Finite Group Databasebeta

← #8701636

Subgroups — #8701636

Order 512.

4315 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59880C212yesmaximal
2#59425C212yesmaximal, complemented
3#59096C212yesmaximal, complemented
4#59036C212yesmaximal, complemented
5#55203C214yesmaximal, complemented
6#54417C214yesmaximal, complemented
7#53936C214yesmaximal, complemented
8#52303C211yesmaximal, characteristic
9#51493C214yesmaximal, complemented
10#49675C214yesmaximal, complemented
11#48952C214yesmaximal, complemented
12#46023C211yesmaximal, characteristic, complemented
13#46006C211yesmaximal, characteristic, complemented
14#46004C211yesmaximal, characteristic, complemented
15#45390C212yesmaximal, complemented
16#45116C212yesmaximal, complemented
17#45078C212yesmaximal, complemented
18#42866C212yesmaximal, complemented
19#42807C212yesmaximal, complemented
20#42672C212yesmaximal, complemented
21#39855C212yesmaximal, complemented
22#38999C212yesmaximal, complemented
23#38974C212yesmaximal, complemented
24#37208C212yesmaximal, complemented
25#37195C212yesmaximal, complemented
26#37136C212yesmaximal, complemented
27#36446C211yesmaximal, characteristic, complemented
28#36313C211yesmaximal, characteristic, complemented
29#36299C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×D4×Q8C2211yescharacteristic
32C2×D4×Q8C2212yes—
33C2×#533C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2862C2212yes—
37#2862C2211yescharacteristic
38#2862C2211yescharacteristic
39#2859C2211yescharacteristic
40#2851C2212yes—
41#2844C2212yes—
42#2844C2212yes—
43#2838C2214yes—
44#2831C2214yes—
45#2820C2212yes—
46#2817C2214yes—
47#2811C2212yes—
48#2808C2211yescharacteristic
49#2808C2212yes—
50#2806C2212yes—
51#2806C2211yescharacteristic
52#2805C2212yes—
53#2804C2212yes—
54#2799C2214yes—
55#2789C2214yes—
56#2786C2214yes—
57#2783C2214yes—
58#2783C2212yes—
59#2781C2212yes—
60#2775C2214yes—
61#2775C2214yes—
62#2775C2214yes—
63#2774C2214yes—
64#2774C2214yes—
65#2774C2214yes—
66#2773C2214yes—
67#2772C2214yes—
68#2768C2214yes—
69#2767C2214yes—
70#2763C2214yes—
71#2763C2214yes—
72#2763C2214yes—
73#2762C2214yes—
74#2762C2214yes—
75#2759C2214yes—
76#2759C2214yes—
77#2758C2214yes—
78#2758C2214yes—
79#2757C2214yes—
80#2755C2214yes—
81#2755C2214yes—
82#2754C2214yes—
83#2751C2214yes—
84#2745C2214yes—
85#2744C2212yes—
86#2744C2214yes—
87#2743C2214yes—
88#2739C2214yes—
89#2738C2214yes—
90#2737C2214yes—
91#2734C2212yes—
92#2734C2214yes—
93#2732C2211yescharacteristic
94#2731C2214yes—
95#2730C2212yes—
96#2729C2214yes—
97#2729C2214yes—
98#2728C2214yes—
99#2719C2214yes—
100#2713C2214yes—
101#2713C2214yes—
102#2713C2214yes—
103#2704C2214yes—
104#2694C2212yes—
105#2692C2214yes—
106#2692C2214yes—
107#2690C2214yes—
108#2686C2212yes—
109#2682C2211yescharacteristic
110#2677C2214yes—
111#2666C2214yes—
112#2666C2214yes—
113#2655C2214yes—
114#2652C2214yes—
115#2650C2214yes—
116#2643C2214yes—
117#2638C2214yes—
118#2638C2214yes—
119#2634C2214yes—
120#2621C2212yes—
121#2612C2214yes—
122#2612C2214yes—
123#2611C2214yes—
124#2610C2214yes—
125#2607C2214yes—
126#2605C2214yes—
127#2605C2214yes—
128#2600C2214yes—
129#2599C2214yes—
130#2595C2214yes—
131#2588C2214yes—
132#2582C2211yescharacteristic
133#2581C2212yes—
134#2573C2214yes—
135#2572C2214yes—
136#2568C2211yescharacteristic
137#2568C2212yes—
138#2568C2211yescharacteristic
139#2568C2212yes—
140#2567C2212yes—
141#2565C2212yes—
142#2563C2212yes—
143#2551C2212yes—
144#2550C2214yes—
145#2550C2212yes—
146#2549C2214yes—
147#2547C2211yescharacteristic
148#2547C2212yes—
149#2546C2211yescharacteristic
150#2538C2212yes—
151#2538C2211yescharacteristic
152#2528C2214yes—
153#2527C2214yes—
154#2527C2214yes—
155#2527C2214yes—
