Finite Group Databasebeta

← #8115464

Subgroups — #8115464

Order 512.

3999 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58870C214yesmaximal, complemented
2#58838C214yesmaximal, complemented
3#57259C214yesmaximal, complemented
4#57030C214yesmaximal
5#56891C214yesmaximal, complemented
6#56827C214yesmaximal, complemented
7#55649C214yesmaximal, complemented
8#54223C214yesmaximal, complemented
9#53070C212yesmaximal, complemented
10#53010C212yesmaximal, complemented
11#45347C211yesmaximal, characteristic, complemented
12#45338C211yesmaximal, characteristic, complemented
13#45306C211yesmaximal, characteristic, complemented
14#45143C211yesmaximal, characteristic, complemented
15#42879C211yesmaximal, characteristic, complemented
16#42878C211yesmaximal, characteristic
17#42793C211yesmaximal, characteristic, complemented
18#42790C211yesmaximal, characteristic
19#42763C212yesmaximal, complemented
20#42747C212yesmaximal, complemented
21#39629C211yesmaximal, characteristic, complemented
22#39619C211yesmaximal, characteristic, complemented
23#39501C211yesmaximal, characteristic, complemented
24#39490C211yesmaximal, characteristic, complemented
25#37955C212yesmaximal, complemented
26#37947C212yesmaximal, complemented
27#37429C212yesmaximal, complemented
28#37395C212yesmaximal, complemented
29#35344C211yesmaximal, characteristic, complemented
30#35319C211yesmaximal, characteristic, complemented
31#34640C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#554C2211yescharacteristic
36C2×#541C2211yescharacteristic
37C2×#541C2211yescharacteristic
38#2868C2211yescharacteristic
39#2864C2212yes—
40#2862C2211yescharacteristic
41#2862C2211yescharacteristic
42#2859C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2841C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2839C2214yes—
49#2837C2214yes—
50#2836C2214yes—
51#2832C2214yes—
52#2831C2214yes—
53#2831C2214yes—
54#2831C2214yes—
55#2822C2212yes—
56#2821C2212yes—
57#2821C2212yes—
58#2820C2212yes—
59#2809C2214yes—
60#2808C2214yes—
61#2806C2214yes—
62#2806C2214yes—
63#2805C2214yes—
64#2805C2214yes—
65#2802C2214yes—
66#2799C2214yes—
67#2798C2214yes—
68#2793C2214yes—
69#2793C2214yes—
70#2793C2214yes—
71#2793C2214yes—
72#2793C2214yes—
73#2791C2214yes—
74#2791C2214yes—
75#2791C2214yes—
76#2791C2214yes—
77#2791C2214yes—
78#2790C2214yes—
79#2788C2214yes—
80#2776C2214yes—
81#2775C2214yes—
82#2770C2214yes—
83#2769C2214yes—
84#2768C2214yes—
85#2767C2214yes—
86#2767C2214yes—
87#2766C2214yes—
88#2764C2214yes—
89#2762C2214yes—
90#2758C2214yes—
91#2758C2214yes—
92#2755C2214yes—
93#2755C2214yes—
94#2755C2214yes—
95#2754C2214yes—
96#2754C2214yes—
97#2754C2214yes—
98#2751C2214yes—
99#2746C2214yes—
100#2744C2214yes—
101#2744C2214yes—
102#2742C2214yes—
103#2740C2214yes—
104#2739C2214yes—
105#2739C2214yes—
106#2737C2214yes—
107#2731C2214yes—
108#2729C2214yes—
109#2727C2214yes—
110#2725C2214yes—
111#2721C2214yes—
112#2719C2214yes—
113#2719C2214yes—
114#2716C2214yes—
115#2716C2214yes—
116#2713C2214yes—
117#2713C2214yes—
118#2713C2214yes—
119#2704C2214yes—
120#2702C2214yes—
121#2689C2214yes—
122#2689C2214yes—
123#2665C2214yes—
124#2664C2212yes—
125#2662C2212yes—
126#2660C2212yes—
127#2660C2212yes—
128#2655C2214yes—
129#2655C2212yes—
130#2654C2214yes—
131#2654C2212yes—
132#2653C2212yes—
133#2652C2212yes—
134#2651C2212yes—
135#2650C2212yes—
136#2649C2212yes—
