Finite Group Databasebeta

← #8096604

Subgroups — #8096604

Order 512.

4793 conjugacy classes of subgroups.

The subgroup lattice has 1488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53130C212yesmaximal, complemented
2#53059C212yesmaximal, complemented
3#52984C212yesmaximal, complemented
4#52621C214yesmaximal, complemented
5#52386C214yesmaximal, complemented
6#52353C214yesmaximal, complemented
7#52306C211yesmaximal, characteristic, complemented
8#52160C212yesmaximal, complemented
9#46343C212yesmaximal, complemented
10#46314C212yesmaximal, complemented
11#46257C214yesmaximal, complemented
12#46063C212yesmaximal, complemented
13#46050C212yesmaximal, complemented
14#46016C211yesmaximal, characteristic, complemented
15#46013C211yesmaximal, characteristic, complemented
16#45997C211yesmaximal, characteristic, complemented
17#45958C212yesmaximal, complemented
18#45952C214yesmaximal, complemented
19#45938C212yesmaximal, complemented
20#45768C214yesmaximal, complemented
21#36496C211yesmaximal, characteristic, complemented
22#36469C212yesmaximal, complemented
23#36313C211yesmaximal, characteristic, complemented
24#36300C211yesmaximal, characteristic, complemented
25#36250C212yesmaximal, complemented
26#36113C212yesmaximal, complemented
27#35844C212yesmaximal, complemented
28#35778C212yesmaximal, complemented
29#35724C212yesmaximal, complemented
30C2×#562C2212yes—
31C2×#559C2212yes—
32C2×#559C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#529C2214yes—
35C2×#520C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2862C2211yescharacteristic
39#2861C2212yes—
40#2860C2212yes—
41#2860C2212yes—
42#2858C2212yes—
43#2858C2211yescharacteristic
44#2858C2211yescharacteristic
45#2855C2214yes—
46#2854C2214yes—
47#2852C2214yes—
48#2838C2214yes—
49#2837C2214yes—
50#2836C2214yes—
51#2832C2214yes—
52#2832C2214yes—
53#2831C2214yes—
54#2829C2214yes—
55#2828C2214yes—
56#2826C2214yes—
57#2825C2214yes—
58#2825C2214yes—
59#2824C2214yes—
60#2820C2212yes—
61#2819C2212yes—
62#2819C2212yes—
63#2818C2214yes—
64#2814C2214yes—
65#2813C2214yes—
66#2809C2211yescharacteristic
67#2808C2212yes—
68#2804C2212yes—
69#2803C2214yes—
70#2800C2214yes—
71#2797C2214yes—
72#2788C2214yes—
73#2775C2212yes—
74#2775C2212yes—
75#2769C2212yes—
76#2764C2214yes—
77#2761C2214yes—
78#2759C2214yes—
79#2757C2214yes—
80#2757C2214yes—
81#2756C2214yes—
82#2753C2214yes—
83#2750C2214yes—
84#2749C2214yes—
85#2749C2214yes—
86#2748C2214yes—
87#2734C2211yescharacteristic
88#2733C2212yes—
89#2732C2212yes—
90#2731C2212yes—
91#2730C2214yes—
92#2727C2211yescharacteristic
93#2727C2211yescharacteristic
94#2721C2214yes—
95#2721C2212yes—
96#2721C2212yes—
97#2720C2214yes—
98#2716C2214yes—
99#2714C2214yes—
100#2714C2214yes—
101#2712C2214yes—
102#2710C2214yes—
103#2705C2214yes—
104#2704C2214yes—
105#2700C2214yes—
106#2699C2214yes—
107#2694C2214yes—
108#2691C2214yes—
109#2691C2214yes—
110#2689C2214yes—
111#2688C2214yes—
112#2687C2214yes—
113#2682C2212yes—
114#2682C2212yes—
115#2676C2214yes—
116#2676C2214yes—
117#2673C2214yes—
118#2638C2214yes—
119#2631C2214yes—
120#2630C2214yes—
121#2625C2212yes—
122#2620C2212yes—
123#2619C2212yes—
124#2610C2214yes—
125#2602C2214yes—
126#2602C2214yes—
127#2600C2214yes—
128#2598C2214yes—
129#2592C2212yes—
130#2592C2212yes—
131#2582C2212yes—
132#2580C2212yes—
133#2579C2214yes—
134#2573C2214yes—
135#2572C2214yes—
136#2568C2211yescharacteristic
