Finite Group Databasebeta

← #8402502

Subgroups — #8402502

Order 512.

4823 conjugacy classes of subgroups.

The subgroup lattice has 1535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59411C212yesmaximal, complemented
2#59101C212yesmaximal, complemented
3#55535C214yesmaximal, complemented
4#55463C214yesmaximal, complemented
5#50842C214yesmaximal, complemented
6#48250C214yesmaximal, complemented
7#48244C214yesmaximal, complemented
8#48074C214yesmaximal, complemented
9#46112C212yesmaximal, complemented
10#45682C212yesmaximal, complemented
11#45421C211yesmaximal, characteristic, complemented
12#45276C211yesmaximal, characteristic, complemented
13#45142C211yesmaximal, characteristic, complemented
14#45141C211yesmaximal, characteristic, complemented
15#43670C214yesmaximal, complemented
16#43448C214yesmaximal, complemented
17#42878C211yesmaximal, characteristic, complemented
18#42877C211yesmaximal, characteristic, complemented
19#40225C212yesmaximal, complemented
20#39985C212yesmaximal, complemented
21#39857C212yesmaximal, complemented
22#39533C212yesmaximal, complemented
23#37321C211yesmaximal, characteristic, complemented
24#36574C211yesmaximal, characteristic, complemented
25#36496C211yesmaximal, characteristic, complemented
26#36419C211yesmaximal, characteristic, complemented
27#36135C211yesmaximal, characteristic, complemented
28#36031C211yesmaximal, characteristic, complemented
29#36029C211yesmaximal, characteristic
30#35622C211yesmaximal, characteristic, complemented
31#34968C211yesmaximal, characteristic, complemented
32C2×#559C2212yes—
33C2×#559C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#554C2211yescharacteristic
36C2×#550C2212yes—
37C2×#550C2211yescharacteristic
38C2×#541C2211yescharacteristic
39C2×#529C2212yes—
40C2×#520C2211yescharacteristic
41#2861C2212yes—
42#2859C2212yes—
43#2859C2211yescharacteristic
44#2858C2211yescharacteristic
45#2851C2212yes—
46#2850C2212yes—
47#2837C2214yes—
48#2827C2214yes—
49#2820C2212yes—
50#2820C2212yes—
51#2800C2214yes—
52#2796C2214yes—
53#2796C2214yes—
54#2783C2214yes—
55#2781C2214yes—
56#2781C2214yes—
57#2780C2214yes—
58#2780C2214yes—
59#2774C2214yes—
60#2772C2214yes—
61#2770C2214yes—
62#2768C2214yes—
63#2761C2214yes—
64#2755C2214yes—
65#2750C2214yes—
66#2748C2214yes—
67#2743C2214yes—
68#2739C2214yes—
69#2732C2214yes—
70#2730C2214yes—
71#2727C2214yes—
72#2727C2214yes—
73#2725C2214yes—
74#2723C2214yes—
75#2715C2214yes—
76#2715C2214yes—
77#2711C2214yes—
78#2711C2214yes—
79#2710C2214yes—
80#2709C2214yes—
81#2709C2214yes—
82#2707C2214yes—
83#2707C2214yes—
84#2706C2214yes—
85#2705C2214yes—
86#2705C2214yes—
87#2705C2214yes—
88#2704C2214yes—
89#2701C2214yes—
90#2701C2214yes—
91#2701C2214yes—
92#2701C2214yes—
93#2695C2214yes—
94#2693C2214yes—
95#2686C2214yes—
96#2672C2214yes—
97#2672C2214yes—
98#2672C2214yes—
99#2667C2214yes—
100#2662C2212yes—
101#2662C2212yes—
102#2651C2214yes—
103#2637C2212yes—
104#2636C2214yes—
105#2636C2212yes—
106#2630C2214yes—
107#2628C2211yescharacteristic
108#2627C2212yes—
109#2619C2211yescharacteristic
110#2619C2212yes—
111#2608C2214yes—
112#2593C2214yes—
113#2590C2214yes—
114#2587C2214yes—
115#2586C2214yes—
116#2584C2214yes—
117#2584C2212yes—
118#2582C2212yes—
119#2581C2212yes—
