Finite Group Databasebeta

← #8751572

Subgroups — #8751572

Order 512.

4059 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59946C211yesmaximal, characteristic
2#59766C212yesmaximal, complemented
3#58923C214yesmaximal, complemented
4#58803C212yesmaximal, complemented
5#58247C214yesmaximal
6#57068C214yesmaximal, complemented
7#56961C214yesmaximal, complemented
8#53142C212yesmaximal, complemented
9#53100C212yesmaximal, complemented
10#53017C211yesmaximal, characteristic
11#52583C214yesmaximal, complemented
12#47544C212yesmaximal, complemented
13#45389C212yesmaximal, complemented
14#45308C211yesmaximal, characteristic
15#45305C212yesmaximal, complemented
16#45293C212yesmaximal, complemented
17#45274C212yesmaximal, complemented
18#42918C211yesmaximal, characteristic
19#42848C212yesmaximal, complemented
20#42832C212yesmaximal, complemented
21#42820C212yesmaximal, complemented
22#42748C212yesmaximal, complemented
23#42347C212yesmaximal, complemented
24#42114C214yesmaximal
25#39978C212yesmaximal, complemented
26#39172C211yesmaximal, characteristic
27#36698C211yesmaximal, characteristic
28#36007C211yesmaximal, characteristic
29#35786C212yesmaximal, complemented
30C2×Q82C2211yescharacteristic
31C2×#557C2212yes—
32C2×#556C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2862C2211yescharacteristic
36#2844C2211yescharacteristic
37#2843C2214yes—
38#2841C2212yes—
39#2839C2214yes—
40#2839C2214yes—
41#2838C2212yes—
42#2838C2212yes—
43#2838C2214yes—
44#2836C2212yes—
45#2836C2212yes—
46#2836C2214yes—
47#2833C2214yes—
48#2833C2211yescharacteristic
49#2833C2211yescharacteristic
50#2833C2214yes—
51#2831C2214yes—
52#2831C2214yes—
53#2830C2212yes—
54#2822C2212yes—
55#2822C2211yescharacteristic
56#2821C2212yes—
57#2820C2212yes—
58#2806C2214yes—
59#2805C2214yes—
60#2799C2214yes—
61#2798C2214yes—
62#2794C2214yes—
63#2793C2214yes—
64#2793C2214yes—
65#2791C2214yes—
66#2791C2214yes—
67#2791C2214yes—
68#2790C2214yes—
69#2789C2212yes—
70#2789C2212yes—
71#2787C2214yes—
72#2783C2214yes—
73#2783C2214yes—
74#2783C2214yes—
75#2776C2214yes—
76#2776C2214yes—
77#2775C2214yes—
78#2775C2214yes—
79#2774C2214yes—
80#2772C2214yes—
81#2769C2212yes—
82#2767C2214yes—
83#2766C2214yes—
84#2764C2212yes—
85#2762C2214yes—
86#2762C2214yes—
87#2762C2214yes—
88#2759C2214yes—
89#2758C2214yes—
90#2758C2214yes—
91#2755C2214yes—
92#2755C2214yes—
93#2747C2214yes—
94#2742C2212yes—
95#2734C2214yes—
96#2734C2214yes—
97#2734C2214yes—
98#2720C2214yes—
99#2717C2212yes—
100#2716C2214yes—
101#2716C2214yes—
102#2713C2214yes—
103#2713C2214yes—
104#2713C2214yes—
105#2713C2214yes—
106#2713C2214yes—
107#2713C2214yes—
108#2707C2214yes—
109#2704C2214yes—
110#2689C2214yes—
111#2674C2214yes—
112#2666C2214yes—
113#2666C2214yes—
114#2664C2212yes—
115#2660C2214yes—
116#2655C2214yes—
117#2654C2214yes—
118#2652C2214yes—
119#2650C2214yes—
120#2650C2214yes—
121#2647C2212yes—
122#2645C2214yes—
123#2640C2212yes—
124#2637C2212yes—
125#2634C2212yes—
126#2629C2212yes—
127#2629C2214yes—
128#2625C2211yescharacteristic
129#2625C2211yescharacteristic
130#2612C2214yes—
131#2612C2212yes—
132#2606C2214yes—
133#2605C2214yes—
134#2605C2214yes—
135#2605C2214yes—
136#2604C2212yes—
137#2590C2214yes—
138#2586C2212yes—
139#2582C2212yes—
140#2582C2214yes—
141#2581C2212yes—
142#2581C2212yes—
143#2581C2212yes—
144#2577C2214yes—
145#2574C2214yes—
146#2570C2212yes—
147#2570C2212yes—
148#2568C2212yes—
149#2568C2212yes—
150#2567C2212yes—
151#2565C2212yes—
152#2565C2214yes—
153#2563C2211yescharacteristic
154#2551C2212yes—
155#2550C2212yes—
156#2550C2212yes—
157#2550C2212yes—
158#2546C2211yescharacteristic
159#2546C2212yes—
160#2545C2212yes—
161#2533C2214yes—
162#2533C2214yes—
163#2532C2214yes—
