Finite Group Databasebeta

← #7712807

Subgroups — #7712807

Order 512.

4588 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59359C214yesmaximal, complemented
2#59353C214yesmaximal, complemented
3#45461C214yesmaximal, complemented
4#45459C214yesmaximal, complemented
5#38073C212yesmaximal, complemented
6#38072C212yesmaximal, complemented
7#38061C212yesmaximal, complemented
8#38060C212yesmaximal, complemented
9#38010C214yesmaximal, complemented
10#38009C214yesmaximal, complemented
11#37931C214yesmaximal, complemented
12#37928C214yesmaximal, complemented
13#37481C211yesmaximal, characteristic, complemented
14#37455C211yesmaximal, characteristic
15#37382C211yesmaximal, characteristic, complemented
16#37288C212yesmaximal, complemented
17#37286C211yesmaximal, characteristic, complemented
18#36626C212yesmaximal, complemented
19#36400C212yesmaximal, complemented
20#36391C212yesmaximal, complemented
21#36379C212yesmaximal, complemented
22#36366C212yesmaximal, complemented
23#35321C211yesmaximal, characteristic, complemented
24#35300C212yesmaximal, complemented
25#35287C211yesmaximal, characteristic, complemented
26#34391C212yesmaximal, complemented
27#34012C211yesmaximal, characteristic, complemented
28C2×#525C2212yes—
29C23×C42C2211yescharacteristic
30#2863C2212yescomplemented
31#2861C2212yescomplemented
32#2860C2212yescomplemented
33#2859C2212yescomplemented
34#2855C2212yes—
35#2855C2212yes—
36#2855C2212yes—
37#2855C2212yes—
38#2854C2212yes—
39#2854C2212yes—
40#2854C2212yes—
41#2854C2212yes—
42#2853C2214yes—
43#2853C2214yes—
44#2849C2214yes—
45#2849C2214yes—
46#2842C2214yes—
47#2812C2214yes—
48#2791C2214yescomplemented
49#2790C2214yescomplemented
50#2783C2214yescomplemented
51#2781C2214yescomplemented
52#2771C2214yes—
53#2767C2214yescomplemented
54#2765C2214yes—
55#2761C2214yes—
56#2752C2214yes—
57#2750C2214yes—
58#2749C2214yes—
59#2746C2214yes—
60#2744C2214yes—
61#2744C2214yescomplemented
62#2743C2214yes—
63#2743C2214yes—
64#2743C2214yes—
65#2743C2214yes—
66#2740C2214yes—
67#2739C2214yes—
68#2739C2214yes—
69#2738C2214yes—
70#2721C2214yescomplemented
71#2718C2214yescomplemented
72#2707C2214yes—
73#2706C2214yes—
74#2705C2214yes—
75#2705C2214yes—
76#2695C2214yes—
77#2695C2214yes—
78#2694C2214yes—
79#2693C2214yes—
80#2667C2214yes—
81#2667C2214yes—
82#2647C2211yescharacteristic, complemented
83#2647C2211yescharacteristic, complemented
84#2645C2212yescomplemented
85#2644C2212yescomplemented
86#2642C2211yescharacteristic, complemented
87#2641C2211yescharacteristic, complemented
88#2630C2214yes—
89#2630C2214yes—
90#2629C2211yescharacteristic
91#2629C2211yescharacteristic
92#2629C2212yes—
93#2621C2211yescharacteristic
94#2620C2212yes—
95#2619C2211yescharacteristic
96#2611C2214yes—
97#2609C2214yes—
98#2608C2214yes—
99#2601C2214yes—
100#2600C2214yes—
101#2598C2214yes—
102#2594C2214yescomplemented
103#2593C2214yescomplemented
104#2587C2214yescomplemented
105#2585C2214yescomplemented
106#2578C2214yescomplemented
107#2576C2214yes—
108#2575C2214yes—
109#2575C2214yescomplemented
110#2573C2214yes—
111#2573C2214yes—
112#2573C2214yescomplemented
113#2558C2214yes—
114#2558C2214yes—
115#2554C2214yes—
116#2553C2214yes—
117#2553C2214yescomplemented
118#2533C2214yescomplemented
119#2533C2214yescomplemented
120#2530C2214yescomplemented
121#2529C2214yescomplemented
122#2529C2214yescomplemented
123#2528C2214yescomplemented
124#2526C2214yes—
