Finite Group Databasebeta

← #7695525

Subgroups — #7695525

Order 512.

4415 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59927C212yesmaximal, complemented
2#59832C211yesmaximal, characteristic, complemented
3#59732C214yesmaximal, complemented
4#59501C212yesmaximal, complemented
5#52306C212yesmaximal
6#52272C211yesmaximal, characteristic
7#45338C212yesmaximal
8#45324C212yesmaximal, complemented
9#45284C212yesmaximal, complemented
10#44425C214yesmaximal, complemented
11#44391C214yesmaximal, complemented
12#44269C214yesmaximal
13#40215C214yesmaximal, complemented
14#39637C211yesmaximal, characteristic, complemented
15#39373C211yesmaximal, characteristic
16#39294C212yesmaximal, complemented
17#38811C212yesmaximal
18#38790C212yesmaximal, complemented
19#38623C214yesmaximal, complemented
20#38229C212yesmaximal, complemented
21#36554C212yesmaximal, complemented
22#36535C211yesmaximal, characteristic, complemented
23#35919C212yesmaximal, complemented
24#35911C212yesmaximal
25#35843C212yesmaximal, complemented
26#34335C212yesmaximal, complemented
27#34328C211yesmaximal, characteristic, complemented
28#34322C211yesmaximal, characteristic
29#34286C212yesmaximal, complemented
30C2×Q82C2212yes—
31C2×#557C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#541C2212yes—
34#2864C2212yes—
35#2863C2214yes—
36#2863C2212yes—
37#2859C2211yescharacteristic
38#2810C2211yescharacteristic
39#2809C2212yes—
40#2808C2211yescharacteristic
41#2806C2212yes—
42#2805C2211yescharacteristic
43#2805C2212yes—
44#2800C2212yes—
45#2798C2212yes—
46#2793C2212yes—
47#2789C2214yes—
48#2777C2214yes—
49#2776C2212yes—
50#2776C2214yes—
51#2775C2214yes—
52#2775C2214yes—
53#2769C2214yes—
54#2769C2214yes—
55#2767C2214yes—
56#2767C2214yes—
57#2767C2214yes—
58#2762C2214yes—
59#2759C2212yes—
60#2754C2214yes—
61#2734C2212yes—
62#2734C2212yes—
63#2731C2214yes—
64#2731C2214yes—
65#2727C2211yescharacteristic
66#2727C2212yes—
67#2727C2212yes—
68#2726C2214yes—
69#2726C2212yes—
70#2726C2212yes—
71#2726C2212yes—
72#2725C2214yes—
73#2721C2214yes—
74#2721C2214yes—
75#2719C2214yes—
76#2716C2214yes—
77#2716C2214yes—
78#2716C2212yes—
79#2716C2214yes—
80#2665C2214yes—
81#2655C2214yes—
82#2655C2214yes—
83#2647C2212yes—
84#2645C2212yes—
85#2629C2212yes—
86#2612C2214yes—
87#2612C2214yes—
88#2608C2214yes—
89#2604C2214yes—
90#2594C2214yes—
91#2590C2214yes—
92#2590C2214yes—
93#2590C2214yes—
94#2589C2214yes—
95#2589C2214yes—
96#2588C2214yes—
97#2588C2214yes—
98#2588C2214yes—
99#2586C2214yes—
100#2585C2214yes—
101#2585C2214yes—
102#2585C2214yes—
103#2585C2214yes—
104#2584C2212yes—
105#2582C2212yes—
106#2581C2212yes—
107#2575C2214yes—
108#2574C2214yes—
109#2571C2211yescharacteristic
110#2570C2212yes—
111#2565C2212yes—
112#2565C2214yes—
113#2552C2211yescharacteristic
114#2551C2212yes—
115#2551C2212yes—
116#2550C2212yes—
117#2546C2214yes—
118#2536C2212yes—
119#2533C2214yes—
120#2532C2214yes—
121#2530C2214yes—
122#2529C2214yes—
123#2528C2214yes—
124#2528C2214yes—
125#2528C2214yes—
126#2527C2214yes—
127#2527C2214yes—
128#2522C2214yes—
129#2520C2214yes—
130#2520C2214yes—
131#2520C2214yes—
132#2519C2214yes—
133#2519C2214yes—
134#2519C2214yes—
135#2519C2214yes—
136#2514C2214yes—
137#2509C2212yes—
138#2508C2212yes—
139#2507C2212yes—
140#2506C2214yes—
141#2506C2212yes—
142#2496C2212yes—
143#2494C2212yes—
144#2492C2212yes—
145#2492C2212yes—
146#2478C2214yes—
147#2475C2214yes—
148#2469C2214yes—
149#2469C2214yes—
150#2469C2214yes—
151#2469C2214yes—
152#2468C2214yes—
153#2462C2214yes—
154#2453C2214yes—
155#2453C2214yes—
156#2451C2212yes—
157#2451C2214yes—
158#2451C2212yes—
159#2446C2214yes—
