Finite Group Databasebeta

← #7658868

Subgroups — #7658868

Order 512.

4432 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42955C211yesmaximal, characteristic, complemented
2#42929C211yesmaximal, characteristic, complemented
3#42911C212yesmaximal, complemented
4#42776C212yesmaximal, complemented
5#42771C212yesmaximal, complemented
6#42747C212yesmaximal, complemented
7#42743C212yesmaximal, complemented
8#42403C212yesmaximal, complemented
9#42354C214yesmaximal, complemented
10#42337C212yesmaximal, complemented
11#41923C214yesmaximal, complemented
12#41918C214yesmaximal, complemented
13#41911C214yesmaximal, complemented
14#41905C214yesmaximal, complemented
15#37638C212yesmaximal, complemented
16#37584C214yesmaximal, complemented
17#37514C211yesmaximal, characteristic, complemented
18#37495C212yesmaximal, complemented
19#36697C212yesmaximal, complemented
20#36670C211yesmaximal, characteristic
21#36080C212yesmaximal, complemented
22#35949C212yesmaximal, complemented
23#35901C212yesmaximal, complemented
24#35804C212yesmaximal, complemented
25#35773C212yesmaximal, complemented
26#35749C211yesmaximal, characteristic, complemented
27#35738C211yesmaximal, characteristic, complemented
28#34307C212yesmaximal, complemented
29#34276C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×#556C2212yes—
32C2×#554C2211yescharacteristic
33C2×#552C2212yes—
34C2×#536C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37#2843C2212yes—
38#2839C2214yes—
39#2838C2214yes—
40#2837C2214yes—
41#2836C2214yes—
42#2833C2211yescharacteristic
43#2833C2212yes—
44#2833C2214yes—
45#2832C2211yescharacteristic
46#2831C2212yes—
47#2831C2214yes—
48#2830C2211yescharacteristic
49#2830C2212yes—
50#2829C2212yes—
51#2828C2211yescharacteristic
52#2827C2212yes—
53#2826C2212yes—
54#2825C2212yes—
55#2824C2212yes—
56#2823C2212yes—
57#2821C2214yes—
58#2799C2214yes—
59#2798C2214yes—
60#2793C2214yes—
61#2791C2214yes—
62#2779C2214yes—
63#2777C2214yes—
64#2773C2214yes—
65#2768C2214yes—
66#2768C2214yes—
67#2767C2214yes—
68#2764C2214yes—
69#2763C2214yes—
70#2763C2212yes—
71#2761C2214yes—
72#2758C2214yes—
73#2753C2214yes—
74#2742C2212yes—
75#2739C2214yes—
76#2738C2214yes—
77#2722C2212yes—
78#2718C2214yes—
79#2718C2214yes—
80#2715C2214yes—
81#2712C2212yes—
82#2710C2214yes—
83#2710C2214yes—
84#2667C2214yes—
85#2666C2214yes—
86#2666C2214yes—
87#2665C2214yes—
88#2664C2214yes—
89#2663C2214yes—
90#2662C2214yes—
91#2653C2214yes—
92#2653C2214yes—
93#2653C2214yes—
94#2650C2214yes—
95#2650C2214yes—
96#2649C2214yes—
97#2649C2214yes—
98#2647C2214yes—
99#2647C2214yes—
100#2646C2214yes—
101#2645C2214yes—
102#2645C2214yes—
103#2645C2212yes—
104#2643C2214yes—
105#2642C2212yes—
106#2637C2214yes—
107#2634C2212yes—
108#2634C2214yes—
109#2634C2212yes—
110#2632C2214yes—
111#2628C2211yescharacteristic
112#2625C2212yes—
113#2621C2212yes—
114#2621C2211yescharacteristic
115#2616C2212yes—
116#2611C2214yes—
117#2611C2212yes—
118#2611C2212yes—
119#2604C2214yes—
120#2602C2214yes—
121#2599C2212yes—
122#2598C2212yes—
123#2598C2214yes—
124#2596C2214yes—
125#2594C2214yes—
126#2593C2212yes—
127#2590C2214yes—
128#2588C2214yes—
129#2586C2212yes—
130#2584C2212yes—
131#2582C2212yes—
132#2581C2211yescharacteristic
133#2571C2212yes—
134#2568C2211yescharacteristic
135#2567C2214yes—
136#2562C2214yes—
137#2560C2214yes—
138#2558C2214yes—
139#2558C2214yes—
140#2556C2214yes—
141#2550C2212yes—
142#2546C2211yescharacteristic
143#2542C2212yes—
144#2542C2212yes—
145#2536C2211yescharacteristic
146#2533C2214yes—
147#2532C2214yes—
148#2532C2214yes—
149#2531C2214yes—
150#2530C2214yes—
151#2529C2214yes—
152#2527C2214yes—
153#2526C2214yes—
154#2523C2214yes—
155#2519C2214yes—
156#2518C2214yes—
157#2514C2214yes—
158#2514C2214yes—
159#2514C2212yes—
160#2510C2214yes—
161#2508C2212yes—
162#2508C2212yes—
163#2506C2214yes—
164#2506C2214yes—
165#2506C2214yes—
166#2505C2214yes—
167#2503C2212yes—
168#2499C2214yes—