125#2526C2214yes—
126#2526C2214yescomplemented
127#2525C2214yescomplemented
128#2524C2214yescomplemented
129#2524C2214yescomplemented
130#2524C2214yescomplemented
131#2522C2214yescomplemented
132#2519C2214yescomplemented
133#2519C2214yescomplemented
134#2518C2214yescomplemented
135#2518C2214yescomplemented
136#2516C2214yes—
137#2516C2214yescomplemented
138#2515C2214yes—
139#2515C2214yescomplemented
140#2512C2212yescomplemented
141#2512C2212yescomplemented
142#2511C2212yescomplemented
143#2511C2212yescomplemented
144#2509C2212yescomplemented
145#2508C2212yescomplemented
146#2508C2214yescomplemented
147#2507C2212yescomplemented
148#2506C2212yescomplemented
149#2505C2214yescomplemented
150#2500C2212yes—
151#2499C2212yes—
152#2495C2214yescomplemented
153#2493C2214yescomplemented
154#2479C2214yes—
155#2479C2214yes—
156#2475C2214yes—
157#2475C2214yescomplemented
158#2471C2214yes—
159#2471C2214yes—
160#2470C2214yes—
161#2468C2214yescomplemented
162#2457C2214yes—
163#2457C2214yes—
164#2454C2212yescomplemented
165#2454C2212yescomplemented
166#2453C2212yescomplemented
167#2453C2212yescomplemented
168#2448C2212yescomplemented
169#2447C2212yescomplemented
170#2446C2212yescomplemented
171#2445C2212yescomplemented
172#2441C2212yes—
173#2441C2212yes—
174#2441C2212yes—
175#2441C2212yes—
176#2432C2212yes—
177#2431C2212yes—
178#2375C2214yes—
179#2375C2214yes—
180#2373C2214yescomplemented
181#2373C2214yescomplemented
182#2373C2214yescomplemented
183#2371C2214yescomplemented
184#2370C2214yescomplemented
185#2363C2212yes—
186#2363C2212yes—
187#2362C2212yes—
188#2362C2212yes—
189#2359C2214yescomplemented
190#2357C2214yes—
191#2353C2214yes—
192#2353C2214yescomplemented
193#2347C2212yes—
194#2346C2212yes—
195#2346C2214yescomplemented
196#2341C2212yes—
197#2339C2212yes—
198#2335C2214yes—
199#2335C2214yes—
200#2330C2212yescomplemented
201#2326C2212yescomplemented
202#2324C2212yes—
203#2324C2212yes—
204#2323C2212yes—
205#2323C2212yes—
206#2320C2212yescomplemented
207#2319C2214yes—
208#2319C2212yescomplemented
209#2318C2214yes—
210C4×C4⋊Q8C2211yescharacteristic, complemented
211C4×#127C2211yescharacteristic, complemented
212C4×#125C2211yescharacteristic, complemented
213C4×#125C2211yescharacteristic, complemented
214C4×#123C2214yes—
215C4×#123C2214yes—
216C4×#123C2214yes—
217C4×#123C2214yes—
218#2297C2212yes—
219#2297C2212yes—
220#2296C2212yes—
221#2296C2212yes—
222#2295C2212yescomplemented
223#2293C2212yescomplemented
224#2285C2211yescharacteristic
225#2285C2212yes—
226#2285C2212yes—
227#2285C2211yescharacteristic
228#2283C2212yes—
229#2283C2212yes—
230#2283C2212yes—
231#2283C2212yes—
232#2283C2212yes—
233#2283C2212yes—
234#2280C2212yes—
235#2280C2211yescharacteristic
236#2280C2211yescharacteristic
237#2280C2212yes—
238#2280C2212yes—
239C4×#117C2212yes—
240C4×#117C2212yes—
241C4×#117C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C22×#41C2312yes—
244C24×C4C2312yes—
245C24×C4C2311yescharacteristic
246C2×C4⋊Q8C2311yescharacteristic
247C2×#127C2311yescharacteristic
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#125C2311yescharacteristic
252C2×#125C2311yescharacteristic
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#124C2312yes—
257#525—216no—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×#121C2312yes—
267C2×#121C2312yes—
268C2×#120C2314yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×#117C2312yes—
