Finite Group Databasebeta

← #8750728

Subgroups — #8750728

Order 512.

4117 conjugacy classes of subgroups.

The subgroup lattice has 1363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59935C211yesmaximal, characteristic, complemented
2#59893C212yesmaximal, complemented
3#57926C214yesmaximal, complemented
4#57434C214yesmaximal, complemented
5#57110C214yesmaximal, complemented
6#56960C212yesmaximal, complemented
7#55770C214yesmaximal, complemented
8#53085C212yesmaximal, complemented
9#53033C211yesmaximal, characteristic, complemented
10#52919C212yesmaximal, complemented
11#52794C214yesmaximal, complemented
12#47820C212yesmaximal, complemented
13#45436C211yesmaximal, characteristic, complemented
14#45391C212yesmaximal, complemented
15#45343C212yesmaximal, complemented
16#45184C212yesmaximal, complemented
17#45175C212yesmaximal
18#42981C212yesmaximal, complemented
19#42884C211yesmaximal, characteristic, complemented
20#42857C212yesmaximal, complemented
21#42791C212yesmaximal, complemented
22#42776C212yesmaximal, complemented
23#42696C212yesmaximal, complemented
24#42250C214yesmaximal, complemented
25#39641C212yesmaximal, complemented
26#39488C211yesmaximal, characteristic
27#36698C211yesmaximal, characteristic, complemented
28#35938C211yesmaximal, characteristic, complemented
29#35886C212yesmaximal, complemented
30C2×#557C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#541C2212yes—
35#2868C2211yescharacteristic
36#2844C2212yes—
37#2844C2211yescharacteristic
38#2843C2212yes—
39#2838C2212yes—
40#2838C2212yes—
41#2837C2214yes—
42#2837C2214yes—
43#2837C2214yes—
44#2836C2214yes—
45#2836C2212yes—
46#2836C2212yes—
47#2834C2214yes—
48#2833C2214yes—
49#2833C2212yes—
50#2830C2214yes—
51#2830C2211yescharacteristic
52#2830C2211yescharacteristic
53#2827C2214yes—
54#2822C2214yes—
55#2822C2211yescharacteristic
56#2821C2212yes—
57#2820C2212yes—
58#2809C2212yes—
59#2808C2214yes—
60#2807C2214yes—
61#2807C2214yes—
62#2807C2214yes—
63#2802C2214yes—
64#2801C2214yes—
65#2800C2214yes—
66#2794C2212yes—
67#2791C2214yes—
68#2791C2214yes—
69#2791C2214yes—
70#2791C2214yes—
71#2791C2214yes—
72#2789C2212yes—
73#2788C2214yes—
74#2788C2214yes—
75#2787C2214yes—
76#2787C2214yes—
77#2784C2212yes—
78#2777C2214yes—
79#2777C2214yes—
80#2776C2214yes—
81#2773C2214yes—
82#2770C2214yes—
83#2769C2214yes—
84#2769C2212yes—
85#2769C2212yes—
86#2768C2214yes—
87#2766C2214yes—
88#2765C2214yes—
89#2762C2214yes—
90#2761C2214yes—
91#2747C2214yes—
92#2742C2214yes—
93#2740C2214yes—
94#2738C2214yes—
95#2737C2214yes—
96#2726C2214yes—
97#2726C2214yes—
98#2725C2214yes—
99#2725C2214yes—
100#2725C2214yes—
101#2721C2214yes—
102#2719C2214yes—
103#2719C2214yes—
104#2718C2214yes—
105#2718C2214yes—
106#2716C2214yes—
107#2707C2214yes—
108#2695C2214yes—
109#2694C2214yes—
110#2691C2214yes—
111#2690C2214yes—
112#2667C2214yes—
113#2664C2214yes—
114#2664C2212yes—
115#2658C2211yescharacteristic
116#2655C2214yes—
117#2653C2214yes—
118#2652C2214yes—
119#2651C2214yes—
120#2649C2214yes—
121#2647C2214yes—
122#2647C2214yes—
123#2645C2212yes—
124#2640C2211yescharacteristic
125#2637C2214yes—
126#2637C2212yes—
127#2628C2212yes—
128#2621C2212yes—
129#2620C2212yes—
130#2612C2214yes—
131#2612C2212yes—
132#2612C2212yes—
133#2612C2212yes—
134#2611C2214yes—
135#2611C2212yes—
136#2608C2214yes—
137#2604C2212yes—
138#2599C2212yes—
139#2596C2214yes—
140#2592C2211yescharacteristic
141#2592C2211yescharacteristic
142#2589C2214yes—
143#2587C2214yes—
144#2584C2214yes—
145#2581C2212yes—
146#2577C2214yes—
147#2577C2214yes—
148#2574C2214yes—
149#2573C2214yes—
