Finite Group Databasebeta

← #8751458

Subgroups — #8751458

Order 512.

4359 conjugacy classes of subgroups.

The subgroup lattice has 1426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59908C211yesmaximal, characteristic, complemented
2#59581C212yesmaximal, complemented
3#58777C212yesmaximal, complemented
4#57756C214yesmaximal, complemented
5#57221C214yesmaximal, complemented
6#57174C214yesmaximal, complemented
7#56159C214yesmaximal, complemented
8#53100C211yesmaximal, characteristic, complemented
9#53004C212yesmaximal, complemented
10#52902C214yesmaximal, complemented
11#52653C212yesmaximal, complemented
12#47664C212yesmaximal, complemented
13#45408C211yesmaximal, characteristic, complemented
14#45289C212yesmaximal, complemented
15#45148C212yesmaximal, complemented
16#45008C212yesmaximal, complemented
17#44883C212yesmaximal, complemented
18#42958C212yesmaximal, complemented
19#42940C212yesmaximal, complemented
20#42812C211yesmaximal, characteristic, complemented
21#42759C212yesmaximal, complemented
22#42705C212yesmaximal, complemented
23#42441C212yesmaximal, complemented
24#41545C214yesmaximal, complemented
25#40098C212yesmaximal, complemented
26#38954C211yesmaximal, characteristic, complemented
27#36697C211yesmaximal, characteristic, complemented
28#35956C211yesmaximal, characteristic, complemented
29#35901C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×D4×Q8C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#542C2212yes—
35#2862C2211yescharacteristic
36#2843C2211yescharacteristic
37#2839C2212yes—
38#2839C2214yes—
39#2838C2212yes—
40#2837C2212yes—
41#2837C2214yes—
42#2836C2212yes—
43#2833C2211yescharacteristic
44#2833C2212yes—
45#2832C2211yescharacteristic
46#2831C2212yes—
47#2831C2214yes—
48#2828C2214yes—
49#2825C2214yes—
50#2824C2214yes—
51#2824C2214yes—
52#2824C2214yes—
53#2823C2211yescharacteristic
54#2822C2212yes—
55#2821C2212yes—
56#2821C2212yes—
57#2814C2214yes—
58#2799C2212yes—
59#2797C2214yes—
60#2795C2212yes—
61#2789C2212yes—
62#2781C2214yes—
63#2775C2214yes—
64#2765C2214yes—
65#2764C2214yes—
66#2764C2214yes—
67#2761C2214yes—
68#2760C2214yes—
69#2759C2214yes—
70#2759C2214yes—
71#2756C2214yes—
72#2753C2214yes—
73#2751C2214yes—
74#2750C2214yes—
75#2748C2214yes—
76#2746C2214yes—
77#2745C2214yes—
78#2743C2214yes—
79#2743C2214yes—
80#2743C2214yes—
81#2741C2214yes—
82#2741C2214yes—
83#2740C2214yes—
84#2740C2214yes—
85#2733C2212yes—
86#2731C2212yes—
87#2730C2214yes—
88#2728C2214yes—
89#2723C2214yes—
90#2716C2214yes—
91#2715C2214yes—
92#2715C2214yes—
93#2713C2214yes—
94#2712C2214yes—
95#2711C2214yes—
96#2702C2214yes—
97#2700C2214yes—
98#2699C2214yes—
99#2699C2212yes—
100#2698C2214yes—
101#2698C2214yes—
102#2695C2214yes—
103#2692C2214yes—
104#2692C2214yes—
105#2690C2214yes—
106#2688C2214yes—
107#2688C2214yes—
108#2688C2214yes—
109#2687C2214yes—
110#2681C2214yes—
111#2672C2214yes—
112#2665C2214yes—
113#2665C2214yes—
114#2662C2212yes—
115#2658C2211yescharacteristic
116#2657C2211yescharacteristic
117#2651C2214yes—
118#2651C2214yes—
119#2650C2214yes—
120#2650C2214yes—
121#2649C2214yes—
122#2648C2214yes—
123#2645C2212yes—
124#2636C2212yes—
125#2630C2214yes—
126#2628C2212yes—
127#2621C2212yes—
128#2620C2212yes—
129#2618C2214yes—
130#2610C2212yes—
131#2603C2212yes—
132#2598C2212yes—
133#2597C2214yes—
134#2594C2214yes—
135#2593C2212yes—
136#2592C2212yes—
137#2592C2211yescharacteristic
138#2591C2214yes—
139#2589C2214yes—
140#2588C2214yes—
141#2582C2212yes—
142#2578C2214yes—
143#2577C2214yes—
144#2576C2214yes—
145#2574C2214yes—
146#2574C2214yes—
147#2572C2212yes—
148#2572C2214yes—
149#2572C2212yes—
150#2568C2211yescharacteristic
151#2568C2211yescharacteristic
152#2560C2214yes—
153#2560C2214yes—
154#2554C2214yes—
155#2548C2211yescharacteristic
156#2548C2212yes—
157#2547C2212yes—
158#2546C2211yescharacteristic
159#2545C2212yes—
160#2545C2212yes—
161#2545C2212yes—
162#2544C2212yes—
163#2544C2212yes—
164#2544C2212yes—
165#2540C2211yescharacteristic
166#2533C2214yes—
167#2532C2214yes—
168#2532C2214yes—
169#2529C2214yes—
