Finite Group Databasebeta

← #7720024

Subgroups — #7720024

Order 512.

4269 conjugacy classes of subgroups.

The subgroup lattice has 1415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51619C214yesmaximal, complemented
2#51618C214yesmaximal, complemented
3#51511C214yesmaximal, complemented
4#51429C214yesmaximal, complemented
5#44795C214yesmaximal, complemented
6#44786C214yesmaximal
7#43600C214yesmaximal, complemented
8#43598C214yesmaximal
9#39695C212yesmaximal, complemented
10#39296C212yesmaximal, complemented
11#38277C212yesmaximal, complemented
12#38069C212yesmaximal, complemented
13#37985C212yesmaximal, complemented
14#37853C212yesmaximal
15#37434C211yesmaximal, characteristic, complemented
16#37433C211yesmaximal, characteristic, complemented
17#37397C211yesmaximal, characteristic, complemented
18#37396C211yesmaximal, characteristic, complemented
19#36307C212yesmaximal, complemented
20#36167C212yesmaximal
21#35344C211yesmaximal, characteristic, complemented
22#35337C211yesmaximal, characteristic, complemented
23#35325C211yesmaximal, characteristic
24#35324C211yesmaximal, characteristic, complemented
25#35320C211yesmaximal, characteristic, complemented
26#35314C211yesmaximal, characteristic, complemented
27#35132C211yesmaximal, characteristic, complemented
28C2×#2628C211yesmaximal, characteristic
29#34399C211yesmaximal, characteristic, complemented
30#34365C211yesmaximal, characteristic, complemented
31#34109C211yesmaximal, characteristic
32C2×#533C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#2864C2212yescomplemented
36#2864C2211yescharacteristic, complemented
37#2864C2211yescharacteristic, complemented
38#2863C2212yescomplemented
39#2862C2211yescharacteristic, complemented
40#2862C2211yescharacteristic, complemented
41#2862C2211yescharacteristic, complemented
42#2862C2211yescharacteristic, complemented
43#2862C2211yescharacteristic, complemented
44#2859C2211yescharacteristic, complemented
45#2855C2212yes—
46#2855C2212yes—
47#2851C2212yes—
48#2848C2212yes—
49#2810C2214yescomplemented
50#2807C2214yes—
51#2805C2214yescomplemented
52#2799C2214yescomplemented
53#2798C2214yes—
54#2798C2214yes—
55#2798C2214yes—
56#2798C2214yes—
57#2789C2214yescomplemented
58#2789C2214yescomplemented
59#2776C2214yescomplemented
60#2776C2214yescomplemented
61#2774C2214yescomplemented
62#2773C2214yes—
63#2773C2214yes—
64#2771C2214yes—
65#2767C2214yescomplemented
66#2767C2214yescomplemented
67#2766C2214yescomplemented
68#2764C2214yes—
69#2763C2214yes—
70#2762C2214yescomplemented
71#2762C2214yescomplemented
72#2762C2214yescomplemented
73#2759C2214yes—
74#2759C2214yes—
75#2758C2214yescomplemented
76#2758C2214yescomplemented
77#2758C2214yescomplemented
78#2758C2214yescomplemented
79#2755C2214yescomplemented
80#2755C2214yescomplemented
81#2754C2214yes—
82#2754C2214yes—
83#2754C2214yes—
84#2754C2214yes—
85#2747C2214yes—
86#2745C2214yes—
87#2742C2214yes—
88#2738C2214yes—
89#2666C2214yescomplemented
90#2647C2212yescomplemented
91#2645C2212yescomplemented
92#2642C2214yescomplemented
93#2628C2211yescharacteristic
94#2628C2211yescharacteristic
95#2628C2212yes—
96#2628C2212yes—
97#2628C2211yescharacteristic
98#2628C2211yescharacteristic
99#2628C2211yescharacteristic
100#2628C2212yes—