164#2531C2214yes—
165#2530C2214yes—
166#2530C2214yes—
167#2528C2214yes—
168#2528C2214yes—
169#2528C2214yes—
170#2527C2214yes—
171#2524C2214yes—
172#2523C2212yes—
173#2523C2214yes—
174#2514C2212yes—
175#2511C2212yes—
176#2511C2214yes—
177#2509C2212yes—
178#2509C2212yes—
179#2508C2212yes—
180#2508C2212yes—
181#2506C2212yes—
182#2506C2214yes—
183#2506C2214yes—
184#2502C2211yescharacteristic
185#2497C2212yes—
186#2495C2212yes—
187#2494C2212yes—
188#2494C2212yes—
189#2492C2214yes—
190#2492C2212yes—
191#2486C2211yescharacteristic
192#2478C2214yes—
193#2474C2214yes—
194#2465C2214yes—
195#2462C2214yes—
196#2462C2214yes—
197#2453C2214yes—
198#2453C2212yes—
199#2453C2212yes—
200#2453C2212yes—
201#2451C2212yes—
202#2451C2212yes—
203#2451C2214yes—
204#2451C2212yes—
205#2451C2212yes—
206#2451C2214yes—
207#2446C2214yes—
208#2446C2214yes—
209#2446C2212yes—
210#2446C2212yes—
211#2442C2212yes—
212#2441C2214yes—
213#2441C2212yes—
214#2439C2212yes—
215#2439C2212yes—
216#2439C2214yes—
217#2434C2211yescharacteristic
218#2429C2212yes—
219#2421C2212yes—
220#2421C2212yes—
221#2421C2212yes—
222#2421C2212yes—
223#2409C2211yescharacteristic
224#2401C2212yes—
225#2401C2212yes—
226#2399C2212yes—
227#2399C2212yes—
228#2396C2212yes—
229#2396C2212yes—
230#2396C2214yes—
231#2395C2211yescharacteristic
232#2395C2211yescharacteristic
233#2374C2212yes—
234#2371C2214yes—
235#2370C2212yes—
236#2365C2212yes—
237#2365C2212yes—
238#2362C2212yes—
239#2360C2212yes—
240#2356C2212yes—
241#2356C2212yes—
242#2351C2212yes—
243Q8×C4⋊C4C2212yes—
244Q8×C4⋊C4C2212yes—
245#2347C2211yescharacteristic
246#2346C2211yescharacteristic
247Q8×C22⋊C4C2212yes—
248Q8×C22⋊C4C2212yes—
249#2331C2214yes—
250#2331C2212yes—
251#2327C2212yes—
252#2327C2212yes—
253#2323C2212yes—
254#2320C2212yes—
255C4×#125C2212yes—
256C4×#124C2211yescharacteristic
257#2295C2211yescharacteristic
258#2295C2212yes—
259C23×Q8C2311yescharacteristic
260Q82—44no—
261#557—48no—
262#556—44no—
263#544—44no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2314yes—
275C2×#126C2312yes—
276C2×#126C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#124C2311yescharacteristic
285C2×#124C2312yes—
286C2×#123C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2311yescharacteristic
290C2×C22⋊Q8C2314yes—
291#519—44no—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×#117C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2314yes—
313C22×C4⋊C4C2311yescharacteristic
314#401C2314yes—
315#401C2314yes—
316#401C2312yes—
317#401C2312yes—
318#401C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2312yes—
322#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2312yes—
337#400C2312yes—
338#400C2311yescharacteristic
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2311yescharacteristic
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#399C2312yes—
363#399C2312yes—
364#399C2314yes—
365#399C2311yescharacteristic
366#399C2311yescharacteristic
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2311yescharacteristic
375#398C2312yes—
376#398C2314yes—
377#398C2312yes—
378#398C2311yescharacteristic
379#398C2312yes—
380#398C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2312yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#397C2312yes—
411#397C2312yes—
412#397C2311yescharacteristic
413#397C2312yes—
414#397C2312yes—
415#397C2312yes—
416#397C2312yes—
417#397C2312yes—
418#397C2312yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2311yescharacteristic
425#397C2312yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#396C2312yes—
431#396C2312yes—
432#396C2312yes—
433#396C2312yes—
434#396C2312yes—
435#396C2312yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#395C2312yes—
