Finite Group Databasebeta

← #7656604

Subgroups — #7656604

Order 512.

4178 conjugacy classes of subgroups.

The subgroup lattice has 1365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42826C212yesmaximal, complemented
2#42825C212yesmaximal, complemented
3#42822C212yesmaximal, complemented
4#42821C212yesmaximal, complemented
5#42185C214yesmaximal, complemented
6#42183C214yesmaximal, complemented
7#42004C214yesmaximal, complemented
8#42002C214yesmaximal, complemented
9#39752C211yesmaximal, characteristic
10#39748C212yesmaximal
11#39624C211yesmaximal, characteristic
12#39620C212yesmaximal
13#39179C212yesmaximal
14#39175C214yesmaximal
15#37623C212yesmaximal
16#37609C214yesmaximal
17#36599C211yesmaximal, characteristic
18#36564C211yesmaximal, characteristic
19#36519C212yesmaximal
20#35972C212yesmaximal, complemented
21#35958C212yesmaximal, complemented
22#35936C212yesmaximal, complemented
23#35867C212yesmaximal, complemented
24#35104C212yesmaximal
25#35104C211yesmaximal, characteristic
26#34595C211yesmaximal, characteristic
27#34595C212yesmaximal
28#34192C212yesmaximal
29C2×#2355C211yesmaximal, characteristic
30C22×C4×Q8C2211yescharacteristic
31#2857C2212yes—
32#2857C2211yescharacteristic
33#2857C2212yes—
34#2857C2211yescharacteristic
35#2851C2214yes—
36#2851C2212yes—
37#2845C2214yes—
38#2845C2214yes—
39#2844C2214yes—
40#2844C2214yes—
41#2843C2214yes—
42#2843C2214yes—
43#2811C2212yes—
44#2809C2214yes—
45#2809C2212yes—
46#2806C2214yes—
47#2806C2212yes—
48#2806C2214yes—
49#2806C2214yes—
50#2806C2212yes—
51#2805C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2799C2214yes—
55#2799C2214yes—
56#2799C2214yes—
57#2792C2214yes—
58#2792C2214yes—
59#2791C2214yes—
60#2791C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2755C2214yes—
64#2755C2214yes—
65#2734C2214yes—
66#2726C2214yes—
67#2713C2214yes—
68#2713C2214yes—
69#2666C2212yes—
70#2666C2214yes—
71#2666C2214yes—
72#2666C2214yes—
73#2666C2212yes—
74#2666C2214yes—
75#2666C2214yes—
76#2666C2214yes—
77#2666C2214yes—
78#2666C2214yes—
79#2666C2212yes—
80#2666C2212yes—
81#2666C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2666C2214yes—
85#2660C2214yes—
86#2660C2212yes—
87#2660C2212yes—
88#2659C2211yescharacteristic
89#2659C2212yes—
90#2659C2211yescharacteristic
91#2659C2212yes—
92#2647C2212yes—
93#2647C2212yes—
94#2647C2214yes—
95#2646C2212yes—
96#2646C2214yes—
97#2627C2211yescharacteristic
98#2627C2212yes—
99#2627C2212yes—
100#2627C2214yes—
101#2627C2211yescharacteristic
102#2627C2212yes—
103#2627C2214yes—
104#2612C2214yes—
105#2612C2214yes—
106#2612C2214yes—
107#2612C2214yes—
108#2606C2214yes—
109#2606C2214yes—
110#2606C2214yes—
111#2605C2214yes—
112#2605C2214yes—
113#2605C2214yes—
114#2590C2214yes—
115#2590C2214yes—
116#2590C2214yes—
117#2588C2214yes—
118#2588C2214yes—
119#2588C2214yes—
120#2586C2214yes—
121#2586C2214yes—
122#2586C2214yes—
123#2585C2214yes—
124#2585C2214yes—
125#2585C2214yes—
126#2584C2212yes—
127#2582C2212yes—
128#2582C2212yes—
129#2581C2212yes—
130#2581C2212yes—
131#2571C2212yes—
132#2570C2214yes—
133#2570C2212yes—
134#2570C2212yes—
135#2570C2214yes—
136#2569C2214yes—
137#2569C2214yes—
138#2569C2214yes—
139#2569C2214yes—
140#2568C2212yes—
141#2567C2211yescharacteristic
142#2567C2212yes—
143#2565C2212yes—
144#2565C2212yes—
145#2552C2212yes—
146#2552C2211yescharacteristic
147#2552C2212yes—
148#2551C2212yes—
149#2551C2211yescharacteristic
150#2550C2214yes—
151#2550C2214yes—
152#2550C2212yes—
153#2550C2212yes—
154#2550C2212yes—
155#2549C2214yes—
156#2549C2214yes—
157#2549C2214yes—
158#2549C2214yes—
159#2546C2211yescharacteristic
160#2520C2214yes—
161#2520C2214yes—
162#2520C2214yes—
163#2511C2214yes—
164#2511C2212yes—
165#2509C2212yes—
166#2508C2212yes—
167#2507C2214yes—
