Finite Group Databasebeta

← #8726332

Subgroups — #8726332

Order 512.

4193 conjugacy classes of subgroups.

The subgroup lattice has 1351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59933C211yesmaximal, characteristic
2#59832C212yesmaximal, complemented
3#59547C212yesmaximal, complemented
4#59496C212yesmaximal, complemented
5#59481C212yesmaximal, complemented
6#58928C214yesmaximal
7#58803C212yesmaximal, complemented
8#56893C214yesmaximal, complemented
9#55137C214yesmaximal, complemented
10#53139C212yesmaximal, complemented
11#53009C211yesmaximal, characteristic
12#52306C211yesmaximal, characteristic
13#47817C212yesmaximal, complemented
14#47623C214yesmaximal, complemented
15#45436C212yesmaximal, complemented
16#45308C211yesmaximal, characteristic
17#44894C212yesmaximal, complemented
18#44268C214yesmaximal
19#42915C211yesmaximal, characteristic
20#42861C212yesmaximal, complemented
21#42376C212yesmaximal, complemented
22#42070C214yesmaximal, complemented
23#40224C212yesmaximal, complemented
24#40155C212yesmaximal, complemented
25#39978C212yesmaximal, complemented
26#39975C212yesmaximal, complemented
27#39172C211yesmaximal, characteristic
28#36007C211yesmaximal, characteristic
29#35711C212yesmaximal, complemented
30C2×Q82C2211yescharacteristic
31C2×Q82C2212yes—
32C2×#556C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2864C2212yes—
36#2862C2211yescharacteristic
37#2844C2212yes—
38#2838C2214yes—
39#2836C2214yes—
40#2836C2214yes—
41#2835C2212yes—
42#2833C2214yes—
43#2833C2214yes—
44#2821C2214yes—
45#2821C2212yes—
46#2809C2211yescharacteristic
47#2806C2214yes—
48#2805C2214yes—
49#2802C2214yes—
50#2802C2214yes—
51#2799C2212yes—
52#2791C2214yes—
53#2789C2212yes—
54#2777C2214yes—
55#2775C2212yes—
56#2775C2214yes—
57#2775C2212yes—
58#2774C2214yes—
59#2774C2214yes—
60#2773C2214yes—
61#2772C2214yes—
62#2769C2212yes—
63#2769C2214yes—
64#2769C2214yes—
65#2769C2211yescharacteristic
66#2769C2211yescharacteristic
67#2769C2214yes—
68#2766C2214yes—
69#2765C2214yes—
70#2762C2214yes—
71#2762C2214yes—
72#2759C2214yes—
73#2759C2214yes—
74#2758C2214yes—
75#2758C2214yes—
76#2755C2214yes—
77#2755C2214yes—
78#2755C2214yes—
79#2754C2214yes—
80#2748C2212yes—
81#2742C2212yes—
82#2734C2214yes—
83#2734C2214yes—
84#2734C2214yes—
85#2734C2211yescharacteristic
86#2734C2214yes—
87#2731C2212yes—
88#2729C2214yes—
89#2727C2212yes—
90#2723C2214yes—
91#2722C2214yes—
92#2721C2212yes—
93#2721C2212yes—
94#2716C2214yes—
95#2716C2214yes—
96#2716C2214yes—
97#2713C2214yes—
98#2713C2214yes—
99#2700C2214yes—
100#2698C2214yes—
101#2689C2214yes—
102#2677C2212yes—
103#2677C2214yes—
104#2666C2214yes—
105#2666C2214yes—
106#2666C2214yes—
107#2664C2212yes—
108#2655C2214yes—
109#2655C2214yes—
110#2640C2212yes—
111#2637C2214yes—
112#2637C2212yes—
113#2634C2212yes—
114#2628C2212yes—
115#2628C2214yes—
116#2625C2211yescharacteristic
117#2625C2211yescharacteristic
118#2612C2214yes—
119#2612C2212yes—
120#2612C2214yes—
121#2612C2214yes—
122#2612C2214yes—
123#2612C2212yes—
124#2606C2214yes—
125#2605C2214yes—
126#2604C2212yes—
127#2604C2214yes—
128#2594C2214yes—
129#2589C2214yes—
130#2588C2214yes—
131#2588C2214yes—
132#2585C2214yes—
133#2584C2212yes—
134#2582C2212yes—
135#2582C2212yes—
136#2581C2212yes—
137#2581C2214yes—
138#2581C2212yes—
139#2577C2214yes—
140#2573C2214yes—
141#2570C2212yes—
142#2570C2212yes—
143#2568C2212yes—
144#2568C2212yes—
145#2568C2214yes—
146#2568C2212yes—
147#2565C2212yes—
148#2563C2211yescharacteristic
149#2551C2214yes—
150#2551C2212yes—
151#2551C2212yes—
152#2550C2212yes—
153#2550C2212yes—
154#2546C2211yescharacteristic
155#2546C2214yes—
156#2546C2214yes—
157#2546C2214yes—
158#2545C2212yes—
159#2531C2214yes—
160#2530C2214yes—