160#2446C2212yes—
161#2446C2212yes—
162#2446C2214yes—
163#2446C2214yes—
164#2446C2214yes—
165#2439C2212yes—
166#2439C2212yes—
167#2439C2214yes—
168#2429C2212yes—
169#2429C2212yes—
170#2423C2212yes—
171#2423C2212yes—
172#2423C2212yes—
173#2421C2212yes—
174#2401C2212yes—
175#2398C2212yes—
176#2396C2212yes—
177#2396C2214yes—
178#2396C2214yes—
179#2395C2214yes—
180#2373C2214yes—
181#2373C2214yes—
182#2373C2214yes—
183#2371C2214yes—
184#2371C2214yes—
185#2371C2214yes—
186#2370C2212yes—
187#2370C2214yes—
188#2370C2212yes—
189#2370C2212yes—
190#2369C2212yes—
191#2369C2214yes—
192#2367C2212yes—
193#2365C2212yes—
194#2365C2212yes—
195#2365C2211yescharacteristic
196#2365C2214yes—
197#2365C2212yes—
198#2365C2211yescharacteristic
199#2365C2214yes—
200#2365C2212yes—
201#2362C2212yes—
202#2362C2212yes—
203#2360C2212yes—
204#2360C2212yes—
205#2360C2212yes—
206#2356C2212yes—
207#2356C2212yes—
208#2355C2211yescharacteristic
209#2355C2211yescharacteristic
210#2355C2211yescharacteristic
211#2355C2212yes—
212#2355C2214yes—
213#2355C2211yescharacteristic
214#2355C2211yescharacteristic
215#2351C2212yes—
216#2351C2212yes—
217#2351C2212yes—
218Q8×C4⋊C4C2212yes—
219D4×C4⋊C4C2211yescharacteristic
220#2346C2212yes—
221#2345C2212yes—
222#2344C2212yes—
223#2336C2214yes—
224#2336C2214yes—
225#2334C2214yes—
226#2334C2214yes—
227#2331C2212yes—
228#2331C2212yes—
229#2331C2214yes—
230#2331C2214yes—
231#2327C2212yes—
232#2323C2212yes—
233#2320C2212yes—
234C4×C4⋊Q8C2211yescharacteristic
235C4×C4⋊Q8C2214yes—
236C4×C4⋊Q8C2211yescharacteristic
237C4×C4⋊Q8C2212yes—
238C4×C4⋊Q8C2211yescharacteristic
239C4×#125C2214yes—
240C4×#125C2212yes—
241C4×#125C2212yes—
242C4×#126C2212yes—
243C4×#126C2214yes—
244C4×#126C2214yes—
245C4×#124C2212yes—
246#2298C2212yes—
247#2295C2212yes—
248#2295C2212yes—
249#2295C2211yescharacteristic
250#2295C2212yes—
251#2295C2214yes—
252#2295C2212yes—
253#2293C2211yescharacteristic
254#2276C2212yes—
255#2276C2212yes—
256#2274C2212yes—
257C42×Q8C2211yescharacteristic
258C42×Q8C2212yes—
259Q82—216no—
260#557—28no—
261#556—28no—
262#541—216no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×#126C2312yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#124C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2314yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2314yes—
313C22×C4⋊C4C2312yes—
314#401C2314yes—
315#401C2312yes—
316#401C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2312yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2312yes—
339#400C2312yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
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#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#397C2312yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2312yes—
375#397C2312yes—
376#397C2312yes—
377#397C2312yes—
378#396C2314yes—
379#396C2314yes—
380#396C2312yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2312yes—
385#396C2314yes—
386#396C2312yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2312yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#394C2312yes—
395#394C2314yes—
396#394C2312yes—
397#393C2314yes—
398#393C2312yes—
399#393C2314yes—
400#393C2312yes—
401#393C2314yes—
402#393C2314yes—
403#393C2312yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2311yescharacteristic
433#391C2314yes—
434#391C2312yes—
435#391C2311yescharacteristic
436#390C2311yescharacteristic
437#390C2311yescharacteristic
438#389C2311yescharacteristic
439#389C2311yescharacteristic
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2312yes—
444#389C2314yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2311yescharacteristic