169#2494C2212yes—
170#2492C2212yes—
171#2492C2212yes—
172#2492C2212yes—
173#2489C2212yes—
174#2487C2212yes—
175#2477C2214yes—
176#2475C2214yes—
177#2468C2214yes—
178#2468C2214yes—
179#2465C2214yes—
180#2462C2214yes—
181#2457C2214yes—
182#2457C2214yes—
183#2451C2212yes—
184#2446C2212yes—
185#2446C2212yes—
186#2442C2212yes—
187#2442C2212yes—
188#2439C2212yes—
189#2434C2212yes—
190#2429C2212yes—
191#2429C2212yes—
192#2429C2212yes—
193#2429C2212yes—
194#2429C2212yes—
195#2421C2212yes—
196#2421C2212yes—
197#2417C2212yes—
198#2417C2212yes—
199#2415C2212yes—
200#2415C2212yes—
201#2415C2212yes—
202#2409C2212yes—
203#2402C2214yes—
204#2401C2212yes—
205#2401C2214yes—
206#2399C2212yes—
207#2398C2212yes—
208#2398C2212yes—
209#2396C2211yescharacteristic
210#2396C2214yes—
211#2396C2214yes—
212#2395C2212yes—
213#2395C2214yes—
214#2392C2212yes—
215#2392C2211yescharacteristic
216#2388C2212yes—
217#2373C2214yes—
218#2373C2214yes—
219#2372C2214yes—
220#2369C2212yes—
221#2365C2212yes—
222#2362C2212yes—
223#2362C2212yes—
224#2362C2212yes—
225#2362C2212yes—
226#2360C2212yes—
227#2360C2212yes—
228#2360C2212yes—
229#2360C2212yes—
230#2359C2214yes—
231#2359C2214yes—
232#2356C2212yes—
233#2356C2214yes—
234#2356C2211yescharacteristic
235#2356C2211yescharacteristic
236#2352C2212yes—
237#2352C2212yes—
238#2347C2212yes—
239#2347C2212yes—
240#2346C2212yes—
241#2337C2214yes—
242#2334C2214yes—
243#2331C2212yes—
244#2327C2212yes—
245#2326C2212yes—
246#2323C2212yes—
247#2317C2211yescharacteristic
248C4×C4⋊Q8C2212yes—
249C4×#126C2214yes—
250C4×#124C2212yes—
251C4×C22⋊Q8C2212yes—
252#2297C2211yescharacteristic
253#2295C2214yes—
254C2×#391C2211yescharacteristic
255#2290C2212yes—
256#2276C2212yes—
257#2274C2212yes—
258C4×#117C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261#557—44no—
262#556—216no—
263#554—44no—
264#552—48no—
265#536—28no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#124C2312yes—
281C2×#124C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294#520—44no—
295#519—44no—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2311yescharacteristic
319C2×#117C2311yescharacteristic
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2314yes—
323C2×#117C2312yes—
324C2×#117C2311yescharacteristic
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2312yes—
328C22×C42C2311yescharacteristic
329#401C2312yes—
330#401C2314yes—
331#401C2314yes—
332#401C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2312yes—
341#400C2312yes—
342#400C2312yes—
343#400C2311yescharacteristic
344#400C2312yes—
345#400C2314yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2311yescharacteristic
371#399C2312yes—
372#399C2314yes—
373#399C2312yes—
374#399C2314yes—
375#399C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2311yescharacteristic
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2312yes—
400#398C2312yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2312yes—
408#397C2312yes—
409#397C2312yes—
410#397C2312yes—
411#397C2312yes—
412#397C2312yes—
413#397C2312yes—
414#397C2311yescharacteristic
415#397C2312yes—
416#397C2312yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2312yes—
423#397C2314yes—
424#397C2312yes—
425#397C2314yes—
426#397C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2312yes—
431#396C2312yes—
432#396C2312yes—
433#396C2312yes—
434#396C2312yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2312yes—
443#395C2314yes—
444#395C2314yes—
445#395C2311yescharacteristic
446#395C2312yes—
447#395C2312yes—
448#395C2314yes—
449#395C2314yes—
450#395C2314yes—
451#394C2312yes—
452#394C2312yes—
453#394C2314yes—
454#394C2311yescharacteristic
455#394C2314yes—
456#394C2312yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2314yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#393C2314yes—
471#393C2312yes—
472#393C2314yes—
473#393C2311yescharacteristic
474#393C2312yes—
475#393C2312yes—