137#2567C2211yescharacteristic
138#2567C2211yescharacteristic
139#2566C2212yes—
140#2557C2214yes—
141#2557C2214yes—
142#2548C2211yescharacteristic
143#2547C2212yes—
144#2546C2211yescharacteristic
145#2545C2212yes—
146#2544C2212yes—
147#2544C2212yes—
148#2544C2212yes—
149#2541C2212yes—
150#2541C2211yescharacteristic
151#2541C2212yes—
152#2530C2214yes—
153#2528C2214yes—
154#2524C2214yes—
155#2523C2214yes—
156#2521C2214yes—
157#2514C2212yes—
158#2514C2212yes—
159#2513C2212yes—
160#2512C2212yes—
161#2509C2212yes—
162#2506C2212yes—
163#2492C2212yes—
164#2491C2212yes—
165#2491C2214yes—
166#2477C2214yes—
167#2477C2214yes—
168#2477C2214yes—
169#2476C2214yes—
170#2475C2214yes—
171#2474C2214yes—
172#2474C2214yes—
173#2473C2214yes—
174#2470C2214yes—
175#2466C2214yes—
176#2461C2214yes—
177#2461C2214yes—
178#2460C2214yes—
179#2459C2214yes—
180#2459C2214yes—
181#2458C2214yes—
182#2457C2214yes—
183#2456C2214yes—
184#2456C2214yes—
185#2455C2214yes—
186#2454C2212yes—
187#2453C2212yes—
188#2452C2212yes—
189#2452C2212yes—
190#2452C2212yes—
191#2451C2212yes—
192#2449C2214yes—
193#2448C2212yes—
194#2448C2212yes—
195#2448C2212yes—
196#2447C2212yes—
197#2447C2212yes—
198#2446C2212yes—
199#2445C2212yes—
200#2445C2212yes—
201#2443C2214yes—
202#2443C2214yes—
203#2432C2212yes—
204#2432C2212yes—
205#2431C2212yes—
206#2431C2212yes—
207#2431C2212yes—
208#2429C2212yes—
209#2428C2212yes—
210#2427C2212yes—
211#2427C2212yes—
212#2426C2212yes—
213#2426C2212yes—
214#2422C2212yes—
215#2422C2214yes—
216#2420C2212yes—
217#2415C2214yes—
218#2413C2214yes—
219#2407C2212yes—
220#2397C2214yes—
221#2396C2212yes—
222#2396C2212yes—
223#2395C2212yes—
224#2392C2214yes—
225#2392C2214yes—
226#2383C2214yes—
227#2379C2212yes—
228#2379C2212yes—
229#2377C2214yes—
230#2376C2214yes—
231#2369C2211yescharacteristic
232#2367C2212yes—
233#2367C2212yes—
234#2366C2211yescharacteristic
235#2366C2212yes—
236#2365C2211yescharacteristic
237#2365C2212yes—
238#2365C2211yescharacteristic
239#2361C2212yes—
240#2361C2212yes—
241#2361C2212yes—
242#2360C2212yes—
243#2356C2212yes—
244#2354C2212yes—
245#2344C2212yes—
246C4×C4⋊Q8C2212yes—
247C4×#127C2212yes—
248C4×#125C2211yescharacteristic
249C4×#125C2211yescharacteristic
250C4×#126C2212yes—
251C4×#126C2212yes—
252C4×#124C2211yescharacteristic
253C4×#121C2214yes—
254#2295C2212yes—
255#2293C2212yes—
256#2290C2214yes—
257C42×Q8C2211yescharacteristic
258C42×D4C2212yes—
259C22×#41C2312yes—
260#562—48no—
261#559—48no—
262#559—44no—
263#554—44no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2312yes—
271C2×#127C2312yes—
272C2×#127C2311yescharacteristic
273C2×#127C2311yescharacteristic
274C2×#127C2312yes—
275#529—416no—
276C2×#126C2312yes—
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2311yescharacteristic
281C2×#125C2311yescharacteristic
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#124C2311yescharacteristic
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2314yes—
295C2×#124C2312yes—
296C2×#124C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×#121C2314yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317#520—48no—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×#117C2314yes—
343C2×#117C2314yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2314yes—
348C22×C42C2314yes—
349#401C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2312yes—
365#399C2312yes—
366#399C2312yes—