120#2581C2211yescharacteristic
121#2581C2211yescharacteristic
122#2570C2212yes—
123#2569C2214yes—
124#2568C2211yescharacteristic
125#2567C2211yescharacteristic
126#2566C2211yescharacteristic
127#2566C2212yes—
128#2565C2211yescharacteristic
129#2564C2212yes—
130#2562C2212yes—
131#2559C2214yes—
132#2559C2214yes—
133#2559C2214yes—
134#2553C2214yes—
135#2548C2211yescharacteristic
136#2547C2211yescharacteristic
137#2546C2211yescharacteristic
138#2545C2212yes—
139#2544C2214yes—
140#2544C2214yes—
141#2544C2212yes—
142#2541C2211yescharacteristic
143#2541C2212yes—
144#2538C2212yes—
145#2538C2212yes—
146#2536C2211yescharacteristic
147#2535C2211yescharacteristic
148#2535C2212yes—
149#2525C2212yes—
150#2521C2212yes—
151#2520C2212yes—
152#2515C2212yes—
153#2512C2212yes—
154#2509C2214yes—
155#2508C2214yes—
156#2503C2211yescharacteristic
157#2502C2211yescharacteristic
158#2500C2212yes—
159#2498C2214yes—
160#2490C2212yes—
161#2489C2212yes—
162#2487C2212yes—
163#2485C2214yes—
164#2481C2214yes—
165#2478C2214yes—
166#2476C2214yes—
167#2475C2214yes—
168#2473C2214yes—
169#2468C2214yes—
170#2468C2212yes—
171#2466C2214yes—
172#2466C2214yes—
173#2466C2214yes—
174#2465C2212yes—
175#2461C2214yes—
176#2461C2214yes—
177#2461C2214yes—
178#2461C2212yes—
179#2458C2212yes—
180#2455C2214yes—
181#2454C2212yes—
182#2454C2212yes—
183#2453C2212yes—
184#2453C2212yes—
185#2453C2212yes—
186#2450C2214yes—
187#2448C2212yes—
188#2447C2214yes—
189#2445C2214yes—
190#2445C2212yes—
191#2445C2214yes—
192#2444C2214yes—
193#2444C2214yes—
194#2442C2212yes—
195#2441C2212yes—
196#2441C2212yes—
197#2438C2214yes—
198#2432C2211yescharacteristic
199#2432C2212yes—
200#2432C2212yes—
201#2432C2211yescharacteristic
202#2429C2212yes—
203#2428C2212yes—
204#2428C2214yes—
205#2427C2212yes—
206#2427C2212yes—
207#2427C2212yes—
208#2426C2212yes—
209#2426C2214yes—
210#2425C2214yes—
211#2425C2214yes—
212#2425C2214yes—
213#2425C2214yes—
214#2423C2212yes—
215#2422C2212yes—
216#2422C2212yes—
217#2421C2214yes—
218#2420C2212yes—
219#2419C2214yes—
220#2416C2212yes—
221#2416C2214yes—
222#2415C2212yes—
223#2399C2211yescharacteristic
224#2398C2211yescharacteristic
225#2396C2211yescharacteristic
226C2×#400C2212yes—
227#2392C2211yescharacteristic
228#2392C2212yes—
229#2377C2214yes—
230#2376C2214yes—
231#2370C2214yes—
232#2367C2214yes—
233#2365C2212yes—
234#2363C2212yes—
235#2361C2214yes—
236#2359C2214yes—
237#2359C2214yes—
238#2351C2211yescharacteristic
239#2351C2211yescharacteristic
240#2351C2211yescharacteristic
241#2349C2214yes—
242#2349C2211yescharacteristic
243#2349C2212yes—
244#2341C2212yes—
245#2339C2212yes—
246#2339C2212yes—
247#2334C2214yes—
248#2331C2211yescharacteristic
249#2329C2214yes—
250#2328C2211yescharacteristic
251#2327C2211yescharacteristic
252#2326C2211yescharacteristic
253#2325C2214yes—
254#2318C2214yes—
255C4×C4⋊Q8C2212yes—
256C4×C4⋊Q8C2211yescharacteristic
257C4×#127C2212yes—
258C4×#126C2212yes—
259C4×#124C2212yes—
260C4×#124C2211yescharacteristic
261C4×C22⋊Q8C2212yes—
262C4×#123C2212yes—
263#2298C2211yescharacteristic
264#2297C2212yes—
265C42×Q8C2211yescharacteristic
266C42×D4C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2312yes—
269#559—48no—
270#559—44no—
271#556—44no—
272#554—44no—
