Finite Group Databasebeta

← #8115404

Subgroups — #8115404

Order 512.

4077 conjugacy classes of subgroups.

The subgroup lattice has 1431 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58962C212yesmaximal, complemented
2#58888C212yesmaximal, complemented
3#58783C212yesmaximal, complemented
4#58767C212yesmaximal, complemented
5#57594C212yesmaximal
6#56659C212yesmaximal
7#56636C214yesmaximal, complemented
8#55610C212yesmaximal, complemented
9#54715C214yesmaximal, complemented
10#54641C214yesmaximal, complemented
11#53975C212yesmaximal, complemented
12#53916C214yesmaximal
13#53140C212yesmaximal, complemented
14#53139C212yesmaximal, complemented
15#45415C212yesmaximal, complemented
16#45390C212yesmaximal, complemented
17#42981C211yesmaximal, characteristic, complemented
18#42941C211yesmaximal, characteristic, complemented
19#42832C212yesmaximal, complemented
20#42817C211yesmaximal, characteristic, complemented
21#42779C212yesmaximal, complemented
22#42695C211yesmaximal, characteristic, complemented
23#37985C212yesmaximal, complemented
24#37859C212yesmaximal
25#37793C212yesmaximal, complemented
26#37663C212yesmaximal
27#37383C212yesmaximal, complemented
28#37377C212yesmaximal, complemented
29#35325C211yesmaximal, characteristic
30#35311C211yesmaximal, characteristic
31#34634C211yesmaximal, characteristic
32C2×#541C2212yes—
33C2×#533C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C22×#117C2211yescharacteristic
37#2855C2212yes—
38#2855C2212yes—
39#2855C2212yes—
40#2848C2212yes—
41#2844C2212yescomplemented
42#2841C2212yes—
43#2839C2214yescomplemented
44#2839C2214yescomplemented
45#2839C2214yescomplemented
46#2838C2214yes—
47#2836C2214yes—
48#2834C2212yes—
49#2833C2212yescomplemented
50#2833C2214yescomplemented
51#2833C2214yescomplemented
52#2831C2214yes—
53#2831C2214yes—
54#2831C2214yes—
55#2811C2212yescomplemented
56#2807C2212yes—
57#2806C2214yescomplemented
58#2805C2214yescomplemented
59#2799C2212yescomplemented
60#2799C2214yescomplemented
61#2798C2214yes—
62#2794C2214yescomplemented
63#2792C2214yescomplemented
64#2792C2214yescomplemented
65#2791C2214yescomplemented
66#2789C2214yescomplemented
67#2789C2212yescomplemented
68#2788C2214yes—
69#2788C2214yes—
70#2783C2214yes—
71#2783C2214yes—
72#2777C2214yes—
73#2777C2214yes—
74#2776C2214yescomplemented
75#2774C2214yescomplemented
76#2772C2214yes—
77#2771C2214yes—
78#2771C2212yes—
79#2769C2214yescomplemented
80#2769C2212yescomplemented
81#2769C2214yescomplemented
82#2767C2214yescomplemented
83#2766C2214yescomplemented
84#2765C2214yes—
85#2764C2214yes—
86#2764C2212yes—
87#2763C2214yes—
88#2762C2214yescomplemented
89#2759C2214yes—
90#2759C2214yes—
91#2758C2214yescomplemented
92#2755C2214yescomplemented
93#2755C2214yescomplemented
94#2755C2214yescomplemented
95#2755C2214yescomplemented
96#2745C2214yes—
97#2745C2214yes—
98#2745C2214yes—
99#2744C2214yes—
100#2742C2212yes—
101#2739C2214yes—
102#2738C2214yes—
103#2738C2214yes—
104#2738C2214yes—
105#2736C2214yes—
106#2735C2214yes—
107#2726C2214yescomplemented
108#2719C2214yescomplemented
109#2719C2214yescomplemented
110#2719C2214yescomplemented
111#2713C2214yescomplemented
112#2713C2214yescomplemented
113#2704C2214yes—
114#2698C2214yes—
115#2698C2214yes—
116#2698C2214yes—
117#2698C2214yes—
118#2690C2214yes—
119#2689C2214yes—
120#2689C2214yes—
121#2689C2214yes—
122#2689C2214yes—
123#2666C2214yescomplemented
124#2666C2214yescomplemented
125#2665C2214yes—
126#2654C2214yes—
127#2652C2214yes—
128#2650C2214yes—
129#2647C2214yescomplemented
130#2645C2214yescomplemented
131#2629C2212yes—
