Finite Group Databasebeta

← #8123035

Subgroups — #8123035

Order 512.

4859 conjugacy classes of subgroups.

The subgroup lattice has 1454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58695C214yesmaximal, complemented
2#55535C214yesmaximal, complemented
3#54930C214yesmaximal, complemented
4#53509C214yesmaximal, complemented
5#53047C212yesmaximal, complemented
6#53016C212yesmaximal, complemented
7#47024C214yesmaximal, complemented
8#46798C214yesmaximal, complemented
9#46676C214yesmaximal, complemented
10#46676C214yesmaximal, complemented
11#45175C212yesmaximal, complemented
12#44920C212yesmaximal, complemented
13#40125C212yesmaximal, complemented
14#39889C212yesmaximal, complemented
15#39816C212yesmaximal, complemented
16#39656C212yesmaximal, complemented
17#39604C212yesmaximal, complemented
18#39340C212yesmaximal, complemented
19#37781C212yesmaximal, complemented
20#37781C212yesmaximal, complemented
21#37393C211yesmaximal, characteristic, complemented
22#37296C211yesmaximal, characteristic, complemented
23#35309C211yesmaximal, characteristic, complemented
24#35273C211yesmaximal, characteristic, complemented
25#35173C211yesmaximal, characteristic, complemented
26#35082C211yesmaximal, characteristic, complemented
27#34744C211yesmaximal, characteristic, complemented
28C2×#547C2212yes—
29C2×#541C2211yescharacteristic
30C2×#537C2212yes—
31C2×#537C2212yes—
32C2×#533C2212yes—
33C2×#532C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2212yes—
38#2857C2211yescharacteristic
39#2857C2211yescharacteristic
40#2856C2211yescharacteristic
41#2856C2211yescharacteristic
42#2855C2212yes—
43#2854C2212yes—
44#2851C2211yescharacteristic
45#2841C2214yes—
46#2837C2214yes—
47#2837C2214yes—
48#2837C2214yes—
49#2829C2214yes—
50#2827C2214yes—
51#2820C2214yes—
52#2814C2214yes—
53#2803C2214yes—
54#2803C2214yes—
55#2800C2214yes—
56#2796C2214yes—
57#2796C2214yes—
58#2792C2214yes—
59#2791C2214yes—
60#2791C2214yes—
61#2790C2214yes—
62#2790C2214yes—
63#2790C2214yes—
64#2784C2214yes—
65#2783C2214yes—
66#2781C2214yes—
67#2781C2214yes—
68#2780C2214yes—
69#2779C2214yes—
70#2779C2214yes—
71#2774C2214yes—
72#2768C2214yes—
73#2768C2214yes—
74#2768C2214yes—
75#2742C2214yes—
76#2732C2214yes—
77#2725C2214yes—
78#2723C2214yes—
79#2720C2214yes—
80#2717C2214yes—
81#2711C2214yes—
82#2711C2214yes—
83#2707C2214yes—
84#2704C2214yes—
85#2704C2214yes—
86#2701C2214yes—
87#2701C2214yes—
88#2701C2214yes—
89#2699C2214yes—
90#2695C2214yes—
91#2694C2214yes—
92#2694C2214yes—
93#2691C2214yes—
94#2686C2214yes—
95#2682C2214yes—
96#2682C2214yes—
97#2682C2214yes—
98#2681C2214yes—
99#2681C2214yes—
100#2672C2214yes—
101#2672C2214yes—
102#2672C2214yes—
103#2672C2214yes—
104#2672C2214yes—
105#2671C2214yes—
106#2671C2214yes—
107#2671C2214yes—
108#2671C2214yes—
109#2667C2214yes—
110#2662C2214yes—
111#2659C2214yes—
112#2651C2214yes—
113#2630C2214yes—
114#2629C2211yescharacteristic
115#2627C2214yes—
116#2621C2211yescharacteristic
117#2620C2212yes—
118#2620C2212yes—
119#2620C2212yes—
120#2616C2212yes—
121#2616C2212yes—
122#2608C2214yes—
123#2602C2214yes—
124#2602C2214yes—
125#2587C2214yes—
126#2584C2214yes—
127#2584C2214yes—
128#2579C2214yes—
129#2567C2212yes—
130#2567C2212yes—
131#2559C2214yes—
132#2559C2214yes—
133#2555C2214yes—
134#2553C2214yes—
135#2553C2214yes—
136#2552C2212yes—
137#2546C2212yes—
138#2546C2212yes—
139#2545C2212yes—
140#2542C2212yes—
141#2538C2214yes—
142#2537C2214yes—
143#2537C2212yes—
144#2537C2214yes—
145#2522C2214yes—
146#2522C2214yes—
