Finite Group Databasebeta

← #7715637

Subgroups — #7715637

Order 512.

4224 conjugacy classes of subgroups.

The subgroup lattice has 1287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#49111C214yesmaximal, complemented
2#49054C214yesmaximal, complemented
3#48274C214yesmaximal, complemented
4#48209C214yesmaximal, complemented
5#47349C214yesmaximal, complemented
6#47345C214yesmaximal, complemented
7#47341C214yesmaximal, complemented
8#47337C214yesmaximal, complemented
9#39765C212yesmaximal, complemented
10#39761C212yesmaximal, complemented
11#39643C212yesmaximal, complemented
12#39630C212yesmaximal, complemented
13#38237C212yesmaximal, complemented
14#38236C212yesmaximal, complemented
15#38229C212yesmaximal, complemented
16#38228C212yesmaximal, complemented
17#37522C211yesmaximal, characteristic, complemented
18#37520C211yesmaximal, characteristic
19#37382C211yesmaximal, characteristic, complemented
20#37286C211yesmaximal, characteristic
21#37275C212yesmaximal, complemented
22#35331C211yesmaximal, characteristic
23#35299C212yesmaximal, complemented
24#35284C211yesmaximal, characteristic, complemented
25#35270C212yesmaximal, complemented
26#34419C212yesmaximal, complemented
27#34074C211yesmaximal, characteristic, complemented
28C2×#542C2212yes—
29C2×#533C2211yescharacteristic
30#2868C2211yescharacteristic
31#2863C2212yes—
32#2862C2211yescharacteristic
33#2860C2212yes—
34#2859C2211yescharacteristic
35#2858C2211yescharacteristic
36#2857C2212yes—
37#2855C2212yes—
38#2854C2212yes—
39#2850C2212yes—
40#2839C2214yes—
41#2837C2214yes—
42#2808C2214yes—
43#2808C2214yes—
44#2807C2214yes—
45#2807C2214yes—
46#2804C2214yes—
47#2799C2214yes—
48#2799C2214yes—
49#2798C2214yes—
50#2798C2214yes—
51#2793C2214yes—
52#2793C2214yes—
53#2793C2214yes—
54#2791C2214yes—
55#2788C2214yes—
56#2788C2214yes—
57#2788C2214yes—
58#2783C2214yes—
59#2781C2214yes—
60#2777C2214yes—
61#2769C2214yes—
62#2767C2214yes—
63#2767C2214yes—
64#2767C2214yes—
65#2762C2214yes—
66#2755C2214yes—
67#2755C2214yes—
68#2750C2214yes—
69#2745C2214yes—
70#2744C2214yes—
71#2741C2214yes—
72#2739C2214yes—
73#2724C2214yes—
74#2721C2214yes—
75#2718C2214yes—
76#2716C2214yes—
77#2716C2214yes—
78#2716C2214yes—
79#2716C2214yes—
80#2705C2214yes—
81#2702C2214yes—
82#2700C2214yes—
83#2695C2214yes—
84#2693C2214yes—
85#2690C2214yes—
86#2687C2214yes—
87#2680C2214yes—
88#2677C2214yes—
89#2674C2214yes—
90#2652C2214yes—
91#2652C2214yes—
92#2647C2212yes—
93#2647C2212yes—
94#2647C2212yes—
95#2645C2212yes—
96#2644C2212yes—
97#2640C2212yes—
98#2640C2212yes—
99#2640C2212yes—
100#2636C2214yes—
101#2630C2214yes—
102#2629C2211yescharacteristic
103#2629C2211yescharacteristic
104#2625C2212yes—
105#2624C2212yes—
106#2621C2211yescharacteristic
107#2619C2211yescharacteristic
108#2609C2214yes—
109#2604C2214yes—
110#2597C2214yes—
111#2597C2214yes—
112#2596C2214yes—
113#2592C2212yes—
114#2592C2212yes—
115#2589C2214yes—
116#2585C2214yes—
117#2585C2214yes—
118#2582C2212yes—
119#2582C2214yes—
120#2581C2212yes—
121#2580C2212yes—
122#2578C2214yes—
123#2577C2214yes—
124#2568C2214yes—
125#2567C2212yes—
126#2560C2214yes—
127#2560C2214yes—
128#2560C2214yes—
129#2557C2214yes—
130#2557C2214yes—
131#2553C2214yes—
132#2546C2212yes—
133#2538C2212yes—
134#2533C2214yes—
135#2532C2214yes—
136#2532C2214yes—
137#2531C2214yes—
138#2530C2214yes—
139#2529C2214yes—
140#2528C2214yes—
141#2527C2214yes—
142#2527C2214yes—
143#2523C2214yes—
144#2522C2214yes—
145#2522C2214yes—
146#2520C2214yes—
147#2512C2212yes—
148#2512C2212yes—
149#2511C2212yes—
150#2511C2212yes—
151#2511C2214yes—
152#2510C2214yes—
153#2509C2212yes—
154#2509C2212yes—
155#2508C2212yes—
