Finite Group Databasebeta

← #8508872

Subgroups — #8508872

Order 512.

4127 conjugacy classes of subgroups.

The subgroup lattice has 1378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59951C211yesmaximal, characteristic, complemented
2#58506C214yesmaximal, complemented
3#58492C214yesmaximal, complemented
4#57557C214yesmaximal, complemented
5#57330C214yesmaximal, complemented
6#57113C214yesmaximal, complemented
7#53326C214yesmaximal, complemented
8#53136C212yesmaximal, complemented
9#52270C211yesmaximal, characteristic
10#52081C212yesmaximal, complemented
11#51999C212yesmaximal, complemented
12#46331C211yesmaximal, characteristic, complemented
13#46196C212yesmaximal, complemented
14#46196C211yesmaximal, characteristic, complemented
15#45416C212yesmaximal, complemented
16#45300C212yesmaximal, complemented
17#42851C212yesmaximal, complemented
18#42714C212yesmaximal, complemented
19#42675C212yesmaximal, complemented
20#39616C211yesmaximal, characteristic, complemented
21#39170C211yesmaximal, characteristic, complemented
22#38267C212yesmaximal, complemented
23#38251C212yesmaximal, complemented
24#38215C212yesmaximal, complemented
25#37400C212yesmaximal, complemented
26#37395C212yesmaximal, complemented
27#37227C212yesmaximal
28#36562C211yesmaximal, characteristic, complemented
29#35204C212yesmaximal, complemented
30C2×#557C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#554C2211yescharacteristic
33C2×#552C2212yes—
34C2×D4×Q8C2211yescharacteristic
35#2868C2211yescharacteristic
36#2865C2214yes—
37#2864C2212yes—
38#2864C2214yes—
39#2863C2212yes—
40#2862C2211yescharacteristic
41#2862C2211yescharacteristic
42#2859C2212yes—
43#2843C2212yes—
44#2838C2214yes—
45#2838C2214yes—
46#2837C2214yes—
47#2831C2214yes—
48#2830C2214yes—
49#2830C2212yes—
50#2827C2214yes—
51#2814C2214yes—
52#2809C2211yescharacteristic
53#2809C2212yes—
54#2808C2212yes—
55#2806C2214yes—
56#2805C2214yes—
57#2803C2212yes—
58#2803C2212yes—
59#2803C2214yes—
60#2802C2214yes—
61#2799C2214yes—
62#2799C2212yes—
63#2797C2214yes—
64#2796C2214yes—
65#2795C2212yes—
66#2793C2214yes—
67#2793C2214yes—
68#2793C2214yes—
69#2793C2214yes—
70#2793C2214yes—
71#2793C2214yes—
72#2792C2214yes—
73#2791C2214yes—
74#2791C2214yes—
75#2791C2214yes—
76#2791C2214yes—
77#2791C2214yes—
78#2790C2214yes—
79#2789C2214yes—
80#2789C2212yes—
81#2787C2214yes—
82#2786C2214yes—
83#2783C2212yes—
84#2783C2212yes—
85#2781C2214yes—
86#2777C2214yes—
87#2777C2214yes—
88#2776C2214yes—
89#2775C2214yes—
90#2774C2214yes—
91#2774C2214yes—
92#2772C2214yes—
93#2770C2214yes—
94#2769C2212yes—
95#2766C2214yes—
96#2765C2214yes—
97#2764C2214yes—
98#2761C2214yes—
99#2759C2214yes—
100#2759C2214yes—
101#2759C2214yes—
102#2751C2214yes—
103#2747C2214yes—
104#2747C2214yes—
105#2745C2214yes—
106#2744C2214yes—
107#2733C2211yescharacteristic
108#2731C2211yescharacteristic
109#2731C2212yes—
110#2731C2211yescharacteristic
111#2731C2212yes—
112#2726C2214yes—
113#2725C2214yes—
114#2725C2214yes—
115#2720C2214yes—
116#2720C2214yes—
117#2719C2214yes—
118#2719C2214yes—
119#2719C2214yes—
120#2716C2214yes—
121#2713C2214yes—
122#2707C2214yes—
123#2704C2214yes—
124#2704C2214yes—
125#2702C2214yes—
126#2698C2214yes—
127#2687C2214yes—
128#2666C2214yes—
129#2660C2212yes—
130#2655C2214yes—
131#2654C2214yes—
132#2651C2214yes—
133#2651C2214yes—
134#2649C2214yes—
135#2645C2212yes—
136#2642C2212yes—
137#2630C2214yes—
138#2625C2212yes—
139#2625C2212yes—
140#2625C2214yes—
141#2621C2212yes—
