Finite Group Databasebeta

← #7655469

Subgroups — #7655469

Order 512.

4308 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#42497C212yesmaximal, complemented
2#42493C212yesmaximal, complemented
3#42184C214yesmaximal, complemented
4#42001C214yesmaximal, complemented
5#39984C212yesmaximal
6#39980C212yesmaximal
7#39978C212yesmaximal, complemented
8#39975C212yesmaximal, complemented
9#39967C214yesmaximal, complemented
10#39964C214yesmaximal, complemented
11#38458C214yesmaximal, complemented
12#38456C214yesmaximal, complemented
13#37567C211yesmaximal, characteristic, complemented
14#37566C212yesmaximal, complemented
15#36479C212yesmaximal, complemented
16#36476C212yesmaximal, complemented
17#36288C212yesmaximal, complemented
18#36284C212yesmaximal, complemented
19#35958C212yesmaximal, complemented
20#35867C212yesmaximal, complemented
21#35344C212yesmaximal, complemented
22#35192C211yesmaximal, characteristic, complemented
23#35120C212yesmaximal, complemented
24#35104C211yesmaximal, characteristic, complemented
25#34966C211yesmaximal, characteristic, complemented
26#34878C212yesmaximal, complemented
27#34197C211yesmaximal, characteristic
28#34123C211yesmaximal, characteristic
29#34121C211yesmaximal, characteristic
30C2×C4×#41C2211yescharacteristic
31#2864C2214yes—
32#2864C2212yes—
33#2862C2214yes—
34#2862C2212yes—
35#2857C2212yes—
36#2855C2214yes—
37#2855C2214yes—
38#2851C2212yes—
39#2841C2214yes—
40#2841C2214yes—
41#2841C2214yes—
42#2807C2214yes—
43#2806C2214yes—
44#2804C2214yes—
45#2802C2214yes—
46#2791C2214yes—
47#2784C2214yes—
48#2780C2214yes—
49#2774C2214yes—
50#2768C2214yes—
51#2768C2214yes—
52#2763C2214yes—
53#2755C2214yes—
54#2755C2214yes—
55#2748C2214yes—
56#2742C2214yes—
57#2734C2214yes—
58#2732C2214yes—
59#2729C2214yes—
60#2729C2214yes—
61#2713C2214yes—
62#2692C2214yes—
63#2692C2214yes—
64#2692C2214yes—
65#2677C2214yes—
66#2667C2212yes—
67#2667C2214yes—
68#2666C2214yes—
69#2666C2214yes—
70#2666C2214yes—
71#2666C2214yes—
72#2666C2214yes—
73#2665C2212yes—
74#2665C2212yes—
75#2665C2214yes—
76#2665C2212yes—
77#2660C2212yes—
78#2659C2214yes—
79#2647C2212yes—
80#2646C2214yes—
81#2628C2214yes—
82#2628C2214yes—
83#2627C2214yes—
84#2612C2214yes—
85#2612C2214yes—
86#2612C2214yes—
87#2612C2214yes—
88#2612C2214yes—
89#2612C2214yes—
90#2612C2214yes—
91#2612C2214yes—
92#2608C2214yes—
93#2607C2214yes—
94#2607C2214yes—
95#2607C2214yes—
96#2607C2214yes—
97#2607C2214yes—
98#2606C2214yes—
99#2606C2212yes—
100#2606C2212yes—
101#2606C2211yescharacteristic
102#2606C2211yescharacteristic
103#2606C2212yes—
104#2605C2211yescharacteristic
105#2605C2214yes—
106#2605C2214yes—
107#2605C2212yes—
108#2605C2212yes—
109#2605C2212yes—
110#2605C2214yes—
111#2605C2212yes—
112#2605C2212yes—
113#2605C2211yescharacteristic
114#2590C2214yes—
115#2589C2214yes—
116#2589C2214yes—
117#2589C2214yes—
118#2588C2214yes—
119#2587C2214yes—
120#2586C2214yes—
121#2585C2214yes—
122#2584C2212yes—
123#2582C2212yes—
124#2581C2212yes—
125#2580C2212yes—
126#2580C2212yes—
127#2574C2214yes—
128#2574C2214yes—
129#2574C2214yes—
130#2571C2212yes—
131#2570C2212yes—
132#2570C2212yes—
133#2570C2212yes—
134#2570C2212yes—
135#2569C2214yes—
136#2568C2212yes—
137#2565C2212yes—
138#2563C2212yes—
139#2556C2214yes—
140#2551C2212yes—
141#2551C2212yes—
142#2550C2212yes—
143#2550C2212yes—
144#2550C2212yes—
145#2550C2212yes—
146#2550C2212yes—
147#2549C2214yes—
148#2546C2212yes—
149#2542C2212yes—
150#2522C2214yes—
151#2522C2214yes—
152#2520C2214yes—
153#2520C2214yes—
154#2509C2212yes—
155#2508C2212yes—
156#2508C2212yes—
157#2507C2212yes—
158#2492C2214yes—
159#2492C2214yes—
160#2465C2214yes—
161#2465C2214yes—
162#2454C2212yes—
163#2454C2212yes—
164#2453C2212yes—
165#2452C2212yes—
166#2452C2212yes—
167#2451C2214yes—
168#2451C2212yes—
169#2451C2212yes—
170#2451C2212yes—
171#2446C2214yes—
172#2442C2212yes—
173#2441C2212yes—