161#2529C2214yes—
162#2528C2214yes—
163#2528C2214yes—
164#2528C2214yes—
165#2525C2214yes—
166#2524C2214yes—
167#2524C2214yes—
168#2523C2212yes—
169#2522C2214yes—
170#2520C2214yes—
171#2514C2212yes—
172#2514C2212yes—
173#2509C2212yes—
174#2508C2212yes—
175#2508C2212yes—
176#2508C2212yes—
177#2507C2212yes—
178#2503C2211yescharacteristic
179#2497C2212yes—
180#2496C2212yes—
181#2495C2212yes—
182#2494C2212yes—
183#2489C2212yes—
184#2487C2211yescharacteristic
185#2478C2214yes—
186#2474C2214yes—
187#2469C2214yes—
188#2465C2214yes—
189#2462C2214yes—
190#2462C2214yes—
191#2453C2212yes—
192#2451C2214yes—
193#2451C2214yes—
194#2451C2212yes—
195#2451C2212yes—
196#2451C2212yes—
197#2451C2214yes—
198#2451C2212yes—
199#2451C2212yes—
200#2451C2212yes—
201#2451C2214yes—
202#2446C2212yes—
203#2446C2212yes—
204#2440C2212yes—
205#2439C2212yes—
206#2439C2212yes—
207#2439C2214yes—
208#2439C2214yes—
209#2439C2212yes—
210#2434C2211yescharacteristic
211#2429C2214yes—
212#2429C2212yes—
213#2423C2212yes—
214#2421C2212yes—
215#2421C2212yes—
216#2421C2212yes—
217#2409C2211yescharacteristic
218#2399C2212yes—
219#2396C2212yes—
220#2396C2212yes—
221#2396C2214yes—
222#2395C2211yescharacteristic
223#2395C2211yescharacteristic
224#2373C2214yes—
225#2372C2212yes—
226#2365C2212yes—
227#2365C2212yes—
228#2365C2214yes—
229#2365C2212yes—
230#2362C2212yes—
231#2360C2212yes—
232#2356C2212yes—
233#2356C2212yes—
234#2356C2214yes—
235#2356C2214yes—
236#2351C2212yes—
237#2351C2212yes—
238#2351C2212yes—
239#2347C2211yescharacteristic
240#2346C2211yescharacteristic
241Q8×C22⋊C4C2212yes—
242Q8×C22⋊C4C2212yes—
243#2332C2214yes—
244#2331C2214yes—
245#2331C2214yes—
246#2327C2212yes—
247#2327C2214yes—
248#2323C2212yes—
249C4×C4⋊Q8C2212yes—
250C4×C4⋊Q8C2212yes—
251C4×C4⋊Q8C2212yes—
252C4×#125C2212yes—
253C4×#126C2212yes—
254C4×#126C2212yes—
255C4×#124C2211yescharacteristic
256#2295C2211yescharacteristic
257#2295C2212yes—
258#2295C2212yes—
259C23×Q8C2311yescharacteristic
260Q82—48no—
261Q82—44no—
262#556—44no—
263#544—44no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2314yes—
280C2×#126C2312yes—
281C2×#126C2312yes—
282C2×#126C2314yes—
283C2×#126C2312yes—
284C2×#126C2312yes—
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×#125C2312yes—
288C2×#124C2311yescharacteristic
289C2×#124C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2314yes—
295#519—44no—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2311yescharacteristic
317C2×#117C2311yescharacteristic
318C2×#117C2314yes—
319C22×C4⋊C4C2311yescharacteristic
320#401C2314yes—
321#401C2314yes—
322#401C2314yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2312yes—
327#400C2314yes—
328#400C2311yescharacteristic
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2311yescharacteristic
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#399C2312yes—
356#399C2311yescharacteristic
357#399C2314yes—
358#399C2314yes—
359#399C2312yes—
360#399C2311yescharacteristic
361#399C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2311yescharacteristic
391#398C2314yes—
392#398C2311yescharacteristic
393#398C2314yes—
394#398C2312yes—
395#398C2312yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#397C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2311yescharacteristic
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2311yescharacteristic
411#397C2312yes—
412#396C2314yes—
413#396C2312yes—
414#396C2312yes—
415#396C2314yes—
416#396C2312yes—
417#396C2314yes—
418#396C2314yes—
419#396C2312yes—
420#396C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2312yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2312yes—
430#395C2312yes—
431#395C2314yes—
432#395C2312yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2312yes—
