Finite Group Databasebeta

← #8115402

Subgroups — #8115402

Order 512.

4479 conjugacy classes of subgroups.

The subgroup lattice has 1507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57787C214yesmaximal, complemented
2#57261C214yesmaximal, complemented
3#56844C214yesmaximal, complemented
4#56587C214yesmaximal, complemented
5#56058C214yesmaximal, complemented
6#56043C214yesmaximal, complemented
7#54565C214yesmaximal, complemented
8#54548C214yesmaximal, complemented
9#53151C212yesmaximal, complemented
10#53136C212yesmaximal, complemented
11#45431C211yesmaximal, characteristic, complemented
12#45429C211yesmaximal, characteristic, complemented
13#45418C211yesmaximal, characteristic, complemented
14#45388C211yesmaximal, characteristic, complemented
15#42878C211yesmaximal, characteristic, complemented
16#42812C212yesmaximal, complemented
17#42792C211yesmaximal, characteristic, complemented
18#42788C211yesmaximal, characteristic, complemented
19#42692C212yesmaximal, complemented
20#42650C211yesmaximal, characteristic, complemented
21#39187C211yesmaximal, characteristic, complemented
22#39186C211yesmaximal, characteristic, complemented
23#39131C212yesmaximal, complemented
24#38958C211yesmaximal, characteristic, complemented
25#38954C211yesmaximal, characteristic, complemented
26#38911C212yesmaximal, complemented
27#37411C212yesmaximal, complemented
28#37400C212yesmaximal, complemented
29#35318C211yesmaximal, characteristic, complemented
30#35314C211yesmaximal, characteristic, complemented
31#34643C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#556C2212yes—
34C2×#555C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2212yes—
38C2×#542C2211yescharacteristic
39C2×#541C2211yescharacteristic
40C2×#529C2212yes—
41#2864C2211yescharacteristic
42#2863C2212yes—
43#2862C2211yescharacteristic
44#2862C2211yescharacteristic
45#2861C2211yescharacteristic
46#2857C2211yescharacteristic
47#2850C2211yescharacteristic
48#2838C2214yes—
49#2838C2214yes—
50#2838C2214yes—
51#2830C2214yes—
52#2830C2214yes—
53#2830C2214yes—
54#2827C2214yes—
55#2825C2214yes—
56#2824C2214yes—
57#2821C2212yes—
58#2821C2212yes—
59#2821C2214yes—
60#2820C2212yes—
61#2813C2212yes—
62#2808C2214yes—
63#2806C2214yes—
64#2802C2214yes—
65#2800C2214yes—
66#2797C2214yes—
67#2797C2214yes—
68#2797C2214yes—
69#2796C2214yes—
70#2792C2214yes—
71#2790C2214yes—
72#2788C2214yes—
73#2787C2214yes—
74#2780C2214yes—
75#2775C2214yes—
76#2775C2214yes—
77#2775C2214yes—
78#2774C2214yes—
79#2772C2214yes—
80#2765C2214yes—
81#2764C2214yes—
82#2762C2214yes—
83#2761C2214yes—
84#2761C2214yes—
85#2759C2214yes—
86#2759C2214yes—
87#2758C2214yes—
88#2754C2214yes—
89#2752C2214yes—
90#2751C2214yes—
91#2751C2214yes—
92#2749C2214yes—
93#2749C2214yes—
94#2743C2214yes—
95#2737C2214yes—
96#2733C2214yes—
97#2732C2214yes—
98#2730C2214yes—
99#2727C2214yes—
100#2725C2214yes—
101#2723C2214yes—
102#2723C2214yes—
103#2723C2214yes—
104#2722C2214yes—
105#2721C2214yes—
106#2720C2214yes—
107#2715C2214yes—
108#2714C2214yes—
109#2714C2214yes—
110#2712C2214yes—
111#2700C2214yes—
112#2700C2214yes—
113#2698C2214yes—
114#2698C2214yes—
115#2698C2214yes—
116#2696C2214yes—
117#2692C2214yes—
118#2692C2214yes—
119#2692C2214yes—
120#2689C2214yes—
121#2689C2214yes—
122#2687C2214yes—
123#2687C2214yes—
124#2677C2214yes—
125#2677C2214yes—
126#2664C2212yes—
127#2664C2212yes—
128#2663C2212yes—
129#2663C2212yes—
130#2662C2212yes—
131#2662C2212yes—
132#2662C2212yes—
133#2661C2212yes—
134#2661C2212yes—