147#2513C2212yes—
148#2512C2212yes—
149#2511C2212yes—
150#2507C2212yes—
151#2507C2214yes—
152#2502C2212yes—
153#2501C2212yes—
154#2497C2212yes—
155#2491C2212yes—
156#2491C2212yes—
157#2489C2212yes—
158#2476C2214yes—
159#2476C2214yes—
160#2476C2214yes—
161#2476C2214yes—
162#2473C2214yes—
163#2473C2214yes—
164#2468C2214yes—
165#2468C2214yes—
166#2466C2214yes—
167#2465C2214yes—
168#2465C2214yes—
169#2462C2214yes—
170#2461C2214yes—
171#2460C2214yes—
172#2460C2214yes—
173#2454C2212yes—
174#2449C2214yes—
175#2448C2212yes—
176#2447C2212yes—
177#2447C2212yes—
178#2446C2212yes—
179#2446C2212yes—
180#2445C2212yes—
181#2445C2212yes—
182#2444C2212yes—
183#2444C2212yes—
184#2443C2214yes—
185#2443C2212yes—
186#2443C2212yes—
187#2442C2214yes—
188#2440C2212yes—
189#2440C2212yes—
190#2440C2214yes—
191#2432C2212yes—
192#2432C2212yes—
193#2432C2212yes—
194#2431C2212yes—
195#2429C2212yes—
196#2429C2212yes—
197#2429C2212yes—
198#2428C2214yes—
199#2426C2212yes—
200#2426C2212yes—
201#2426C2214yes—
202#2426C2214yes—
203#2425C2214yes—
204#2423C2212yes—
205#2423C2212yes—
206#2421C2212yes—
207#2417C2212yes—
208#2417C2212yes—
209#2416C2214yes—
210#2416C2214yes—
211#2416C2214yes—
212#2407C2212yes—
213#2407C2212yes—
214#2395C2212yes—
215#2395C2212yes—
216#2367C2212yes—
217#2360C2212yes—
218#2360C2212yes—
219#2355C2212yes—
220D4×C4⋊C4C2212yes—
221#2341C2212yes—
222#2341C2212yes—
223#2335C2214yes—
224#2335C2214yes—
225#2335C2214yes—
226#2323C2212yes—
227#2323C2212yes—
228#2322C2214yes—
229#2322C2214yes—
230#2316C2214yes—
231#2314C2211yescharacteristic
232#2311C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×#123C2212yes—
235C4×#123C2212yes—
236C4×#121C2212yes—
237#2297C2211yescharacteristic
238#2297C2211yescharacteristic
239#2297C2211yescharacteristic
240#2296C2211yescharacteristic
241C2×#384C2211yescharacteristic
242C2×C4×C4⋊C4C2211yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2312yes—
245C22×#41C2311yescharacteristic
246C22×#41C2312yes—
247#547—48no—
248#541—44no—
249#537—48no—
250#537—48no—
251#533—48no—
252#532—44no—
253#532—44no—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2311yescharacteristic
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2312yes—
260C2×#127C2311yescharacteristic
261C2×#127C2311yescharacteristic
262C2×#126C2314yes—
263C2×#126C2314yes—
264C2×#125C2314yes—
265C2×#125C2311yescharacteristic
266C2×#125C2314yes—
267C2×#125C2314yes—
268C2×#124C2312yes—
269C2×#124C2312yes—
270C2×#124C2311yescharacteristic
271C2×#124C2311yescharacteristic
272C2×#124C2314yes—
273C2×#124C2314yes—
274C2×#123C2312yes—
275C2×#123C2314yes—
276C2×#123C2312yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
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⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C4×#41—44no—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×#117C2311yescharacteristic
328C2×#117C2314yes—
329C2×#117C2311yescharacteristic
330C2×#117C2311yescharacteristic
331C2×#117C2311yescharacteristic
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2314yes—
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2314yes—
337C22×C42C2311yescharacteristic
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2311yescharacteristic
341C22×C42C2311yescharacteristic
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2312yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2312yes—
359#398C2314yes—
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#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#397C2312yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2312yes—