137#2648C2212yes—
138#2647C2212yes—
139#2645C2214yes—
140#2642C2211yescharacteristic
141#2642C2212yes—
142#2642C2211yescharacteristic
143#2637C2212yes—
144#2636C2212yes—
145#2634C2212yes—
146#2634C2212yes—
147#2628C2212yes—
148#2628C2211yescharacteristic
149#2628C2211yescharacteristic
150#2621C2211yescharacteristic
151#2621C2212yes—
152#2621C2212yes—
153#2621C2211yescharacteristic
154#2612C2214yes—
155#2612C2214yes—
156#2607C2214yes—
157#2607C2214yes—
158#2606C2214yes—
159#2605C2214yes—
160#2605C2214yes—
161#2604C2212yes—
162#2604C2212yes—
163#2584C2212yes—
164#2581C2211yescharacteristic
165#2581C2211yescharacteristic
166#2578C2214yes—
167#2574C2214yes—
168#2571C2212yes—
169#2570C2212yes—
170#2568C2211yescharacteristic
171#2568C2211yescharacteristic
172#2568C2212yes—
173#2567C2211yescharacteristic
174#2567C2211yescharacteristic
175#2565C2212yes—
176#2562C2212yes—
177#2552C2212yes—
178#2550C2212yes—
179#2538C2212yes—
180#2536C2211yescharacteristic
181#2536C2212yes—
182#2536C2211yescharacteristic
183#2533C2214yes—
184#2533C2214yes—
185#2532C2214yes—
186#2532C2214yes—
187#2531C2214yes—
188#2530C2214yes—
189#2529C2214yes—
190#2527C2214yes—
191#2522C2214yes—
192#2520C2214yes—
193#2520C2214yes—
194#2520C2214yes—
195#2514C2212yes—
196#2511C2212yes—
197#2511C2214yes—
198#2506C2214yes—
199#2506C2214yes—
200#2503C2212yes—
201#2499C2212yes—
202#2496C2214yes—
203#2496C2214yes—
204#2492C2212yes—
205#2492C2212yes—
206#2492C2212yes—
207#2492C2212yes—
208#2489C2212yes—
209#2489C2212yes—
210#2469C2214yes—
211#2460C2214yes—
212#2453C2214yes—
213#2451C2212yes—
214#2451C2212yes—
215#2451C2214yes—
216#2447C2214yes—
217#2446C2212yes—
218#2446C2212yes—
219#2446C2212yes—
220#2446C2212yes—
221#2446C2214yes—
222#2446C2214yes—
223#2442C2212yes—
224#2442C2212yes—
225#2441C2212yes—
226#2439C2212yes—
227#2429C2212yes—
228#2429C2212yes—
229#2429C2212yes—
230#2429C2212yes—
231#2423C2212yes—
232#2421C2212yes—
233#2421C2214yes—
234#2417C2212yes—
235#2415C2212yes—
236#2402C2211yescharacteristic
237#2401C2212yes—
238#2398C2211yescharacteristic
239#2396C2211yescharacteristic
240#2395C2212yes—
241#2392C2211yescharacteristic
242#2362C2212yes—
243#2360C2212yes—
244#2356C2211yescharacteristic
245#2356C2211yescharacteristic
246#2356C2212yes—
247#2355C2212yes—
248#2351C2211yescharacteristic
249#2351C2211yescharacteristic
250#2331C2212yes—
251#2331C2211yescharacteristic
252#2331C2211yescharacteristic
253#2327C2212yes—
254#2327C2212yes—
255#2327C2211yescharacteristic
256#2327C2211yescharacteristic
257#2317C2212yes—
258#2314C2212yes—
259C4×C4⋊Q8C2211yescharacteristic
260C4×C4⋊Q8C2211yescharacteristic
261#2298C2212yes—
262#2295C2211yescharacteristic
263#2293C2211yescharacteristic
264#2290C2212yes—
265#2283C2212yes—
266C4×#117C2211yescharacteristic
267Q82—44no—
268#557—44no—
269#556—44no—
270#554—44no—
271#541—44no—
272#541—44no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2311yescharacteristic
285C2×C4⋊Q8C2314yes—
286C2×#126C2312yes—
287C2×#126C2312yes—
288C2×#126C2312yes—
289C2×#126C2312yes—
290C2×#126C2314yes—
291C2×#125C2312yes—
292C2×#125C2312yes—
293C2×#125C2312yes—
294C2×#125C2312yes—
295C2×#125C2311yescharacteristic
296C2×#125C2311yescharacteristic
297C2×#125C2312yes—
298C2×#125C2312yes—
299C2×#125C2314yes—
300C2×#124C2312yes—
301C2×C22⋊Q8C2311yescharacteristic
302C2×C22⋊Q8C2311yescharacteristic
