Finite Group Databasebeta

← #7674846

Subgroups — #7674846

Order 512.

4596 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59934C212yesmaximal, complemented
2#59867C212yesmaximal, complemented
3#59499C212yesmaximal, complemented
4#59477C212yesmaximal, complemented
5#59445C212yesmaximal, complemented
6#59376C212yesmaximal, complemented
7#59274C212yesmaximal, complemented
8#59259C212yesmaximal, complemented
9#44639C214yesmaximal, complemented
10#44583C214yesmaximal, complemented
11#43572C214yesmaximal, complemented
12#43565C214yesmaximal, complemented
13#39678C212yesmaximal, complemented
14#39670C212yesmaximal
15#39624C211yesmaximal, characteristic, complemented
16#39615C211yesmaximal, characteristic
17#39604C212yesmaximal, complemented
18#39601C214yesmaximal, complemented
19#36552C211yesmaximal, characteristic, complemented
20#36551C211yesmaximal, characteristic
21Q8×#123C212yesmaximal, complemented
22#35401C214yesmaximal, complemented
23#35015C211yesmaximal, characteristic, complemented
24#35013C212yesmaximal, complemented
25#34772C212yesmaximal, complemented
26#34334C212yesmaximal, complemented
27#34278C212yesmaximal
28C2×#2355C211yesmaximal, characteristic, complemented
29C4×#539C211yesmaximal, characteristic
30C2×D4×Q8C2212yes—
31C2×#539C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2855C2214yes—
36#2855C2212yes—
37#2851C2212yes—
38#2851C2212yes—
39#2811C2212yes—
40#2806C2212yes—
41#2806C2214yes—
42#2799C2214yes—
43#2792C2214yes—
44#2791C2214yes—
45#2791C2214yes—
46#2791C2214yes—
47#2790C2214yes—
48#2774C2214yes—
49#2774C2214yes—
50#2774C2214yes—
51#2768C2214yes—
52#2768C2214yes—
53#2768C2214yes—
54#2763C2214yes—
55#2763C2214yes—
56#2755C2214yes—
57#2755C2214yes—
58#2755C2214yes—
59#2748C2214yes—
60#2742C2214yes—
61#2734C2212yes—
62#2732C2212yes—
63#2729C2214yes—
64#2720C2214yes—
65#2659C2212yes—
66#2659C2212yes—
67#2646C2212yes—
68#2627C2212yes—
69#2627C2214yes—
70#2612C2214yes—
71#2607C2214yes—
72#2606C2214yes—
73#2605C2214yes—
74#2590C2214yes—
75#2590C2214yes—
76#2590C2214yes—
77#2589C2214yes—
78#2589C2214yes—
79#2588C2214yes—
80#2588C2214yes—
81#2588C2214yes—
82#2586C2214yes—
83#2586C2214yes—
84#2585C2214yes—
85#2585C2214yes—
86#2585C2214yes—
87#2582C2212yes—
88#2574C2214yes—
89#2574C2214yes—
90#2574C2214yes—
91#2570C2214yes—
92#2569C2214yes—
93#2568C2211yescharacteristic
94#2567C2212yes—
95#2567C2212yes—
96#2565C2214yes—
97#2564C2214yes—
98#2564C2214yes—
99#2563C2211yescharacteristic
100#2556C2214yes—
101#2552C2211yescharacteristic
102#2552C2212yes—
103#2552C2211yescharacteristic
104#2549C2214yes—
105#2522C2214yes—
106#2522C2214yes—
107#2520C2214yes—
108#2520C2214yes—
109#2520C2214yes—
110#2520C2214yes—
111#2520C2214yes—
112#2520C2214yes—
113#2511C2214yes—
114#2511C2212yes—
115#2511C2212yes—
116#2511C2212yes—
117#2511C2212yes—
118#2509C2212yes—
119#2508C2212yes—
120#2508C2214yes—
121#2508C2214yes—
122#2507C2212yes—
123#2507C2212yes—
124#2507C2212yes—
125#2506C2214yes—
126#2505C2214yes—
127#2505C2214yes—
128#2505C2214yes—
129#2505C2214yes—
130#2505C2214yes—
131#2502C2214yes—
132#2502C2212yes—
133#2502C2212yes—
134#2497C2212yes—
135#2497C2212yes—
136#2497C2212yes—
137#2492C2212yes—
138#2487C2214yes—
139#2487C2212yes—
140#2473C2214yes—
141#2462C2214yes—
142#2462C2214yes—
143#2462C2214yes—
144#2454C2212yes—
145#2453C2212yes—
146#2451C2212yes—
