Finite Group Databasebeta

← #7696305

Subgroups — #7696305

Order 512.

4679 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59924C211yesmaximal, characteristic, complemented
2#59923C212yesmaximal, complemented
3#59921C212yesmaximal, complemented
4#59736C214yesmaximal, complemented
5#52291C212yesmaximal, complemented
6#52267C211yesmaximal, characteristic, complemented
7#45360C212yesmaximal, complemented
8#45281C212yesmaximal, complemented
9#44879C212yesmaximal, complemented
10#43569C214yesmaximal, complemented
11#43563C214yesmaximal, complemented
12#43561C214yesmaximal, complemented
13#39981C214yesmaximal, complemented
14#39711C212yesmaximal, complemented
15#39688C212yesmaximal, complemented
16#39659C214yesmaximal, complemented
17#39637C211yesmaximal, characteristic, complemented
18#39365C211yesmaximal, characteristic, complemented
19#38444C212yesmaximal, complemented
20#38105C212yesmaximal, complemented
21#36564C212yesmaximal, complemented
22#36477C211yesmaximal, characteristic, complemented
23#35871C212yesmaximal, complemented
24#35843C212yesmaximal, complemented
25#35783C212yesmaximal, complemented
26#34334C211yesmaximal, characteristic, complemented
27#34316C211yesmaximal, characteristic
28#34298C212yesmaximal
29#34271C212yesmaximal, complemented
30C2×D4×Q8C2211yescharacteristic
31C2×#547C2211yescharacteristic
32C2×#544C2212yes—
33#2859C2211yescharacteristic
34#2857C2212yes—
35#2857C2214yes—
36#2855C2212yes—
37#2811C2212yes—
38#2811C2212yes—
39#2809C2212yes—
40#2809C2214yes—
41#2807C2212yes—
42#2806C2211yescharacteristic
43#2806C2212yes—
44#2805C2211yescharacteristic
45#2805C2214yes—
46#2805C2212yes—
47#2804C2211yescharacteristic
48#2802C2212yes—
49#2799C2214yes—
50#2790C2212yes—
51#2790C2214yes—
52#2788C2214yes—
53#2788C2212yes—
54#2788C2214yes—
55#2788C2214yes—
56#2784C2214yes—
57#2784C2214yes—
58#2784C2214yes—
59#2784C2214yes—
60#2780C2214yes—
61#2780C2212yes—
62#2755C2214yes—
63#2734C2212yes—
64#2732C2214yes—
65#2732C2214yes—
66#2732C2211yescharacteristic
67#2732C2212yes—
68#2729C2214yes—
69#2729C2214yes—
70#2729C2214yes—
71#2729C2212yes—
72#2726C2212yes—
73#2726C2212yes—
74#2704C2214yes—
75#2692C2214yes—
76#2692C2214yes—
77#2683C2214yes—
78#2683C2212yes—
79#2665C2214yes—
80#2665C2214yes—
81#2665C2214yes—
82#2647C2212yes—
83#2629C2212yes—
84#2628C2212yes—
85#2608C2214yes—
86#2608C2214yes—
87#2607C2214yes—
88#2590C2214yes—
89#2589C2214yes—
90#2588C2214yes—
91#2588C2214yes—
92#2587C2214yes—
93#2587C2214yes—
94#2587C2214yes—
95#2586C2214yes—
96#2586C2214yes—
97#2586C2214yes—
98#2586C2214yes—
99#2586C2214yes—
100#2585C2214yes—
101#2585C2214yes—
102#2584C2212yes—
103#2583C2214yes—
104#2581C2214yes—
105#2574C2214yes—
106#2570C2212yes—
107#2567C2212yes—
108#2567C2214yes—
109#2567C2214yes—
110#2567C2212yes—
111#2566C2212yes—
112#2566C2214yes—
113#2564C2214yes—
114#2556C2214yes—
115#2556C2214yes—
116#2556C2214yes—
117#2551C2212yes—
118#2551C2212yes—
119#2551C2212yes—
120#2551C2212yes—
121#2550C2212yes—
122#2550C2212yes—
123#2549C2214yes—
124#2549C2214yes—
125#2549C2214yes—
126#2549C2214yes—
127#2538C2211yescharacteristic
128#2538C2214yes—
129#2538C2211yescharacteristic
130#2522C2214yes—
131#2520C2214yes—
132#2511C2214yes—
133#2509C2212yes—
134#2509C2212yes—
135#2508C2212yes—
136#2507C2212yes—
137#2507C2214yes—
138#2507C2212yes—
139#2506C2212yes—
140#2497C2214yes—
141#2497C2212yes—
142#2492C2214yes—
143#2492C2214yes—
144#2465C2214yes—
145#2462C2214yes—
146#2454C2212yes—
147#2453C2214yes—
148#2452C2212yes—
149#2452C2212yes—
150#2452C2214yes—
151#2452C2212yes—
152#2452C2214yes—
153#2451C2214yes—
154#2451C2214yes—
155#2450C2214yes—
156#2449C2214yes—
157#2446C2214yes—
158#2446C2214yes—
159#2441C2212yes—
160#2441C2214yes—
161#2440C2212yes—
162#2440C2212yes—
163#2439C2212yes—
164#2439C2214yes—
165#2439C2212yes—
166#2439C2212yes—
167#2438C2214yes—
168#2434C2214yes—
169#2429C2214yes—
