Finite Group Databasebeta

← #8402613

Subgroups — #8402613

Order 512.

4831 conjugacy classes of subgroups.

The subgroup lattice has 1540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59410C212yesmaximal, complemented
2#59102C212yesmaximal, complemented
3#55410C214yesmaximal, complemented
4#55287C214yesmaximal, complemented
5#51919C214yesmaximal, complemented
6#48746C214yesmaximal, complemented
7#48510C214yesmaximal, complemented
8#48304C214yesmaximal, complemented
9#46104C212yesmaximal, complemented
10#45695C212yesmaximal, complemented
11#45429C211yesmaximal, characteristic, complemented
12#45270C211yesmaximal, characteristic, complemented
13#45269C211yesmaximal, characteristic, complemented
14#44947C211yesmaximal, characteristic, complemented
15#44339C214yesmaximal, complemented
16#43152C214yesmaximal, complemented
17#42646C211yesmaximal, characteristic, complemented
18#42645C211yesmaximal, characteristic, complemented
19#40153C212yesmaximal, complemented
20#39985C212yesmaximal, complemented
21#39882C212yesmaximal, complemented
22#39791C212yesmaximal, complemented
23#37397C211yesmaximal, characteristic, complemented
24#36573C211yesmaximal, characteristic, complemented
25#36508C211yesmaximal, characteristic, complemented
26#36415C211yesmaximal, characteristic, complemented
27#36135C211yesmaximal, characteristic, complemented
28#36040C211yesmaximal, characteristic, complemented
29#36020C211yesmaximal, characteristic, complemented
30#35534C211yesmaximal, characteristic, complemented
31#34968C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#556C2212yes—
34C2×#556C2211yescharacteristic
35C2×#555C2211yescharacteristic
36C2×#547C2212yes—
37C2×#547C2211yescharacteristic
38C2×#540C2211yescharacteristic
39C2×#529C2212yes—
40C2×#520C2211yescharacteristic
41#2862C2211yescharacteristic
42#2861C2212yes—
43#2859C2211yescharacteristic
44#2859C2212yes—
45#2851C2212yes—
46#2850C2212yes—
47#2837C2214yes—
48#2827C2214yes—
49#2814C2212yes—
50#2813C2212yes—
51#2802C2214yes—
52#2798C2214yes—
53#2786C2214yes—
54#2783C2214yes—
55#2780C2214yes—
56#2780C2214yes—
57#2773C2214yes—
58#2773C2214yes—
59#2768C2214yes—
60#2767C2214yes—
61#2767C2214yes—
62#2761C2214yes—
63#2755C2214yes—
64#2754C2214yes—
65#2752C2214yes—
66#2749C2214yes—
67#2748C2214yes—
68#2748C2214yes—
69#2747C2214yes—
70#2744C2214yes—
71#2741C2214yes—
72#2732C2214yes—
73#2731C2214yes—
74#2727C2214yes—
75#2722C2214yes—
76#2714C2214yes—
77#2714C2214yes—
78#2711C2214yes—
79#2710C2214yes—
80#2708C2214yes—
81#2706C2214yes—
82#2706C2214yes—
83#2705C2214yes—
84#2705C2214yes—
85#2705C2214yes—
86#2703C2214yes—
87#2703C2214yes—
88#2702C2214yes—
89#2698C2214yes—
90#2696C2214yes—
91#2695C2214yes—
92#2694C2214yes—
93#2694C2214yes—
94#2692C2214yes—
95#2691C2214yes—
96#2681C2214yes—
97#2676C2214yes—
98#2672C2214yes—
99#2667C2214yes—
100#2664C2214yes—
101#2656C2212yes—
102#2639C2212yes—
103#2636C2214yes—
104#2635C2214yes—
105#2628C2211yescharacteristic
106#2628C2212yes—
107#2624C2212yes—
108#2624C2212yes—
109#2621C2211yescharacteristic
110#2618C2212yes—
111#2609C2214yes—
112#2608C2214yes—
113#2601C2214yes—
114#2596C2214yes—
115#2585C2214yes—
116#2582C2212yes—
117#2580C2212yes—
118#2580C2214yes—
119#2580C2211yescharacteristic