170#2526C2214yes—
171#2526C2214yes—
172#2518C2214yes—
173#2516C2214yes—
174#2515C2214yes—
175#2514C2214yes—
176#2514C2212yes—
177#2511C2212yes—
178#2511C2212yes—
179#2508C2212yes—
180#2506C2212yes—
181#2503C2214yes—
182#2500C2212yes—
183#2499C2212yes—
184#2492C2212yes—
185#2492C2214yes—
186#2491C2214yes—
187#2491C2212yes—
188#2490C2214yes—
189#2476C2214yes—
190#2473C2214yes—
191#2467C2214yes—
192#2461C2214yes—
193#2461C2214yes—
194#2459C2214yes—
195#2457C2214yes—
196#2452C2212yes—
197#2451C2212yes—
198#2451C2212yes—
199#2451C2212yes—
200#2448C2212yes—
201#2447C2212yes—
202#2447C2212yes—
203#2447C2212yes—
204#2447C2212yes—
205#2446C2212yes—
206#2446C2212yes—
207#2436C2212yes—
208#2436C2212yes—
209#2436C2212yes—
210#2436C2214yes—
211#2434C2212yes—
212#2434C2212yes—
213#2429C2212yes—
214#2428C2212yes—
215#2428C2212yes—
216#2428C2212yes—
217#2427C2212yes—
218#2427C2212yes—
219#2427C2212yes—
220#2421C2212yes—
221#2417C2214yes—
222#2414C2212yes—
223#2409C2214yes—
224#2402C2214yes—
225#2402C2212yes—
226#2401C2212yes—
227#2399C2211yescharacteristic
228#2398C2211yescharacteristic
229#2396C2212yes—
230#2396C2212yes—
231#2395C2212yes—
232#2392C2212yes—
233#2372C2212yes—
234#2369C2212yes—
235#2367C2212yes—
236#2367C2212yes—
237#2366C2212yes—
238#2365C2212yes—
239#2363C2212yes—
240#2362C2212yes—
241#2362C2212yes—
242#2357C2212yes—
243#2356C2212yes—
244#2352C2214yes—
245D4×C4⋊C4C2212yes—
246#2347C2212yes—
247Q8×C22⋊C4C2212yes—
248#2337C2214yes—
249#2324C2212yes—
250#2320C2211yescharacteristic
251#2319C2212yes—
252#2310C2212yes—
253#2310C2212yes—
254C4×C4⋊Q8C2211yescharacteristic
255C4×#126C2212yes—
256C4×#124C2212yes—
257#2293C2211yescharacteristic
258#2276C2211yescharacteristic
259C23×Q8C2312yes—
260C23×Q8C2312yes—
261#559—44no—
262#556—44no—
263D4×Q8—44no—
264D4×Q8—44no—
265#542—48no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×#127C2312yes—
275C2×#127C2311yescharacteristic
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#126C2312yes—
279C2×#126C2312yes—
280C2×#125C2314yes—
281C2×#124C2311yescharacteristic
282C2×#124C2312yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2311yescharacteristic
290C2×#124C2314yes—
291C2×#124C2312yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2311yescharacteristic
325C2×#117C2312yes—
326C2×#117C2312yes—
327C2×#117C2312yes—
328C2×#117C2312yes—
329C22×C4⋊C4C2314yes—
330#401C2314yes—
331#401C2314yes—
332#401C2312yes—
333#400C2311yescharacteristic
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2311yescharacteristic
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2312yes—
351#400C2312yes—
352#400C2314yes—
353#400C2312yes—
354#400C2312yes—
355#400C2314yes—
356#400C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#399C2312yes—
363#399C2312yes—
364#399C2312yes—
365#399C2312yes—
366#399C2312yes—
367#399C2314yes—
368#399C2312yes—
369#399C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2311yescharacteristic
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2312yes—
381#398C2311yescharacteristic
382#398C2312yes—
383#398C2312yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#397C2312yes—
395#397C2314yes—
396#397C2312yes—
397#397C2312yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2312yes—
407#397C2312yes—
408#397C2314yes—
409#397C2314yes—
410#397C2312yes—
411#397C2314yes—
412#397C2314yes—
413#397C2312yes—
414#397C2314yes—
415#397C2312yes—
416#397C2314yes—
417#397C2314yes—
418#396C2312yes—
419#396C2312yes—
420#396C2312yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2312yes—
425#396C2312yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#395C2314yes—
434#395C2312yes—
435#395C2312yes—
436#395C2314yes—
437#395C2311yescharacteristic
438#395C2314yes—
439#395C2311yescharacteristic
440#395C2312yes—
441#395C2314yes—
442#395C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2312yes—
446#394C2311yescharacteristic
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2312yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2312yes—
463#394C2311yescharacteristic