132#2629C2212yes—
133#2628C2212yes—
134#2628C2211yescharacteristic
135#2628C2211yescharacteristic
136#2628C2211yescharacteristic
137#2628C2211yescharacteristic
138#2628C2211yescharacteristic
139#2628C2211yescharacteristic
140#2627C2211yescharacteristic
141#2627C2212yes—
142#2627C2211yescharacteristic
143#2626C2211yescharacteristic
144#2626C2212yes—
145#2626C2211yescharacteristic
146#2625C2212yes—
147#2625C2212yes—
148#2625C2212yes—
149#2625C2212yes—
150#2621C2212yes—
151#2621C2211yescharacteristic
152#2621C2211yescharacteristic
153#2612C2212yescomplemented
154#2612C2214yescomplemented
155#2612C2214yescomplemented
156#2611C2212yes—
157#2611C2212yes—
158#2607C2212yes—
159#2605C2214yescomplemented
160#2599C2212yes—
161#2599C2212yes—
162#2590C2214yescomplemented
163#2587C2214yes—
164#2586C2212yescomplemented
165#2584C2212yescomplemented
166#2584C2212yescomplemented
167#2583C2212yes—
168#2582C2212yescomplemented
169#2582C2212yescomplemented
170#2581C2212yescomplemented
171#2581C2212yescomplemented
172#2575C2214yes—
173#2575C2214yes—
174#2574C2214yes—
175#2573C2214yes—
176#2570C2212yescomplemented
177#2568C2212yescomplemented
178#2568C2212yescomplemented
179#2568C2212yescomplemented
180#2561C2212yes—
181#2550C2212yescomplemented
182#2546C2212yescomplemented
183#2533C2214yescomplemented
184#2530C2214yes—
185#2529C2214yes—
186#2527C2214yes—
187#2527C2214yes—
188#2527C2214yes—
189#2523C2212yes—
190#2522C2214yes—
191#2514C2212yescomplemented
192#2514C2212yescomplemented
193#2514C2212yescomplemented
194#2511C2214yescomplemented
195#2511C2212yescomplemented
196#2509C2212yescomplemented
197#2509C2212yescomplemented
198#2509C2212yescomplemented
199#2508C2214yescomplemented
200#2508C2212yescomplemented
201#2503C2212yes—
202#2502C2212yes—
203#2499C2212yes—
204#2499C2212yes—
205#2499C2212yes—
206#2497C2212yes—
207#2494C2212yes—
208#2492C2212yes—
209#2489C2212yes—
210#2484C2212yes—
211#2484C2212yes—
212#2484C2212yes—
213#2483C2212yes—
214#2483C2212yes—
215#2482C2212yes—
216#2480C2214yes—
217#2480C2214yes—
218#2478C2214yes—
219#2478C2214yes—
220#2473C2214yes—
221#2462C2214yescomplemented
222#2453C2214yescomplemented
223#2453C2212yescomplemented
224#2451C2212yescomplemented
225#2451C2212yescomplemented
226#2451C2212yescomplemented
227#2446C2212yescomplemented
228#2446C2212yescomplemented
229#2446C2212yescomplemented
230#2446C2212yescomplemented
231#2442C2212yes—
232#2442C2214yes—
233#2439C2212yes—
234#2434C2212yes—
235#2429C2212yes—
236#2429C2212yes—
237#2421C2212yes—
238#2421C2212yes—
239#2396C2211yescharacteristic
240#2396C2211yescharacteristic
241#2396C2212yes—
242#2396C2211yescharacteristic
243#2396C2212yes—
244#2396C2211yescharacteristic
245#2369C2212yescomplemented
246#2365C2212yescomplemented
247#2362C2212yes—
248#2360C2212yes—
249#2356C2212yescomplemented
250#2351C2212yescomplemented
251#2346C2212yes—
252Q8×C22⋊C4C2212yes—
253#2323C2212yes—
254#2323C2212yes—
255#2323C2212yes—
256#2323C2212yes—
257#2317C2211yescharacteristic
258#2317C2211yescharacteristic
259#2314C2212yes—
260#2310C2211yescharacteristic
261#2310C2211yescharacteristic
262#2296C2212yes—
263#2285C2211yescharacteristic
264#2283C2211yescharacteristic
265#2280C2212yes—
266#2280C2211yescharacteristic
267C23×Q8C2311yescharacteristic
268C24×C4C2311yescharacteristic
269#541—48no—
270#533—44no—
271#533—44no—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×C22⋊Q8—44no—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×#117—44no—
308C2×#117C2311yescharacteristic
309C2×#117C2312yes—
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2311yescharacteristic
