Finite Group Databasebeta

← #8115480

Subgroups — #8115480

Order 512.

4463 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58871C214yesmaximal, complemented
2#58839C214yesmaximal, complemented
3#57319C214yesmaximal, complemented
4#57027C214yesmaximal, complemented
5#56886C214yesmaximal, complemented
6#56779C214yesmaximal, complemented
7#55820C214yesmaximal, complemented
8#54161C214yesmaximal, complemented
9#53073C212yesmaximal, complemented
10#53008C212yesmaximal, complemented
11#45307C212yesmaximal, complemented
12#45156C212yesmaximal, complemented
13#42853C212yesmaximal, complemented
14#42802C212yesmaximal, complemented
15#42800C212yesmaximal, complemented
16#42749C212yesmaximal, complemented
17#39762C211yesmaximal, characteristic, complemented
18#39740C211yesmaximal, characteristic, complemented
19#39379C211yesmaximal, characteristic, complemented
20#39356C211yesmaximal, characteristic, complemented
21#37774C212yesmaximal, complemented
22#37750C212yesmaximal, complemented
23#37435C212yesmaximal, complemented
24#37390C212yesmaximal, complemented
25#35343C211yesmaximal, characteristic, complemented
26#35319C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#548C2212yes—
30C2×#541C2212yes—
31C2×#541C2212yes—
32C2×#536C2212yes—
33C2×#529C2212yes—
34#2868C2211yescharacteristic
35#2861C2212yes—
36#2859C2211yescharacteristic
37#2859C2211yescharacteristic
38#2858C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2843C2214yes—
42#2838C2214yes—
43#2838C2214yes—
44#2834C2214yes—
45#2833C2214yes—
46#2829C2214yes—
47#2828C2214yes—
48#2827C2214yes—
49#2826C2214yes—
50#2825C2214yes—
51#2823C2214yes—
52#2820C2214yes—
53#2807C2214yes—
54#2805C2214yes—
55#2801C2214yes—
56#2800C2214yes—
57#2797C2214yes—
58#2793C2214yes—
59#2792C2214yes—
60#2790C2214yes—
61#2787C2214yes—
62#2783C2214yes—
63#2779C2214yes—
64#2778C2214yes—
65#2777C2214yes—
66#2776C2214yes—
67#2776C2214yes—
68#2774C2214yes—
69#2772C2214yes—
70#2770C2214yes—
71#2765C2214yes—
72#2765C2214yes—
73#2757C2214yes—
74#2757C2214yes—
75#2757C2214yes—
76#2756C2214yes—
77#2750C2214yes—
78#2749C2214yes—
79#2749C2214yes—
80#2746C2214yes—
81#2743C2214yes—
82#2739C2214yes—
83#2732C2214yes—
84#2727C2214yes—
85#2727C2214yes—
86#2727C2214yes—
87#2725C2214yes—
88#2725C2214yes—
89#2725C2214yes—
90#2723C2214yes—
91#2721C2214yes—
92#2720C2214yes—
93#2720C2214yes—
94#2720C2214yes—
95#2720C2214yes—
96#2720C2214yes—
97#2718C2214yes—
98#2718C2214yes—
99#2718C2214yes—
100#2718C2214yes—
101#2715C2214yes—
102#2714C2214yes—
103#2711C2214yes—
104#2705C2214yes—
105#2704C2214yes—
106#2702C2214yes—
107#2700C2214yes—
108#2695C2214yes—
109#2694C2214yes—
110#2693C2214yes—
111#2691C2214yes—
112#2689C2214yes—
113#2689C2214yes—
114#2687C2214yes—
115#2683C2214yes—
116#2682C2214yes—
117#2666C2214yes—
118#2664C2214yes—
119#2662C2214yes—
120#2658C2212yes—
121#2655C2212yes—
122#2654C2212yes—
123#2653C2212yes—
124#2652C2212yes—
125#2652C2214yes—
126#2651C2212yes—
127#2650C2212yes—
128#2649C2212yes—
129#2648C2212yes—
130#2648C2214yes—
131#2643C2214yes—
132#2642C2212yes—
133#2642C2212yes—
134#2636C2214yes—
135#2629C2214yes—
136#2629C2212yes—
137#2621C2211yescharacteristic
138#2621C2212yes—
139#2620C2212yes—
140#2620C2212yes—
141#2619C2211yescharacteristic
142#2602C2214yes—
143#2602C2214yes—
144#2601C2214yes—
145#2601C2214yes—
146#2601C2214yes—
147#2594C2214yes—
148#2587C2214yes—
149#2587C2214yes—
150#2582C2212yes—
151#2573C2214yes—
152#2566C2214yes—
153#2546C2212yes—
154#2546C2212yes—
155#2546C2212yes—
156#2545C2212yes—
157#2545C2212yes—
158#2545C2212yes—
159#2545C2212yes—
160#2544C2212yes—
161#2542C2212yes—
