Finite Group Databasebeta

← #8115479

Subgroups — #8115479

Order 512.

4259 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58024C214yesmaximal, complemented
2#57462C214yesmaximal, complemented
3#57126C214yesmaximal, complemented
4#56937C214yesmaximal, complemented
5#56757C214yesmaximal, complemented
6#55795C214yesmaximal, complemented
7#54296C214yesmaximal, complemented
8#54132C214yesmaximal, complemented
9#53068C212yesmaximal, complemented
10#52959C212yesmaximal, complemented
11#45071C212yesmaximal, complemented
12#44967C212yesmaximal, complemented
13#42798C212yesmaximal, complemented
14#42781C212yesmaximal, complemented
15#42561C212yesmaximal, complemented
16#42442C212yesmaximal, complemented
17#39635C211yesmaximal, characteristic, complemented
18#39611C211yesmaximal, characteristic, complemented
19#39507C211yesmaximal, characteristic, complemented
20#39484C211yesmaximal, characteristic, complemented
21#37955C212yesmaximal, complemented
22#37946C212yesmaximal, complemented
23#37432C212yesmaximal, complemented
24#37312C212yesmaximal, complemented
25#35345C211yesmaximal, characteristic, complemented
26#35277C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic, complemented
28C2×#554C2212yes—
29C2×#552C2212yes—
30C2×#542C2212yes—
31#2868C2211yescharacteristic
32#2864C2212yes—
33#2859C2211yescharacteristic
34#2859C2211yescharacteristic
35#2858C2211yescharacteristic
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2838C2214yes—
39#2837C2214yes—
40#2837C2214yes—
41#2836C2214yes—
42#2836C2214yes—
43#2830C2214yes—
44#2829C2214yes—
45#2827C2214yes—
46#2826C2214yes—
47#2823C2214yes—
48#2814C2214yes—
49#2814C2214yes—
50#2803C2214yes—
51#2803C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2800C2214yes—
55#2797C2214yes—
56#2797C2214yes—
57#2796C2214yes—
58#2793C2214yes—
59#2792C2214yes—
60#2791C2214yes—
61#2790C2214yes—
62#2786C2214yes—
63#2786C2214yes—
64#2786C2214yes—
65#2775C2214yes—
66#2775C2214yes—
67#2772C2214yes—
68#2770C2214yes—
69#2769C2214yes—
70#2768C2214yes—
71#2761C2214yes—
72#2757C2214yes—
73#2757C2214yes—
74#2752C2214yes—
75#2752C2214yes—
76#2751C2214yes—
77#2749C2214yes—
78#2744C2214yes—
79#2744C2214yes—
80#2740C2214yes—
81#2740C2214yes—
82#2737C2214yes—
83#2734C2214yes—
84#2732C2214yes—
85#2732C2214yes—
86#2729C2214yes—
87#2729C2214yes—
88#2726C2214yes—
89#2724C2214yes—
90#2723C2214yes—
91#2723C2214yes—
92#2721C2214yes—
93#2720C2214yes—
94#2713C2214yes—
95#2711C2214yes—
96#2707C2214yes—
97#2704C2214yes—
98#2704C2214yes—
99#2702C2214yes—
100#2701C2214yes—
101#2700C2214yes—
102#2698C2214yes—
103#2698C2214yes—
104#2690C2214yes—
105#2689C2214yes—
106#2688C2214yes—
107#2683C2214yes—
108#2682C2214yes—
109#2681C2214yes—
110#2681C2214yes—
111#2681C2214yes—
112#2677C2214yes—
113#2674C2214yes—
114#2662C2214yes—
115#2660C2212yes—
116#2655C2212yes—
117#2654C2214yes—
118#2654C2212yes—
119#2653C2212yes—
120#2652C2214yes—
121#2652C2212yes—
122#2651C2212yes—
123#2650C2212yes—
124#2649C2212yes—
125#2648C2212yes—
126#2647C2212yes—
127#2644C2214yes—
128#2640C2212yes—
129#2638C2214yes—
130#2629C2212yes—
131#2629C2211yescharacteristic
132#2629C2211yescharacteristic
133#2627C2214yes—
134#2621C2214yes—
135#2621C2212yes—
136#2620C2214yes—
137#2620C2212yes—
138#2619C2212yes—
139#2612C2214yes—
140#2611C2214yes—
141#2608C2214yes—
142#2608C2214yes—
143#2606C2214yes—
144#2606C2214yes—
145#2603C2214yes—
146#2601C2214yes—
147#2582C2212yes—
148#2574C2214yes—
149#2570C2212yes—
150#2566C2212yes—
151#2566C2212yes—
152#2565C2212yes—
153#2559C2214yes—
154#2552C2212yes—
155#2551C2212yes—
156#2550C2212yes—
157#2542C2212yes—
158#2538C2212yes—
159#2537C2212yes—
160#2536C2212yes—
161#2531C2214yes—
162#2529C2214yes—
163#2529C2214yes—
164#2527C2214yes—