101#2628C2212yes—
102#2628C2212yes—
103#2628C2212yes—
104#2628C2212yes—
105#2628C2211yescharacteristic
106#2625C2212yes—
107#2621C2211yescharacteristic
108#2621C2211yescharacteristic
109#2612C2214yescomplemented
110#2612C2214yescomplemented
111#2611C2212yes—
112#2611C2212yes—
113#2607C2214yes—
114#2607C2214yes—
115#2605C2214yescomplemented
116#2605C2214yescomplemented
117#2605C2214yescomplemented
118#2599C2212yes—
119#2599C2212yes—
120#2596C2214yes—
121#2596C2214yes—
122#2590C2214yescomplemented
123#2589C2214yes—
124#2589C2214yes—
125#2589C2214yes—
126#2589C2214yes—
127#2588C2214yescomplemented
128#2588C2214yescomplemented
129#2588C2214yescomplemented
130#2586C2214yescomplemented
131#2583C2212yes—
132#2577C2214yes—
133#2575C2214yes—
134#2575C2214yes—
135#2570C2212yescomplemented
136#2568C2212yescomplemented
137#2568C2214yescomplemented
138#2568C2212yescomplemented
139#2561C2212yes—
140#2561C2214yes—
141#2550C2212yescomplemented
142#2533C2214yescomplemented
143#2533C2214yescomplemented
144#2533C2214yescomplemented
145#2533C2214yescomplemented
146#2532C2214yes—
147#2532C2214yes—
148#2530C2214yes—
149#2528C2214yescomplemented
150#2528C2214yescomplemented
151#2527C2214yes—
152#2527C2214yes—
153#2524C2214yescomplemented
154#2523C2214yes—
155#2520C2214yescomplemented
156#2520C2214yescomplemented
157#2517C2214yes—
158#2514C2212yescomplemented
159#2514C2214yescomplemented
160#2511C2212yescomplemented
161#2509C2212yescomplemented
162#2509C2214yescomplemented
163#2509C2212yescomplemented
164#2508C2212yescomplemented
165#2508C2212yescomplemented
166#2505C2214yes—
167#2503C2212yes—
168#2503C2214yes—
169#2503C2214yes—
170#2503C2212yes—
171#2495C2212yes—
172#2495C2212yes—
173#2494C2212yes—
174#2494C2212yes—
175#2493C2214yes—
176#2493C2214yes—
177#2493C2214yes—
178#2493C2214yes—
179#2493C2214yes—
180#2492C2212yes—
181#2489C2212yes—
182#2484C2214yes—
183#2484C2214yes—
184#2484C2212yes—
185#2483C2214yes—
186#2482C2214yes—
187#2482C2212yes—
188#2453C2212yescomplemented
189#2451C2212yescomplemented
190#2442C2212yes—
191#2440C2212yes—
192#2438C2214yes—
193#2438C2214yes—
194#2438C2214yes—
195#2423C2212yes—
196#2421C2212yes—
197C2×#400C2212yes—
198C2×#399C2212yes—
199C2×#395C2212yes—
200C2×#393C2212yes—
201#2382C2214yescomplemented
202#2381C2214yescomplemented
203#2369C2212yescomplemented
204#2369C2212yescomplemented
205#2360C2212yes—
206#2360C2212yes—
207#2356C2212yescomplemented
208#2351C2212yescomplemented
209#2347C2212yes—
210#2346C2212yes—
211#2345C2212yes—
212#2344C2212yes—
213#2344C2212yes—
214#2344C2214yes—
215#2344C2212yes—
216#2344C2214yes—
217#2343C2212yes—
218#2343C2212yes—
219#2343C2214yes—
220#2343C2214yes—
221#2343C2214yes—
222#2342C2212yes—
223#2342C2212yes—
224#2342C2214yes—
225#2331C2211yescharacteristic, complemented
226#2331C2211yescharacteristic, complemented
227#2331C2211yescharacteristic, complemented
228#2331C2211yescharacteristic, complemented
229#2331C2212yescomplemented
230#2331C2211yescharacteristic, complemented
231#2331C2211yescharacteristic, complemented
232#2331C2214yescomplemented
233#2329C2214yes—
234#2329C2214yes—
235#2327C2211yescharacteristic, complemented
236#2327C2211yescharacteristic, complemented
237#2323C2212yes—
238#2323C2212yes—
239#2323C2212yes—