162#2540C2212yes—
163#2538C2212yes—
164#2525C2214yes—
165#2514C2212yes—
166#2514C2212yes—
167#2514C2212yes—
168#2514C2214yes—
169#2513C2212yes—
170#2512C2214yes—
171#2510C2214yes—
172#2509C2214yes—
173#2506C2214yes—
174#2506C2214yes—
175#2506C2214yes—
176#2496C2214yes—
177#2496C2214yes—
178#2490C2212yes—
179#2489C2212yes—
180#2479C2214yes—
181#2479C2214yes—
182#2479C2214yes—
183#2476C2214yes—
184#2470C2214yes—
185#2467C2214yes—
186#2466C2214yes—
187#2461C2214yes—
188#2461C2214yes—
189#2457C2214yes—
190#2454C2214yes—
191#2454C2212yes—
192#2453C2212yes—
193#2450C2214yes—
194#2450C2214yes—
195#2447C2212yes—
196#2446C2212yes—
197#2441C2214yes—
198#2438C2214yes—
199#2438C2214yes—
200#2434C2212yes—
201#2434C2212yes—
202#2434C2212yes—
203#2432C2212yes—
204#2432C2212yes—
205#2431C2212yes—
206#2429C2212yes—
207#2429C2212yes—
208#2429C2212yes—
209#2427C2212yes—
210#2427C2212yes—
211#2426C2212yes—
212#2421C2212yes—
213#2421C2212yes—
214#2421C2212yes—
215#2420C2212yes—
216#2409C2212yes—
217#2407C2212yes—
218#2402C2211yescharacteristic
219#2401C2212yes—
220#2398C2211yescharacteristic
221#2396C2211yescharacteristic
222#2395C2212yes—
223#2392C2211yescharacteristic
224#2367C2212yes—
225#2365C2212yes—
226#2355C2212yes—
227Q8×C4⋊C4C2212yes—
228Q8×C22⋊C4C2212yes—
229#2339C2212yes—
230#2330C2212yes—
231#2328C2211yescharacteristic
232#2327C2211yescharacteristic
233#2327C2212yes—
234#2326C2212yes—
235#2326C2212yes—
236C4×C4⋊Q8C2211yescharacteristic
237C4×C4⋊Q8C2211yescharacteristic
238#2298C2212yes—
239#2295C2211yescharacteristic
240#2293C2211yescharacteristic
241#2290C2212yes—
242C4×#117C2211yescharacteristic
243C22×#41C2312yes—
244C23×Q8C2312yes—
245#556—48no—
246#548—48no—
247#541—48no—
248#541—48no—
249#536—48no—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2312yes—
257C2×C4⋊Q8C2312yes—
258C2×#127C2311yescharacteristic
259#529—48no—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#125C2312yes—
268C2×#125C2314yes—
269C2×#125C2312yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#125C2314yes—
273C2×#124C2312yes—
274C2×#124C2312yes—
275C2×#124C2314yes—
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×#117C2311yescharacteristic
309C2×#117C2312yes—
310C2×#117C2314yes—
311C2×#117C2314yes—
312C2×#117C2311yescharacteristic
313C22×C42C2311yescharacteristic
314#401C2314yes—
315#401C2312yes—
316#401C2314yes—
317#401C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2311yescharacteristic
341#400C2312yes—
342#400C2312yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2312yes—
347#399C2314yes—
348#399C2311yescharacteristic
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2311yescharacteristic
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2312yes—
391#397C2312yes—
392#397C2314yes—
393#397C2311yescharacteristic
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2312yes—
398#397C2312yes—
399#396C2312yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2312yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2312yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2311yescharacteristic
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2312yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2312yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2312yes—
451#394C2311yescharacteristic
452#394C2312yes—
453#393C2314yes—
454#393C2312yes—
455#393C2311yescharacteristic
456#392C2314yes—
457#392C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2311yescharacteristic
462#391C2312yes—
463#391C2312yes—
464#391C2314yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2314yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#390C2314yes—
