Finite Group Databasebeta

← #8701611

Subgroups — #8701611

Order 512.

4543 conjugacy classes of subgroups.

The subgroup lattice has 1464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59886C212yesmaximal, complemented
2#59381C212yesmaximal, complemented
3#59145C212yesmaximal, complemented
4#59064C212yesmaximal, complemented
5#55469C214yesmaximal, complemented
6#55390C214yesmaximal, complemented
7#54888C214yesmaximal, complemented
8#52304C211yesmaximal, characteristic, complemented
9#50045C214yesmaximal, complemented
10#49737C214yesmaximal, complemented
11#49343C214yesmaximal, complemented
12#46016C211yesmaximal, characteristic, complemented
13#46013C211yesmaximal, characteristic, complemented
14#46007C211yesmaximal, characteristic, complemented
15#45192C212yesmaximal, complemented
16#45151C212yesmaximal, complemented
17#44998C212yesmaximal, complemented
18#42857C212yesmaximal, complemented
19#42560C212yesmaximal, complemented
20#42481C212yesmaximal, complemented
21#40151C212yesmaximal, complemented
22#39889C212yesmaximal, complemented
23#39665C212yesmaximal, complemented
24#37219C212yesmaximal, complemented
25#37209C212yesmaximal, complemented
26#37140C212yesmaximal, complemented
27#36463C211yesmaximal, characteristic, complemented
28#36454C211yesmaximal, characteristic, complemented
29#36303C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×D4×Q8C2211yescharacteristic
32C2×#547C2211yescharacteristic
33C2×#532C2212yes—
34#2862C2211yescharacteristic
35#2862C2211yescharacteristic
36#2858C2211yescharacteristic
37#2855C2212yes—
38#2855C2212yes—
39#2854C2212yes—
40#2850C2212yes—
41#2845C2212yes—
42#2830C2214yes—
43#2824C2214yes—
44#2820C2212yes—
45#2819C2212yes—
46#2814C2214yes—
47#2808C2212yes—
48#2808C2214yes—
49#2806C2212yes—
50#2806C2212yes—
51#2805C2211yescharacteristic
52#2805C2211yescharacteristic
53#2804C2212yes—
54#2800C2214yes—
55#2799C2214yes—
56#2797C2214yes—
57#2793C2214yes—
58#2790C2214yes—
59#2789C2212yes—
60#2788C2214yes—
61#2787C2214yes—
62#2786C2214yes—
63#2775C2214yes—
64#2775C2214yes—
65#2774C2214yes—
66#2765C2212yes—
67#2765C2212yes—
68#2763C2214yes—
69#2761C2214yes—
70#2761C2214yes—
71#2759C2214yes—
72#2755C2214yes—
73#2755C2214yes—
74#2753C2214yes—
75#2752C2214yes—
76#2751C2214yes—
77#2751C2214yes—
78#2750C2214yes—
79#2746C2214yes—
80#2745C2214yes—
81#2745C2214yes—
82#2744C2214yes—
83#2744C2214yes—
84#2737C2214yes—
85#2737C2214yes—
86#2733C2212yes—
87#2732C2212yes—
88#2730C2214yes—
89#2724C2211yescharacteristic
90#2717C2212yes—
91#2712C2214yes—
92#2708C2214yes—
93#2708C2214yes—
94#2706C2214yes—
95#2703C2214yes—
96#2701C2214yes—
97#2701C2214yes—
98#2700C2214yes—
99#2700C2214yes—
100#2700C2214yes—
101#2700C2214yes—
102#2699C2214yes—
103#2696C2214yes—
104#2690C2212yes—
105#2690C2212yes—
106#2683C2211yescharacteristic
107#2682C2214yes—
108#2680C2214yes—
109#2680C2214yes—
110#2676C2214yes—
111#2665C2214yes—
112#2652C2214yes—
113#2651C2214yes—
114#2643C2214yes—
115#2640C2212yes—
116#2638C2214yes—
117#2638C2214yes—
118#2630C2214yes—
119#2630C2214yes—
120#2614C2214yes—
121#2602C2214yes—
122#2595C2214yes—
123#2592C2212yes—
124#2592C2212yes—
125#2589C2214yes—
126#2579C2214yes—
127#2576C2214yes—
128#2575C2214yes—
129#2574C2214yes—
130#2574C2214yes—
131#2569C2214yes—
132#2568C2211yescharacteristic
133#2568C2212yes—
134#2567C2212yes—
135#2564C2214yes—
136#2563C2211yescharacteristic
137#2557C2214yes—
138#2557C2214yes—
139#2547C2212yes—
140#2547C2211yescharacteristic
141#2547C2211yescharacteristic
142#2546C2212yes—
143#2546C2212yes—
144#2545C2212yes—
145#2545C2212yes—
146#2544C2212yes—
147#2542C2211yescharacteristic
148#2541C2211yescharacteristic
149#2531C2214yes—
150#2529C2214yes—
151#2529C2214yes—
152#2527C2214yes—
153#2527C2214yes—
154#2520C2214yes—
155#2517C2214yes—
156#2516C2214yes—
157#2513C2212yes—
158#2511C2212yes—
159#2511C2214yes—
160#2503C2212yes—
161#2497C2212yes—
162#2494C2212yes—
163#2493C2214yes—
164#2492C2212yes—
165#2492C2212yes—
166#2492C2212yes—
167#2491C2212yes—