476#393C2312yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#392C2312yes—
481#392C2311yescharacteristic
482#392C2312yes—
483#392C2312yes—
484#392C2312yes—
485#391C2314yes—
486#391C2311yescharacteristic
487#391C2312yes—
488#391C2314yes—
489#391C2314yes—
490#391C2312yes—
491#391C2314yes—
492#391C2311yescharacteristic
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2314yes—
497#391C2314yes—
498#391C2314yes—
499#391C2314yes—
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2314yes—
510#390C2314yes—
511#390C2311yescharacteristic
512#390C2311yescharacteristic
513#390C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#388C2312yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
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#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#386C2314yes—
615#386C2312yes—
616#386C2312yes—
617#386C2312yes—
618#386C2312yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#385C2312yes—
625#385C2312yes—
626#385C2312yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#384C2312yes—
640#384C2314yes—
641#384C2314yes—
642#383C2314yes—
643#383C2314yes—
644#383C2314yes—
645#383C2312yes—
646#383C2312yes—
647#383C2314yes—
648#382C2312yes—
649#382C2314yes—
650#382C2314yes—
651#382C2312yes—
652#382C2311yescharacteristic
653#382C2314yes—
654#382C2312yes—
655#382C2311yescharacteristic
656#382C2314yes—
657#381C2314yes—
658#381C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710#376C2312yes—
711#376C2312yes—
712#376C2314yes—
713#376C2314yes—
714#376C2312yes—
715#376C2312yes—
716#376C2314yes—
717C2×#95C2314yes—
718C43C2312yes—
719C2×#41—24no—
720C2×#41—42no—
721C2×#41—42no—
722C22×Q8—24no—
723C22×Q8—42no—
724C22×Q8—42no—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2414yes—
731C22×Q8C2411yescharacteristic
732C22×Q8C2412yes—
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2412yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2414yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C4⋊Q8—28no—
748C4⋊Q8—28no—
749C4⋊Q8—42no—
750C4⋊Q8—44no—
751C4⋊Q8—42no—
752C4⋊Q8—44no—
753#126—216no—
754#126—216no—
755#126—48no—
756#125—48no—
757#125—44no—
758#125—44no—
759#125—44no—
760#125—48no—
761#124—216no—
762#124—28no—
763#123—216no—
764#123—48no—
765C22⋊Q8—28no—
766C22⋊Q8—28no—
767C22⋊Q8—28no—
768C22⋊Q8—28no—
769C22⋊Q8—48no—
770C22⋊Q8—44no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775C4×Q8—28no—
776C4×Q8—24no—
777C4×Q8—24no—
778C4×Q8—28no—
779C4×Q8—216no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—42no—
784C4×Q8—44no—
785C4×Q8—44no—
786C4×Q8—42no—
787C4×Q8—42no—
788C4×D4—28no—
789C4×D4—48no—
790C4×D4—44no—
791C4×D4—44no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—42no—
795#117—28no—
796#117—24no—
797#117—28no—
798#117—44no—
799#117—42no—
800#117—48no—
801#117—44no—
802#117—44no—
803#117#4118yes—
804C2×C4⋊C4—28no—
805C2×C4⋊C4—44no—
806C2×C4⋊C4—42no—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C42—42no—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2411yescharacteristic
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2411yescharacteristic
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2411yescharacteristic
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2411yescharacteristic
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2411yescharacteristic
948#95C2411yescharacteristic
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2411yescharacteristic
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2411yescharacteristic
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015C24C2512yes—
1016C24C2512yes—
1017C24C2511yescharacteristic
1018#41—416no—
1019C2×Q8—24no—
1020C2×Q8—22no—
1021C2×Q8—22no—
1022C2×Q8—24no—
1023C2×Q8—22no—
1024C2×Q8—28no—
1025C2×Q8—22no—
1026C2×Q8—22no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—22no—
1030C2×Q8—22no—
1031C2×Q8—41no—
