Finite Group Databasebeta

← #7652254

Subgroups — #7652254

Order 512.

4110 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42941C211yesmaximal, characteristic
2#42941C211yesmaximal, characteristic
3#42701C212yesmaximal, complemented
4#42701C212yesmaximal, complemented
5#42697C211yesmaximal, characteristic
6#42695C211yesmaximal, characteristic
7#41584C214yesmaximal, complemented
8#41577C214yesmaximal
9#41547C214yesmaximal, complemented
10#41536C214yesmaximal
11#40062C214yesmaximal
12#40028C212yesmaximal
13#40024C212yesmaximal, complemented
14#39647C214yesmaximal, complemented
15#39641C212yesmaximal, complemented
16#39640C212yesmaximal
17#38620C214yesmaximal
18#38614C214yesmaximal, complemented
19#35670C212yesmaximal
20#35656C212yesmaximal, complemented
21#35656C212yesmaximal, complemented
22#35319C211yesmaximal, characteristic
23#35187C212yesmaximal, complemented
24#34951C212yesmaximal, complemented
25#34882C211yesmaximal, characteristic
26#34286C212yesmaximal
27#34254C211yesmaximal, characteristic
28C2×#541C2212yes—
29C2×#519C2211yescharacteristic
30#2868C2211yescharacteristic
31#2864C2214yes—
32#2863C2214yes—
33#2859C2211yescharacteristic
34#2857C2212yes—
35#2839C2214yes—
36#2839C2214yes—
37#2835C2212yes—
38#2834C2212yes—
39#2833C2212yes—
40#2833C2212yes—
41#2806C2214yes—
42#2805C2214yes—
43#2802C2214yes—
44#2794C2212yes—
45#2792C2212yes—
46#2791C2214yes—
47#2791C2214yes—
48#2791C2214yes—
49#2791C2214yes—
50#2791C2214yes—
51#2789C2212yes—
52#2787C2214yes—
53#2776C2214yes—
54#2774C2214yes—
55#2774C2214yes—
56#2774C2214yes—
57#2774C2214yes—
58#2771C2212yes—
59#2771C2212yes—
60#2770C2214yes—
61#2769C2212yes—
62#2767C2214yes—
63#2767C2214yes—
64#2767C2214yes—
65#2766C2214yes—
66#2766C2214yes—
67#2766C2214yes—
68#2765C2214yes—
69#2765C2214yes—
70#2764C2212yes—
71#2764C2212yes—
72#2758C2214yes—
73#2758C2214yes—
74#2747C2214yes—
75#2719C2214yes—
76#2690C2214yes—
77#2666C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2655C2214yes—
82#2655C2214yes—
83#2655C2214yes—
84#2655C2214yes—
85#2655C2214yes—
86#2655C2214yes—
87#2652C2214yes—
88#2652C2214yes—
89#2647C2214yes—
90#2646C2214yes—
91#2642C2212yes—
92#2621C2211yescharacteristic
93#2621C2211yescharacteristic
94#2590C2214yes—
95#2590C2214yes—
96#2590C2214yes—
97#2588C2214yes—
98#2588C2214yes—
99#2588C2214yes—
100#2586C2212yes—
101#2586C2212yes—
102#2586C2212yes—
103#2585C2212yes—
104#2585C2214yes—
105#2585C2214yes—
106#2582C2212yes—
107#2582C2212yes—
108#2581C2212yes—
109#2581C2212yes—
110#2574C2212yes—
111#2571C2212yes—
112#2570C2212yes—
113#2570C2212yes—
114#2568C2212yes—
115#2568C2212yes—
116#2568C2212yes—
117#2568C2212yes—
118#2565C2212yes—
119#2565C2212yes—
120#2556C2212yes—
121#2552C2212yes—
122#2546C2212yes—
123#2546C2212yes—
124#2546C2212yes—
125#2546C2212yes—
126#2546C2212yes—
127#2546C2212yes—
128#2533C2214yes—
129#2533C2214yes—
130#2533C2214yes—
131#2533C2214yes—
132#2533C2214yes—
133#2528C2214yes—
134#2528C2214yes—
135#2528C2214yes—
136#2528C2214yes—
137#2528C2214yes—
138#2524C2214yes—
139#2524C2214yes—
140#2524C2214yes—
141#2524C2214yes—
142#2523C2212yes—
143#2522C2212yes—
144#2520C2214yes—
145#2520C2212yes—
146#2520C2214yes—
147#2520C2214yes—
148#2520C2214yes—
149#2517C2212yes—
150#2514C2212yes—
151#2514C2212yes—
152#2514C2212yes—
153#2514C2212yes—
154#2514C2214yes—
155#2511C2212yes—
156#2511C2212yes—
157#2511C2212yes—
158#2511C2212yes—
159#2509C2214yes—
160#2508C2214yes—
161#2507C2214yes—
162#2507C2214yes—
163#2506C2214yes—
164#2506C2214yes—
165#2505C2214yes—
166#2505C2214yes—
167#2499C2212yes—
168#2499C2212yes—