303C2×C22⋊Q8C2311yescharacteristic
304C2×C22⋊Q8C2311yescharacteristic
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×#117C2312yes—
326C2×#117C2311yescharacteristic
327C2×#117C2312yes—
328C2×#117C2311yescharacteristic
329C22×C4⋊C4C2312yes—
330C22×C42C2311yescharacteristic
331#401C2312yes—
332#401C2314yes—
333#400C2312yes—
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2312yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2312yes—
368#400C2311yescharacteristic
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2312yes—
373#400C2312yes—
374#400C2312yes—
375#400C2312yes—
376#400C2312yes—
377#400C2314yes—
378#400C2314yes—
379#399C2314yes—
380#399C2311yescharacteristic
381#399C2314yes—
382#399C2312yes—
383#399C2314yes—
384#399C2312yes—
385#399C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2311yescharacteristic
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2312yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2312yes—
414#398C2314yes—
415#398C2314yes—
416#398C2312yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2312yes—
421#398C2312yes—
422#398C2314yes—
423#398C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2312yes—
428#397C2312yes—
429#397C2312yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2312yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2311yescharacteristic
441#397C2312yes—
442#397C2312yes—
443#397C2312yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2312yes—
454#396C2312yes—
455#396C2312yes—
456#395C2312yes—
457#395C2312yes—
458#395C2312yes—
459#395C2312yes—
460#395C2314yes—
461#395C2312yes—
462#395C2312yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#395C2312yes—
468#395C2312yes—
469#395C2314yes—
470#395C2311yescharacteristic
471#394C2311yescharacteristic
472#394C2312yes—
473#394C2312yes—
474#394C2312yes—
475#394C2314yes—
476#394C2314yes—
477#394C2312yes—
478#394C2312yes—
479#394C2312yes—
480#393C2311yescharacteristic
481#393C2314yes—
482#393C2312yes—
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2312yes—
488#393C2312yes—
489#393C2314yes—
490#392C2311yescharacteristic
491#391C2311yescharacteristic
492#391C2311yescharacteristic
493#391C2311yescharacteristic
494#391C2311yescharacteristic
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2312yes—
500#391C2314yes—
501#391C2314yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2312yes—
508#391C2312yes—
509#391C2311yescharacteristic
510#391C2311yescharacteristic
511#391C2311yescharacteristic
512#391C2311yescharacteristic
513#391C2314yes—
514#391C2314yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2314yes—
519#391C2314yes—
520#391C2312yes—
521#391C2312yes—
522#391C2314yes—
523#391C2314yes—
524#391C2314yes—
525#391C2314yes—
526#391C2312yes—
527#391C2314yes—
528#390C2312yes—
529#390C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2312yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#389C2314yes—
562#389C2314yes—
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#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2312yes—
582#388C2312yes—
583#388C2312yes—
584#388C2312yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
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#387C2312yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2312yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2312yes—
645#387C2312yes—
646#387C2312yes—
647#387C2312yes—
