Finite Group Databasebeta

← #7900955

Subgroups — #7900955

Order 512.

4617 conjugacy classes of subgroups.

The subgroup lattice has 1452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59440C212yesmaximal, complemented
3#52160C211yesmaximal, characteristic
4#52028C214yesmaximal, complemented
5#51701C214yesmaximal, complemented
6#50076C214yesmaximal, complemented
7#46705C214yesmaximal, complemented
8#46286C212yesmaximal, complemented
9#45397C212yesmaximal, complemented
10#45078C212yesmaximal, complemented
11#44981C212yesmaximal, complemented
12#43398C214yesmaximal, complemented
13#42862C212yesmaximal, complemented
14#42808C212yesmaximal, complemented
15#41136C214yesmaximal, complemented
16#39757C211yesmaximal, characteristic, complemented
17#39666C212yesmaximal, complemented
18#39509C211yesmaximal, characteristic, complemented
19#39493C212yesmaximal, complemented
20#39274C212yesmaximal, complemented
21#38474C212yesmaximal, complemented
22#38040C212yesmaximal, complemented
23#37199C212yesmaximal, complemented
24#36270C211yesmaximal, characteristic, complemented
25#35738C212yesmaximal, complemented
26#35663C212yesmaximal, complemented
27#35199C211yesmaximal, characteristic, complemented
28#34465C212yesmaximal, complemented
29#34311C211yesmaximal, characteristic, complemented
30C2×#554C2212yes—
31C2×#552C2212yes—
32C2×D4×Q8C2211yescharacteristic
33C2×#529C2212yes—
34C2×#519C2212yes—
35#2863C2212yes—
36#2862C2212yes—
37#2860C2212yes—
38#2859C2211yescharacteristic
39#2855C2212yes—
40#2831C2214yes—
41#2821C2214yes—
42#2810C2212yes—
43#2810C2212yes—
44#2810C2212yes—
45#2808C2212yes—
46#2806C2214yes—
47#2805C2212yes—
48#2805C2212yes—
49#2805C2212yes—
50#2804C2214yes—
51#2798C2214yes—
52#2798C2214yes—
53#2797C2214yes—
54#2795C2214yes—
55#2794C2214yes—
56#2784C2214yes—
57#2783C2214yes—
58#2781C2214yes—
59#2780C2214yes—
60#2775C2214yes—
61#2774C2214yes—
62#2773C2214yes—
63#2772C2214yes—
64#2772C2214yes—
65#2771C2214yes—
66#2753C2214yes—
67#2751C2214yes—
68#2751C2214yes—
69#2739C2214yes—
70#2737C2214yes—
71#2733C2211yescharacteristic
72#2732C2211yescharacteristic
73#2732C2212yes—
74#2732C2212yes—
75#2731C2214yes—
76#2730C2212yes—
77#2727C2212yes—
78#2727C2211yescharacteristic
79#2721C2214yes—
80#2721C2212yes—
81#2720C2214yes—
82#2720C2214yes—
83#2719C2214yes—
84#2715C2214yes—
85#2714C2212yes—
86#2710C2214yes—
87#2705C2212yes—
88#2696C2214yes—
89#2696C2214yes—
90#2695C2214yes—
91#2694C2212yes—
92#2689C2214yes—
93#2682C2211yescharacteristic
94#2674C2214yes—
95#2673C2212yes—
96#2666C2214yes—
97#2665C2214yes—
98#2665C2214yes—
99#2652C2214yes—
100#2642C2212yes—
101#2636C2214yes—
102#2634C2214yes—
103#2628C2214yes—
104#2628C2212yes—
105#2625C2212yes—
106#2612C2214yes—
107#2611C2214yes—
108#2610C2214yes—
109#2602C2214yes—
110#2601C2214yes—
111#2601C2214yes—
112#2598C2214yes—
113#2598C2214yes—
114#2597C2214yes—
115#2596C2214yes—
116#2596C2214yes—
117#2595C2214yes—
118#2590C2214yes—
119#2589C2214yes—
120#2589C2214yes—
121#2589C2214yes—
122#2582C2211yescharacteristic
123#2581C2212yes—
124#2575C2214yes—
125#2574C2214yes—
126#2570C2214yes—
127#2569C2214yes—
128#2568C2211yescharacteristic
129#2563C2212yes—
130#2562C2212yes—
131#2562C2212yes—
132#2558C2214yes—
133#2557C2214yes—
134#2552C2212yes—
135#2551C2211yescharacteristic
136#2547C2212yes—
137#2546C2211yescharacteristic
138#2542C2212yes—
139#2538C2212yes—
140#2538C2211yescharacteristic
141#2538C2214yes—
142#2538C2211yescharacteristic
143#2536C2212yes—
144#2533C2214yes—
145#2533C2214yes—
146#2530C2214yes—
147#2529C2214yes—
148#2526C2214yes—
149#2520C2214yes—
150#2511C2212yes—
151#2511C2212yes—
152#2511C2214yes—
153#2508C2212yes—
154#2506C2212yes—
155#2497C2212yes—
156#2496C2212yes—
157#2492C2212yes—
158#2492C2212yes—
159#2488C2214yes—
160#2487C2212yes—
161#2486C2212yes—
162#2485C2212yes—
163#2485C2212yes—