444#395C2312yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#395C2312yes—
450#395C2314yes—
451#395C2312yes—
452#395C2314yes—
453#395C2314yes—
454#395C2312yes—
455#395C2314yes—
456#395C2312yes—
457#395C2312yes—
458#395C2312yes—
459#395C2312yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#394C2312yes—
466#394C2312yes—
467#393C2312yes—
468#393C2312yes—
469#393C2314yes—
470#393C2312yes—
471#393C2312yes—
472#393C2312yes—
473#393C2314yes—
474#393C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2312yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2312yes—
490#391C2311yescharacteristic
491#391C2314yes—
492#391C2312yes—
493#391C2314yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2314yes—
498#391C2314yes—
499#391C2314yes—
500#391C2314yes—
501#391C2312yes—
502#391C2312yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2312yes—
510#390C2312yes—
511#390C2311yescharacteristic
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2312yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2314yes—
551#389C2312yes—
552#389C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2312yes—
561#388C2312yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
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#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#386C2312yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2312yes—
644#384C2312yes—
645#384C2314yes—
646#384C2314yes—
647#384C2312yes—
648#384C2314yes—
649#383C2312yes—
650#383C2314yes—
651#383C2314yes—
652#383C2314yes—
653#383C2314yes—
654#383C2314yes—
655#382C2312yes—
656#382C2312yes—
657#382C2312yes—
658#382C2314yes—
659#382C2311yescharacteristic
660#382C2312yes—
661#382C2312yes—
662#382C2312yes—
663#382C2312yes—
664#382C2314yes—
665#382C2312yes—
666#382C2314yes—
667#382C2314yes—
668#381C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2312yes—
675#380C2311yescharacteristic
676#380C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2312yes—
711#376C2312yes—
712#376C2314yes—
713#376C2312yes—
714#376C2314yes—
715#376C2314yes—
716C43C2311yescharacteristic
717C22×Q8—28no—
718C22×Q8—42no—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2414yes—
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×D4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2412yes—
732C23×C4C2412yes—
733C4⋊Q8—28no—
734C4⋊Q8—28no—
735C4⋊Q8—44no—
736C4⋊Q8—44no—
737C4⋊Q8—42no—
738C4⋊Q8—42no—
739C4⋊Q8—44no—
740C4⋊Q8—44no—
741C4⋊Q8—48no—
742C4⋊Q8—48no—
743C4⋊Q8—48no—
744#126—44no—
745#126—44no—
746#125—28no—
747#125—44no—
748#125—48no—
749#125—44no—
750#125—44no—
751#125—48no—
752#125—48no—
753#124—44no—
754#124—42no—
755#123—44no—
756C22⋊Q8—28no—
757C22⋊Q8—48no—
758C22⋊Q8—42no—
759C22⋊Q8—42no—
760C4×Q8—28no—
761C4×Q8—28no—
762C4×Q8—28no—
763C4×Q8—24no—
764C4×Q8—44no—
765C4×Q8—44no—
766C4×Q8—44no—
767C4×Q8—42no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×Q8—44no—
771C4×Q8—48no—
772C4×Q8—44no—
773C4×Q8—44no—
774C4×Q8—44no—
775C4×D4—42no—
776#117—24no—
777#117—24no—
778#117—42no—
779#117—42no—
780#117—48no—
781C2×C4⋊C4—42no—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2411yescharacteristic
864C2×C22⋊C4C2411yescharacteristic
865C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908#95C2411yescharacteristic
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2411yescharacteristic
932#95C2411yescharacteristic
933#95C2412yes—
934#95C2412yes—
935#95C2411yescharacteristic
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
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—
997C24C2511yescharacteristic
998C24C2511yescharacteristic
999C2×Q8—24no—
1000C2×Q8—22no—
1001C2×Q8—28no—
1002C2×Q8—24no—
1003C2×Q8—24no—
1004C2×Q8—28no—
1005C2×Q8—22no—