464#394C2314yes—
465#394C2312yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2312yes—
473#393C2312yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2312yes—
479#393C2312yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#392C2312yes—
484#392C2314yes—
485#392C2312yes—
486#392C2314yes—
487#392C2314yes—
488#392C2314yes—
489#392C2312yes—
490#392C2314yes—
491#391C2314yes—
492#391C2314yes—
493#391C2311yescharacteristic
494#391C2311yescharacteristic
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2314yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2314yes—
504#391C2314yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2314yes—
510#391C2314yes—
511#391C2312yes—
512#391C2314yes—
513#391C2314yes—
514#391C2314yes—
515#391C2312yes—
516#391C2312yes—
517#391C2312yes—
518#391C2312yes—
519#391C2312yes—
520#391C2314yes—
521#390C2314yes—
522#390C2314yes—
523#390C2314yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2314yes—
531#390C2314yes—
532#390C2314yes—
533#390C2314yes—
534#390C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2314yes—
549#388C2312yes—
550#388C2312yes—
551#388C2312yes—
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#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
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#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#384C2311yescharacteristic
649#384C2312yes—
650#383C2312yes—
651#383C2312yes—
652#383C2314yes—
653#383C2314yes—
654#383C2314yes—
655#382C2312yes—
656#382C2312yes—
657#382C2314yes—
658#382C2312yes—
659#382C2314yes—
660#382C2312yes—
661#381C2314yes—
662#381C2314yes—
663#381C2314yes—
664#381C2314yes—
665#381C2314yes—
666#381C2314yes—
667#381C2314yes—
668#381C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712#376C2311yescharacteristic
713#376C2312yes—
714#376C2314yes—
715#376C2311yescharacteristic
716C43C2311yescharacteristic
717C22×Q8—44no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8—44no—
721C22×Q8—44no—
722C22×Q8—82no—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2414yes—
729C22×Q8C2412yes—
730C22×Q8C2411yescharacteristic
731C22×Q8C2414yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C22×D4C2412yes—
741C22×D4C2414yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C4⋊Q8—28no—
750C4⋊Q8—44no—
751C4⋊Q8—42no—
752C4⋊Q8—44no—
753C4⋊Q8—42no—
754C4⋊Q8—42no—
755C4⋊Q8—42no—
756C4⋊Q8—82no—
757#127—44no—
758#127—42no—
759#126—44no—
760#126—44no—
761#126—44no—
762#126—48no—
763#125—84no—
764#124—44no—
765#124—44no—
766#124—44no—
767#124—44no—
768#124—44no—
769#124—42no—
770#124—42no—
771#124—44no—
772#124—44no—
773#124—48no—
774#124—48no—
775#123—48no—
776#123—48no—
777C22⋊Q8—28no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—48no—
784C22⋊Q8—84no—
785#121—44no—
786#121—44no—
787#121—44no—
788#121—84no—
789#121—84no—
790#121—84no—
791C4×Q8—24no—
792C4×Q8—24no—
793C4×Q8—42no—
794C4×Q8—42no—
795C4×Q8—42no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×D4—28no—
800C4×D4—24no—
801C4×D4—44no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—42no—
806C4×D4—44no—
807C4×D4—48no—
808#117—44no—
809#117—44no—
810#117—44no—
811#117—82no—
812C2×C4⋊C4—84no—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2414yes—
943#95C2411yescharacteristic
944#95C2412yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2411yescharacteristic
949#95C2412yes—
950#95C2412yes—
951#95C2411yescharacteristic
952#95C2414yes—
953#95C2411yescharacteristic
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24C2512yes—
1017C24C2512yes—
1018C24C2514yes—
1019C2×Q8—22no—
1020C2×Q8—22no—
1021C2×Q8—24no—
1022C2×Q8—28no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—22no—
1028C2×Q8—22no—
1029C2×Q8—24no—
1030C2×Q8—41no—
1031C2×Q8—41no—
1032C2×Q8—41no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—44no—
1040C2×Q8—44no—
1041C2×Q8—44no—
1042C2×Q8—42no—
1043C2×Q8—816no—
1044C2×Q8—816no—
1045C2×D4—22no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—41no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—42no—
