Finite Group Databasebeta

← #8751480

Subgroups — #8751480

Order 512.

4113 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59934C212yesmaximal, complemented
2#59933C211yesmaximal, characteristic
3#58932C214yesmaximal, complemented
4#58710C214yesmaximal, complemented
5#58665C214yesmaximal, complemented
6#58592C212yesmaximal, complemented
7#58016C214yesmaximal
8#53107C212yesmaximal, complemented
9#53100C212yesmaximal, complemented
10#52961C211yesmaximal, characteristic
11#52580C214yesmaximal, complemented
12#47817C212yesmaximal, complemented
13#45351C211yesmaximal, characteristic
14#45340C212yesmaximal, complemented
15#45339C212yesmaximal, complemented
16#45277C212yesmaximal, complemented
17#45099C212yesmaximal, complemented
18#42915C211yesmaximal, characteristic
19#42863C212yesmaximal, complemented
20#42840C212yesmaximal, complemented
21#42822C212yesmaximal, complemented
22#42780C212yesmaximal, complemented
23#42347C212yesmaximal, complemented
24#42062C214yesmaximal
25#39753C212yesmaximal, complemented
26#39744C211yesmaximal, characteristic
27#36698C211yesmaximal, characteristic
28#36007C211yesmaximal, characteristic
29#35786C212yesmaximal, complemented
30C2×#557C2212yes—
31C2×#557C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2868C2211yescharacteristic
36#2845C2214yes—
37#2844C2211yescharacteristic
38#2839C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2838C2212yes—
42#2838C2212yes—
43#2836C2212yes—
44#2836C2214yes—
45#2836C2214yes—
46#2836C2212yes—
47#2834C2212yes—
48#2833C2211yescharacteristic
49#2833C2211yescharacteristic
50#2833C2212yes—
51#2831C2214yes—
52#2831C2214yes—
53#2830C2212yes—
54#2822C2214yes—
55#2822C2211yescharacteristic
56#2821C2212yes—
57#2820C2212yes—
58#2809C2212yes—
59#2806C2214yes—
60#2802C2214yes—
61#2802C2214yes—
62#2799C2212yes—
63#2799C2212yes—
64#2798C2214yes—
65#2791C2214yes—
66#2791C2214yes—
67#2791C2214yes—
68#2791C2214yes—
69#2791C2214yes—
70#2789C2214yes—
71#2777C2214yes—
72#2774C2214yes—
73#2774C2214yes—
74#2773C2214yes—
75#2771C2214yes—
76#2767C2214yes—
77#2766C2214yes—
78#2762C2214yes—
79#2755C2214yes—
80#2755C2214yes—
81#2754C2214yes—
82#2754C2214yes—
83#2748C2212yes—
84#2747C2214yes—
85#2744C2214yes—
86#2734C2214yes—
87#2729C2214yes—
88#2726C2214yes—
89#2726C2214yes—
90#2726C2214yes—
91#2726C2214yes—
92#2726C2214yes—
93#2725C2214yes—
94#2725C2214yes—
95#2722C2212yes—
96#2722C2212yes—
97#2721C2214yes—
98#2721C2214yes—
99#2721C2214yes—
100#2721C2214yes—
101#2721C2214yes—
102#2719C2214yes—
103#2715C2214yes—
104#2713C2214yes—
105#2713C2214yes—
106#2713C2214yes—
107#2713C2214yes—
108#2713C2214yes—
109#2704C2214yes—
110#2700C2214yes—
111#2698C2214yes—
112#2667C2214yes—
113#2666C2214yes—
114#2666C2214yes—
115#2664C2214yes—
116#2664C2212yes—
117#2664C2214yes—
118#2660C2214yes—
119#2658C2212yes—
120#2655C2214yes—
121#2654C2214yes—
122#2647C2212yes—
123#2645C2214yes—
124#2637C2212yes—
125#2634C2212yes—
126#2629C2214yes—
127#2629C2212yes—
128#2625C2211yescharacteristic
129#2625C2211yescharacteristic
130#2612C2212yes—
131#2612C2214yes—
132#2604C2212yes—
133#2590C2214yes—
134#2589C2214yes—
135#2588C2214yes—
136#2586C2212yes—
137#2585C2214yes—
138#2585C2214yes—
139#2584C2212yes—
140#2582C2212yes—
141#2582C2212yes—
142#2582C2214yes—
143#2582C2212yes—
144#2581C2212yes—
145#2577C2214yes—
146#2575C2214yes—
147#2571C2212yes—
148#2570C2214yes—
149#2568C2212yes—
150#2565C2212yes—
151#2565C2212yes—
152#2565C2214yes—
153#2556C2214yes—
154#2552C2212yes—
155#2552C2214yes—
156#2552C2212yes—
157#2550C2212yes—
158#2550C2212yes—
159#2550C2214yes—
160#2550C2212yes—
161#2547C2211yescharacteristic