1032C2×Q8—42no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—41no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—42no—
1040C2×Q8—44no—
1041C2×Q8—416no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—22no—
1045C2×D4—41no—
1046C2×D4—41no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C2×D4—41no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C22×C4—22no—
1060C22×C4—22no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—28no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4C2×#4114yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2512yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—22no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—41no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—41no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4C2×#4118yes—
1169C4⋊C4H(5,𝔽2)14yes—
1170C22⋊C4—24no—
1171C22⋊C4—28no—
1172C22⋊C4—28no—
1173C22⋊C4—24no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—42no—
1183C22⋊C4—44no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—41no—
1201C22⋊C4—41no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4C2×#4118yes—
1213C42—28no—
1214C42—24no—
1215C42—28no—
1216C42—28no—
1217C42—24no—
1218C42—24no—
1219C42—22no—
1220C42—24no—
1221C42—22no—
1222C42—28no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—41no—
1227C42—41no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—42no—
1236C42—42no—
1237C42—44no—
1238C42C2×#4118yes—
1239C23—21no—
1240C23—21no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23C22×#4112yes—
1258C23C2611yescharacteristic
1259Q8—48no—
1260Q8—44no—
1261Q8—44no—
1262Q8—48no—
1263Q8—44no—
1264Q8—44no—
1265Q8—88no—
1266Q8—162no—
1267D4—44no—
1268D4—48no—
1269D4—44no—
1270D4—84no—
1271D4—84no—
1272D4—84no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—28no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—48no—
1341C2×C4—48no—
1342C2×C4—48no—
1343C2×C4—88no—
1344C2×C4—84no—
1345C2×C4—162no—
1346C2×C4—164no—
1347C2×C4C22×#4118yes—
1348C2×C4C22×#4112yes—
1349C2×C4C22×#4112yes—
1350C2×C4C2×H(5,𝔽2)14yes—
1351C2×C4C2×H(5,𝔽2)12yes—
1352C2×C4#58512yes—
1353C22—24no—
1354C22—22no—
1355C22—41no—
1356C22—42no—
1357C22—41no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22C23×#4111yescharacteristic
1373C22C22×H(5,𝔽2)11yescharacteristic
1374C22C2×#58511yescharacteristic
1375C222−1+612yes—
1376C222−1+612yes—
1377C4—24no—
1378C4—28no—
1379C4—22no—
1380C4—42no—
1381C4—44no—
1382C4—41no—
1383C4—42no—
1384C4—41no—
1385C4—42no—
1386C4—44no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—41no—
1391C4—44no—
1392C4—42no—
1393C4—41no—
1394C4—42no—
1395C4—42no—
1396C4—44no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—44no—
1402C4#346014yes—
1403C2—42no—
1404C2—82no—
1405C2—82no—
1406C2C2×#346011yescharacteristic
1407C2#6286112yes—
1408C2#6304811yescharacteristic
1409C2#6305312yes—
1410C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36670C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42955C2semidirect
2. #42929C2semidirect
3. #42911C2semidirect
4. #42776C2semidirect
5. #42771C2semidirect
6. #42747C2semidirect
7. #42743C2semidirect
8. #42403C2semidirect
9. #42354C2semidirect
10. #42337C2semidirect
11. #41923C2semidirect
12. #41918C2semidirect
13. #41911C2semidirect
14. #41905C2semidirect
15. #37638C2semidirect
16. #37584C2semidirect
17. #37514C2semidirect
18. #37495C2semidirect
19. #36697C2semidirect
21. #36080C2semidirect
22. #35949C2semidirect
23. #35901C2semidirect
24. #35804C2semidirect
25. #35773C2semidirect
26. #35749C2semidirect
27. #35738C2semidirect
28. #34307C2semidirect
29. #34276C2semidirect

Maximal subgroups

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

subgroupindex
#429552
#429292
#429112
#427762
#427712
#427472
#427432
#424032
#423542
#423372
#419232
#419182
#419112
#419052
#376382
#375842
#375142
#374952
#366972
#366702
#360802
#359492
#359012
#358042
#357732
#357492
#357382
#343072
#342762