Finite Group Databasebeta

← #7695679

Subgroups — #7695679

Order 512.

4493 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59937C214yesmaximal, complemented
2#59923C212yesmaximal, complemented
3#59832C211yesmaximal, characteristic, complemented
4#59461C212yesmaximal
5#52290C212yesmaximal, complemented
6#52274C211yesmaximal, characteristic, complemented
7#45279C212yesmaximal, complemented
8#45213C212yesmaximal
9#44934C212yesmaximal
10#44597C214yesmaximal, complemented
11#44317C214yesmaximal, complemented
12#43141C214yesmaximal, complemented
13#39711C212yesmaximal, complemented
14#39674C212yesmaximal
15#39663C214yesmaximal, complemented
16#39629C211yesmaximal, characteristic, complemented
17#39621C211yesmaximal, characteristic, complemented
18#39181C212yesmaximal, complemented
19#38456C214yesmaximal, complemented
20#38446C212yesmaximal, complemented
21#36565C212yesmaximal, complemented
22#36476C211yesmaximal, characteristic
23#35958C212yesmaximal, complemented
24#35871C212yesmaximal
25#35867C212yesmaximal, complemented
26#34335C212yesmaximal, complemented
27#34334C211yesmaximal, characteristic
28#34326C212yesmaximal
29#34324C211yesmaximal, characteristic
30C2×Q82C2212yes—
31C2×#556C2211yescharacteristic
32C2×D4×Q8C2211yescharacteristic
33#2862C2214yes—
34#2862C2211yescharacteristic
35#2859C2212yes—
36#2855C2212yes—
37#2811C2212yes—
38#2809C2211yescharacteristic
39#2806C2211yescharacteristic
40#2806C2212yes—
41#2806C2214yes—
42#2806C2212yes—
43#2806C2212yes—
44#2806C2212yes—
45#2805C2212yes—
46#2805C2211yescharacteristic
47#2805C2212yes—
48#2802C2214yes—
49#2802C2212yes—
50#2799C2212yes—
51#2791C2212yes—
52#2791C2214yes—
53#2788C2214yes—
54#2788C2214yes—
55#2788C2214yes—
56#2774C2214yes—
57#2774C2214yes—
58#2774C2212yes—
59#2768C2214yes—
60#2768C2214yes—
61#2768C2214yes—
62#2763C2214yes—
63#2763C2214yes—
64#2755C2214yes—
65#2755C2212yes—
66#2734C2212yes—
67#2734C2212yes—
68#2734C2212yes—
69#2729C2214yes—
70#2729C2214yes—
71#2729C2214yes—
72#2726C2211yescharacteristic
73#2720C2214yes—
74#2713C2214yes—
75#2713C2214yes—
76#2713C2212yes—
77#2677C2214yes—
78#2677C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2665C2214yes—
82#2660C2212yes—
83#2647C2212yes—
84#2647C2212yes—
85#2612C2214yes—
86#2612C2214yes—
87#2607C2214yes—
88#2605C2214yes—
89#2605C2214yes—
90#2590C2214yes—
91#2589C2214yes—
92#2589C2214yes—
93#2589C2214yes—
94#2589C2214yes—
95#2588C2214yes—
96#2588C2214yes—
97#2587C2214yes—
98#2586C2214yes—
99#2586C2214yes—
100#2586C2214yes—
101#2586C2214yes—
102#2586C2214yes—
103#2586C2214yes—
104#2586C2214yes—
105#2585C2214yes—
106#2583C2214yes—
107#2582C2212yes—
108#2581C2214yes—
109#2581C2212yes—
110#2580C2212yes—
111#2574C2214yes—
112#2571C2212yes—
113#2570C2212yes—
114#2570C2212yes—
115#2568C2212yes—
116#2565C2212yes—
117#2563C2211yescharacteristic
118#2556C2214yes—
119#2551C2212yes—
120#2551C2212yes—
121#2551C2212yes—
122#2551C2212yes—
123#2551C2212yes—
124#2550C2212yes—
125#2550C2214yes—
126#2550C2212yes—
127#2550C2214yes—
128#2549C2214yes—
129#2549C2214yes—
130#2549C2214yes—
131#2546C2214yes—
132#2546C2214yes—
133#2542C2211yescharacteristic
134#2522C2214yes—
135#2520C2214yes—
136#2520C2214yes—
137#2520C2214yes—
138#2520C2214yes—
139#2520C2214yes—
140#2511C2214yes—
141#2509C2214yes—
142#2505C2214yes—
143#2492C2214yes—
144#2492C2212yes—
145#2492C2214yes—
146#2473C2214yes—
147#2465C2214yes—
148#2465C2214yes—
149#2465C2214yes—
150#2454C2212yes—
151#2453C2212yes—
152#2452C2212yes—
153#2452C2212yes—
154#2452C2212yes—
155#2451C2214yes—
156#2451C2214yes—
157#2451C2212yes—
158#2451C2212yes—
159#2451C2212yes—
160#2451C2214yes—
161#2451C2214yes—
162#2451C2212yes—
163#2451C2212yes—
164#2451C2212yes—