168#2490C2212yes—
169#2489C2212yes—
170#2488C2214yes—
171#2488C2214yes—
172#2488C2214yes—
173#2465C2214yes—
174#2464C2214yes—
175#2461C2214yes—
176#2461C2214yes—
177#2459C2214yes—
178#2459C2214yes—
179#2457C2214yes—
180#2456C2214yes—
181#2452C2212yes—
182#2452C2212yes—
183#2451C2212yes—
184#2451C2212yes—
185#2451C2212yes—
186#2451C2212yes—
187#2450C2214yes—
188#2448C2212yes—
189#2447C2214yes—
190#2447C2212yes—
191#2447C2212yes—
192#2447C2212yes—
193#2446C2212yes—
194#2446C2212yes—
195#2445C2212yes—
196#2445C2212yes—
197#2436C2212yes—
198#2432C2212yes—
199#2432C2212yes—
200#2432C2212yes—
201#2431C2212yes—
202#2431C2212yes—
203#2429C2212yes—
204#2427C2214yes—
205#2426C2212yes—
206#2425C2214yes—
207#2422C2212yes—
208#2421C2212yes—
209#2421C2212yes—
210#2420C2214yes—
211#2420C2212yes—
212#2419C2214yes—
213#2419C2214yes—
214#2419C2214yes—
215#2409C2214yes—
216#2407C2212yes—
217#2401C2212yes—
218#2401C2212yes—
219#2399C2212yes—
220#2382C2212yes—
221#2379C2212yes—
222#2379C2212yes—
223#2369C2211yescharacteristic
224#2368C2214yes—
225#2367C2212yes—
226#2366C2211yescharacteristic
227#2366C2212yes—
228#2365C2211yescharacteristic
229#2365C2211yescharacteristic
230#2364C2214yes—
231#2357C2212yes—
232#2356C2212yes—
233#2355C2212yes—
234#2355C2212yes—
235#2349C2214yes—
236#2341C2212yes—
237#2341C2212yes—
238#2339C2212yes—
239#2339C2212yes—
240#2339C2212yes—
241#2332C2214yes—
242#2327C2212yes—
243#2326C2212yes—
244#2326C2214yes—
245#2322C2214yes—
246#2319C2212yes—
247C4×#125C2211yescharacteristic
248C4×#125C2211yescharacteristic
249C4×#124C2211yescharacteristic
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×#123C2212yes—
255C4×#121C2212yes—
256C4×#121C2212yes—
257C2×#391C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261C23×Q8C2312yes—
262#559—48no—
263D4×Q8—44no—
264#547—44no—
265#532—48no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×#127C2312yes—
275C2×#127C2311yescharacteristic
276C2×#125C2311yescharacteristic
277C2×#125C2311yescharacteristic
278C2×#124C2312yes—
279C2×#124C2311yescharacteristic
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2314yes—
287C2×#124C2312yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2312yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2314yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C42C2312yes—
333C22×C42C2312yes—
334#401C2314yes—
335#401C2312yes—
336#401C2312yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#399C2314yes—
356#399C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#397C2314yes—
373#397C2312yes—
374#397C2314yes—
375#397C2312yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2314yes—
393#397C2312yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2312yes—
406#396C2314yes—
407#396C2312yes—
408#396C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2312yes—
414#395C2312yes—
415#395C2314yes—
416#395C2312yes—
417#395C2314yes—
418#395C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#392C2314yes—
450#392C2314yes—
451#392C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2311yescharacteristic
484#390C2312yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2314yes—
489#390C2312yes—
490#390C2312yes—
491#390C2311yescharacteristic
492#390C2314yes—
493#390C2312yes—
494#390C2314yes—
495#390C2314yes—
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2314yes—
502#389C2311yescharacteristic
503#389C2311yescharacteristic
504#389C2311yescharacteristic
505#389C2311yescharacteristic
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2314yes—
520#389C2312yes—
521#388C2314yes—
522#388C2314yes—
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#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2312yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2312yes—
554#388C2314yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2312yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2312yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2314yes—
634#385C2312yes—
635#385C2312yes—
636#384C2314yes—
637#384C2312yes—