313C2×#117C2312yes—
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2311yescharacteristic
317C2×#117C2311yescharacteristic
318C2×#117C2311yescharacteristic
319C2×#117C2311yescharacteristic
320C2×#117C2312yes—
321C22×C4⋊C4C2311yescharacteristic
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2311yescharacteristic
324C22×C4⋊C4C2312yes—
325C22×C22⋊C4C2311yescharacteristic
326C22×C22⋊C4C2311yescharacteristic
327C22×C22⋊C4C2312yes—
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330#401C2314yes—
331#401C2314yes—
332#401C2314yes—
333#401C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2311yescharacteristic
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2311yescharacteristic
374#400C2312yes—
375#400C2311yescharacteristic
376#400C2311yescharacteristic
377#400C2314yes—
378#400C2314yes—
379#399C2314yes—
380#399C2311yescharacteristic
381#399C2312yes—
382#399C2312yes—
383#399C2312yes—
384#399C2311yescharacteristic
385#399C2312yes—
386#399C2311yescharacteristic
387#399C2311yescharacteristic
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2312yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2312yes—
407#398C2312yes—
408#398C2312yes—
409#398C2312yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2312yes—
418#398C2312yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2312yes—
424#398C2312yes—
425#398C2312yes—
426#398C2312yes—
427#398C2314yes—
428#397C2312yes—
429#397C2312yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2312yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2312yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#396C2312yes—
449#396C2314yes—
450#396C2312yes—
451#396C2312yes—
452#396C2314yes—
453#396C2314yes—
454#396C2312yes—
455#396C2314yes—
456#396C2312yes—
457#396C2312yes—
458#396C2312yes—
459#396C2312yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2312yes—
465#395C2312yes—
466#395C2314yes—
467#395C2314yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#395C2312yes—
472#395C2314yes—
473#395C2311yescharacteristic
474#395C2314yes—
475#395C2312yes—
476#395C2311yescharacteristic
477#395C2311yescharacteristic
478#395C2311yescharacteristic
479#393C2312yes—
480#393C2312yes—
481#393C2314yes—
482#393C2312yes—
483#393C2311yescharacteristic
484#393C2314yes—
485#393C2311yescharacteristic
486#393C2311yescharacteristic
487#393C2311yescharacteristic
488#393C2312yes—
489#393C2314yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2314yes—
500#391C2314yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2312yes—
513#391C2312yes—
514#391C2314yes—
515#391C2314yes—
516#391C2314yes—
517#391C2312yes—
518#391C2314yes—
519#391C2312yes—
520#391C2314yes—
521#391C2314yes—
522#391C2314yes—
523#391C2314yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2312yes—
554#389C2314yes—
555#389C2312yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
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#387C2314yes—
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#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#385C2312yes—
641#385C2312yes—
642#385C2312yes—
643#385C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2312yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2312yes—
655#385C2312yes—
656#385C2312yes—
657#385C2314yes—
658#384C2312yes—
659#384C2312yes—
660#384C2312yes—
661#384C2312yes—
662#383C2314yes—
663#383C2312yes—
664#383C2314yes—
665#383C2314yes—
666#383C2314yes—
667#382C2311yescharacteristic
668#382C2312yes—
669#382C2314yes—
670#382C2314yes—
671#382C2311yescharacteristic
672#382C2312yes—
673#382C2312yes—
