C2211yescharacteristic, complemented
31#2864C2211yescharacteristic, complemented
32#2863C2212yescomplemented
33#2862C2211yescharacteristic, complemented
34#2860C2212yescomplemented
35#2858C2211yescharacteristic, complemented
36#2855C2212yes—
37#2854C2212yes—
38#2848C2212yes—
39#2847C2212yes—
40#2844C2212yescomplemented
41#2844C2212yescomplemented
42#2823C2212yescomplemented
43#2823C2212yescomplemented
44#2803C2214yes—
45#2800C2214yes—
46#2800C2214yes—
47#2795C2214yes—
48#2794C2214yescomplemented
49#2793C2214yes—
50#2793C2214yescomplemented
51#2789C2214yescomplemented
52#2788C2214yes—
53#2788C2214yescomplemented
54#2785C2214yes—
55#2784C2214yes—
56#2784C2214yescomplemented
57#2783C2214yescomplemented
58#2779C2214yes—
59#2779C2214yes—
60#2779C2214yescomplemented
61#2778C2214yes—
62#2778C2214yes—
63#2776C2214yescomplemented
64#2775C2214yes—
65#2775C2214yescomplemented
66#2772C2214yes—
67#2772C2214yescomplemented
68#2771C2212yes—
69#2770C2214yes—
70#2770C2214yescomplemented
71#2766C2214yescomplemented
72#2764C2212yes—
73#2761C2214yes—
74#2760C2212yes—
75#2753C2214yes—
76#2752C2212yes—
77#2751C2214yes—
78#2750C2214yes—
79#2750C2214yescomplemented
80#2743C2214yes—
81#2739C2214yescomplemented
82#2736C2212yes—
83#2735C2212yes—
84#2731C2214yes—
85#2731C2214yescomplemented
86#2716C2214yes—
87#2716C2214yescomplemented
88#2715C2214yes—
89#2715C2214yes—
90#2686C2214yes—
91#2686C2214yes—
92#2685C2214yes—
93#2684C2214yes—
94#2670C2212yes—
95#2668C2212yes—
96#2647C2212yescomplemented
97#2645C2212yescomplemented
98#2644C2212yescomplemented
99#2640C2212yescomplemented
100#2630C2214yes—
101#2630C2214yes—
102#2629C2212yes—
103#2629C2212yes—
104#2628C2211yescharacteristic
105#2628C2214yes—
106#2628C2214yes—
107#2628C2212yes—
108#2628C2211yescharacteristic
109#2621C2211yescharacteristic
110#2620C2212yes—
111#2620C2212yes—
112#2620C2212yes—
113#2619C2211yescharacteristic
114#2610C2214yes—
115#2609C2214yes—
116#2609C2214yes—
117#2609C2212yescomplemented
118#2609C2212yescomplemented
119#2608C2214yescomplemented
120#2601C2214yes—
121#2601C2214yes—
122#2601C2214yes—
123#2599C2214yescomplemented
124#2595C2214yes—
125#2595C2214yescomplemented
126#2594C2214yes—
127#2591C2214yes—
128#2590C2214yescomplemented
129#2588C2214yescomplemented
130#2588C2214yescomplemented
131#2579C2214yes—
132#2576C2214yescomplemented
133#2575C2214yes—
134#2574C2214yescomplemented
135#2574C2214yescomplemented
136#2573C2214yescomplemented
137#2573C2214yescomplemented
138#2572C2214yes—
139#2571C2212yescomplemented
140#2571C2212yescomplemented
141#2571C2212yescomplemented
142#2566C2212yescomplemented
143#2565C2212yescomplemented
144#2559C2214yes—
145#2557C2214yes—
146#2553C2214yes—
147#2551C2212yescomplemented
148#2551C2212yescomplemented
149#2551C2212yescomplemented
150#2545C2214yes—
151#2545C2212yescomplemented
152#2544C2212yescomplemented
153#2534C2214yes—
154#2529C2214yes—
155#2528C2214yescomplemented
156#2528C2214yescomplemented
157#2527C2214yes—
158#2526C2214yescomplemented
159#2525C2214yes—
160#2525C2214yescomplemented
161#2525C2214yescomplemented
162#2518C2214yes—
163#2518C2214yes—
164#2516C2214yes—
165#2515C2214yescomplemented
166#2497C2212yes—
167#2496C2212yes—
168#2495C2212yes—
169#2494C2212yes—
170#2492C2212yes—
171#2492C2212yes—
172#2491C2212yes—
173#2491C2212yes—
174#2491C2214yes—
175#2484C2214yescomplemented
176#2481C2214yes—
177#2481C2214yescomplemented
178#2474C2214yes—
179#2474C2214yes—