162#2546C2211yescharacteristic
163#2546C2212yes—
164#2545C2212yes—
165#2528C2214yes—
166#2524C2214yes—
167#2522C2214yes—
168#2522C2214yes—
169#2521C2214yes—
170#2520C2214yes—
171#2520C2214yes—
172#2519C2214yes—
173#2517C2214yes—
174#2517C2212yes—
175#2511C2212yes—
176#2511C2214yes—
177#2511C2212yes—
178#2507C2212yes—
179#2507C2212yes—
180#2506C2214yes—
181#2506C2212yes—
182#2506C2212yes—
183#2506C2212yes—
184#2506C2214yes—
185#2503C2211yescharacteristic
186#2497C2212yes—
187#2496C2212yes—
188#2496C2212yes—
189#2494C2212yes—
190#2489C2212yes—
191#2487C2211yescharacteristic
192#2478C2214yes—
193#2474C2214yes—
194#2462C2214yes—
195#2462C2214yes—
196#2453C2212yes—
197#2453C2212yes—
198#2453C2214yes—
199#2453C2212yes—
200#2451C2212yes—
201#2451C2212yes—
202#2451C2212yes—
203#2451C2214yes—
204#2451C2212yes—
205#2451C2214yes—
206#2451C2214yes—
207#2446C2212yes—
208#2446C2212yes—
209#2446C2214yes—
210#2442C2212yes—
211#2441C2212yes—
212#2441C2212yes—
213#2441C2214yes—
214#2439C2212yes—
215#2439C2214yes—
216#2434C2211yescharacteristic
217#2429C2212yes—
218#2423C2212yes—
219#2423C2212yes—
220#2423C2212yes—
221#2423C2214yes—
222#2423C2212yes—
223#2409C2211yescharacteristic
224#2401C2212yes—
225#2401C2212yes—
226#2399C2212yes—
227#2399C2212yes—
228#2396C2212yes—
229#2396C2214yes—
230#2396C2212yes—
231#2395C2211yescharacteristic
232#2395C2211yescharacteristic
233#2372C2212yes—
234#2371C2214yes—
235#2369C2212yes—
236#2365C2212yes—
237#2365C2212yes—
238#2362C2212yes—
239#2360C2212yes—
240#2355C2212yes—
241#2355C2212yes—
242#2351C2212yes—
243Q8×C4⋊C4C2212yes—
244Q8×C4⋊C4C2212yes—
245#2347C2211yescharacteristic
246#2346C2211yescharacteristic
247Q8×C22⋊C4C2212yes—
248Q8×C22⋊C4C2212yes—
249#2331C2214yes—
250#2330C2212yes—
251#2327C2212yes—
252#2327C2212yes—
253#2323C2212yes—
254#2320C2212yes—
255C4×#125C2212yes—
256C4×#124C2211yescharacteristic
257#2295C2212yes—
258#2295C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260#557—44no—
261#557—48no—
262#556—44no—
263#544—44no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×#126C2312yes—
275C2×#126C2312yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#124C2311yescharacteristic
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2314yes—
297#519—44no—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
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#401C2312yes—
322#401C2312yes—
323#400C2312yes—
324#400C2312yes—
325#400C2314yes—
326#400C2312yes—
327#400C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2311yescharacteristic
332#400C2312yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2311yescharacteristic
348#400C2312yes—
349#400C2312yes—
350#400C2312yes—
351#400C2314yes—
352#400C2312yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#399C2312yes—
360#399C2312yes—
361#399C2311yescharacteristic
362#399C2312yes—
363#399C2314yes—
364#399C2311yescharacteristic
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2314yes—
382#398C2311yescharacteristic
383#398C2311yescharacteristic
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2312yes—
398#398C2312yes—
399#398C2312yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2312yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#397C2312yes—
428#397C2312yes—
429#397C2314yes—
430#397C2312yes—
431#397C2312yes—
432#397C2312yes—
433#397C2312yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2312yes—
439#397C2312yes—
440#397C2311yescharacteristic
441#397C2311yescharacteristic
442#397C2312yes—
443#397C2312yes—
444#397C2314yes—
445#396C2312yes—
446#396C2312yes—
447#396C2312yes—
448#396C2312yes—
449#396C2312yes—
450#396C2312yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#395C2312yes—
