Finite Group Databasebeta

← #7657706

Subgroups — #7657706

Order 512.

4342 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42231C214yesmaximal, complemented
2#42062C214yesmaximal, complemented
3#41965C214yesmaximal, complemented
4#41024C214yesmaximal, complemented
5#41014C214yesmaximal, complemented
6#40547C212yesmaximal, complemented
7#40545C212yesmaximal
8#39682C212yesmaximal, complemented
9#39680C212yesmaximal, complemented
10#37963C212yesmaximal, complemented
11#37960C212yesmaximal, complemented
12#37884C212yesmaximal, complemented
13#37882C212yesmaximal, complemented
14#37617C211yesmaximal, characteristic
15#37597C212yesmaximal, complemented
16#37592C212yesmaximal, complemented
17#37549C211yesmaximal, characteristic
18#36189C212yesmaximal, complemented
19#36171C212yesmaximal, complemented
20#35999C214yesmaximal, complemented
21#35743C212yesmaximal, complemented
22#35742C212yesmaximal
23#35304C211yesmaximal, characteristic, complemented
24#35282C212yesmaximal, complemented
25#34625C212yesmaximal, complemented
26C2×#2660C211yesmaximal, characteristic, complemented
27#34239C211yesmaximal, characteristic, complemented
28#34216C211yesmaximal, characteristic, complemented
29#34149C211yesmaximal, characteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C22×#125C2211yescharacteristic
33#2864C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2851C2212yes—
38#2851C2212yes—
39#2839C2214yes—
40#2836C2214yes—
41#2833C2214yes—
42#2831C2214yes—
43#2822C2212yes—
44#2821C2214yes—
45#2820C2212yes—
46#2809C2214yes—
47#2802C2214yes—
48#2802C2214yes—
49#2799C2214yes—
50#2794C2214yes—
51#2794C2214yes—
52#2789C2214yes—
53#2787C2214yes—
54#2783C2214yes—
55#2777C2214yes—
56#2773C2214yes—
57#2767C2214yes—
58#2762C2214yes—
59#2758C2214yes—
60#2755C2214yes—
61#2754C2214yes—
62#2726C2214yes—
63#2721C2214yes—
64#2721C2214yes—
65#2715C2214yes—
66#2713C2214yes—
67#2713C2214yes—
68#2700C2214yes—
69#2689C2214yes—
70#2667C2214yes—
71#2666C2214yes—
72#2666C2214yes—
73#2666C2214yes—
74#2665C2214yes—
75#2664C2214yes—
76#2664C2214yes—
77#2660C2212yes—
78#2660C2212yes—
79#2660C2212yes—
80#2660C2212yes—
81#2660C2211yescharacteristic
82#2660C2214yes—
83#2660C2211yescharacteristic
84#2660C2211yescharacteristic
85#2660C2211yescharacteristic
86#2660C2212yes—
87#2658C2212yes—
88#2655C2214yes—
89#2655C2214yes—
90#2654C2214yes—
91#2650C2214yes—
92#2647C2212yes—
93#2647C2212yes—
94#2647C2212yes—
95#2642C2212yes—
96#2637C2214yes—
97#2634C2214yes—
98#2629C2212yes—
99#2629C2212yes—
100#2629C2212yes—
101#2628C2212yes—
102#2628C2212yes—
103#2628C2212yes—
104#2627C2212yes—
105#2623C2214yes—
106#2618C2212yes—
107#2612C2214yes—
108#2606C2212yes—
109#2605C2212yes—
110#2605C2214yes—
111#2594C2214yes—
112#2590C2214yes—
113#2590C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2586C2214yes—
117#2585C2214yes—
118#2584C2211yescharacteristic
119#2584C2211yescharacteristic
120#2577C2214yes—
121#2575C2214yes—
122#2574C2214yes—
123#2570C2214yes—
124#2569C2212yes—
125#2562C2211yescharacteristic
126#2562C2211yescharacteristic
127#2556C2214yes—
128#2550C2214yes—
129#2549C2212yes—
130#2547C2212yes—
131#2546C2212yes—
132#2532C2214yes—
133#2528C2214yes—
134#2524C2214yes—
135#2524C2214yes—
136#2522C2214yes—
137#2521C2214yes—
138#2520C2214yes—
139#2520C2214yes—
140#2519C2214yes—
141#2517C2214yes—
142#2511C2214yes—
143#2509C2212yes—
144#2509C2212yes—
145#2508C2214yes—
146#2508C2212yes—
147#2508C2212yes—
148#2507C2212yes—
149#2507C2212yes—
150#2506C2212yes—
151#2506C2212yes—
152#2498C2214yes—
153#2497C2212yes—
154#2497C2212yes—
155#2496C2212yes—
156#2496C2212yes—
157#2495C2212yes—
158#2495C2212yes—
159#2494C2212yes—
160#2494C2212yes—
161#2493C2214yes—
162#2493C2214yes—
163#2488C2214yes—
164#2487C2212yes—
165#2487C2212yes—
166#2487C2212yes—
167#2486C2212yes—