150#2568C2212yes—
151#2568C2211yescharacteristic
152#2568C2211yescharacteristic
153#2567C2211yescharacteristic
154#2559C2214yes—
155#2556C2214yes—
156#2553C2214yes—
157#2550C2214yes—
158#2546C2212yes—
159#2546C2212yes—
160#2546C2212yes—
161#2546C2212yes—
162#2546C2212yes—
163#2546C2212yes—
164#2546C2212yes—
165#2545C2212yes—
166#2542C2211yescharacteristic
167#2533C2214yes—
168#2530C2214yes—
169#2530C2214yes—
170#2530C2214yes—
171#2528C2214yes—
172#2526C2214yes—
173#2526C2214yes—
174#2525C2214yes—
175#2519C2214yes—
176#2519C2214yes—
177#2518C2214yes—
178#2517C2214yes—
179#2516C2214yes—
180#2515C2214yes—
181#2514C2212yes—
182#2513C2212yes—
183#2513C2212yes—
184#2509C2212yes—
185#2509C2214yes—
186#2509C2214yes—
187#2508C2212yes—
188#2507C2214yes—
189#2507C2214yes—
190#2503C2212yes—
191#2502C2212yes—
192#2500C2212yes—
193#2497C2214yes—
194#2492C2212yes—
195#2489C2212yes—
196#2473C2214yes—
197#2469C2214yes—
198#2454C2212yes—
199#2453C2212yes—
200#2453C2214yes—
201#2453C2212yes—
202#2451C2212yes—
203#2448C2212yes—
204#2448C2212yes—
205#2448C2212yes—
206#2446C2212yes—
207#2446C2212yes—
208#2446C2212yes—
209#2446C2212yes—
210#2442C2214yes—
211#2432C2212yes—
212#2432C2212yes—
213#2432C2212yes—
214#2432C2212yes—
215#2429C2212yes—
216#2429C2212yes—
217#2429C2212yes—
218#2429C2212yes—
219#2429C2212yes—
220#2429C2212yes—
221#2429C2212yes—
222#2421C2212yes—
223#2417C2212yes—
224#2401C2214yes—
225#2401C2212yes—
226#2401C2212yes—
227#2399C2211yescharacteristic
228#2399C2211yescharacteristic
229#2396C2212yes—
230#2396C2212yes—
231#2396C2212yes—
232#2395C2212yes—
233#2372C2212yes—
234#2370C2212yes—
235#2367C2212yes—
236#2365C2212yes—
237#2365C2212yes—
238#2365C2212yes—
239#2360C2212yes—
240#2360C2212yes—
241#2360C2212yes—
242#2356C2212yes—
243#2356C2212yes—
244#2351C2212yes—
245#2346C2214yes—
246#2345C2212yes—
247#2341C2212yes—
248#2330C2214yes—
249#2327C2212yes—
250#2323C2212yes—
251#2320C2211yescharacteristic
252#2317C2212yes—
253#2311C2212yes—
254C4×#125C2212yes—
255C4×#124C2211yescharacteristic
256#2295C2212yes—
257#2293C2211yescharacteristic
258#2276C2211yescharacteristic
259C22×#41C2312yes—
260#557—44no—
261#557—44no—
262#556—44no—
263#547—44no—
264#541—48no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×#126C2312yes—
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#124C2311yescharacteristic
288C2×#124C2311yescharacteristic
289C2×#124C2311yescharacteristic
290C2×#124C2312yes—
291C2×#123C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×#121C2312yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2312yes—
320#401C2312yes—
321#401C2314yes—
322#401C2312yes—
323#401C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2314yes—
327#400C2312yes—
328#400C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
343#400C2312yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#399C2312yes—
359#399C2312yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2312yes—
365#399C2312yes—
366#399C2314yes—
367#399C2314yes—
368#399C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2311yescharacteristic
372#398C2311yescharacteristic
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2311yescharacteristic
395#398C2311yescharacteristic
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#397C2312yes—
413#397C2312yes—
414#397C2314yes—
415#397C2312yes—
416#397C2314yes—
417#397C2314yes—
418#397C2312yes—
419#397C2312yes—
420#397C2314yes—
421#397C2314yes—
422#397C2312yes—
423#397C2312yes—
424#397C2314yes—
425#397C2312yes—
426#397C2314yes—
427#397C2314yes—
428#397C2312yes—
429#397C2312yes—