389#397C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2312yes—
394#397C2312yes—
395#397C2314yes—
396#397C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2312yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2312yes—
451#394C2312yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#393C2314yes—
457#393C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2314yes—
476#390C2314yes—
477#390C2314yes—
478#390C2312yes—
479#390C2312yes—
480#390C2314yes—
481#390C2312yes—
482#390C2314yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#390C2312yes—
487#390C2314yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
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#388C2314yes—
544#388C2314yes—
545#388C2312yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2314yes—
550#388C2312yes—
551#388C2314yes—
552#388C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2314yes—
562#387C2312yes—
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#387C2312yes—
576#387C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2312yes—
589#386C2312yes—
590#386C2311yescharacteristic
591#386C2312yes—
592#386C2311yescharacteristic
593#386C2311yescharacteristic
594#386C2312yes—
595#386C2311yescharacteristic
596#386C2312yes—
597#386C2312yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
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#385C2314yes—
620#385C2312yes—
621#385C2312yes—
622#385C2312yes—
623#385C2312yes—
624#384C2311yescharacteristic
625#384C2311yescharacteristic
626#384C2312yes—
627#384C2311yescharacteristic
628#384C2312yes—
629#384C2312yes—
630#384C2314yes—
631#384C2314yes—
632#382C2314yes—
633#382C2311yescharacteristic
634#382C2314yes—
635#381C2314yes—
636#381C2314yes—
637#381C2312yes—
638#381C2312yes—
639#380C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2312yes—
652#380C2314yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C2×#95C2312yes—
682C2×#41—24no—
683C2×#41—24no—
684C2×#41—28no—
685C2×#41—24no—
686C2×#41—42no—
687C2×#41—42no—
688C2×#41—42no—
689C2×#41—44no—
690C2×#41—44no—
691C2×#41—44no—
692C2×#41—44no—
693C2×#41—44no—
694C22×Q8C2412yes—
695C22×Q8C2412yes—
696C22×Q8C2411yescharacteristic
697C22×Q8C2411yescharacteristic
698C22×Q8C2414yes—
699C22×D4C2412yes—
700C22×D4C2412yes—
701C22×D4C2411yescharacteristic
702C22×D4C2411yescharacteristic
703C22×D4C2411yescharacteristic
704C22×D4C2414yes—
705C22×D4C2414yes—
706C22×D4C2412yes—
707C22×D4C2412yes—
708C22×D4C2414yes—
709C22×D4C2411yescharacteristic
710C22×D4C2414yes—
711C22×D4C2414yes—
712C22×D4C2414yes—
713C23×C4C2411yescharacteristic
714C23×C4C2412yes—
715C23×C4C2411yescharacteristic
716C23×C4C2412yes—
717C23×C4C2411yescharacteristic
718C23×C4C2411yescharacteristic
719C23×C4C2414yes—
720C23×C4C2412yes—
721C23×C4C2412yes—
722C23×C4C2414yes—
723C23×C4C2412yes—
724C23×C4C2411yescharacteristic
725C23×C4C2414yes—
726C23×C4C2414yes—
727C23×C4C2414yes—
728C4⋊Q8—44no—
729C4⋊Q8—42no—
730C4⋊Q8—44no—
731C4⋊Q8—42no—
732C4⋊Q8—44no—
733C4⋊Q8—42no—
734#127—42no—
735#127—42no—
736#126—48no—
737#126—84no—
738#125—48no—
739#125—42no—
740#125—48no—
741#125—84no—
742#124—44no—
743#124—44no—
744#124—42no—
745#124—42no—
746#124—84no—
747#124—84no—
748#123—28no—
749#123—216no—
750#123—28no—
751#123—48no—
752#123—48no—
753#123—84no—
754#123—84no—
755#123—84no—
756C22⋊Q8—28no—
757C22⋊Q8—28no—
758C22⋊Q8—28no—
759C22⋊Q8—48no—
760C22⋊Q8—48no—
761C22⋊Q8—48no—
762C22⋊Q8—44no—
