Finite Group Databasebeta

← #7895487

Subgroups — #7895487

Order 512.

4683 conjugacy classes of subgroups.

The subgroup lattice has 1440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59822C211yesmaximal, characteristic
2#59821C212yesmaximal, complemented
3#52287C211yesmaximal, characteristic, complemented
4#51674C214yesmaximal, complemented
5#50611C214yesmaximal, complemented
6#50127C214yesmaximal, complemented
7#47645C214yesmaximal, complemented
8#45956C212yesmaximal, complemented
9#45370C212yesmaximal, complemented
10#44965C212yesmaximal, complemented
11#44963C212yesmaximal, complemented
12#44679C214yesmaximal, complemented
13#42699C212yesmaximal, complemented
14#42524C212yesmaximal, complemented
15#42140C214yesmaximal, complemented
16#40021C212yesmaximal, complemented
17#39801C212yesmaximal, complemented
18#39756C211yesmaximal, characteristic, complemented
19#39611C211yesmaximal, characteristic, complemented
20#39161C212yesmaximal, complemented
21#38830C212yesmaximal, complemented
22#38435C212yesmaximal, complemented
23#37207C212yesmaximal, complemented
24#36285C211yesmaximal, characteristic, complemented
25#35934C212yesmaximal, complemented
26#35562C212yesmaximal, complemented
27#35186C211yesmaximal, characteristic, complemented
28#34484C212yesmaximal, complemented
29#34331C211yesmaximal, characteristic, complemented
30C2×#559C2211yescharacteristic
31C2×#556C2214yes—
32C2×#555C2212yes—
33C2×#554C2212yes—
34#2863C2212yes—
35#2861C2212yes—
36#2861C2212yes—
37#2860C2212yes—
38#2859C2211yescharacteristic
39#2837C2214yes—
40#2829C2214yes—
41#2811C2211yescharacteristic
42#2808C2212yes—
43#2808C2212yes—
44#2806C2211yescharacteristic
45#2806C2211yescharacteristic
46#2806C2212yes—
47#2806C2212yes—
48#2801C2214yes—
49#2792C2212yes—
50#2792C2212yes—
51#2792C2212yes—
52#2788C2214yes—
53#2788C2214yes—
54#2787C2214yes—
55#2787C2214yes—
56#2786C2214yes—
57#2786C2214yes—
58#2783C2214yes—
59#2777C2214yes—
60#2775C2214yes—
61#2759C2214yes—
62#2757C2214yes—
63#2756C2214yes—
64#2756C2214yes—
65#2734C2211yescharacteristic
66#2734C2212yes—
67#2733C2212yes—
68#2733C2212yes—
69#2732C2212yes—
70#2732C2212yes—
71#2731C2214yes—
72#2730C2214yes—
73#2730C2214yes—
74#2727C2212yes—
75#2727C2214yes—
76#2727C2212yes—
77#2727C2214yes—
78#2718C2214yes—
79#2715C2214yes—
80#2715C2214yes—
81#2702C2214yes—
82#2701C2214yes—
83#2700C2214yes—
84#2692C2214yes—
85#2691C2214yes—
86#2687C2214yes—
87#2686C2214yes—
88#2686C2214yes—
89#2686C2214yes—
90#2683C2212yes—
91#2683C2212yes—
92#2681C2214yes—
93#2681C2214yes—
94#2672C2214yes—
95#2667C2214yes—
96#2663C2214yes—
97#2662C2214yes—
98#2660C2212yes—
99#2653C2214yes—
100#2651C2214yes—
101#2651C2214yes—
102#2641C2212yes—
103#2640C2212yes—
104#2630C2214yes—
105#2610C2214yes—
106#2610C2214yes—
107#2606C2214yes—
108#2604C2214yes—
109#2601C2214yes—
110#2601C2214yes—
111#2599C2214yes—
112#2599C2214yes—
113#2594C2214yes—
114#2592C2212yes—
115#2592C2212yes—
116#2590C2214yes—
117#2582C2211yescharacteristic
118#2582C2211yescharacteristic
119#2582C2211yescharacteristic
120#2580C2212yes—
121#2580C2212yes—
122#2570C2212yes—
123#2566C2212yes—
124#2566C2212yes—
125#2566C2212yes—
126#2565C2212yes—
127#2559C2214yes—
128#2557C2214yes—
129#2556C2214yes—
130#2556C2214yes—
131#2552C2211yescharacteristic
132#2549C2214yes—
133#2548C2212yes—
134#2548C2212yes—
135#2548C2212yes—
136#2548C2211yescharacteristic
137#2548C2211yescharacteristic
138#2548C2212yes—
139#2544C2212yes—
140#2544C2212yes—
141#2542C2212yes—
142#2542C2212yes—
143#2541C2212yes—
144#2541C2212yes—
145#2538C2212yes—
146#2538C2214yes—
147#2537C2212yes—
148#2532C2214yes—
149#2522C2214yes—
150#2521C2214yes—
151#2514C2212yes—
152#2513C2212yes—