168#2507C2212yes—
169#2507C2212yes—
170#2506C2212yes—
171#2462C2214yes—
172#2462C2214yes—
173#2462C2214yes—
174#2453C2212yes—
175#2453C2212yes—
176#2453C2212yes—
177#2453C2212yes—
178#2451C2212yes—
179#2451C2212yes—
180#2451C2214yes—
181#2451C2212yes—
182#2451C2212yes—
183#2451C2212yes—
184#2446C2214yes—
185#2446C2212yes—
186#2442C2214yes—
187#2442C2212yes—
188#2442C2212yes—
189#2440C2214yes—
190#2440C2212yes—
191#2440C2212yes—
192#2402C2212yes—
193#2402C2212yes—
194#2402C2214yes—
195#2402C2214yes—
196#2399C2214yes—
197#2399C2214yes—
198#2399C2212yes—
199#2399C2212yes—
200#2370C2212yes—
201#2370C2212yes—
202#2370C2212yes—
203#2369C2212yes—
204#2369C2211yescharacteristic
205#2365C2211yescharacteristic
206#2365C2212yes—
207#2356C2214yes—
208#2356C2214yes—
209#2356C2212yes—
210#2356C2212yes—
211#2355C2214yes—
212#2355C2214yes—
213#2355C2212yes—
214#2355C2212yes—
215#2355C2212yes—
216#2355C2212yes—
217#2355C2212yes—
218#2355C2211yescharacteristic
219#2351C2212yes—
220#2351C2212yes—
221Q8×C4⋊C4C2211yescharacteristic
222#2345C2214yes—
223#2345C2214yes—
224#2345C2212yes—
225#2345C2212yes—
226Q8×C22⋊C4C2212yes—
227Q8×C22⋊C4C2212yes—
228#2329C2212yes—
229#2329C2214yes—
230#2329C2212yes—
231#2329C2212yes—
232#2329C2212yes—
233#2320C2214yes—
234#2320C2212yes—
235#2320C2212yes—
236#2320C2214yes—
237C4×C22⋊Q8C2214yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2211yescharacteristic
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2211yescharacteristic
243C2×#391C2211yescharacteristic
244C2×#391C2211yescharacteristic
245C2×#387C2212yes—
246C2×#387C2212yes—
247C2×#384C2211yescharacteristic
248#2283C2214yes—
249#2283C2212yes—
250#2283C2214yes—
251#2283C2212yes—
252C2×#382C2212yes—
253#2276C2212yes—
254#2276C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2311yescharacteristic
274C2×C22⋊Q8C2311yescharacteristic
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C4×Q8Q8116yescomplemented
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2314yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2312yes—
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2312yes—
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2312yes—
304C22×C42C2312yes—
305C22×C42C2312yes—
306C22×C42C2311yescharacteristic
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2312yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2314yes—
329#400C2312yes—
330#400C2312yes—
331#400C2314yes—
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
335#400C2314yes—
336#400C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2312yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2312yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2312yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2314yes—
396#398C2312yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2312yes—
404#395C2312yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2312yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2312yes—
420#395C2314yes—
421#395C2312yes—
422#395C2314yes—
423#395C2312yes—
424#395C2314yes—
425#395C2312yes—
426#395C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2312yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2311yescharacteristic
464#391C2311yescharacteristic
465#391C2312yes—
466#391C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2311yescharacteristic
518#389C2312yes—
519#389C2311yescharacteristic
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
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#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#385C2314yes—
583#385C2312yes—
584#385C2312yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2312yes—
590#385C2314yes—
591#385C2312yes—
592#384C2311yescharacteristic
593#384C2312yes—