142#2621C2212yes—
143#2606C2214yes—
144#2605C2214yes—
145#2596C2214yes—
146#2593C2212yes—
147#2590C2214yes—
148#2589C2214yes—
149#2585C2214yes—
150#2582C2212yes—
151#2568C2211yescharacteristic
152#2568C2211yescharacteristic
153#2567C2212yes—
154#2567C2211yescharacteristic
155#2566C2212yes—
156#2566C2212yes—
157#2565C2212yes—
158#2565C2212yes—
159#2556C2214yes—
160#2556C2214yes—
161#2546C2212yes—
162#2546C2211yescharacteristic
163#2542C2211yescharacteristic
164#2542C2211yescharacteristic
165#2538C2212yes—
166#2533C2214yes—
167#2532C2214yes—
168#2531C2214yes—
169#2530C2214yes—
170#2529C2214yes—
171#2529C2214yes—
172#2528C2214yes—
173#2527C2214yes—
174#2525C2214yes—
175#2520C2214yes—
176#2515C2214yes—
177#2514C2212yes—
178#2511C2212yes—
179#2508C2212yes—
180#2507C2214yes—
181#2507C2212yes—
182#2499C2212yes—
183#2495C2212yes—
184#2495C2214yes—
185#2494C2214yes—
186#2494C2212yes—
187#2492C2212yes—
188#2489C2212yes—
189#2485C2214yes—
190#2485C2212yes—
191#2477C2214yes—
192#2475C2214yes—
193#2466C2214yes—
194#2458C2214yes—
195#2457C2214yes—
196#2453C2212yes—
197#2453C2212yes—
198#2453C2214yes—
199#2451C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2446C2212yes—
203#2446C2212yes—
204#2446C2212yes—
205#2442C2212yes—
206#2439C2212yes—
207#2439C2214yes—
208#2439C2212yes—
209#2439C2214yes—
210#2434C2212yes—
211#2434C2212yes—
212#2429C2212yes—
213#2429C2212yes—
214#2429C2212yes—
215#2429C2212yes—
216#2429C2212yes—
217#2429C2212yes—
218#2429C2212yes—
219#2423C2212yes—
220#2417C2212yes—
221#2415C2212yes—
222#2415C2212yes—
223#2415C2212yes—
224#2415C2212yes—
225#2409C2212yes—
226#2409C2212yes—
227#2398C2212yes—
228#2392C2212yes—
229#2392C2212yes—
230#2381C2212yes—
231#2381C2212yes—
232#2369C2212yes—
233#2362C2212yes—
234#2362C2212yes—
235#2360C2212yes—
236#2360C2212yes—
237#2347C2212yes—
238Q8×C22⋊C4C2212yes—
239#2330C2212yes—
240#2327C2212yes—
241#2327C2212yes—
242#2327C2212yes—
243#2326C2212yes—
244#2323C2212yes—
245#2323C2212yes—
246#2316C2212yes—
247#2310C2212yes—
248C4×C4⋊Q8C2211yescharacteristic
249C4×#124C2211yescharacteristic
250C4×#124C2211yescharacteristic
251C4×#124C2212yes—
252#2298C2212yes—
253#2298C2212yes—
254#2295C2211yescharacteristic
255#2295C2212yes—
256#2295C2211yescharacteristic
257#2293C2212yes—
258C42×Q8C2211yescharacteristic
259C23×Q8C2312yes—
260#557—44no—
261#557—44no—
262#554—44no—
263#552—48no—
264D4×Q8—44no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2312yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#124C2311yescharacteristic
286C2×#124C2311yescharacteristic
287C2×#123C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2314yes—
320C22×C4⋊C4C2312yes—
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2312yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2312yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2312yes—
417#396C2314yes—
418#396C2312yes—
419#396C2312yes—
420#396C2312yes—
421#396C2314yes—
422#396C2314yes—
423#395C2314yes—
424#395C2312yes—
425#395C2312yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#394C2312yes—
433#394C2314yes—
434#394C2312yes—
435#394C2314yes—
436#394C2314yes—
437#394C2312yes—
438#394C2314yes—
439#394C2314yes—
440#394C2312yes—
441#394C2312yes—
442#394C2312yes—
443#394C2312yes—
444#394C2312yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2312yes—
449#393C2312yes—
450#393C2314yes—
451#393C2314yes—
452#392C2312yes—
453#392C2312yes—
454#391C2311yescharacteristic
455#391C2311yescharacteristic