135#2660C2212yes—
136#2660C2211yescharacteristic
137#2658C2211yescharacteristic
138#2655C2214yes—
139#2651C2214yes—
140#2640C2212yes—
141#2639C2212yes—
142#2637C2212yes—
143#2636C2214yes—
144#2633C2212yes—
145#2631C2212yes—
146#2628C2214yes—
147#2628C2211yescharacteristic
148#2625C2212yes—
149#2625C2212yes—
150#2625C2212yes—
151#2625C2212yes—
152#2621C2212yes—
153#2621C2211yescharacteristic
154#2621C2211yescharacteristic
155#2620C2212yes—
156#2620C2211yescharacteristic
157#2605C2214yes—
158#2603C2212yes—
159#2603C2212yes—
160#2598C2214yes—
161#2584C2212yes—
162#2582C2212yes—
163#2568C2211yescharacteristic
164#2568C2212yes—
165#2567C2211yescharacteristic
166#2556C2214yes—
167#2554C2214yes—
168#2553C2214yes—
169#2550C2214yes—
170#2547C2211yescharacteristic
171#2546C2211yescharacteristic
172#2542C2212yes—
173#2540C2212yes—
174#2540C2212yes—
175#2538C2212yes—
176#2536C2211yescharacteristic
177#2536C2211yescharacteristic
178#2536C2211yescharacteristic
179#2536C2212yes—
180#2535C2211yescharacteristic
181#2535C2212yes—
182#2531C2214yes—
183#2529C2214yes—
184#2528C2214yes—
185#2525C2214yes—
186#2524C2214yes—
187#2523C2214yes—
188#2521C2214yes—
189#2520C2214yes—
190#2520C2214yes—
191#2519C2214yes—
192#2517C2214yes—
193#2514C2212yes—
194#2512C2214yes—
195#2511C2212yes—
196#2510C2214yes—
197#2499C2212yes—
198#2499C2212yes—
199#2498C2212yes—
200#2497C2212yes—
201#2494C2212yes—
202#2492C2214yes—
203#2492C2212yes—
204#2489C2212yes—
205#2479C2214yes—
206#2479C2214yes—
207#2478C2214yes—
208#2471C2214yes—
209#2463C2214yes—
210#2463C2214yes—
211#2451C2214yes—
212#2448C2214yes—
213#2447C2214yes—
214#2447C2214yes—
215#2447C2212yes—
216#2446C2212yes—
217#2441C2212yes—
218#2439C2214yes—
219#2439C2212yes—
220#2438C2214yes—
221#2436C2212yes—
222#2436C2212yes—
223#2434C2212yes—
224#2434C2212yes—
225#2429C2212yes—
226#2429C2212yes—
227#2427C2212yes—
228#2427C2212yes—
229#2420C2214yes—
230#2420C2214yes—
231#2415C2212yes—
232#2415C2212yes—
233#2415C2212yes—
234#2414C2212yes—
235#2409C2212yes—
236#2409C2212yes—
237#2409C2212yes—
238#2409C2212yes—
239#2399C2211yescharacteristic
240#2398C2212yes—
241#2397C2211yescharacteristic
242#2392C2211yescharacteristic
243#2392C2211yescharacteristic
244#2392C2212yes—
245#2356C2211yescharacteristic
246#2356C2211yescharacteristic
247#2355C2212yes—
248#2354C2212yes—
249#2351C2211yescharacteristic
250#2349C2211yescharacteristic
251#2331C2211yescharacteristic
252#2327C2211yescharacteristic
253#2327C2211yescharacteristic
254#2326C2211yescharacteristic
255#2324C2212yes—
256#2323C2212yes—
257#2320C2212yes—
258#2310C2212yes—
259#2310C2212yes—
260C4×C4⋊Q8C2211yescharacteristic
261C4×#124C2211yescharacteristic
262C4×C22⋊Q8C2212yes—
263#2293C2211yescharacteristic
264#2293C2211yescharacteristic
265#2293C2212yes—
266C4×#117C2211yescharacteristic
267C23×Q8C2312yes—
268C23×Q8C2312yes—
269#556—44no—
270#556—48no—
271#555—44no—
272D4×Q8—48no—
273D4×Q8—44no—
274D4×Q8—44no—
275#542—44no—
276#541—44no—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2311yescharacteristic
285C2×C4⋊Q8C2311yescharacteristic
286C2×C4⋊Q8C2312yes—
287#529—48no—
288C2×#126C2312yes—
289C2×#126C2312yes—
290C2×#126C2314yes—
291C2×#126C2312yes—
292C2×#126C2312yes—
293C2×#126C2312yes—
294C2×#126C2314yes—
295C2×#126C2314yes—
296C2×#125C2312yes—
297C2×#125C2311yescharacteristic
298C2×#125C2312yes—
299C2×#125C2312yes—
300C2×#124C2311yescharacteristic
301C2×#124C2312yes—
302C2×#124C2311yescharacteristic
303C2×#124C2311yescharacteristic