120#2580C2212yes—
121#2580C2211yescharacteristic
122#2570C2212yes—
123#2569C2214yes—
124#2566C2211yescharacteristic
125#2565C2212yes—
126#2565C2211yescharacteristic
127#2564C2214yes—
128#2563C2211yescharacteristic
129#2563C2212yes—
130#2557C2214yes—
131#2557C2214yes—
132#2554C2214yes—
133#2554C2214yes—
134#2554C2214yes—
135#2553C2214yes—
136#2548C2211yescharacteristic
137#2547C2211yescharacteristic
138#2546C2211yescharacteristic
139#2545C2212yes—
140#2544C2212yes—
141#2543C2212yes—
142#2542C2211yescharacteristic
143#2541C2211yescharacteristic
144#2540C2214yes—
145#2538C2212yes—
146#2537C2212yes—
147#2536C2211yescharacteristic
148#2535C2211yescharacteristic
149#2535C2214yes—
150#2525C2212yes—
151#2521C2212yes—
152#2520C2212yes—
153#2519C2214yes—
154#2519C2214yes—
155#2515C2212yes—
156#2511C2212yes—
157#2504C2211yescharacteristic
158#2501C2211yescharacteristic
159#2499C2212yes—
160#2498C2212yes—
161#2498C2212yes—
162#2490C2212yes—
163#2489C2212yes—
164#2486C2212yes—
165#2481C2214yes—
166#2481C2214yes—
167#2478C2214yes—
168#2478C2214yes—
169#2475C2214yes—
170#2471C2214yes—
171#2471C2214yes—
172#2471C2214yes—
173#2468C2212yes—
174#2465C2212yes—
175#2464C2214yes—
176#2461C2212yes—
177#2458C2212yes—
178#2457C2214yes—
179#2456C2214yes—
180#2456C2214yes—
181#2456C2214yes—
182#2455C2214yes—
183#2454C2212yes—
184#2454C2212yes—
185#2454C2214yes—
186#2454C2214yes—
187#2454C2214yes—
188#2454C2212yes—
189#2453C2212yes—
190#2453C2212yes—
191#2450C2214yes—
192#2448C2214yes—
193#2447C2212yes—
194#2446C2212yes—
195#2444C2214yes—
196#2443C2214yes—
197#2442C2212yes—
198#2442C2214yes—
199#2441C2212yes—
200#2441C2212yes—
201#2438C2214yes—
202#2431C2211yescharacteristic
203#2431C2212yes—
204#2431C2211yescharacteristic
205#2431C2212yes—
206#2429C2214yes—
207#2429C2212yes—
208#2428C2212yes—
209#2427C2212yes—
210#2426C2212yes—
211#2426C2212yes—
212#2426C2212yes—
213#2425C2214yes—
214#2423C2212yes—
215#2423C2212yes—
216#2422C2212yes—
217#2421C2212yes—
218#2417C2214yes—
219#2417C2212yes—
220#2414C2214yes—
221#2414C2212yes—
222#2413C2214yes—
223#2399C2211yescharacteristic
224#2398C2211yescharacteristic
225#2396C2212yes—
226#2396C2211yescharacteristic
227#2392C2211yescharacteristic
228C2×#398C2212yes—
229#2377C2214yes—
230#2376C2214yes—
231#2366C2212yes—
232#2362C2214yes—
233#2362C2212yes—
234#2359C2214yes—
235#2352C2214yes—
236#2352C2214yes—
237#2352C2214yes—
238#2351C2211yescharacteristic
239#2351C2212yes—
240#2349C2211yescharacteristic
241#2349C2211yescharacteristic
242#2349C2214yes—
243#2349C2211yescharacteristic
244#2341C2212yes—
245#2341C2212yes—
246#2339C2212yes—
247#2336C2214yes—
248#2331C2211yescharacteristic
249#2329C2214yes—
250#2328C2211yescharacteristic
251#2327C2211yescharacteristic
252#2326C2211yescharacteristic
253#2325C2214yes—
254#2324C2214yes—
255C4×C4⋊Q8C2212yes—
256C4×#127C2212yes—
257C4×#127C2211yescharacteristic
258C4×#126C2212yes—
259C4×#124C2212yes—
260C4×#124C2211yescharacteristic
261C4×C22⋊Q8C2212yes—
262C4×#123C2212yes—
263#2298C2211yescharacteristic
264#2297C2212yes—
265C42×Q8C2211yescharacteristic
266C42×D4C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2312yes—
269#557—44no—
270#556—44no—
271#556—48no—
272#555—44no—
273#547—44no—
274#547—48no—