367#399C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2312yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2312yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2312yes—
413#396C2314yes—
414#396C2314yes—
415#396C2312yes—
416#396C2312yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2312yes—
421#395C2312yes—
422#394C2312yes—
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#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2312yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2312yes—
455#393C2314yes—
456#393C2314yes—
457#393C2312yes—
458#393C2314yes—
459#393C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2314yes—
464#392C2314yes—
465#392C2314yes—
466#392C2314yes—
467#392C2314yes—
468#392C2314yes—
469#392C2314yes—
470#392C2314yes—
471#392C2314yes—
472#392C2314yes—
473#392C2314yes—
474#392C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2311yescharacteristic
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2314yes—
496#390C2311yescharacteristic
497#390C2312yes—
498#390C2314yes—
499#390C2314yes—
500#390C2312yes—
501#390C2312yes—
502#390C2314yes—
503#390C2314yes—
504#390C2312yes—
505#390C2312yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2314yes—
510#390C2314yes—
511#390C2314yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2312yes—
522#389C2311yescharacteristic
523#389C2311yescharacteristic
524#389C2311yescharacteristic
525#389C2311yescharacteristic
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2314yes—
537#389C2312yes—
538#389C2314yes—
539#389C2314yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2314yes—
549#388C2312yes—
550#388C2312yes—
551#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
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#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2312yes—
586#388C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
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#387C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#384C2312yes—
658#384C2312yes—
659#384C2312yes—
660#383C2312yes—
661#383C2312yes—
662#383C2314yes—
663#383C2314yes—
664#383C2314yes—
665#382C2311yescharacteristic
666#382C2311yescharacteristic
667#382C2312yes—
668#382C2312yes—
669#382C2311yescharacteristic
670#382C2312yes—
671#381C2314yes—
672#381C2314yes—
673#381C2314yes—
674#381C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2312yes—
679#380C2314yes—
680#380C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714#376C2314yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C43C2312yes—
718C2×#41—44no—
719C2×#41—44no—
720C2×#41—44no—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2414yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2412yes—
741C22×D4C2412yes—
742C22×D4C2414yes—
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C4⋊Q8—42no—
752C4⋊Q8—42no—
753C4⋊Q8—42no—
754C4⋊Q8—44no—
755C4⋊Q8—42no—
756C4⋊Q8—44no—
757#127—44no—
758#127—42no—
759#127—44no—
760#127—44no—
761#127—42no—
762#126—28no—
763#126—48no—
764#126—48no—
765#126—44no—
766#125—24no—
767#125—42no—
768#125—44no—
769#125—48no—
770#124—44no—
771#124—44no—
772#124—48no—
773#124—44no—
774#124—44no—
775#124—44no—
776#124—44no—
777#124—44no—
778#124—42no—
779#124—44no—
780#124—44no—
781#124—44no—
782#124—48no—
783#123—216no—
784#123—48no—
785#123—48no—
786#123—48no—
787#123—48no—
788#123—48no—
789C22⋊Q8—48no—
790C22⋊Q8—48no—
791C22⋊Q8—48no—
792C22⋊Q8—48no—
