Finite Group Databasebeta

← #8701678

Subgroups — #8701678

Order 512.

3877 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59927C212yesmaximal, complemented
2#59402C212yesmaximal
3#59330C212yesmaximal, complemented
4#59245C212yesmaximal, complemented
5#55855C214yesmaximal, complemented
6#55282C214yesmaximal
7#54911C214yesmaximal, complemented
8#52304C211yesmaximal, characteristic
9#50568C214yesmaximal, complemented
10#50333C214yesmaximal, complemented
11#49535C214yesmaximal, complemented
12#46157C211yesmaximal, characteristic, complemented
13#46023C211yesmaximal, characteristic
14#46006C211yesmaximal, characteristic, complemented
15#45342C212yesmaximal, complemented
16#45284C212yesmaximal, complemented
17#45276C212yesmaximal, complemented
18#42854C212yesmaximal, complemented
19#42597C212yesmaximal, complemented
20#42511C212yesmaximal, complemented
21#40220C212yesmaximal, complemented
22#39939C212yesmaximal
23#39667C212yesmaximal, complemented
24#37153C212yesmaximal
25#37146C212yesmaximal, complemented
26#37143C212yesmaximal
27#36447C211yesmaximal, characteristic, complemented
28#36313C211yesmaximal, characteristic, complemented
29#36312C211yesmaximal, characteristic
30#2863C2212yes—
31#2862C2211yescharacteristic
32#2860C2212yes—
33#2859C2212yes—
34#2859C2211yescharacteristic
35#2859C2211yescharacteristic
36#2855C2212yes—
37#2844C2212yes—
38#2839C2214yes—
39#2836C2214yes—
40#2831C2214yes—
41#2822C2212yes—
42#2820C2212yes—
43#2810C2212yes—
44#2810C2214yes—
45#2809C2214yes—
46#2809C2214yes—
47#2808C2212yes—
48#2807C2214yes—
49#2806C2212yes—
50#2805C2212yes—
51#2805C2211yescharacteristic
52#2805C2211yescharacteristic
53#2798C2214yes—
54#2794C2214yes—
55#2793C2214yes—
56#2793C2214yes—
57#2791C2214yes—
58#2790C2214yes—
59#2789C2212yes—
60#2788C2214yes—
61#2788C2214yes—
62#2783C2214yes—
63#2783C2214yes—
64#2777C2214yes—
65#2776C2214yes—
66#2776C2214yes—
67#2776C2214yes—
68#2775C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2774C2214yes—
72#2772C2214yes—
73#2772C2214yes—
74#2772C2214yes—
75#2767C2214yes—
76#2767C2214yes—
77#2767C2214yes—
78#2765C2212yes—
79#2765C2212yes—
80#2762C2214yes—
81#2762C2214yes—
82#2758C2214yes—
83#2755C2214yes—
84#2755C2214yes—
85#2755C2214yes—
86#2754C2214yes—
87#2754C2214yes—
88#2747C2214yes—
89#2745C2214yes—
90#2744C2214yes—
91#2739C2214yes—
92#2737C2214yes—
93#2734C2212yes—
94#2726C2212yes—
95#2724C2211yescharacteristic
96#2719C2214yes—
97#2719C2214yes—
98#2717C2212yes—
99#2716C2214yes—
100#2713C2214yes—
101#2707C2214yes—
102#2690C2214yes—
103#2690C2212yes—
104#2690C2212yes—
105#2689C2214yes—
106#2683C2211yescharacteristic
107#2667C2214yes—
108#2655C2214yes—
109#2655C2214yes—
110#2655C2214yes—
111#2652C2214yes—
112#2650C2214yes—
113#2650C2214yes—
114#2647C2212yes—
115#2637C2214yes—
116#2634C2214yes—
117#2612C2214yes—
118#2595C2214yes—
119#2594C2214yes—
120#2594C2214yes—
121#2590C2214yes—
122#2590C2214yes—
123#2590C2214yes—
124#2590C2214yes—
125#2588C2214yes—
126#2588C2214yes—
127#2588C2214yes—
128#2588C2214yes—
129#2588C2214yes—
130#2587C2214yes—
131#2586C2214yes—
132#2586C2214yes—
133#2585C2214yes—
134#2585C2214yes—
135#2585C2214yes—
136#2582C2212yes—
137#2582C2212yes—
138#2582C2211yescharacteristic
139#2581C2212yes—
140#2581C2212yes—
141#2577C2214yes—
142#2571C2212yes—
143#2571C2211yescharacteristic
144#2570C2212yes—
145#2570C2214yes—