147#2451C2212yes—
148#2451C2212yes—
149#2450C2214yes—
150#2450C2214yes—
151#2449C2214yes—
152#2446C2212yes—
153#2446C2212yes—
154#2446C2214yes—
155#2446C2214yes—
156#2446C2212yes—
157#2446C2212yes—
158#2441C2214yes—
159#2440C2212yes—
160#2440C2212yes—
161#2438C2214yes—
162#2434C2212yes—
163#2423C2214yes—
164#2423C2214yes—
165#2423C2214yes—
166#2423C2212yes—
167#2423C2212yes—
168#2423C2212yes—
169#2423C2212yes—
170#2417C2212yes—
171#2409C2212yes—
172#2402C2214yes—
173#2396C2214yes—
174#2374C2214yes—
175#2373C2214yes—
176#2373C2214yes—
177#2371C2214yes—
178#2370C2214yes—
179#2369C2214yes—
180#2369C2211yescharacteristic
181#2368C2214yes—
182#2368C2214yes—
183#2368C2214yes—
184#2365C2212yes—
185#2365C2211yescharacteristic
186#2362C2214yes—
187#2360C2212yes—
188#2360C2212yes—
189#2359C2214yes—
190#2355C2212yes—
191#2355C2212yes—
192#2355C2214yes—
193#2355C2214yes—
194#2355C2212yes—
195#2355C2212yes—
196#2355C2212yes—
197#2355C2212yes—
198Q8×C4⋊C4C2212yes—
199Q8×C4⋊C4C2212yes—
200Q8×C4⋊C4C2211yescharacteristic
201#2349C2214yes—
202D4×C4⋊C4C2212yes—
203D4×C4⋊C4C2211yescharacteristic
204#2345C2212yes—
205Q8×C22⋊C4C2212yes—
206Q8×C22⋊C4C2212yes—
207Q8×C22⋊C4C2212yes—
208Q8×C22⋊C4C2212yes—
209#2336C2212yes—
210#2335C2212yes—
211#2334C2212yes—
212#2332C2212yes—
213#2331C2214yes—
214#2329C2214yes—
215#2329C2214yes—
216#2329C2211yescharacteristic
217#2329C2212yes—
218#2329C2212yes—
219#2325C2211yescharacteristic
220#2325C2212yes—
221#2322C2212yes—
222#2322C2214yes—
223#2318C2212yes—
224#2313C2211yescharacteristic
225#2313C2212yes—
226C4×C4⋊Q8C2212yes—
227C4×C4⋊Q8C2212yes—
228C4×#125C2212yes—
229C4×#126C2212yes—
230C4×C22⋊Q8C2212yes—
231C4×C22⋊Q8C2212yes—
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2211yescharacteristic
234C4×C22⋊Q8C2214yes—
235C4×C22⋊Q8C2212yes—
236C4×C22⋊Q8C2212yes—
237C4×#123C2212yes—
238C4×#123C2212yes—
239C4×#123C2214yes—
240C4×#121C2211yescharacteristic
241C4×#121C2212yes—
242#2295C2212yes—
243#2295C2212yes—
244C2×#391C2211yescharacteristic
245C2×#391C2212yes—
246C2×#391C2211yescharacteristic
247#2290C2214yes—
248C2×#387C2212yes—
249C2×#387C2212yes—
250#2285C2212yes—
251C2×#384C2211yescharacteristic
252C2×#382C2212yes—
253#2275C2214yes—
254C42×D4C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2312yes—
260C23×Q8C2311yescharacteristic
261D4×Q8—216no—
262#539Q8116yescomplemented
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×#126C2312yes—
269C2×#125C2314yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#123C2312yes—
274C2×#123C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2312yes—
285C2×#121C2311yescharacteristic
286C2×C4×Q8—28no—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×#117C2314yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2311yescharacteristic
315C22×C42C2312yes—
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2312yes—
320C22×C42C2312yes—
321C22×C42C2312yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
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#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#391C2312yes—
395#391C2312yes—
396#391C2314yes—
397#391C2312yes—
398#391C2314yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2312yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2311yescharacteristic
419#391C2312yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#390C2312yes—