165#2526C2214yes—
166#2525C2214yes—
167#2513C2212yes—
168#2512C2212yes—
169#2512C2214yes—
170#2511C2214yes—
171#2507C2214yes—
172#2502C2212yes—
173#2499C2212yes—
174#2492C2212yes—
175#2492C2212yes—
176#2491C2214yes—
177#2490C2212yes—
178#2490C2212yes—
179#2489C2212yes—
180#2489C2212yes—
181#2485C2214yes—
182#2478C2214yes—
183#2478C2214yes—
184#2478C2214yes—
185#2477C2214yes—
186#2464C2214yes—
187#2453C2212yes—
188#2453C2212yes—
189#2452C2214yes—
190#2452C2214yes—
191#2449C2214yes—
192#2449C2214yes—
193#2448C2212yes—
194#2448C2212yes—
195#2447C2212yes—
196#2447C2212yes—
197#2443C2214yes—
198#2442C2214yes—
199#2441C2212yes—
200#2440C2212yes—
201#2440C2212yes—
202#2439C2212yes—
203#2427C2212yes—
204#2427C2212yes—
205#2426C2212yes—
206#2426C2212yes—
207#2422C2212yes—
208#2422C2214yes—
209#2420C2212yes—
210#2416C2212yes—
211#2415C2214yes—
212#2414C2212yes—
213#2414C2214yes—
214#2413C2214yes—
215#2402C2211yescharacteristic
216#2401C2212yes—
217#2398C2211yescharacteristic
218#2396C2211yescharacteristic
219#2395C2212yes—
220#2392C2211yescharacteristic
221#2363C2212yes—
222#2361C2212yes—
223#2356C2212yes—
224#2355C2212yes—
225#2354C2212yes—
226Q8×C4⋊C4C2212yes—
227#2330C2212yes—
228#2330C2211yescharacteristic
229#2330C2211yescharacteristic
230#2328C2212yes—
231#2327C2212yes—
232#2326C2212yes—
233#2317C2212yes—
234#2314C2212yes—
235C4×C4⋊Q8C2211yescharacteristic
236C4×#127C2211yescharacteristic
237#2298C2212yes—
238#2295C2211yescharacteristic
239#2293C2211yescharacteristic
240#2290C2212yes—
241#2283C2212yes—
242C4×#117C2211yescharacteristic
243#554—48no—
244#552—48no—
245#542—48no—
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2314yes—
251C2×#127C2311yescharacteristic
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2311yescharacteristic
258C2×#125C2311yescharacteristic
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×#117C2312yes—
296C2×#117C2311yescharacteristic
297C2×#117C2312yes—
298C2×#117C2314yes—
299C2×#117C2311yescharacteristic
300C2×#117C2314yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2314yes—
303C22×C42C2311yescharacteristic
304#401C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2312yes—
316#400C2312yes—
317#400C2312yes—
318#400C2311yescharacteristic
319#400C2312yes—
320#400C2312yes—
321#400C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2312yes—
327#399C2314yes—
328#399C2311yescharacteristic
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2312yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2311yescharacteristic
354#398C2312yes—
355#398C2314yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2312yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2312yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2311yescharacteristic
385#397C2312yes—
386#397C2312yes—
387#397C2312yes—
388#397C2312yes—
389#397C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2312yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2312yes—
410#396C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2311yescharacteristic
418#395C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2312yes—
439#394C2311yescharacteristic
440#394C2312yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2312yes—
447#393C2311yescharacteristic
448#392C2314yes—
449#392C2314yes—
450#392C2314yes—
451#392C2311yescharacteristic
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2312yes—
464#390C2312yes—
465#390C2314yes—
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2312yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2314yes—
475#390C2312yes—
476#390C2312yes—
477#390C2314yes—
478#390C2314yes—
479#390C2312yes—
480#390C2314yes—
481#390C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2312yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#388C2312yes—