168#2481C2214yes—
169#2481C2214yes—
170#2478C2214yes—
171#2474C2214yes—
172#2473C2214yes—
173#2473C2214yes—
174#2469C2214yes—
175#2465C2214yes—
176#2462C2214yes—
177#2462C2214yes—
178#2453C2214yes—
179#2451C2214yes—
180#2442C2214yes—
181#2441C2214yes—
182#2438C2214yes—
183#2438C2214yes—
184#2436C2212yes—
185#2434C2212yes—
186#2423C2214yes—
187#2419C2214yes—
188#2417C2214yes—
189#2413C2214yes—
190#2402C2214yes—
191#2399C2214yes—
192#2396C2214yes—
193#2396C2214yes—
194C2×#398C2214yes—
195C2×#395C2212yes—
196C2×#395C2212yes—
197#2373C2212yes—
198#2373C2212yes—
199#2372C2212yes—
200#2371C2214yes—
201#2371C2212yes—
202#2370C2212yes—
203#2370C2212yes—
204#2369C2212yes—
205#2369C2212yes—
206#2368C2211yescharacteristic
207#2368C2211yescharacteristic
208#2365C2214yes—
209#2364C2211yescharacteristic
210#2364C2211yescharacteristic
211#2360C2214yes—
212#2359C2214yes—
213#2359C2212yes—
214#2359C2212yes—
215#2352C2214yes—
216#2345C2212yes—
217#2345C2211yescharacteristic
218#2345C2212yes—
219#2345C2211yescharacteristic
220#2344C2211yescharacteristic
221#2344C2212yes—
222#2344C2212yes—
223#2344C2211yescharacteristic
224#2343C2214yes—
225Q8×C22⋊C4C2212yes—
226Q8×C22⋊C4C2212yes—
227#2336C2214yes—
228#2331C2212yes—
229#2331C2212yes—
230#2331C2214yes—
231#2330C2212yes—
232#2330C2212yes—
233#2316C2212yes—
234#2314C2212yes—
235#2314C2212yes—
236#2313C2212yes—
237C4×C4⋊Q8C2212yes—
238C4×C4⋊Q8C2212yes—
239C4×C4⋊Q8C2212yes—
240C4×#125C2212yes—
241C4×#125C2212yes—
242C4×#125C2212yes—
243#2298C2212yes—
244#2295C2212yes—
245#2290C2212yes—
246#2290C2212yes—
247#2285C2212yes—
248#2285C2211yescharacteristic
249C2×#384C2212yes—
250#2283C2212yes—
251#2283C2211yescharacteristic
252C2×#382C2212yes—
253#2274C2212yes—
254#2274C2212yes—
255C42×D4C2212yes—
256C4×#117C2212yes—
257C4×#117C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C23×Q8C2312yes—
260C2×C4⋊Q8—28no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268#529—28no—
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125—28no—
273C2×#125C2311yescharacteristic
274C2×#125C2311yescharacteristic
275C2×#125C2312yes—
276C2×#125C2311yescharacteristic
277C2×#125C2311yescharacteristic
278C2×#125C2312yes—
279C2×#125C2311yescharacteristic
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#124C2311yescharacteristic
285C2×#124C2314yes—
286C2×#123C2312yes—
287C2×#123C2314yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2314yes—
295C2×C4×Q8C2314yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2311yescharacteristic
303C2×#117C2312yes—
304C2×#117C2311yescharacteristic
305C2×#117C2312yes—
306C2×#117C2312yes—
307C2×#117C2314yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2314yes—
316C22×C42C2312yes—
317C22×C42C2312yes—
318C22×C42C2311yescharacteristic
319#401C2314yes—
320#401C2314yes—
321#400C2312yes—
322#400C2312yes—
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#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2312yes—
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#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#395C2312yes—
408#395C2312yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#395C2312yes—
413#395C2312yes—
414#395C2312yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2312yes—
422#395C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2314yes—
426#394C2312yes—
427#394C2312yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2312yes—
500#388C2314yes—
501#388C2312yes—
502#388C2312yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2312yes—
507#388C2312yes—
508#388C2312yes—
509#388C2312yes—
510#388C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
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#387C2312yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2312yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2312yes—