180#2474C2214yescomplemented
181#2474C2214yescomplemented
182#2471C2214yes—
183#2469C2214yes—
184#2469C2214yescomplemented
185#2458C2214yes—
186#2446C2214yescomplemented
187#2439C2214yescomplemented
188#2429C2212yes—
189#2428C2212yes—
190#2427C2212yes—
191#2426C2212yes—
192#2421C2212yes—
193#2421C2212yes—
194#2420C2212yes—
195#2420C2212yes—
196#2413C2214yes—
197#2411C2214yes—
198#2376C2214yes—
199#2376C2214yes—
200#2370C2212yescomplemented
201#2370C2212yescomplemented
202#2367C2212yescomplemented
203#2367C2212yescomplemented
204#2355C2212yescomplemented
205#2354C2214yes—
206#2354C2212yescomplemented
207#2352C2214yes—
208Q8×C4⋊C4C2212yescomplemented
209D4×C4⋊C4C2212yescomplemented
210#2334C2214yescomplemented
211#2334C2214yescomplemented
212#2331C2211yescharacteristic, complemented
213#2331C2211yescharacteristic, complemented
214#2328C2211yescharacteristic, complemented
215#2327C2211yescharacteristic, complemented
216#2324C2212yes—
217#2324C2212yes—
218#2324C2212yes—
219#2324C2212yes—
220#2323C2212yes—
221#2323C2212yes—
222#2323C2212yes—
223#2323C2212yes—
224#2320C2212yescomplemented
225#2319C2212yescomplemented
226#2317C2214yescomplemented
227#2314C2212yes—
228#2314C2212yes—
229#2314C2212yes—
230#2314C2212yes—
231#2314C2214yescomplemented
232#2313C2212yes—
233#2313C2212yes—
234#2312C2212yes—
235#2312C2212yes—
236C4×C4⋊Q8C2212yescomplemented
237C4×#124C2212yescomplemented
238#2298C2212yes—
239#2298C2212yes—
240#2298C2212yes—
241#2298C2212yes—
242#2295C2212yescomplemented
243#2293C2212yescomplemented
244#2285C2211yescharacteristic
245#2285C2211yescharacteristic
246#2285C2212yes—
247#2280C2211yescharacteristic
248#2280C2211yescharacteristic
249C4×#117C2211yescharacteristic
250C4×#117C2211yescharacteristic
251C24×C4C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2311yescharacteristic
256C2×C4⋊Q8C2314yes—
257C2×C4⋊Q8C2314yes—
258C2×#127C2311yescharacteristic
259#529—216no—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#125C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2314yes—
267C2×#124C2314yes—
268C2×#124C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2314yes—
278C2×#120C2314yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×#117—28no—
288C2×#117C2312yes—
289C2×#117C2312yes—
290C2×#117C2314yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2311yescharacteristic
294C2×#117C2311yescharacteristic
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2314yes—
298C2×#117C2314yes—
299C2×#117C2314yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2314yes—
302C22×C22⋊C4C2312yes—
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305#401C2314yes—
306#401C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2312yes—
312#400C2314yes—
313#400C2312yes—
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#399C2312yes—
327#399C2314yes—
328#399C2312yes—
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2312yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2312yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2312yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2312yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2312yes—
380#394C2314yes—
381#394C2312yes—
382#394C2312yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2312yes—
402#393C2312yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#392C2314yes—
407#392C2312yes—
408#392C2312yes—
409#391C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#390C2312yes—