538#388C2312yes—
539#388C2312yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2314yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2312yes—
594#386C2312yes—
595#386C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2312yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2312yes—
613#385C2314yes—
614#384C2311yescharacteristic
615#384C2311yescharacteristic
616#384C2312yes—
617#384C2311yescharacteristic
618#384C2312yes—
619#384C2314yes—
620#384C2312yes—
621#384C2312yes—
622#384C2311yescharacteristic
623#384C2314yes—
624#383C2314yes—
625#383C2314yes—
626#382C2312yes—
627#382C2312yes—
628#382C2312yes—
629#382C2312yes—
630#382C2314yes—
631#382C2314yes—
632#382C2314yes—
633#381C2314yes—
634#381C2314yes—
635#381C2314yes—
636#381C2314yes—
637#380C2312yes—
638#380C2312yes—
639#380C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2312yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2311yescharacteristic
648C4×C4⋊C4C2311yescharacteristic
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670#376C2311yescharacteristic
671#376C2312yes—
672#376C2311yescharacteristic
673#376C2314yes—
674#376C2314yes—
675C43C2311yescharacteristic
676C43C2311yescharacteristic
677C22×Q8C2412yes—
678C22×Q8C2411yescharacteristic
679C22×Q8C2414yes—
680C22×Q8C2414yes—
681C22×D4C2412yes—
682C22×D4C2411yescharacteristic
683C22×D4C2414yes—
684C22×D4C2412yes—
685C22×D4C2414yes—
686C22×D4C2414yes—
687C22×D4C2414yes—
688C23×C4C2412yes—
689C23×C4C2411yescharacteristic
690C23×C4C2414yes—
691C23×C4C2412yes—
692C23×C4C2414yes—
693C23×C4C2414yes—
694C23×C4C2414yes—
695C4⋊Q8—24no—
696C4⋊Q8—44no—
697C4⋊Q8—44no—
698C4⋊Q8—84no—
699C4⋊Q8—84no—
700#127—24no—
701#126—48no—
702#126—48no—
703#126—84no—
704#125—28no—
705#125—42no—
706#125—42no—
707#125—44no—
708#125—48no—
709#125—84no—
710#124—48no—
711#124—44no—
712#124—44no—
713#123—48no—
714#123—48no—
715#123—84no—
716C22⋊Q8—48no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720C22⋊Q8—44no—
721C22⋊Q8—44no—
722C22⋊Q8—44no—
723C22⋊Q8—84no—
724C22⋊Q8—84no—
725C22⋊Q8—84no—
726C22⋊Q8—84no—
727#121—44no—
728#121—44no—
729#121—44no—
730#121—84no—
731#121—84no—
732#121—84no—
733C4×Q8—28no—
734C4×Q8—24no—
735C4×Q8—44no—
736C4×Q8—44no—
737C4×D4—28no—
738C4×D4—24no—
739C4×D4—44no—
740C4×D4—44no—
741C4×D4—44no—
742C4×D4—84no—
743C4×D4—84no—
744#117—24no—
745#117—28no—
746#117—42no—
747#117—48no—
748#117—44no—
749#117—84no—
750C2×C4⋊C4—44no—
751C2×C4⋊C4—48no—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C42—24no—
862C2×C42C2414yes—
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2411yescharacteristic
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2412yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2411yescharacteristic
883C2×C42C2411yescharacteristic
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2412yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2411yescharacteristic
922#95C2411yescharacteristic
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2411yescharacteristic
931#95C2411yescharacteristic
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950C24C2511yescharacteristic
951C24C2512yes—
952C24C2514yes—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—42no—
958C2×Q8—44no—
959C2×Q8—44no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—44no—
964C2×D4—24no—
965C2×D4—22no—
966C2×D4—24no—
967C2×D4—28no—
968C2×D4—24no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—42no—
974C2×D4—42no—
975C2×D4—44no—
976C2×D4—42no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C22×C4—24no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—24no—
988C22×C4—22no—
989C22×C4—24no—
990C22×C4—28no—