169#2496C2214yes—
170#2496C2214yes—
171#2478C2214yes—
172#2478C2214yes—
173#2478C2214yes—
174#2478C2214yes—
175#2465C2212yes—
176#2462C2212yes—
177#2462C2214yes—
178#2462C2214yes—
179#2462C2214yes—
180#2462C2214yes—
181#2453C2214yes—
182#2446C2212yes—
183#2446C2212yes—
184#2446C2212yes—
185#2446C2212yes—
186#2446C2212yes—
187#2446C2212yes—
188#2446C2212yes—
189#2446C2212yes—
190#2434C2212yes—
191#2434C2212yes—
192#2402C2214yes—
193#2402C2214yes—
194#2399C2211yescharacteristic
195#2399C2211yescharacteristic
196#2396C2211yescharacteristic
197#2396C2211yescharacteristic
198#2373C2214yes—
199#2373C2214yes—
200#2371C2214yes—
201#2370C2212yes—
202#2370C2212yes—
203#2370C2214yes—
204#2365C2212yes—
205#2365C2212yes—
206#2362C2212yes—
207#2362C2212yes—
208#2360C2212yes—
209#2360C2212yes—
210#2356C2214yes—
211#2355C2214yes—
212#2343C2214yes—
213#2343C2214yes—
214#2336C2214yes—
215#2336C2214yes—
216#2336C2214yes—
217#2334C2214yes—
218#2330C2214yes—
219#2329C2214yes—
220#2327C2212yes—
221#2327C2211yescharacteristic
222#2327C2212yes—
223#2327C2211yescharacteristic
224#2320C2212yes—
225#2320C2212yes—
226#2320C2212yes—
227#2317C2211yescharacteristic
228#2310C2211yescharacteristic
229C4×C4⋊Q8C2212yes—
230C4×C4⋊Q8C2212yes—
231C4×C4⋊Q8C2212yes—
232C4×#125C2212yes—
233C4×#125C2214yes—
234C4×#125C2214yes—
235C4×#126C2214yes—
236C4×C22⋊Q8C2212yes—
237#2298C2212yes—
238#2296C2211yescharacteristic
239#2295C2211yescharacteristic
240#2295C2212yes—
241#2295C2212yes—
242#2295C2212yes—
243#2295C2212yes—
244#2295C2214yes—
245C2×#391C2211yescharacteristic
246#2276C2212yes—
247#2274C2211yescharacteristic
248C42×Q8C2211yescharacteristic
249C42×Q8C2212yes—
250C4×#117C2211yescharacteristic
251C23×Q8C2311yescharacteristic
252#541—216no—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2312yes—
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2312yes—
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2311yescharacteristic
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#125C2312yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2312yes—
267C2×#125C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271#519—28no—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×#117C2311yescharacteristic
286C2×#117C2314yes—
287C2×#117C2311yescharacteristic
288C2×#117C2311yescharacteristic
289C2×#117C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C42C2311yescharacteristic
292#401C2314yes—
293#401C2314yes—
294#401C2314yes—
295#401C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2311yescharacteristic
309#400C2311yescharacteristic
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
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#400C2314yes—
336#399C2311yescharacteristic
337#399C2311yescharacteristic
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2312yes—
345#398C2312yes—
346#398C2312yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#397C2312yes—
381#397C2314yes—
382#397C2312yes—
383#397C2314yes—
384#397C2312yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#396C2312yes—
389#396C2312yes—
390#395C2312yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2311yescharacteristic
396#395C2311yescharacteristic
397#395C2312yes—
398#395C2314yes—
399#395C2314yes—
400#395C2312yes—
401#395C2312yes—
402#393C2311yescharacteristic
403#393C2311yescharacteristic
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#391C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#388C2312yes—
484#388C2314yes—
485#388C2314yes—
486#388C2312yes—
487#388C2312yes—
488#388C2314yes—
489#388C2314yes—