674#382C2312yes—
675#382C2314yes—
676#382C2314yes—
677#382C2312yes—
678#382C2314yes—
679#382C2311yescharacteristic
680#382C2311yescharacteristic
681#382C2314yes—
682#381C2314yes—
683#381C2312yes—
684#381C2312yes—
685#381C2312yes—
686#381C2312yes—
687#381C2312yes—
688#381C2314yes—
689#381C2314yes—
690#381C2312yes—
691#381C2312yes—
692#381C2312yes—
693#380C2312yes—
694#380C2312yes—
695#380C2312yes—
696#380C2312yes—
697#380C2312yes—
698#380C2314yes—
699#380C2312yes—
700#380C2311yescharacteristic
701#380C2312yes—
702#380C2311yescharacteristic
703#380C2312yes—
704#380C2312yes—
705#380C2312yes—
706#380C2314yes—
707#379C2314yes—
708#379C2312yes—
709#379C2312yes—
710#379C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2314yes—
721C4×C4⋊C4C2312yes—
722C4×C4⋊C4C2312yes—
723C4×C4⋊C4C2311yescharacteristic
724C4×C4⋊C4C2312yes—
725C4×C4⋊C4C2311yescharacteristic
726C4×C4⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2314yes—
732C4×C22⋊C4C2312yes—
733C4×C22⋊C4C2312yes—
734C4×C22⋊C4C2312yes—
735C4×C22⋊C4C2312yes—
736#376C2314yes—
737#376C2312yes—
738#376C2314yes—
739C25C2411yescharacteristic
740C22×Q8—24no—
741C22×Q8—42no—
742C22×Q8—42no—
743C22×Q8C2412yes—
744C22×Q8C2412yes—
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2412yes—
748C22×Q8C2411yescharacteristic
749C22×Q8C2412yes—
750C22×Q8C2414yes—
751C23×C4—24no—
752C23×C4—24no—
753C23×C4—42no—
754C23×C4C2411yescharacteristic
755C23×C4C2411yescharacteristic
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C23×C4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C23×C4C2411yescharacteristic
761C23×C4C2411yescharacteristic
762C23×C4C2411yescharacteristic
763C23×C4C2411yescharacteristic
764C23×C4C2412yes—
765C23×C4C2412yes—
766C4⋊Q8—44no—
767C4⋊Q8—42no—
768C4⋊Q8—42no—
769C4⋊Q8—42no—
770C4⋊Q8—44no—
771C4⋊Q8—42no—
772C4⋊Q8—44no—
773#126—48no—
774#126—48no—
775#125—44no—
776#125—44no—
777#125—44no—
778#125—48no—
779#125—48no—
780C22⋊Q8—28no—
781C22⋊Q8—28no—
782C22⋊Q8—28no—
783C22⋊Q8—44no—
784C22⋊Q8—42no—
785C22⋊Q8—44no—
786C22⋊Q8—42no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789C22⋊Q8—44no—
790C22⋊Q8—44no—
791C4×Q8—42no—
792C4×Q8—44no—
793C4×Q8—42no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—44no—
800#117—28no—
801#117—24no—
802#117—42no—
803#117—42no—
804#117—42no—
805#117—42no—
806#117—42no—
807#117—42no—
808#117—42no—
809#117—42no—
810#117—44no—
811#117—44no—
812#117—42no—
813C2×C4⋊C4—42no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4—42no—
816C2×C4⋊C4—42no—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
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×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C22⋊C4—44no—
892C2×C22⋊C4—42no—
893C2×C22⋊C4—42no—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2411yescharacteristic
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2411yescharacteristic
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2411yescharacteristic
905C2×C22⋊C4C2411yescharacteristic
906C2×C22⋊C4C2411yescharacteristic
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C42—24no—
927C2×C42—24no—
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2411yescharacteristic
980#95C2412yes—
981#95C2411yescharacteristic
982#95C2411yescharacteristic
983#95C2412yes—
984#95C2411yescharacteristic
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
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—
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—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036C24—22no—
1037C24—22no—
1038C24—41no—
1039C24—42no—
1040C24—42no—