440#395C2314yes—
441#395C2314yes—
442#394C2312yes—
443#394C2312yes—
444#393C2312yes—
445#393C2312yes—
446#393C2314yes—
447#393C2314yes—
448#393C2312yes—
449#393C2314yes—
450#393C2314yes—
451#393C2312yes—
452#393C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2312yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2312yes—
473#391C2314yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2311yescharacteristic
485#391C2312yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2314yes—
490#391C2312yes—
491#390C2312yes—
492#390C2311yescharacteristic
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#388C2312yes—
541#388C2312yes—
542#388C2312yes—
543#388C2312yes—
544#388C2312yes—
545#388C2312yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2312yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2314yes—
574#387C2314yes—
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#386C2312yes—
632#386C2312yes—
633#385C2314yes—
634#385C2314yes—
635#385C2312yes—
636#385C2314yes—
637#385C2312yes—
638#384C2312yes—
639#384C2312yes—
640#384C2312yes—
641#383C2312yes—
642#383C2312yes—
643#383C2312yes—
644#383C2314yes—
645#383C2314yes—
646#383C2314yes—
647#383C2314yes—
648#383C2314yes—
649#382C2312yes—
650#382C2312yes—
651#382C2312yes—
652#382C2311yescharacteristic
653#382C2312yes—
654#382C2312yes—
655#382C2314yes—
656#382C2314yes—
657#382C2314yes—
658#382C2312yes—
659#382C2312yes—
660#382C2312yes—
661#382C2314yes—
662#382C2314yes—
663#382C2314yes—
664#382C2314yes—
665#381C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2311yescharacteristic
672#380C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C22⋊C4C2311yescharacteristic
701C4×C22⋊C4C2311yescharacteristic
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709#376C2312yes—
710#376C2312yes—
711#376C2314yes—
712#376C2314yes—
713#376C2314yes—
714#376C2314yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C22×Q8—28no—
718C22×Q8—42no—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×D4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2412yes—
733C23×C4C2412yes—
734C4⋊Q8—28no—
735C4⋊Q8—28no—
736C4⋊Q8—28no—
737C4⋊Q8—28no—
738C4⋊Q8—28no—
739C4⋊Q8—48no—
740C4⋊Q8—48no—
741C4⋊Q8—42no—
742C4⋊Q8—44no—
743C4⋊Q8—42no—
744C4⋊Q8—44no—
745C4⋊Q8—48no—
746C4⋊Q8—44no—
747C4⋊Q8—48no—
748C4⋊Q8—48no—
749C4⋊Q8—48no—
750#126—44no—
751#126—48no—
752#126—44no—
753#126—44no—
754#126—44no—
755#125—44no—
756#125—44no—
757#125—44no—
758#124—24no—
759#124—44no—
760C22⋊Q8—28no—
761C22⋊Q8—48no—
762C22⋊Q8—48no—
763C22⋊Q8—42no—
764C22⋊Q8—42no—
765C4×Q8—28no—
766C4×Q8—28no—
767C4×Q8—28no—
768C4×Q8—24no—
769C4×Q8—48no—
770C4×Q8—44no—
771C4×Q8—44no—
772C4×Q8—44no—
773C4×Q8—42no—
774C4×Q8—48no—
775C4×Q8—44no—
776C4×Q8—48no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×D4—42no—
783#117—24no—
784#117—24no—
785#117—42no—
786#117—42no—
787#117—48no—
788C2×C4⋊C4—42no—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C22⋊C4C2412yes—
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⋊C4C2411yescharacteristic
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2411yescharacteristic
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916C2×C42C2412yes—
917C2×C42C2414yes—
918#95C2411yescharacteristic
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2411yescharacteristic
939#95C2414yes—
940#95C2411yescharacteristic
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
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—
1003C24C2511yescharacteristic
1004C24C2511yescharacteristic
1005C2×Q8—24no—
1006C2×Q8—22no—
1007C2×Q8—28no—
1008C2×Q8—28no—
1009C2×Q8—24no—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—28no—
1013C2×Q8—24no—