174#2440C2212yes—
175#2439C2214yes—
176#2439C2212yes—
177#2439C2212yes—
178#2439C2212yes—
179#2438C2214yes—
180#2438C2212yes—
181#2438C2212yes—
182#2438C2214yes—
183#2429C2214yes—
184#2423C2214yes—
185#2402C2212yes—
186#2402C2214yes—
187#2399C2214yes—
188#2399C2212yes—
189#2370C2212yes—
190#2370C2212yes—
191#2369C2212yes—
192#2369C2212yes—
193#2365C2212yes—
194#2365C2212yes—
195#2357C2212yes—
196#2357C2212yes—
197#2357C2212yes—
198#2357C2211yescharacteristic
199#2357C2211yescharacteristic
200#2356C2211yescharacteristic
201#2356C2212yes—
202#2356C2211yescharacteristic
203#2355C2212yes—
204#2355C2212yes—
205#2355C2212yes—
206#2354C2212yes—
207#2353C2212yes—
208#2353C2214yes—
209#2353C2212yes—
210#2352C2214yes—
211#2351C2211yescharacteristic
212#2351C2211yescharacteristic
213#2349C2211yescharacteristic
214#2349C2211yescharacteristic
215#2346C2214yes—
216#2346C2212yes—
217#2346C2212yes—
218#2343C2214yes—
219#2341C2212yes—
220#2339C2212yes—
221#2331C2214yes—
222#2331C2214yes—
223#2331C2214yes—
224#2329C2214yes—
225#2329C2214yes—
226#2329C2214yes—
227#2319C2212yes—
228#2319C2214yes—
229C4×C4⋊Q8C2212yes—
230C4×#125C2212yes—
231C4×C22⋊Q8C2214yes—
232C4×C22⋊Q8C2214yes—
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2212yes—
235#2298C2212yes—
236#2298C2212yes—
237#2297C2211yescharacteristic
238#2297C2211yescharacteristic
239#2295C2212yes—
240#2295C2214yes—
241#2295C2214yes—
242#2290C2214yes—
243#2285C2211yescharacteristic
244#2283C2212yes—
245#2283C2212yes—
246#2283C2211yescharacteristic
247#2283C2211yescharacteristic
248#2283C2212yes—
249#2283C2212yes—
250#2283C2211yescharacteristic
251#2276C2212yes—
252C42×D4C2212yes—
253C4×#117C2212yes—
254C4×#117C2211yescharacteristic
255C4×#117C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×#376C2212yes—
259C22×#41C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2314yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C4×#41Q8116yescomplemented
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2311yescharacteristic
293C2×#117C2314yes—
294C2×#117C2312yes—
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2312yes—
298C2×#117C2311yescharacteristic
299C22×C4⋊C4C2312yes—
300C22×C42C2311yescharacteristic
301C22×C42C2314yes—
302C22×C42C2311yescharacteristic
303C22×C42C2312yes—
304C22×C42C2311yescharacteristic
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2312yes—
311#400C2314yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2312yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2312yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2312yes—
360#398C2314yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2312yes—
379#395C2314yes—
380#395C2314yes—
381#395C2312yes—
382#395C2314yes—
383#395C2314yes—
384#395C2312yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2312yes—
391#395C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#390C2312yes—
437#390C2312yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#387C2312yes—
500#387C2312yes—
501#387C2312yes—
502#387C2312yes—
503#387C2314yes—
504#387C2314yes—
505#387C2312yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2312yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2312yes—
516#387C2312yes—
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#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2312yes—
562#385C2312yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2312yes—
571#385C2312yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#384C2312yes—
576#384C2312yes—
577#384C2312yes—
578#384C2312yes—
579#383C2312yes—
580#383C2311yescharacteristic
581#383C2312yes—
582#383C2312yes—
583#383C2312yes—
584#383C2311yescharacteristic
585#383C2314yes—
586#382C2312yes—
587#382C2312yes—
588#382C2312yes—
589#382C2312yes—
590#382C2312yes—
591#382C2311yescharacteristic
592#382C2311yescharacteristic
593#382C2312yes—