763C22⋊Q8—44no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766C22⋊Q8—44no—
767C22⋊Q8—84no—
768C22⋊Q8—84no—
769#121—28no—
770#121—44no—
771#121—48no—
772#121—48no—
773#121—44no—
774#121—48no—
775#121—48no—
776#121—48no—
777#121—48no—
778#121—48no—
779#121—44no—
780#121—44no—
781#121—48no—
782#121—84no—
783#121—84no—
784#121—84no—
785C4×Q8—48no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×D4—28no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—48no—
795C4×D4—44no—
796C4×D4—44no—
797C4×D4—44no—
798C4×D4—84no—
799C4×D4—84no—
800#117—24no—
801#117—42no—
802#117—42no—
803#117—42no—
804#117—48no—
805C2×C4⋊C4—28no—
806C2×C4⋊C4—44no—
807C2×C4⋊C4—44no—
808C2×C4⋊C4—48no—
809C2×C4⋊C4—84no—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C42—24no—
921C2×C42—24no—
922C2×C42—42no—
923C2×C42—42no—
924C2×C42—42no—
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2411yescharacteristic
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2411yescharacteristic
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2411yescharacteristic
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996C24C2512yes—
997C24C2514yes—
998C24C2511yescharacteristic
999C24C2511yescharacteristic
1000C24C2511yescharacteristic
1001#41—416no—
1002#41—88no—
1003#41—816no—
1004#41—816no—
1005C2×Q8—22no—
1006C2×Q8—24no—
1007C2×Q8—24no—
1008C2×Q8—24no—
1009C2×Q8—22no—
1010C2×Q8—24no—
1011C2×Q8—22no—
1012C2×Q8—24no—
1013C2×Q8—24no—
1014C2×Q8—41no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×Q8—44no—
1018C2×Q8—41no—
1019C2×Q8—41no—
1020C2×D4—24no—
1021C2×D4—22no—
1022C2×D4—22no—
1023C2×D4—22no—
1024C2×D4—22no—
1025C2×D4—28no—
1026C2×D4—24no—
1027C2×D4—28no—
1028C2×D4—22no—
1029C2×D4—24no—
1030C2×D4—24no—
1031C2×D4—22no—
1032C2×D4—22no—
1033C2×D4—24no—
1034C2×D4—28no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—42no—
1038C2×D4—41no—
1039C2×D4—41no—
1040C2×D4—41no—
1041C2×D4—44no—
1042C2×D4—42no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—42no—
1047C2×D4—44no—
1048C2×D4—42no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—41no—
1052C2×D4—41no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—42no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C22×C4—22no—
1063C22×C4—22no—
1064C22×C4—22no—
1065C22×C4—24no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—24no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—22no—
1074C22×C4—24no—
1075C22×C4—22no—
1076C22×C4—24no—
1077C22×C4—28no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—28no—
1081C22×C4—24no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4H(5,𝔽2)14yes—
1104C22×C4H(5,𝔽2)14yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2514yes—
1117C22×C4C2514yes—
1118C22×C4C2514yes—
1119C22×C4C2514yes—
1120C22×C4C2514yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2511yescharacteristic
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2511yescharacteristic
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C42−1+418yes—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—24no—
1187C22⋊C4—28no—
1188C22⋊C4—24no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—28no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—28no—
1199C22⋊C4—41no—
1200C22⋊C4—41no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C42—22no—
1238C42—22no—
1239C42—24no—
1240C42—24no—
1241C42—24no—
1242C42—22no—
1243C42—22no—
1244C42—24no—
1245C42—24no—
1246C42—42no—
1247C42—42no—
1248C42—41no—
1249C42—41no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C23—21no—