430#397C2312yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#396C2312yes—
436#396C2312yes—
437#396C2312yes—
438#396C2312yes—
439#396C2312yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2312yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#395C2312yes—
453#395C2312yes—
454#395C2311yescharacteristic
455#395C2312yes—
456#395C2312yes—
457#395C2314yes—
458#395C2311yescharacteristic
459#395C2311yescharacteristic
460#395C2314yes—
461#395C2311yescharacteristic
462#395C2312yes—
463#395C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#393C2312yes—
475#393C2312yes—
476#393C2314yes—
477#393C2312yes—
478#393C2312yes—
479#393C2312yes—
480#393C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2314yes—
492#391C2314yes—
493#391C2312yes—
494#391C2311yescharacteristic
495#391C2314yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2311yescharacteristic
505#390C2314yes—
506#390C2312yes—
507#390C2314yes—
508#390C2312yes—
509#390C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2314yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2312yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2312yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2312yes—
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#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2312yes—
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#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#384C2312yes—
648#384C2312yes—
649#384C2312yes—
650#384C2314yes—
651#384C2312yes—
652#383C2312yes—
653#383C2314yes—
654#383C2314yes—
655#383C2314yes—
656#382C2312yes—
657#382C2311yescharacteristic
658#382C2314yes—
659#382C2312yes—
660#382C2312yes—
661#382C2314yes—
662#382C2312yes—
663#382C2312yes—
664#382C2312yes—
665#382C2314yes—
666#382C2314yes—
667#381C2314yes—
668#381C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2314yes—
675#380C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710#376C2311yescharacteristic
711#376C2314yes—
712#376C2314yes—
713#376C2312yes—
714#376C2314yes—
715#376C2311yescharacteristic
716C43C2311yescharacteristic
717C2×#41—44no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×D4C2411yescharacteristic
729C22×D4C2411yescharacteristic
730C22×D4C2414yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2414yes—
734C23×C4C2414yes—
735C4⋊Q8—44no—
736C4⋊Q8—42no—
737C4⋊Q8—44no—
738C4⋊Q8—44no—
739C4⋊Q8—44no—
740C4⋊Q8—44no—
741C4⋊Q8—44no—
742C4⋊Q8—42no—
743C4⋊Q8—42no—
744C4⋊Q8—44no—
745C4⋊Q8—42no—
746#126—48no—
747#126—44no—
748#126—44no—
749#126—48no—
750#125—28no—
751#125—28no—
752#125—48no—
753#125—44no—
754#125—48no—
755#125—48no—
756#125—48no—
757#124—24no—
758#124—44no—
759#124—42no—
760#124—42no—
761#123—48no—
762C22⋊Q8—28no—
763C22⋊Q8—44no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766C22⋊Q8—44no—
767C22⋊Q8—44no—
768#121—44no—
769C4×Q8—28no—
770C4×Q8—24no—
771C4×Q8—24no—
772C4×Q8—42no—
773C4×Q8—42no—
774C4×Q8—44no—
775C4×Q8—42no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×D4—24no—
784C4×D4—42no—
785#117—28no—
786#117—44no—
787#117—44no—
788C2×C4⋊C4—44no—
789C2×C4⋊C4—44no—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2411yescharacteristic
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925#95C2411yescharacteristic
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2414yes—
932#95C2412yes—
933#95C2411yescharacteristic
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2411yescharacteristic
939#95C2411yescharacteristic
940#95C2414yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004C24C2512yes—
1005C24C2512yes—
1006#41—816no—
1007C2×Q8—22no—