479#390C2314yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2314yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2314yes—
489#390C2314yes—
490#390C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2312yes—
545#388C2314yes—
546#388C2312yes—
547#388C2312yes—
548#388C2312yes—
549#388C2312yes—
550#388C2312yes—
551#388C2312yes—
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#387C2312yes—
578#387C2314yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2312yes—
601#386C2312yes—
602#386C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2312yes—
620#385C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#384C2311yescharacteristic
625#384C2311yescharacteristic
626#384C2314yes—
627#384C2314yes—
628#384C2312yes—
629#384C2314yes—
630#384C2314yes—
631#383C2314yes—
632#383C2314yes—
633#383C2314yes—
634#382C2314yes—
635#382C2314yes—
636#382C2311yescharacteristic
637#382C2312yes—
638#382C2311yescharacteristic
639#381C2314yes—
640#381C2314yes—
641#381C2314yes—
642#380C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674#376C2311yescharacteristic
675#376C2312yes—
676#376C2311yescharacteristic
677C2×#95C2314yes—
678C43C2311yescharacteristic
679C43C2311yescharacteristic
680C2×#41—44no—
681C2×#41—44no—
682C2×#41—44no—
683C22×Q8—44no—
684C22×Q8—44no—
685C22×Q8—44no—
686C22×Q8C2412yes—
687C22×Q8C2412yes—
688C22×Q8C2412yes—
689C22×Q8C2411yescharacteristic
690C22×Q8C2414yes—
691C22×D4C2412yes—
692C22×D4C2411yescharacteristic
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2412yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C23×C4C2411yescharacteristic
699C23×C4C2412yes—
700C23×C4C2412yes—
701C23×C4C2414yes—
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2414yes—
705C4⋊Q8—24no—
706C4⋊Q8—24no—
707C4⋊Q8—42no—
708C4⋊Q8—44no—
709C4⋊Q8—44no—
710C4⋊Q8—44no—
711C4⋊Q8—44no—
712C4⋊Q8—44no—
713#127—42no—
714#126—48no—
715#126—48no—
716#126—48no—
717#126—48no—
718#126—48no—
719#126—48no—
720#126—48no—
721#125—28no—
722#125—44no—
723#125—48no—
724#125—48no—
725#125—48no—
726#125—48no—
727#124—28no—
728#124—28no—
729#124—48no—
730#124—44no—
731#124—44no—
732#124—44no—
733#123—48no—
734#123—48no—
735#123—48no—
736C22⋊Q8—48no—
737C22⋊Q8—48no—
738C22⋊Q8—48no—
739C22⋊Q8—48no—
740C22⋊Q8—44no—
741C22⋊Q8—44no—
742C22⋊Q8—44no—
743C22⋊Q8—44no—
744C22⋊Q8—44no—
745C22⋊Q8—44no—
746#121—48no—
747#121—44no—
748#121—44no—
749C4×Q8—28no—
750C4×Q8—28no—
751C4×Q8—24no—
752C4×Q8—44no—
753C4×Q8—44no—
754C4×Q8—44no—
755C4×Q8—44no—
756C4×D4—24no—
757C4×D4—48no—
758C4×D4—44no—
759C4×D4—44no—
760C4×D4—44no—
761C4×D4—48no—
762#117—28no—
763#117—24no—
764#117—42no—
765#117—48no—
766#117—48no—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C42—24no—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
881C2×C42C2411yescharacteristic
882C2×C42C2411yescharacteristic
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2411yescharacteristic
941#95C2411yescharacteristic
942#95C2412yes—
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964C24C2511yescharacteristic
965C24C2512yes—
966C24C2514yes—
967#41—816no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—24no—
971C2×Q8—24no—
972C2×Q8—24no—
973C2×Q8—24no—
974C2×Q8—22no—
975C2×Q8—24no—
976C2×Q8—24no—
977C2×Q8—24no—
978C2×Q8—44no—
979C2×Q8—44no—
980C2×Q8—44no—
981C2×Q8—42no—
982C2×Q8—816no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—22no—
986C2×D4—24no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—42no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—42no—
993C2×D4—44no—
994C2×D4—42no—
995C2×D4—44no—
