Finite Group Databasebeta

← #7645085

Subgroups — #7645085

Order 512.

4468 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40637C214yesmaximal, complemented
2#40636C214yesmaximal, complemented
3#40633C214yesmaximal, complemented
4#40632C214yesmaximal, complemented
5#39967C214yesmaximal, complemented
6#39966C214yesmaximal, complemented
7#39965C214yesmaximal, complemented
8#39964C214yesmaximal, complemented
9#37609C212yesmaximal, complemented
10#37478C211yesmaximal, characteristic, complemented
11#37478C211yesmaximal, characteristic, complemented
12#37134C214yesmaximal
13#36750C212yesmaximal, complemented
14#36749C212yesmaximal, complemented
15#35402C214yesmaximal, complemented
16#35235C212yesmaximal, complemented
17#35079C211yesmaximal, characteristic, complemented
18#35079C211yesmaximal, characteristic, complemented
19#35065C212yesmaximal, complemented
20#35015C212yesmaximal, complemented
21#35013C212yesmaximal, complemented
22#34958C212yesmaximal, complemented
23#34185C211yesmaximal, characteristic
24C2×#2357C211yesmaximal, characteristic
25#34057C211yesmaximal, characteristic
26C22×C4×D4C2211yescharacteristic
27#2857C2212yes—
28#2857C2212yes—
29#2855C2214yes—
30#2855C2214yes—
31#2855C2214yescomplemented
32#2855C2214yescomplemented
33#2851C2212yes—
34#2851C2212yes—
35#2845C2214yescomplemented
36#2844C2214yescomplemented
37#2841C2214yescomplemented
38#2841C2214yescomplemented
39#2807C2214yescomplemented
40#2804C2214yes—
41#2790C2214yescomplemented
42#2790C2214yescomplemented
43#2788C2214yescomplemented
44#2788C2214yescomplemented
45#2784C2214yes—
46#2784C2214yes—
47#2780C2214yes—
48#2780C2214yes—
49#2780C2214yes—
50#2780C2214yes—
51#2768C2214yescomplemented
52#2768C2214yescomplemented
53#2763C2214yescomplemented
54#2748C2214yes—
55#2748C2214yes—
56#2742C2214yescomplemented
57#2732C2214yes—
58#2732C2214yes—
59#2729C2214yescomplemented
60#2729C2214yescomplemented
61#2720C2214yescomplemented
62#2720C2214yescomplemented
63#2704C2214yescomplemented
64#2704C2214yescomplemented
65#2692C2214yes—
66#2692C2214yes—
67#2692C2214yes—
68#2692C2214yes—
69#2683C2214yes—
70#2677C2214yescomplemented
71#2667C2212yescomplemented
72#2667C2212yescomplemented
73#2667C2212yescomplemented
74#2667C2212yescomplemented
75#2667C2214yescomplemented
76#2666C2214yescomplemented
77#2666C2214yescomplemented
78#2666C2214yescomplemented
79#2666C2214yescomplemented
80#2666C2214yescomplemented
81#2666C2214yescomplemented
82#2665C2212yescomplemented
83#2665C2212yescomplemented
84#2665C2212yescomplemented
85#2665C2212yescomplemented
86#2665C2214yescomplemented
87#2659C2212yes—
88#2659C2212yes—
89#2646C2212yes—
90#2646C2212yes—
91#2627C2214yes—
92#2627C2214yes—
93#2627C2214yescomplemented
94#2627C2214yescomplemented
95#2612C2214yescomplemented
96#2612C2214yescomplemented
97#2608C2214yescomplemented
98#2608C2214yescomplemented
99#2607C2214yescomplemented
100#2607C2214yescomplemented
101#2606C2214yescomplemented
102#2605C2214yescomplemented
103#2590C2214yescomplemented
104#2590C2214yescomplemented
105#2589C2214yescomplemented
106#2589C2214yescomplemented
107#2588C2214yescomplemented
108#2588C2214yescomplemented
109#2587C2214yescomplemented
110#2587C2214yescomplemented
111#2586C2214yescomplemented
112#2586C2214yescomplemented
113#2585C2214yescomplemented
114#2585C2214yescomplemented
115#2574C2214yescomplemented