425#390C2314yes—
426#390C2314yes—
427#390C2312yes—
428#390C2312yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#389C2314yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#388C2312yes—
460#388C2312yes—
461#388C2312yes—
462#388C2312yes—
463#388C2312yes—
464#388C2312yes—
465#388C2312yes—
466#388C2312yes—
467#388C2312yes—
468#388C2312yes—
469#388C2312yes—
470#388C2312yes—
471#388C2312yes—
472#388C2312yes—
473#388C2312yes—
474#388C2312yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
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#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2312yes—
520#387C2312yes—
521#387C2312yes—
522#387C2312yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
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#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#384C2312yes—
598#384C2311yescharacteristic
599#384C2311yescharacteristic
600#384C2312yes—
601#384C2312yes—
602#384C2314yes—
603#384C2312yes—
604#383C2314yes—
605#383C2314yes—
606#383C2314yes—
607#382C2311yescharacteristic
608#382C2311yescharacteristic
609#382C2311yescharacteristic
610#382C2311yescharacteristic
611#382C2312yes—
612#382C2314yes—
613#382C2314yes—
614#382C2311yescharacteristic
615#382C2311yescharacteristic
616#382C2312yes—
617#382C2314yes—
618#382C2314yes—
619#382C2314yes—
620#382C2314yes—
621#381C2312yes—
622#381C2311yescharacteristic
623#381C2311yescharacteristic
624#381C2314yes—
625#381C2314yes—
626#381C2314yes—
627#381C2314yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2312yes—
646#380C2312yes—
647#379C2311yescharacteristic
648#379C2311yescharacteristic
649#379C2312yes—
650#379C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685#376C2312yes—
686#376C2311yescharacteristic
687#376C2311yescharacteristic
688#376C2314yes—
689C43C2312yes—
690C43C2311yescharacteristic
691C43C2311yescharacteristic
692C25C2411yescharacteristic
693C22×Q8C2412yes—
694C22×Q8C2414yes—
695C22×Q8C2412yes—
696C22×Q8C2412yes—
697C22×D4C2412yes—
698C22×D4C2414yes—
699C22×D4C2414yes—
700C22×D4C2414yes—
701C22×D4C2412yes—
702C22×D4C2412yes—
703C23×C4—24no—
704C23×C4—42no—
705C23×C4—42no—
706C23×C4C2412yes—
707C23×C4C2411yescharacteristic
708C23×C4C2412yes—
709C23×C4C2411yescharacteristic
710C23×C4C2414yes—
711C23×C4C2412yes—
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2412yes—
715C4⋊Q8—44no—
716C4⋊Q8—42no—
717C4⋊Q8—42no—
718C4⋊Q8—42no—
719C4⋊Q8—84no—
720C4⋊Q8—84no—
721#127—42no—
722#126—216no—
723#126—84no—
724#126—84no—
725#125—28no—
726#124—28no—
727#124—44no—
728#124—84no—
729#124—84no—
730#124—84no—
731#123—216no—
732#123—84no—
733C22⋊Q8—28no—
734C22⋊Q8—44no—
735C22⋊Q8—44no—
736#121—28no—
737#121—44no—
738#121—44no—
739#121—84no—
740#120—84no—
741C4×Q8—28no—
742C4×Q8—44no—
743C4×Q8—44no—
744C4×Q8—84no—
745C4×D4—216no—
746C4×D4—28no—
747C4×D4—44no—
748C4×D4—44no—
749#117—28no—
750#117—28no—
751#117—28no—
752#117—28no—
753#117—216no—
754#117—42no—
755#117—42no—
756#117—42no—
757#117—42no—
758#117—84no—
759#117—84no—
760#117—84no—
761C2×C4⋊C4—28no—
762C2×C4⋊C4—84no—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C22⋊C4—28no—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2411yescharacteristic
837C2×C22⋊C4C2411yescharacteristic
838C2×C22⋊C4C2411yescharacteristic
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C42—24no—
869C2×C42#4118yes—
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2412yes—