648#387C2312yes—
649#387C2312yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#386C2312yes—
656#386C2314yes—
657#386C2312yes—
658#385C2314yes—
659#385C2314yes—
660#385C2312yes—
661#385C2314yes—
662#385C2314yes—
663#385C2312yes—
664#385C2314yes—
665#384C2311yescharacteristic
666#384C2311yescharacteristic
667#384C2312yes—
668#384C2312yes—
669#384C2314yes—
670#384C2314yes—
671#384C2314yes—
672#383C2312yes—
673#383C2312yes—
674#383C2314yes—
675#383C2314yes—
676#383C2314yes—
677#382C2312yes—
678#382C2312yes—
679#382C2312yes—
680#382C2312yes—
681#382C2312yes—
682#382C2312yes—
683#382C2311yescharacteristic
684#382C2311yescharacteristic
685#382C2314yes—
686#382C2312yes—
687#382C2314yes—
688#382C2311yescharacteristic
689#382C2311yescharacteristic
690#382C2314yes—
691#382C2314yes—
692#381C2314yes—
693#381C2314yes—
694#381C2314yes—
695#380C2314yes—
696#380C2314yes—
697#380C2312yes—
698#380C2312yes—
699#380C2314yes—
700#380C2314yes—
701#380C2314yes—
702#380C2312yes—
703#380C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2314yes—
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731#376C2311yescharacteristic
732#376C2312yes—
733#376C2311yescharacteristic
734#376C2312yes—
735#376C2312yes—
736#376C2314yes—
737#376C2314yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C22×Q8C2411yescharacteristic
741C22×Q8C2411yescharacteristic
742C22×Q8C2411yescharacteristic
743C22×Q8C2411yescharacteristic
744C22×Q8C2411yescharacteristic
745C22×Q8C2412yes—
746C22×Q8C2412yes—
747C22×Q8C2414yes—
748C22×Q8C2414yes—
749C22×D4C2411yescharacteristic
750C22×D4C2412yes—
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2412yes—
754C23×C4C2414yes—
755C4⋊Q8—24no—
756C4⋊Q8—24no—
757C4⋊Q8—24no—
758C4⋊Q8—24no—
759C4⋊Q8—44no—
760C4⋊Q8—44no—
761C4⋊Q8—44no—
762C4⋊Q8—42no—
763C4⋊Q8—42no—
764C4⋊Q8—42no—
765C4⋊Q8—42no—
766C4⋊Q8—44no—
767C4⋊Q8—48no—
768#126—44no—
769#126—44no—
770#126—44no—
771#126—44no—
772#126—48no—
773#125—42no—
774#125—42no—
775#125—44no—
776#125—44no—
777#125—44no—
778#125—44no—
779#125—44no—
780#125—44no—
781#125—48no—
782#124—44no—
783C22⋊Q8—48no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—42no—
787C22⋊Q8—42no—
788C22⋊Q8—42no—
789C22⋊Q8—42no—
790C22⋊Q8—44no—
791C22⋊Q8—44no—
792C4×Q8—24no—
793C4×Q8—24no—
794C4×Q8—24no—
795C4×Q8—24no—
796C4×Q8—24no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×Q8—44no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×D4—24no—
805C4×D4—44no—
806C4×D4—44no—
807#117—24no—
808#117—28no—
809#117—42no—
810#117—44no—
811C2×C4⋊C4—44no—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C42—24no—
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947#95C2411yescharacteristic
948#95C2411yescharacteristic
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2411yescharacteristic
984#95C2411yescharacteristic
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
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—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033C24C2511yescharacteristic
1034C24C2512yes—
1035C2×Q8—22no—
1036C2×Q8—22no—
1037C2×Q8—22no—
1038C2×Q8—22no—
1039C2×Q8—22no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—22no—
1043C2×Q8—22no—
1044C2×Q8—22no—
1045C2×Q8—22no—
1046C2×Q8—22no—
1047C2×Q8—22no—
1048C2×Q8—22no—
1049C2×Q8—22no—
1050C2×Q8—42no—
1051C2×Q8—44no—
1052C2×Q8—44no—