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2314yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2312yes—
287C2×#117C2312yes—
288C22×C42—28no—
289C22×C42C2312yes—
290C22×C42C2312yes—
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2312yes—
294C22×C42C2312yes—
295C22×C42C2312yes—
296#401C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#392C2314yes—
374#392C2314yes—
375#392C2314yes—
376#391C2312yes—
377#391C2312yes—
378#391C2312yes—
379#391C2312yes—
380#391C2312yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#390C2314yes—
385#390C2312yes—
386#390C2314yes—
387#390C2314yes—
388#390C2312yes—
389#390C2312yes—
390#390C2312yes—
391#390C2312yes—
392#390C2314yes—
393#390C2314yes—
394#390C2314yes—
395#390C2314yes—
396#390C2312yes—
397#390C2312yes—
398#390C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2312yes—
429#389C2312yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#384C2311yescharacteristic
549#384C2311yescharacteristic
550#384C2312yes—
551#384C2312yes—
552#384C2312yes—
553#384C2311yescharacteristic
554#384C2311yescharacteristic
555#383C2314yes—
556#383C2312yes—
557#383C2314yes—
558#383C2314yes—
559#383C2312yes—
560#383C2312yes—
561#383C2312yes—
562#382C2311yescharacteristic
563#382C2311yescharacteristic
564#382C2314yes—
565#382C2314yes—
566#382C2312yes—
567#382C2314yes—
568#382C2314yes—
569#382C2311yescharacteristic
570#382C2312yes—
571#382C2312yes—
572#382C2312yes—
573#382C2311yescharacteristic
574#382C2312yes—
575#381C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2312yes—
583#381C2311yescharacteristic
584#381C2314yes—
585#381C2311yescharacteristic
586#381C2312yes—
587#381C2312yes—
588#381C2312yes—
589#381C2312yes—
590#380C2312yes—
591#380C2312yes—
592#380C2314yes—
593#380C2314yes—
594#380C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2314yes—
599#380C2314yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2312yes—
604#380C2312yes—
605#380C2312yes—
606#380C2312yes—
607#380C2312yes—
608#380C2312yes—
609#380C2312yes—
610#379C2314yes—
611#379C2312yes—
612#379C2311yescharacteristic
613#379C2311yescharacteristic
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C22⋊C4C2312yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663#376C2314yes—
664#376C2311yescharacteristic
665#376C2311yescharacteristic
666#376C2312yes—
667#376C2312yes—
668#376C2312yes—
669#376C2314yes—
670#376C2312yes—
671#376C2312yes—
672C2×#95C2314yes—
673C43C2311yescharacteristic
674C43C2311yescharacteristic
675C43C2312yes—
676C25C2411yescharacteristic
677C2×#41—28no—
678C2×#41—44no—
679C2×#41—44no—
680C22×Q8C2412yes—
681C22×D4C2412yes—
682C22×D4C2414yes—
683C22×D4C2414yes—
684C22×D4C2414yes—
685C22×D4C2414yes—
686C23×C4—28no—
687C23×C4—42no—
688C23×C4—42no—
689C23×C4—44no—
690C23×C4—44no—
691C23×C4#4118yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2411yescharacteristic
698C23×C4C2412yes—
699C23×C4C2414yes—
700C23×C4C2412yes—
701C23×C4C2414yes—
702C23×C4C2414yes—
703C23×C4C2411yescharacteristic
704C23×C4C2412yes—
705C4⋊Q8—42no—
706#127—42no—
707#126—48no—
708#126—48no—
709#126—48no—
710#125—44no—
711#125—48no—
712#125—42no—
713#125—42no—
714#125—48no—
715#124—44no—
716#123—216no—
717#123—48no—
718#123—48no—
719#123—48no—
720#123—48no—
721#123—48no—
722C22⋊Q8—28no—
723C22⋊Q8—28no—
724#121—28no—
725#121—28no—
726#120—216no—
727C4×Q8—44no—
728C4×Q8—44no—
729C4×D4—216no—
730C4×D4—216no—
731C4×D4—48no—
732C4×D4—44no—