304C2×#124C2312yes—
305C2×#124C2312yes—
306C2×#124C2312yes—
307C2×#124C2314yes—
308C2×#123C2312yes—
309C2×#123C2312yes—
310C2×#123C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2311yescharacteristic
313C2×C22⋊Q8C2311yescharacteristic
314C2×C22⋊Q8C2311yescharacteristic
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×#121C2312yes—
329C2×#121C2311yescharacteristic
330C2×#121C2312yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×#117C2311yescharacteristic
352C2×#117C2312yes—
353C2×#117C2312yes—
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2314yes—
357C2×#117C2311yescharacteristic
358C2×#117C2312yes—
359C22×C42C2311yescharacteristic
360#401C2314yes—
361#401C2314yes—
362#400C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2312yes—
368#400C2312yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2312yes—
376#400C2314yes—
377#400C2314yes—
378#400C2312yes—
379#399C2314yes—
380#399C2314yes—
381#399C2314yes—
382#399C2314yes—
383#399C2314yes—
384#399C2314yes—
385#399C2314yes—
386#399C2312yes—
387#399C2312yes—
388#399C2312yes—
389#398C2311yescharacteristic
390#398C2314yes—
391#398C2312yes—
392#398C2312yes—
393#398C2314yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2312yes—
401#398C2312yes—
402#398C2312yes—
403#398C2312yes—
404#398C2314yes—
405#398C2314yes—
406#398C2311yescharacteristic
407#398C2312yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2312yes—
412#398C2312yes—
413#398C2314yes—
414#397C2314yes—
415#397C2311yescharacteristic
416#397C2314yes—
417#397C2312yes—
418#397C2314yes—
419#397C2312yes—
420#397C2312yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2312yes—
436#397C2312yes—
437#397C2312yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2311yescharacteristic
445#397C2312yes—
446#397C2312yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2312yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2312yes—
456#396C2314yes—
457#396C2314yes—
458#396C2312yes—
459#396C2312yes—
460#396C2314yes—
461#395C2312yes—
462#395C2312yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#395C2312yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#395C2314yes—
472#395C2314yes—
473#395C2312yes—
474#395C2312yes—
475#394C2311yescharacteristic
476#394C2312yes—
477#394C2312yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2312yes—
483#394C2314yes—
484#394C2312yes—
485#394C2312yes—
486#394C2314yes—
487#394C2314yes—
488#394C2312yes—
489#394C2314yes—
490#394C2314yes—
491#394C2311yescharacteristic
492#394C2312yes—
493#394C2314yes—
494#394C2312yes—
495#394C2312yes—
496#394C2312yes—
497#393C2314yes—
498#393C2314yes—
499#393C2314yes—
500#393C2314yes—
501#393C2314yes—
502#393C2314yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#393C2312yes—
508#393C2312yes—
509#393C2312yes—
510#392C2314yes—
511#392C2312yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2311yescharacteristic
516#392C2312yes—
517#392C2311yescharacteristic
518#392C2312yes—
519#392C2312yes—
520#391C2311yescharacteristic
521#391C2311yescharacteristic
522#391C2311yescharacteristic
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2312yes—
527#391C2312yes—
528#391C2314yes—
529#391C2314yes—
530#391C2314yes—
531#391C2314yes—
532#391C2314yes—
533#391C2314yes—
534#391C2312yes—
535#391C2312yes—
536#391C2312yes—
537#391C2312yes—
538#391C2311yescharacteristic
539#391C2314yes—
540#391C2311yescharacteristic
541#391C2311yescharacteristic
542#391C2312yes—
543#391C2314yes—
544#391C2314yes—
545#391C2314yes—