1006C2×Q8—24no—
1007C2×Q8—41no—
1008C2×Q8—42no—
1009C2×Q8—41no—
1010C2×Q8—42no—
1011C2×Q8—42no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—42no—
1015C2×Q8—42no—
1016C2×Q8—42no—
1017C2×Q8—44no—
1018C2×Q8—42no—
1019C2×Q8—44no—
1020C2×Q8—44no—
1021C2×Q8—44no—
1022C2×Q8—416no—
1023C2×Q82−1+418yes—
1024C2×D4—22no—
1025C2×D4—41no—
1026C2×D4—41no—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—24no—
1030C22×C4—28no—
1031C22×C4—24no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4C2511yescharacteristic
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C4⋊C4—24no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—28no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—41no—
1107C4⋊C4—41no—
1108C4⋊C4—41no—
1109C4⋊C4—41no—
1110C4⋊C4—41no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4H(5,𝔽2)14yes—
1139C22⋊C4—24no—
1140C22⋊C4—24no—
1141C22⋊C4—28no—
1142C22⋊C4—42no—
1143C22⋊C4—42no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—42no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
1153C22⋊C4—42no—
1154C22⋊C4—42no—
1155C22⋊C4—41no—
1156C22⋊C4—41no—
1157C22⋊C4—42no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—42no—
1162C22⋊C4—42no—
1163C42—24no—
1164C42—24no—
1165C42—28no—
1166C42—24no—
1167C42—24no—
1168C42—22no—
1169C42—24no—
1170C42—24no—
1171C42—28no—
1172C42—28no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—22no—
1177C42—24no—
1178C42—44no—
1179C42—41no—
1180C42—44no—
1181C42—44no—
1182C42—44no—
1183C42—42no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C23—21no—
1190C23—21no—
1191C23—22no—
1192C23—22no—
1193C23—21no—
1194C23—21no—
1195C23—22no—
1196C23—22no—
1197C23—21no—
1198C23—21no—
1199C23C2611yescharacteristic
1200Q8—216no—
1201Q8—48no—
1202Q8—44no—
1203Q8—44no—
1204Q8—88no—
1205Q8—84no—
1206Q8—84no—
1207Q8—162no—
1208Q8—164no—
1209D4—82no—
1210C2×C4—21no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
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—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—48no—
1281C2×C4—44no—
1282C2×C4—44no—
1283C2×C4—162no—
1284C2×C4C2×H(5,𝔽2)14yes—
1285C2×C4C2×H(5,𝔽2)12yes—
1286C2×C4C2×2−1+418yes—
1287C2×C4C2×2−1+414yes—
1288C2×C4#58512yes—
1289C22—41no—
1290C22—41no—
1291C22—42no—
1292C22—42no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—42no—
1299C22C22×H(5,𝔽2)11yescharacteristic
1300C22C22×2−1+412yes—
1301C22C2×#58511yescharacteristic
1302C222−1+611yescharacteristic
1303C222−1+612yes—
1304C4—28no—
1305C4—24no—
1306C4—22no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—44no—
1318C4—41no—
1319C4—42no—
1320C4—44no—
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—44no—
1327C4—42no—
1328C4—44no—
1329C4—42no—
1330C4#353814yes—
1331C2—81no—
1332C2—81no—
1333C2C2×#353811yescharacteristic
1334C2#6291911yescharacteristic
1335C2#6295312yes—
1336C2#6305712yes—
1337C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59766C2semidirect
3. #58923C2semidirect
4. #58803C2semidirect
6. #57068C2semidirect
7. #56961C2semidirect
8. #53142C2semidirect
9. #53100C2semidirect
11. #52583C2semidirect
12. #47544C2semidirect
13. #45389C2semidirect
15. #45305C2semidirect
16. #45293C2semidirect
17. #45274C2semidirect
19. #42848C2semidirect
20. #42832C2semidirect
21. #42820C2semidirect
22. #42748C2semidirect
23. #42347C2semidirect
25. #39978C2semidirect
29. #35786C2semidirect

Maximal subgroups

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

subgroupindex
#599462
#597662
#589232
#588032
#582472
#570682
#569612
#531422
#531002
#530172
#525832
#475442
#453892
#453082
#453052
#452932
#452742
#429182
#428482
#428322
#428202
#427482
#423472
#421142
#399782
#391722
#366982
#360072
#357862