Finite Group Databasebeta

← #8750756

Subgroups — #8750756

Order 512.

4220 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59201C211yesmaximal, characteristic, complemented
2#59025C212yesmaximal, complemented
3#58879C212yesmaximal, complemented
4#58762C214yesmaximal, complemented
5#58681C214yesmaximal, complemented
6#57397C214yesmaximal, complemented
7#56159C214yesmaximal, complemented
8#53092C212yesmaximal, complemented
9#52993C211yesmaximal, characteristic, complemented
10#52927C212yesmaximal, complemented
11#52819C214yesmaximal, complemented
12#47418C212yesmaximal, complemented
13#45397C212yesmaximal, complemented
14#45308C211yesmaximal, characteristic, complemented
15#45228C212yesmaximal, complemented
16#45098C212yesmaximal, complemented
17#45005C212yesmaximal, complemented
18#42964C211yesmaximal, characteristic, complemented
19#42929C212yesmaximal, complemented
20#42866C212yesmaximal, complemented
21#42726C212yesmaximal, complemented
22#42695C212yesmaximal, complemented
23#42668C212yesmaximal, complemented
24#41888C214yesmaximal, complemented
25#39935C212yesmaximal, complemented
26#38917C211yesmaximal, characteristic, complemented
27#36676C211yesmaximal, characteristic
28#36065C211yesmaximal, characteristic, complemented
29#35901C212yesmaximal, complemented
30C2×#556C2212yes—
31C2×#556C2211yescharacteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#544C2211yescharacteristic, complemented
34C22×C22⋊Q8C2211yescharacteristic
35#2848C2211yescharacteristic
36#2842C2211yescharacteristic
37#2841C2212yescomplemented
38#2841C2214yescomplemented
39#2839C2214yescomplemented
40#2838C2214yes—
41#2836C2214yes—
42#2836C2214yes—
43#2836C2214yes—
44#2834C2212yes—
45#2834C2211yescharacteristic
46#2831C2214yes—
47#2831C2214yescomplemented
48#2827C2212yes—
49#2827C2212yes—
50#2827C2212yes—
51#2826C2211yescharacteristic
52#2826C2212yes—
53#2825C2212yes—
54#2823C2214yes—
55#2822C2212yescomplemented
56#2812C2212yes—
57#2812C2211yescharacteristic
58#2800C2214yes—
59#2797C2214yes—
60#2795C2214yes—
61#2795C2214yes—
62#2794C2214yescomplemented
63#2793C2214yes—
64#2793C2214yescomplemented
65#2791C2214yescomplemented
66#2791C2214yescomplemented
67#2791C2214yescomplemented
68#2789C2214yescomplemented
69#2789C2212yescomplemented
70#2786C2214yes—
71#2786C2214yes—
72#2783C2214yes—
73#2781C2214yes—
74#2775C2214yescomplemented
75#2774C2214yescomplemented
76#2774C2214yescomplemented
77#2772C2214yescomplemented
78#2769C2214yescomplemented
79#2768C2214yes—
80#2765C2214yes—
81#2762C2214yescomplemented
82#2760C2212yescomplemented
83#2759C2214yescomplemented
84#2756C2214yes—
85#2753C2214yes—
86#2745C2214yescomplemented
87#2743C2214yes—
88#2742C2212yes—
89#2741C2214yes—
90#2741C2214yescomplemented
91#2736C2212yes—
92#2735C2214yes—
93#2731C2214yes—
94#2730C2214yes—
95#2725C2214yescomplemented
96#2723C2214yes—
97#2722C2214yescomplemented
98#2720C2214yes—
99#2715C2214yes—
100#2715C2214yescomplemented
101#2712C2214yes—
102#2702C2214yes—
103#2700C2214yes—
104#2698C2214yescomplemented
105#2697C2212yes—
106#2697C2214yes—
107#2693C2214yes—
108#2693C2212yes—
109#2689C2214yes—
110#2687C2214yes—
111#2680C2214yes—
112#2666C2214yescomplemented
113#2662C2212yescomplemented
114#2660C2211yescharacteristic, complemented
115#2660C2212yescomplemented
116#2654C2214yescomplemented
117#2652C2214yes—
118#2652C2214yes—
119#2651C2214yes—
120#2650C2214yes—
121#2649C2214yescomplemented
122#2648C2214yes—
123#2645C2212yescomplemented
124#2637C2214yes—
125#2637C2214yescomplemented
126#2625C2211yescharacteristic, complemented
127#2623C2212yes—
128#2621C2212yes—
129#2621C2212yescomplemented
130#2612C2212yescomplemented
131#2611C2212yes—
132#2610C2212yes—
133#2604C2212yescomplemented