273#550—44no—
274#550—48no—
275#541—44no—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×#127C2312yes—
281C2×#127C2311yescharacteristic
282C2×#127C2312yes—
283C2×#127C2314yes—
284#529—48no—
285C2×#126C2312yes—
286C2×#126C2314yes—
287C2×#126C2312yes—
288C2×#126C2312yes—
289C2×#126C2314yes—
290C2×#126C2314yes—
291C2×#125C2312yes—
292C2×#125C2312yes—
293C2×#125C2311yescharacteristic
294C2×#125C2312yes—
295C2×#125C2314yes—
296C2×#125C2312yes—
297C2×#124C2311yescharacteristic
298C2×#124C2311yescharacteristic
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#124C2312yes—
302C2×#124C2314yes—
303C2×#124C2312yes—
304C2×#124C2314yes—
305C2×#124C2312yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×#123C2314yes—
313C2×#123C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2311yescharacteristic
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2311yescharacteristic
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2312yes—
325C2×#121C2314yes—
326C2×#121C2312yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331#520—44no—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2312yes—
345C2×C4×D4C2311yescharacteristic
346C2×C4×D4C2312yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2314yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2311yescharacteristic
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×#117C2311yescharacteristic
362C2×#117C2314yes—
363C2×#117C2312yes—
364C2×#117C2312yes—
365C22×C4⋊C4C2312yes—
366C22×C4⋊C4C2312yes—
367C22×C4⋊C4C2311yescharacteristic
368C22×C42C2312yes—
369#400C2311yescharacteristic
370#400C2312yes—
371#400C2312yes—
372#400C2312yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2312yes—
379#400C2314yes—
380#400C2312yes—
381#400C2314yes—
382#400C2312yes—
383#400C2314yes—
384#399C2312yes—
385#399C2314yes—
386#399C2314yes—
387#399C2314yes—
388#399C2314yes—
389#399C2314yes—
390#399C2311yescharacteristic
391#399C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2311yescharacteristic
400#398C2312yes—
401#398C2314yes—
402#398C2314yes—
403#398C2312yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2312yes—
408#398C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2311yescharacteristic
416#397C2312yes—
417#397C2314yes—
418#397C2312yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2312yes—
440#396C2312yes—
441#396C2314yes—
442#396C2314yes—
443#395C2312yes—
444#395C2311yescharacteristic
445#395C2312yes—
446#395C2312yes—
447#395C2312yes—
448#395C2312yes—
449#395C2314yes—
450#395C2312yes—
451#395C2312yes—
452#394C2312yes—
453#394C2312yes—
454#394C2311yescharacteristic
455#394C2312yes—
456#394C2312yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2312yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2312yes—
471#394C2314yes—
472#394C2314yes—
473#394C2312yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#393C2311yescharacteristic
484#393C2312yes—
485#393C2312yes—
486#392C2314yes—
487#392C2312yes—
488#392C2312yes—
489#392C2312yes—
490#392C2312yes—
491#392C2311yescharacteristic
492#392C2312yes—
493#391C2311yescharacteristic
494#391C2312yes—
495#391C2312yes—
496#391C2311yescharacteristic
497#391C2311yescharacteristic
498#391C2312yes—
499#391C2312yes—
500#391C2314yes—