578#386C2312yes—
579#386C2314yes—
580#386C2312yes—
581#386C2312yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2312yes—
586#385C2314yes—
587#385C2314yes—
588#385C2312yes—
589#385C2312yes—
590#385C2312yes—
591#385C2314yes—
592#385C2314yes—
593#384C2312yes—
594#384C2312yes—
595#384C2312yes—
596#384C2312yes—
597#384C2314yes—
598#384C2314yes—
599#384C2312yes—
600#384C2312yes—
601#383C2312yes—
602#383C2314yes—
603#383C2314yes—
604#383C2314yes—
605#382C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2312yes—
609#382C2312yes—
610#382C2314yes—
611#382C2314yes—
612#382C2314yes—
613#382C2314yes—
614#382C2314yes—
615#382C2312yes—
616#382C2312yes—
617#382C2314yes—
618#381C2312yes—
619#381C2312yes—
620#381C2314yes—
621#381C2314yes—
622#381C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2314yes—
631#380C2312yes—
632#380C2312yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2311yescharacteristic
637#380C2312yes—
638#380C2311yescharacteristic
639#380C2312yes—
640#380C2312yes—
641#380C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2311yescharacteristic
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⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C22⋊C4C2311yescharacteristic
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2311yescharacteristic
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2311yescharacteristic
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698#376C2312yes—
699#376C2312yes—
700#376C2312yes—
701#376C2314yes—
702#376C2311yescharacteristic
703#376C2311yescharacteristic
704#376C2312yes—
705#376C2312yes—
706#376C2311yescharacteristic
707#376C2311yescharacteristic
708C2×#95C2311yescharacteristic
709C2×#95C2314yes—
710C2×#95C2312yes—
711C2×#95C2314yes—
712C2×#95C2311yescharacteristic
713C43C2312yes—
714C43C2312yes—
715C22×Q8—28no—
716C22×Q8—84no—
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×Q8C2414yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2414yes—
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2412yes—
732C23×C4C2414yes—
733C23×C4C2412yes—
734C23×C4C2411yescharacteristic
735C4⋊Q8—24no—
736C4⋊Q8—24no—
737C4⋊Q8—28no—
738C4⋊Q8—28no—
739C4⋊Q8—28no—
740C4⋊Q8—28no—
741C4⋊Q8—84no—
742#126—28no—
743#126—84no—
744#126—84no—
745#125—24no—
746#125—24no—
747#125—24no—
748#125—24no—
749#125—28no—
750#125—28no—
751#125—24no—
752#125—28no—
753#125—84no—
754#125—84no—
755#125—84no—
756#124—24no—
757#124—84no—
758#123—28no—
759#123—48no—
760C22⋊Q8—24no—
761C22⋊Q8—48no—
762C22⋊Q8—84no—
763#121—24no—
764C4×Q8—24no—
765C4×Q8—84no—
766C4×Q8—84no—
767C4×Q8—84no—
768C4×D4—28no—
769C4×D4—28no—
770C4×D4—24no—
771C4×D4—44no—
772#117—24no—
773#117—28no—
774#117—28no—
775#117—28no—
776#117—42no—
777#117—44no—
778#117—44no—
779#117—84no—
780C2×C4⋊C4—24no—
781C2×C4⋊C4—28no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4—24no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—28no—
786C2×C4⋊C4—84no—
787C2×C4⋊C4—84no—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C22⋊C4C2411yescharacteristic
862C2×C22⋊C4C2411yescharacteristic
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2411yescharacteristic
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2411yescharacteristic
887C2×C42—28no—
888C2×C42—28no—
889C2×C42#4118yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2412yes—
922#95C2411yescharacteristic
923#95C2411yescharacteristic
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2411yescharacteristic
930#95C2411yescharacteristic
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002C24C2512yes—
1003C24C2511yescharacteristic
1004C2×Q8—24no—
1005C2×Q8—24no—
1006C2×Q8—22no—
1007C2×Q8—28no—
1008C2×Q8—28no—
1009C2×Q8—44no—
1010C2×Q8—44no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—42no—
1015C2×Q8—44no—
1016C2×Q8—816no—
1017C2×D4—24no—