153#2513C2212yes—
154#2512C2212yes—
155#2512C2212yes—
156#2512C2212yes—
157#2512C2212yes—
158#2512C2212yes—
159#2511C2212yes—
160#2507C2212yes—
161#2479C2214yes—
162#2478C2214yes—
163#2478C2214yes—
164#2476C2214yes—
165#2476C2214yes—
166#2476C2214yes—
167#2474C2214yes—
168#2474C2214yes—
169#2471C2214yes—
170#2470C2214yes—
171#2469C2214yes—
172#2468C2214yes—
173#2467C2214yes—
174#2466C2214yes—
175#2466C2214yes—
176#2465C2214yes—
177#2463C2214yes—
178#2463C2214yes—
179#2461C2214yes—
180#2459C2214yes—
181#2454C2212yes—
182#2449C2214yes—
183#2449C2214yes—
184#2448C2212yes—
185#2448C2214yes—
186#2448C2214yes—
187#2447C2212yes—
188#2446C2212yes—
189#2445C2212yes—
190#2445C2212yes—
191#2444C2214yes—
192#2443C2214yes—
193#2443C2214yes—
194#2438C2214yes—
195#2425C2214yes—
196#2415C2214yes—
197#2415C2214yes—
198#2414C2214yes—
199#2414C2214yes—
200#2399C2212yes—
201#2399C2212yes—
202#2399C2212yes—
203#2396C2214yes—
204#2378C2214yes—
205#2378C2214yes—
206#2370C2212yes—
207#2370C2212yes—
208#2369C2212yes—
209#2367C2212yes—
210#2367C2212yes—
211#2366C2211yescharacteristic
212#2362C2214yes—
213#2359C2214yes—
214#2357C2212yes—
215#2356C2212yes—
216#2355C2211yescharacteristic
217#2355C2212yes—
218#2355C2211yescharacteristic
219#2354C2212yes—
220#2354C2212yes—
221#2354C2212yes—
222#2354C2212yes—
223#2354C2212yes—
224Q8×C4⋊C4C2211yescharacteristic
225Q8×C4⋊C4C2212yes—
226Q8×C4⋊C4C2211yescharacteristic
227#2349C2212yes—
228#2344C2214yes—
229#2337C2214yes—
230#2335C2214yes—
231#2330C2212yes—
232#2330C2212yes—
233#2328C2212yes—
234#2328C2212yes—
235#2326C2212yes—
236#2326C2212yes—
237#2323C2214yes—
238#2323C2214yes—
239#2323C2214yes—
240#2319C2212yes—
241#2319C2212yes—
242#2316C2214yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2212yes—
246C4×#127C2211yescharacteristic
247C4×#127C2211yescharacteristic
248C4×#127C2212yes—
249C4×#124C2212yes—
250#2295C2211yescharacteristic
251#2295C2212yes—
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2295C2212yes—
255#2293C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×Q8C2211yescharacteristic
259#559—28no—
260#556—416no—
261#555—48no—
262#554—216no—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×#127C2311yescharacteristic
267C2×#127C2311yescharacteristic
268C2×#127C2312yes—
269C2×#127C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#124C2312yes—
279C2×#124C2314yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2314yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2314yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2312yes—
328C2×#117C2314yes—
329C2×#117C2314yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C2×#117C2314yes—
333C2×#117C2314yes—
334C22×C4⋊C4C2314yes—
335#401C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2312yes—
356#398C2312yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#395C2312yes—
396#395C2314yes—
397#395C2314yes—
398#395C2312yes—
399#395C2312yes—
400#395C2312yes—
401#395C2312yes—
402#395C2312yes—
403#395C2312yes—
404#395C2312yes—
405#395C2312yes—
406#395C2312yes—
407#395C2312yes—
408#395C2312yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#391C2312yes—
442#391C2311yescharacteristic
443#391C2314yes—
444#391C2312yes—
445#391C2311yescharacteristic
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2311yescharacteristic
457#391C2312yes—
458#391C2314yes—
459#391C2312yes—
460#391C2311yescharacteristic
461#391C2311yescharacteristic
462#391C2312yes—
463#391C2311yescharacteristic
464#391C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2314yes—
473#390C2314yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2312yes—
487#390C2314yes—
488#390C2314yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2314yes—