733C4×D4—44no—
734#117—28no—
735#117—44no—
736#117—42no—
737#117—44no—
738#117—42no—
739#117—42no—
740#117—42no—
741#117—48no—
742#117—44no—
743#117—44no—
744#117—44no—
745#117—44no—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
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×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C42—28no—
843C2×C42—28no—
844C2×C42—28no—
845C2×C42—24no—
846C2×C42—24no—
847C2×C42—28no—
848C2×C42—28no—
849C2×C42C2412yes—
850C2×C42C2411yescharacteristic
851C2×C42C2412yes—
852C2×C42C2414yes—
853C2×C42C2412yes—
854C2×C42C2411yescharacteristic
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2411yescharacteristic
858C2×C42C2411yescharacteristic
859C2×C42C2412yes—
860C2×C42C2411yescharacteristic
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882#95C2412yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948C24—41no—
949C24—41no—
950C24—42no—
951C24—42no—
952C24C2×#4114yes—
953C24C2514yes—
954C24C2512yes—
955C24C2511yescharacteristic
956#41—816no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—24no—
964C2×D4—24no—
965C2×D4—24no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C22×C4—24no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—28no—
992C22×C4—416no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—41no—
996C22×C4—41no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—432no—
1012C22×C4C2×#4118yes—
1013C22×C4C2×#4114yes—
1014C22×C4C2×#4114yes—
1015C22×C4C2×#4118yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2512yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—28no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—41no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—41no—
1060C4⋊C4—42no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—44no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C42—24no—
1137C42—22no—
1138C42—22no—
1139C42—24no—
1140C42—24no—
1141C42—24no—
1142C42—24no—
1143C42—24no—
1144C42—22no—
1145C42—22no—
1146C42—28no—
1147C42—24no—
1148C42—22no—
1149C42—24no—
1150C42—24no—
1151C42—22no—
1152C42—24no—
1153C42—24no—
1154C42—22no—
1155C42—22no—
1156C42—24no—
1157C42—42no—
1158C42—42no—
1159C42—42no—
1160C42—42no—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C23—21no—
1170C23—21no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—24no—
1184C23—24no—
1185C23—24no—
1186C23—44no—
1187C23—48no—
1188C23—48no—
1189C23—44no—
1190C23—44no—
1191C23C22×#4114yes—
1192C23C22×#4112yes—
1193C23C2611yescharacteristic
1194Q8—48no—
1195D4—48no—
1196D4—88no—
1197D4—88no—
1198D4—88no—
1199D4—88no—
1200C2×C4—216no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—28no—
1210C2×C4—216no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—44no—
1265C2×C4—48no—
1266C2×C4—48no—
1267C2×C4—48no—
1268C2×C4—48no—
1269C2×C4—48no—
1270C2×C4—48no—
1271C2×C4—88no—
1272C2×C4—88no—
1273C2×C4—164no—
1274C2×C4C22×#4114yes—
1275C2×C4C22×#4112yes—
1276C2×C4C22×#4112yes—
1277C2×C4#58514yes—
1278C2×C4#58514yes—
1279C2×C4#58512yes—
1280C2×C4#58512yes—
1281C22—24no—
1282C22—22no—
1283C22—24no—
1284C22—24no—
1285C22—24no—
1286C22—416no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—41no—
1292C22—42no—
1293C22—41no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22C23×#4111yescharacteristic
1302C22C2×#58511yescharacteristic
1303C22C2×#58512yes—
1304C22C2×#58512yes—
1305C22C2×#58511yescharacteristic
1306C4—24no—
1307C4—22no—
1308C4—24no—