456#391C2311yescharacteristic
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2314yes—
466#391C2311yescharacteristic
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2314yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2312yes—
484#391C2314yes—
485#391C2312yes—
486#391C2314yes—
487#391C2314yes—
488#390C2311yescharacteristic
489#390C2311yescharacteristic
490#390C2312yes—
491#390C2312yes—
492#390C2314yes—
493#390C2312yes—
494#390C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2312yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2312yes—
567#388C2312yes—
568#388C2312yes—
569#388C2312yes—
570#388C2312yes—
571#388C2312yes—
572#388C2312yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2312yes—
577#388C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2314yes—
607#387C2312yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2312yes—
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#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2312yes—
635#387C2312yes—
636#387C2312yes—
637#387C2312yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#384C2311yescharacteristic
651#384C2312yes—
652#384C2312yes—
653#384C2312yes—
654#384C2312yes—
655#384C2312yes—
656#384C2312yes—
657#384C2314yes—
658#383C2314yes—
659#383C2314yes—
660#383C2314yes—
661#383C2314yes—
662#382C2312yes—
663#382C2312yes—
664#382C2312yes—
665#382C2312yes—
666#382C2312yes—
667#382C2311yescharacteristic
668#382C2312yes—
669#382C2314yes—
670#382C2314yes—
671#382C2314yes—
672#382C2311yescharacteristic
673#381C2314yes—
674#381C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2314yes—
681#380C2312yes—
682#380C2314yes—
683#380C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2312yes—
710#376C2312yes—
711#376C2312yes—
712#376C2314yes—
713C43C2311yescharacteristic
714C43C2312yes—
715C43C2311yescharacteristic
716C43C2311yescharacteristic
717C22×Q8—44no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2414yes—
728C22×Q8C2411yescharacteristic
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C4⋊Q8—24no—
738C4⋊Q8—28no—
739C4⋊Q8—44no—
740C4⋊Q8—42no—
741C4⋊Q8—44no—
742C4⋊Q8—42no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745C4⋊Q8—42no—
746C4⋊Q8—42no—
747C4⋊Q8—42no—
748C4⋊Q8—42no—
749#126—48no—
750#125—28no—
751#125—44no—
752#125—44no—
753#125—44no—
754#125—44no—
755#125—48no—
756#125—48no—
757#124—24no—
758#124—24no—
759#123—48no—
760C22⋊Q8—28no—
761C22⋊Q8—48no—
762C22⋊Q8—48no—
763C22⋊Q8—44no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766C22⋊Q8—44no—
767C22⋊Q8—44no—
768C22⋊Q8—44no—
769C22⋊Q8—44no—
770C4×Q8—24no—
771C4×Q8—24no—
772C4×Q8—24no—
773C4×Q8—44no—
774C4×Q8—42no—
775C4×Q8—42no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×D4—44no—
782C4×D4—44no—
783C4×D4—42no—
784C4×D4—44no—
785C4×D4—44no—
786C4×D4—42no—
787#117—44no—
788#117—44no—
789#117—44no—
790#117—44no—
791#117—48no—
792C2×C4⋊C4—28no—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2411yescharacteristic
922C2×C42C2414yes—
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2412yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
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—
1004#95C2414yes—
1005C24C2512yes—
1006C24C2512yes—
1007C2×Q8—22no—
1008C2×Q8—22no—
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—41no—
1020C2×Q8—41no—
1021C2×Q8—42no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—42no—
1026C2×Q8—41no—
1027C2×Q8—42no—
1028C2×Q8—44no—