240#2320C2214yescomplemented
241#2320C2212yescomplemented
242#2314C2212yes—
243#2310C2214yes—
244#2310C2214yes—
245C4×#125C2212yescomplemented
246C4×C22⋊Q8C2212yes—
247#2298C2211yescharacteristic
248#2298C2211yescharacteristic
249#2298C2211yescharacteristic
250#2298C2211yescharacteristic
251#2296C2211yescharacteristic
252#2296C2211yescharacteristic
253#2295C2212yescomplemented
254C2×#389C2212yes—
255#2283C2212yes—
256#2283C2211yescharacteristic
257#2283C2211yescharacteristic
258#2283C2211yescharacteristic
259C2×#382C2211yescharacteristic
260#2280C2211yescharacteristic
261C2×#380C2212yes—
262C4×#117C2211yescharacteristic
263C4×#117C2211yescharacteristic
264C4×#117C2211yescharacteristic
265C4×#117C2211yescharacteristic
266C2×C4×C22⋊C4C2211yescharacteristic
267C23×Q8C2312yes—
268C24×C4C2311yescharacteristic
269#533—28no—
270C2×C4⋊Q8—28no—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×#117—28no—
291C2×#117C2312yes—
292C2×#117C2311yescharacteristic
293C2×#117C2311yescharacteristic
294C2×#117C2311yescharacteristic
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2314yes—
303C2×#117C2314yes—
304C2×#117C2311yescharacteristic
305C2×#117C2312yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2314yes—
311C22×C4⋊C4C2312yes—
312C22×C22⋊C4C2311yescharacteristic
313C22×C22⋊C4C2311yescharacteristic
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2312yes—
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320#401C2314yes—
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
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#400C2312yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#399C2312yes—
365#399C2314yes—
366#399C2312yes—
367#399C2314yes—
368#399C2314yes—
369#399C2312yes—
370#399C2312yes—
371#399C2312yes—
372#399C2312yes—
373#399C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2312yes—
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#397C2312yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2312yes—
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#395C2312yes—
403#395C2312yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2312yes—
408#395C2312yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#395C2312yes—
413#395C2314yes—
414#393C2312yes—
415#393C2314yes—
416#393C2312yes—
417#393C2314yes—
418#393C2312yes—
419#393C2314yes—
420#393C2312yes—
421#393C2312yes—
422#393C2314yes—
423#393C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2312yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2312yes—
509#388C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2312yes—
518#388C2312yes—
519#388C2314yes—
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#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
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#385C2312yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2312yes—
604#385C2312yes—
605#385C2314yes—
606#385C2312yes—
607#385C2314yes—
608#384C2312yes—
609#383C2312yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#383C2312yes—
614#383C2314yes—
615#383C2314yes—
616#383C2312yes—
617#383C2314yes—
618#383C2314yes—
619#382C2312yes—
620#382C2312yes—
621#382C2314yes—
622#382C2312yes—
623#382C2312yes—
624#382C2314yes—
625#382C2312yes—
626#382C2312yes—