594#384C2311yescharacteristic
595#384C2312yes—
596#384C2312yes—
597#384C2312yes—
598#384C2312yes—
599#384C2314yes—
600#384C2312yes—
601#384C2314yes—
602#383C2314yes—
603#383C2314yes—
604#383C2314yes—
605#383C2312yes—
606#383C2312yes—
607#383C2314yes—
608#383C2314yes—
609#382C2312yes—
610#382C2312yes—
611#382C2312yes—
612#382C2314yes—
613#382C2314yes—
614#382C2312yes—
615#382C2314yes—
616#382C2314yes—
617#382C2312yes—
618#382C2312yes—
619#382C2314yes—
620#382C2314yes—
621#382C2314yes—
622#382C2314yes—
623#382C2312yes—
624#382C2314yes—
625#382C2314yes—
626#381C2312yes—
627#381C2314yes—
628#381C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#380C2314yes—
634#380C2314yes—
635#380C2312yes—
636#380C2311yescharacteristic
637#380C2312yes—
638#380C2312yes—
639#380C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2312yes—
643#380C2311yescharacteristic
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2311yescharacteristic
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
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⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698#376C2314yes—
699#376C2314yes—
700#376C2312yes—
701#376C2312yes—
702#376C2314yes—
703#376C2314yes—
704#376C2314yes—
705C2×#95C2312yes—
706C2×#95C2312yes—
707C2×#95C2312yes—
708C2×#95C2312yes—
709C2×#95C2311yescharacteristic
710C2×#95C2312yes—
711C2×#95C2311yescharacteristic
712C2×#95C2312yes—
713C22×Q8—42no—
714C22×Q8—42no—
715C22×Q8C2×Q818yes—
716C22×Q8C2412yes—
717C22×Q8C2411yescharacteristic
718C22×Q8C2411yescharacteristic
719C22×Q8C2412yes—
720C22×Q8C2414yes—
721C22×Q8C2412yes—
722C22×Q8C2414yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C23×C4C2411yescharacteristic
726C23×C4C2411yescharacteristic
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2411yescharacteristic
736C4⋊Q8—42no—
737C4⋊Q8—42no—
738C4⋊Q8—44no—
739C4⋊Q8—44no—
740C4⋊Q8—82no—
741C4⋊Q8—82no—
742C4⋊Q8—84no—
743#125—44no—
744#125—44no—
745#125—44no—
746#125—84no—
747#125—84no—
748C22⋊Q8—24no—
749C22⋊Q8—28no—
750C22⋊Q8—24no—
751C22⋊Q8—48no—
752C22⋊Q8—44no—
753C22⋊Q8—48no—
754C22⋊Q8—44no—
755C4×Q8—44no—
756C4×Q8—42no—
757C4×Q8—42no—
758C4×Q8—44no—
759C4×Q8—44no—
760C4×Q8—44no—
761C4×Q8—44no—
762C4×Q8—84no—
763C4×Q8—82no—
764C4×Q8—82no—
765C4×Q8C2×Q8116yes—
766C4×Q8C2×Q8116yes—
767C4×Q8C2×Q8132yes—
768C2×C4⋊C4—24no—
769C2×C4⋊C4—42no—
770C2×C4⋊C4—42no—
771C2×C4⋊C4—42no—
772C2×C4⋊C4—44no—
773C2×C4⋊C4—82no—
774C2×C4⋊C4C2×Q818yes—
775C2×C4⋊C4C2×Q8116yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C42—42no—
868C2×C42—42no—
869C2×C42—82no—
870C2×C42—82no—
871C2×C42C2×Q818yes—
872C2×C42C2×Q8116yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2414yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903#95C2412yes—
904#95C2414yes—
905#95C2412yes—
906#95C2412yes—
907#95C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2414yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991C24C2511yescharacteristic
992C2×Q8—22no—
993C2×Q8—22no—
994C2×Q8—24no—
995C2×Q8—24no—
996C2×Q8—24no—
997C2×Q8—41no—
998C2×Q8—41no—
999C2×Q8—42no—
1000C2×Q8—42no—
1001C2×Q8—41no—
1002C2×Q8—42no—
1003C2×Q8—42no—
1004C2×Q8—44no—
1005C2×Q8—42no—
1006C2×Q8—44no—
1007C2×Q8—42no—
1008C2×Q8—44no—
1009C2×Q8—41no—
1010C2×Q8—42no—
1011C2×Q8—42no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—42no—
1015C2×Q8—44no—
1016C2×Q8—42no—
1017C2×Q8—416no—
1018C2×Q8C22×Q818yes—
1019C2×Q8C22×Q818yes—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—24no—
1026C22×C4—22no—
1027C22×C4—24no—
1028C22×C4—22no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—42no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—42no—
1036C22×C4—41no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—41no—
1040C22×C4—41no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4C22×Q814yes—