165#2451C2212yes—
166#2446C2214yes—
167#2438C2214yes—
168#2434C2214yes—
169#2434C2214yes—
170#2429C2214yes—
171#2423C2212yes—
172#2423C2214yes—
173#2402C2212yes—
174#2402C2212yes—
175#2402C2214yes—
176#2399C2214yes—
177#2399C2212yes—
178#2396C2214yes—
179#2373C2214yes—
180#2373C2214yes—
181#2373C2214yes—
182#2370C2212yes—
183#2369C2214yes—
184#2369C2212yes—
185#2369C2212yes—
186#2369C2212yes—
187#2369C2211yescharacteristic
188#2368C2214yes—
189#2368C2214yes—
190#2368C2214yes—
191#2367C2212yes—
192#2367C2212yes—
193#2367C2212yes—
194#2365C2211yescharacteristic
195#2365C2212yes—
196#2365C2211yescharacteristic
197#2365C2212yes—
198#2365C2214yes—
199#2365C2211yescharacteristic
200#2365C2214yes—
201#2365C2212yes—
202#2362C2212yes—
203#2360C2212yes—
204#2357C2212yes—
205#2356C2212yes—
206#2355C2212yes—
207#2355C2212yes—
208#2355C2212yes—
209#2355C2211yescharacteristic
210#2355C2214yes—
211#2355C2212yes—
212#2354C2211yescharacteristic
213#2351C2212yes—
214#2351C2212yes—
215Q8×C4⋊C4C2211yescharacteristic
216Q8×C4⋊C4C2212yes—
217#2349C2212yes—
218D4×C4⋊C4C2211yescharacteristic
219#2346C2212yes—
220#2343C2214yes—
221Q8×C22⋊C4C2212yes—
222#2334C2214yes—
223#2334C2214yes—
224#2332C2214yes—
225#2331C2212yes—
226#2331C2212yes—
227#2331C2214yes—
228#2331C2214yes—
229#2331C2212yes—
230#2329C2214yes—
231#2327C2212yes—
232#2326C2212yes—
233#2326C2212yes—
234C4×C4⋊Q8C2212yes—
235C4×C4⋊Q8C2211yescharacteristic
236C4×C4⋊Q8C2211yescharacteristic
237C4×C4⋊Q8C2214yes—
238C4×C4⋊Q8C2211yescharacteristic
239C4×#125C2214yes—
240C4×#125C2212yes—
241C4×#126C2214yes—
242C4×#124C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2212yes—
246#2298C2214yes—
247#2296C2212yes—
248#2295C2212yes—
249#2295C2211yescharacteristic
250#2295C2211yescharacteristic
251#2295C2214yes—
252#2295C2212yes—
253C2×#391C2212yes—
254#2276C2212yes—
255#2276C2212yes—
256#2275C2212yes—
257C42×Q8C2212yes—
258C42×D4C2211yescharacteristic
259C23×Q8C2312yes—
260Q82—216no—
261#556Q8116yescomplemented
262D4×Q8—28no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2314yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×#126C2314yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#124C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×#117C2312yes—
315C2×#117C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C42C2312yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
329#400C2314yes—
330#400C2312yes—
331#400C2312yes—
332#400C2312yes—
333#400C2314yes—
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#400C2312yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2312yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2314yes—
367#398C2312yes—
368#398C2312yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2312yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2312yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2312yes—
401#395C2314yes—
402#395C2312yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2314yes—
420#391C2312yes—
421#391C2314yes—
422#391C2312yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2312yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2311yescharacteristic
449#391C2312yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2311yescharacteristic
456#391C2312yes—
457#391C2312yes—
458#391C2311yescharacteristic
459#391C2311yescharacteristic
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#389C2314yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2311yescharacteristic
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2311yescharacteristic
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2312yes—
517#389C2311yescharacteristic
518#389C2311yescharacteristic