627#382C2314yes—
628#382C2312yes—
629#382C2314yes—
630#382C2314yes—
631#382C2311yescharacteristic
632#382C2311yescharacteristic
633#382C2312yes—
634#382C2311yescharacteristic
635#382C2311yescharacteristic
636#382C2312yes—
637#382C2314yes—
638#382C2314yes—
639#382C2312yes—
640#381C2314yes—
641#381C2314yes—
642#381C2314yes—
643#381C2312yes—
644#381C2312yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2312yes—
651#381C2312yes—
652#381C2314yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#379C2314yes—
668#379C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2311yescharacteristic
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2311yescharacteristic
712C4×C22⋊C4C2311yescharacteristic
713C4×C22⋊C4C2311yescharacteristic
714C4×C22⋊C4C2311yescharacteristic
715C4×C22⋊C4C2311yescharacteristic
716C4×C22⋊C4C2311yescharacteristic
717C4×C22⋊C4C2311yescharacteristic
718#376C2311yescharacteristic
719#376C2314yes—
720#376C2311yescharacteristic
721#376C2311yescharacteristic
722#376C2312yes—
723#376C2311yescharacteristic
724#376C2312yes—
725#376C2312yes—
726#376C2314yes—
727#376C2314yes—
728C2×#95C2312yes—
729C2×#95C2312yes—
730C2×#95C2312yes—
731C2×#95C2314yes—
732C2×#95C2314yes—
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C25C2411yescharacteristic
738C22×Q8—28no—
739C22×Q8—48no—
740C22×Q8C2412yes—
741C22×Q8C2412yes—
742C22×Q8C2414yes—
743C22×Q8C2412yes—
744C22×Q8C2412yes—
745C22×Q8C2414yes—
746C23×C4—24no—
747C23×C4—24no—
748C23×C4—42no—
749C23×C4C2411yescharacteristic
750C23×C4C2414yes—
751C23×C4C2411yescharacteristic
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2411yescharacteristic
755C23×C4C2411yescharacteristic
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C23×C4C2414yes—
759C23×C4C2411yescharacteristic
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2411yescharacteristic
763C4⋊Q8—28no—
764C4⋊Q8—28no—
765C4⋊Q8—28no—
766C4⋊Q8—24no—
767C4⋊Q8—24no—
768C4⋊Q8—24no—
769C4⋊Q8—24no—
770C4⋊Q8—44no—
771#125—28no—
772#125—44no—
773C22⋊Q8—28no—
774C22⋊Q8—28no—
775C22⋊Q8—28no—
776C22⋊Q8—48no—
777C22⋊Q8—44no—
778C4×Q8—28no—
779C4×Q8—28no—
780C4×Q8—44no—
781C4×Q8—44no—
782#117—28no—
783#117—24no—
784#117—24no—
785#117—24no—
786#117—24no—
787#117—24no—
788#117—24no—
789#117—24no—
790#117—24no—
791#117—24no—
792#117—42no—
793#117—44no—
794#117—48no—
795#117—44no—
796#117—48no—
797C2×C4⋊C4—24no—
798C2×C4⋊C4—24no—
799C2×C4⋊C4—28no—
800C2×C4⋊C4—28no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4—48no—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C22⋊C4—24no—
864C2×C22⋊C4—24no—
865C2×C22⋊C4—44no—
866C2×C22⋊C4—48no—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2411yescharacteristic
870C2×C22⋊C4C2411yescharacteristic
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2411yescharacteristic
876C2×C22⋊C4C2411yescharacteristic
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C42—24no—
896C2×C42—24no—
897C2×C42—42no—
898C2×C42#4118yes—
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2414yes—
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025C24—22no—
1026C24—22no—
1027C24—24no—
1028C24—41no—
1029C24—42no—
1030C24C2511yescharacteristic
1031C24C2511yescharacteristic
1032C24C2511yescharacteristic