1309C4—24no—
1310C4—42no—
1311C4—42no—
1312C4—44no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4—42no—
1318C4—42no—
1319C4—44no—
1320C4—44no—
1321C4—41no—
1322C4—42no—
1323C4—44no—
1324C4—41no—
1325C4—41no—
1326C4—42no—
1327C4—41no—
1328C4—44no—
1329C4#349114yes—
1330C2—44no—
1331C2—42no—
1332C2—84no—
1333C2#6276212yes—
1334C2C2×#349111yescharacteristic
1335C2#6281412yes—
1336C2#6283911yescharacteristic
1337C2#6284011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37455C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59359C2semidirect
2. #59353C2semidirect
3. #45461C2semidirect
4. #45459C2semidirect
5. #38073C2semidirect
6. #38072C2semidirect
7. #38061C2semidirect
8. #38060C2semidirect
9. #38010C2semidirect
10. #38009C2semidirect
11. #37931C2semidirect
12. #37928C2semidirect
13. #37481C2semidirect
15. #37382C2semidirect
16. #37288C2semidirect
17. #37286C2semidirect
18. #36626C2semidirect
19. #36400C2semidirect
20. #36391C2semidirect
21. #36379C2semidirect
22. #36366C2semidirect
23. #35321C2semidirect
24. #35300C2semidirect
25. #35287C2semidirect
26. #34391C2semidirect
27. #34012C2semidirect
30. #2863C22semidirect
31. #2861C22semidirect
32. #2860C22semidirect
33. #2859C22semidirect
48. #2791C22semidirect
49. #2790C22semidirect
50. #2783C22semidirect
51. #2781C22semidirect
53. #2767C22semidirect
61. #2744C22semidirect
70. #2721C22semidirect
71. #2718C22semidirect
82. #2647C22semidirect
83. #2647C22semidirect
84. #2645C22semidirect
85. #2644C22semidirect
86. #2642C22semidirect
87. #2641C22semidirect
102. #2594C22semidirect
103. #2593C22semidirect
104. #2587C22semidirect
105. #2585C22semidirect
106. #2578C22semidirect
109. #2575C22semidirect
112. #2573C22semidirect
117. #2553C22semidirect
118. #2533C22semidirect
119. #2533C22semidirect
120. #2530C22semidirect
121. #2529C22semidirect
122. #2529C22semidirect
123. #2528C22semidirect
126. #2526C22semidirect
127. #2525C22semidirect
128. #2524C22semidirect
129. #2524C22semidirect
130. #2524C22semidirect
131. #2522C22semidirect
132. #2519C22semidirect
133. #2519C22semidirect
134. #2518C22semidirect
135. #2518C22semidirect
137. #2516C22semidirect
139. #2515C22semidirect
140. #2512C22semidirect
141. #2512C22semidirect
142. #2511C22semidirect
143. #2511C22semidirect
144. #2509C22semidirect
145. #2508C22semidirect
146. #2508C22semidirect
147. #2507C22semidirect
148. #2506C22semidirect
149. #2505C22semidirect
152. #2495C22semidirect
153. #2493C22semidirect
157. #2475C22semidirect
161. #2468C22semidirect
164. #2454C22semidirect
165. #2454C22semidirect
166. #2453C22semidirect
167. #2453C22semidirect
168. #2448C22semidirect
169. #2447C22semidirect
170. #2446C22semidirect
171. #2445C22semidirect
180. #2373C22semidirect
181. #2373C22semidirect
182. #2373C22semidirect
183. #2371C22semidirect
184. #2370C22semidirect
189. #2359C22semidirect
192. #2353C22semidirect
195. #2346C22semidirect
200. #2330C22semidirect
201. #2326C22semidirect
206. #2320C22semidirect
208. #2319C22semidirect
210. C4×C4⋊Q8C22semidirect
211. C4×#127C22semidirect
212. C4×#125C22semidirect
213. C4×#125C22semidirect
222. #2295C22semidirect
223. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#593592
#593532
#454612
#454592
#380732
#380722
#380612
#380602
#380102
#380092
#379312
#379282
#374812
#374552
#373822
#372882
#372862
#366262
#364002
#363912
#363792
#363662
#353212
#353002
#352872
#343912
#340122