170#2429C2214yes—
171#2429C2212yes—
172#2409C2214yes—
173#2402C2212yes—
174#2396C2214yes—
175#2396C2212yes—
176#2396C2214yes—
177#2396C2214yes—
178#2396C2212yes—
179#2374C2214yes—
180#2374C2214yes—
181#2370C2212yes—
182#2370C2212yes—
183#2370C2212yes—
184#2370C2212yes—
185#2370C2214yes—
186#2370C2214yes—
187#2369C2212yes—
188#2369C2214yes—
189#2369C2212yes—
190#2369C2212yes—
191#2369C2212yes—
192#2369C2212yes—
193#2369C2212yes—
194#2368C2214yes—
195#2368C2214yes—
196#2368C2214yes—
197#2365C2212yes—
198#2365C2211yescharacteristic
199#2365C2211yescharacteristic
200#2365C2214yes—
201#2365C2212yes—
202#2363C2212yes—
203#2363C2212yes—
204#2362C2212yes—
205#2361C2212yes—
206#2360C2212yes—
207#2359C2214yes—
208#2357C2212yes—
209#2355C2211yescharacteristic
210#2355C2211yescharacteristic
211#2354C2211yescharacteristic
212#2354C2211yescharacteristic
213#2352C2212yes—
214Q8×C4⋊C4C2211yescharacteristic
215#2349C2212yes—
216D4×C4⋊C4C2211yescharacteristic
217#2345C2212yes—
218#2345C2212yes—
219#2344C2212yes—
220#2341C2212yes—
221Q8×C22⋊C4C2212yes—
222#2339C2214yes—
223#2335C2214yes—
224#2335C2214yes—
225#2332C2214yes—
226#2331C2212yes—
227#2331C2212yes—
228#2329C2214yes—
229#2329C2214yes—
230#2329C2214yes—
231#2324C2212yes—
232#2324C2212yes—
233#2316C2212yes—
234C4×C4⋊Q8C2211yescharacteristic
235C4×C4⋊Q8C2211yescharacteristic
236C4×C4⋊Q8C2211yescharacteristic
237C4×C22⋊Q8C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2212yes—
241C4×C22⋊Q8C2214yes—
242C4×C22⋊Q8C2214yes—
243C4×C22⋊Q8C2214yes—
244C4×#123C2214yes—
245C4×#121C2212yes—
246#2297C2212yes—
247#2297C2214yes—
248#2296C2212yes—
249#2296C2212yes—
250#2295C2211yescharacteristic
251C2×#391C2212yes—
252#2293C2211yescharacteristic
253#2290C2212yes—
254#2275C2212yes—
255#2274C2212yes—
256#2274C2212yes—
257C42×D4C2211yescharacteristic
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2312yes—
260C23×Q8C2312yes—
261D4×Q8—28no—
262#547Q8116yescomplemented
263#544—216no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#123C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×#121C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2314yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2311yescharacteristic
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C2×#117C2312yes—
317C2×#117C2314yes—
318C2×#117C2312yes—
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C42C2312yes—
323C22×C42C2312yes—
324C22×C42C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2312yes—
345#399C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2314yes—
360#398C2312yes—
361#398C2312yes—
362#398C2314yes—
363#398C2312yes—
364#398C2314yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2312yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2312yes—
384#396C2312yes—
385#396C2312yes—
386#396C2314yes—
387#396C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2312yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2312yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2312yes—
410#393C2314yes—
411#393C2314yes—
412#393C2312yes—
413#393C2314yes—
414#393C2314yes—
415#391C2311yescharacteristic
416#391C2312yes—
417#391C2311yescharacteristic
418#391C2312yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2311yescharacteristic
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2311yescharacteristic
450#390C2312yes—
451#390C2314yes—
452#390C2312yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2312yes—
457#390C2311yescharacteristic
458#390C2312yes—
459#390C2311yescharacteristic
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2311yescharacteristic
520#389C2311yescharacteristic
521#389C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2312yes—
531#388C2312yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2312yes—
536#388C2312yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2312yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2312yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2312yes—