156#2527C2214yes—
157#2526C2214yes—
158#2525C2214yes—
159#2524C2214yes—
160#2515C2214yes—
161#2514C2212yes—
162#2514C2212yes—
163#2514C2212yes—
164#2514C2212yes—
165#2511C2212yes—
166#2511C2212yes—
167#2509C2212yes—
168#2505C2214yes—
169#2503C2212yes—
170#2499C2212yes—
171#2495C2212yes—
172#2493C2214yes—
173#2493C2214yes—
174#2492C2212yes—
175#2492C2212yes—
176#2492C2212yes—
177#2489C2214yes—
178#2489C2214yes—
179#2489C2212yes—
180#2489C2212yes—
181#2489C2212yes—
182#2475C2214yes—
183#2465C2214yes—
184#2465C2214yes—
185#2465C2214yes—
186#2458C2214yes—
187#2454C2214yes—
188#2453C2212yes—
189#2451C2214yes—
190#2451C2212yes—
191#2450C2214yes—
192#2447C2212yes—
193#2446C2212yes—
194#2446C2212yes—
195#2446C2212yes—
196#2446C2212yes—
197#2444C2214yes—
198#2439C2214yes—
199#2439C2214yes—
200#2439C2212yes—
201#2438C2214yes—
202#2438C2214yes—
203#2434C2212yes—
204#2434C2212yes—
205#2434C2212yes—
206#2429C2212yes—
207#2423C2212yes—
208#2423C2212yes—
209#2421C2212yes—
210#2421C2212yes—
211#2417C2212yes—
212#2415C2212yes—
213#2415C2212yes—
214#2409C2212yes—
215#2409C2212yes—
216#2409C2212yes—
217#2396C2212yes—
218#2395C2212yes—
219#2392C2212yes—
220#2382C2212yes—
221#2382C2212yes—
222#2379C2212yes—
223#2365C2212yes—
224#2365C2212yes—
225#2365C2211yescharacteristic
226#2365C2211yescharacteristic
227#2363C2214yes—
228#2360C2212yes—
229#2359C2214yes—
230#2356C2212yes—
231#2356C2212yes—
232#2355C2211yescharacteristic
233#2352C2212yes—
234D4×C4⋊C4C2211yescharacteristic
235#2346C2212yes—
236#2344C2212yes—
237#2343C2214yes—
238Q8×C22⋊C4C2212yes—
239Q8×C22⋊C4C2212yes—
240Q8×C22⋊C4C2212yes—
241#2327C2214yes—
242#2323C2212yes—
243#2320C2214yes—
244#2318C2214yes—
245#2314C2212yes—
246#2310C2212yes—
247C4×#125C2211yescharacteristic
248C4×#124C2211yescharacteristic
249C4×#124C2211yescharacteristic
250C4×#124C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×#123C2212yes—
254C4×#121C2212yes—
255#2295C2212yes—
256C2×#391C2212yes—
257#2293C2212yes—
258C42×Q8C2211yescharacteristic
259C23×Q8C2312yes—
260C23×Q8C2312yes—
261#557—44no—
262D4×Q8—44no—
263D4×Q8—48no—
264#533—48no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2314yes—
276C2×#125C2311yescharacteristic
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#124C2311yescharacteristic
282C2×#124C2311yescharacteristic
283C2×#124C2312yes—
284C2×#123C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×#121C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2314yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2314yes—
319C2×#117C2314yes—
320C22×C4⋊C4C2312yes—
321C22×C42C2312yes—
322#401C2314yes—
323#401C2314yes—
324#401C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#399C2314yes—
355#399C2312yes—
356#399C2314yes—
357#399C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2312yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2312yes—
398#396C2314yes—
399#396C2312yes—
400#396C2314yes—
401#396C2312yes—
402#396C2312yes—
403#396C2314yes—
404#396C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2312yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#394C2314yes—
423#394C2312yes—
424#394C2314yes—
425#394C2312yes—
426#394C2312yes—
427#394C2312yes—
428#394C2312yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2312yes—
438#393C2314yes—
439#392C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2312yes—
456#391C2314yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2312yes—
474#391C2312yes—
475#391C2311yescharacteristic
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2311yescharacteristic
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2314yes—
484#391C2314yes—
485#391C2312yes—
486#391C2314yes—
487#390C2314yes—
488#390C2314yes—