116#2574C2214yescomplemented
117#2570C2214yescomplemented
118#2569C2212yes—
119#2569C2212yes—
120#2569C2214yes—
121#2569C2212yes—
122#2569C2212yes—
123#2569C2214yescomplemented
124#2556C2214yescomplemented
125#2556C2214yescomplemented
126#2550C2214yescomplemented
127#2549C2212yes—
128#2549C2212yes—
129#2549C2214yes—
130#2549C2212yes—
131#2549C2212yes—
132#2549C2214yescomplemented
133#2522C2214yescomplemented
134#2522C2214yescomplemented
135#2520C2214yescomplemented
136#2520C2214yescomplemented
137#2511C2214yescomplemented
138#2507C2214yescomplemented
139#2497C2214yescomplemented
140#2492C2214yescomplemented
141#2465C2214yescomplemented
142#2465C2214yescomplemented
143#2462C2214yescomplemented
144#2462C2214yescomplemented
145#2451C2214yescomplemented
146#2446C2214yescomplemented
147#2442C2214yes—
148#2442C2212yescomplemented
149#2442C2212yescomplemented
150#2441C2212yescomplemented
151#2441C2212yescomplemented
152#2440C2214yes—
153#2440C2212yescomplemented
154#2440C2212yescomplemented
155#2439C2212yescomplemented
156#2439C2212yescomplemented
157#2438C2214yescomplemented
158#2438C2214yescomplemented
159#2438C2214yescomplemented
160#2438C2214yescomplemented
161#2437C2214yes—
162#2437C2214yes—
163#2437C2214yes—
164#2437C2214yes—
165#2437C2214yes—
166#2437C2214yes—
167#2437C2214yes—
168#2437C2214yes—
169#2429C2214yescomplemented
170#2423C2214yescomplemented
171#2396C2214yescomplemented
172#2396C2214yescomplemented
173#2357C2214yes—
174#2357C2214yes—
175#2357C2212yes—
176#2357C2212yes—
177#2357C2212yes—
178#2357C2212yes—
179#2353C2212yes—
180#2353C2212yes—
181#2353C2212yes—
182#2353C2212yes—
183#2352C2214yes—
184#2352C2214yes—
185#2331C2214yescomplemented
186#2330C2214yescomplemented
187#2329C2214yes—
188#2329C2214yes—
189#2329C2214yescomplemented
190#2329C2214yescomplemented
191#2318C2214yes—
192#2318C2214yes—
193#2315C2211yescharacteristic
194#2315C2211yescharacteristic
195#2313C2211yescharacteristic
196#2313C2211yescharacteristic
197#2313C2212yes—
198#2312C2212yes—
199#2312C2212yes—
200#2308C2212yes—
201#2308C2212yes—
202C4×C22⋊Q8C2214yes—
203C4×C22⋊Q8C2214yes—
204C4×C22⋊Q8C2214yescomplemented
205C4×C22⋊Q8C2214yescomplemented
206C2×#390C2212yes—
207#2290C2214yes—
208#2290C2214yes—
209C2×#388C2212yes—
210C2×#388C2212yes—
211#2283C2212yes—
212#2283C2212yes—
213C2×#382C2211yescharacteristic
214#2280C2211yescharacteristic
215#2280C2211yescharacteristic
216#2280C2212yes—
217C2×#381C2211yescharacteristic
218C2×#381C2211yescharacteristic
219C2×#380C2211yescharacteristic
220C2×#380C2211yescharacteristic
221#2273C2212yes—
222C2×C4×C4⋊C4C2211yescharacteristic
223C2×C4×C4⋊C4C2212yes—
224C2×C4×C22⋊C4C2211yescharacteristic
225C2×C4×C22⋊C4C2212yes—
226C2×C4×C22⋊C4C2211yescharacteristic
227C23×D4C2311yescharacteristic
228C24×C4C2311yescharacteristic
229C24×C4C2311yescharacteristic
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×#125C2314yes—
234C2×#125C2312yes—
235C2×#125C2312yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×D4Q8116yescomplemented
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×#117C2314yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2312yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2311yescharacteristic
272C22×C22⋊C4C2311yescharacteristic
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2314yes—
276C22×C42C2312yes—
277C22×C42C2311yescharacteristic