594#382C2312yes—
595#382C2314yes—
596#382C2314yes—
597#382C2314yes—
598#382C2314yes—
599#382C2314yes—
600#382C2311yescharacteristic
601#382C2311yescharacteristic
602#382C2312yes—
603#382C2312yes—
604#382C2314yes—
605#381C2314yes—
606#381C2312yes—
607#381C2312yes—
608#381C2314yes—
609#381C2312yes—
610#381C2312yes—
611#381C2314yes—
612#381C2311yescharacteristic
613#381C2311yescharacteristic
614#380C2314yes—
615#380C2314yes—
616#380C2314yes—
617#380C2314yes—
618#380C2314yes—
619#380C2312yes—
620#380C2314yes—
621#380C2314yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2314yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631C4×C4⋊C4C2311yescharacteristic
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2311yescharacteristic
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2311yescharacteristic
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2311yescharacteristic
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⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2311yescharacteristic
691C4×C22⋊C4C2311yescharacteristic
692#376C2314yes—
693#376C2312yes—
694#376C2312yes—
695#376C2314yes—
696#376C2314yes—
697#376C2314yes—
698#376C2311yescharacteristic
699#376C2311yescharacteristic
700#376C2312yes—
701#376C2314yes—
702#376C2312yes—
703#376C2312yes—
704#376C2312yes—
705#376C2312yes—
706C2×#95C2314yes—
707C2×#95C2312yes—
708C2×#95C2312yes—
709C2×#95C2312yes—
710C43C2312yes—
711C43C2312yes—
712C43C2312yes—
713C2×#41—42no—
714C2×#41—42no—
715C2×#41C2×Q818yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2414yes—
718C22×Q8C2414yes—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×D4C2411yescharacteristic
724C22×D4C2412yes—
725C23×C4C2411yescharacteristic
726C23×C4C2412yes—
727C23×C4C2414yes—
728C23×C4C2412yes—
729C23×C4C2414yes—
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C4⋊Q8—44no—
736C4⋊Q8—48no—
737C4⋊Q8—44no—
738C4⋊Q8—44no—
739C4⋊Q8—44no—
740C4⋊Q8—48no—
741C4⋊Q8—44no—
742C4⋊Q8—48no—
743#125—44no—
744#125—44no—
745#125—44no—
746C22⋊Q8—44no—
747C22⋊Q8—44no—
748C22⋊Q8—48no—
749C22⋊Q8—48no—
750C22⋊Q8—48no—
751C22⋊Q8—48no—
752C22⋊Q8—48no—
753C4×Q8—44no—
754C4×Q8—44no—
755C4×Q8—48no—
756C4×Q8—48no—
757C4×Q8—44no—
758C4×Q8—44no—
759C4×Q8C2×Q818yes—
760C4×Q8C2×Q818yes—
761C4×D4—44no—
762C4×D4—44no—
763C4×D4C2×Q818yes—
764C4×D4C2×Q818yes—
765C4×D4C2×Q8116yes—
766C4×D4C2×Q8116yes—
767#117—44no—
768#117—48no—
769#117—42no—
770#117—42no—
771#117C2×Q818yes—
772#117C2×Q8116yes—
773C2×C4⋊C4—44no—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C42—48no—
864C2×C42—42no—
865C2×C42—42no—
866C2×C42C2×Q818yes—
867C2×C42C2×Q8116yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2411yescharacteristic
891C2×C42C2411yescharacteristic
892C2×C42C2411yescharacteristic
893C2×C42C2414yes—
894C2×C42C2411yescharacteristic
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903#95C2412yes—
904#95C2411yescharacteristic
905#95C2411yescharacteristic
906#95C2412yes—
907#95C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2411yescharacteristic
921#95C2411yescharacteristic
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2411yescharacteristic
942#95C2412yes—
943#95C2411yescharacteristic
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2411yescharacteristic
954#95C2411yescharacteristic
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989C24C2511yescharacteristic
990C24C2512yes—
991#41—416no—
992C2×Q8—22no—
993C2×Q8—22no—
994C2×Q8—28no—
995C2×Q8—28no—
996C2×Q8—24no—
997C2×Q8—42no—
998C2×Q8—44no—
999C2×Q8—42no—
1000C2×Q8—42no—
1001C2×Q8—44no—
1002C2×Q8—42no—
1003C2×Q8—44no—
1004C2×Q8—44no—
1005C2×Q8—42no—
1006C2×Q8—44no—
1007C2×Q8—44no—
1008C2×Q8—44no—
1009C2×Q8—44no—
1010C2×Q8—44no—
1011C2×Q8—44no—
1012C2×Q8C22×Q814yes—
1013C2×D4—22no—
1014C2×D4—22no—
1015C2×D4—42no—
1016C2×D4—42no—
1017C2×D4C22×Q814yes—