1018C2×D4—24no—
1019C2×D4—24no—
1020C2×D4—22no—
1021C2×D4—42no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—28no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4C2×#4114yes—
1050C22×C4C2×#4114yes—
1051C22×C4C2×#4114yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—22no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—22no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—22no—
1102C4⋊C4—24no—
1103C4⋊C4—22no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—28no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
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—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C22⋊C4—24no—
1153C22⋊C4—22no—
1154C22⋊C4—24no—
1155C22⋊C4—22no—
1156C22⋊C4—22no—
1157C22⋊C4—24no—
1158C22⋊C4—28no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—42no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C42−1+414yes—
1178C42—24no—
1179C42—24no—
1180C42—24no—
1181C42—24no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—28no—
1187C42—24no—
1188C42—24no—
1189C42—42no—
1190C42—42no—
1191C42—42no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—42no—
1196C42—42no—
1197C42—42no—
1198C42—44no—
1199C42—42no—
1200C42—44no—
1201C42—44no—
1202C42—44no—
1203C42—42no—
1204C42—44no—
1205C42C2×#4114yes—
1206C42C2×#4114yes—
1207C42C2×#4114yes—
1208C42C2×#4114yes—
1209C422−1+418yes—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23C22×#4112yes—
1220C23C2×2−1+412yes—
1221C23#58512yes—
1222C23C2611yescharacteristic
1223Q8—48no—
1224Q8—48no—
1225Q8—82no—
1226Q8—88no—
1227Q8—88no—
1228D4—48no—
1229D4—82no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—28no—
1244C2×C4—28no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—44no—
1298C2×C4—48no—
1299C2×C4—48no—
1300C2×C4—48no—
1301C2×C4—48no—
1302C2×C4—48no—
1303C2×C4—84no—
1304C2×C4—84no—
1305C2×C4—88no—
1306C2×C4C22×#4112yes—
1307C2×C4C22×#4112yes—
1308C2×C4C22×#4112yes—
1309C2×C4C22×#4112yes—
1310C2×C4C22×#4112yes—
1311C2×C4C22×#4112yes—
1312C2×C4C2×2−1+414yes—
1313C2×C4C2×2−1+414yes—
1314C2×C4C2×2−1+414yes—
1315C2×C4C2×2−1+414yes—
1316C22—22no—
1317C22—22no—
1318C22—24no—
1319C22—24no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22#346114yes—
1328C22C23×#4111yescharacteristic
1329C22C22×2−1+412yes—
1330C22C22×2−1+411yescharacteristic
1331C22C2×#58511yescharacteristic
1332C22H(7,𝔽2)12yes—
1333C4—22no—
1334C4—22no—
1335C4—22no—
1336C4—22no—
1337C4—22no—
1338C4—24no—
1339C4—24no—
1340C4—24no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4—44no—
1346C4—42no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—44no—
1352C4—42no—
1353C4—42no—
1354C4—44no—
1355C4—42no—
1356C4—42no—
1357C4—44no—
1358C4—44no—
1359C4#350914yes—
1360C2—24no—
1361C2—82no—
1362C2C2×#346111yescharacteristic
1363C2C2×#350911yescharacteristic
1364C2#6285511yescharacteristic
1365C2#6294512yes—
1366C2#6295812yes—
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. #42231C2semidirect
2. #42062C2semidirect
3. #41965C2semidirect
4. #41024C2semidirect
5. #41014C2semidirect
6. #40547C2semidirect
8. #39682C2semidirect
9. #39680C2semidirect
10. #37963C2semidirect
11. #37960C2semidirect
12. #37884C2semidirect
13. #37882C2semidirect
15. #37597C2semidirect
16. #37592C2semidirect
18. #36189C2semidirect
19. #36171C2semidirect
20. #35999C2semidirect
21. #35743C2semidirect
23. #35304C2semidirect
24. #35282C2semidirect
25. #34625C2semidirect
26. C2×#2660C2semidirect
27. #34239C2semidirect
28. #34216C2semidirect

Maximal subgroups

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

subgroupindex
#422312
#420622
#419652
#410242
#410142
#405472
#405452
#396822
#396802
#379632
#379602
#378842
#378822
#376172
#375972
#375922
#375492
#361892
#361712
#359992
#357432
#357422
#353042
#352822
#346252
C2×#26602
#342392
#342162
#341492