134#2597C2214yescomplemented
135#2595C2214yes—
136#2594C2214yes—
137#2588C2214yescomplemented
138#2587C2214yes—
139#2582C2214yescomplemented
140#2576C2214yes—
141#2575C2214yes—
142#2572C2214yes—
143#2570C2214yescomplemented
144#2570C2212yescomplemented
145#2565C2212yescomplemented
146#2563C2211yescharacteristic
147#2562C2212yes—
148#2562C2211yescharacteristic, complemented
149#2560C2214yes—
150#2560C2214yescomplemented
151#2554C2214yes—
152#2552C2212yescomplemented
153#2542C2212yes—
154#2538C2212yes—
155#2538C2212yes—
156#2536C2212yescomplemented
157#2533C2214yescomplemented
158#2532C2214yes—
159#2531C2214yes—
160#2531C2214yes—
161#2530C2214yescomplemented
162#2529C2214yes—
163#2529C2214yes—
164#2529C2214yescomplemented
165#2523C2212yes—
166#2523C2212yes—
167#2522C2214yescomplemented
168#2519C2214yes—
169#2519C2214yescomplemented
170#2518C2214yescomplemented
171#2515C2214yes—
172#2515C2214yescomplemented
173#2514C2214yescomplemented
174#2511C2212yescomplemented
175#2509C2212yescomplemented
176#2508C2212yescomplemented
177#2502C2211yescharacteristic, complemented
178#2499C2214yes—
179#2499C2212yes—
180#2497C2212yes—
181#2497C2214yescomplemented
182#2497C2214yescomplemented
183#2495C2212yes—
184#2494C2212yes—
185#2492C2212yes—
186#2489C2212yes—
187#2489C2212yes—
188#2489C2212yescomplemented
189#2486C2211yescharacteristic
190#2486C2212yes—
191#2485C2212yes—
192#2482C2212yes—
193#2481C2214yes—
194#2480C2214yes—
195#2472C2214yes—
196#2470C2214yes—
197#2465C2214yes—
198#2451C2212yescomplemented
199#2451C2212yescomplemented
200#2446C2214yescomplemented
201#2446C2212yescomplemented
202#2441C2212yes—
203#2440C2212yes—
204#2439C2212yes—
205#2439C2212yescomplemented
206#2434C2211yescharacteristic
207#2429C2212yes—
208#2429C2212yescomplemented
209#2421C2212yes—
210#2421C2212yes—
211#2421C2214yescomplemented
212#2421C2212yescomplemented
213#2417C2212yes—
214#2417C2212yescomplemented
215#2417C2212yescomplemented
216#2417C2212yescomplemented
217#2415C2212yes—
218#2415C2212yes—
219#2415C2212yes—
220#2415C2212yes—
221#2411C2212yes—
222#2409C2211yescharacteristic
223#2409C2212yes—
224#2402C2214yescomplemented
225#2401C2212yes—
226#2397C2211yescharacteristic
227#2396C2212yes—
228#2395C2212yes—
229#2395C2211yescharacteristic
230#2392C2212yes—
231#2392C2212yes—
232#2392C2212yes—
233#2374C2212yes—
234#2369C2212yescomplemented
235#2365C2212yescomplemented
236#2362C2212yes—
237#2362C2212yes—
238#2360C2214yes—
239#2356C2212yescomplemented
240#2354C2212yescomplemented
241#2352C2212yes—
242#2352C2212yes—
243#2352C2212yes—
244#2347C2212yes—
245#2346C2211yescharacteristic, complemented
246#2345C2212yescomplemented
247#2344C2211yescharacteristic
248Q8×C22⋊C4C2212yes—
249#2335C2214yes—
250#2323C2212yescomplemented
251#2323C2212yescomplemented
252#2317C2212yes—
253#2317C2212yescomplemented
254#2314C2212yescomplemented
255C4×#120C2211yescharacteristic
256C4×#120C2212yes—
257#2280C2212yes—
258#2276C2211yescharacteristic, complemented
259C23×Q8C2311yescharacteristic
260C24×C4C2311yescharacteristic
261#556—44no—
262#556—48no—
263#552—44no—
264#544—44no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2312yes—
273C2×#125C2312yes—
274C2×#125C2311yescharacteristic
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#124C2312yes—
278C2×#124C2314yes—
279C2×#123C2314yes—
280C2×#123C2312yes—
281C2×#123C2312yes—
282C2×C22⋊Q8—44no—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2311yescharacteristic
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2312yes—
295C2×#120C2311yescharacteristic
296C2×#120C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×#117C2312yes—
311C2×#117C2311yescharacteristic
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2312yes—