501#391C2311yescharacteristic
502#391C2311yescharacteristic
503#391C2314yes—
504#391C2312yes—
505#391C2314yes—
506#391C2311yescharacteristic
507#391C2312yes—
508#390C2311yescharacteristic
509#390C2312yes—
510#390C2314yes—
511#390C2314yes—
512#390C2311yescharacteristic
513#390C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2314yes—
517#390C2312yes—
518#390C2314yes—
519#390C2314yes—
520#390C2314yes—
521#390C2314yes—
522#390C2314yes—
523#390C2314yes—
524#390C2314yes—
525#390C2312yes—
526#390C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2314yes—
554#389C2312yes—
555#389C2314yes—
556#389C2314yes—
557#389C2312yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
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#388C2312yes—
584#388C2314yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2314yes—
590#388C2312yes—
591#388C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
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#387C2314yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
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#386C2312yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2312yes—
649#385C2314yes—
650#385C2314yes—
651#385C2312yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2312yes—
666#385C2314yes—
667#384C2312yes—
668#384C2311yescharacteristic
669#384C2312yes—
670#384C2311yescharacteristic
671#383C2312yes—
672#382C2312yes—
673#382C2312yes—
674#382C2311yescharacteristic
675#382C2311yescharacteristic
676#382C2312yes—
677#382C2314yes—
678#382C2311yescharacteristic
679#382C2311yescharacteristic
680#382C2314yes—
681#382C2312yes—
682#382C2312yes—
683#381C2314yes—
684#381C2314yes—
685#381C2314yes—
686#381C2314yes—
687#381C2312yes—
688#380C2314yes—
689#380C2314yes—
690#380C2314yes—
691#380C2314yes—
692#380C2314yes—
693#380C2314yes—
694#380C2314yes—
695#380C2312yes—
696#380C2312yes—
697#380C2312yes—
698#380C2312yes—
699#380C2314yes—
700#380C2314yes—
701#380C2314yes—
702#380C2312yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2311yescharacteristic
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2311yescharacteristic
713C4×C4⋊C4C2311yescharacteristic
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2314yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2314yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2314yes—
733C4×C22⋊C4C2311yescharacteristic
734C4×C22⋊C4C2311yescharacteristic
735C4×C22⋊C4C2312yes—
736#376C2311yescharacteristic
737C2×#95C2312yes—
738C2×#95C2314yes—
739C2×#95C2314yes—
740C2×#95C2314yes—
741C43C2312yes—
742C43C2311yescharacteristic
743C2×#41—24no—
744C2×#41—28no—
745C2×#41—24no—
746C2×#41—42no—
747C2×#41—44no—
748C2×#41—44no—
749C22×Q8C2411yescharacteristic
750C22×Q8C2411yescharacteristic
751C22×Q8C2411yescharacteristic
752C22×Q8C2411yescharacteristic
753C22×Q8C2412yes—
754C22×Q8C2412yes—
755C22×D4C2412yes—
756C22×D4C2414yes—
757C22×D4C2412yes—
758C22×D4C2411yescharacteristic
759C22×D4C2411yescharacteristic
760C22×D4C2412yes—
761C22×D4C2414yes—
762C22×D4C2414yes—
763C22×D4C2412yes—
764C22×D4C2412yes—
765C22×D4C2414yes—
766C22×D4C2414yes—
767C22×D4C2414yes—
768C23×C4C2411yescharacteristic
769C23×C4C2412yes—
770C23×C4C2412yes—
771C23×C4C2412yes—
772C23×C4C2414yes—
773C23×C4C2414yes—