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#399C2314yes—
295#399C2314yes—
296#399C2314yes—
297#399C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#393C2314yes—
367#393C2314yes—
368#393C2314yes—
369#393C2314yes—
370#393C2314yes—
371#393C2314yes—
372#393C2314yes—
373#393C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#390C2314yes—
393#390C2314yes—
394#390C2314yes—
395#390C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2312yes—
415#389C2312yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2314yes—
425#389C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#384C2314yes—
523#384C2312yes—
524#384C2312yes—
525#383C2314yes—
526#383C2312yes—
527#383C2312yes—
528#382C2314yes—
529#382C2314yes—
530#382C2312yes—
531#382C2314yes—
532#382C2312yes—
533#382C2312yes—
534#382C2312yes—
535#382C2314yes—
536#381C2314yes—
537#381C2312yes—
538#381C2312yes—
539#381C2312yes—
540#381C2312yes—
541#381C2312yes—
542#381C2312yes—
543#381C2312yes—
544#381C2314yes—
545#381C2312yes—
546#381C2312yes—
547#381C2312yes—
548#381C2312yes—
549#381C2312yes—
550#380C2312yes—
551#380C2312yes—
552#380C2312yes—
553#380C2312yes—
554#380C2311yescharacteristic
555#380C2311yescharacteristic
556#380C2311yescharacteristic
557#380C2311yescharacteristic
558#380C2314yes—
559#380C2314yes—
560#380C2312yes—
561#380C2312yes—
562#380C2314yes—
563#380C2314yes—
564#380C2314yes—
565#380C2314yes—
566#380C2314yes—
567#380C2312yes—
568#380C2312yes—
569#380C2314yes—
570#380C2314yes—
571#380C2312yes—
572#380C2312yes—
573#380C2314yes—
574#380C2314yes—
575#380C2311yescharacteristic
576#380C2311yescharacteristic
577#380C2311yescharacteristic
578#380C2311yescharacteristic
579#380C2314yes—
580#380C2314yes—
581#379C2314yes—
582#379C2312yes—
583#379C2312yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2312yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2312yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2311yescharacteristic
621C4×C22⋊C4C2311yescharacteristic
622C4×C22⋊C4C2311yescharacteristic
623C4×C22⋊C4C2311yescharacteristic
624#376C2312yes—
625#376C2312yes—
626#376C2314yes—
627C2×#95C2311yescharacteristic
628C2×#95C2311yescharacteristic
629C2×#95C2311yescharacteristic
630C2×#95C2311yescharacteristic
631C2×#95C2312yes—
632C2×#95C2314yes—
633C2×#95C2312yes—
634C2×#95C2312yes—
635C2×#95C2312yes—
636C2×#95C2312yes—
637C25C2411yescharacteristic
638C25C2411yescharacteristic
639C22×Q8C2414yes—
640C22×Q8C2414yes—
641C22×Q8C2414yes—
642C22×Q8C2414yes—
643C22×D4—42no—
644C22×D4—42no—
645C22×D4C2×Q818yes—
646C22×D4C2412yes—
647C22×D4C2412yes—
648C23×C4—82no—
649C23×C4—82no—
650C23×C4C2×Q818yes—
651C23×C4C2×Q818yes—
652C23×C4C2412yes—
653C23×C4C2411yescharacteristic
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2411yescharacteristic
662C23×C4C2411yescharacteristic
663C23×C4C2411yescharacteristic
664C23×C4C2411yescharacteristic
665C23×C4C2411yescharacteristic
666C23×C4C2411yescharacteristic
667C23×C4C2411yescharacteristic
668C23×C4C2412yes—
669C23×C4C2412yes—
670C23×C4C2411yescharacteristic
671C4⋊Q8—48no—
672C4⋊Q8—82no—
673C4⋊Q8—82no—
674#125—48no—
675#125—82no—
676#125—82no—
677C22⋊Q8—48no—
678C22⋊Q8—48no—
679C22⋊Q8—48no—
680C22⋊Q8—48no—
681C22⋊Q8—48no—
682C22⋊Q8—48no—
683C22⋊Q8—48no—
684C22⋊Q8—48no—
685C22⋊Q8—84no—
686C22⋊Q8—84no—
687C22⋊Q8—84no—
688C22⋊Q8—84no—
689C4×Q8—84no—
690C4×Q8—84no—
691C4×D4C2×Q8116yes—
692C4×D4C2×Q8116yes—
