Finite Group Databasebeta

← #8504949

Subgroups — #8504949

Order 512.

4445 conjugacy classes of subgroups.

The subgroup lattice has 1448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59935C211yesmaximal, characteristic, complemented
2#58889C212yesmaximal, complemented
3#58543C212yesmaximal, complemented
4#57718C214yesmaximal, complemented
5#57389C214yesmaximal, complemented
6#57378C214yesmaximal, complemented
7#54898C214yesmaximal, complemented
8#53372C214yesmaximal, complemented
9#53033C211yesmaximal, characteristic, complemented
10#53031C211yesmaximal, characteristic, complemented
11#52228C211yesmaximal, characteristic, complemented
12#49109C214yesmaximal, complemented
13#46330C212yesmaximal, complemented
14#45593C212yesmaximal, complemented
15#45337C212yesmaximal, complemented
16#44996C212yesmaximal, complemented
17#42858C212yesmaximal, complemented
18#42683C211yesmaximal, characteristic, complemented
19#42541C212yesmaximal, complemented
20#42481C211yesmaximal, characteristic, complemented
21#39614C212yesmaximal, complemented
22#38249C212yesmaximal, complemented
23#38125C212yesmaximal, complemented
24#38068C212yesmaximal, complemented
25#37384C212yesmaximal, complemented
26#37338C212yesmaximal, complemented
27#37242C212yesmaximal, complemented
28#36496C211yesmaximal, characteristic, complemented
29#35217C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#554C2212yes—
32C2×#554C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#547C2211yescharacteristic
35#2866C2214yes—
36#2863C2214yes—
37#2861C2212yes—
38#2858C2211yescharacteristic
39#2857C2212yes—
40#2854C2212yes—
41#2850C2212yes—
42#2844C2212yes—
43#2843C2212yes—
44#2843C2212yes—
45#2843C2212yes—
46#2836C2214yes—
47#2833C2214yes—
48#2830C2214yes—
49#2825C2214yes—
50#2817C2214yes—
51#2814C2212yes—
52#2813C2212yes—
53#2809C2212yes—
54#2801C2214yes—
55#2800C2214yes—
56#2797C2214yes—
57#2797C2214yes—
58#2794C2212yes—
59#2789C2212yes—
60#2788C2214yes—
61#2787C2214yes—
62#2785C2211yescharacteristic
63#2784C2211yescharacteristic
64#2784C2212yes—
65#2784C2214yes—
66#2784C2214yes—
67#2781C2212yes—
68#2779C2214yes—
69#2779C2214yes—
70#2778C2214yes—
71#2778C2214yes—
72#2777C2214yes—
73#2777C2214yes—
74#2775C2212yes—
75#2775C2214yes—
76#2773C2214yes—
77#2772C2214yes—
78#2770C2214yes—
79#2770C2214yes—
80#2769C2211yescharacteristic
81#2768C2214yes—
82#2764C2214yes—
83#2762C2214yes—
84#2761C2214yes—
85#2757C2214yes—
86#2756C2212yes—
87#2756C2214yes—
88#2748C2214yes—
89#2748C2214yes—
90#2748C2214yes—
91#2744C2212yes—
92#2743C2214yes—
93#2741C2214yes—
94#2740C2214yes—
95#2740C2214yes—
96#2739C2214yes—
97#2738C2214yes—
98#2737C2212yes—
99#2730C2214yes—
100#2728C2214yes—
101#2728C2214yes—
102#2726C2214yes—
103#2717C2214yes—
104#2710C2214yes—
105#2707C2214yes—
106#2706C2214yes—
107#2704C2214yes—
108#2704C2214yes—
109#2703C2214yes—
110#2703C2214yes—
111#2702C2214yes—
112#2700C2214yes—
113#2699C2211yescharacteristic
114#2698C2214yes—
115#2696C2214yes—
116#2696C2214yes—
117#2695C2214yes—
118#2693C2214yes—
119#2690C2214yes—
120#2690C2214yes—
121#2687C2214yes—
122#2686C2212yes—
123#2683C2214yes—
124#2681C2214yes—
125#2680C2212yes—
126#2680C2212yes—
127#2680C2214yes—
128#2673C2214yes—
129#2659C2214yes—
130#2658C2211yescharacteristic
131#2655C2214yes—
132#2652C2214yes—
133#2650C2214yes—
134#2648C2214yes—
135#2648C2214yes—
136#2647C2212yes—
137#2645C2212yes—
138#2644C2212yes—
139#2640C2211yescharacteristic
140#2638C2212yes—
141#2635C2212yes—
142#2630C2214yes—
143#2624C2212yes—
144#2623C2212yes—
145#2614C2212yes—
146#2612C2212yes—
147#2603C2214yes—
148#2594C2214yes—
149#2592C2211yescharacteristic
150#2591C2214yes—
151#2588C2214yes—
152#2581C2212yes—
153#2578C2214yes—
154#2574C2214yes—
155#2568C2211yescharacteristic
156#2567C2211yescharacteristic
157#2567C2211yescharacteristic
158#2566C2212yes—
159#2544C2212yes—
160#2541C2211yescharacteristic
161#2540C2211yescharacteristic
162#2535C2212yes—
163#2533C2214yes—
164#2532C2214yes—