156#2508C2212yes—
157#2507C2214yes—
158#2505C2214yes—
159#2505C2214yes—
160#2499C2214yes—
161#2498C2214yes—
162#2497C2214yes—
163#2496C2214yes—
164#2496C2214yes—
165#2492C2214yes—
166#2488C2214yes—
167#2488C2214yes—
168#2478C2214yes—
169#2478C2214yes—
170#2477C2214yes—
171#2470C2214yes—
172#2469C2214yes—
173#2458C2214yes—
174#2458C2214yes—
175#2454C2212yes—
176#2454C2212yes—
177#2453C2212yes—
178#2453C2212yes—
179#2450C2214yes—
180#2446C2212yes—
181#2446C2212yes—
182#2446C2214yes—
183#2446C2214yes—
184#2445C2212yes—
185#2445C2212yes—
186#2439C2214yes—
187#2439C2214yes—
188#2429C2214yes—
189#2419C2214yes—
190#2379C2214yes—
191#2376C2214yes—
192#2369C2212yes—
193#2367C2212yes—
194#2367C2212yes—
195#2367C2214yes—
196#2365C2212yes—
197#2359C2214yes—
198#2355C2212yes—
199#2354C2212yes—
200#2351C2212yes—
201#2349C2212yes—
202#2334C2214yes—
203#2334C2214yes—
204#2331C2212yes—
205#2331C2212yes—
206#2331C2212yes—
207#2331C2212yes—
208#2330C2212yes—
209#2330C2212yes—
210#2330C2211yescharacteristic
211#2330C2211yescharacteristic
212#2329C2212yes—
213#2329C2212yes—
214#2329C2212yes—
215#2329C2212yes—
216#2329C2214yes—
217#2328C2211yescharacteristic
218#2327C2211yescharacteristic
219#2326C2212yes—
220#2326C2212yes—
221#2324C2212yes—
222#2323C2212yes—
223#2323C2214yes—
224#2320C2212yes—
225#2319C2212yes—
226#2314C2212yes—
227C4×C4⋊Q8C2212yes—
228C4×#124C2212yes—
229C4×C22⋊Q8C2212yes—
230C4×#121C2212yes—
231#2296C2211yescharacteristic
232#2296C2211yescharacteristic
233#2295C2212yes—
234#2295C2212yes—
235#2295C2212yes—
236#2295C2212yes—
237#2295C2212yes—
238#2293C2212yes—
239#2285C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C2×#376C2211yescharacteristic
243#542—216no—
244#533—28no—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2311yescharacteristic
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2314yes—
251C2×#127C2311yescharacteristic
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#125C2312yes—
257C2×#125C2311yescharacteristic
258C2×#125C2311yescharacteristic
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×#121C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2314yes—
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2314yes—
288C2×#117C2314yes—
289C2×#117C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293#401C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
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#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
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#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#393C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#392C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2312yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2314yes—
402#391C2312yes—
403#391C2312yes—
404#391C2314yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#390C2312yes—
423#390C2312yes—
424#390C2312yes—
425#390C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2312yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2312yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2312yes—
583#385C2312yes—
584#385C2312yes—
585#385C2312yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#384C2312yes—
594#384C2314yes—
595#384C2312yes—
596#384C2312yes—
597#384C2311yescharacteristic
598#384C2311yescharacteristic
599#384C2314yes—
600#383C2314yes—
601#383C2314yes—
602#382C2314yes—
603#382C2314yes—
604#382C2312yes—
605#382C2314yes—
606#382C2311yescharacteristic
607#382C2311yescharacteristic
608#382C2312yes—
609#382C2312yes—
610#382C2314yes—
611#382C2314yes—
612#381C2314yes—
613#381C2314yes—
614#380C2312yes—
615#380C2312yes—