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2311yescharacteristic
491#389C2314yes—
492#389C2312yes—
493#389C2311yescharacteristic
494#389C2314yes—
495#389C2311yescharacteristic
496#388C2312yes—
497#388C2312yes—
498#388C2314yes—
499#388C2312yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2312yes—
512#388C2312yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2312yes—
517#388C2314yes—
518#388C2314yes—
519#388C2312yes—
520#388C2312yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2312yes—
529#387C2314yes—
530#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2312yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2312yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#384C2312yes—
610#384C2314yes—
611#384C2311yescharacteristic
612#384C2311yescharacteristic
613#384C2311yescharacteristic
614#384C2311yescharacteristic
615#384C2311yescharacteristic
616#383C2314yes—
617#383C2312yes—
618#383C2314yes—
619#383C2314yes—
620#382C2312yes—
621#382C2314yes—
622#382C2312yes—
623#382C2312yes—
624#382C2314yes—
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2312yes—
629#382C2314yes—
630#382C2314yes—
631#382C2312yes—
632#382C2314yes—
633#381C2314yes—
634#380C2314yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2311yescharacteristic
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2314yes—
708#376C2314yes—
709#376C2314yes—
710#376C2314yes—
711#376C2314yes—
712C43C2314yes—
713C43C2312yes—
714C43C2312yes—
715C43C2311yescharacteristic
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2414yes—
721C22×Q8C2414yes—
722C22×Q8C2412yes—
723C22×D4C2411yescharacteristic
724C23×C4C2412yes—
725C23×C4C2414yes—
726C4⋊Q8—28no—
727C4⋊Q8—216no—
728C4⋊Q8—216no—
729C4⋊Q8—28no—
730C4⋊Q8—28no—
731C4⋊Q8—216no—
732C4⋊Q8—24no—
733C4⋊Q8—84no—
734C4⋊Q8#4118yes—
735C4⋊Q8#4118yes—
736#126—216no—
737#126—216no—
738#126—216no—
739#126—28no—
740#126—84no—
741#125—216no—
742#125—216no—
743#125—216no—
744#125—28no—
745#125—28no—
746#125—28no—
747#125—84no—
748#124—28no—
749C22⋊Q8—28no—
750C22⋊Q8—28no—
751C22⋊Q8—28no—
752C4×Q8—28no—
753C4×Q8—28no—
754C4×Q8—28no—
755C4×Q8—28no—
756C4×Q8—28no—
757C4×Q8—28no—
758C4×Q8—28no—
759C4×Q8—216no—
760C4×Q8—28no—
761C4×Q8—24no—
762C4×Q8—24no—
763C4×Q8—24no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—28no—
767C4×Q8—84no—
768C4×Q8—82no—
769C4×Q8—84no—
770C4×Q8—82no—
771C4×D4—24no—
772C4×D4—82no—
773#117—28no—
774#117—28no—
775#117—84no—
776C2×C4⋊C4—28no—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2414yes—
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2411yescharacteristic
912C2×C42C2414yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996C24C2512yes—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—22no—
1000C2×Q8—22no—
1001C2×Q8—22no—
1002C2×Q8—28no—
1003C2×Q8—28no—
1004C2×Q8—24no—
1005C2×Q8—22no—
1006C2×Q8—24no—
1007C2×Q8—42no—
1008C2×Q8—42no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C2×Q8—42no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—44no—
1015C2×Q8—44no—
1016C2×Q8C2×#4118yes—
1017C2×Q8C2×#4118yes—
1018C2×D4—22no—
1019C2×D4—41no—
1020C2×D4—41no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—28no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2512yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2514yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2514yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C4⋊C4—22no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—22no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—22no—
1096C4⋊C4—42no—
1097C4⋊C4—41no—
1098C4⋊C4—42no—
