Finite Group Databasebeta

← #8749863

Subgroups — #8749863

Order 512.

4499 conjugacy classes of subgroups.

The subgroup lattice has 1490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59865C211yesmaximal, characteristic, complemented
2#59505C212yesmaximal, complemented
3#58543C212yesmaximal, complemented
4#57091C214yesmaximal, complemented
5#55851C214yesmaximal, complemented
6#55603C214yesmaximal, complemented
7#53880C214yesmaximal, complemented
8#53134C212yesmaximal, complemented
9#53017C211yesmaximal, characteristic, complemented
10#52761C212yesmaximal, complemented
11#52489C214yesmaximal, complemented
12#47535C212yesmaximal, complemented
13#45236C212yesmaximal, complemented
14#45060C212yesmaximal, complemented
15#44922C212yesmaximal, complemented
16#44921C212yesmaximal, complemented
17#44914C211yesmaximal, characteristic, complemented
18#42985C211yesmaximal, characteristic, complemented
19#42949C212yesmaximal, complemented
20#42906C212yesmaximal, complemented
21#42736C212yesmaximal, complemented
22#42448C212yesmaximal, complemented
23#42227C212yesmaximal, complemented
24#42116C214yesmaximal, complemented
25#40050C212yesmaximal, complemented
26#39169C211yesmaximal, characteristic, complemented
27#36696C211yesmaximal, characteristic, complemented
28#36005C211yesmaximal, characteristic, complemented
29#35772C212yesmaximal, complemented
30C2×#554C2211yescharacteristic
31C2×#552C2212yes—
32C2×#550C2211yescharacteristic
33C2×#537C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2858C2211yescharacteristic
36#2843C2211yescharacteristic
37#2841C2212yes—
38#2836C2214yes—
39#2836C2214yes—
40#2831C2214yes—
41#2830C2212yes—
42#2830C2211yescharacteristic
43#2829C2212yes—
44#2829C2214yes—
45#2829C2212yes—
46#2829C2212yes—
47#2828C2214yes—
48#2828C2212yes—
49#2828C2214yes—
50#2828C2211yescharacteristic
51#2827C2214yes—
52#2826C2214yes—
53#2823C2211yescharacteristic
54#2822C2212yes—
55#2818C2212yes—
56#2815C2212yes—
57#2813C2214yes—
58#2803C2214yes—
59#2803C2214yes—
60#2803C2214yes—
61#2796C2214yes—
62#2794C2212yes—
63#2793C2214yes—
64#2788C2214yes—
65#2786C2214yes—
66#2786C2214yes—
67#2782C2212yes—
68#2782C2214yes—
69#2781C2214yes—
70#2780C2214yes—
71#2777C2214yes—
72#2770C2214yes—
73#2769C2212yes—
74#2767C2214yes—
75#2764C2212yes—
76#2763C2212yes—
77#2757C2214yes—
78#2756C2214yes—
79#2753C2214yes—
80#2753C2214yes—
81#2751C2214yes—
82#2740C2214yes—
83#2739C2214yes—
84#2730C2214yes—
85#2726C2214yes—
86#2723C2214yes—
87#2720C2214yes—
88#2717C2214yes—
89#2714C2214yes—
90#2711C2214yes—
91#2709C2212yes—
92#2708C2214yes—
93#2708C2214yes—
94#2707C2214yes—
95#2706C2214yes—
96#2706C2214yes—
97#2705C2214yes—
98#2703C2214yes—
99#2703C2214yes—
100#2701C2214yes—
101#2691C2214yes—
102#2691C2214yes—
103#2690C2214yes—
104#2689C2214yes—
105#2688C2214yes—
106#2682C2214yes—
107#2680C2214yes—
108#2676C2214yes—
109#2676C2214yes—
110#2673C2214yes—
111#2673C2214yes—
112#2661C2214yes—
113#2652C2214yes—
114#2651C2214yes—
115#2651C2214yes—
116#2649C2214yes—
117#2649C2214yes—
118#2641C2212yes—
119#2641C2214yes—
120#2639C2212yes—
121#2638C2212yes—
122#2636C2214yes—
123#2635C2214yes—
124#2630C2214yes—
125#2629C2212yes—
126#2624C2212yes—
127#2624C2211yescharacteristic
128#2624C2212yes—
129#2615C2211yescharacteristic
130#2612C2212yes—
131#2609C2214yes—
132#2603C2214yes—
133#2602C2214yes—
134#2601C2214yes—
135#2598C2214yes—
136#2596C2214yes—
137#2595C2214yes—
138#2595C2214yes—
139#2593C2212yes—
140#2570C2214yes—
141#2570C2212yes—
142#2566C2212yes—
143#2566C2212yes—
144#2563C2211yescharacteristic
145#2562C2212yes—
146#2562C2212yes—