433#390C2311yescharacteristic
434#389C2312yes—
435#389C2312yes—
436#389C2314yes—
437#389C2312yes—
438#389C2314yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2311yescharacteristic
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2311yescharacteristic
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#388C2312yes—
480#388C2312yes—
481#388C2312yes—
482#388C2312yes—
483#388C2312yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2312yes—
489#388C2312yes—
490#388C2314yes—
491#388C2314yes—
492#388C2312yes—
493#388C2314yes—
494#388C2314yes—
495#387C2312yes—
496#387C2312yes—
497#387C2312yes—
498#387C2312yes—
499#387C2312yes—
500#387C2312yes—
501#387C2312yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2312yes—
511#387C2314yes—
512#387C2314yes—
513#387C2312yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2312yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2312yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2312yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#386C2312yes—
567#386C2312yes—
568#386C2314yes—
569#386C2314yes—
570#386C2312yes—
571#386C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2312yes—
577#385C2312yes—
578#385C2314yes—
579#385C2312yes—
580#385C2312yes—
581#385C2314yes—
582#385C2314yes—
583#385C2312yes—
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#384C2312yes—
597#384C2312yes—
598#384C2314yes—
599#384C2311yescharacteristic
600#384C2312yes—
601#384C2312yes—
602#384C2314yes—
603#384C2311yescharacteristic
604#384C2312yes—
605#384C2312yes—
606#384C2314yes—
607#383C2312yes—
608#382C2312yes—
609#382C2312yes—
610#382C2314yes—
611#382C2312yes—
612#382C2314yes—
613#382C2314yes—
614#382C2314yes—
615#382C2314yes—
616#382C2314yes—
617#382C2314yes—
618#381C2314yes—
619#381C2312yes—
620#381C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2312yes—
624#380C2314yes—
625#380C2314yes—
626#380C2314yes—
627#380C2311yescharacteristic
628#380C2312yes—
629#380C2311yescharacteristic
630#380C2312yes—
631#380C2312yes—
632#380C2314yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639C4×C4⋊C4C2311yescharacteristic
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2311yescharacteristic
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2311yescharacteristic
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702#376C2314yes—
703#376C2314yes—
704C2×#95C2312yes—
705C2×#95C2314yes—
706C2×#95C2314yes—
707C2×#95C2311yescharacteristic
708C2×#95C2311yescharacteristic
709C2×#95C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C43C2312yes—
715C22×Q8—28no—
716C22×Q8—42no—
717C22×Q8—42no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8#4118yes—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2414yes—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×D4C2412yes—
729C22×D4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2411yescharacteristic
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2411yescharacteristic
738C23×C4C2411yescharacteristic
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2412yes—
745C23×C4C2412yes—
746C4⋊Q8—28no—
747C4⋊Q8—216no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750C4⋊Q8—42no—
751#126C2×Q8116yescomplemented
752#125—82no—
753#125—82no—
754#125—84no—
755#125C2×Q8116yescomplemented
756#123C2×Q8116yescomplemented
757#123C2×Q8116yescomplemented
