Finite Group Databasebeta

← #7656594

Subgroups — #7656594

Order 512.

4600 conjugacy classes of subgroups.

The subgroup lattice has 1448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42473C212yesmaximal, complemented
2#42470C212yesmaximal, complemented
3#42469C212yesmaximal, complemented
4#42466C212yesmaximal, complemented
5#41024C214yesmaximal, complemented
6#41020C214yesmaximal, complemented
7#41014C214yesmaximal, complemented
8#41010C214yesmaximal, complemented
9#39504C211yesmaximal, characteristic, complemented
10#39376C211yesmaximal, characteristic, complemented
11#39266C214yesmaximal, complemented
12#39190C212yesmaximal, complemented
13#37959C212yesmaximal, complemented
14#37771C212yesmaximal
15#37632C212yesmaximal, complemented
16#37518C214yesmaximal, complemented
17#36486C212yesmaximal, complemented
18#36176C211yesmaximal, characteristic, complemented
19#36116C211yesmaximal, characteristic, complemented
20#35828C212yesmaximal, complemented
21#35815C212yesmaximal, complemented
22#35783C212yesmaximal, complemented
23#35770C212yesmaximal, complemented
24#35104C211yesmaximal, characteristic, complemented
25#35092C212yesmaximal, complemented
26#34602C212yesmaximal, complemented
27#34594C211yesmaximal, characteristic
28#34241C212yesmaximal, complemented
29C2×#2365C211yesmaximal, characteristic, complemented
30C2×#539C2212yes—
31C22×C4⋊Q8C2211yescharacteristic
32C2×#529C2212yes—
33C2×#529C2212yes—
34C22×C4×Q8C2212yes—
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2855C2212yes—
38#2854C2212yes—
39#2853C2214yes—
40#2851C2212yes—
41#2833C2214yes—
42#2832C2214yes—
43#2831C2214yes—
44#2831C2214yes—
45#2821C2214yes—
46#2821C2214yes—
47#2809C2212yes—
48#2808C2212yes—
49#2802C2214yes—
50#2798C2214yes—
51#2796C2214yes—
52#2796C2214yes—
53#2794C2214yes—
54#2794C2214yes—
55#2789C2214yes—
56#2787C2214yes—
57#2783C2214yes—
58#2777C2214yes—
59#2773C2214yes—
60#2767C2214yes—
61#2762C2214yes—
62#2758C2214yes—
63#2754C2214yes—
64#2754C2214yes—
65#2751C2214yes—
66#2730C2214yes—
67#2726C2212yes—
68#2724C2212yes—
69#2721C2214yes—
70#2721C2214yes—
71#2705C2214yes—
72#2689C2214yes—
73#2666C2214yes—
74#2666C2214yes—
75#2665C2214yes—
76#2665C2214yes—
77#2664C2212yes—
78#2664C2212yes—
79#2662C2212yes—
80#2662C2212yes—
81#2660C2214yes—
82#2659C2211yescharacteristic
83#2656C2211yescharacteristic
84#2653C2214yes—
85#2653C2214yes—
86#2650C2214yes—
87#2650C2214yes—
88#2640C2214yes—
89#2639C2212yes—
90#2637C2214yes—
91#2637C2214yes—
92#2634C2214yes—
93#2632C2214yes—
94#2628C2212yes—
95#2628C2212yes—
96#2628C2212yes—
97#2628C2212yes—
98#2627C2212yes—
99#2627C2212yes—
100#2627C2212yes—
101#2623C2214yes—
102#2618C2211yescharacteristic
103#2618C2211yescharacteristic
104#2618C2212yes—
105#2618C2212yes—
106#2614C2214yes—
107#2614C2214yes—
108#2607C2214yes—
109#2606C2214yes—
110#2605C2214yes—
111#2605C2214yes—
112#2597C2214yes—
113#2595C2214yes—
114#2594C2214yes—
115#2590C2214yes—
116#2589C2214yes—
117#2588C2214yes—
118#2586C2214yes—
119#2577C2214yes—
120#2575C2214yes—
121#2574C2214yes—
122#2574C2214yes—
123#2572C2214yes—
124#2571C2211yescharacteristic
125#2570C2212yes—
126#2570C2212yes—
127#2570C2214yes—
128#2570C2212yes—
129#2567C2212yes—
130#2567C2212yes—
131#2563C2212yes—
132#2563C2212yes—
133#2563C2211yescharacteristic
134#2562C2212yes—
135#2552C2211yescharacteristic
136#2550C2212yes—
137#2550C2212yes—
138#2547C2211yescharacteristic
139#2532C2214yes—
140#2528C2214yes—
141#2524C2214yes—
142#2517C2214yes—
143#2516C2214yes—
144#2513C2212yes—
145#2511C2214yes—
146#2509C2212yes—
147#2508C2212yes—
148#2508C2212yes—
149#2507C2212yes—
150#2506C2212yes—
151#2503C2214yes—
152#2501C2214yes—
153#2497C2212yes—
154#2497C2212yes—
155#2496C2212yes—
156#2496C2212yes—
157#2495C2212yes—
158#2495C2212yes—
159#2494C2212yes—
160#2494C2212yes—
161#2493C2214yes—
162#2493C2214yes—
163#2488C2214yes—
164#2488C2214yes—
165#2487C2212yes—
166#2486C2212yes—
167#2486C2212yes—
168#2486C2212yes—
169#2486C2212yes—
170#2486C2212yes—