1041C24C2511yescharacteristic
1042C24C2511yescharacteristic
1043C24C2511yescharacteristic
1044C2×Q8—24no—
1045C2×Q8—24no—
1046C2×Q8—24no—
1047C2×Q8—24no—
1048C2×Q8—24no—
1049C2×Q8—24no—
1050C2×Q8—24no—
1051C2×Q8—41no—
1052C2×Q8—42no—
1053C2×Q8—41no—
1054C2×Q8—42no—
1055C2×Q8—42no—
1056C2×Q8—42no—
1057C2×Q8—42no—
1058C2×Q8—42no—
1059C2×Q8—44no—
1060C2×Q8—42no—
1061C2×Q8—42no—
1062C2×Q8—44no—
1063C2×Q8—44no—
1064C2×Q8—44no—
1065C2×Q8—88no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—22no—
1075C22×C4—22no—
1076C22×C4—24no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—22no—
1080C22×C4—22no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—22no—
1084C22×C4—41no—
1085C22×C4—41no—
1086C22×C4—41no—
1087C22×C4—42no—
1088C22×C4—416no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—44no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4H(5,𝔽2)14yes—
1097C22×C42−1+414yes—
1098C22×C4C2514yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2514yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2514yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2514yes—
1118C22×C4C2514yes—
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2514yes—
1123C22×C4C2511yescharacteristic
1124C22×C4C2511yescharacteristic
1125C22×C4C2511yescharacteristic
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—41no—
1138C4⋊C4—41no—
1139C4⋊C4—41no—
1140C4⋊C4—41no—
1141C4⋊C4—41no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
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—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—41no—
1187C4⋊C4—42no—
1188C4⋊C4—41no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C22⋊C4—28no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—28no—
1204C22⋊C4—24no—
1205C22⋊C4—28no—
1206C22⋊C4—41no—
1207C22⋊C4—41no—
1208C22⋊C4—41no—
1209C22⋊C4—41no—
1210C22⋊C4—41no—
1211C22⋊C4—41no—
1212C22⋊C4—41no—
1213C22⋊C4—41no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C42—22no—
1233C42—22no—
1234C42—22no—
1235C42—22no—
1236C42—22no—
1237C42—22no—
1238C42—22no—
1239C42—22no—
1240C42—24no—
1241C42—24no—
1242C42—24no—
1243C42—24no—
1244C42—24no—
1245C42—44no—
1246C42—44no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—42no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C23—21no—
1257C23—21no—
1258C23—21no—
1259C23—21no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—21no—
1265C23—21no—
1266C23—21no—
1267C23—22no—
1268C23—22no—
1269C23—44no—
1270C23—44no—
1271C23—82no—
1272C23—84no—
1273C23—84no—
1274C23C2×H(5,𝔽2)12yes—
1275C23C2×2−1+412yes—
1276C23C2611yescharacteristic
1277Q8—48no—
1278Q8—48no—
1279Q8—84no—
1280Q8—82no—
1281Q8—84no—
1282Q8—82no—
1283Q8—84no—
1284Q8—164no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—28no—
1290C2×C4—28no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—21no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—21no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—21no—
1322C2×C4—24no—
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—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—44no—
1359C2×C4—44no—
1360C2×C4—44no—
1361C2×C4—44no—
1362C2×C4—44no—
1363C2×C4—82no—
1364C2×C4—82no—
1365C2×C4—82no—
1366C2×C4—84no—
1367C2×C4—84no—
1368C2×C4C2×H(5,𝔽2)12yes—
1369C2×C4C2×H(5,𝔽2)12yes—
1370C2×C4C2×2−1+412yes—
1371C2×C4C2×2−1+412yes—
1372C2×C4#58512yes—
1373C22—22no—
1374C22—22no—
1375C22—22no—
1376C22—22no—
1377C22—24no—
1378C22—41no—
1379C22—41no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—41no—
1384C22—41no—
1385C22—41no—
1386C22—42no—
1387C22—42no—
1388C22—88no—