587#386C2314yes—
588#386C2314yes—
589#386C2312yes—
590#386C2314yes—
591#385C2312yes—
592#385C2314yes—
593#385C2312yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2312yes—
602#385C2312yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2312yes—
609#385C2314yes—
610#385C2314yes—
611#385C2312yes—
612#385C2312yes—
613#385C2314yes—
614#385C2312yes—
615#384C2311yescharacteristic
616#384C2311yescharacteristic
617#384C2311yescharacteristic
618#384C2314yes—
619#384C2312yes—
620#384C2314yes—
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#382C2312yes—
624#382C2314yes—
625#382C2312yes—
626#382C2312yes—
627#381C2314yes—
628#381C2314yes—
629#380C2312yes—
630#380C2314yes—
631#380C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2314yes—
643#380C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710#376C2312yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C43C2311yescharacteristic
715C2×#41—82no—
716C2×#41—82no—
717C2×#41C2×Q8116yescomplemented
718C22×Q8—28no—
719C22×Q8—82no—
720C22×Q8—82no—
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2414yes—
725C22×Q8C2414yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2414yes—
732C22×D4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2412yes—
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C4⋊Q8—216no—
744C4⋊Q8—24no—
745C4⋊Q8—28no—
746C4⋊Q8—28no—
747C4⋊Q8—44no—
748C4⋊Q8—44no—
749C4⋊Q8—84no—
750C4⋊Q8—84no—
751C4⋊Q8—84no—
752C4⋊Q8C2×Q818yescomplemented
753C4⋊Q8#4118yescomplemented
754#125—216no—
755#125—28no—
756#125—28no—
757#125—84no—
758#123C2×Q8132yescomplemented
759C22⋊Q8—216no—
760C22⋊Q8—28no—
761C22⋊Q8—28no—
762C22⋊Q8—28no—
763C22⋊Q8—216no—
764C22⋊Q8—216no—
765C22⋊Q8—84no—
766C22⋊Q8—82no—
767C22⋊Q8—84no—
768C22⋊Q8—84no—
769C22⋊Q8—84no—
770C22⋊Q8—84no—
771C22⋊Q8—84no—
772C22⋊Q8C2×Q8116yescomplemented
773#121C2×Q8116yes—
774C4×Q8—24no—
775C4×Q8—42no—
776C4×Q8—42no—
777C4×Q8—82no—
778C4×Q8—82no—
779C4×Q8—84no—
780C4×Q8—82no—
781C4×Q8—84no—
782C4×Q8—82no—
783C4×Q8—82no—
784C4×D4—28no—
785C4×D4—24no—
786C4×D4—44no—
787C4×D4—42no—
788C4×D4—84no—
789C4×D4—84no—
790C4×D4C2×Q818yes—
791C4×D4C2×Q818yescomplemented
792#117—28no—
793#117—28no—
794#117—44no—
795#117—44no—
796#117—84no—
797#117—82no—
798C2×C4⋊C4—28no—
799C2×C4⋊C4—82no—
800C2×C4⋊C4C2×Q8116yescomplemented
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C42—44no—
909C2×C42—82no—
910C2×C42—84no—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2411yescharacteristic
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2411yescharacteristic
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011C24C2512yes—
1012C24C2512yes—
1013#41—816no—
1014C2×Q8—22no—
1015C2×Q8—28no—
1016C2×Q8—28no—
1017C2×Q8—22no—
1018C2×Q8—41no—
1019C2×Q8—41no—
1020C2×Q8—42no—
1021C2×Q8—42no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—41no—
1025C2×Q8—41no—
1026C2×Q8—41no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—41no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—816no—
1039C2×Q8C22×Q818yes—
1040C2×Q8C2×#4118yes—
1041C2×Q82−1+414yes—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—41no—
1047C2×D4—41no—
1048C2×D4C22×Q814yes—
1049C2×D4C22×Q814yes—
1050C2×D4C22×Q8116yes—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—28no—
1056C22×C4—28no—
1057C22×C4—24no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4C22×Q818yes—
1079C22×C4C22×Q8116yes—
1080C22×C4C22×Q818yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2514yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—22no—
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—22no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—41no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—41no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4C22×Q814yes—
1181C4⋊C4C22×Q818yes—
1182C4⋊C4C22×Q8116yes—