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#387C2312yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
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#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2312yes—
590#387C2314yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#384C2312yes—
613#384C2311yescharacteristic
614#384C2311yescharacteristic
615#384C2314yes—
616#384C2311yescharacteristic
617#384C2312yes—
618#384C2312yes—
619#383C2314yes—
620#382C2314yes—
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2314yes—
627#382C2312yes—
628#382C2314yes—
629#382C2314yes—
630#382C2314yes—
631#382C2314yes—
632#381C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2314yes—
636#380C2312yes—
637#380C2312yes—
638#380C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2311yescharacteristic
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704#376C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2314yes—
708#376C2314yes—
709#376C2314yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C43C2314yes—
713C43C2312yes—
714C43C2311yescharacteristic
715C22×Q8—28no—
716C22×Q8—82no—
717C22×Q8—82no—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2414yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×D4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2414yes—
732C23×C4C2412yes—
733C23×C4C2414yes—
734C23×C4C2412yes—
735C4⋊Q8—216no—
736C4⋊Q8—216no—
737C4⋊Q8—28no—
738C4⋊Q8—28no—
739C4⋊Q8—28no—
740C4⋊Q8—216no—
741C4⋊Q8—24no—
742C4⋊Q8—42no—
743C4⋊Q8—42no—
744C4⋊Q8—44no—
745C4⋊Q8—84no—
746C4⋊Q8—84no—
747C4⋊Q8—84no—
748C4⋊Q8—84no—
749C4⋊Q8C2×Q818yescomplemented
750C4⋊Q8#4118yes—
751#126C2×Q8132yescomplemented
752#125—28no—
753#125—44no—
754#125—84no—
755#124C2×Q8116yes—
756C22⋊Q8—28no—
757C22⋊Q8—216no—
758C22⋊Q8—28no—
759C22⋊Q8—84no—
760C22⋊Q8—82no—
761C22⋊Q8—84no—
762C22⋊Q8—84no—
763C22⋊Q8C2×Q8116yescomplemented
764C4×Q8—28no—
765C4×Q8—28no—
766C4×Q8—216no—
767C4×Q8—24no—
768C4×Q8—28no—
769C4×Q8—28no—
770C4×Q8—44no—
771C4×Q8—44no—
772C4×Q8—44no—
773C4×Q8—82no—
774C4×Q8—82no—
775C4×Q8—82no—
776C4×Q8—84no—
777C4×Q8—84no—
778C4×Q8—82no—
779C4×Q8C2×Q8116yescomplemented
780C4×Q8C2×Q818yescomplemented
781C4×D4—28no—
782C4×D4—24no—
783C4×D4—44no—
784C4×D4—42no—
785C4×D4C2×Q818yes—
786#117—82no—
787#117C2×Q8116yescomplemented
788C2×C4⋊C4—82no—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C42—82no—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2411yescharacteristic
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2411yescharacteristic
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2414yes—
915C2×C42C2411yescharacteristic
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2411yescharacteristic
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002C24C2512yes—
1003C2×Q8—24no—
1004C2×Q8—24no—
1005C2×Q8—22no—
1006C2×Q8—28no—
1007C2×Q8—28no—
1008C2×Q8—28no—
1009C2×Q8—24no—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—41no—
1013C2×Q8—42no—
1014C2×Q8—42no—
1015C2×Q8—41no—
1016C2×Q8—41no—
1017C2×Q8—42no—
1018C2×Q8—41no—
1019C2×Q8—42no—
1020C2×Q8—44no—
1021C2×Q8—44no—
1022C2×Q8—44no—
1023C2×Q8—42no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—44no—
1033C2×Q8—816no—
1034C2×Q8C22×Q818yes—
1035C2×Q8C22×Q814yes—
1036C2×Q8C2×#4118yes—
1037C2×D4—22no—
1038C2×D4—22no—
1039C2×D4C22×Q814yes—
1040C22×C4—24no—
1041C22×C4—28no—
1042C22×C4—24no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4C22×Q818yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2511yescharacteristic
1078C22×C4C2514yes—
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—22no—
1104C4⋊C4—22no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—41no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—41no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—41no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—41no—