1099C4⋊C4—41no—
1100C4⋊C4—41no—
1101C4⋊C4—41no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—41no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—41no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4C2×#4118yes—
1129C4⋊C4C2×#4118yes—
1130C4⋊C4C2×#4118yes—
1131C4⋊C4C2×#4118yes—
1132C4⋊C42−1+414yes—
1133C4⋊C42−1+414yes—
1134C22⋊C4—28no—
1135C22⋊C4—24no—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—24no—
1142C22⋊C4—24no—
1143C22⋊C4—24no—
1144C22⋊C4—42no—
1145C22⋊C4—42no—
1146C22⋊C4—42no—
1147C22⋊C4—44no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—42no—
1154C42—24no—
1155C42—28no—
1156C42—24no—
1157C42—28no—
1158C42—24no—
1159C42—28no—
1160C42—28no—
1161C42—28no—
1162C42—24no—
1163C42—24no—
1164C42—24no—
1165C42—28no—
1166C42—28no—
1167C42—22no—
1168C42—24no—
1169C42—28no—
1170C42—24no—
1171C42—24no—
1172C42—24no—
1173C42—22no—
1174C42—42no—
1175C42—44no—
1176C42—41no—
1177C42—42no—
1178C42—41no—
1179C42—44no—
1180C42—44no—
1181C42—42no—
1182C42—44no—
1183C42—44no—
1184C42—42no—
1185C42—44no—
1186C42—41no—
1187C42—42no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42C2×#4114yes—
1192C42C2×#4114yes—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23C2611yescharacteristic
1201Q8—216no—
1202Q8—48no—
1203Q8—48no—
1204Q8—44no—
1205Q8—44no—
1206Q8—88no—
1207Q8—88no—
1208D4—44no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—24no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—21no—
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—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—48no—
1282C2×C4—88no—
1283C2×C4C22×#4112yes—
1284C2×C4C22×#4118yes—
1285C2×C4C22×#4118yes—
1286C2×C4C22×#4112yes—
1287C2×C4C22×#4112yes—
1288C2×C4C22×#4112yes—
1289C2×C4C22×#4112yes—
1290C2×C4C22×#4112yes—
1291C2×C4C2×2−1+412yes—
1292C2×C4C2×2−1+414yes—
1293C2×C4C2×2−1+414yes—
1294C2×C4C2×2−1+412yes—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22C23×#4111yescharacteristic
1303C22C23×#4111yescharacteristic
1304C22C22×2−1+411yescharacteristic
1305C22C22×2−1+411yescharacteristic
1306C22H(7,𝔽2)11yescharacteristic
1307C222−1+611yescharacteristic
1308C222−1+611yescharacteristic
1309C4—22no—
1310C4—24no—
1311C4—22no—
1312C4—24no—
1313C4—22no—
1314C4—28no—
1315C4—22no—
1316C4—22no—
1317C4—28no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—44no—
1323C4—42no—
1324C4—42no—
1325C4—41no—
1326C4—44no—
1327C4—42no—
1328C4—44no—
1329C4—42no—
1330C4—42no—
1331C4—44no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4#348214yes—
1337C2—82no—
1338C2C2×#348211yescharacteristic
1339C2#6284711yescharacteristic
1340C2#6285011yescharacteristic
1341C2#6294711yescharacteristic
1342C2#6299811yescharacteristic
1343C2#6299911yescharacteristic
1344C2#6305811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59927C2semidirect
2. #59832C2semidirect
3. #59732C2semidirect
4. #59501C2semidirect
8. #45324C2semidirect
9. #45284C2semidirect
10. #44425C2semidirect
11. #44391C2semidirect
13. #40215C2semidirect
14. #39637C2semidirect
16. #39294C2semidirect
18. #38790C2semidirect
19. #38623C2semidirect
20. #38229C2semidirect
21. #36554C2semidirect
22. #36535C2semidirect
23. #35919C2semidirect
25. #35843C2semidirect
26. #34335C2semidirect
27. #34328C2semidirect
29. #34286C2semidirect

Maximal subgroups

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

subgroupindex
#599272
#598322
#597322
#595012
#523062
#522722
#453382
#453242
#452842
#444252
#443912
#442692
#402152
#396372
#393732
#392942
#388112
#387902
#386232
#382292
#365542
#365352
#359192
#359112
#358432
#343352
#343282
#343222
#342862