165#2531C2214yes—
166#2521C2214yes—
167#2514C2212yes—
168#2512C2212yes—
169#2510C2214yes—
170#2509C2212yes—
171#2508C2212yes—
172#2504C2212yes—
173#2497C2214yes—
174#2495C2212yes—
175#2495C2212yes—
176#2492C2212yes—
177#2492C2212yes—
178#2488C2214yes—
179#2487C2214yes—
180#2487C2212yes—
181#2486C2212yes—
182#2481C2214yes—
183#2473C2214yes—
184#2463C2214yes—
185#2463C2214yes—
186#2461C2214yes—
187#2461C2214yes—
188#2461C2214yes—
189#2457C2214yes—
190#2456C2214yes—
191#2452C2212yes—
192#2451C2212yes—
193#2451C2212yes—
194#2448C2212yes—
195#2447C2212yes—
196#2446C2212yes—
197#2446C2212yes—
198#2445C2212yes—
199#2444C2214yes—
200#2440C2212yes—
201#2440C2212yes—
202#2440C2212yes—
203#2432C2212yes—
204#2431C2212yes—
205#2429C2212yes—
206#2429C2212yes—
207#2429C2212yes—
208#2427C2212yes—
209#2427C2212yes—
210#2426C2212yes—
211#2426C2212yes—
212#2421C2212yes—
213#2420C2214yes—
214#2419C2214yes—
215#2417C2212yes—
216#2417C2214yes—
217#2417C2212yes—
218#2417C2212yes—
219#2417C2214yes—
220#2417C2214yes—
221#2417C2212yes—
222#2417C2214yes—
223#2416C2212yes—
224#2409C2214yes—
225#2409C2212yes—
226#2409C2214yes—
227#2407C2212yes—
228#2407C2212yes—
229#2399C2211yescharacteristic
230#2398C2212yes—
231#2398C2211yescharacteristic
232#2392C2212yes—
233#2380C2214yes—
234#2372C2212yes—
235#2361C2212yes—
236#2361C2212yes—
237#2361C2212yes—
238#2360C2212yes—
239#2345C2212yes—
240#2341C2212yes—
241#2331C2212yes—
242#2327C2212yes—
243#2326C2212yes—
244#2325C2214yes—
245#2323C2212yes—
246#2323C2212yes—
247#2319C2211yescharacteristic
248#2319C2211yescharacteristic
249#2311C2212yes—
250C4×#127C2212yes—
251C4×#124C2211yescharacteristic
252C4×#121C2212yes—
253#2298C2212yes—
254#2295C2212yes—
255C2×#389C2212yes—
256#2290C2212yes—
257#2283C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261#559—44no—
262#554—44no—
263#554—48no—
264D4×Q8—44no—
265#547—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×#127C2312yes—
272C2×#127C2311yescharacteristic
273C2×#126C2314yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#124C2311yescharacteristic
277C2×#124C2312yes—
278C2×#124C2311yescharacteristic
279C2×#124C2312yes—
280C2×#124C2311yescharacteristic
281C2×#124C2314yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2314yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×#117C2312yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2314yes—
333C22×C42C2312yes—
334#401C2314yes—
335#401C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2311yescharacteristic
348#400C2311yescharacteristic
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#399C2312yes—
360#399C2312yes—
361#399C2314yes—
362#399C2314yes—
363#399C2312yes—
364#399C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2311yescharacteristic
383#398C2311yescharacteristic
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2312yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2312yes—
408#397C2314yes—
409#397C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2312yes—
418#396C2312yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#395C2312yes—
426#395C2312yes—
427#395C2314yes—
428#395C2314yes—
429#395C2312yes—
430#395C2312yes—
431#395C2314yes—
432#395C2314yes—
433#395C2311yescharacteristic
434#395C2314yes—
435#395C2311yescharacteristic
436#395C2312yes—
437#395C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2312yes—
448#394C2311yescharacteristic
449#394C2314yes—
450#394C2312yes—
451#394C2312yes—
452#394C2312yes—
453#394C2314yes—
454#394C2314yes—
455#394C2311yescharacteristic
456#394C2312yes—
457#394C2314yes—
458#393C2314yes—
459#393C2312yes—
460#393C2312yes—
461#393C2312yes—
462#393C2314yes—
463#393C2312yes—
464#393C2314yes—
465#393C2312yes—
466#393C2312yes—
467#392C2314yes—
468#392C2314yes—
469#392C2314yes—
470#392C2314yes—
471#392C2314yes—
472#392C2312yes—
473#392C2312yes—
474#392C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2314yes—
489#391C2314yes—
490#391C2314yes—
491#391C2311yescharacteristic
492#391C2314yes—