1018C2×D4C22×Q818yes—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—28no—
1022C22×C4—24no—
1023C22×C4—44no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—44no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—44no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—44no—
1039C22×C4C22×Q814yes—
1040C22×C4C22×Q818yes—
1041C22×C4C22×Q814yes—
1042C22×C4C22×Q814yes—
1043C22×C4C22×Q818yes—
1044C22×C4C22×Q818yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
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—44no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4C22×Q818yes—
1137C4⋊C4C22×Q818yes—
1138C4⋊C4C22×Q814yes—
1139C4⋊C4C22×Q814yes—
1140C22⋊C4—28no—
1141C22⋊C4—24no—
1142C22⋊C4—42no—
1143C22⋊C4—44no—
1144C22⋊C4—42no—
1145C22⋊C4—42no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4C22×Q818yes—
1159C22⋊C4C22×Q818yes—
1160C22⋊C4C22×Q818yes—
1161C42—24no—
1162C42—28no—
1163C42—24no—
1164C42—24no—
1165C42—28no—
1166C42—24no—
1167C42—24no—
1168C42—24no—
1169C42—24no—
1170C42—44no—
1171C42—44no—
1172C42—41no—
1173C42—41no—
1174C42—41no—
1175C42—41no—
1176C42—42no—
1177C42—44no—
1178C42—42no—
1179C42—42no—
1180C42—44no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—42no—
1187C42—42no—
1188C42—44no—
1189C42C22×Q814yes—
1190C42C22×Q818yes—
1191C42C22×Q814yes—
1192C42C22×Q818yes—
1193C42C22×Q818yes—
1194C42C22×Q814yes—
1195C42C22×Q814yes—
1196C23—22no—
1197C23—24no—
1198C23—22no—
1199C23—24no—
1200C23—21no—
1201C23—22no—
1202C23—22no—
1203C23—21no—
1204C23C23×Q812yes—
1205C23C23×Q814yes—
1206C23C2611yescharacteristic
1207Q8—28no—
1208Q8—88no—
1209Q8—84no—
1210Q8—88no—
1211Q8—84no—
1212Q8—164no—
1213Q8—164no—
1214D4—28no—
1215D4—48no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—28no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—48no—
1280C2×C4—44no—
1281C2×C4—44no—
1282C2×C4—48no—
1283C2×C4—48no—
1284C2×C4—84no—
1285C2×C4—88no—
1286C2×C4—84no—
1287C2×C4—88no—
1288C2×C4C23×Q812yes—
1289C2×C4C23×Q812yes—
1290C2×C4C23×Q812yes—
1291C2×C4C23×Q814yes—
1292C2×C4C23×Q814yes—
1293C2×C4C23×Q812yes—
1294C2×C4C23×Q812yes—
1295C2×C4C23×Q814yes—
1296C2×C4C23×Q812yes—
1297C2×C4#58514yes—
1298C2×C4#58514yes—
1299C2×C4#58512yes—
1300C2×C4#58512yes—
1301C22—22no—
1302C22—24no—
1303C22—22no—
1304C22—24no—
1305C22—22no—
1306C22—24no—
1307C22—42no—
1308C22—44no—
1309C22—44no—
1310C22—42no—
1311C22C24×Q811yescharacteristic
1312C22C2×#58511yescharacteristic
1313C22C2×#58512yes—
1314C22C2×#58512yes—
1315C22C2×#58511yescharacteristic
1316C4—24no—
1317C4—24no—
1318C4—22no—
1319C4—22no—
1320C4—24no—
1321C4—24no—
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—24no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—44no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—44no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4#345814yes—
1343C2—42no—
1344C2—44no—
1345C2C2×#345811yescharacteristic
1346C2#6281311yescharacteristic
1347C2#6281311yescharacteristic
1348C2#6302812yes—
1349C2#6303012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42497C2semidirect
2. #42493C2semidirect
3. #42184C2semidirect
4. #42001C2semidirect
7. #39978C2semidirect
8. #39975C2semidirect
9. #39967C2semidirect
10. #39964C2semidirect
11. #38458C2semidirect
12. #38456C2semidirect
13. #37567C2semidirect
14. #37566C2semidirect
15. #36479C2semidirect
16. #36476C2semidirect
17. #36288C2semidirect
18. #36284C2semidirect
19. #35958C2semidirect
20. #35867C2semidirect
21. #35344C2semidirect
22. #35192C2semidirect
23. #35120C2semidirect
24. #35104C2semidirect
25. #34966C2semidirect
26. #34878C2semidirect
278. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#424972
#424932
#421842
#420012
#399842
#399802
#399782
#399752
#399672
#399642
#384582
#384562
#375672
#375662
#364792
#364762
#362882
#362842
#359582
#358672
#353442
#351922
#351202
#351042
#349662
#348782
#341972
#341232
#341212