1124C4⋊C4—41no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—41no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4C22×Q814yes—
1157C4⋊C4C22×Q818yes—
1158C4⋊C4C22×Q814yes—
1159C4⋊C4C22×Q8116yes—
1160C4⋊C4C22×Q818yes—
1161C4⋊C4C22×Q818yes—
1162C4⋊C4C2×#4118yes—
1163C4⋊C4C2×#4118yes—
1164C4⋊C42−1+414yes—
1165C22⋊C4—28no—
1166C22⋊C4—24no—
1167C22⋊C4—28no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4C22×Q8116yes—
1176C22⋊C4C22×Q818yes—
1177C22⋊C4C22×Q8116yes—
1178C42—24no—
1179C42—28no—
1180C42—28no—
1181C42—28no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—22no—
1186C42—24no—
1187C42—22no—
1188C42—24no—
1189C42—41no—
1190C42—42no—
1191C42—42no—
1192C42—42no—
1193C42—44no—
1194C42—44no—
1195C42—42no—
1196C42—41no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—44no—
1201C42—44no—
1202C42—44no—
1203C42—41no—
1204C42—44no—
1205C42—42no—
1206C42—44no—
1207C42—44no—
1208C42—42no—
1209C42—44no—
1210C42C22×Q8116yes—
1211C42C22×Q814yes—
1212C42C22×Q818yes—
1213C42C2×#4114yes—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23C23×Q814yes—
1221C23C2611yescharacteristic
1222Q8—216no—
1223Q8—48no—
1224Q8—44no—
1225Q8—48no—
1226Q8—44no—
1227Q8—88no—
1228Q8—88no—
1229Q8—84no—
1230Q8—88no—
1231Q8—164no—
1232Q8—162no—
1233D4—28no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—48no—
1305C2×C4—48no—
1306C2×C4—84no—
1307C2×C4—88no—
1308C2×C4—164no—
1309C2×C4C23×Q814yes—
1310C2×C4C23×Q814yes—
1311C2×C4C23×Q812yes—
1312C2×C4C23×Q814yes—
1313C2×C4C23×Q818yes—
1314C2×C4C23×Q812yes—
1315C2×C4C23×Q812yes—
1316C2×C4C22×#4112yes—
1317C2×C4C22×#4118yes—
1318C2×C4C22×#4112yes—
1319C2×C4C22×#4112yes—
1320C2×C4C2×2−1+414yes—
1321C2×C4C2×2−1+412yes—
1322C2×C4#58512yes—
1323C22—24no—
1324C22—24no—
1325C22—24no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22C24×Q811yescharacteristic
1331C22C23×#4111yescharacteristic
1332C22C22×2−1+411yescharacteristic
1333C22C2×#58511yescharacteristic
1334C22H(7,𝔽2)11yescharacteristic
1335C22H(7,𝔽2)11yescharacteristic
1336C222−1+611yescharacteristic
1337C4—22no—
1338C4—24no—
1339C4—22no—
1340C4—24no—
1341C4—22no—
1342C4—28no—
1343C4—22no—
1344C4—24no—
1345C4—24no—
1346C4—22no—
1347C4—28no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—44no—
1352C4—42no—
1353C4—41no—
1354C4—44no—
1355C4—42no—
1356C4—42no—
1357C4—44no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4Q8×#4114yes—
1365C2—44no—
1366C2C2×Q8×#4111yescharacteristic
1367C2#6284611yescharacteristic
1368C2#6285411yescharacteristic
1369C2#6296211yescharacteristic
1370C2Q8×2−1+411yescharacteristic
1371C2#6299811yescharacteristic
1372C2#6306911yescharacteristic
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. #59937C2semidirect
2. #59923C2semidirect
3. #59832C2semidirect
5. #52290C2semidirect
6. #52274C2semidirect
7. #45279C2semidirect
10. #44597C2semidirect
11. #44317C2semidirect
12. #43141C2semidirect
13. #39711C2semidirect
15. #39663C2semidirect
16. #39629C2semidirect
17. #39621C2semidirect
18. #39181C2semidirect
19. #38456C2semidirect
20. #38446C2semidirect
21. #36565C2semidirect
23. #35958C2semidirect
25. #35867C2semidirect
26. #34335C2semidirect
261. #556Q8semidirect
749. C4⋊Q8C2×Q8semidirect
751. #126C2×Q8semidirect
763. C22⋊Q8C2×Q8semidirect
779. C4×Q8C2×Q8semidirect
780. C4×Q8C2×Q8semidirect
787. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599372
#599232
#598322
#594612
#522902
#522742
#452792
#452132
#449342
#445972
#443172
#431412
#397112
#396742
#396632
#396292
#396212
#391812
#384562
#384462
#365652
#364762
#359582
#358712
#358672
#343352
#343342
#343262
#343242