275#540—44no—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2312yes—
280C2×#127C2311yescharacteristic
281C2×#127C2311yescharacteristic
282C2×#127C2311yescharacteristic
283#529—48no—
284C2×#126C2312yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#126C2314yes—
288C2×#126C2314yes—
289C2×#125C2311yescharacteristic
290C2×#125C2312yes—
291C2×#125C2314yes—
292C2×#125C2312yes—
293C2×#125C2314yes—
294C2×#124C2311yescharacteristic
295C2×#124C2311yescharacteristic
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2314yes—
299C2×#124C2312yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2312yes—
306C2×#123C2314yes—
307C2×#123C2312yes—
308C2×#123C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2312yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2312yes—
325C2×#121C2311yescharacteristic
326C2×#121C2312yes—
327C2×#121C2314yes—
328C2×#121C2311yescharacteristic
329#520—44no—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2314yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2314yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×#117C2311yescharacteristic
358C2×#117C2314yes—
359C2×#117C2314yes—
360C2×#117C2312yes—
361C2×#117C2312yes—
362C2×#117C2312yes—
363C2×#117C2312yes—
364C22×C4⋊C4C2314yes—
365C22×C4⋊C4C2312yes—
366C22×C4⋊C4C2312yes—
367C22×C4⋊C4C2311yescharacteristic
368C22×C42C2312yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2312yes—
377#400C2311yescharacteristic
378#400C2312yes—
379#400C2314yes—
380#400C2314yes—
381#399C2312yes—
382#399C2314yes—
383#399C2311yescharacteristic
384#399C2312yes—
385#399C2314yes—
386#399C2312yes—
387#399C2314yes—
388#399C2314yes—
389#399C2314yes—
390#399C2312yes—
391#399C2312yes—
392#399C2314yes—
393#399C2314yes—
394#399C2314yes—
395#399C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2312yes—
407#398C2312yes—
408#398C2312yes—
409#398C2311yescharacteristic
410#398C2314yes—
411#398C2312yes—
412#398C2312yes—
413#398C2314yes—
414#398C2312yes—
415#398C2312yes—
416#398C2312yes—
417#398C2314yes—
418#398C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2312yes—
426#397C2312yes—
427#397C2311yescharacteristic
428#397C2312yes—
429#397C2312yes—
430#397C2312yes—
431#397C2312yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2312yes—
450#396C2312yes—
451#396C2314yes—
452#396C2314yes—
453#395C2312yes—
454#395C2312yes—
455#395C2311yescharacteristic
456#395C2312yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2311yescharacteristic
465#394C2312yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2312yes—
473#394C2312yes—
474#393C2311yescharacteristic
475#393C2312yes—
476#393C2312yes—
477#393C2312yes—
478#393C2312yes—
479#393C2314yes—
480#393C2312yes—
481#393C2312yes—
482#392C2314yes—
483#392C2314yes—
484#392C2314yes—
485#392C2314yes—
486#392C2311yescharacteristic
487#392C2314yes—
488#392C2312yes—
489#392C2314yes—
490#392C2314yes—
491#392C2314yes—
492#392C2314yes—
493#391C2311yescharacteristic
494#391C2312yes—
495#391C2311yescharacteristic
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2312yes—
504#391C2314yes—
505#391C2312yes—
506#390C2311yescharacteristic
507#390C2312yes—
508#390C2312yes—
509#390C2314yes—
510#390C2314yes—
511#390C2311yescharacteristic
512#390C2314yes—
513#390C2312yes—
514#390C2314yes—