1048C22×C4C22×Q814yes—
1049C22×C4C22×Q814yes—
1050C22×C4C22×Q818yes—
1051C22×C4C22×Q818yes—
1052C22×C42−1+414yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2514yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—22no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—22no—
1090C4⋊C4—24no—
1091C4⋊C4—22no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—41no—
1114C4⋊C4—41no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—41no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
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—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4C22×Q818yes—
1162C4⋊C4C22×Q8116yes—
1163C4⋊C4C22×Q8116yes—
1164C4⋊C4C22×Q814yes—
1165C4⋊C4C22×Q814yes—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—28no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—28no—
1172C42—24no—
1173C42—22no—
1174C42—22no—
1175C42—24no—
1176C42—24no—
1177C42—24no—
1178C42—24no—
1179C42—41no—
1180C42—41no—
1181C42—42no—
1182C42—42no—
1183C42—42no—
1184C42—44no—
1185C42—44no—
1186C42—42no—
1187C42—42no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42C22×Q8116yes—
1199C42C22×Q818yes—
1200C42C22×Q8116yes—
1201C42C22×Q818yes—
1202C23—21no—
1203C23—21no—
1204C23—21no—
1205C23—21no—
1206C23C23×Q812yes—
1207C23C2×2−1+412yes—
1208C23#58512yes—
1209C23C2611yescharacteristic
1210Q8—216no—
1211Q8—48no—
1212Q8—44no—
1213Q8—82no—
1214Q8—84no—
1215Q8—84no—
1216Q8—88no—
1217Q8—162no—
1218Q8—164no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—28no—
1236C2×C4—28no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
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—21no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—21no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—21no—
1294C2×C4—48no—
1295C2×C4—44no—
1296C2×C4—48no—
1297C2×C4—44no—
1298C2×C4—44no—
1299C2×C4—82no—
1300C2×C4—82no—
1301C2×C4—84no—
1302C2×C4—84no—
1303C2×C4C23×Q814yes—
1304C2×C4C23×Q814yes—
1305C2×C4C23×Q814yes—
1306C2×C4C23×Q814yes—
1307C2×C4C23×Q812yes—
1308C2×C4C23×Q818yes—
1309C2×C4C23×Q812yes—
1310C2×C4C2×2−1+412yes—
1311C2×C4C2×2−1+412yes—
1312C2×C4#58512yes—
1313C2×C4#58512yes—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—22no—
1318C22—22no—
1319C22—22no—
1320C22#350214yes—
1321C22C24×Q811yescharacteristic
1322C22C22×2−1+411yescharacteristic
1323C22C2×#58511yescharacteristic
1324C22C2×#58511yescharacteristic
1325C22C2×#58511yescharacteristic
1326C22H(7,𝔽2)11yescharacteristic
1327C222−1+611yescharacteristic
1328C4—24no—
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—22no—
1333C4—22no—
1334C4—22no—
1335C4—28no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—41no—
1341C4—42no—
1342C4—41no—
1343C4—42no—
1344C4—42no—
1345C4—44no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4—42no—
1350C4—44no—
1351C4—42no—
1352C4—42no—
1353C4—44no—
1354C4—42no—
1355C4#345814yes—
1356C2—24no—
1357C2C2×#345811yescharacteristic
1358C2C2×#350211yescharacteristic
1359C2#6285411yescharacteristic
1360C2#6290211yescharacteristic
1361C2#6291111yescharacteristic
1362C2#6295611yescharacteristic
1363C2#6296511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42826C2semidirect
2. #42825C2semidirect
3. #42822C2semidirect
4. #42821C2semidirect
5. #42185C2semidirect
6. #42183C2semidirect
7. #42004C2semidirect
8. #42002C2semidirect
20. #35972C2semidirect
21. #35958C2semidirect
22. #35936C2semidirect
23. #35867C2semidirect
279. C2×C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#428262
#428252
#428222
#428212
#421852
#421832
#420042
#420022
#397522
#397482
#396242
#396202
#391792
#391752
#376232
#376092
#365992
#365642
#365192
#359722
#359582
#359362
#358672
#351042
#345952
#341922
C2×#23552