459#395C2312yes—
460#395C2314yes—
461#395C2312yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2312yes—
466#395C2312yes—
467#395C2312yes—
468#395C2312yes—
469#395C2312yes—
470#395C2314yes—
471#395C2312yes—
472#395C2314yes—
473#395C2314yes—
474#395C2314yes—
475#394C2312yes—
476#394C2312yes—
477#393C2314yes—
478#393C2312yes—
479#393C2312yes—
480#393C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2314yes—
490#391C2314yes—
491#391C2312yes—
492#391C2311yescharacteristic
493#391C2312yes—
494#391C2312yes—
495#391C2314yes—
496#391C2314yes—
497#391C2314yes—
498#391C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2314yes—
504#391C2312yes—
505#391C2312yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2312yes—
511#390C2311yescharacteristic
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2314yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2312yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2312yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2312yes—
556#389C2314yes—
557#389C2314yes—
558#389C2312yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#388C2312yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
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#387C2314yes—
639#386C2312yes—
640#386C2312yes—
641#385C2314yes—
642#385C2314yes—
643#385C2312yes—
644#385C2314yes—
645#385C2312yes—
646#384C2312yes—
647#384C2314yes—
648#384C2312yes—
649#384C2314yes—
650#384C2312yes—
651#384C2314yes—
652#384C2312yes—
653#384C2312yes—
654#384C2314yes—
655#383C2312yes—
656#383C2314yes—
657#382C2312yes—
658#382C2312yes—
659#382C2312yes—
660#382C2314yes—
661#382C2314yes—
662#382C2311yescharacteristic
663#382C2314yes—
664#382C2314yes—
665#382C2314yes—
666#382C2312yes—
667#382C2314yes—
668#381C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673#380C2314yes—
674#380C2311yescharacteristic
675#380C2311yescharacteristic
676#380C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2312yes—
714#376C2314yes—
715#376C2312yes—
716C43C2311yescharacteristic
717C22×Q8—28no—
718C22×Q8—42no—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2414yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×D4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2412yes—
732C4⋊Q8—28no—
733C4⋊Q8—28no—
734C4⋊Q8—28no—
735C4⋊Q8—42no—
736C4⋊Q8—42no—
737C4⋊Q8—44no—
738C4⋊Q8—44no—
739C4⋊Q8—48no—
740C4⋊Q8—82no—
741C4⋊Q8—82no—
742#126—44no—
743#126—44no—
744#126—84no—
745#126—84no—
746#125—28no—
747#125—28no—
748#125—44no—
749#125—44no—
750#125—44no—
751#125—48no—
752#125—48no—
753#125—48no—
754#125—84no—
755#125—84no—
756#125—84no—
757#125—84no—
758#124—24no—
759#124—44no—
760#124—82no—
761C22⋊Q8—28no—
762C22⋊Q8—48no—
763C22⋊Q8—42no—
764C22⋊Q8—42no—
765C4×Q8—28no—
766C4×Q8—28no—
767C4×Q8—28no—
768C4×Q8—24no—
769C4×Q8—44no—
770C4×Q8—44no—
771C4×Q8—44no—
772C4×Q8—42no—
773C4×Q8—44no—
774C4×Q8—44no—
775C4×Q8—44no—
776C4×Q8—48no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—44no—
780C4×D4—42no—
781#117—24no—
782#117—24no—
783#117—42no—
784#117—42no—
785#117—48no—
786C2×C4⋊C4—42no—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2411yescharacteristic
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2411yescharacteristic
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2411yescharacteristic
920#95C2411yescharacteristic
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2411yescharacteristic
935#95C2411yescharacteristic
936#95C2412yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2411yescharacteristic
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
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—24no—