147#2560C2214yes—
148#2553C2214yes—
149#2550C2212yes—
150#2543C2212yes—
151#2541C2212yes—
152#2541C2211yescharacteristic
153#2537C2212yes—
154#2536C2212yes—
155#2535C2212yes—
156#2533C2214yes—
157#2531C2214yes—
158#2529C2214yes—
159#2519C2214yes—
160#2516C2214yes—
161#2516C2214yes—
162#2513C2212yes—
163#2508C2212yes—
164#2506C2212yes—
165#2505C2214yes—
166#2504C2212yes—
167#2504C2211yescharacteristic
168#2501C2212yes—
169#2501C2211yescharacteristic
170#2498C2214yes—
171#2497C2212yes—
172#2497C2212yes—
173#2496C2212yes—
174#2495C2212yes—
175#2490C2212yes—
176#2490C2212yes—
177#2490C2214yes—
178#2487C2211yescharacteristic
179#2487C2212yes—
180#2486C2211yescharacteristic
181#2486C2212yes—
182#2485C2212yes—
183#2485C2212yes—
184#2479C2214yes—
185#2476C2214yes—
186#2476C2214yes—
187#2475C2214yes—
188#2474C2214yes—
189#2473C2214yes—
190#2470C2214yes—
191#2468C2214yes—
192#2463C2212yes—
193#2461C2214yes—
194#2460C2214yes—
195#2456C2214yes—
196#2456C2214yes—
197#2456C2214yes—
198#2455C2214yes—
199#2454C2212yes—
200#2453C2212yes—
201#2445C2214yes—
202#2445C2212yes—
203#2443C2214yes—
204#2442C2212yes—
205#2442C2212yes—
206#2441C2212yes—
207#2440C2212yes—
208#2428C2212yes—
209#2423C2212yes—
210#2422C2212yes—
211#2422C2214yes—
212#2422C2212yes—
213#2421C2212yes—
214#2421C2212yes—
215#2416C2212yes—
216#2416C2212yes—
217#2415C2214yes—
218#2414C2212yes—
219#2414C2212yes—
220#2414C2212yes—
221#2407C2212yes—
222#2407C2212yes—
223#2407C2212yes—
224#2395C2212yes—
225#2395C2212yes—
226#2395C2211yescharacteristic
227#2392C2214yes—
228#2392C2212yes—
229#2392C2212yes—
230#2392C2212yes—
231#2388C2211yescharacteristic
232#2388C2212yes—
233#2374C2212yes—
234#2371C2214yes—
235#2363C2212yes—
236#2362C2212yes—
237#2361C2212yes—
238#2355C2212yes—
239#2354C2212yes—
240#2352C2212yes—
241#2352C2212yes—
242Q8×C4⋊C4C2212yes—
243D4×C4⋊C4C2212yes—
244D4×C4⋊C4C2212yes—
245#2346C2212yes—
246#2341C2212yes—
247#2341C2211yescharacteristic
248#2339C2211yescharacteristic
249#2328C2212yes—
250#2324C2212yes—
251#2324C2214yes—
252#2323C2212yes—
253#2317C2212yes—
254#2311C2212yes—
255C4×#127C2211yescharacteristic
256C4×#125C2212yes—
257C4×#126C2212yes—
258#2295C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C22×#41C2311yescharacteristic
262#554—44no—
263#552—48no—
264#550—44no—
265#537—44no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×#127C2311yescharacteristic
268C2×#127C2312yes—
269C2×#127C2311yescharacteristic
270C2×#127C2312yes—
271C2×#126C2312yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#124C2314yes—
280C2×#123C2312yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×#121C2312yes—
293C2×#121C2314yes—
294C2×#121C2312yes—
295C2×#121C2311yescharacteristic
296C2×#121C2312yes—
297C2×#121C2311yescharacteristic
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306#520—44no—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×#117C2312yes—
326C2×#117C2312yes—
327C2×#117C2312yes—
328C2×#117C2312yes—
329C2×#117C2314yes—
330C2×#117C2311yescharacteristic
331C2×#117C2314yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2311yescharacteristic
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2314yes—
354#399C2314yes—
355#399C2311yescharacteristic
356#399C2312yes—
357#399C2314yes—
358#399C2312yes—
359#399C2314yes—
360#399C2312yes—
361#399C2312yes—
362#399C2314yes—
363#399C2312yes—
364#398C2314yes—
365#398C2311yescharacteristic
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2314yes—
388#397C2312yes—
389#397C2312yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2311yescharacteristic
396#397C2312yes—