493#390C2311yescharacteristic
494#390C2312yes—
495#390C2314yes—
496#390C2314yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2314yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2314yes—
507#390C2314yes—
508#390C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#388C2312yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2312yes—
567#388C2312yes—
568#388C2312yes—
569#388C2312yes—
570#388C2314yes—
571#388C2312yes—
572#387C2314yes—
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#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#387C2312yes—
602#387C2312yes—
603#386C2314yes—
604#386C2314yes—
605#386C2312yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2312yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2312yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2312yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2312yes—
647#385C2312yes—
648#384C2312yes—
649#384C2312yes—
650#384C2312yes—
651#383C2314yes—
652#383C2314yes—
653#383C2314yes—
654#383C2312yes—
655#383C2312yes—
656#382C2311yescharacteristic
657#382C2312yes—
658#382C2312yes—
659#382C2312yes—
660#382C2314yes—
661#382C2312yes—
662#382C2312yes—
663#381C2314yes—
664#381C2312yes—
665#381C2312yes—
666#381C2314yes—
667#381C2312yes—
668#381C2312yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2312yes—
673#380C2312yes—
674#380C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2314yes—
678#380C2312yes—
679#380C2314yes—
680#380C2312yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684#380C2312yes—
685#380C2314yes—
686#380C2314yes—
687#380C2314yes—
688#380C2312yes—
689#380C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2311yescharacteristic
711#376C2311yescharacteristic
712#376C2312yes—
713#376C2314yes—
714C2×#95C2314yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C2×#41—44no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8—44no—
721C22×Q8—84no—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2414yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2414yes—
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2414yes—
752C4⋊Q8—28no—
753C4⋊Q8—42no—
754C4⋊Q8—42no—
755C4⋊Q8—44no—
756C4⋊Q8—42no—
757#127—28no—
758#127—42no—
759#126—84no—
760#125—44no—
761#125—48no—
762#124—24no—
763#124—44no—
764#124—44no—
765#124—42no—
766#124—42no—
767#124—84no—
768#123—48no—
769#123—44no—
770#123—44no—
771#123—84no—
772#123—84no—
773#123—84no—
774C22⋊Q8—28no—
775C22⋊Q8—48no—
776C22⋊Q8—48no—
777C22⋊Q8—44no—
778C22⋊Q8—48no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—48no—
784C22⋊Q8—84no—
785C22⋊Q8—84no—
786C22⋊Q8—84no—
787C22⋊Q8—84no—
788#121—28no—
789#121—44no—
790#121—44no—
791#121—44no—
792#121—44no—
793#121—84no—
794C4×Q8—24no—
795C4×Q8—42no—
796C4×Q8—42no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×D4—24no—
801C4×D4—24no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—42no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—42no—
808C4×D4—44no—
809C4×D4—48no—
810C4×D4—84no—
811C4×D4—84no—
812C4×D4—84no—
813#117—44no—
814C2×C4⋊C4—28no—
815C2×C4⋊C4—44no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—44no—
818C2×C4⋊C4—84no—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C42—44no—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2411yescharacteristic
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2411yescharacteristic
956#95C2411yescharacteristic
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2411yescharacteristic
962#95C2411yescharacteristic
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019C24C2512yes—
1020C24C2512yes—
1021C24C2512yes—
1022C24C2512yes—
1023#41—816no—
1024C2×Q8—22no—
1025C2×Q8—24no—
1026C2×Q8—28no—
1027C2×Q8—22no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—41no—
1032C2×Q8—42no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—41no—
1039C2×Q8—42no—
1040C2×Q8—44no—
1041C2×Q8—816no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—28no—
1045C2×D4—28no—
1046C2×D4—22no—