1258C23—21no—
1259C23—22no—
1260C23—22no—
1261C23—21no—
1262C23—21no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—24no—
1267C23—21no—
1268C23—21no—
1269C23—24no—
1270C23—22no—
1271C23—22no—
1272C23—24no—
1273C23—22no—
1274C23—24no—
1275C23—22no—
1276C23—21no—
1277C23—22no—
1278C23—24no—
1279C23—24no—
1280C23—22no—
1281C23—22no—
1282C23—24no—
1283C23—22no—
1284C23C2×H(5,𝔽2)12yes—
1285C23C2×H(5,𝔽2)12yes—
1286C23C2611yescharacteristic
1287Q8—44no—
1288Q8—48no—
1289Q8—48no—
1290Q8—82no—
1291Q8—88no—
1292D4—48no—
1293D4—44no—
1294D4—44no—
1295D4—44no—
1296D4—48no—
1297D4—88no—
1298D4—84no—
1299D4—82no—
1300D4—88no—
1301D4—84no—
1302D4—88no—
1303D4—88no—
1304D4—164no—
1305D4—164no—
1306C2×C4—28no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—22no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—28no—
1318C2×C4—28no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—21no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—21no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—21no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—48no—
1368C2×C4—44no—
1369C2×C4—48no—
1370C2×C4—84no—
1371C2×C4—84no—
1372C2×C4—84no—
1373C2×C4—88no—
1374C2×C4—88no—
1375C2×C4—82no—
1376C2×C4—88no—
1377C2×C4—164no—
1378C2×C4—164no—
1379C2×C4C2×H(5,𝔽2)12yes—
1380C2×C4C2×H(5,𝔽2)12yes—
1381C2×C4C2×H(5,𝔽2)12yes—
1382C2×C4C2×H(5,𝔽2)12yes—
1383C2×C4C2×2−1+414yes—
1384C2×C4C2×2−1+414yes—
1385C2×C4C2×2−1+414yes—
1386C2×C4#58512yes—
1387C22—22no—
1388C22—22no—
1389C22—22no—
1390C22—22no—
1391C22—24no—
1392C22—41no—
1393C22—41no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—41no—
1398C22—42no—
1399C22—44no—
1400C22—44no—
1401C22—41no—
1402C22—42no—
1403C22—42no—
1404C22—44no—
1405C22—41no—
1406C22—42no—
1407C22—44no—
1408C22—42no—
1409C22—42no—
1410C22—44no—
1411C22—42no—
1412C22—42no—
1413C22—44no—
1414C22—42no—
1415C22—44no—
1416C22C22×H(5,𝔽2)11yescharacteristic
1417C22C22×H(5,𝔽2)11yescharacteristic
1418C22C22×2−1+412yes—
1419C22C2×#58511yescharacteristic
1420C22H(7,𝔽2)12yes—
1421C4—22no—
1422C4—22no—
1423C4—24no—
1424C4—24no—
1425C4—24no—
1426C4—42no—
1427C4—41no—
1428C4—44no—
1429C4—44no—
1430C4—42no—
1431C4—44no—
1432C4—44no—
1433C4—44no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—42no—
1438C4—44no—
1439C4—42no—
1440C4—42no—
1441C4—44no—
1442C4#353414yes—
1443C2—42no—
1444C2—42no—
1445C2—81no—
1446C2—82no—
1447C2—84no—
1448C2C2×#353411yescharacteristic
1449C2#6283311yescharacteristic
1450C2#6288011yescharacteristic
1451C2#6294412yes—
1452C2#6295212yes—
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. #58695C2semidirect
2. #55535C2semidirect
3. #54930C2semidirect
4. #53509C2semidirect
5. #53047C2semidirect
6. #53016C2semidirect
7. #47024C2semidirect
8. #46798C2semidirect
9. #46676C2semidirect
10. #46676C2semidirect
11. #45175C2semidirect
12. #44920C2semidirect
13. #40125C2semidirect
14. #39889C2semidirect
15. #39816C2semidirect
16. #39656C2semidirect
17. #39604C2semidirect
18. #39340C2semidirect
19. #37781C2semidirect
20. #37781C2semidirect
21. #37393C2semidirect
22. #37296C2semidirect
23. #35309C2semidirect
24. #35273C2semidirect
25. #35173C2semidirect
26. #35082C2semidirect
27. #34744C2semidirect

Maximal subgroups

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

subgroupindex
#586952
#555352
#549302
#535092
#530472
#530162
#470242
#467982
#466762
#451752
#449202
#401252
#398892
#398162
#396562
#396042
#393402
#377812
#373932
#372962
#353092
#352732
#351732
#350822
#347442