397#397C2312yes—
398#397C2312yes—
399#397C2312yes—
400#397C2314yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2312yes—
410#397C2314yes—
411#397C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2312yes—
417#396C2312yes—
418#396C2312yes—
419#396C2314yes—
420#396C2312yes—
421#396C2312yes—
422#396C2312yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#395C2311yescharacteristic
429#395C2312yes—
430#395C2314yes—
431#395C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2312yes—
436#394C2312yes—
437#394C2312yes—
438#394C2312yes—
439#394C2312yes—
440#394C2312yes—
441#394C2312yes—
442#394C2311yescharacteristic
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2312yes—
449#394C2312yes—
450#394C2312yes—
451#394C2312yes—
452#394C2314yes—
453#394C2312yes—
454#394C2312yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#393C2312yes—
475#393C2312yes—
476#393C2312yes—
477#393C2311yescharacteristic
478#393C2312yes—
479#392C2312yes—
480#392C2312yes—
481#392C2312yes—
482#392C2312yes—
483#392C2312yes—
484#392C2312yes—
485#392C2312yes—
486#392C2314yes—
487#392C2312yes—
488#392C2311yescharacteristic
489#392C2314yes—
490#392C2314yes—
491#392C2314yes—
492#392C2314yes—
493#392C2314yes—
494#392C2314yes—
495#392C2314yes—
496#392C2314yes—
497#392C2314yes—
498#391C2314yes—
499#391C2314yes—
500#391C2312yes—
501#391C2312yes—
502#390C2314yes—
503#390C2311yescharacteristic
504#390C2312yes—
505#390C2311yescharacteristic
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2312yes—
510#390C2312yes—
511#390C2312yes—
512#390C2314yes—
513#390C2314yes—
514#390C2314yes—
515#390C2314yes—
516#390C2312yes—
517#390C2312yes—
518#390C2314yes—
519#390C2314yes—
520#390C2314yes—
521#390C2312yes—
522#390C2312yes—
523#390C2314yes—
524#390C2314yes—
525#390C2314yes—
526#390C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#389C2314yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2314yes—
543#389C2312yes—
544#389C2314yes—
545#389C2312yes—
546#389C2312yes—
547#388C2312yes—
548#388C2312yes—
549#388C2312yes—
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#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
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#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2312yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2312yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#384C2311yescharacteristic
652#384C2312yes—
653#384C2312yes—
654#384C2314yes—
655#384C2312yes—
656#383C2312yes—
657#383C2314yes—
658#382C2312yes—
659#382C2312yes—
660#382C2312yes—
661#382C2314yes—
662#382C2314yes—
663#382C2312yes—
664#382C2314yes—
665#381C2312yes—
666#381C2312yes—
667#381C2314yes—
668#380C2312yes—
669#380C2311yescharacteristic
670#380C2311yescharacteristic
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2314yes—
680#380C2314yes—
681#380C2312yes—
682#380C2314yes—
683#380C2312yes—
684#380C2314yes—
685#380C2314yes—
686#380C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713#376C2312yes—
714#376C2314yes—
715C2×#95C2312yes—
716C43C2311yescharacteristic
717C2×#41—24no—
718C2×#41—24no—
719C2×#41—42no—
720C2×#41—44no—
721C2×#41—44no—
722C2×#41—44no—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×D4C2411yescharacteristic
727C22×D4C2411yescharacteristic
728C22×D4C2411yescharacteristic
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2412yes—
741C22×D4C2414yes—
742C22×D4C2414yes—
743C22×D4C2412yes—
744C22×D4C2414yes—
745C22×D4C2411yescharacteristic
746C22×D4C2412yes—
747C23×C4C2412yes—
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C23×C4C2414yes—
757C23×C4C2412yes—