171#2485C2212yes—
172#2485C2212yes—
173#2478C2214yes—
174#2471C2214yes—
175#2469C2214yes—
176#2469C2214yes—
177#2467C2214yes—
178#2465C2214yes—
179#2465C2214yes—
180#2462C2214yes—
181#2462C2214yes—
182#2458C2214yes—
183#2458C2214yes—
184#2453C2212yes—
185#2447C2212yes—
186#2442C2212yes—
187#2441C2212yes—
188#2441C2214yes—
189#2440C2212yes—
190#2439C2212yes—
191#2425C2214yes—
192#2425C2214yes—
193#2423C2214yes—
194#2419C2214yes—
195#2419C2214yes—
196#2399C2214yes—
197#2398C2214yes—
198#2396C2212yes—
199#2396C2212yes—
200#2396C2214yes—
201#2396C2214yes—
202#2392C2212yes—
203#2392C2212yes—
204#2373C2214yes—
205#2373C2214yes—
206#2370C2212yes—
207#2369C2211yescharacteristic
208#2368C2214yes—
209#2365C2211yescharacteristic
210#2365C2214yes—
211#2365C2214yes—
212#2365C2212yes—
213#2365C2212yes—
214#2365C2212yes—
215#2365C2212yes—
216#2364C2214yes—
217#2355C2212yes—
218#2355C2212yes—
219#2354C2211yescharacteristic
220#2352C2212yes—
221#2352C2212yes—
222#2352C2212yes—
223#2352C2212yes—
224#2352C2212yes—
225D4×C4⋊C4C2212yes—
226D4×C4⋊C4C2211yescharacteristic
227D4×C4⋊C4C2212yes—
228#2347C2212yes—
229#2346C2212yes—
230#2345C2212yes—
231#2344C2212yes—
232#2337C2214yes—
233#2336C2214yes—
234#2329C2212yes—
235#2329C2212yes—
236#2322C2214yes—
237#2314C2212yes—
238#2314C2212yes—
239#2313C2212yes—
240C4×#123C2214yes—
241C4×#123C2214yes—
242C4×#123C2214yes—
243C4×#121C2211yescharacteristic
244C4×#121C2212yes—
245C4×#121C2211yescharacteristic
246C2×#391C2212yes—
247C2×#389C2211yescharacteristic
248C2×#389C2211yescharacteristic
249C2×#387C2212yes—
250C2×#387C2212yes—
251#2283C2212yes—
252#2283C2212yes—
253#2274C2212yes—
254#2274C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2312yes—
260#539—48no—
261C2×C4⋊Q8—28no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267#529—216no—
268#529—48no—
269C2×#126C2312yes—
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#123C2312yes—
280C2×#123C2312yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×#121C2311yescharacteristic
291C2×#121C2311yescharacteristic
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×C4×Q8—48no—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C2×#117C2314yes—
314C2×#117C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2311yescharacteristic
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2311yescharacteristic
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2311yescharacteristic
326C22×C42C2312yes—
327C22×C42C2311yescharacteristic
328C22×C42C2312yes—
329C22×C42C2311yescharacteristic
330C22×C42C2312yes—
331C22×C42C2311yescharacteristic
332#401C2314yes—
333#401C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2312yes—
364#399C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2312yes—
387#398C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2312yes—
404#396C2312yes—
405#396C2312yes—
406#396C2314yes—
407#396C2314yes—
408#396C2312yes—
409#396C2312yes—
410#396C2314yes—
411#396C2314yes—
412#396C2312yes—
413#396C2312yes—
414#396C2312yes—
415#396C2312yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2312yes—
424#395C2312yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#394C2314yes—
430#394C2312yes—
431#394C2314yes—
432#394C2312yes—
433#394C2312yes—
434#394C2314yes—
435#394C2312yes—
436#394C2312yes—
437#394C2312yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2312yes—
447#393C2312yes—
448#393C2314yes—
449#393C2314yes—
450#392C2312yes—
451#392C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#390C2314yes—
469#390C2312yes—
470#390C2314yes—
471#390C2312yes—
472#390C2312yes—
473#390C2311yescharacteristic
474#390C2311yescharacteristic
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2311yescharacteristic
510#389C2311yescharacteristic
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2312yes—
538#388C2312yes—
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#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
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#387C2314yes—