616#380C2314yes—
617#380C2314yes—
618#380C2314yes—
619#380C2314yes—
620#380C2312yes—
621#380C2312yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C22⋊C4C2311yescharacteristic
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2311yescharacteristic
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2311yescharacteristic
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2311yescharacteristic
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660#376C2312yes—
661#376C2312yes—
662#376C2312yes—
663#376C2311yescharacteristic
664#376C2311yescharacteristic
665#376C2311yescharacteristic
666#376C2311yescharacteristic
667#376C2311yescharacteristic
668#376C2311yescharacteristic
669#376C2314yes—
670C2×#95C2312yes—
671C2×#95C2312yes—
672C2×#95C2314yes—
673C43C2311yescharacteristic
674C43C2311yescharacteristic
675C43C2312yes—
676C22×Q8C2412yes—
677C22×Q8C2412yes—
678C22×Q8C2414yes—
679C22×Q8C2412yes—
680C22×Q8C2414yes—
681C22×D4C2412yes—
682C22×D4C2414yes—
683C22×D4C2414yes—
684C23×C4C2411yescharacteristic
685C23×C4C2414yes—
686C23×C4C2411yescharacteristic
687C23×C4C2412yes—
688C23×C4C2411yescharacteristic
689C23×C4C2414yes—
690C23×C4C2414yes—
691C23×C4C2412yes—
692C4⋊Q8—28no—
693C4⋊Q8—28no—
694C4⋊Q8—28no—
695C4⋊Q8—42no—
696C4⋊Q8—84no—
697C4⋊Q8—84no—
698#127—42no—
699#126—216no—
700#126—84no—
701#126—84no—
702#126—84no—
703#125—28no—
704#125—42no—
705#125—42no—
706#124—216no—
707#124—28no—
708#124—28no—
709#123—216no—
710#123—84no—
711#123—84no—
712#123—84no—
713C22⋊Q8—28no—
714C22⋊Q8—216no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—84no—
718C22⋊Q8—84no—
719#121—28no—
720C4×Q8—28no—
721C4×Q8—28no—
722C4×Q8—28no—
723C4×Q8—44no—
724C4×Q8—44no—
725C4×Q8—84no—
726C4×Q8—84no—
727C4×D4—28no—
728C4×D4—44no—
729C4×D4—44no—
730C4×D4—84no—
731#117—24no—
732#117—42no—
733#117—42no—
734#117—84no—
735#117—84no—
736#117#4118yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2411yescharacteristic
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⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
829C2×C42—24no—
830C2×C42—24no—
831C2×C42—42no—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2411yescharacteristic
835C2×C42C2411yescharacteristic
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2414yes—
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842C2×C42C2411yescharacteristic
843C2×C42C2411yescharacteristic
844C2×C42C2412yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865#95C2412yes—
866#95C2412yes—
867#95C2412yes—
868#95C2412yes—
869#95C2412yes—
870#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2412yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2412yes—
905#95C2412yes—
906#95C2414yes—
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
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—
939C24C2514yes—
940C24C2511yescharacteristic
941C2×Q8—24no—
942C2×Q8—24no—
943C2×Q8—24no—
944C2×Q8—28no—
945C2×Q8—24no—
946C2×Q8—28no—
947C2×Q8—24no—
948C2×Q8—44no—
949C2×Q8—44no—
950C2×Q8—42no—
951C2×Q8—44no—
952C2×Q8—42no—
953C2×Q8—42no—
954C2×Q8—42no—
955C2×Q8—44no—
956C2×D4—28no—
957C2×D4—24no—
958C2×D4—24no—
959C2×D4—24no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C22×C4—22no—
966C22×C4—22no—
967C22×C4—24no—
968C22×C4—28no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4C2×#4114yes—
987C22×C4C2511yescharacteristic
988C22×C4C2512yes—
989C22×C4C2514yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2511yescharacteristic
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2514yes—
1000C22×C4C2514yes—
1001C22×C4C2512yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2512yes—