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—28no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—44no—
1041C2×Q8—44no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—44no—
1045C2×Q8—44no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×Q8—816no—
1049C22×C4—24no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—22no—
1056C22×C4—28no—
1057C22×C4—22no—
1058C22×C4—28no—
1059C22×C4—24no—
1060C22×C4—28no—
1061C22×C4—22no—
1062C22×C4—24no—
1063C22×C4—28no—
1064C22×C4—22no—
1065C22×C4—22no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—41no—
1074C22×C4—42no—
1075C22×C4—416no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4C2×#4114yes—
1085C22×C4C2×#4114yes—
1086C22×C4C2×#4114yes—
1087C22×C42−1+414yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2514yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—22no—
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—22no—
1122C4⋊C4—22no—
1123C4⋊C4—22no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—28no—
1183C22⋊C4—24no—
1184C22⋊C4—22no—
1185C22⋊C4—22no—
1186C22⋊C4—22no—
1187C22⋊C4—22no—
1188C22⋊C4—22no—
1189C22⋊C4—22no—
1190C22⋊C4—22no—
1191C22⋊C4—22no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C42—22no—
1205C42—22no—
1206C42—22no—
1207C42—22no—
1208C42—28no—
1209C42—24no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—22no—
1216C42—22no—
1217C42—22no—
1218C42—42no—
1219C42—44no—
1220C42—42no—
1221C42—42no—
1222C42—42no—
1223C42—44no—
1224C42—42no—
1225C42—44no—
1226C42—42no—
1227C42—42no—
1228C42—42no—
1229C42—42no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42C2×#4114yes—
1237C42C2×#4114yes—
1238C42C2×#4114yes—
1239C42C2×#4114yes—
1240C23—21no—
1241C23—21no—
1242C23—22no—
1243C23—21no—
1244C23—22no—
1245C23—21no—
1246C23—22no—
1247C23—21no—
1248C23—21no—
1249C23—22no—
1250C23—21no—
1251C23—22no—
1252C23—44no—
1253C23—48no—
1254C23—44no—
1255C23—82no—
1256C23—84no—
1257C23C22×#4112yes—
1258C23C2×2−1+412yes—
1259C23#58514yes—
1260C23C2611yescharacteristic
1261Q8—48no—
1262Q8—84no—
1263Q8—84no—
1264Q8—84no—
1265Q8—88no—
1266Q8—164no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—28no—
1276C2×C4—28no—
1277C2×C4—28no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—21no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—44no—
1338C2×C4—44no—
1339C2×C4—44no—
1340C2×C4—44no—
1341C2×C4—44no—
1342C2×C4—416no—
1343C2×C4—44no—
1344C2×C4—82no—
1345C2×C4—84no—
1346C2×C4—88no—
1347C2×C4—84no—
1348C2×C4C22×#4112yes—
1349C2×C4C22×#4112yes—
1350C2×C4C22×#4112yes—
1351C2×C4C22×#4112yes—
1352C2×C4C22×#4112yes—
1353C2×C4C22×#4112yes—
1354C2×C4C2×2−1+412yes—
1355C2×C4C2×2−1+412yes—
1356C2×C4#58512yes—
1357C22—22no—
1358C22—22no—
1359C22—24no—
1360C22—24no—
1361C22—22no—
1362C22—24no—
1363C22—41no—
1364C22—41no—
1365C22—42no—
1366C22—41no—
1367C22—41no—
1368C22—41no—
1369C22—42no—
1370C22—42no—
1371C22—88no—
1372C22#351014yes—
1373C22C23×#4111yescharacteristic
1374C22C22×2−1+411yescharacteristic
1375C22C2×#58511yescharacteristic
1376C22C2×#58512yes—
1377C222−1+612yes—
1378C4—22no—
1379C4—22no—
1380C4—22no—
1381C4—22no—
1382C4—22no—
1383C4—22no—
1384C4—41no—
1385C4—44no—
1386C4—41no—
1387C4—41no—
1388C4—44no—
1389C4—44no—
1390C4—41no—
1391C4—41no—
1392C4—44no—