164#2481C2214yes—
165#2478C2214yes—
166#2477C2214yes—
167#2477C2214yes—
168#2476C2214yes—
169#2474C2214yes—
170#2470C2214yes—
171#2469C2214yes—
172#2469C2214yes—
173#2465C2214yes—
174#2465C2214yes—
175#2465C2214yes—
176#2462C2214yes—
177#2459C2214yes—
178#2458C2214yes—
179#2454C2214yes—
180#2451C2212yes—
181#2451C2212yes—
182#2446C2212yes—
183#2445C2212yes—
184#2444C2214yes—
185#2443C2214yes—
186#2440C2214yes—
187#2439C2214yes—
188#2421C2212yes—
189#2421C2212yes—
190#2419C2214yes—
191#2417C2212yes—
192#2417C2212yes—
193#2417C2212yes—
194#2417C2212yes—
195#2415C2212yes—
196#2415C2212yes—
197#2409C2212yes—
198#2409C2212yes—
199#2409C2212yes—
200#2409C2212yes—
201#2398C2214yes—
202#2397C2212yes—
203#2392C2212yes—
204#2392C2212yes—
205#2383C2214yes—
206#2382C2214yes—
207#2370C2212yes—
208#2366C2212yes—
209#2365C2211yescharacteristic
210#2365C2212yes—
211#2362C2212yes—
212#2362C2214yes—
213#2360C2212yes—
214#2360C2212yes—
215#2359C2214yes—
216#2356C2212yes—
217#2354C2212yes—
218#2354C2211yescharacteristic
219#2354C2211yescharacteristic
220#2352C2212yes—
221#2352C2214yes—
222#2352C2212yes—
223#2352C2212yes—
224Q8×C4⋊C4C2211yescharacteristic
225D4×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2212yes—
227#2346C2212yes—
228#2344C2212yes—
229#2343C2214yes—
230Q8×C22⋊C4C2212yes—
231#2334C2214yes—
232#2333C2214yes—
233#2331C2212yes—
234#2330C2212yes—
235#2330C2214yes—
236#2323C2212yes—
237#2323C2214yes—
238#2323C2212yes—
239#2323C2212yes—
240#2322C2214yes—
241#2320C2212yes—
242#2317C2214yes—
243#2317C2212yes—
244#2314C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2211yescharacteristic
248C4×#127C2211yescharacteristic
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×#121C2212yes—
252#2295C2211yescharacteristic
253#2293C2212yes—
254#2293C2211yescharacteristic
255#2293C2212yes—
256C2×#389C2212yes—
257#2290C2212yes—
258C42×Q8C2211yescharacteristic
259C23×Q8C2312yes—
260#554—48no—
261#552—216no—
262D4×Q8—28no—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×#127C2311yescharacteristic
270#529—48no—
271C2×#126C2314yes—
272C2×#126C2312yes—
273C2×#126C2312yes—
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#125C2312yes—
279C2×#124C2312yes—
280C2×#124C2314yes—
281C2×#123C2314yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×#123C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298#519—48no—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2314yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×#117C2312yes—
323C2×#117C2314yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C2×#117C2314yes—
327C2×#117C2314yes—
328C2×#117C2312yes—
329C2×#117C2314yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2314yes—
334C22×C42C2312yes—
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#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#399C2312yes—
358#399C2314yes—
359#399C2312yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2312yes—
364#399C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2312yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2312yes—
399#396C2312yes—
400#396C2312yes—
401#396C2312yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2312yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2312yes—
423#394C2312yes—
424#394C2312yes—
425#394C2312yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#392C2312yes—
436#392C2312yes—
437#392C2312yes—
438#392C2312yes—
439#392C2312yes—
440#392C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2311yescharacteristic
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2311yescharacteristic
464#390C2312yes—
465#390C2311yescharacteristic
466#390C2311yescharacteristic
467#390C2312yes—
468#390C2314yes—
469#390C2312yes—
470#390C2314yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2311yescharacteristic
476#390C2314yes—
477#390C2311yescharacteristic