873C2×C42C2411yescharacteristic
874C2×C42C2412yes—
875C2×C42C2414yes—
876C2×C42C2411yescharacteristic
877C2×C42C2412yes—
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2411yescharacteristic
897C2×C42C2412yes—
898C2×C42C2411yescharacteristic
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969C24—22no—
970C24—41no—
971C24—41no—
972C24—42no—
973C24—42no—
974C24C2512yes—
975C24C2514yes—
976C24C2511yescharacteristic
977C2×Q8—24no—
978C2×Q8—24no—
979C2×Q8—24no—
980C2×Q8—44no—
981C2×Q8—44no—
982C2×Q8—44no—
983C2×Q8—44no—
984C2×Q8—44no—
985C2×Q8—42no—
986C2×Q8—42no—
987C2×D4—28no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—42no—
1000C2×D4—42no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—22no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—28no—
1010C22×C4—24no—
1011C22×C4—24no—
1012C22×C4—44no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—416no—
1029C22×C4C2×#4114yes—
1030C22×C4C2×#4118yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2511yescharacteristic
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2514yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—24no—
1064C4⋊C4—28no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C22⋊C4—28no—
1111C22⋊C4—24no—
1112C22⋊C4—24no—
1113C22⋊C4—24no—
1114C22⋊C4—24no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—44no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—44no—
1127C22⋊C4—42no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—42no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—42no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—42no—
1154C22⋊C4—42no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—42no—
1159C42—24no—
1160C42—22no—
1161C42—22no—
1162C42—28no—
1163C42—22no—
1164C42—24no—
1165C42—22no—
1166C42—24no—
1167C42—22no—
1168C42—22no—
1169C42—42no—
1170C42—42no—
1171C42—42no—
1172C42—42no—
1173C42—42no—
1174C42—44no—
1175C42—44no—
1176C42—44no—
1177C42—44no—
1178C42—44no—
1179C42—44no—
1180C42—44no—
1181C42—42no—
1182C42—44no—
1183C42—42no—
1184C42—42no—
1185C42C2×#4114yes—
1186C42C2×#4118yes—
1187C42C2×#4114yes—
1188C23—21no—
1189C23—21no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—24no—
1194C23—24no—
1195C23—24no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—24no—
1200C23—24no—
1201C23—22no—
1202C23—22no—
1203C23—24no—
1204C23—22no—
1205C23—24no—
1206C23—44no—
1207C23—84no—
1208C23—84no—
1209C23—82no—
1210C23—82no—
1211C23C22×#4112yes—
1212C23C2611yescharacteristic
1213Q8—48no—
1214Q8—88no—
1215Q8—162no—
1216Q8—162no—
1217D4—48no—
1218D4—88no—
1219D4—164no—
1220D4—162no—
1221D4—164no—
1222D4—162no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—28no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—48no—
1287C2×C4—416no—
1288C2×C4—48no—
1289C2×C4—44no—
1290C2×C4—48no—
1291C2×C4—84no—
1292C2×C4—88no—
1293C2×C4—164no—
1294C2×C4C22×#4112yes—
1295C2×C4C22×#4114yes—
1296C2×C4C22×#4114yes—
1297C2×C4C22×#4112yes—
1298C2×C4#58512yes—
1299C2×C4#58512yes—
1300C22—22no—
1301C22—24no—
1302C22—42no—
1303C22—41no—
1304C22—41no—
1305C22—42no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—42no—
1310C22—42no—
1311C22—44no—
1312C22—42no—
1313C22—44no—
1314C22—42no—
1315C22—44no—
1316C22—42no—
1317C22—44no—
1318C22—42no—
1319C22—88no—
1320C22C23×#4111yescharacteristic
1321C22C2×#58511yescharacteristic
1322C22C2×#58511yescharacteristic
1323C22H(7,𝔽2)12yes—
1324C222−1+612yes—
1325C4—22no—
1326C4—24no—
1327C4—24no—