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2311yescharacteristic
322C22×C22⋊C4C2312yes—
323#401C2312yes—
324#401C2314yes—
325#401C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2311yescharacteristic
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#399C2312yes—
354#399C2311yescharacteristic
355#399C2311yescharacteristic
356#399C2312yes—
357#399C2311yescharacteristic
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2311yescharacteristic
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2312yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#397C2312yes—
399#397C2312yes—
400#397C2312yes—
401#397C2312yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2312yes—
409#397C2311yescharacteristic
410#397C2312yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2312yes—
429#396C2312yes—
430#396C2312yes—
431#396C2312yes—
432#396C2312yes—
433#396C2312yes—
434#396C2312yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#395C2312yes—
444#395C2314yes—
445#395C2312yes—
446#395C2314yes—
447#395C2312yes—
448#395C2314yes—
449#395C2314yes—
450#395C2314yes—
451#394C2314yes—
452#394C2312yes—
453#394C2314yes—
454#394C2312yes—
455#394C2312yes—
456#394C2314yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2312yes—
474#393C2312yes—
475#393C2314yes—
476#393C2312yes—
477#393C2314yes—
478#392C2311yescharacteristic
479#392C2312yes—
480#392C2312yes—
481#392C2312yes—
482#392C2311yescharacteristic
483#392C2312yes—
484#391C2314yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#391C2314yes—
489#391C2314yes—
490#391C2312yes—
491#391C2314yes—
492#391C2314yes—
493#391C2314yes—
494#391C2312yes—
495#391C2314yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2314yes—
501#390C2314yes—
502#390C2314yes—
503#390C2312yes—
504#390C2314yes—
505#390C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#386C2312yes—
611#386C2314yes—
612#386C2312yes—
613#386C2312yes—
614#386C2312yes—
615#386C2311yescharacteristic
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2312yes—
623#386C2314yes—
624#385C2311yescharacteristic
625#385C2312yes—
626#385C2312yes—
627#385C2312yes—
628#385C2312yes—
629#385C2312yes—
630#385C2312yes—
631#385C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#385C2314yes—
639#384C2312yes—
640#384C2314yes—
641#384C2312yes—
642#384C2314yes—
643#384C2314yes—
644#383C2314yes—
645#383C2314yes—
646#383C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2312yes—
652#382C2314yes—
653#382C2314yes—
654#382C2314yes—
655#382C2314yes—
656#382C2314yes—
657#381C2312yes—
658#381C2314yes—
659#381C2312yes—
660#381C2314yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2311yescharacteristic
673#380C2314yes—
674#380C2314yes—
675#380C2311yescharacteristic
676#380C2312yes—
677#380C2312yes—
678#379C2312yes—
679#379C2311yescharacteristic
680#379C2312yes—
681#379C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2312yes—
715#376C2314yes—
716#376C2311yescharacteristic
717C25C2411yescharacteristic
718C22×Q8—42no—
719C22×Q8—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2414yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×D4C2411yescharacteristic
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C23×C4—42no—
733C23×C4—44no—
734C23×C4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2412yes—
744C4⋊Q8—28no—
745C4⋊Q8—42no—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748#126—44no—
749#126—48no—
750#126—48no—
751#126—48no—
752#125—44no—
753#125—44no—
754#125—44no—
755#125—42no—
756#124—44no—
757#124—48no—
758#123—48no—
759#123—44no—
760#123—44no—
761C22⋊Q8—28no—
762C22⋊Q8—48no—
763C22⋊Q8—48no—
764C22⋊Q8—48no—
765C22⋊Q8—44no—
766C22⋊Q8—44no—
767C22⋊Q8—44no—
768C22⋊Q8—44no—
769C22⋊Q8—42no—
770C22⋊Q8—42no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773#120—42no—