1047C2×D4—22no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—41no—
1052C2×D4—42no—
1053C2×D4—41no—
1054C2×D4—42no—
1055C2×D4—41no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—42no—
1072C2×D4—44no—
1073C2×D42−1+414yes—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—28no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—42no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—44no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2512yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C4⋊C4—24no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—41no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—41no—
1155C4⋊C4—41no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—41no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—41no—
1167C4⋊C4—41no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4H(5,𝔽2)14yes—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—24no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C42—22no—
1240C42—22no—
1241C42—24no—
1242C42—24no—
1243C42—22no—
1244C42—22no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—24no—
1249C42—42no—
1250C42—42no—
1251C42—41no—
1252C42—42no—
1253C42—42no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—42no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—24no—
1273C23—22no—
1274C23—22no—
1275C23—24no—
1276C23—22no—
1277C23—24no—
1278C23—24no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23C2×2−1+414yes—
1284C23C2611yescharacteristic
1285Q8—44no—
1286Q8—44no—
1287Q8—48no—
1288Q8—82no—
1289Q8—88no—
1290Q8—84no—
1291Q8—162no—
1292D4—44no—
1293D4—48no—
1294D4—44no—
1295D4—44no—
1296D4—84no—
1297D4—84no—
1298D4—88no—
1299D4—88no—
1300D4—82no—
1301D4—88no—
1302D4—88no—
1303D4—162no—
1304C2×C4—21no—
1305C2×C4—24no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—48no—
1370C2×C4—48no—
1371C2×C4—84no—
1372C2×C4—88no—
1373C2×C4—84no—
1374C2×C4—84no—
1375C2×C4—84no—
1376C2×C4—88no—
1377C2×C4—88no—
1378C2×C4—164no—
1379C2×C4—164no—
1380C2×C4C2×H(5,𝔽2)14yes—
1381C2×C4C2×H(5,𝔽2)12yes—
1382C2×C4C2×2−1+412yes—
1383C2×C4#58514yes—
1384C22—24no—
1385C22—24no—
1386C22—24no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—44no—
1399C22—42no—
1400C22—44no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—44no—
1406C22—44no—
1407C22—42no—
1408C22C22×H(5,𝔽2)11yescharacteristic
1409C22C22×2−1+411yescharacteristic
1410C22C2×#58512yes—
1411C22H(7,𝔽2)12yes—
1412C222−1+611yescharacteristic
1413C4—24no—
1414C4—22no—
1415C4—42no—
1416C4—42no—
1417C4—44no—
1418C4—42no—
1419C4—41no—
1420C4—41no—
1421C4—42no—
1422C4—44no—
1423C4—44no—
1424C4—41no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—44no—
1429C4—44no—
1430C4—42no—
1431C4—41no—
1432C4—41no—
1433C4—42no—
1434C4—42no—
1435C4—42no—
1436C4—44no—
1437C4#355114yes—
1438C2—44no—
1439C2—82no—
1440C2—82no—
1441C2—82no—
1442C2C2×#355111yescharacteristic
1443C2#6288412yes—
1444C2#6289311yescharacteristic
1445C2#6295112yes—
1446C2#6304111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59935C2semidirect
2. #58889C2semidirect
3. #58543C2semidirect
4. #57718C2semidirect
5. #57389C2semidirect
6. #57378C2semidirect
7. #54898C2semidirect
8. #53372C2semidirect
9. #53033C2semidirect
10. #53031C2semidirect
11. #52228C2semidirect
12. #49109C2semidirect
13. #46330C2semidirect
14. #45593C2semidirect
15. #45337C2semidirect
16. #44996C2semidirect
17. #42858C2semidirect
18. #42683C2semidirect
19. #42541C2semidirect
20. #42481C2semidirect
21. #39614C2semidirect
22. #38249C2semidirect
23. #38125C2semidirect
24. #38068C2semidirect
25. #37384C2semidirect
26. #37338C2semidirect
27. #37242C2semidirect
28. #36496C2semidirect
29. #35217C2semidirect

Maximal subgroups

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

subgroupindex
#599352
#588892
#585432
#577182
#573892
#573782
#548982
#533722
#530332
#530312
#522282
#491092
#463302
#455932
#453372
#449962
#428582
#426832
#425412
#424812
#396142
#382492
#381252
#380682
#373842
#373382
#372422
#364962
#352172