1029C2×Q8—816no—
1030C2×Q82−1+414yes—
1031C2×D4—22no—
1032C2×D4—22no—
1033C2×D4—41no—
1034C2×D4—41no—
1035C2×D4—41no—
1036C2×D4—41no—
1037C2×D4—42no—
1038C2×D4—42no—
1039C2×D4—42no—
1040C2×D4—42no—
1041C2×D4—42no—
1042C2×D4—42no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—28no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—41no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—41no—
1127C4⋊C4—44no—
1128C4⋊C4—41no—
1129C4⋊C4—41no—
1130C4⋊C4—41no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4H(5,𝔽2)14yes—
1153C22⋊C4—28no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—42no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—42no—
1168C22⋊C4—42no—
1169C22⋊C4—44no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—42no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C42—24no—
1190C42—24no—
1191C42—22no—
1192C42—22no—
1193C42—24no—
1194C42—24no—
1195C42—22no—
1196C42—22no—
1197C42—22no—
1198C42—22no—
1199C42—24no—
1200C42—24no—
1201C42—24no—
1202C42—24no—
1203C42—41no—
1204C42—42no—
1205C42—42no—
1206C42—41no—
1207C42—44no—
1208C42—41no—
1209C42—44no—
1210C42—42no—
1211C42—42no—
1212C42—42no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—22no—
1233C23C2611yescharacteristic
1234Q8—44no—
1235Q8—44no—
1236Q8—44no—
1237Q8—48no—
1238Q8—44no—
1239Q8—82no—
1240Q8—84no—
1241Q8—88no—
1242Q8—162no—
1243D4—44no—
1244D4—44no—
1245D4—84no—
1246D4—84no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—24no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—48no—
1315C2×C4—48no—
1316C2×C4—88no—
1317C2×C4—88no—
1318C2×C4C2×H(5,𝔽2)14yes—
1319C2×C4C2×H(5,𝔽2)12yes—
1320C2×C4C2×2−1+412yes—
1321C2×C4C2×2−1+412yes—
1322C2×C4C2×2−1+412yes—
1323C2×C4#58514yes—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22C22×H(5,𝔽2)11yescharacteristic
1339C22C22×2−1+411yescharacteristic
1340C22C2×#58512yes—
1341C222−1+612yes—
1342C222−1+611yescharacteristic
1343C4—24no—
1344C4—22no—
1345C4—22no—
1346C4—22no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—44no—
1351C4—42no—
1352C4—42no—
1353C4—41no—
1354C4—41no—
1355C4—44no—
1356C4—42no—
1357C4—41no—
1358C4—42no—
1359C4—42no—
1360C4—44no—
1361C4—44no—
1362C4—42no—
1363C4—42no—
1364C4—44no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—44no—
1369C4#355114yes—
1370C2—82no—
1371C2—82no—
1372C2C2×#355111yescharacteristic
1373C2#6289012yes—
1374C2#6289311yescharacteristic
1375C2#6295312yes—
1376C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2733C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59951C2semidirect
2. #58506C2semidirect
3. #58492C2semidirect
4. #57557C2semidirect
5. #57330C2semidirect
6. #57113C2semidirect
7. #53326C2semidirect
8. #53136C2semidirect
10. #52081C2semidirect
11. #51999C2semidirect
12. #46331C2semidirect
13. #46196C2semidirect
14. #46196C2semidirect
15. #45416C2semidirect
16. #45300C2semidirect
17. #42851C2semidirect
18. #42714C2semidirect
19. #42675C2semidirect
20. #39616C2semidirect
21. #39170C2semidirect
22. #38267C2semidirect
23. #38251C2semidirect
24. #38215C2semidirect
25. #37400C2semidirect
26. #37395C2semidirect
28. #36562C2semidirect
29. #35204C2semidirect

Maximal subgroups

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

subgroupindex
#599512
#585062
#584922
#575572
#573302
#571132
#533262
#531362
#522702
#520812
#519992
#463312
#461962
#454162
#453002
#428512
#427142
#426752
#396162
#391702
#382672
#382512
#382152
#374002
#373952
#372272
#365622
#352042