515#390C2311yescharacteristic
516#390C2314yes—
517#390C2314yes—
518#390C2314yes—
519#390C2311yescharacteristic
520#390C2314yes—
521#390C2312yes—
522#390C2311yescharacteristic
523#390C2314yes—
524#390C2314yes—
525#390C2311yescharacteristic
526#390C2314yes—
527#390C2314yes—
528#390C2314yes—
529#390C2314yes—
530#390C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2312yes—
553#389C2314yes—
554#389C2314yes—
555#389C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
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#388C2312yes—
581#388C2314yes—
582#388C2314yes—
583#388C2312yes—
584#388C2312yes—
585#388C2314yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
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#387C2314yes—
619#387C2314yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
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#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2312yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2312yes—
652#385C2314yes—
653#385C2312yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2312yes—
667#384C2311yescharacteristic
668#384C2312yes—
669#384C2312yes—
670#384C2311yescharacteristic
671#383C2312yes—
672#382C2312yes—
673#382C2314yes—
674#382C2311yescharacteristic
675#382C2311yescharacteristic
676#382C2311yescharacteristic
677#382C2311yescharacteristic
678#382C2314yes—
679#382C2312yes—
680#382C2314yes—
681#382C2312yes—
682#382C2314yes—
683#381C2314yes—
684#381C2314yes—
685#381C2312yes—
686#380C2314yes—
687#380C2314yes—
688#380C2314yes—
689#380C2314yes—
690#380C2314yes—
691#380C2314yes—
692#380C2314yes—
693#380C2312yes—
694#380C2312yes—
695#380C2312yes—
696#380C2314yes—
697#380C2312yes—
698#380C2312yes—
699#380C2312yes—
700#380C2314yes—
701#380C2314yes—
702#380C2314yes—
703#380C2314yes—
704#380C2312yes—
705C4×C4⋊C4C2311yescharacteristic
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2311yescharacteristic
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2311yescharacteristic
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2311yescharacteristic
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×#95C2312yes—
740C2×#95C2312yes—
741C43C2312yes—
742C43C2311yescharacteristic
743C2×#41—24no—
744C2×#41—24no—
745C2×#41—28no—
746C2×#41—42no—
747C2×#41—44no—
748C2×#41—44no—
749C22×Q8C2412yes—
750C22×Q8C2411yescharacteristic
751C22×Q8C2411yescharacteristic
752C22×Q8C2412yes—
753C22×Q8C2412yes—
754C22×D4C2411yescharacteristic
755C22×D4C2411yescharacteristic
756C22×D4C2414yes—
757C22×D4C2412yes—
758C22×D4C2411yescharacteristic
759C22×D4C2411yescharacteristic
760C22×D4C2412yes—
761C22×D4C2414yes—
762C22×D4C2414yes—
763C22×D4C2414yes—
764C22×D4C2412yes—
765C22×D4C2414yes—
766C22×D4C2412yes—
767C22×D4C2412yes—
768C22×D4C2412yes—
769C23×C4C2411yescharacteristic
770C23×C4C2412yes—
771C23×C4C2412yes—
772C23×C4C2412yes—
773C23×C4C2414yes—
774C23×C4C2414yes—
775C23×C4C2414yes—
776C23×C4C2412yes—
777C23×C4C2412yes—
778C23×C4C2412yes—
779C23×C4C2412yes—
780C23×C4C2414yes—
781C23×C4C2412yes—
782C23×C4C2412yes—
783C4⋊Q8—28no—
784C4⋊Q8—24no—
785C4⋊Q8—24no—
786C4⋊Q8—44no—
787#127—24no—
788#127—24no—
789#127—42no—
790#126—44no—
791#126—48no—
792#126—48no—
793#126—48no—
794#126—48no—
795#125—48no—
796#125—44no—
797#125—42no—