693C4×D4C2×Q8116yes—
694C4×D4C2×Q8116yes—
695#117—82no—
696#117—82no—
697#117—84no—
698C2×C4⋊C4—44no—
699C2×C4⋊C4—44no—
700C2×C4⋊C4—82no—
701C2×C4⋊C4—82no—
702C2×C4⋊C4C2×Q818yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C22⋊C4—44no—
758C2×C22⋊C4—44no—
759C2×C22⋊C4—44no—
760C2×C22⋊C4—44no—
761C2×C22⋊C4—44no—
762C2×C22⋊C4—44no—
763C2×C22⋊C4—82no—
764C2×C22⋊C4—82no—
765C2×C22⋊C4C2×Q818yes—
766C2×C22⋊C4C2×Q818yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C42—44no—
802C2×C42—84no—
803C2×C42—82no—
804C2×C42—82no—
805C2×C42C2×Q818yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824#95C2412yes—
825#95C2412yes—
826#95C2412yes—
827#95C2412yes—
828#95C2412yes—
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2414yes—
832#95C2414yes—
833#95C2412yes—
834#95C2412yes—
835#95C2411yescharacteristic
836#95C2412yes—
837#95C2411yescharacteristic
838#95C2414yes—
839#95C2414yes—
840#95C2412yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892C24—22no—
893C24—22no—
894C24—22no—
895C24—22no—
896C24—42no—
897C24—42no—
898C24—42no—
899C24—42no—
900C24C22×Q814yes—
901C24C22×Q814yes—
902C24C2511yescharacteristic
903C24C2511yescharacteristic
904C24C2512yes—
905C24C2511yescharacteristic
906C2×Q8—28no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—44no—
910C2×Q8—44no—
911C2×Q8—44no—
912C2×Q8—44no—
913C2×Q8—44no—
914C2×Q8—44no—
915C2×Q8—44no—
916C2×Q8—44no—
917C2×Q8—44no—
918C2×D4—416no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4C22×Q818yes—
924C2×D4C22×Q818yes—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—44no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—44no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—88no—
962C22×C4—88no—
963C22×C4C22×Q814yes—
964C22×C4C22×Q814yes—
965C22×C4C22×Q814yes—
966C22×C4C22×Q814yes—
967C22×C4C22×Q814yes—
968C22×C4C22×Q814yes—
969C22×C4C22×Q814yes—
970C22×C4C22×Q814yes—
971C22×C4C22×Q814yes—
972C22×C4C22×Q818yes—
973C22×C4C22×Q818yes—
974C22×C4C2514yes—
975C22×C4C2512yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2514yes—
986C22×C4C2512yes—
987C22×C4C2511yescharacteristic
988C22×C4C2512yes—
989C22×C4C2511yescharacteristic
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2512yes—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4C22×Q818yes—
1048C4⋊C4C22×Q818yes—
1049C22⋊C4—28no—
1050C22⋊C4—24no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—28no—
1057C22⋊C4—24no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4C22×Q818yes—
1080C22⋊C4C22×Q818yes—
1081C22⋊C4C22×Q818yes—
1082C22⋊C4C22×Q818yes—
1083C42—44no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—42no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42C22×Q818yes—
1100C42C22×Q818yes—
1101C23—22no—
1102C23—22no—
1103C23—24no—
1104C23—22no—
1105C23—22no—
1106C23—21no—
1107C23—21no—
1108C23—22no—
1109C23—22no—
1110C23—21no—
1111C23—21no—
1112C23—24no—
1113C23—22no—
1114C23—22no—
1115C23—28no—
1116C23—28no—
1117C23—44no—
1118C23—44no—
1119C23—44no—
1120C23—44no—
1121C23—84no—
1122C23—84no—
1123C23—84no—
1124C23—84no—
1125C23C23×Q812yes—
1126C23C23×Q812yes—
1127C23C23×Q814yes—
1128C23C23×Q812yes—
1129C23#58512yes—
1130C23#58512yes—
1131C23C2611yescharacteristic
1132Q8—88no—
1133Q8—88no—
1134Q8—164no—
1135Q8—164no—
1136D4—48no—
1137D4—48no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—28no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—44no—