1014C2×Q8—41no—
1015C2×Q8—42no—
1016C2×Q8—42no—
1017C2×Q8—41no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—44no—
1021C2×Q8—44no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—42no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—42no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—416no—
1031C2×Q82−1+418yes—
1032C2×Q82−1+414yes—
1033C2×D4—22no—
1034C2×D4—41no—
1035C2×D4—41no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—24no—
1039C22×C4—28no—
1040C22×C4—24no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—44no—
1044C22×C4C2511yescharacteristic
1045C22×C4C2512yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2511yescharacteristic
1071C4⋊C4—24no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—41no—
1109C4⋊C4—41no—
1110C4⋊C4—41no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4H(5,𝔽2)14yes—
1146C22⋊C4—24no—
1147C22⋊C4—24no—
1148C22⋊C4—28no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—42no—
1154C22⋊C4—42no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4—42no—
1159C22⋊C4—41no—
1160C22⋊C4—41no—
1161C22⋊C4—44no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4—44no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C42—24no—
1171C42—24no—
1172C42—28no—
1173C42—24no—
1174C42—24no—
1175C42—22no—
1176C42—24no—
1177C42—24no—
1178C42—28no—
1179C42—28no—
1180C42—24no—
1181C42—24no—
1182C42—22no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—28no—
1188C42—28no—
1189C42—42no—
1190C42—41no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42—42no—
1199C42—42no—
1200C23—21no—
1201C23—21no—
1202C23—22no—
1203C23—21no—
1204C23—21no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—21no—
1209C23—21no—
1210C23C2611yescharacteristic
1211Q8—216no—
1212Q8—44no—
1213Q8—48no—
1214Q8—48no—
1215Q8—44no—
1216Q8—88no—
1217Q8—88no—
1218Q8—84no—
1219Q8—164no—
1220Q8—162no—
1221D4—82no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—48no—
1291C2×C4—44no—
1292C2×C4—44no—
1293C2×C4—162no—
1294C2×C4C2×H(5,𝔽2)14yes—
1295C2×C4C2×H(5,𝔽2)12yes—
1296C2×C4C2×2−1+412yes—
1297C2×C4C2×2−1+418yes—
1298C2×C4C2×2−1+414yes—
1299C2×C4C2×2−1+414yes—
1300C2×C4#58514yes—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—42no—
1306C22—42no—
1307C22—41no—
1308C22—41no—
1309C22—42no—
1310C22—42no—
1311C22C22×H(5,𝔽2)11yescharacteristic
1312C22C22×2−1+412yes—
1313C22C22×2−1+411yescharacteristic
1314C22C2×#58512yes—
1315C222−1+611yescharacteristic
1316C4—28no—
1317C4—24no—
1318C4—24no—
1319C4—22no—
1320C4—24no—
1321C4—41no—
1322C4—41no—
1323C4—42no—
1324C4—44no—
1325C4—42no—
1326C4—42no—
1327C4—44no—
1328C4—42no—
1329C4—41no—
1330C4—42no—
1331C4—44no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4#353814yes—
1343C2—81no—
1344C2—81no—
1345C2C2×#353811yescharacteristic
1346C2#6289311yescharacteristic
1347C2#6295312yes—
1348C2#6302411yescharacteristic
1349C2#6303812yes—
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. #59832C2semidirect
3. #59547C2semidirect
4. #59496C2semidirect
5. #59481C2semidirect
7. #58803C2semidirect
8. #56893C2semidirect
9. #55137C2semidirect
10. #53139C2semidirect
13. #47817C2semidirect
14. #47623C2semidirect
15. #45436C2semidirect
17. #44894C2semidirect
20. #42861C2semidirect
21. #42376C2semidirect
22. #42070C2semidirect
23. #40224C2semidirect
24. #40155C2semidirect
25. #39978C2semidirect
26. #39975C2semidirect
29. #35711C2semidirect

Maximal subgroups

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

subgroupindex
#599332
#598322
#595472
#594962
#594812
#589282
#588032
#568932
#551372
#531392
#530092
#523062
#478172
#476232
#454362
#453082
#448942
#442682
#429152
#428612
#423762
#420702
#402242
#401552
#399782
#399752
#391722
#360072
#357112