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2511yescharacteristic
1008C22×C4C2512yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—24no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—24no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—24no—
1026C4⋊C4—24no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—44no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—42no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—42no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4C2×#4118yes—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—41no—
1085C22⋊C4—42no—
1086C22⋊C4—41no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
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⋊C4C2×#4118yes—
1104C42—24no—
1105C42—22no—
1106C42—22no—
1107C42—24no—
1108C42—28no—
1109C42—22no—
1110C42—22no—
1111C42—22no—
1112C42—24no—
1113C42—24no—
1114C42—22no—
1115C42—22no—
1116C42—41no—
1117C42—41no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—44no—
1123C42—42no—
1124C42—44no—
1125C42—44no—
1126C42—44no—
1127C42—44no—
1128C42—42no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—42no—
1133C42—42no—
1134C42C2×#4114yes—
1135C42C2×#4114yes—
1136C422−1+414yes—
1137C23—21no—
1138C23—21no—
1139C23—22no—
1140C23—22no—
1141C23—24no—
1142C23—24no—
1143C23—24no—
1144C23—24no—
1145C23—24no—
1146C23—24no—
1147C23—24no—
1148C23C22×#4112yes—
1149C23C2611yescharacteristic
1150Q8—48no—
1151Q8—84no—
1152Q8—88no—
1153Q8—84no—
1154Q8—88no—
1155D4—48no—
1156D4—88no—
1157D4—164no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—28no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—88no—
1223C2×C4—82no—
1224C2×C4—82no—
1225C2×C4—84no—
1226C2×C4—88no—
1227C2×C4—84no—
1228C2×C4—164no—
1229C2×C4C22×#4114yes—
1230C2×C4C22×#4112yes—
1231C2×C4C22×#4114yes—
1232C2×C4C22×#4112yes—
1233C2×C4C2×2−1+412yes—
1234C2×C4C2×2−1+412yes—
1235C2×C4C2×2−1+412yes—
1236C2×C4#58512yes—
1237C22—22no—
1238C22—24no—
1239C22—41no—
1240C22—42no—
1241C22—41no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22C23×#4111yescharacteristic
1250C22C22×2−1+411yescharacteristic
1251C22C2×#58511yescharacteristic
1252C22H(7,𝔽2)12yes—
1253C222−1+612yes—
1254C4—22no—
1255C4—24no—
1256C4—24no—
1257C4—22no—
1258C4—22no—
1259C4—44no—
1260C4—42no—
1261C4—44no—
1262C4—42no—
1263C4—44no—
1264C4—42no—
1265C4—42no—
1266C4—41no—
1267C4—44no—
1268C4—44no—
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4—44no—
1273C4—42no—
1274C4—42no—
1275C4—44no—
1276C4—42no—
1277C4—41no—
1278C4#350714yes—
1279C2—42no—
1280C2—84no—
1281C2C2×#350711yescharacteristic
1282C2#6285712yes—
1283C2#6288111yescharacteristic
1284C2#6288212yes—
1285C2#6288911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2619C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #49111C2semidirect
2. #49054C2semidirect
3. #48274C2semidirect
4. #48209C2semidirect
5. #47349C2semidirect
6. #47345C2semidirect
7. #47341C2semidirect
8. #47337C2semidirect
9. #39765C2semidirect
10. #39761C2semidirect
11. #39643C2semidirect
12. #39630C2semidirect
13. #38237C2semidirect
14. #38236C2semidirect
15. #38229C2semidirect
16. #38228C2semidirect
17. #37522C2semidirect
19. #37382C2semidirect
21. #37275C2semidirect
23. #35299C2semidirect
24. #35284C2semidirect
25. #35270C2semidirect
26. #34419C2semidirect
27. #34074C2semidirect

Maximal subgroups

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

subgroupindex
#491112
#490542
#482742
#482092
#473492
#473452
#473412
#473372
#397652
#397612
#396432
#396302
#382372
#382362
#382292
#382282
#375222
#375202
#373822
#372862
#372752
#353312
#352992
#352842
#352702
#344192
#340742