588#387C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2312yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2312yes—
597#386C2312yes—
598#386C2312yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#384C2314yes—
610#384C2314yes—
611#384C2312yes—
612#384C2312yes—
613#384C2311yescharacteristic
614#384C2311yescharacteristic
615#383C2314yes—
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#382C2314yes—
620#382C2312yes—
621#382C2314yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2314yes—
627#382C2314yes—
628#382C2312yes—
629#382C2312yes—
630#381C2314yes—
631#381C2314yes—
632#381C2314yes—
633#381C2314yes—
634#381C2314yes—
635#381C2314yes—
636#381C2314yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2311yescharacteristic
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2311yescharacteristic
657#380C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708#376C2314yes—
709#376C2314yes—
710C2×#95C2311yescharacteristic
711C2×#95C2311yescharacteristic
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C2×#95C2312yes—
716C2×#95C2312yes—
717C22×Q8—28no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8C2414yes—
721C22×Q8C2414yes—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2411yescharacteristic
728C22×D4C2411yescharacteristic
729C22×D4C2412yes—
730C22×D4C2412yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2411yescharacteristic
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740C23×C4C2414yes—
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2414yes—
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C4⋊Q8—28no—
747C4⋊Q8—28no—
748C4⋊Q8—216no—
749C4⋊Q8—42no—
750C4⋊Q8—42no—
751#126—28no—
752#126—28no—
753#126—48no—
754#126—48no—
755#125—28no—
756#125—44no—
757#125—44no—
758#125—48no—
759#124—28no—
760#124—44no—
761#123—28no—
762#123—28no—
763#123—48no—
764#123—48no—
765#123—48no—
766#123—48no—
767#123—48no—
768C22⋊Q8—28no—
769C22⋊Q8—28no—
770C22⋊Q8—44no—
771C22⋊Q8—48no—
772#121—28no—
773#121—24no—
774#121—24no—
775#121—44no—
776C4×Q8—28no—
777C4×Q8—48no—
778C4×Q8—48no—
779C4×Q8—48no—
780C4×Q8—48no—
781C4×Q8—44no—
782C4×D4—28no—
783C4×D4—28no—
784C4×D4—28no—
785C4×D4—44no—
786C4×D4—44no—
787C4×D4—42no—
788C4×D4—42no—
789C4×D4—48no—
790C4×D4—48no—
791#117—28no—
792#117—28no—
793#117—28no—
794#117—48no—
795#117—44no—
796C2×C4⋊C4—24no—
797C2×C4⋊C4—24no—
798C2×C4⋊C4—28no—
799C2×C4⋊C4—24no—
800C2×C4⋊C4—28no—
801C2×C4⋊C4—24no—
802C2×C4⋊C4—28no—
803C2×C4⋊C4—42no—
804C2×C4⋊C4—44no—
805C2×C4⋊C4—42no—
806C2×C4⋊C4—44no—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C42—28no—
915C2×C42—42no—
916C2×C42—42no—
917C2×C42—44no—
918C2×C42—44no—
919C2×C42#4118yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2412yes—
945C2×C42C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24C2512yes—
1017C24C2512yes—
1018C24C2511yescharacteristic
1019C2×Q8—28no—
1020C2×Q8—28no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—42no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—432no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—24no—
1038C2×D4—24no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—41no—
1045C2×D4—41no—
1046C2×D4—41no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—41no—
1052C2×D4—42no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—22no—
1056C22×C4—22no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—22no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—28no—
1076C22×C4—41no—
1077C22×C4—41no—
1078C22×C4—42no—
1079C22×C4—41no—
1080C22×C4—41no—
1081C22×C4—41no—
1082C22×C4—41no—
1083C22×C4—41no—
1084C22×C4—41no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—41no—
1090C22×C4—41no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4C2×#4114yes—
1095C22×C4C2×#4114yes—
1096C22×C4C2×#4114yes—
1097C22×C4H(5,𝔽2)14yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2514yes—
1110C22×C4C2514yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2512yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2512yes—