1053C2×Q8—44no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—44no—
1057C2×Q8—44no—
1058C2×Q8—44no—
1059C2×D4—22no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C22×C4—24no—
1065C22×C4—22no—
1066C22×C4—22no—
1067C22×C4—24no—
1068C22×C4—22no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2512yes—
1104C22×C4C2511yescharacteristic
1105C4⋊C4—22no—
1106C4⋊C4—24no—
1107C4⋊C4—22no—
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—24no—
1111C4⋊C4—22no—
1112C4⋊C4—24no—
1113C4⋊C4—22no—
1114C4⋊C4—24no—
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C22⋊C4—22no—
1182C22⋊C4—22no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C42—22no—
1213C42—24no—
1214C42—24no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—22no—
1220C42—24no—
1221C42—22no—
1222C42—22no—
1223C42—24no—
1224C42—42no—
1225C42—42no—
1226C42—42no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42H(5,𝔽2)14yes—
1238C422−1+414yes—
1239C23—21no—
1240C23—22no—
1241C23—22no—
1242C23—21no—
1243C23—22no—
1244C23—21no—
1245C23—22no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23C2611yescharacteristic
1252Q8—44no—
1253Q8—44no—
1254Q8—44no—
1255Q8—44no—
1256Q8—44no—
1257Q8—84no—
1258Q8—84no—
1259Q8—164no—
1260Q8—164no—
1261D4—44no—
1262D4—84no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—22no—
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—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—48no—
1337C2×C4—44no—
1338C2×C4—84no—
1339C2×C4—164no—
1340C2×C4C2×H(5,𝔽2)12yes—
1341C2×C4C2×H(5,𝔽2)12yes—
1342C2×C4C2×H(5,𝔽2)12yes—
1343C2×C4C2×2−1+414yes—
1344C2×C4C2×2−1+412yes—
1345C2×C4#58512yes—
1346C22—41no—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22—41no—
1351C22—41no—
1352C22—42no—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22C22×H(5,𝔽2)11yescharacteristic
1359C22C22×2−1+411yescharacteristic
1360C22C2×#58511yescharacteristic
1361C222−1+612yes—
1362C222−1+612yes—
1363C4—22no—
1364C4—22no—
1365C4—24no—
1366C4—42no—
1367C4—41no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—41no—
1374C4—41no—
1375C4—42no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4—44no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—44no—
1389C4—44no—
1390C4—42no—
1391C4#354714yes—
1392C2—82no—
1393C2—81no—
1394C2C2×#354711yescharacteristic
1395C2#6288711yescharacteristic
1396C2#6288711yescharacteristic
1397C2#6288912yes—
1398C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58870C2semidirect
2. #58838C2semidirect
3. #57259C2semidirect
5. #56891C2semidirect
6. #56827C2semidirect
7. #55649C2semidirect
8. #54223C2semidirect
9. #53070C2semidirect
10. #53010C2semidirect
11. #45347C2semidirect
12. #45338C2semidirect
13. #45306C2semidirect
14. #45143C2semidirect
15. #42879C2semidirect
17. #42793C2semidirect
19. #42763C2semidirect
20. #42747C2semidirect
21. #39629C2semidirect
22. #39619C2semidirect
23. #39501C2semidirect
24. #39490C2semidirect
25. #37955C2semidirect
26. #37947C2semidirect
27. #37429C2semidirect
28. #37395C2semidirect
29. #35344C2semidirect
30. #35319C2semidirect

Maximal subgroups

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

subgroupindex
#588702
#588382
#572592
#570302
#568912
#568272
#556492
#542232
#530702
#530102
#453472
#453382
#453062
#451432
#428792
#428782
#427932
#427902
#427632
#427472
#396292
#396192
#395012
#394902
#379552
#379472
#374292
#373952
#353442
#353192
#346402