758C23×C4C2414yes—
759C4⋊Q8—42no—
760#127—44no—
761#127—42no—
762#127—44no—
763#127—42no—
764#126—44no—
765#126—48no—
766#126—84no—
767#125—44no—
768#125—48no—
769#125—44no—
770#125—44no—
771#125—48no—
772#124—84no—
773#123—48no—
774#123—44no—
775#123—84no—
776#123—84no—
777#123—84no—
778#123—84no—
779#123—84no—
780C22⋊Q8—28no—
781C22⋊Q8—28no—
782C22⋊Q8—48no—
783C22⋊Q8—44no—
784C22⋊Q8—84no—
785#121—44no—
786#121—48no—
787#121—48no—
788#121—44no—
789#121—44no—
790#121—44no—
791#121—44no—
792#121—42no—
793#121—42no—
794#121—44no—
795#121—44no—
796#121—84no—
797#121—84no—
798#121—84no—
799C4×Q8—28no—
800C4×Q8—24no—
801C4×Q8—44no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—48no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—44no—
811C4×D4—42no—
812C4×D4—44no—
813C4×D4—42no—
814C4×D4—84no—
815C4×D4—84no—
816C4×D4—84no—
817#117—44no—
818#117—44no—
819#117—42no—
820#117—48no—
821#117—44no—
822#117—44no—
823#117—84no—
824C2×C4⋊C4—42no—
825C2×C4⋊C4—44no—
826C2×C4⋊C4—42no—
827C2×C4⋊C4—44no—
828C2×C4⋊C4—44no—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2411yescharacteristic
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2411yescharacteristic
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2411yescharacteristic
964C2×C42C2414yes—
965#95C2411yescharacteristic
966#95C2412yes—
967#95C2414yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2411yescharacteristic
977#95C2414yes—
978#95C2412yes—
979#95C2411yescharacteristic
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2411yescharacteristic
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022C24C2512yes—
1023C24C2512yes—
1024C24C2511yescharacteristic
1025C24C2512yes—
1026C24C2512yes—
1027C24C2511yescharacteristic
1028#41—416no—
1029#41—88no—
1030#41—88no—
1031C2×Q8—24no—
1032C2×Q8—41no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8H(5,𝔽2)14yes—
1037C2×D4—24no—
1038C2×D4—22no—
1039C2×D4—22no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—22no—
1044C2×D4—24no—
1045C2×D4—22no—
1046C2×D4—41no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—41no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—41no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—44no—
1061C2×D4—42no—
1062C2×D4—41no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—41no—
1073C2×D4—44no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—42no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—22no—
1095C22×C4—24no—
1096C22×C4—22no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—42no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—42no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—42no—
1122C22×C4—42no—
1123C22×C4C2511yescharacteristic
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2514yes—
1128C22×C4C2514yes—
1129C22×C4C2514yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2511yescharacteristic
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2511yescharacteristic
1145C22×C4C2511yescharacteristic
1146C4⋊C4—24no—
1147C4⋊C4—22no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—28no—
1151C4⋊C4—28no—
1152C4⋊C4—24no—
1153C4⋊C4—28no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—28no—
1158C4⋊C4—24no—
1159C4⋊C4—42no—
1160C4⋊C4—41no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—41no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—41no—
1176C4⋊C4—41no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C22⋊C4—28no—
1201C22⋊C4—28no—
1202C22⋊C4—24no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—41no—
1230C22⋊C4—41no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—42no—