798#125—44no—
799#125—48no—
800#124—24no—
801#124—24no—
802#124—44no—
803#124—44no—
804#124—44no—
805#124—48no—
806#123—48no—
807#123—48no—
808#123—48no—
809#123—48no—
810#123—44no—
811#123—44no—
812#123—48no—
813#123—44no—
814#123—48no—
815C22⋊Q8—28no—
816C22⋊Q8—48no—
817C22⋊Q8—48no—
818C22⋊Q8—44no—
819C22⋊Q8—48no—
820C22⋊Q8—44no—
821C22⋊Q8—44no—
822C22⋊Q8—44no—
823#121—48no—
824#121—44no—
825#121—44no—
826#121—48no—
827#121—48no—
828#121—48no—
829#121—44no—
830#121—42no—
831#121—42no—
832#121—44no—
833#121—44no—
834#121—44no—
835C4×Q8—28no—
836C4×Q8—24no—
837C4×Q8—24no—
838C4×Q8—44no—
839C4×Q8—44no—
840C4×Q8—42no—
841C4×Q8—44no—
842C4×Q8—44no—
843C4×Q8—44no—
844C4×Q8—44no—
845C4×D4—24no—
846C4×D4—24no—
847C4×D4—24no—
848C4×D4—24no—
849C4×D4—44no—
850C4×D4—44no—
851C4×D4—48no—
852C4×D4—48no—
853C4×D4—48no—
854C4×D4—42no—
855C4×D4—44no—
856C4×D4—44no—
857C4×D4—44no—
858C4×D4—48no—
859C4×D4—44no—
860C4×D4—48no—
861C4×D4—44no—
862#117—24no—
863#117—44no—
864#117—48no—
865#117—48no—
866#117—44no—
867#117—44no—
868#117—44no—
869C2×C4⋊C4—44no—
870C2×C4⋊C4—42no—
871C2×C4⋊C4—44no—
872C2×C4⋊C4—48no—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C22⋊C4C2411yescharacteristic
935C2×C22⋊C4C2411yescharacteristic
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2414yes—
984C2×C22⋊C4C2414yes—
985C2×C22⋊C4C2412yes—
986C2×C22⋊C4C2412yes—
987C2×C22⋊C4C2412yes—
988C2×C22⋊C4C2412yes—
989C2×C42—44no—
990C2×C42C2414yes—
991C2×C42C2412yes—
992C2×C42C2411yescharacteristic
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2411yescharacteristic
999C2×C42C2412yes—
1000C2×C42C2411yescharacteristic
1001C2×C42C2412yes—
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004C2×C42C2414yes—
1005C2×C42C2412yes—
1006C2×C42C2412yes—
1007C2×C42C2414yes—
1008C2×C42C2414yes—
1009C2×C42C2414yes—
1010C2×C42C2414yes—
1011C2×C42C2412yes—
1012C2×C42C2412yes—
1013C2×C42C2412yes—
1014C2×C42C2411yescharacteristic
1015#95C2411yescharacteristic
1016#95C2411yescharacteristic
1017#95C2412yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2411yescharacteristic
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2412yes—
1047#95C2414yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2411yescharacteristic
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2412yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2414yes—
1075C24C2512yes—
1076C24C2512yes—
1077C24C2512yes—
1078C24C2511yescharacteristic
1079C24C2512yes—
1080#41—416no—
1081#41—816no—
1082C2×Q8—22no—
1083C2×Q8—22no—
1084C2×Q8—24no—
1085C2×Q8—24no—
1086C2×Q8—24no—
1087C2×Q8—22no—
1088C2×Q8—24no—
1089C2×Q8—24no—
1090C2×Q8—42no—
1091C2×Q8—42no—
1092C2×Q8—44no—
1093C2×Q8—42no—
1094C2×Q8H(5,𝔽2)14yes—
1095C2×D4—28no—
1096C2×D4—24no—
1097C2×D4—28no—
1098C2×D4—28no—
1099C2×D4—22no—
1100C2×D4—22no—
1101C2×D4—22no—
1102C2×D4—22no—
1103C2×D4—22no—
1104C2×D4—22no—
1105C2×D4—22no—
1106C2×D4—24no—
1107C2×D4—22no—
1108C2×D4—22no—
1109C2×D4—28no—
1110C2×D4—24no—
1111C2×D4—42no—
1112C2×D4—44no—
1113C2×D4—42no—
1114C2×D4—42no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—42no—
1123C2×D4—42no—
1124C2×D4—42no—
1125C2×D4—44no—
1126C2×D4—42no—
1127C2×D4—42no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D42−1+414yes—
1135C22×C4—24no—
1136C22×C4—28no—