478#389C2311yescharacteristic
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2311yescharacteristic
518#389C2312yes—
519#389C2312yes—
520#389C2311yescharacteristic
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2312yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
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#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2314yes—
602#387C2312yes—
603#387C2312yes—
604#387C2314yes—
605#386C2312yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2312yes—
618#386C2312yes—
619#386C2314yes—
620#386C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#384C2311yescharacteristic
639#384C2311yescharacteristic
640#384C2312yes—
641#384C2311yescharacteristic
642#384C2314yes—
643#384C2311yescharacteristic
644#384C2311yescharacteristic
645#384C2314yes—
646#383C2314yes—
647#383C2314yes—
648#382C2314yes—
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#382C2314yes—
654#382C2314yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2312yes—
673#380C2314yes—
674#380C2314yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711#376C2312yes—
712#376C2314yes—
713#376C2314yes—
714C2×#95C2314yes—
715C43C2311yescharacteristic
716C43C2312yes—
717C22×Q8—28no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2414yes—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2414yes—
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2411yescharacteristic
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C4⋊Q8—28no—
745C4⋊Q8—24no—
746C4⋊Q8—24no—
747C4⋊Q8—44no—
748C4⋊Q8—82no—
749C4⋊Q8—82no—
750#127—24no—
751#126—216no—
752#126—44no—
753#126—44no—
754#126—84no—
755#125—216no—
756#125—28no—
757#125—48no—
758#125—44no—
759#124—44no—
760#124—84no—
761#123—216no—
762#123—44no—
763#123—44no—
764#123—84no—
765C22⋊Q8—28no—
766C22⋊Q8—28no—
767C22⋊Q8—28no—
768C22⋊Q8—216no—
769C22⋊Q8—44no—
770C22⋊Q8—48no—
771C22⋊Q8—48no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775C22⋊Q8—44no—
776#121—28no—
777#121—44no—
778C4×Q8—24no—
779C4×Q8—28no—
780C4×Q8—24no—
781C4×Q8—48no—
782C4×Q8—48no—
783C4×Q8—42no—
784C4×Q8—44no—
785C4×Q8—44no—
786C4×Q8—82no—
787C4×Q8#4118yes—
788C4×D4—28no—
789C4×D4—28no—
790C4×D4—24no—
791C4×D4—28no—
792C4×D4—28no—
793C4×D4—48no—
794C4×D4—42no—
795C4×D4—42no—
796C4×D4—44no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—84no—
801#117—28no—
802#117—216no—
803#117—28no—
804#117—44no—
805#117—48no—
806#117—48no—
807#117—44no—
808#117—84no—
809C2×C4⋊C4—28no—
810C2×C4⋊C4—44no—
811C2×C4⋊C4—44no—
812C2×C4⋊C4—84no—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C42—44no—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2411yescharacteristic
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2411yescharacteristic
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2411yescharacteristic
949C2×C42C2412yes—
950C2×C42C2411yescharacteristic
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2412yes—
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019C24C2512yes—
1020C24C2512yes—
1021C24C2512yes—
1022C2×Q8—28no—
1023C2×Q8—24no—
1024C2×Q8—22no—
1025C2×Q8—24no—
1026C2×Q8—22no—
1027C2×Q8—24no—
1028C2×Q8—22no—
1029C2×Q8—24no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—42no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—41no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—432no—
1040C2×Q8C2×#4114yes—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—22no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—22no—
1049C2×D4—41no—
1050C2×D4—42no—
1051C2×D4—41no—
1052C2×D4—41no—
1053C2×D4—41no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—41no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—41no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D42−1+414yes—