493#390C2312yes—
494#390C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2311yescharacteristic
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2311yescharacteristic
536#389C2311yescharacteristic
537#389C2312yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2312yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2314yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#384C2312yes—
645#384C2311yescharacteristic
646#384C2311yescharacteristic
647#384C2312yes—
648#384C2312yes—
649#384C2311yescharacteristic
650#384C2311yescharacteristic
651#384C2312yes—
652#384C2312yes—
653#384C2311yescharacteristic
654#383C2314yes—
655#383C2314yes—
656#382C2312yes—
657#382C2312yes—
658#382C2312yes—
659#382C2312yes—
660#381C2314yes—
661#381C2314yes—
662#381C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708#376C2312yes—
709#376C2312yes—
710#376C2312yes—
711#376C2314yes—
712C2×#95C2314yes—
713C43C2311yescharacteristic
714C43C2312yes—
715C43C2312yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2414yes—
730C22×D4C2412yes—
731C22×D4C2414yes—
732C22×D4C2414yes—
733C22×D4C2414yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C4⋊Q8—24no—
741C4⋊Q8—28no—
742C4⋊Q8—28no—
743#127—24no—
744#127—24no—
745#127—44no—
746#127—44no—
747#126—48no—
748#126—48no—
749#126—48no—
750#126—48no—
751#126—84no—
752#125—28no—
753#125—28no—
754#125—82no—
755#124—28no—
756#124—216no—
757#124—28no—
758#124—44no—
759#124—48no—
760#124—48no—
761#124—84no—
762#124—82no—
763#123—216no—
764#123—84no—
765#123—84no—
766C22⋊Q8—216no—
767C22⋊Q8—216no—
768C22⋊Q8—216no—
769C22⋊Q8—48no—
770C22⋊Q8—48no—
771C22⋊Q8—84no—
772C22⋊Q8—84no—
773C22⋊Q8—84no—
774#121—48no—
775#121—48no—
776#121—84no—
777#121—84no—
778C4×Q8—28no—
779C4×Q8—24no—
780C4×Q8—24no—
781C4×Q8—24no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×Q8—42no—
785C4×Q8—42no—
786C4×Q8—48no—
787C4×Q8—42no—
788C4×Q8—48no—
789C4×Q8—82no—
790C4×Q8#4118yes—
791C4×D4—28no—
792C4×D4—28no—
793C4×D4—28no—
794C4×D4—28no—
795C4×D4—28no—
796C4×D4—28no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—48no—
801C4×D4—82no—
802C4×D4—84no—
803C4×D4—82no—
804C4×D4—82no—
805#117—48no—
806#117—48no—
807#117—48no—
808#117—48no—
809#117—84no—
810#117—84no—
811C2×C4⋊C4—216no—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C42C2414yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2411yescharacteristic
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017C24C2514yes—
1018C24C2514yes—
1019C2×Q8—22no—
1020C2×Q8—28no—
1021C2×Q8—24no—
1022C2×Q8—22no—
1023C2×Q8—22no—
1024C2×Q8—22no—
1025C2×Q8—22no—
1026C2×Q8—41no—
1027C2×Q8—42no—
1028C2×Q8—41no—
1029C2×Q8—41no—
1030C2×Q8—41no—
1031C2×Q8—42no—
1032C2×Q8—44no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—42no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—41no—
1040C2×Q8—41no—
1041C2×Q8C2×#4114yes—
1042C2×Q8H(5,𝔽2)14yes—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—28no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—44no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—42no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C22×C4—28no—
1074C22×C4—28no—
1075C22×C4—28no—
1076C22×C4—28no—
1077C22×C4—28no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C22×C4C2511yescharacteristic
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—22no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—22no—
1138C4⋊C4—22no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—41no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—41no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—41no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4C2×#4118yes—