489#390C2312yes—
490#390C2311yescharacteristic
491#390C2311yescharacteristic
492#390C2312yes—
493#389C2311yescharacteristic
494#389C2311yescharacteristic
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2314yes—
544#388C2312yes—
545#388C2312yes—
546#388C2312yes—
547#388C2314yes—
548#388C2312yes—
549#388C2312yes—
550#388C2312yes—
551#388C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
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#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2312yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2312yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2312yes—
631#384C2312yes—
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#383C2314yes—
635#383C2314yes—
636#383C2314yes—
637#383C2314yes—
638#383C2314yes—
639#383C2314yes—
640#382C2311yescharacteristic
641#382C2314yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2311yescharacteristic
646#382C2312yes—
647#382C2314yes—
648#382C2314yes—
649#382C2314yes—
650#382C2312yes—
651#382C2314yes—
652#382C2311yescharacteristic
653#382C2312yes—
654#382C2312yes—
655#382C2312yes—
656#382C2312yes—
657#382C2314yes—
658#381C2314yes—
659#381C2314yes—
660#381C2314yes—
661#381C2314yes—
662#381C2314yes—
663#381C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2312yes—
675#380C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2314yes—
710#376C2314yes—
711#376C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C43C2311yescharacteristic
715C43C2312yes—
716C22×Q8—28no—
717C22×Q8—44no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8—44no—
721C22×Q8—44no—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2414yes—
730C22×Q8C2414yes—
731C22×Q8C2414yes—
732C22×D4C2412yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C4⋊Q8—28no—
744C4⋊Q8—42no—
745C4⋊Q8—44no—
746C4⋊Q8—44no—
747C4⋊Q8—42no—
748C4⋊Q8—44no—
749C4⋊Q8—42no—
750C4⋊Q8—42no—
751C4⋊Q8—44no—
752C4⋊Q8—48no—
753C4⋊Q8—48no—
754#125—24no—
755#125—44no—
756#125—44no—
757#125—48no—
758#125—48no—
759#124—24no—
760#124—44no—
761#124—42no—
762#123—28no—
763C22⋊Q8—28no—
764C22⋊Q8—48no—
765C22⋊Q8—44no—
766C22⋊Q8—48no—
767C22⋊Q8—48no—
768C22⋊Q8—44no—
769C22⋊Q8—44no—
770C22⋊Q8—44no—
771C22⋊Q8—44no—
772C22⋊Q8—48no—
773C22⋊Q8—44no—
774#121—28no—
775C4×Q8—28no—
776C4×Q8—24no—
777C4×Q8—28no—
778C4×Q8—42no—
779C4×Q8—42no—
780C4×Q8—44no—
781C4×Q8—48no—
782C4×Q8—44no—
783C4×Q8—42no—
784C4×Q8—42no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×D4—28no—
788C4×D4—44no—
789C4×D4—42no—
790C4×D4—44no—
791C4×D4—42no—
792C4×D4—44no—
793C4×D4—48no—
794#117—44no—
795#117—48no—
796#117—48no—
797#117—44no—
798C2×C4⋊C4—44no—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C42—44no—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2411yescharacteristic
928C2×C42C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24C2512yes—
1009C24C2512yes—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—28no—
1013C2×Q8—24no—
1014C2×Q8—22no—
1015C2×Q8—22no—
1016C2×Q8—22no—
1017C2×Q8—24no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—22no—
1022C2×Q8—24no—
1023C2×Q8—44no—
1024C2×Q8—41no—
1025C2×Q8—42no—
1026C2×Q8—41no—
1027C2×Q8—44no—
1028C2×Q8—42no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—41no—
1035C2×Q8—42no—
1036C2×Q8—42no—
1037C2×Q8—41no—
1038C2×Q8—44no—
1039C2×Q8—816no—
1040C2×Q8—816no—
1041C2×Q8H(5,𝔽2)14yes—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—22no—
1046C2×D4—41no—
1047C2×D4—42no—
1048C2×D4—41no—
1049C2×D4—41no—
1050C2×D4—41no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D42−1+414yes—
1054C22×C4—24no—
1055C22×C4—28no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—28no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—22no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—22no—