638#383C2314yes—
639#382C2311yescharacteristic
640#382C2311yescharacteristic
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2314yes—
650#382C2311yescharacteristic
651#381C2314yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2314yes—
660#381C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2314yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2311yescharacteristic
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
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—
709C4×C22⋊C4C2312yes—
710#376C2312yes—
711#376C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C43C2311yescharacteristic
716C2×#41—28no—
717C2×#41—44no—
718C2×#41—44no—
719C2×#41—44no—
720C2×#41—44no—
721C2×#41—44no—
722C22×Q8—44no—
723C22×Q8—44no—
724C22×Q8—82no—
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2414yes—
732C22×Q8C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2411yescharacteristic
736C22×D4C2414yes—
737C22×D4C2411yescharacteristic
738C22×D4C2412yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2414yes—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2414yes—
754C4⋊Q8—42no—
755C4⋊Q8—42no—
756C4⋊Q8—42no—
757C4⋊Q8—44no—
758C4⋊Q8—44no—
759C4⋊Q8—42no—
760C4⋊Q8—44no—
761C4⋊Q8—42no—
762#127—28no—
763#127—42no—
764#125—24no—
765#125—42no—
766#124—28no—
767#124—44no—
768#124—44no—
769#124—44no—
770#124—42no—
771#124—44no—
772#124—44no—
773#124—48no—
774#124—48no—
775#124—82no—
776#123—48no—
777#123—48no—
778#123—48no—
779#123—48no—
780#123—44no—
781#123—84no—
782#123—84no—
783C22⋊Q8—28no—
784C22⋊Q8—48no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787C22⋊Q8—48no—
788C22⋊Q8—44no—
789C22⋊Q8—44no—
790C22⋊Q8—44no—
791C22⋊Q8—84no—
792C22⋊Q8—82no—
793#121—28no—
794#121—48no—
795#121—48no—
796#121—44no—
797#121—44no—
798#121—82no—
799C4×Q8—42no—
800C4×Q8—44no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×Q8—82no—
806C4×D4—24no—
807C4×D4—28no—
808C4×D4—44no—
809C4×D4—42no—
810C4×D4—42no—
811C4×D4—44no—
812C4×D4—42no—
813C4×D4—48no—
814C4×D4—48no—
815C4×D4—48no—
816C4×D4—48no—
817C4×D4—82no—
818C4×D4—84no—
819C2×C4⋊C4—44no—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C42—44no—
926C2×C42—82no—
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2411yescharacteristic
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022C24C2514yes—
1023C24C2512yes—
1024C24C2512yes—
1025#41—816no—
1026#41—816no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—22no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—41no—
1038C2×Q8—41no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—42no—
1044C2×Q8—44no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—44no—
1048C2×Q8—42no—
1049C2×Q8—42no—
1050C2×Q8—42no—
1051C2×Q8—816no—
1052C2×D4—28no—
1053C2×D4—28no—
1054C2×D4—28no—
1055C2×D4—24no—
1056C2×D4—28no—
1057C2×D4—24no—
1058C2×D4—22no—
1059C2×D4—22no—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—22no—
1063C2×D4—44no—
1064C2×D4—41no—
1065C2×D4—42no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—41no—
1073C2×D4—42no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4H(5,𝔽2)14yes—
1082C22×C4—24no—
1083C22×C4—28no—
1084C22×C4—28no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4C2511yescharacteristic
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2511yescharacteristic
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2514yes—
1127C22×C4C2514yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2512yes—
1132C22×C4C2511yescharacteristic
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2511yescharacteristic
1137C22×C4C2512yes—
1138C22×C4C2511yescharacteristic
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C4⋊C4—24no—
1142C4⋊C4—22no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—22no—
1148C4⋊C4—22no—
1149C4⋊C4—24no—
1150C4⋊C4—22no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—22no—
1155C4⋊C4—22no—
1156C4⋊C4—24no—
1157C4⋊C4—41no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—41no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—41no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—41no—