1009C2×Q8—24no—
1010C2×Q8—28no—
1011C2×Q8—22no—
1012C2×Q8—24no—
1013C2×Q8—24no—
1014C2×Q8—42no—
1015C2×Q8—42no—
1016C2×Q8—41no—
1017C2×Q8—42no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—42no—
1021C2×Q8—41no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—42no—
1025C2×Q8—42no—
1026C2×Q8—416no—
1027C2×Q82−1+418yes—
1028C2×D4—22no—
1029C2×D4—41no—
1030C2×D4—41no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—28no—
1035C22×C4—24no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—44no—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2514yes—
1065C22×C4C2511yescharacteristic
1066C4⋊C4—24no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—41no—
1109C4⋊C4—41no—
1110C4⋊C4—41no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—41no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4H(5,𝔽2)14yes—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—28no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—42no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4—44no—
1159C22⋊C4—42no—
1160C22⋊C4—42no—
1161C22⋊C4—42no—
1162C22⋊C4—42no—
1163C22⋊C4—41no—
1164C22⋊C4—41no—
1165C22⋊C4—42no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C42—24no—
1174C42—24no—
1175C42—28no—
1176C42—24no—
1177C42—24no—
1178C42—22no—
1179C42—24no—
1180C42—24no—
1181C42—28no—
1182C42—24no—
1183C42—28no—
1184C42—24no—
1185C42—24no—
1186C42—44no—
1187C42—42no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C42—42no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—41no—
1198C422−1+414yes—
1199C23—21no—
1200C23—21no—
1201C23—22no—
1202C23—21no—
1203C23—21no—
1204C23—22no—
1205C23—21no—
1206C23—21no—
1207C23—22no—
1208C23—22no—
1209C23C2611yescharacteristic
1210Q8—216no—
1211Q8—48no—
1212Q8—44no—
1213Q8—88no—
1214Q8—82no—
1215Q8—84no—
1216Q8—84no—
1217Q8—84no—
1218D4—82no—
1219C2×C4—21no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—48no—
1289C2×C4—44no—
1290C2×C4—44no—
1291C2×C4—162no—
1292C2×C4C2×H(5,𝔽2)14yes—
1293C2×C4C2×H(5,𝔽2)12yes—
1294C2×C4C2×2−1+418yes—
1295C2×C4C2×2−1+414yes—
1296C2×C4C2×2−1+412yes—
1297C2×C4C2×2−1+414yes—
1298C22—41no—
1299C22—41no—
1300C22—42no—
1301C22—42no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—42no—
1307C22—42no—
1308C22C22×H(5,𝔽2)11yescharacteristic
1309C22C22×2−1+412yes—
1310C22C22×2−1+411yescharacteristic
1311C22H(7,𝔽2)11yescharacteristic
1312C222−1+612yes—
1313C4—28no—
1314C4—24no—
1315C4—22no—
1316C4—24no—
1317C4—41no—
1318C4—41no—
1319C4—42no—
1320C4—44no—
1321C4—42no—
1322C4—44no—
1323C4—42no—
1324C4—42no—
1325C4—44no—
1326C4—41no—
1327C4—44no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4#353814yes—
1340C2—81no—
1341C2—81no—
1342C2C2×#353811yescharacteristic
1343C2#6291711yescharacteristic
1344C2#6294712yes—
1345C2#6306112yes—
1346C2#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
1. #59934C2semidirect
3. #58932C2semidirect
4. #58710C2semidirect
5. #58665C2semidirect
6. #58592C2semidirect
8. #53107C2semidirect
9. #53100C2semidirect
11. #52580C2semidirect
12. #47817C2semidirect
14. #45340C2semidirect
15. #45339C2semidirect
16. #45277C2semidirect
17. #45099C2semidirect
19. #42863C2semidirect
20. #42840C2semidirect
21. #42822C2semidirect
22. #42780C2semidirect
23. #42347C2semidirect
25. #39753C2semidirect
29. #35786C2semidirect

Maximal subgroups

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

subgroupindex
#599342
#599332
#589322
#587102
#586652
#585922
#580162
#531072
#531002
#529612
#525802
#478172
#453512
#453402
#453392
#452772
#450992
#429152
#428632
#428402
#428222
#427802
#423472
#420622
#397532
#397442
#366982
#360072
#357862