1064C2×D4—44no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—28no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2514yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—41no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—41no—
1147C4⋊C4—42no—
1148C4⋊C4—41no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—41no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—41no—
1156C4⋊C4—41no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4H(5,𝔽2)14yes—
1175C22⋊C4—24no—
1176C22⋊C4—28no—
1177C22⋊C4—28no—
1178C22⋊C4—28no—
1179C22⋊C4—24no—
1180C22⋊C4—42no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—42no—
1185C22⋊C4—44no—
1186C22⋊C4—42no—
1187C22⋊C4—44no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C42—24no—
1227C42—24no—
1228C42—24no—
1229C42—24no—
1230C42—22no—
1231C42—22no—
1232C42—22no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—22no—
1237C42—44no—
1238C42—42no—
1239C42—44no—
1240C42—41no—
1241C42—42no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42—44no—
1246C42—42no—
1247C42—44no—
1248C42—42no—
1249C23—22no—
1250C23—22no—
1251C23—24no—
1252C23—22no—
1253C23—24no—
1254C23—24no—
1255C23—24no—
1256C23—24no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—24no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—24no—
1266C23—24no—
1267C23—24no—
1268C23C2611yescharacteristic
1269Q8—44no—
1270Q8—44no—
1271Q8—48no—
1272Q8—44no—
1273Q8—82no—
1274Q8—84no—
1275Q8—88no—
1276Q8—82no—
1277Q8—88no—
1278D4—44no—
1279D4—44no—
1280D4—48no—
1281D4—84no—
1282D4—88no—
1283D4—164no—
1284D4—164no—
1285D4—164no—
1286D4—164no—
1287D4—162no—
1288C2×C4—21no—
1289C2×C4—22no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—21no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—21no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—48no—
1357C2×C4—48no—
1358C2×C4—88no—
1359C2×C4—88no—
1360C2×C4—88no—
1361C2×C4—164no—
1362C2×C4—164no—
1363C2×C4C2×H(5,𝔽2)14yes—
1364C2×C4C2×H(5,𝔽2)12yes—
1365C2×C4#58512yes—
1366C2×C4#58514yes—
1367C22—42no—
1368C22—42no—
1369C22—44no—
1370C22—42no—
1371C22—44no—
1372C22—42no—
1373C22—44no—
1374C22—44no—
1375C22—44no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—44no—
1380C22—42no—
1381C22—44no—
1382C22—44no—
1383C22—42no—
1384C22—42no—
1385C22—44no—
1386C22C22×H(5,𝔽2)11yescharacteristic
1387C22C2×#58512yes—
1388C22C2×#58511yescharacteristic
1389C22H(7,𝔽2)11yescharacteristic
1390C222−1+612yes—
1391C4—22no—
1392C4—24no—
1393C4—42no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—41no—
1398C4—42no—
1399C4—41no—
1400C4—41no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—44no—
1405C4—44no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—44no—
1410C4—41no—
1411C4—41no—
1412C4—42no—
1413C4—42no—
1414C4—44no—
1415C4—42no—
1416C4#355114yes—
1417C2—82no—
1418C2—84no—
1419C2—82no—
1420C2C2×#355111yescharacteristic
1421C2#6291811yescharacteristic
1422C2#6296712yes—
1423C2#6304411yescharacteristic
1424C2#6306912yes—
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. #59908C2semidirect
2. #59581C2semidirect
3. #58777C2semidirect
4. #57756C2semidirect
5. #57221C2semidirect
6. #57174C2semidirect
7. #56159C2semidirect
8. #53100C2semidirect
9. #53004C2semidirect
10. #52902C2semidirect
11. #52653C2semidirect
12. #47664C2semidirect
13. #45408C2semidirect
14. #45289C2semidirect
15. #45148C2semidirect
16. #45008C2semidirect
17. #44883C2semidirect
18. #42958C2semidirect
19. #42940C2semidirect
20. #42812C2semidirect
21. #42759C2semidirect
22. #42705C2semidirect
23. #42441C2semidirect
24. #41545C2semidirect
25. #40098C2semidirect
26. #38954C2semidirect
27. #36697C2semidirect
28. #35956C2semidirect
29. #35901C2semidirect

Maximal subgroups

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

subgroupindex
#599082
#595812
#587772
#577562
#572212
#571742
#561592
#531002
#530042
#529022
#526532
#476642
#454082
#452892
#451482
#450082
#448832
#429582
#429402
#428122
#427592
#427052
#424412
#415452
#400982
#389542
#366972
#359562
#359012