1137C22×C4—24no—
1138C22×C4—24no—
1139C22×C4—22no—
1140C22×C4—24no—
1141C22×C4—22no—
1142C22×C4—22no—
1143C22×C4—24no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—24no—
1147C22×C4—28no—
1148C22×C4—28no—
1149C22×C4—42no—
1150C22×C4—42no—
1151C22×C4—42no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—42no—
1162C22×C4—42no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—42no—
1166C22×C4—42no—
1167C22×C4—44no—
1168C22×C4—42no—
1169C22×C4—42no—
1170C22×C4—44no—
1171C22×C4—44no—
1172C22×C4C2512yes—
1173C22×C4C2511yescharacteristic
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2514yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2512yes—
1179C22×C4C2514yes—
1180C22×C4C2511yescharacteristic
1181C22×C4C2512yes—
1182C22×C4C2514yes—
1183C22×C4C2512yes—
1184C22×C4C2512yes—
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2514yes—
1188C22×C4C2512yes—
1189C22×C4C2512yes—
1190C22×C4C2512yes—
1191C22×C4C2512yes—
1192C22×C4C2511yescharacteristic
1193C22×C4C2511yescharacteristic
1194C22×C4C2512yes—
1195C22×C4C2512yes—
1196C22×C4C2512yes—
1197C22×C4C2511yescharacteristic
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—28no—
1201C4⋊C4—28no—
1202C4⋊C4—22no—
1203C4⋊C4—24no—
1204C4⋊C4—22no—
1205C4⋊C4—24no—
1206C4⋊C4—22no—
1207C4⋊C4—22no—
1208C4⋊C4—22no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—22no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—28no—
1216C4⋊C4—24no—
1217C4⋊C4—28no—
1218C4⋊C4—24no—
1219C4⋊C4—28no—
1220C4⋊C4—28no—
1221C4⋊C4—24no—
1222C4⋊C4—24no—
1223C4⋊C4—24no—
1224C4⋊C4—28no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—42no—
1234C4⋊C4—44no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—44no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—44no—
1246C4⋊C4—42no—
1247C4⋊C4—42no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C22⋊C4—22no—
1260C22⋊C4—22no—
1261C22⋊C4—24no—
1262C22⋊C4—28no—
1263C22⋊C4—28no—
1264C22⋊C4—24no—
1265C22⋊C4—24no—
1266C22⋊C4—24no—
1267C22⋊C4—28no—
1268C22⋊C4—28no—
1269C22⋊C4—24no—
1270C22⋊C4—24no—
1271C22⋊C4—24no—
1272C22⋊C4—28no—
1273C22⋊C4—24no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—42no—
1288C22⋊C4—44no—
1289C22⋊C4—42no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—42no—
1298C22⋊C4—42no—
1299C22⋊C4—42no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—42no—
1306C22⋊C4—42no—
1307C22⋊C4—42no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—42no—
1311C22⋊C4—42no—
1312C22⋊C4—42no—
1313C22⋊C4—42no—
1314C42—22no—
1315C42—24no—
1316C42—22no—
1317C42—28no—
1318C42—24no—
1319C42—24no—
1320C42—24no—
1321C42—22no—
1322C42—22no—
1323C42—22no—
1324C42—24no—
1325C42—24no—
1326C42—24no—
1327C42—24no—
1328C42—42no—
1329C42—42no—
1330C42—44no—
1331C42—42no—
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—22no—
1344C23—22no—
1345C23—22no—
1346C23—21no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—21no—
1351C23—21no—
1352C23—22no—
1353C23—22no—
1354C23—22no—
1355C23—22no—
1356C23—22no—
1357C23—24no—
1358C23—22no—
1359C23—22no—
1360C23—24no—
1361C23—22no—
1362C23—24no—
1363C23—22no—
1364C23—24no—
1365C23C2×2−1+414yes—
1366C23C2611yescharacteristic
1367Q8—28no—
1368Q8—44no—
1369Q8—48no—
1370Q8—84no—
1371Q8—84no—
1372D4—28no—
1373D4—416no—
1374D4—48no—