1393C4—42no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—44no—
1402C4—44no—
1403C4—44no—
1404C4—42no—
1405C4#349514yes—
1406C2—24no—
1407C2—42no—
1408C2—81no—
1409C2C2×#349511yescharacteristic
1410C2C2×#351011yescharacteristic
1411C2#6286011yescharacteristic
1412C2#6292812yes—
1413C2#6294012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51619C2semidirect
2. #51618C2semidirect
3. #51511C2semidirect
4. #51429C2semidirect
5. #44795C2semidirect
7. #43600C2semidirect
9. #39695C2semidirect
10. #39296C2semidirect
11. #38277C2semidirect
12. #38069C2semidirect
13. #37985C2semidirect
15. #37434C2semidirect
16. #37433C2semidirect
17. #37397C2semidirect
18. #37396C2semidirect
19. #36307C2semidirect
21. #35344C2semidirect
22. #35337C2semidirect
24. #35324C2semidirect
25. #35320C2semidirect
26. #35314C2semidirect
27. #35132C2semidirect
29. #34399C2semidirect
30. #34365C2semidirect
35. #2864C22semidirect
36. #2864C22semidirect
37. #2864C22semidirect
38. #2863C22semidirect
39. #2862C22semidirect
40. #2862C22semidirect
41. #2862C22semidirect
42. #2862C22semidirect
43. #2862C22semidirect
44. #2859C22semidirect
49. #2810C22semidirect
51. #2805C22semidirect
52. #2799C22semidirect
57. #2789C22semidirect
58. #2789C22semidirect
59. #2776C22semidirect
60. #2776C22semidirect
61. #2774C22semidirect
65. #2767C22semidirect
66. #2767C22semidirect
67. #2766C22semidirect
70. #2762C22semidirect
71. #2762C22semidirect
72. #2762C22semidirect
75. #2758C22semidirect
76. #2758C22semidirect
77. #2758C22semidirect
78. #2758C22semidirect
79. #2755C22semidirect
80. #2755C22semidirect
89. #2666C22semidirect
90. #2647C22semidirect
91. #2645C22semidirect
92. #2642C22semidirect
109. #2612C22semidirect
110. #2612C22semidirect
115. #2605C22semidirect
116. #2605C22semidirect
117. #2605C22semidirect
122. #2590C22semidirect
127. #2588C22semidirect
128. #2588C22semidirect
129. #2588C22semidirect
130. #2586C22semidirect
135. #2570C22semidirect
136. #2568C22semidirect
137. #2568C22semidirect
138. #2568C22semidirect
141. #2550C22semidirect
142. #2533C22semidirect
143. #2533C22semidirect
144. #2533C22semidirect
145. #2533C22semidirect
149. #2528C22semidirect
150. #2528C22semidirect
153. #2524C22semidirect
155. #2520C22semidirect
156. #2520C22semidirect
158. #2514C22semidirect
159. #2514C22semidirect
160. #2511C22semidirect
161. #2509C22semidirect
162. #2509C22semidirect
163. #2509C22semidirect
164. #2508C22semidirect
165. #2508C22semidirect
188. #2453C22semidirect
189. #2451C22semidirect
201. #2382C22semidirect
202. #2381C22semidirect
203. #2369C22semidirect
204. #2369C22semidirect
207. #2356C22semidirect
208. #2351C22semidirect
225. #2331C22semidirect
226. #2331C22semidirect
227. #2331C22semidirect
228. #2331C22semidirect
229. #2331C22semidirect
230. #2331C22semidirect
231. #2331C22semidirect
232. #2331C22semidirect
235. #2327C22semidirect
236. #2327C22semidirect
240. #2320C22semidirect
241. #2320C22semidirect
245. C4×#125C22semidirect
253. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#516192
#516182
#515112
#514292
#447952
#447862
#436002
#435982
#396952
#392962
#382772
#380692
#379852
#378532
#374342
#374332
#373972
#373962
#363072
#361672
#353442
#353372
#353252
#353242
#353202
#353142
#351322
C2×#26282
#343992
#343652
#341092