758C22⋊Q8—28no—
759C22⋊Q8—216no—
760C22⋊Q8—28no—
761C22⋊Q8—216no—
762C22⋊Q8—48no—
763C22⋊Q8—44no—
764C22⋊Q8—44no—
765C22⋊Q8—84no—
766C22⋊Q8C2×Q818yescomplemented
767C22⋊Q8C2×Q8116yescomplemented
768#121C2×Q818yes—
769C4×Q8—28no—
770C4×Q8—28no—
771C4×Q8—216no—
772C4×Q8—28no—
773C4×Q8—42no—
774C4×Q8—44no—
775C4×Q8—44no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—84no—
779C4×Q8—82no—
780C4×D4—28no—
781C4×D4—216no—
782C4×D4—42no—
783C4×D4—44no—
784C4×D4—48no—
785C4×D4—82no—
786C4×D4C2×Q8116yescomplemented
787#117—84no—
788C2×C4⋊C4—24no—
789C2×C4⋊C4—28no—
790C2×C4⋊C4—42no—
791C2×C4⋊C4—44no—
792C2×C4⋊C4—42no—
793C2×C4⋊C4—42no—
794C2×C4⋊C4—44no—
795C2×C4⋊C4—82no—
796C2×C4⋊C4C2×Q818yescomplemented
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C42—24no—
893C2×C42—28no—
894C2×C42—42no—
895C2×C42—44no—
896C2×C42—42no—
897C2×C42—82no—
898C2×C42—82no—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2411yescharacteristic
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24C2512yes—
1009C24C2511yescharacteristic
1010C2×Q8—24no—
1011C2×Q8—28no—
1012C2×Q8—24no—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—41no—
1017C2×Q8—41no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—44no—
1021C2×Q8—44no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—42no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×Q8—416no—
1029C2×Q8—816no—
1030C2×Q8C22×Q814yes—
1031C2×Q8C2×#4118yes—
1032C2×Q8C2×#4118yes—
1033C2×D4—24no—
1034C2×D4—24no—
1035C2×D4—41no—
1036C2×D4—41no—
1037C2×D4C22×Q818yes—
1038C2×D4C22×Q814yes—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—28no—
1053C22×C4—41no—
1054C22×C4—42no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—42no—
1059C22×C4—41no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—41no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—41no—
1066C22×C4—42no—
1067C22×C4—41no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—41no—
1074C22×C4—42no—
1075C22×C4—41no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4C22×Q814yes—
1082C22×C4C22×Q814yes—
1083C22×C4C22×Q814yes—
1084C22×C4C22×Q818yes—
1085C22×C4C2×#4114yes—
1086C22×C4C2×#4118yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2514yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—24no—
1117C4⋊C4—22no—
1118C4⋊C4—22no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—22no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—41no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—41no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—41no—
1173C4⋊C4—41no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4C22×Q818yes—
1181C4⋊C4C22×Q818yes—
1182C4⋊C4C22×Q818yes—
1183C4⋊C4C22×Q814yes—
1184C4⋊C4C22×Q818yes—
1185C4⋊C4C22×Q818yes—
1186C4⋊C4C22×Q814yes—
1187C4⋊C4C22×Q818yes—
1188C22⋊C4—24no—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—24no—
1192C22⋊C4—28no—
1193C22⋊C4—24no—
1194C22⋊C4—42no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4C22×Q818yes—
1205C22⋊C4C22×Q818yes—
1206C22⋊C4C22×Q818yes—
1207C22⋊C4C22×Q818yes—
1208C22⋊C4C22×Q818yes—
1209C42—28no—
1210C42—28no—
1211C42—24no—
1212C42—24no—
1213C42—28no—
1214C42—24no—
1215C42—24no—
1216C42—22no—
1217C42—24no—
1218C42—22no—
1219C42—24no—
1220C42—42no—
1221C42—42no—
1222C42—42no—
1223C42—41no—
1224C42—41no—
1225C42—44no—
1226C42—42no—
1227C42—44no—
1228C42—42no—
1229C42—42no—