774#120—44no—
775C4×Q8—24no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—48no—
780C4×Q8—44no—
781C4×D4—44no—
782C4×D4—44no—
783C4×D4—44no—
784C4×D4—44no—
785C4×D4—42no—
786C4×D4—44no—
787C4×D4—42no—
788#117—24no—
789#117—28no—
790#117—44no—
791#117—42no—
792#117—44no—
793#117—44no—
794#117—44no—
795#117—44no—
796C2×C4⋊C4—24no—
797C2×C4⋊C4—44no—
798C2×C4⋊C4—44no—
799C2×C4⋊C4—42no—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C22⋊C4—44no—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2411yescharacteristic
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936#95C2411yescharacteristic
937#95C2411yescharacteristic
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2411yescharacteristic
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2411yescharacteristic
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007C24—22no—
1008C24—41no—
1009C24—42no—
1010C24—42no—
1011C24—41no—
1012C24C2512yes—
1013C24C2512yes—
1014C24C2511yescharacteristic
1015C24C2511yescharacteristic
1016C2×Q8—22no—
1017C2×Q8—24no—
1018C2×Q8—28no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8—88no—
1029C2×D4—22no—
1030C2×D4—24no—
1031C2×D4—41no—
1032C2×D4—41no—
1033C2×D4—42no—
1034C2×D4—42no—
1035C2×D4—42no—
1036C2×D4—42no—
1037C2×D4—42no—
1038C2×D4—42no—
1039C2×D4—42no—
1040C2×D4—42no—
1041C2×D4—42no—
1042C2×D4—41no—
1043C2×D4—42no—
1044C2×D4—42no—
1045C2×D4—42no—
1046C2×D4—42no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—41no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—88no—
1076C22×C4C2512yes—
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2514yes—
1088C22×C4C2512yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C4⋊C4—22no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—41no—
1133C4⋊C4—42no—
1134C4⋊C4—41no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—41no—
1140C4⋊C4—42no—
1141C4⋊C4—41no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4H(5,𝔽2)14yes—
1164C22⋊C4—22no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—24no—
1170C22⋊C4—28no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—41no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—42no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—41no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—41no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C42—24no—
1218C42—28no—
1219C42—24no—
1220C42—24no—
1221C42—22no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—44no—
1226C42—42no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C23—21no—
1237C23—22no—
1238C23—22no—
1239C23—21no—
1240C23—22no—
1241C23—21no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—21no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—21no—
1259C23—44no—
1260C23—82no—
1261C23—84no—
1262C23—82no—
1263C23—84no—
1264C23#58512yes—
1265C23C2611yescharacteristic
1266Q8—44no—
1267Q8—48no—
1268Q8—88no—
1269Q8—84no—
1270Q8—84no—
1271D4—82no—
1272D4—84no—
1273D4—82no—
1274D4—84no—
1275D4—84no—
1276D4—84no—
1277D4—84no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—21no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—21no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—48no—
1345C2×C4—44no—
1346C2×C4—48no—
1347C2×C4—48no—
1348C2×C4—44no—
1349C2×C4—82no—
1350C2×C4—84no—
1351C2×C4—84no—
1352C2×C4—162no—
1353C2×C4—164no—
1354C2×C4C2×H(5,𝔽2)14yes—
1355C2×C4C2×H(5,𝔽2)12yes—
1356C2×C4#58514yes—
1357C22—22no—
1358C22—24no—
1359C22—41no—
1360C22—41no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—41no—
1365C22—42no—
1366C22—41no—
1367C22—42no—
1368C22—42no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—41no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—88no—
1382C22C22×H(5,𝔽2)11yescharacteristic
1383C22C2×#58512yes—