546#391C2314yes—
547#391C2314yes—
548#391C2314yes—
549#390C2314yes—
550#390C2314yes—
551#390C2314yes—
552#390C2311yescharacteristic
553#390C2314yes—
554#390C2311yescharacteristic
555#390C2314yes—
556#390C2312yes—
557#390C2312yes—
558#390C2312yes—
559#390C2312yes—
560#390C2314yes—
561#390C2314yes—
562#390C2314yes—
563#390C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2314yes—
570#389C2312yes—
571#389C2312yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2312yes—
579#389C2314yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
610#388C2312yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#384C2311yescharacteristic
681#384C2312yes—
682#384C2311yescharacteristic
683#384C2314yes—
684#383C2314yes—
685#383C2312yes—
686#383C2312yes—
687#383C2314yes—
688#383C2314yes—
689#382C2312yes—
690#382C2312yes—
691#382C2314yes—
692#382C2314yes—
693#382C2311yescharacteristic
694#382C2311yescharacteristic
695#382C2311yescharacteristic
696#382C2314yes—
697#382C2314yes—
698#382C2311yescharacteristic
699#382C2314yes—
700#381C2314yes—
701#381C2314yes—
702#381C2314yes—
703#381C2314yes—
704#381C2314yes—
705#380C2312yes—
706#380C2312yes—
707#380C2314yes—
708#380C2312yes—
709#380C2312yes—
710#380C2312yes—
711#380C2312yes—
712#380C2314yes—
713#380C2314yes—
714#380C2314yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2311yescharacteristic
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2311yescharacteristic
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C4⋊C4C2314yes—
723C4×C4⋊C4C2314yes—
724C4×C4⋊C4C2312yes—
725C4×C4⋊C4C2312yes—
726C4×C4⋊C4C2312yes—
727C4×C4⋊C4C2314yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2312yes—
733C4×C22⋊C4C2312yes—
734C4×C22⋊C4C2314yes—
735C4×C22⋊C4C2314yes—
736#376C2311yescharacteristic
737#376C2311yescharacteristic
738#376C2312yes—
739#376C2312yes—
740C2×#95C2312yes—
741C43C2311yescharacteristic
742C43C2311yescharacteristic
743C22×Q8—44no—
744C22×Q8—44no—
745C22×Q8—44no—
746C22×Q8—44no—
747C22×Q8—44no—
748C22×Q8—44no—
749C22×Q8C2411yescharacteristic
750C22×Q8C2411yescharacteristic
751C22×Q8C2411yescharacteristic
752C22×Q8C2412yes—
753C22×Q8C2412yes—
754C22×Q8C2412yes—
755C22×Q8C2414yes—
756C22×Q8C2414yes—
757C22×Q8C2412yes—
758C22×D4C2411yescharacteristic
759C22×D4C2411yescharacteristic
760C22×D4C2412yes—
761C22×D4C2411yescharacteristic
762C22×D4C2412yes—
763C22×D4C2412yes—
764C22×D4C2412yes—
765C22×D4C2414yes—
766C22×D4C2412yes—
767C22×D4C2414yes—
768C23×C4C2411yescharacteristic
769C23×C4C2412yes—
770C23×C4C2412yes—
771C23×C4C2412yes—
772C23×C4C2412yes—
773C23×C4C2414yes—
774C23×C4C2414yes—
775C23×C4C2414yes—
776C4⋊Q8—24no—
777C4⋊Q8—24no—
778C4⋊Q8—24no—
779C4⋊Q8—42no—
780C4⋊Q8—48no—
781C4⋊Q8—44no—
782C4⋊Q8—44no—
783C4⋊Q8—42no—
784C4⋊Q8—42no—
785C4⋊Q8—44no—
786#126—44no—
787#126—44no—
788#126—44no—
789#126—44no—
790#126—44no—
791#126—48no—
792#126—48no—
793#126—48no—
794#125—44no—
795#125—42no—
796#125—44no—
797#125—44no—
798#124—24no—
799#124—44no—
800#124—42no—
801#124—44no—
802#124—42no—
803#124—44no—
804#124—44no—
805#124—48no—
806#123—44no—
807#123—44no—
808#123—44no—
809C22⋊Q8—48no—
810C22⋊Q8—48no—
811C22⋊Q8—48no—
812C22⋊Q8—48no—
813C22⋊Q8—48no—
814C22⋊Q8—44no—
815C22⋊Q8—44no—
816C22⋊Q8—44no—
817C22⋊Q8—44no—
818C22⋊Q8—42no—
819C22⋊Q8—42no—
820C22⋊Q8—42no—
821C22⋊Q8—44no—
822C22⋊Q8—44no—
823C22⋊Q8—44no—
824C22⋊Q8—44no—
825C22⋊Q8—44no—
826#121—44no—
827#121—44no—
828#121—42no—
829#121—44no—
830#121—44no—
831C4×Q8—28no—
832C4×Q8—24no—
833C4×Q8—24no—