1188C4⋊C4C2×#4114yes—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—28no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
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—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C42—24no—
1232C42—24no—
1233C42—28no—
1234C42—28no—
1235C42—22no—
1236C42—24no—
1237C42—24no—
1238C42—24no—
1239C42—24no—
1240C42—22no—
1241C42—24no—
1242C42—24no—
1243C42—24no—
1244C42—41no—
1245C42—42no—
1246C42—44no—
1247C42—44no—
1248C42—44no—
1249C42—42no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—41no—
1254C42—41no—
1255C42—42no—
1256C42—42no—
1257C42—42no—
1258C42—42no—
1259C42C2×#4118yes—
1260C42C2×#4114yes—
1261C422−1+414yes—
1262C23—24no—
1263C23—24no—
1264C23—24no—
1265C23—24no—
1266C23—24no—
1267C23—24no—
1268C23—24no—
1269C23—24no—
1270C23—24no—
1271C23—24no—
1272C23—24no—
1273C23—24no—
1274C23—24no—
1275C23—24no—
1276C23C2611yescharacteristic
1277Q8—44no—
1278Q8—44no—
1279Q8—48no—
1280Q8—44no—
1281Q8—88no—
1282Q8—82no—
1283Q8—82no—
1284Q8—84no—
1285D4—48no—
1286D4—48no—
1287D4—48no—
1288D4—84no—
1289D4—84no—
1290D4—88no—
1291D4—84no—
1292D4—88no—
1293D4—164no—
1294D4—164no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—21no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—416no—
1366C2×C4—88no—
1367C2×C4—88no—
1368C2×C4—88no—
1369C2×C4—88no—
1370C2×C4—164no—
1371C2×C4C22×#4112yes—
1372C2×C4C22×#4114yes—
1373C2×C4C22×#4114yes—
1374C2×C4C22×#4112yes—
1375C2×C4C22×#4112yes—
1376C2×C4C2×H(5,𝔽2)14yes—
1377C2×C4C2×H(5,𝔽2)12yes—
1378C2×C4C2×2−1+412yes—
1379C2×C4C2×2−1+412yes—
1380C2×C4C2×2−1+412yes—
1381C2×C4#58512yes—
1382C22—44no—
1383C22—44no—
1384C22—44no—
1385C22—44no—
1386C22—44no—
1387C22—44no—
1388C22—44no—
1389C22—44no—
1390C22—44no—
1391C22—44no—
1392C22—44no—
1393C22—44no—
1394C22—44no—
1395C22—44no—
1396C22C23×#4111yescharacteristic
1397C22C22×H(5,𝔽2)11yescharacteristic
1398C22C22×2−1+411yescharacteristic
1399C22C2×#58511yescharacteristic
1400C22H(7,𝔽2)11yescharacteristic
1401C22H(7,𝔽2)11yescharacteristic
1402C222−1+611yescharacteristic
1403C4—22no—
1404C4—24no—
1405C4—24no—
1406C4—22no—
1407C4—22no—
1408C4—24no—
1409C4—22no—
1410C4—22no—
1411C4—42no—
1412C4—44no—
1413C4—44no—
1414C4—42no—
1415C4—41no—
1416C4—42no—
1417C4—42no—
1418C4—42no—
1419C4—42no—
1420C4—42no—
1421C4—44no—
1422C4—42no—
1423C4—42no—
1424C4—42no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—44no—
1429C4#351814yes—
1430C2—84no—
1431C2—84no—
1432C2C2×#351811yescharacteristic
1433C2#6284511yescharacteristic
1434C2#6287911yescharacteristic
1435C2#6290111yescharacteristic
1436C2#6291711yescharacteristic
1437C2#6298611yescharacteristic
1438C2#6305111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59822C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59821C2semidirect
3. #52287C2semidirect
4. #51674C2semidirect
5. #50611C2semidirect
6. #50127C2semidirect
7. #47645C2semidirect
8. #45956C2semidirect
9. #45370C2semidirect
10. #44965C2semidirect
11. #44963C2semidirect
12. #44679C2semidirect
13. #42699C2semidirect
14. #42524C2semidirect
15. #42140C2semidirect
16. #40021C2semidirect
17. #39801C2semidirect
18. #39756C2semidirect
19. #39611C2semidirect
20. #39161C2semidirect
21. #38830C2semidirect
22. #38435C2semidirect
23. #37207C2semidirect
24. #36285C2semidirect
25. #35934C2semidirect
26. #35562C2semidirect
27. #35186C2semidirect
28. #34484C2semidirect
29. #34331C2semidirect

Maximal subgroups

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

subgroupindex
#598222
#598212
#522872
#516742
#506112
#501272
#476452
#459562
#453702
#449652
#449632
#446792
#426992
#425242
#421402
#400212
#398012
#397562
#396112
#391612
#388302
#384352
#372072
#362852
#359342
#355622
#351862
#344842
#343312