146#2570C2212yes—
147#2570C2212yes—
148#2568C2212yes—
149#2568C2211yescharacteristic
150#2567C2212yes—
151#2558C2214yes—
152#2552C2212yes—
153#2552C2211yescharacteristic
154#2551C2212yes—
155#2546C2211yescharacteristic
156#2538C2211yescharacteristic
157#2533C2214yes—
158#2530C2214yes—
159#2529C2214yes—
160#2529C2214yes—
161#2528C2214yes—
162#2528C2214yes—
163#2525C2214yes—
164#2524C2214yes—
165#2524C2214yes—
166#2520C2214yes—
167#2519C2214yes—
168#2515C2214yes—
169#2514C2212yes—
170#2514C2214yes—
171#2514C2212yes—
172#2511C2212yes—
173#2511C2212yes—
174#2511C2212yes—
175#2511C2214yes—
176#2511C2212yes—
177#2509C2212yes—
178#2509C2212yes—
179#2508C2212yes—
180#2508C2212yes—
181#2508C2214yes—
182#2508C2212yes—
183#2507C2212yes—
184#2507C2212yes—
185#2506C2212yes—
186#2506C2212yes—
187#2506C2214yes—
188#2499C2212yes—
189#2499C2212yes—
190#2497C2212yes—
191#2497C2214yes—
192#2496C2212yes—
193#2494C2212yes—
194#2492C2214yes—
195#2462C2214yes—
196#2453C2212yes—
197#2451C2212yes—
198#2448C2212yes—
199#2446C2214yes—
200#2446C2212yes—
201#2446C2212yes—
202#2439C2212yes—
203#2439C2212yes—
204#2439C2212yes—
205#2429C2212yes—
206#2429C2212yes—
207#2429C2212yes—
208#2423C2212yes—
209#2423C2212yes—
210#2421C2212yes—
211#2421C2212yes—
212#2415C2212yes—
213#2401C2212yes—
214#2401C2212yes—
215#2399C2212yes—
216#2382C2212yes—
217#2382C2212yes—
218#2382C2212yes—
219#2371C2214yes—
220#2370C2214yes—
221#2369C2214yes—
222#2365C2212yes—
223#2365C2211yescharacteristic
224#2365C2212yes—
225#2365C2211yescharacteristic
226#2362C2212yes—
227#2362C2212yes—
228#2362C2212yes—
229#2356C2212yes—
230#2355C2212yes—
231#2354C2211yescharacteristic
232#2351C2212yes—
233#2351C2212yes—
234Q8×C4⋊C4C2211yescharacteristic
235Q8×C4⋊C4C2212yes—
236Q8×C4⋊C4C2211yescharacteristic
237Q8×C4⋊C4C2211yescharacteristic
238#2347C2212yes—
239#2346C2212yes—
240#2336C2214yes—
241#2334C2214yes—
242#2332C2214yes—
243#2331C2212yes—
244#2327C2212yes—
245#2320C2212yes—
246C4×#125C2212yes—
247C4×#125C2211yescharacteristic
248C4×#125C2211yescharacteristic
249C4×#124C2211yescharacteristic
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×#123C2212yes—
255#2295C2212yes—
256#2295C2212yes—
257#2285C2212yes—
258C42×Q8C2211yescharacteristic
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2314yes—
264C2×#126C2314yes—
265C2×#125C2312yes—
266C2×#125C2311yescharacteristic
267C2×#125C2311yescharacteristic
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#124C2311yescharacteristic
273C2×#123C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×D4C2311yescharacteristic
292C2×#117C2312yes—
293C2×#117C2312yes—
294C22×C42C2312yes—
295#401C2314yes—
296#401C2314yes—
297#401C2312yes—
298#401C2312yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
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#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#399C2314yes—
340#399C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2312yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2312yes—
387#397C2312yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2312yes—
396#396C2312yes—
397#396C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2312yes—
404#395C2312yes—
405#395C2314yes—
406#395C2314yes—
407#395C2312yes—
408#395C2312yes—
409#394C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2312yes—
441#391C2314yes—
442#391C2311yescharacteristic