1122C4⋊C4—24no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—41no—
1126C4⋊C4—41no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—41no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—41no—
1138C4⋊C4—42no—
1139C4⋊C4—41no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C42−1+414yes—
1170C22⋊C4—28no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—28no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—42no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—42no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—42no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C42—24no—
1204C42—24no—
1205C42—28no—
1206C42—24no—
1207C42—22no—
1208C42—24no—
1209C42—24no—
1210C42—28no—
1211C42—22no—
1212C42—22no—
1213C42—24no—
1214C42—24no—
1215C42—24no—
1216C42—22no—
1217C42—22no—
1218C42—22no—
1219C42—42no—
1220C42—42no—
1221C42—41no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—42no—
1228C42—42no—
1229C42—44no—
1230C42—44no—
1231C23—22no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23C2×2−1+414yes—
1245C23C2611yescharacteristic
1246Q8—28no—
1247Q8—48no—
1248Q8—48no—
1249Q8—82no—
1250Q8—84no—
1251Q8—82no—
1252Q8—84no—
1253Q8—88no—
1254Q8—88no—
1255Q8—88no—
1256D4—44no—
1257D4—48no—
1258D4—44no—
1259D4—84no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—48no—
1334C2×C4—48no—
1335C2×C4—48no—
1336C2×C4—88no—
1337C2×C4—88no—
1338C2×C4—84no—
1339C2×C4—88no—
1340C2×C4C2×H(5,𝔽2)14yes—
1341C2×C4C2×H(5,𝔽2)12yes—
1342C2×C4C2×2−1+412yes—
1343C2×C4C2×2−1+412yes—
1344C2×C4C2×2−1+414yes—
1345C2×C4#58512yes—
1346C2×C4#58512yes—
1347C2×C4#58512yes—
1348C22—24no—
1349C22—24no—
1350C22—24no—
1351C22—42no—
1352C22—42no—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22C22×H(5,𝔽2)11yescharacteristic
1363C22C22×2−1+411yescharacteristic
1364C22C22×2−1+411yescharacteristic
1365C22C2×#58511yescharacteristic
1366C22C2×#58511yescharacteristic
1367C22C2×#58511yescharacteristic
1368C222−1+611yescharacteristic
1369C4—24no—
1370C4—24no—
1371C4—22no—
1372C4—22no—
1373C4—22no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—44no—
1378C4—42no—
1379C4—41no—
1380C4—42no—
1381C4—41no—
1382C4—44no—
1383C4—42no—
1384C4—42no—
1385C4—41no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—44no—
1391C4—44no—
1392C4—42no—
1393C4—42no—
1394C4—44no—
1395C4#354514yes—
1396C2—44no—
1397C2—82no—
1398C2C2×#354511yescharacteristic
1399C2#6289711yescharacteristic
1400C2#6290411yescharacteristic
1401C2#6295911yescharacteristic
1402C2#6301611yescharacteristic
1403C2#6302511yescharacteristic
1404C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2682C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59425C2semidirect
3. #59096C2semidirect
4. #59036C2semidirect
5. #55203C2semidirect
6. #54417C2semidirect
7. #53936C2semidirect
9. #51493C2semidirect
10. #49675C2semidirect
11. #48952C2semidirect
12. #46023C2semidirect
13. #46006C2semidirect
14. #46004C2semidirect
15. #45390C2semidirect
16. #45116C2semidirect
17. #45078C2semidirect
18. #42866C2semidirect
19. #42807C2semidirect
20. #42672C2semidirect
21. #39855C2semidirect
22. #38999C2semidirect
23. #38974C2semidirect
24. #37208C2semidirect
25. #37195C2semidirect
26. #37136C2semidirect
27. #36446C2semidirect
28. #36313C2semidirect
29. #36299C2semidirect

Maximal subgroups

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

subgroupindex
#598802
#594252
#590962
#590362
#552032
#544172
#539362
#523032
#514932
#496752
#489522
#460232
#460062
#460042
#453902
#451162
#450782
#428662
#428072
#426722
#398552
#389992
#389742
#372082
#371952
#371362
#364462
#363132
#362992