834C4×Q8—24no—
835C4×Q8—28no—
836C4×Q8—44no—
837C4×Q8—44no—
838C4×D4—28no—
839C4×D4—24no—
840C4×D4—24no—
841C4×D4—24no—
842C4×D4—48no—
843C4×D4—44no—
844C4×D4—44no—
845C4×D4—44no—
846C4×D4—44no—
847C4×D4—44no—
848C4×D4—44no—
849#117—24no—
850#117—42no—
851#117—44no—
852#117—44no—
853#117—48no—
854#117—44no—
855#117—44no—
856#117—44no—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2411yescharacteristic
923C2×C22⋊C4C2411yescharacteristic
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C42—24no—
977C2×C42C2411yescharacteristic
978C2×C42C2412yes—
979C2×C42C2411yescharacteristic
980C2×C42C2412yes—
981C2×C42C2414yes—
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2414yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2414yes—
996C2×C42C2414yes—
997C2×C42C2414yes—
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000#95C2411yescharacteristic
1001#95C2412yes—
1002#95C2414yes—
1003#95C2411yescharacteristic
1004#95C2411yescharacteristic
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2411yescharacteristic
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2414yes—
1066C24C2511yescharacteristic
1067C24C2512yes—
1068C24C2512yes—
1069C24C2512yes—
1070C2×Q8—22no—
1071C2×Q8—22no—
1072C2×Q8—22no—
1073C2×Q8—24no—
1074C2×Q8—22no—
1075C2×Q8—22no—
1076C2×Q8—22no—
1077C2×Q8—24no—
1078C2×Q8—24no—
1079C2×Q8—24no—
1080C2×Q8—22no—
1081C2×Q8—24no—
1082C2×Q8—22no—
1083C2×Q8—22no—
1084C2×Q8—44no—
1085C2×Q8—44no—
1086C2×Q8—44no—
1087C2×Q8—44no—
1088C2×Q8—44no—
1089C2×Q8—44no—
1090C2×Q8—42no—
1091C2×Q8—44no—
1092C2×Q8—42no—
1093C2×Q8—42no—
1094C2×Q8—44no—
1095C2×Q8—816no—
1096C2×Q8—816no—
1097C2×D4—22no—
1098C2×D4—24no—
1099C2×D4—22no—
1100C2×D4—22no—
1101C2×D4—22no—
1102C2×D4—22no—
1103C2×D4—42no—
1104C2×D4—42no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—42no—
1111C2×D4—42no—
1112C2×D4—42no—
1113C2×D4—42no—
1114C2×D4—42no—
1115C2×D4—42no—
1116C2×D4—44no—
1117C2×D4—42no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C22×C4—22no—
1125C22×C4—22no—
1126C22×C4—24no—
1127C22×C4—24no—
1128C22×C4—24no—
1129C22×C4—24no—
1130C22×C4—22no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—24no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—42no—
1141C22×C4—44no—
1142C22×C4—42no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4C2512yes—
1148C22×C4C2514yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2512yes—
1153C22×C4C2514yes—
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2514yes—
1160C22×C4C2512yes—
1161C22×C4C2514yes—
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2511yescharacteristic
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2511yescharacteristic
1170C22×C4C2511yescharacteristic
1171C22×C4C2512yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C4⋊C4—22no—
1175C4⋊C4—22no—
1176C4⋊C4—22no—
1177C4⋊C4—22no—
1178C4⋊C4—22no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—22no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—28no—
1187C4⋊C4—24no—
1188C4⋊C4—22no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—22no—
1192C4⋊C4—28no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—42no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C22⋊C4—22no—
1239C22⋊C4—22no—
1240C22⋊C4—28no—
1241C22⋊C4—24no—
1242C22⋊C4—24no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—42no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—42no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—42no—