1384C22C2×#58511yescharacteristic
1385C222−1+612yes—
1386C222−1+611yescharacteristic
1387C4—24no—
1388C4—42no—
1389C4—41no—
1390C4—42no—
1391C4—41no—
1392C4—44no—
1393C4—42no—
1394C4—42no—
1395C4—42no—
1396C4—41no—
1397C4—44no—
1398C4—42no—
1399C4—42no—
1400C4—44no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—41no—
1405C4—42no—
1406C4—44no—
1407C4—44no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4#355114yes—
1412C2—42no—
1413C2—82no—
1414C2—81no—
1415C2—82no—
1416C2C2×#355111yescharacteristic
1417C2#6289811yescharacteristic
1418C2#6291112yes—
1419C2#6304411yescharacteristic
1420C2#6305312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36676C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59201C2semidirect
2. #59025C2semidirect
3. #58879C2semidirect
4. #58762C2semidirect
5. #58681C2semidirect
6. #57397C2semidirect
7. #56159C2semidirect
8. #53092C2semidirect
9. #52993C2semidirect
10. #52927C2semidirect
11. #52819C2semidirect
12. #47418C2semidirect
13. #45397C2semidirect
14. #45308C2semidirect
15. #45228C2semidirect
16. #45098C2semidirect
17. #45005C2semidirect
18. #42964C2semidirect
19. #42929C2semidirect
20. #42866C2semidirect
21. #42726C2semidirect
22. #42695C2semidirect
23. #42668C2semidirect
24. #41888C2semidirect
25. #39935C2semidirect
26. #38917C2semidirect
28. #36065C2semidirect
29. #35901C2semidirect
31. C2×#556C22semidirect
33. C2×#544C22semidirect
37. #2841C22semidirect
38. #2841C22semidirect
39. #2839C22semidirect
47. #2831C22semidirect
55. #2822C22semidirect
62. #2794C22semidirect
64. #2793C22semidirect
65. #2791C22semidirect
66. #2791C22semidirect
67. #2791C22semidirect
68. #2789C22semidirect
69. #2789C22semidirect
74. #2775C22semidirect
75. #2774C22semidirect
76. #2774C22semidirect
77. #2772C22semidirect
78. #2769C22semidirect
81. #2762C22semidirect
82. #2760C22semidirect
83. #2759C22semidirect
86. #2745C22semidirect
90. #2741C22semidirect
95. #2725C22semidirect
97. #2722C22semidirect
100. #2715C22semidirect
104. #2698C22semidirect
112. #2666C22semidirect
113. #2662C22semidirect
114. #2660C22semidirect
115. #2660C22semidirect
116. #2654C22semidirect
121. #2649C22semidirect
123. #2645C22semidirect
125. #2637C22semidirect
126. #2625C22semidirect
129. #2621C22semidirect
130. #2612C22semidirect
133. #2604C22semidirect
134. #2597C22semidirect
137. #2588C22semidirect
139. #2582C22semidirect
143. #2570C22semidirect
144. #2570C22semidirect
145. #2565C22semidirect
148. #2562C22semidirect
150. #2560C22semidirect
152. #2552C22semidirect
156. #2536C22semidirect
157. #2533C22semidirect
161. #2530C22semidirect
164. #2529C22semidirect
167. #2522C22semidirect
169. #2519C22semidirect
170. #2518C22semidirect
172. #2515C22semidirect
173. #2514C22semidirect
174. #2511C22semidirect
175. #2509C22semidirect
176. #2508C22semidirect
177. #2502C22semidirect
181. #2497C22semidirect
182. #2497C22semidirect
188. #2489C22semidirect
198. #2451C22semidirect
199. #2451C22semidirect
200. #2446C22semidirect
201. #2446C22semidirect
205. #2439C22semidirect
208. #2429C22semidirect
211. #2421C22semidirect
212. #2421C22semidirect
214. #2417C22semidirect
215. #2417C22semidirect
216. #2417C22semidirect
224. #2402C22semidirect
234. #2369C22semidirect
235. #2365C22semidirect
239. #2356C22semidirect
240. #2354C22semidirect
245. #2346C22semidirect
246. #2345C22semidirect
250. #2323C22semidirect
251. #2323C22semidirect
253. #2317C22semidirect
254. #2314C22semidirect
258. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#592012
#590252
#588792
#587622
#586812
#573972
#561592
#530922
#529932
#529272
#528192
#474182
#453972
#453082
#452282
#450982
#450052
#429642
#429292
#428662
#427262
#426952
#426682
#418882
#399352
#389172
#366762
#360652
#359012