1375D4—44no—
1376D4—44no—
1377D4—44no—
1378D4—84no—
1379D4—88no—
1380D4—88no—
1381D4—88no—
1382D4—162no—
1383D4—162no—
1384D4—162no—
1385D4—162no—
1386D4—164no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—21no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—22no—
1418C2×C4—21no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—24no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—24no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—24no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—24no—
1442C2×C4—24no—
1443C2×C4—24no—
1444C2×C4—24no—
1445C2×C4—22no—
1446C2×C4—24no—
1447C2×C4—24no—
1448C2×C4—22no—
1449C2×C4—48no—
1450C2×C4—44no—
1451C2×C4—48no—
1452C2×C4—88no—
1453C2×C4—88no—
1454C2×C4—84no—
1455C2×C4—84no—
1456C2×C4—84no—
1457C2×C4—88no—
1458C2×C4—84no—
1459C2×C4—88no—
1460C2×C4—84no—
1461C2×C4—162no—
1462C2×C4—162no—
1463C2×C4C2×H(5,𝔽2)12yes—
1464C2×C4C2×H(5,𝔽2)14yes—
1465C2×C4C2×H(5,𝔽2)12yes—
1466C2×C4C2×H(5,𝔽2)12yes—
1467C2×C4C2×H(5,𝔽2)12yes—
1468C2×C4C2×2−1+412yes—
1469C2×C4#58514yes—
1470C2×C4#58514yes—
1471C22—24no—
1472C22—28no—
1473C22—44no—
1474C22—42no—
1475C22—42no—
1476C22—41no—
1477C22—42no—
1478C22—42no—
1479C22—42no—
1480C22—42no—
1481C22—42no—
1482C22—44no—
1483C22—44no—
1484C22—42no—
1485C22—44no—
1486C22—44no—
1487C22—42no—
1488C22—42no—
1489C22—42no—
1490C22—42no—
1491C22—42no—
1492C22—41no—
1493C22—42no—
1494C22—42no—
1495C22—41no—
1496C22—42no—
1497C22—42no—
1498C22C22×H(5,𝔽2)11yescharacteristic
1499C22C22×H(5,𝔽2)11yescharacteristic
1500C22C22×2−1+411yescharacteristic
1501C22C2×#58512yes—
1502C22C2×#58512yes—
1503C4—24no—
1504C4—24no—
1505C4—24no—
1506C4—22no—
1507C4—22no—
1508C4—41no—
1509C4—42no—
1510C4—44no—
1511C4—42no—
1512C4—42no—
1513C4—44no—
1514C4—42no—
1515C4—44no—
1516C4—42no—
1517C4—42no—
1518C4—42no—
1519C4—42no—
1520C4—42no—
1521C4—42no—
1522C4—42no—
1523C4—42no—
1524C4—41no—
1525C4—41no—
1526C4—44no—
1527C4—42no—
1528C4#353614yes—
1529C2—44no—
1530C2—81no—
1531C2—82no—
1532C2—82no—
1533C2—82no—
1534C2C2×#353611yescharacteristic
1535C2#6283611yescharacteristic
1536C2#6283611yescharacteristic
1537C2#6301912yes—
1538C2#6302312yes—
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. #59410C2semidirect
2. #59102C2semidirect
3. #55410C2semidirect
4. #55287C2semidirect
5. #51919C2semidirect
6. #48746C2semidirect
7. #48510C2semidirect
8. #48304C2semidirect
9. #46104C2semidirect
10. #45695C2semidirect
11. #45429C2semidirect
12. #45270C2semidirect
13. #45269C2semidirect
14. #44947C2semidirect
15. #44339C2semidirect
16. #43152C2semidirect
17. #42646C2semidirect
18. #42645C2semidirect
19. #40153C2semidirect
20. #39985C2semidirect
21. #39882C2semidirect
22. #39791C2semidirect
23. #37397C2semidirect
24. #36573C2semidirect
25. #36508C2semidirect
26. #36415C2semidirect
27. #36135C2semidirect
28. #36040C2semidirect
29. #36020C2semidirect
30. #35534C2semidirect
31. #34968C2semidirect

Maximal subgroups

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

subgroupindex
#594102
#591022
#554102
#552872
#519192
#487462
#485102
#483042
#461042
#456952
#454292
#452702
#452692
#449472
#443392
#431522
#426462
#426452
#401532
#399852
#398822
#397912
#373972
#365732
#365082
#364152
#361352
#360402
#360202
#355342
#349682