1271C22⋊C4—42no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—42no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—44no—
1293C42—22no—
1294C42—24no—
1295C42—22no—
1296C42—24no—
1297C42—24no—
1298C42—28no—
1299C42—24no—
1300C42—24no—
1301C42—24no—
1302C42—22no—
1303C42—22no—
1304C42—44no—
1305C42—42no—
1306C42—42no—
1307C42—42no—
1308C42—44no—
1309C42—42no—
1310C42—44no—
1311C42—44no—
1312C42—44no—
1313C42—44no—
1314C42H(5,𝔽2)14yes—
1315C42H(5,𝔽2)14yes—
1316C23—21no—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—22no—
1323C23—21no—
1324C23—21no—
1325C23—22no—
1326C23—22no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—24no—
1336C23—24no—
1337C23—22no—
1338C23—22no—
1339C23—22no—
1340C23C2611yescharacteristic
1341Q8—44no—
1342Q8—44no—
1343Q8—44no—
1344Q8—48no—
1345Q8—84no—
1346Q8—84no—
1347Q8—88no—
1348Q8—88no—
1349Q8—162no—
1350D4—48no—
1351D4—44no—
1352D4—44no—
1353D4—44no—
1354D4—84no—
1355D4—84no—
1356D4—84no—
1357D4—164no—
1358D4—162no—
1359D4—164no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—21no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—21no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—22no—
1427C2×C4—44no—
1428C2×C4—48no—
1429C2×C4—48no—
1430C2×C4—84no—
1431C2×C4—84no—
1432C2×C4—88no—
1433C2×C4—88no—
1434C2×C4—88no—
1435C2×C4C2×H(5,𝔽2)12yes—
1436C2×C4C2×H(5,𝔽2)14yes—
1437C2×C4C2×H(5,𝔽2)12yes—
1438C2×C4C2×H(5,𝔽2)12yes—
1439C2×C4C2×H(5,𝔽2)12yes—
1440C2×C4#58512yes—
1441C22—42no—
1442C22—42no—
1443C22—41no—
1444C22—42no—
1445C22—42no—
1446C22—44no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—41no—
1455C22—42no—
1456C22—42no—
1457C22—41no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—44no—
1463C22—42no—
1464C22—42no—
1465C22C22×H(5,𝔽2)11yescharacteristic
1466C22C22×H(5,𝔽2)11yescharacteristic
1467C22C2×#58511yescharacteristic
1468C222−1+612yes—
1469C222−1+612yes—
1470C4—24no—
1471C4—22no—
1472C4—22no—
1473C4—41no—
1474C4—42no—
1475C4—42no—
1476C4—42no—
1477C4—44no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—44no—
1482C4—42no—
1483C4—42no—
1484C4—42no—
1485C4—42no—
1486C4—42no—
1487C4—41no—
1488C4—42no—
1489C4—42no—
1490C4—44no—
1491C4—42no—
1492C4—41no—
1493C4—42no—
1494C4—42no—
1495C4—44no—
1496C4#354614yes—
1497C2—82no—
1498C2—82no—
1499C2—81no—
1500C2—82no—
1501C2C2×#354611yescharacteristic
1502C2#6288612yes—
1503C2#6288711yescharacteristic
1504C2#6288711yescharacteristic
1505C2#6289112yes—
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. #57787C2semidirect
2. #57261C2semidirect
3. #56844C2semidirect
4. #56587C2semidirect
5. #56058C2semidirect
6. #56043C2semidirect
7. #54565C2semidirect
8. #54548C2semidirect
9. #53151C2semidirect
10. #53136C2semidirect
11. #45431C2semidirect
12. #45429C2semidirect
13. #45418C2semidirect
14. #45388C2semidirect
15. #42878C2semidirect
16. #42812C2semidirect
17. #42792C2semidirect
18. #42788C2semidirect
19. #42692C2semidirect
20. #42650C2semidirect
21. #39187C2semidirect
22. #39186C2semidirect
23. #39131C2semidirect
24. #38958C2semidirect
25. #38954C2semidirect
26. #38911C2semidirect
27. #37411C2semidirect
28. #37400C2semidirect
29. #35318C2semidirect
30. #35314C2semidirect
31. #34643C2semidirect

Maximal subgroups

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

subgroupindex
#577872
#572612
#568442
#565872
#560582
#560432
#545652
#545482
#531512
#531362
#454312
#454292
#454182
#453882
#428782
#428122
#427922
#427882
#426922
#426502
#391872
#391862
#391312
#389582
#389542
#389112
#374112
#374002
#353182
#353142
#346432