1230C42—42no—
1231C42—42no—
1232C42—44no—
1233C42—44no—
1234C42—42no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—44no—
1239C42—42no—
1240C42—44no—
1241C42C22×Q818yes—
1242C23—21no—
1243C23—21no—
1244C23—21no—
1245C23—21no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23C23×Q814yes—
1253C23C23×Q812yes—
1254C23C22×#4112yes—
1255C23#58512yes—
1256C23C2611yescharacteristic
1257Q8—216no—
1258Q8—48no—
1259Q8—44no—
1260Q8—48no—
1261Q8—88no—
1262Q8—88no—
1263Q8—162no—
1264D4—216no—
1265D4—44no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—28no—
1285C2×C4—28no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—22no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—21no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—44no—
1338C2×C4—48no—
1339C2×C4—44no—
1340C2×C4—48no—
1341C2×C4—48no—
1342C2×C4—44no—
1343C2×C4—48no—
1344C2×C4—88no—
1345C2×C4—82no—
1346C2×C4—82no—
1347C2×C4—84no—
1348C2×C4—84no—
1349C2×C4—84no—
1350C2×C4—164no—
1351C2×C4C23×Q814yes—
1352C2×C4C23×Q814yes—
1353C2×C4C23×Q814yes—
1354C2×C4C23×Q814yes—
1355C2×C4C23×Q814yes—
1356C2×C4C23×Q812yes—
1357C2×C4C23×Q812yes—
1358C2×C4C22×#4118yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4#58512yes—
1362C2×C4#58512yes—
1363C22—22no—
1364C22—22no—
1365C22—22no—
1366C22—22no—
1367C22—22no—
1368C22—22no—
1369C22—24no—
1370C22—24no—
1371C22—24no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22Q8×#4114yes—
1377C22C24×Q811yescharacteristic
1378C22C23×#4111yescharacteristic
1379C22C2×#58511yescharacteristic
1380C22C2×#58511yescharacteristic
1381C22C2×#58511yescharacteristic
1382C22H(7,𝔽2)11yescharacteristic
1383C222−1+611yescharacteristic
1384C4—24no—
1385C4—22no—
1386C4—24no—
1387C4—22no—
1388C4—24no—
1389C4—22no—
1390C4—28no—
1391C4—24no—
1392C4—24no—
1393C4—42no—
1394C4—44no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—41no—
1402C4—42no—
1403C4—41no—
1404C4—44no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—44no—
1409C4—42no—
1410C4#349114yes—
1411C2—24no—
1412C2—44no—
1413C2C2×Q8×#4111yescharacteristic
1414C2C2×#349111yescharacteristic
1415C2#6285111yescharacteristic
1416C2#6291111yescharacteristic
1417C2#6296511yescharacteristic
1418C2#6298911yescharacteristic
1419C2#6300411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59934C2semidirect
2. #59867C2semidirect
3. #59499C2semidirect
4. #59477C2semidirect
5. #59445C2semidirect
6. #59376C2semidirect
7. #59274C2semidirect
8. #59259C2semidirect
9. #44639C2semidirect
10. #44583C2semidirect
11. #43572C2semidirect
12. #43565C2semidirect
13. #39678C2semidirect
15. #39624C2semidirect
17. #39604C2semidirect
18. #39601C2semidirect
19. #36552C2semidirect
21. Q8×#123C2semidirect
22. #35401C2semidirect
23. #35015C2semidirect
24. #35013C2semidirect
25. #34772C2semidirect
26. #34334C2semidirect
28. C2×#2355C2semidirect
262. #539Q8semidirect
751. #126C2×Q8semidirect
755. #125C2×Q8semidirect
756. #123C2×Q8semidirect
757. #123C2×Q8semidirect
766. C22⋊Q8C2×Q8semidirect
767. C22⋊Q8C2×Q8semidirect
786. C4×D4C2×Q8semidirect
796. C2×C4⋊C4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599342
#598672
#594992
#594772
#594452
#593762
#592742
#592592
#446392
#445832
#435722
#435652
#396782
#396702
#396242
#396152
#396042
#396012
#365522
#365512
Q8×#1232
#354012
#350152
#350132
#347722
#343342
#342782
C2×#23552
C4×#5392