1068C22×C4—28no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—28no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—42no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—22no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—22no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—22no—
1147C4⋊C4—24no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—41no—
1155C4⋊C4—42no—
1156C4⋊C4—41no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—41no—
1171C4⋊C4—41no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—41no—
1188C4⋊C4C2×#4114yes—
1189C4⋊C4C2×#4118yes—
1190C22⋊C4—28no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C42—28no—
1236C42—24no—
1237C42—24no—
1238C42—24no—
1239C42—28no—
1240C42—24no—
1241C42—22no—
1242C42—22no—
1243C42—24no—
1244C42—42no—
1245C42—42no—
1246C42—41no—
1247C42—42no—
1248C42—41no—
1249C42—44no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—42no—
1258C42—41no—
1259C42—42no—
1260C42C2×#4118yes—
1261C42C2×#4114yes—
1262C42H(5,𝔽2)14yes—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23C2×2−1+414yes—
1284C23C2611yescharacteristic
1285Q8—28no—
1286Q8—416no—
1287Q8—48no—
1288Q8—82no—
1289Q8—84no—
1290Q8—164no—
1291D4—44no—
1292D4—48no—
1293D4—48no—
1294D4—44no—
1295D4—82no—
1296D4—84no—
1297D4—84no—
1298D4—84no—
1299D4—84no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—22no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—21no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—21no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—416no—
1369C2×C4—416no—
1370C2×C4—48no—
1371C2×C4—48no—
1372C2×C4—48no—
1373C2×C4—84no—
1374C2×C4—84no—
1375C2×C4—164no—
1376C2×C4—164no—
1377C2×C4C22×#4114yes—
1378C2×C4C22×#4112yes—
1379C2×C4C22×#4114yes—
1380C2×C4C22×#4112yes—
1381C2×C4C22×#4112yes—
1382C2×C4C2×H(5,𝔽2)12yes—
1383C2×C4C2×H(5,𝔽2)12yes—
1384C2×C4C2×H(5,𝔽2)12yes—
1385C2×C4C2×2−1+412yes—
1386C2×C4#58512yes—
1387C22—24no—
1388C22—24no—
1389C22—24no—
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—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22C23×#4111yescharacteristic
1409C22C22×H(5,𝔽2)11yescharacteristic
1410C22C22×2−1+411yescharacteristic
1411C22C2×#58511yescharacteristic
1412C22H(7,𝔽2)11yescharacteristic
1413C222−1+611yescharacteristic
1414C222−1+611yescharacteristic
1415C4—24no—
1416C4—22no—
1417C4—24no—
1418C4—22no—
1419C4—22no—
1420C4—22no—
1421C4—22no—
1422C4—44no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—42no—
1427C4—41no—
1428C4—42no—
1429C4—44no—
1430C4—42no—
1431C4—44no—
1432C4—42no—
1433C4—42no—
1434C4—44no—
1435C4—44no—
1436C4—42no—
1437C4—42no—
1438C4—42no—
1439C4—42no—
1440C4#350614yes—
1441C2—44no—
1442C2—82no—
1443C2—82no—
1444C2C2×#350611yescharacteristic
1445C2#6285011yescharacteristic
1446C2#6287811yescharacteristic
1447C2#6290411yescharacteristic
1448C2#6294211yescharacteristic
1449C2#6300011yescharacteristic
1450C2#6306511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52160C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59823C2semidirect
2. #59440C2semidirect
4. #52028C2semidirect
5. #51701C2semidirect
6. #50076C2semidirect
7. #46705C2semidirect
8. #46286C2semidirect
9. #45397C2semidirect
10. #45078C2semidirect
11. #44981C2semidirect
12. #43398C2semidirect
13. #42862C2semidirect
14. #42808C2semidirect
15. #41136C2semidirect
16. #39757C2semidirect
17. #39666C2semidirect
18. #39509C2semidirect
19. #39493C2semidirect
20. #39274C2semidirect
21. #38474C2semidirect
22. #38040C2semidirect
23. #37199C2semidirect
24. #36270C2semidirect
25. #35738C2semidirect
26. #35663C2semidirect
27. #35199C2semidirect
28. #34465C2semidirect
29. #34311C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#594402
#521602
#520282
#517012
#500762
#467052
#462862
#453972
#450782
#449812
#433982
#428622
#428082
#411362
#397572
#396662
#395092
#394932
#392742
#384742
#380402
#371992
#362702
#357382
#356632
#351992
#344652
#343112