443#390C2312yes—
444#390C2311yescharacteristic
445#390C2312yes—
446#389C2311yescharacteristic
447#389C2311yescharacteristic
448#389C2312yes—
449#389C2311yescharacteristic
450#389C2311yescharacteristic
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2312yes—
527#388C2312yes—
528#388C2312yes—
529#387C2314yes—
530#387C2314yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
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#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2312yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#386C2312yes—
611#385C2312yes—
612#385C2312yes—
613#385C2314yes—
614#385C2312yes—
615#385C2314yes—
616#385C2312yes—
617#385C2312yes—
618#385C2314yes—
619#384C2311yescharacteristic
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2314yes—
623#384C2311yescharacteristic
624#384C2312yes—
625#384C2312yes—
626#384C2311yescharacteristic
627#384C2312yes—
628#384C2312yes—
629#383C2314yes—
630#383C2314yes—
631#383C2314yes—
632#383C2314yes—
633#382C2311yescharacteristic
634#382C2312yes—
635#382C2311yescharacteristic
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2314yes—
643#382C2314yes—
644#382C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#382C2314yes—
650#382C2314yes—
651#382C2311yescharacteristic
652#381C2314yes—
653#381C2312yes—
654#380C2314yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707#376C2312yes—
708#376C2314yes—
709#376C2314yes—
710C43C2311yescharacteristic
711C43C2312yes—
712C22×Q8C2412yes—
713C22×Q8C2411yescharacteristic
714C22×Q8C2411yescharacteristic
715C22×Q8C2412yes—
716C22×Q8C2412yes—
717C22×Q8C2414yes—
718C22×D4C2411yescharacteristic
719C23×C4C2412yes—
720C23×C4C2412yes—
721C23×C4C2412yes—
722C4⋊Q8—28no—
723C4⋊Q8—44no—
724C4⋊Q8—42no—
725C4⋊Q8—42no—
726C4⋊Q8—48no—
727#126—48no—
728#125—28no—
729#125—24no—
730#125—48no—
731#125—44no—
732#125—42no—
733#125—44no—
734#125—48no—
735#124—42no—
736#123—44no—
737C22⋊Q8—28no—
738C22⋊Q8—28no—
739C22⋊Q8—44no—
740C22⋊Q8—44no—
741C22⋊Q8—44no—
742C4×Q8—24no—
743C4×Q8—44no—
744C4×Q8—42no—
745C4×Q8—44no—
746C4×Q8—44no—
747C4×Q8—42no—
748C4×Q8—44no—
749C4×Q8—44no—
750C4×Q8—44no—
751C4×Q8—44no—
752C4×Q8—44no—
753C4×Q8—42no—
754C4×D4—42no—
755#117—44no—
756#117—44no—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C42—44no—
858C2×C42C2411yescharacteristic
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2411yescharacteristic
866C2×C42C2411yescharacteristic
867C2×C42C2412yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2412yes—
871C2×C42C2411yescharacteristic
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2411yescharacteristic
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2414yes—
893#95C2414yes—
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977C24C2512yes—
978C2×Q8—24no—
979C2×Q8—24no—
980C2×Q8—22no—
981C2×Q8—22no—
982C2×Q8—24no—
983C2×Q8—22no—
984C2×Q8—24no—
985C2×Q8—24no—
986C2×Q8—41no—
987C2×Q8—41no—
988C2×Q8—42no—
989C2×Q8—42no—
990C2×Q8—42no—
991C2×Q8—42no—
992C2×Q8—44no—
993C2×Q8—44no—
994C2×Q8—44no—
995C2×Q82−1+414yes—
996C2×D4—22no—
997C2×D4—41no—
998C2×D4—41no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2514yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2512yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2512yes—
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2514yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2511yescharacteristic