793C22⋊Q8—44no—
794C22⋊Q8—44no—
795#121—48no—
796#121—48no—
797#121—48no—
798#121—48no—
799#121—44no—
800#121—44no—
801#121—44no—
802#121—48no—
803C4×Q8—28no—
804C4×Q8—28no—
805C4×Q8—24no—
806C4×Q8—44no—
807C4×Q8—42no—
808C4×Q8—42no—
809C4×Q8—42no—
810C4×Q8—44no—
811C4×D4—28no—
812C4×D4—28no—
813C4×D4—48no—
814C4×D4—48no—
815C4×D4—48no—
816C4×D4—44no—
817C4×D4—44no—
818C4×D4—44no—
819C4×D4—44no—
820C4×D4—48no—
821C4×D4—48no—
822C4×D4—44no—
823C4×D4—42no—
824C4×D4—48no—
825C4×D4—44no—
826C4×D4—48no—
827#117—44no—
828#117—48no—
829#117—48no—
830#117—48no—
831C2×C4⋊C4—28no—
832C2×C4⋊C4—48no—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2411yescharacteristic
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
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⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C42—48no—
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2411yescharacteristic
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2414yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2411yescharacteristic
973C2×C42C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033C24C2512yes—
1034C24C2514yes—
1035C24C2514yes—
1036#41—432no—
1037C2×Q8—24no—
1038C2×Q8—22no—
1039C2×Q8—24no—
1040C2×Q8—22no—
1041C2×Q8—22no—
1042C2×Q8—24no—
1043C2×Q8—24no—
1044C2×Q8—22no—
1045C2×Q8—41no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—42no—
1050C2×Q8—41no—
1051C2×Q8—42no—
1052C2×Q8—42no—
1053C2×Q8—42no—
1054C2×Q8—42no—
1055C2×Q8—42no—
1056C2×Q8—42no—
1057C2×Q8—42no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—28no—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—22no—
1065C2×D4—24no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—41no—
1069C2×D4—44no—
1070C2×D4—41no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—42no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—42no—
1088C2×D4—42no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—44no—
1101C2×D4—42no—
1102C2×D4—44no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—24no—
1106C22×C4—28no—
1107C22×C4—28no—
1108C22×C4—28no—
1109C22×C4—28no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2511yescharacteristic
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2511yescharacteristic
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2514yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C4⋊C4—28no—
1154C4⋊C4—24no—
1155C4⋊C4—28no—
1156C4⋊C4—24no—
1157C4⋊C4—28no—
1158C4⋊C4—24no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—22no—
1164C4⋊C4—22no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—22no—
1168C4⋊C4—22no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—24no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—41no—
1176C4⋊C4—41no—
1177C4⋊C4—41no—
1178C4⋊C4—41no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—41no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—41no—
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—44no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4H(5,𝔽2)14yes—
1211C4⋊C4H(5,𝔽2)14yes—
1212C22⋊C4—24no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—24no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—42no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C42—24no—
1267C42—28no—
1268C42—24no—
1269C42—24no—
1270C42—28no—
1271C42—24no—
1272C42—24no—
1273C42—24no—
1274C42—22no—
1275C42—22no—
1276C42—24no—
1277C42—24no—
1278C42—24no—