1328C4—42no—
1329C4—44no—
1330C4—44no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—41no—
1341C4—44no—
1342C4—42no—
1343C4—44no—
1344C4—41no—
1345C4—42no—
1346C4—41no—
1347C4—41no—
1348C4#349314yes—
1349C2—42no—
1350C2—84no—
1351C2—82no—
1352C2C2×#349311yescharacteristic
1353C2#6285612yes—
1354C2#6288212yes—
1355C2#6288511yescharacteristic
1356C2#6289111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37284C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #49616C2semidirect
2. #49614C2semidirect
3. #47909C2semidirect
4. #47907C2semidirect
5. #47806C2semidirect
6. #47805C2semidirect
7. #47784C2semidirect
8. #47751C2semidirect
9. #39295C2semidirect
10. #39294C2semidirect
11. #39285C2semidirect
12. #39284C2semidirect
13. #38285C2semidirect
14. #38284C2semidirect
15. #38279C2semidirect
16. #38278C2semidirect
17. #37642C2semidirect
18. #37542C2semidirect
19. #37381C2semidirect
21. #37282C2semidirect
22. #35324C2semidirect
23. #35302C2semidirect
24. #35296C2semidirect
25. #35290C2semidirect
26. #34383C2semidirect
27. #34048C2semidirect
30. #2864C22semidirect
31. #2864C22semidirect
32. #2863C22semidirect
33. #2862C22semidirect
34. #2860C22semidirect
35. #2858C22semidirect
40. #2844C22semidirect
41. #2844C22semidirect
42. #2823C22semidirect
43. #2823C22semidirect
48. #2794C22semidirect
50. #2793C22semidirect
51. #2789C22semidirect
53. #2788C22semidirect
56. #2784C22semidirect
57. #2783C22semidirect
60. #2779C22semidirect
63. #2776C22semidirect
65. #2775C22semidirect
67. #2772C22semidirect
70. #2770C22semidirect
71. #2766C22semidirect
79. #2750C22semidirect
81. #2739C22semidirect
85. #2731C22semidirect
87. #2716C22semidirect
96. #2647C22semidirect
97. #2645C22semidirect
98. #2644C22semidirect
99. #2640C22semidirect
117. #2609C22semidirect
118. #2609C22semidirect
119. #2608C22semidirect
123. #2599C22semidirect
125. #2595C22semidirect
128. #2590C22semidirect
129. #2588C22semidirect
130. #2588C22semidirect
132. #2576C22semidirect
134. #2574C22semidirect
135. #2574C22semidirect
136. #2573C22semidirect
137. #2573C22semidirect
139. #2571C22semidirect
140. #2571C22semidirect
141. #2571C22semidirect
142. #2566C22semidirect
143. #2565C22semidirect
147. #2551C22semidirect
148. #2551C22semidirect
149. #2551C22semidirect
151. #2545C22semidirect
152. #2544C22semidirect
155. #2528C22semidirect
156. #2528C22semidirect
158. #2526C22semidirect
160. #2525C22semidirect
161. #2525C22semidirect
165. #2515C22semidirect
175. #2484C22semidirect
177. #2481C22semidirect
180. #2474C22semidirect
181. #2474C22semidirect
184. #2469C22semidirect
186. #2446C22semidirect
187. #2439C22semidirect
200. #2370C22semidirect
201. #2370C22semidirect
202. #2367C22semidirect
203. #2367C22semidirect
204. #2355C22semidirect
206. #2354C22semidirect
208. Q8×C4⋊C4C22semidirect
209. D4×C4⋊C4C22semidirect
210. #2334C22semidirect
211. #2334C22semidirect
212. #2331C22semidirect
213. #2331C22semidirect
214. #2328C22semidirect
215. #2327C22semidirect
224. #2320C22semidirect
225. #2319C22semidirect
226. #2317C22semidirect
231. #2314C22semidirect
236. C4×C4⋊Q8C22semidirect
237. C4×#124C22semidirect
242. #2295C22semidirect
243. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#496162
#496142
#479092
#479072
#478062
#478052
#477842
#477512
#392952
#392942
#392852
#392842
#382852
#382842
#382792
#382782
#376422
#375422
#373812
#372842
#372822
#353242
#353022
#352962
#352902
#343832
#340482