1008C2×Q8—24no—
1009C2×Q8—22no—
1010C2×Q8—24no—
1011C2×Q8—22no—
1012C2×Q8—24no—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—41no—
1019C2×Q8—42no—
1020C2×Q8—41no—
1021C2×Q8—41no—
1022C2×Q8—42no—
1023C2×Q8—41no—
1024C2×Q8—42no—
1025C2×Q8—44no—
1026C2×D4—22no—
1027C2×D4—22no—
1028C2×D4—24no—
1029C2×D4—41no—
1030C2×D4—44no—
1031C2×D4—41no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4C2514yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—41no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—41no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—41no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—41no—
1127C4⋊C4—41no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4H(5,𝔽2)14yes—
1148C22⋊C4—24no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4—44no—
1166C22⋊C4—42no—
1167C22⋊C4—42no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—42no—
1178C22⋊C4—42no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—22no—
1187C42—22no—
1188C42—22no—
1189C42—28no—
1190C42—24no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—44no—
1195C42—42no—
1196C42—44no—
1197C42—41no—
1198C42—44no—
1199C42—42no—
1200C42—42no—
1201C42—44no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C422−1+414yes—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—24no—
1215C23—22no—
1216C23—24no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23C2611yescharacteristic
1221Q8—44no—
1222Q8—44no—
1223Q8—48no—
1224Q8—44no—
1225Q8—48no—
1226Q8—82no—
1227Q8—82no—
1228Q8—84no—
1229D4—44no—
1230D4—82no—
1231D4—88no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—48no—
1303C2×C4—48no—
1304C2×C4—88no—
1305C2×C4—164no—
1306C2×C4C2×H(5,𝔽2)14yes—
1307C2×C4C2×H(5,𝔽2)12yes—
1308C2×C4C2×2−1+412yes—
1309C2×C4C2×2−1+414yes—
1310C2×C4#58514yes—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—44no—
1318C22—42no—
1319C22—42no—
1320C22—44no—
1321C22—42no—
1322C22—42no—
1323C22C22×H(5,𝔽2)11yescharacteristic
1324C22C22×2−1+411yescharacteristic
1325C22C2×#58512yes—
1326C222−1+612yes—
1327C222−1+611yescharacteristic
1328C4—22no—
1329C4—24no—
1330C4—24no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—42no—
1335C4—44no—
1336C4—41no—
1337C4—41no—
1338C4—42no—
1339C4—42no—
1340C4—44no—
1341C4—41no—
1342C4—42no—
1343C4—42no—
1344C4—42no—
1345C4—44no—
1346C4—44no—
1347C4—42no—
1348C4—42no—
1349C4—41no—
1350C4—41no—
1351C4—44no—
1352C4—42no—
1353C4—42no—
1354C4#355114yes—
1355C2—82no—
1356C2—82no—
1357C2C2×#355111yescharacteristic
1358C2#6291511yescharacteristic
1359C2#6295612yes—
1360C2#6304411yescharacteristic
1361C2#6306212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59935C2semidirect
2. #59893C2semidirect
3. #57926C2semidirect
4. #57434C2semidirect
5. #57110C2semidirect
6. #56960C2semidirect
7. #55770C2semidirect
8. #53085C2semidirect
9. #53033C2semidirect
10. #52919C2semidirect
11. #52794C2semidirect
12. #47820C2semidirect
13. #45436C2semidirect
14. #45391C2semidirect
15. #45343C2semidirect
16. #45184C2semidirect
18. #42981C2semidirect
19. #42884C2semidirect
20. #42857C2semidirect
21. #42791C2semidirect
22. #42776C2semidirect
23. #42696C2semidirect
24. #42250C2semidirect
25. #39641C2semidirect
27. #36698C2semidirect
28. #35938C2semidirect
29. #35886C2semidirect

Maximal subgroups

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

subgroupindex
#599352
#598932
#579262
#574342
#571102
#569602
#557702
#530852
#530332
#529192
#527942
#478202
#454362
#453912
#453432
#451842
#451752
#429812
#428842
#428572
#427912
#427762
#426962
#422502
#396412
#394882
#366982
#359382
#358862