774C23×C4C2414yes—
775C23×C4C2412yes—
776C23×C4C2412yes—
777C23×C4C2414yes—
778C23×C4C2412yes—
779C23×C4C2414yes—
780C23×C4C2412yes—
781C4⋊Q8—24no—
782C4⋊Q8—24no—
783C4⋊Q8—24no—
784C4⋊Q8—42no—
785#127—28no—
786#127—24no—
787#127—44no—
788#127—48no—
789#126—44no—
790#126—44no—
791#126—44no—
792#126—48no—
793#126—48no—
794#126—48no—
795#125—48no—
796#125—44no—
797#125—42no—
798#125—44no—
799#125—44no—
800#125—44no—
801#124—24no—
802#124—24no—
803#124—44no—
804#124—48no—
805#124—44no—
806#124—44no—
807#124—44no—
808#124—44no—
809#124—48no—
810#123—48no—
811#123—48no—
812#123—48no—
813#123—48no—
814#123—48no—
815#123—44no—
816#123—48no—
817#123—48no—
818C22⋊Q8—44no—
819C22⋊Q8—48no—
820C22⋊Q8—48no—
821C22⋊Q8—44no—
822C22⋊Q8—42no—
823C22⋊Q8—42no—
824C22⋊Q8—44no—
825C22⋊Q8—44no—
826#121—28no—
827#121—48no—
828#121—48no—
829#121—48no—
830#121—48no—
831#121—48no—
832#121—44no—
833#121—44no—
834#121—48no—
835C4×Q8—24no—
836C4×Q8—24no—
837C4×Q8—24no—
838C4×Q8—24no—
839C4×Q8—44no—
840C4×Q8—44no—
841C4×Q8—42no—
842C4×Q8—44no—
843C4×Q8—44no—
844C4×Q8—44no—
845C4×Q8—44no—
846C4×D4—28no—
847C4×D4—24no—
848C4×D4—24no—
849C4×D4—48no—
850C4×D4—48no—
851C4×D4—44no—
852C4×D4—44no—
853C4×D4—42no—
854C4×D4—44no—
855C4×D4—44no—
856C4×D4—44no—
857C4×D4—44no—
858C4×D4—44no—
859C4×D4—44no—
860C4×D4—44no—
861C4×D4—48no—
862C4×D4—48no—
863C4×D4—48no—
864#117—24no—
865#117—44no—
866#117—48no—
867#117—44no—
868C2×C4⋊C4—44no—
869C2×C4⋊C4—42no—
870C2×C4⋊C4—44no—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2411yescharacteristic
936C2×C22⋊C4C2411yescharacteristic
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2414yes—
983C2×C22⋊C4C2414yes—
984C2×C22⋊C4C2414yes—
985C2×C22⋊C4C2412yes—
986C2×C22⋊C4C2412yes—
987C2×C22⋊C4C2414yes—
988C2×C42—44no—
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2412yes—
1000C2×C42C2412yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004C2×C42C2412yes—
1005C2×C42C2412yes—
1006C2×C42C2414yes—
1007C2×C42C2414yes—
1008C2×C42C2414yes—
1009C2×C42C2414yes—
1010C2×C42C2412yes—
1011C2×C42C2412yes—
1012C2×C42C2412yes—
1013C2×C42C2414yes—
1014C2×C42C2411yescharacteristic
1015#95C2411yescharacteristic
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2411yescharacteristic
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2412yes—
1044#95C2414yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2414yes—
1048#95C2411yescharacteristic
1049#95C2412yes—
1050#95C2411yescharacteristic
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2414yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2414yes—
1075C24C2511yescharacteristic
1076C24C2512yes—
1077C24C2514yes—
1078C24C2512yes—
1079#41—416no—
1080#41—816no—
1081C2×Q8—22no—
1082C2×Q8—22no—
1083C2×Q8—22no—
1084C2×Q8—22no—
1085C2×Q8—22no—
1086C2×Q8—22no—
1087C2×Q8—22no—
1088C2×Q8—24no—
1089C2×Q8—22no—
1090C2×Q8—22no—
1091C2×Q8—24no—
1092C2×Q8—42no—
1093C2×Q8—42no—
1094C2×Q8—42no—
1095C2×Q8—44no—
1096C2×Q82−1+414yes—
1097C2×D4—28no—
1098C2×D4—24no—
1099C2×D4—28no—
1100C2×D4—28no—
1101C2×D4—22no—
1102C2×D4—22no—
1103C2×D4—24no—
1104C2×D4—24no—
1105C2×D4—24no—
1106C2×D4—24no—
1107C2×D4—22no—
1108C2×D4—24no—
1109C2×D4—24no—
1110C2×D4—28no—
1111C2×D4—28no—
1112C2×D4—24no—
1113C2×D4—42no—