1279C42—22no—
1280C42—22no—
1281C42—22no—
1282C42—22no—
1283C42—24no—
1284C42—44no—
1285C42—44no—
1286C42—41no—
1287C42—42no—
1288C42—44no—
1289C42—42no—
1290C42—42no—
1291C42—42no—
1292C42—42no—
1293C23—22no—
1294C23—24no—
1295C23—24no—
1296C23—24no—
1297C23—24no—
1298C23—22no—
1299C23—24no—
1300C23—22no—
1301C23—24no—
1302C23—24no—
1303C23—24no—
1304C23—22no—
1305C23—24no—
1306C23—24no—
1307C23—22no—
1308C23—24no—
1309C23—22no—
1310C23—24no—
1311C23—22no—
1312C23—24no—
1313C23—24no—
1314C23C2611yescharacteristic
1315Q8—44no—
1316Q8—48no—
1317Q8—82no—
1318Q8—84no—
1319Q8—84no—
1320Q8—162no—
1321Q8—162no—
1322D4—44no—
1323D4—416no—
1324D4—48no—
1325D4—48no—
1326D4—88no—
1327D4—84no—
1328D4—84no—
1329D4—88no—
1330D4—88no—
1331D4—88no—
1332D4—88no—
1333D4—164no—
1334D4—162no—
1335D4—162no—
1336D4—164no—
1337C2×C4—22no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—416no—
1408C2×C4—48no—
1409C2×C4—88no—
1410C2×C4—88no—
1411C2×C4—88no—
1412C2×C4—88no—
1413C2×C4—88no—
1414C2×C4—164no—
1415C2×C4C2×H(5,𝔽2)12yes—
1416C2×C4C2×H(5,𝔽2)14yes—
1417C2×C4C2×H(5,𝔽2)14yes—
1418C2×C4C2×H(5,𝔽2)12yes—
1419C2×C4#58512yes—
1420C2×C4#58512yes—
1421C2×C4#58512yes—
1422C2×C4#58512yes—
1423C22—42no—
1424C22—44no—
1425C22—44no—
1426C22—44no—
1427C22—42no—
1428C22—44no—
1429C22—42no—
1430C22—44no—
1431C22—44no—
1432C22—42no—
1433C22—44no—
1434C22—44no—
1435C22—44no—
1436C22—42no—
1437C22—44no—
1438C22—44no—
1439C22—42no—
1440C22—44no—
1441C22—44no—
1442C22—44no—
1443C22—42no—
1444C22C22×H(5,𝔽2)11yescharacteristic
1445C22C22×H(5,𝔽2)11yescharacteristic
1446C22C2×#58511yescharacteristic
1447C22C2×#58511yescharacteristic
1448C22C2×#58511yescharacteristic
1449C22C2×#58511yescharacteristic
1450C222−1+611yescharacteristic
1451C4—24no—
1452C4—24no—
1453C4—22no—
1454C4—22no—
1455C4—22no—
1456C4—42no—
1457C4—42no—
1458C4—44no—
1459C4—42no—
1460C4—41no—
1461C4—44no—
1462C4—42no—
1463C4—41no—
1464C4—41no—
1465C4—42no—
1466C4—42no—
1467C4—42no—
1468C4—42no—
1469C4—42no—
1470C4—42no—
1471C4—44no—
1472C4—42no—
1473C4—42no—
1474C4—44no—
1475C4—42no—
1476C4#352914yes—
1477C2—82no—
1478C2—84no—
1479C2—84no—
1480C2C2×#352911yescharacteristic
1481C2#6289711yescharacteristic
1482C2#6296011yescharacteristic
1483C2#6296411yescharacteristic
1484C2#6301411yescharacteristic
1485C2#6302111yescharacteristic
1486C2#6303111yescharacteristic
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. #53130C2semidirect
2. #53059C2semidirect
3. #52984C2semidirect
4. #52621C2semidirect
5. #52386C2semidirect
6. #52353C2semidirect
7. #52306C2semidirect
8. #52160C2semidirect
9. #46343C2semidirect
10. #46314C2semidirect
11. #46257C2semidirect
12. #46063C2semidirect
13. #46050C2semidirect
14. #46016C2semidirect
15. #46013C2semidirect
16. #45997C2semidirect
17. #45958C2semidirect
18. #45952C2semidirect
19. #45938C2semidirect
20. #45768C2semidirect
21. #36496C2semidirect
22. #36469C2semidirect
23. #36313C2semidirect
24. #36300C2semidirect
25. #36250C2semidirect
26. #36113C2semidirect
27. #35844C2semidirect
28. #35778C2semidirect
29. #35724C2semidirect

Maximal subgroups

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

subgroupindex
#531302
#530592
#529842
#526212
#523862
#523532
#523062
#521602
#463432
#463142
#462572
#460632
#460502
#460162
#460132
#459972
#459582
#459522
#459382
#457682
#364962
#364692
#363132
#363002
#362502
#361132
#358442
#357782
#357242