991C22×C4—24no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—42no—
998C22×C4—44no—
999C22×C4—42no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2511yescharacteristic
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2512yes—
1028C22×C4C2511yescharacteristic
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—24no—
1036C4⋊C4—28no—
1037C4⋊C4—24no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—28no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—24no—
1093C22⋊C4—28no—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—42no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—42no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—42no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C42—22no—
1139C42—28no—
1140C42—24no—
1141C42—24no—
1142C42—22no—
1143C42—24no—
1144C42—22no—
1145C42—22no—
1146C42—24no—
1147C42—42no—
1148C42—42no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C42—42no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—42no—
1158C42H(5,𝔽2)14yes—
1159C422−1+414yes—
1160C23—21no—
1161C23—22no—
1162C23—24no—
1163C23—22no—
1164C23—21no—
1165C23—24no—
1166C23—21no—
1167C23—24no—
1168C23—22no—
1169C23—24no—
1170C23—22no—
1171C23—24no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—24no—
1176C23—22no—
1177C23—22no—
1178C23—24no—
1179C23C2611yescharacteristic
1180Q8—48no—
1181Q8—82no—
1182Q8—164no—
1183Q8—164no—
1184D4—48no—
1185D4—88no—
1186D4—82no—
1187D4—88no—
1188D4—84no—
1189D4—164no—
1190D4—164no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—21no—
1205C2×C4—24no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—48no—
1254C2×C4—44no—
1255C2×C4—84no—
1256C2×C4—88no—
1257C2×C4—88no—
1258C2×C4—88no—
1259C2×C4—164no—
1260C2×C4C2×H(5,𝔽2)12yes—
1261C2×C4C2×H(5,𝔽2)12yes—
1262C2×C4C2×H(5,𝔽2)12yes—
1263C2×C4C2×2−1+414yes—
1264C2×C4C2×2−1+412yes—
1265C2×C4#58512yes—
1266C22—41no—
1267C22—42no—
1268C22—44no—
1269C22—42no—
1270C22—44no—
1271C22—44no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—44no—
1276C22—41no—
1277C22—42no—
1278C22—42no—
1279C22—44no—
1280C22—42no—
1281C22—44no—
1282C22—44no—
1283C22—41no—
1284C22—42no—
1285C22C22×H(5,𝔽2)11yescharacteristic
1286C22C22×2−1+411yescharacteristic
1287C22C2×#58511yescharacteristic
1288C22H(7,𝔽2)12yes—
1289C222−1+612yes—
1290C4—24no—
1291C4—22no—
1292C4—22no—
1293C4—42no—
1294C4—41no—
1295C4—44no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—44no—
1300C4—44no—
1301C4—44no—
1302C4—42no—
1303C4—41no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—44no—
1309C4—44no—
1310C4—41no—
1311C4—44no—
1312C4—42no—
1313C4#354714yes—
1314C2—81no—
1315C2—82no—
1316C2—84no—
1317C2C2×#354711yescharacteristic
1318C2#6287912yes—
1319C2#6288011yescharacteristic
1320C2#6288412yes—
1321C2#6288811yescharacteristic
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. #58024C2semidirect
2. #57462C2semidirect
3. #57126C2semidirect
4. #56937C2semidirect
5. #56757C2semidirect
6. #55795C2semidirect
7. #54296C2semidirect
8. #54132C2semidirect
9. #53068C2semidirect
10. #52959C2semidirect
11. #45071C2semidirect
12. #44967C2semidirect
13. #42798C2semidirect
14. #42781C2semidirect
15. #42561C2semidirect
16. #42442C2semidirect
17. #39635C2semidirect
18. #39611C2semidirect
19. #39507C2semidirect
20. #39484C2semidirect
21. #37955C2semidirect
22. #37946C2semidirect
23. #37432C2semidirect
24. #37312C2semidirect
25. #35345C2semidirect
26. #35277C2semidirect
27. #34640C2semidirect

Maximal subgroups

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

subgroupindex
#580242
#574622
#571262
#569372
#567572
#557952
#542962
#541322
#530682
#529592
#450712
#449672
#427982
#427812
#425612
#424422
#396352
#396112
#395072
#394842
#379552
#379462
#374322
#373122
#353452
#352772
#346402