1114C2×D4—44no—
1115C2×D4—42no—
1116C2×D4—42no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—42no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4H(5,𝔽2)14yes—
1133C22×C4—24no—
1134C22×C4—28no—
1135C22×C4—24no—
1136C22×C4—22no—
1137C22×C4—24no—
1138C22×C4—22no—
1139C22×C4—24no—
1140C22×C4—22no—
1141C22×C4—24no—
1142C22×C4—24no—
1143C22×C4—28no—
1144C22×C4—42no—
1145C22×C4—42no—
1146C22×C4—42no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—42no—
1150C22×C4—42no—
1151C22×C4—44no—
1152C22×C4—42no—
1153C22×C4—42no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—42no—
1157C22×C4—42no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2511yescharacteristic
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2514yes—
1179C22×C4C2512yes—
1180C22×C4C2514yes—
1181C22×C4C2511yescharacteristic
1182C22×C4C2512yes—
1183C22×C4C2514yes—
1184C22×C4C2512yes—
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2511yescharacteristic
1189C22×C4C2512yes—
1190C22×C4C2511yescharacteristic
1191C22×C4C2511yescharacteristic
1192C22×C4C2512yes—
1193C22×C4C2512yes—
1194C22×C4C2512yes—
1195C22×C4C2511yescharacteristic
1196C4⋊C4—22no—
1197C4⋊C4—22no—
1198C4⋊C4—22no—
1199C4⋊C4—24no—
1200C4⋊C4—22no—
1201C4⋊C4—24no—
1202C4⋊C4—22no—
1203C4⋊C4—22no—
1204C4⋊C4—24no—
1205C4⋊C4—22no—
1206C4⋊C4—24no—
1207C4⋊C4—22no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—28no—
1213C4⋊C4—28no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—28no—
1217C4⋊C4—28no—
1218C4⋊C4—24no—
1219C4⋊C4—28no—
1220C4⋊C4—24no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—42no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—42no—
1236C4⋊C4—42no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—42no—
1253C4⋊C4—42no—
1254C4⋊C4—42no—
1255C4⋊C4—42no—
1256C4⋊C4—42no—
1257C4⋊C4—42no—
1258C4⋊C4—44no—
1259C22⋊C4—28no—
1260C22⋊C4—28no—
1261C22⋊C4—28no—
1262C22⋊C4—28no—
1263C22⋊C4—22no—
1264C22⋊C4—22no—
1265C22⋊C4—24no—
1266C22⋊C4—24no—
1267C22⋊C4—28no—
1268C22⋊C4—24no—
1269C22⋊C4—28no—
1270C22⋊C4—28no—
1271C22⋊C4—24no—
1272C22⋊C4—28no—
1273C22⋊C4—24no—
1274C22⋊C4—24no—
1275C22⋊C4—42no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—42no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—42no—
1296C22⋊C4—42no—
1297C22⋊C4—42no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—42no—
1309C22⋊C4—42no—
1310C22⋊C4—42no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C42—22no—
1314C42—24no—
1315C42—22no—
1316C42—24no—
1317C42—24no—
1318C42—22no—
1319C42—24no—
1320C42—24no—
1321C42—24no—
1322C42—22no—
1323C42—22no—
1324C42—24no—
1325C42—24no—
1326C42—24no—
1327C42—24no—
1328C42—42no—
1329C42—42no—
1330C42—42no—
1331C42—44no—
1332C42—44no—
1333C42—44no—
1334C42—44no—
1335C42—42no—
1336C42—42no—
1337C42—44no—
1338C42H(5,𝔽2)14yes—
1339C23—22no—
1340C23—22no—
1341C23—24no—
1342C23—24no—
1343C23—21no—
1344C23—22no—
1345C23—24no—
1346C23—24no—
1347C23—22no—
1348C23—21no—
1349C23—21no—
1350C23—22no—
1351C23—24no—
1352C23—22no—
1353C23—24no—
1354C23—22no—
1355C23—22no—
1356C23—24no—
1357C23—22no—
1358C23—24no—
1359C23—24no—
1360C23—22no—
1361C23—22no—
1362C23C2×H(5,𝔽2)14yes—
1363C23C2611yescharacteristic
1364Q8—28no—
1365Q8—44no—
1366Q8—44no—
1367Q8—44no—
1368Q8—84no—
1369Q8—84no—