490#388C2312yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2312yes—
495#387C2312yes—
496#387C2314yes—
497#387C2314yes—
498#387C2312yes—
499#387C2314yes—
500#387C2314yes—
501#387C2312yes—
502#387C2314yes—
503#387C2314yes—
504#387C2312yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2312yes—
514#387C2312yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2312yes—
548#387C2314yes—
549#387C2314yes—
550#387C2312yes—
551#387C2314yes—
552#387C2312yes—
553#387C2312yes—
554#387C2314yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2314yes—
562#387C2312yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
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#387C2312yes—
586#387C2312yes—
587#385C2312yes—
588#385C2312yes—
589#385C2312yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2312yes—
598#384C2312yes—
599#384C2312yes—
600#384C2312yes—
601#384C2312yes—
602#384C2314yes—
603#384C2314yes—
604#383C2314yes—
605#383C2314yes—
606#383C2314yes—
607#383C2314yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#382C2314yes—
612#382C2312yes—
613#382C2314yes—
614#382C2312yes—
615#382C2312yes—
616#382C2314yes—
617#382C2314yes—
618#382C2314yes—
619#382C2311yescharacteristic
620#382C2311yescharacteristic
621#382C2314yes—
622#382C2312yes—
623#382C2314yes—
624#382C2314yes—
625#381C2312yes—
626#381C2312yes—
627#380C2312yes—
628#380C2314yes—
629#380C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680#376C2311yescharacteristic
681#376C2311yescharacteristic
682#376C2312yes—
683#376C2314yes—
684#376C2314yes—
685#376C2314yes—
686#376C2314yes—
687C2×#95C2314yes—
688C43C2314yes—
689C43C2311yescharacteristic
690C43C2311yescharacteristic
691C43C2312yes—
692C22×Q8—24no—
693C22×Q8—42no—
694C22×Q8—42no—
695C22×Q8C2412yes—
696C22×Q8C2412yes—
697C22×Q8C2412yes—
698C22×Q8C2411yescharacteristic
699C22×Q8C2412yes—
700C22×Q8C2412yes—
701C22×Q8C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2412yes—
706C4⋊Q8—28no—
707C4⋊Q8—44no—
708C4⋊Q8—42no—
709C4⋊Q8—42no—
710C4⋊Q8—44no—
711C4⋊Q8—44no—
712C4⋊Q8—44no—
713C4⋊Q8—44no—
714#126—216no—
715#126—216no—
716#125—216no—
717#125—216no—
718#125—28no—
719#125—216no—
720#125—28no—
721C22⋊Q8—28no—
722C22⋊Q8—28no—
723C22⋊Q8—28no—
724C4×Q8—216no—
725C4×Q8—28no—
726C4×Q8—28no—
727C4×Q8—28no—
728C4×Q8—28no—
729C4×Q8—28no—
730C4×Q8—44no—
731C4×Q8—42no—
732C4×Q8—42no—
733C4×Q8—44no—
734C4×Q8—44no—
735C4×Q8—44no—
736C4×Q8—44no—
737#117—24no—
738#117—216no—
739#117—42no—
740#117—42no—
741#117#4118yes—
742C2×C4⋊C4—42no—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2411yescharacteristic
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C42—42no—
829C2×C42C2411yescharacteristic
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2412yes—
833C2×C42C2411yescharacteristic
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2411yescharacteristic
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2414yes—
846C2×C42C2411yescharacteristic
847C2×C42C2412yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2412yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2414yes—
876#95C2412yes—
877#95C2412yes—
878#95C2414yes—
879#95C2412yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2412yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2414yes—
899#95C2411yescharacteristic
900#95C2412yes—
901#95C2412yes—
902#95C2414yes—
903#95C2411yescharacteristic
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2414yes—
918#95C2411yescharacteristic
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2411yescharacteristic
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956C24C2511yescharacteristic