1260C22⋊C4—44no—
1261C22⋊C4—42no—
1262C22⋊C4—42no—
1263C22⋊C4—42no—
1264C42—28no—
1265C42—24no—
1266C42—24no—
1267C42—22no—
1268C42—24no—
1269C42—24no—
1270C42—24no—
1271C42—24no—
1272C42—22no—
1273C42—41no—
1274C42—44no—
1275C42—44no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42—44no—
1280C42—44no—
1281C42—42no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—21no—
1286C23—22no—
1287C23—21no—
1288C23—22no—
1289C23—21no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—24no—
1295C23—21no—
1296C23—24no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—24no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—24no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—21no—
1313C23—21no—
1314C23—22no—
1315C23—22no—
1316C23C2611yescharacteristic
1317Q8—28no—
1318Q8—82no—
1319Q8—162no—
1320D4—44no—
1321D4—48no—
1322D4—48no—
1323D4—48no—
1324D4—44no—
1325D4—44no—
1326D4—82no—
1327D4—84no—
1328D4—84no—
1329D4—84no—
1330D4—88no—
1331D4—84no—
1332D4—84no—
1333D4—82no—
1334D4—84no—
1335D4—162no—
1336D4—162no—
1337D4—162no—
1338D4—164no—
1339D4—164no—
1340D4—164no—
1341C2×C4—21no—
1342C2×C4—24no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—48no—
1401C2×C4—48no—
1402C2×C4—44no—
1403C2×C4—48no—
1404C2×C4—44no—
1405C2×C4—84no—
1406C2×C4—88no—
1407C2×C4—88no—
1408C2×C4—162no—
1409C2×C4—164no—
1410C2×C4—164no—
1411C2×C4—162no—
1412C2×C4C2×H(5,𝔽2)14yes—
1413C2×C4C2×H(5,𝔽2)12yes—
1414C2×C4#58512yes—
1415C2×C4#58514yes—
1416C22—42no—
1417C22—41no—
1418C22—41no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—44no—
1428C22—44no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—41no—
1433C22—42no—
1434C22—42no—
1435C22—41no—
1436C22—41no—
1437C22—42no—
1438C22—42no—
1439C22—41no—
1440C22—42no—
1441C22—42no—
1442C22—44no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—44no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22C22×H(5,𝔽2)11yescharacteristic
1451C22C2×#58512yes—
1452C22C2×#58511yescharacteristic
1453C22H(7,𝔽2)12yes—
1454C222−1+611yescharacteristic
1455C4—24no—
1456C4—22no—
1457C4—42no—
1458C4—41no—
1459C4—41no—
1460C4—42no—
1461C4—42no—
1462C4—44no—
1463C4—42no—
1464C4—42no—
1465C4—44no—
1466C4—44no—
1467C4—42no—
1468C4—42no—
1469C4—41no—
1470C4—42no—
1471C4—44no—
1472C4—42no—
1473C4—42no—
1474C4—44no—
1475C4—42no—
1476C4—44no—
1477C4#353314yes—
1478C2—81no—
1479C2—82no—
1480C2—81no—
1481C2—82no—
1482C2—82no—
1483C2—82no—
1484C2C2×#353311yescharacteristic
1485C2#6291911yescharacteristic
1486C2#6293812yes—
1487C2#6304712yes—
1488C2#6306611yescharacteristic
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. #59865C2semidirect
2. #59505C2semidirect
3. #58543C2semidirect
4. #57091C2semidirect
5. #55851C2semidirect
6. #55603C2semidirect
7. #53880C2semidirect
8. #53134C2semidirect
9. #53017C2semidirect
10. #52761C2semidirect
11. #52489C2semidirect
12. #47535C2semidirect
13. #45236C2semidirect
14. #45060C2semidirect
15. #44922C2semidirect
16. #44921C2semidirect
17. #44914C2semidirect
18. #42985C2semidirect
19. #42949C2semidirect
20. #42906C2semidirect
21. #42736C2semidirect
22. #42448C2semidirect
23. #42227C2semidirect
24. #42116C2semidirect
25. #40050C2semidirect
26. #39169C2semidirect
27. #36696C2semidirect
28. #36005C2semidirect
29. #35772C2semidirect

Maximal subgroups

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

subgroupindex
#598652
#595052
#585432
#570912
#558512
#556032
#538802
#531342
#530172
#527612
#524892
#475352
#452362
#450602
#449222
#449212
#449142
#429852
#429492
#429062
#427362
#424482
#422272
#421162
#400502
#391692
#366962
#360052
#357722