1370D4—28no—
1371D4—416no—
1372D4—48no—
1373D4—44no—
1374D4—48no—
1375D4—84no—
1376D4—84no—
1377D4—84no—
1378D4—88no—
1379D4—88no—
1380D4—88no—
1381D4—164no—
1382D4—164no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—21no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—21no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—21no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—24no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—24no—
1434C2×C4—24no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—22no—
1441C2×C4—24no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—24no—
1446C2×C4—22no—
1447C2×C4—24no—
1448C2×C4—48no—
1449C2×C4—44no—
1450C2×C4—48no—
1451C2×C4—84no—
1452C2×C4—88no—
1453C2×C4—88no—
1454C2×C4—84no—
1455C2×C4—84no—
1456C2×C4—164no—
1457C2×C4—162no—
1458C2×C4—164no—
1459C2×C4—162no—
1460C2×C4—164no—
1461C2×C4C2×H(5,𝔽2)12yes—
1462C2×C4C2×H(5,𝔽2)12yes—
1463C2×C4C2×H(5,𝔽2)12yes—
1464C2×C4C2×H(5,𝔽2)12yes—
1465C2×C4C2×2−1+414yes—
1466C2×C4C2×2−1+412yes—
1467C2×C4#58514yes—
1468C2×C4#58514yes—
1469C22—24no—
1470C22—28no—
1471C22—44no—
1472C22—42no—
1473C22—42no—
1474C22—41no—
1475C22—42no—
1476C22—44no—
1477C22—42no—
1478C22—42no—
1479C22—44no—
1480C22—44no—
1481C22—42no—
1482C22—42no—
1483C22—44no—
1484C22—42no—
1485C22—42no—
1486C22—44no—
1487C22—41no—
1488C22—44no—
1489C22—42no—
1490C22—44no—
1491C22—42no—
1492C22—41no—
1493C22C22×H(5,𝔽2)11yescharacteristic
1494C22C22×H(5,𝔽2)11yescharacteristic
1495C22C22×2−1+411yescharacteristic
1496C22C2×#58512yes—
1497C22C2×#58512yes—
1498C4—24no—
1499C4—24no—
1500C4—24no—
1501C4—22no—
1502C4—22no—
1503C4—41no—
1504C4—42no—
1505C4—42no—
1506C4—42no—
1507C4—42no—
1508C4—42no—
1509C4—44no—
1510C4—42no—
1511C4—42no—
1512C4—42no—
1513C4—44no—
1514C4—42no—
1515C4—41no—
1516C4—42no—
1517C4—42no—
1518C4—41no—
1519C4—42no—
1520C4—42no—
1521C4—42no—
1522C4—44no—
1523C4—42no—
1524C4#353614yes—
1525C2—44no—
1526C2—81no—
1527C2—82no—
1528C2—84no—
1529C2C2×#353611yescharacteristic
1530C2#6283611yescharacteristic
1531C2#6283611yescharacteristic
1532C2#6301812yes—
1533C2#6303312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36029C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59411C2semidirect
2. #59101C2semidirect
3. #55535C2semidirect
4. #55463C2semidirect
5. #50842C2semidirect
6. #48250C2semidirect
7. #48244C2semidirect
8. #48074C2semidirect
9. #46112C2semidirect
10. #45682C2semidirect
11. #45421C2semidirect
12. #45276C2semidirect
13. #45142C2semidirect
14. #45141C2semidirect
15. #43670C2semidirect
16. #43448C2semidirect
17. #42878C2semidirect
18. #42877C2semidirect
19. #40225C2semidirect
20. #39985C2semidirect
21. #39857C2semidirect
22. #39533C2semidirect
23. #37321C2semidirect
24. #36574C2semidirect
25. #36496C2semidirect
26. #36419C2semidirect
27. #36135C2semidirect
28. #36031C2semidirect
30. #35622C2semidirect
31. #34968C2semidirect

Maximal subgroups

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

subgroupindex
#594112
#591012
#555352
#554632
#508422
#482502
#482442
#480742
#461122
#456822
#454212
#452762
#451422
#451412
#436702
#434482
#428782
#428772
#402252
#399852
#398572
#395332
#373212
#365742
#364962
#364192
#361352
#360312
#360292
#356222
#349682