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—24no—
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—24no—
968C2×Q8—24no—
969C2×Q8—41no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—42no—
973C2×Q8—41no—
974C2×Q8—42no—
975C2×Q8—42no—
976C2×Q8—416no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—44no—
987C22×C4C2×#4114yes—
988C22×C4C2511yescharacteristic
989C22×C4C2512yes—
990C22×C4C2511yescharacteristic
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2514yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2514yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2512yes—
1002C22×C4C2514yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2512yes—
1005C22×C4C2514yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2511yescharacteristic
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—24no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—41no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—41no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4C2×#4118yes—
1087C4⋊C42−1+418yes—
1088C22⋊C4—24no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—24no—
1092C22⋊C4—24no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—42no—
1098C22⋊C4C2×#4118yes—
1099C42—24no—
1100C42—28no—
1101C42—28no—
1102C42—28no—
1103C42—28no—
1104C42—24no—
1105C42—24no—
1106C42—24no—
1107C42—24no—
1108C42—28no—
1109C42—22no—
1110C42—22no—
1111C42—22no—
1112C42—22no—
1113C42—24no—
1114C42—24no—
1115C42—24no—
1116C42—24no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—44no—
1121C42—42no—
1122C42—42no—
1123C42—44no—
1124C42—44no—
1125C42—44no—
1126C42—44no—
1127C42—42no—
1128C42—44no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42C2×#4114yes—
1133C42C2×#4114yes—
1134C23—22no—
1135C23—21no—
1136C23—21no—
1137C23—22no—
1138C23C22×#4112yes—
1139C23C2611yescharacteristic
1140Q8—44no—
1141Q8—48no—
1142Q8—48no—
1143Q8—48no—
1144Q8—48no—
1145Q8—84no—
1146Q8—82no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—28no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—48no—
1214C2×C4—84no—
1215C2×C4—162no—
1216C2×C4C22×#4114yes—
1217C2×C4C22×#4114yes—
1218C2×C4C22×#4112yes—
1219C2×C4C22×#4112yes—
1220C2×C4C2×2−1+414yes—
1221C2×C4C2×2−1+414yes—
1222C2×C4C2×2−1+414yes—
1223C2×C4#58512yes—
1224C2×C4#58512yes—
1225C22—24no—
1226C22—22no—
1227C22—41no—
1228C22—41no—
1229C22—42no—
1230C22C23×#4111yescharacteristic
1231C22C22×2−1+412yes—
1232C22C2×#58511yescharacteristic
1233C22C2×#58511yescharacteristic
1234C222−1+612yes—
1235C4—24no—
1236C4—24no—
1237C4—24no—
1238C4—22no—
1239C4—24no—
1240C4—24no—
1241C4—44no—
1242C4—44no—
1243C4—44no—
1244C4—41no—
1245C4—42no—
1246C4—41no—
1247C4—41no—
1248C4—42no—
1249C4—44no—
1250C4—41no—
1251C4—42no—
1252C4—44no—
1253C4—44no—
1254C4—44no—
1255C4—42no—
1256C4—44no—
1257C4—42no—
1258C4—42no—
1259C4—42no—
1260C4#345514yes—
1261C2—42no—
1262C2C2×#345511yescharacteristic
1263C2#6283711yescharacteristic
1264C2#6289111yescharacteristic
1265C2#6295012yes—
1266C2#6300112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #42701C2semidirect
4. #42701C2semidirect
7. #41584C2semidirect
9. #41547C2semidirect
13. #40024C2semidirect
14. #39647C2semidirect
15. #39641C2semidirect
18. #38614C2semidirect
20. #35656C2semidirect
21. #35656C2semidirect
23. #35187C2semidirect
24. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#429412
#427012
#426972
#426952
#415842
#415772
#415472
#415362
#400622
#400282
#400242
#396472
#396412
#396402
#386202
#386142
#356702
#356562
#353192
#351872
#349512
#348822
#342862
#342542