1036C4⋊C4—24no—
1037C4⋊C4—22no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—22no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—22no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—22no—
1055C4⋊C4—24no—
1056C4⋊C4—22no—
1057C4⋊C4—24no—
1058C4⋊C4—22no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—42no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—42no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—42no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—41no—
1076C4⋊C4—42no—
1077C4⋊C4—41no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C42−1+414yes—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—42no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C42—24no—
1137C42—22no—
1138C42—24no—
1139C42—22no—
1140C42—24no—
1141C42—24no—
1142C42—24no—
1143C42—22no—
1144C42—24no—
1145C42—24no—
1146C42—24no—
1147C42—24no—
1148C42—22no—
1149C42—22no—
1150C42—22no—
1151C42—42no—
1152C42—42no—
1153C42—41no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—42no—
1159C42—42no—
1160C42—44no—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23C2611yescharacteristic
1176Q8—28no—
1177Q8—44no—
1178Q8—48no—
1179Q8—84no—
1180Q8—84no—
1181Q8—164no—
1182D4—82no—
1183C2×C4—21no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—24no—
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—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—48no—
1260C2×C4—84no—
1261C2×C4—84no—
1262C2×C4C2×2−1+412yes—
1263C2×C4C2×2−1+414yes—
1264C2×C4C2×2−1+414yes—
1265C2×C4C2×2−1+412yes—
1266C2×C4#58512yes—
1267C2×C4#58512yes—
1268C2×C4#58512yes—
1269C2×C4#58512yes—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22C22×2−1+411yescharacteristic
1278C22C22×2−1+411yescharacteristic
1279C22C2×#58511yescharacteristic
1280C22C2×#58511yescharacteristic
1281C22C2×#58511yescharacteristic
1282C22C2×#58511yescharacteristic
1283C222−1+611yescharacteristic
1284C4—24no—
1285C4—24no—
1286C4—22no—
1287C4—22no—
1288C4—22no—
1289C4—42no—
1290C4—44no—
1291C4—42no—
1292C4—41no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—41no—
1298C4—41no—
1299C4—42no—
1300C4—44no—
1301C4—42no—
1302C4—44no—
1303C4—44no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—44no—
1309C4—44no—
1310C4—42no—
1311C4#355314yes—
1312C2—82no—
1313C2C2×#355311yescharacteristic
1314C2#6290711yescharacteristic
1315C2#6294711yescharacteristic
1316C2#6296411yescharacteristic
1317C2#6302511yescharacteristic
1318C2#6303411yescharacteristic
1319C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59927C2semidirect
3. #59330C2semidirect
4. #59245C2semidirect
5. #55855C2semidirect
7. #54911C2semidirect
9. #50568C2semidirect
10. #50333C2semidirect
11. #49535C2semidirect
12. #46157C2semidirect
14. #46006C2semidirect
15. #45342C2semidirect
16. #45284C2semidirect
17. #45276C2semidirect
18. #42854C2semidirect
19. #42597C2semidirect
20. #42511C2semidirect
21. #40220C2semidirect
23. #39667C2semidirect
25. #37146C2semidirect
27. #36447C2semidirect
28. #36313C2semidirect

Maximal subgroups

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

subgroupindex
#599272
#594022
#593302
#592452
#558552
#552822
#549112
#523042
#505682
#503332
#495352
#461572
#460232
#460062
#453422
#452842
#452762
#428542
#425972
#425112
#402202
#399392
#396672
#371532
#371462
#371432
#364472
#363132
#363122