1123C22×C4C2511yescharacteristic
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—22no—
1130C4⋊C4—22no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—28no—
1144C4⋊C4—28no—
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—22no—
1148C4⋊C4—22no—
1149C4⋊C4—24no—
1150C4⋊C4—28no—
1151C4⋊C4—22no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—41no—
1165C4⋊C4—41no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—41no—
1174C4⋊C4—41no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C42−1+414yes—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—28no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C42—24no—
1232C42—24no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—24no—
1237C42—28no—
1238C42—24no—
1239C42—22no—
1240C42—22no—
1241C42—41no—
1242C42—41no—
1243C42—42no—
1244C42—44no—
1245C42—44no—
1246C42—44no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42C2×#4118yes—
1256C42C2×#4118yes—
1257C23—21no—
1258C23—21no—
1259C23—21no—
1260C23—21no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23C22×#4112yes—
1276C23C2×H(5,𝔽2)12yes—
1277C23#58512yes—
1278C23C2611yescharacteristic
1279Q8—416no—
1280Q8—416no—
1281Q8—84no—
1282Q8—84no—
1283Q8—162no—
1284D4—44no—
1285D4—48no—
1286D4—48no—
1287D4—84no—
1288D4—82no—
1289D4—84no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—28no—
1303C2×C4—28no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—21no—
1356C2×C4—22no—
1357C2×C4—21no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—44no—
1362C2×C4—44no—
1363C2×C4—48no—
1364C2×C4—44no—
1365C2×C4—48no—
1366C2×C4—48no—
1367C2×C4—48no—
1368C2×C4—48no—
1369C2×C4—88no—
1370C2×C4—84no—
1371C2×C4—82no—
1372C2×C4—82no—
1373C2×C4—164no—
1374C2×C4C22×#4112yes—
1375C2×C4C22×#4114yes—
1376C2×C4C22×#4114yes—
1377C2×C4C22×#4112yes—
1378C2×C4C2×H(5,𝔽2)12yes—
1379C2×C4C2×H(5,𝔽2)12yes—
1380C2×C4C2×2−1+414yes—
1381C2×C4C2×2−1+412yes—
1382C2×C4#58512yes—
1383C22—22no—
1384C22—22no—
1385C22—22no—
1386C22—22no—
1387C22—22no—
1388C22—22no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22#350614yes—
1404C22C23×#4111yescharacteristic
1405C22C22×H(5,𝔽2)11yescharacteristic
1406C22C22×2−1+411yescharacteristic
1407C22C2×#58511yescharacteristic
1408C22C2×#58511yescharacteristic
1409C222−1+611yescharacteristic
1410C222−1+611yescharacteristic
1411C4—24no—
1412C4—24no—
1413C4—22no—
1414C4—22no—
1415C4—22no—
1416C4—24no—
1417C4—42no—
1418C4—42no—
1419C4—44no—
1420C4—42no—
1421C4—42no—
1422C4—42no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—44no—
1427C4—41no—
1428C4—42no—
1429C4—41no—
1430C4—44no—
1431C4—42no—
1432C4—42no—
1433C4—42no—
1434C4—44no—
1435C4—44no—
1436C4#346114yes—
1437C2—24no—
1438C2—82no—
1439C2—82no—
1440C2C2×#346111yescharacteristic
1441C2C2×#350611yescharacteristic
1442C2#6286011yescharacteristic
1443C2#6290111yescharacteristic
1444C2#6291111yescharacteristic
1445C2#6294211yescharacteristic
1446C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2656C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42473C2semidirect
2. #42470C2semidirect
3. #42469C2semidirect
4. #42466C2semidirect
5. #41024C2semidirect
6. #41020C2semidirect
7. #41014C2semidirect
8. #41010C2semidirect
9. #39504C2semidirect
10. #39376C2semidirect
11. #39266C2semidirect
12. #39190C2semidirect
13. #37959C2semidirect
15. #37632C2semidirect
16. #37518C2semidirect
17. #36486C2semidirect
18. #36176C2semidirect
19. #36116C2semidirect
20. #35828C2semidirect
21. #35815C2semidirect
22. #35783C2semidirect
23. #35770C2semidirect
24. #35104C2semidirect
25. #35092C2semidirect
26. #34602C2semidirect
28. #34241C2semidirect
29. C2×#2365C2semidirect

Maximal subgroups

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

subgroupindex
#424732
#424702
#424692
#424662
#410242
#410202
#410142
#410102
#395042
#393762
#392662
#391902
#379592
#377712
#376322
#375182
#364862
#361762
#361162
#358282
#358152
#357832
#357702
#351042
#350922
#346022
#345942
#342412
C2×#23652