1183C4⋊C4C22×Q814yes—
1184C4⋊C4C22×Q818yes—
1185C4⋊C4C2×#4118yes—
1186C4⋊C4C2×#4118yes—
1187C22⋊C4—28no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—28no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—28no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4C22×Q818yes—
1213C22⋊C4C22×Q818yes—
1214C22⋊C4C22×Q8116yes—
1215C42—28no—
1216C42—24no—
1217C42—24no—
1218C42—22no—
1219C42—24no—
1220C42—24no—
1221C42—24no—
1222C42—22no—
1223C42—42no—
1224C42—42no—
1225C42—41no—
1226C42—44no—
1227C42—42no—
1228C42—42no—
1229C42—44no—
1230C42—44no—
1231C42—42no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—44no—
1239C42—41no—
1240C42—41no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42C22×Q814yes—
1245C42C2×#4114yes—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23C23×Q814yes—
1259C23C23×Q814yes—
1260C23C2611yescharacteristic
1261Q8—48no—
1262Q8—48no—
1263Q8—44no—
1264Q8—44no—
1265Q8—88no—
1266Q8—82no—
1267Q8—88no—
1268Q8—88no—
1269Q8—164no—
1270D4—28no—
1271D4—416no—
1272D4—44no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—24no—
1293C2×C4—216no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—21no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—21no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—21no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—48no—
1343C2×C4—416no—
1344C2×C4—48no—
1345C2×C4—48no—
1346C2×C4—88no—
1347C2×C4—84no—
1348C2×C4—88no—
1349C2×C4—84no—
1350C2×C4—164no—
1351C2×C4C23×Q812yes—
1352C2×C4C23×Q812yes—
1353C2×C4C23×Q814yes—
1354C2×C4C23×Q814yes—
1355C2×C4C23×Q818yes—
1356C2×C4C23×Q812yes—
1357C2×C4C22×#4118yes—
1358C2×C4C22×#4112yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C2×2−1+412yes—
1362C2×C4C2×2−1+414yes—
1363C2×C4#58512yes—
1364C22—24no—
1365C22—24no—
1366C22—24no—
1367C22—24no—
1368C22—24no—
1369C22—24no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22C24×Q811yescharacteristic
1379C22C23×#4111yescharacteristic
1380C22C22×2−1+411yescharacteristic
1381C22C2×#58511yescharacteristic
1382C22H(7,𝔽2)11yescharacteristic
1383C22H(7,𝔽2)11yescharacteristic
1384C22H(7,𝔽2)11yescharacteristic
1385C4—22no—
1386C4—22no—
1387C4—24no—
1388C4—22no—
1389C4—28no—
1390C4—22no—
1391C4—28no—
1392C4—24no—
1393C4—22no—
1394C4—24no—
1395C4—42no—
1396C4—42no—
1397C4—44no—
1398C4—41no—
1399C4—42no—
1400C4—42no—
1401C4—44no—
1402C4—42no—
1403C4—44no—
1404C4—42no—
1405C4—42no—
1406C4—44no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4Q8×#4114yes—
1412C2—44no—
1413C2—44no—
1414C2C2×Q8×#4111yescharacteristic
1415C2#6284311yescharacteristic
1416C2#6284611yescharacteristic
1417C2#6290211yescharacteristic
1418C2Q8×2−1+411yescharacteristic
1419C2#6299911yescharacteristic
1420C2#6305111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59924C2semidirect
2. #59923C2semidirect
3. #59921C2semidirect
4. #59736C2semidirect
5. #52291C2semidirect
6. #52267C2semidirect
7. #45360C2semidirect
8. #45281C2semidirect
9. #44879C2semidirect
10. #43569C2semidirect
11. #43563C2semidirect
12. #43561C2semidirect
13. #39981C2semidirect
14. #39711C2semidirect
15. #39688C2semidirect
16. #39659C2semidirect
17. #39637C2semidirect
18. #39365C2semidirect
19. #38444C2semidirect
20. #38105C2semidirect
21. #36564C2semidirect
22. #36477C2semidirect
23. #35871C2semidirect
24. #35843C2semidirect
25. #35783C2semidirect
26. #34334C2semidirect
29. #34271C2semidirect
262. #547Q8semidirect
717. C2×#41C2×Q8semidirect
752. C4⋊Q8C2×Q8semidirect
753. C4⋊Q8#41semidirect
758. #123C2×Q8semidirect
772. C22⋊Q8C2×Q8semidirect
791. C4×D4C2×Q8semidirect
800. C2×C4⋊C4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599242
#599232
#599212
#597362
#522912
#522672
#453602
#452812
#448792
#435692
#435632
#435612
#399812
#397112
#396882
#396592
#396372
#393652
#384442
#381052
#365642
#364772
#358712
#358432
#357832
#343342
#343162
#342982
#342712