1174C4⋊C4—44no—
1175C4⋊C4—41no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—44no—
1183C4⋊C4—41no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C42−1+414yes—
1199C22⋊C4—24no—
1200C22⋊C4—28no—
1201C22⋊C4—28no—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—28no—
1207C22⋊C4—28no—
1208C22⋊C4—24no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
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—44no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C42—24no—
1247C42—24no—
1248C42—22no—
1249C42—24no—
1250C42—22no—
1251C42—24no—
1252C42—22no—
1253C42—22no—
1254C42—24no—
1255C42—22no—
1256C42—22no—
1257C42—42no—
1258C42—42no—
1259C42—41no—
1260C42—42no—
1261C42—42no—
1262C42—42no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—44no—
1269C42—44no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—24no—
1277C23—22no—
1278C23—22no—
1279C23—24no—
1280C23—22no—
1281C23—24no—
1282C23—24no—
1283C23—22no—
1284C23—22no—
1285C23—24no—
1286C23—24no—
1287C23—22no—
1288C23—22no—
1289C23—24no—
1290C23C2×H(5,𝔽2)14yes—
1291C23C2611yescharacteristic
1292Q8—44no—
1293Q8—48no—
1294Q8—48no—
1295Q8—84no—
1296Q8—84no—
1297Q8—84no—
1298Q8—88no—
1299Q8—162no—
1300D4—28no—
1301D4—416no—
1302D4—48no—
1303D4—82no—
1304D4—84no—
1305D4—88no—
1306D4—88no—
1307D4—88no—
1308D4—88no—
1309D4—162no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—21no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—48no—
1382C2×C4—48no—
1383C2×C4—84no—
1384C2×C4—84no—
1385C2×C4—84no—
1386C2×C4—88no—
1387C2×C4—88no—
1388C2×C4—84no—
1389C2×C4—88no—
1390C2×C4—164no—
1391C2×C4—164no—
1392C2×C4C2×H(5,𝔽2)12yes—
1393C2×C4C2×2−1+412yes—
1394C2×C4C2×2−1+414yes—
1395C2×C4#58512yes—
1396C2×C4#58512yes—
1397C2×C4#58512yes—
1398C2×C4#58512yes—
1399C22—24no—
1400C22—24no—
1401C22—24no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—44no—
1408C22—42no—
1409C22—44no—
1410C22—42no—
1411C22—44no—
1412C22—44no—
1413C22—42no—
1414C22—42no—
1415C22—44no—
1416C22—44no—
1417C22—42no—
1418C22—44no—
1419C22—42no—
1420C22C22×H(5,𝔽2)11yescharacteristic
1421C22C22×2−1+411yescharacteristic
1422C22C2×#58511yescharacteristic
1423C22C2×#58511yescharacteristic
1424C22C2×#58511yescharacteristic
1425C22C2×#58511yescharacteristic
1426C22H(7,𝔽2)11yescharacteristic
1427C4—24no—
1428C4—22no—
1429C4—22no—
1430C4—22no—
1431C4—42no—
1432C4—44no—
1433C4—44no—
1434C4—41no—
1435C4—42no—
1436C4—42no—
1437C4—41no—
1438C4—42no—
1439C4—42no—
1440C4—41no—
1441C4—44no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—44no—
1446C4—42no—
1447C4—42no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—44no—
1452C4#354514yes—
1453C2—44no—
1454C2—82no—
1455C2—84no—
1456C2C2×#354511yescharacteristic
1457C2#6289611yescharacteristic
1458C2#6296211yescharacteristic
1459C2#6296511yescharacteristic
1460C2#6301311yescharacteristic
1461C2#6303411yescharacteristic
1462C2#6303611yescharacteristic
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. #59886C2semidirect
2. #59381C2semidirect
3. #59145C2semidirect
4. #59064C2semidirect
5. #55469C2semidirect
6. #55390C2semidirect
7. #54888C2semidirect
8. #52304C2semidirect
9. #50045C2semidirect
10. #49737C2semidirect
11. #49343C2semidirect
12. #46016C2semidirect
13. #46013C2semidirect
14. #46007C2semidirect
15. #45192C2semidirect
16. #45151C2semidirect
17. #44998C2semidirect
18. #42857C2semidirect
19. #42560C2semidirect
20. #42481C2semidirect
21. #40151C2semidirect
22. #39889C2semidirect
23. #39665C2semidirect
24. #37219C2semidirect
25. #37209C2semidirect
26. #37140C2semidirect
27. #36463C2semidirect
28. #36454C2semidirect
29. #36303C2semidirect

Maximal subgroups

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

subgroupindex
#598862
#593812
#591452
#590642
#554692
#553902
#548882
#523042
#500452
#497372
#493432
#460162
#460132
#460072
#451922
#451512
#449982
#428572
#425602
#424812
#401512
#398892
#396652
#372192
#372092
#371402
#364632
#364542
#363032