996C2×D4—42no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—22no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2512yes—
1047C22×C4C2511yescharacteristic
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—24no—
1053C4⋊C4—28no—
1054C4⋊C4—22no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—28no—
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—22no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C22⋊C4—24no—
1109C22⋊C4—24no—
1110C22⋊C4—22no—
1111C22⋊C4—22no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—24no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—42no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C42—24no—
1157C42—22no—
1158C42—24no—
1159C42—22no—
1160C42—28no—
1161C42—24no—
1162C42—28no—
1163C42—22no—
1164C42—22no—
1165C42—24no—
1166C42—42no—
1167C42—42no—
1168C42—42no—
1169C42—42no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42—44no—
1176C42H(5,𝔽2)14yes—
1177C42H(5,𝔽2)14yes—
1178C23—21no—
1179C23—22no—
1180C23—24no—
1181C23—24no—
1182C23—22no—
1183C23—21no—
1184C23—21no—
1185C23—24no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—24no—
1190C23—24no—
1191C23—24no—
1192C23—22no—
1193C23—24no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23C2611yescharacteristic
1198Q8—48no—
1199Q8—48no—
1200Q8—48no—
1201Q8—82no—
1202Q8—88no—
1203D4—48no—
1204D4—82no—
1205D4—88no—
1206D4—88no—
1207D4—84no—
1208D4—88no—
1209D4—164no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—24no—
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—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—44no—
1273C2×C4—48no—
1274C2×C4—84no—
1275C2×C4—88no—
1276C2×C4—88no—
1277C2×C4—88no—
1278C2×C4—88no—
1279C2×C4C2×H(5,𝔽2)12yes—
1280C2×C4C2×H(5,𝔽2)12yes—
1281C2×C4C2×H(5,𝔽2)14yes—
1282C2×C4C2×H(5,𝔽2)12yes—
1283C2×C4C2×H(5,𝔽2)12yes—
1284C2×C4#58512yes—
1285C22—42no—
1286C22—41no—
1287C22—44no—
1288C22—42no—
1289C22—44no—
1290C22—44no—
1291C22—42no—
1292C22—44no—
1293C22—44no—
1294C22—41no—
1295C22—41no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—44no—
1302C22—44no—
1303C22—42no—
1304C22C22×H(5,𝔽2)11yescharacteristic
1305C22C22×H(5,𝔽2)11yescharacteristic
1306C22C2×#58511yescharacteristic
1307C222−1+612yes—
1308C222−1+612yes—
1309C4—24no—
1310C4—22no—
1311C4—22no—
1312C4—41no—
1313C4—42no—
1314C4—44no—
1315C4—44no—
1316C4—44no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—41no—
1321C4—41no—
1322C4—44no—
1323C4—44no—
1324C4—42no—
1325C4—42no—
1326C4—44no—
1327C4—44no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4#354614yes—
1333C2—82no—
1334C2—81no—
1335C2—84no—
1336C2C2×#354611yescharacteristic
1337C2#6288812yes—
1338C2#6288811yescharacteristic
1339C2#6288811yescharacteristic
1340C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58871C2semidirect
2. #58839C2semidirect
3. #57319C2semidirect
4. #57027C2semidirect
5. #56886C2semidirect
6. #56779C2semidirect
7. #55820C2semidirect
8. #54161C2semidirect
9. #53073C2semidirect
10. #53008C2semidirect
11. #45307C2semidirect
12. #45156C2semidirect
13. #42853C2semidirect
14. #42802C2semidirect
15. #42800C2semidirect
16. #42749C2semidirect
17. #39762C2semidirect
18. #39740C2semidirect
19. #39379C2semidirect
20. #39356C2semidirect
21. #37774C2semidirect
22. #37750C2semidirect
23. #37435C2semidirect
24. #37390C2semidirect
25. #35343C2semidirect
26. #35319C2semidirect
27. #34640C2semidirect

Maximal subgroups

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

subgroupindex
#588712
#588392
#573192
#570272
#568862
#567792
#558202
#541612
#530732
#530082
#453072
#451562
#428532
#428022
#428002
#427492
#397622
#397402
#393792
#393562
#377742
#377502
#374352
#373902
#353432
#353192
#346402