1389C22C22×H(5,𝔽2)11yescharacteristic
1390C22C22×2−1+411yescharacteristic
1391C22C2×#58511yescharacteristic
1392C222−1+612yes—
1393C222−1+612yes—
1394C4—22no—
1395C4—22no—
1396C4—41no—
1397C4—44no—
1398C4—44no—
1399C4—41no—
1400C4—41no—
1401C4—41no—
1402C4—41no—
1403C4—41no—
1404C4—44no—
1405C4—41no—
1406C4—41no—
1407C4—41no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—44no—
1413C4—44no—
1414C4—44no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4—44no—
1420C4—42no—
1421C4#353514yes—
1422C2—42no—
1423C2—42no—
1424C2—81no—
1425C2C2×#353511yescharacteristic
1426C2#6288611yescharacteristic
1427C2#6288611yescharacteristic
1428C2#6288912yes—
1429C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58962C2semidirect
2. #58888C2semidirect
3. #58783C2semidirect
4. #58767C2semidirect
7. #56636C2semidirect
8. #55610C2semidirect
9. #54715C2semidirect
10. #54641C2semidirect
11. #53975C2semidirect
13. #53140C2semidirect
14. #53139C2semidirect
15. #45415C2semidirect
16. #45390C2semidirect
17. #42981C2semidirect
18. #42941C2semidirect
19. #42832C2semidirect
20. #42817C2semidirect
21. #42779C2semidirect
22. #42695C2semidirect
23. #37985C2semidirect
25. #37793C2semidirect
27. #37383C2semidirect
28. #37377C2semidirect
41. #2844C22semidirect
43. #2839C22semidirect
44. #2839C22semidirect
45. #2839C22semidirect
49. #2833C22semidirect
50. #2833C22semidirect
51. #2833C22semidirect
55. #2811C22semidirect
57. #2806C22semidirect
58. #2805C22semidirect
59. #2799C22semidirect
60. #2799C22semidirect
62. #2794C22semidirect
63. #2792C22semidirect
64. #2792C22semidirect
65. #2791C22semidirect
66. #2789C22semidirect
67. #2789C22semidirect
74. #2776C22semidirect
75. #2774C22semidirect
79. #2769C22semidirect
80. #2769C22semidirect
81. #2769C22semidirect
82. #2767C22semidirect
83. #2766C22semidirect
88. #2762C22semidirect
91. #2758C22semidirect
92. #2755C22semidirect
93. #2755C22semidirect
94. #2755C22semidirect
95. #2755C22semidirect
107. #2726C22semidirect
108. #2719C22semidirect
109. #2719C22semidirect
110. #2719C22semidirect
111. #2713C22semidirect
112. #2713C22semidirect
123. #2666C22semidirect
124. #2666C22semidirect
129. #2647C22semidirect
130. #2645C22semidirect
153. #2612C22semidirect
154. #2612C22semidirect
155. #2612C22semidirect
159. #2605C22semidirect
162. #2590C22semidirect
164. #2586C22semidirect
165. #2584C22semidirect
166. #2584C22semidirect
168. #2582C22semidirect
169. #2582C22semidirect
170. #2581C22semidirect
171. #2581C22semidirect
176. #2570C22semidirect
177. #2568C22semidirect
178. #2568C22semidirect
179. #2568C22semidirect
181. #2550C22semidirect
182. #2546C22semidirect
183. #2533C22semidirect
191. #2514C22semidirect
192. #2514C22semidirect
193. #2514C22semidirect
194. #2511C22semidirect
195. #2511C22semidirect
196. #2509C22semidirect
197. #2509C22semidirect
198. #2509C22semidirect
199. #2508C22semidirect
200. #2508C22semidirect
221. #2462C22semidirect
222. #2453C22semidirect
223. #2453C22semidirect
224. #2451C22semidirect
225. #2451C22semidirect
226. #2451C22semidirect
227. #2446C22semidirect
228. #2446C22semidirect
229. #2446C22semidirect
230. #2446C22semidirect
245. #2369C22semidirect
246. #2365C22semidirect
249. #2356C22semidirect
250. #2351C22semidirect

Maximal subgroups

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

subgroupindex
#589622
#588882
#587832
#587672
#575942
#566592
#566362
#556102
#547152
#546412
#539752
#539162
#531402
#531392
#454152
#453902
#429812
#429412
#428322
#428172
#427792
#426952
#379852
#378592
#377932
#376632
#373832
#373772
#353252
#353112
#346342