1189C2×C4—48no—
1190C2×C4—44no—
1191C2×C4—44no—
1192C2×C4—44no—
1193C2×C4—44no—
1194C2×C4—48no—
1195C2×C4—44no—
1196C2×C4—44no—
1197C2×C4—44no—
1198C2×C4—48no—
1199C2×C4—84no—
1200C2×C4—84no—
1201C2×C4—84no—
1202C2×C4—88no—
1203C2×C4—88no—
1204C2×C4—164no—
1205C2×C4—164no—
1206C2×C4C23×Q814yes—
1207C2×C4C23×Q814yes—
1208C2×C4C23×Q812yes—
1209C2×C4C23×Q812yes—
1210C2×C4C23×Q814yes—
1211C2×C4C23×Q812yes—
1212C2×C4C23×Q812yes—
1213C2×C4#58514yes—
1214C22—22no—
1215C22—22no—
1216C22—24no—
1217C22—24no—
1218C22—24no—
1219C22—22no—
1220C22—22no—
1221C22—24no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—24no—
1227C22—44no—
1228C22—42no—
1229C22—42no—
1230C22—44no—
1231C22—42no—
1232C22—42no—
1233C22—88no—
1234C22—88no—
1235C22#345814yes—
1236C22C24×Q811yescharacteristic
1237C22C2×#58512yes—
1238C22C2×#58511yescharacteristic
1239C22C2×#58511yescharacteristic
1240C22H(7,𝔽2)12yes—
1241C4—24no—
1242C4—22no—
1243C4—22no—
1244C4—24no—
1245C4—22no—
1246C4—22no—
1247C4—24no—
1248C4—24no—
1249C4—42no—
1250C4—44no—
1251C4—44no—
1252C4—44no—
1253C4—44no—
1254C4—44no—
1255C4—42no—
1256C4—44no—
1257C4—44no—
1258C4—44no—
1259C4—42no—
1260C4—44no—
1261C4—44no—
1262C2—24no—
1263C2—44no—
1264C2—42no—
1265C2—42no—
1266C2C2×#345811yescharacteristic
1267C2#6281311yescharacteristic
1268C2#6284311yescharacteristic
1269C2#6296312yes—
1270C2#6296512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40637C2semidirect
2. #40636C2semidirect
3. #40633C2semidirect
4. #40632C2semidirect
5. #39967C2semidirect
6. #39966C2semidirect
7. #39965C2semidirect
8. #39964C2semidirect
9. #37609C2semidirect
10. #37478C2semidirect
11. #37478C2semidirect
13. #36750C2semidirect
14. #36749C2semidirect
15. #35402C2semidirect
16. #35235C2semidirect
17. #35079C2semidirect
18. #35079C2semidirect
19. #35065C2semidirect
20. #35015C2semidirect
21. #35013C2semidirect
22. #34958C2semidirect
31. #2855C22semidirect
32. #2855C22semidirect
35. #2845C22semidirect
36. #2844C22semidirect
37. #2841C22semidirect
38. #2841C22semidirect
39. #2807C22semidirect
41. #2790C22semidirect
42. #2790C22semidirect
43. #2788C22semidirect
44. #2788C22semidirect
51. #2768C22semidirect
52. #2768C22semidirect
53. #2763C22semidirect
56. #2742C22semidirect
59. #2729C22semidirect
60. #2729C22semidirect
61. #2720C22semidirect
62. #2720C22semidirect
63. #2704C22semidirect
64. #2704C22semidirect
70. #2677C22semidirect
71. #2667C22semidirect
72. #2667C22semidirect
73. #2667C22semidirect
74. #2667C22semidirect
75. #2667C22semidirect
76. #2666C22semidirect
77. #2666C22semidirect
78. #2666C22semidirect
79. #2666C22semidirect
80. #2666C22semidirect
81. #2666C22semidirect
82. #2665C22semidirect
83. #2665C22semidirect
84. #2665C22semidirect
85. #2665C22semidirect
86. #2665C22semidirect
93. #2627C22semidirect
94. #2627C22semidirect
95. #2612C22semidirect
96. #2612C22semidirect
97. #2608C22semidirect
98. #2608C22semidirect
99. #2607C22semidirect
100. #2607C22semidirect
101. #2606C22semidirect
102. #2605C22semidirect
103. #2590C22semidirect
104. #2590C22semidirect
105. #2589C22semidirect
106. #2589C22semidirect
107. #2588C22semidirect
108. #2588C22semidirect
109. #2587C22semidirect
110. #2587C22semidirect
111. #2586C22semidirect
112. #2586C22semidirect
113. #2585C22semidirect
114. #2585C22semidirect
115. #2574C22semidirect
116. #2574C22semidirect
117. #2570C22semidirect
123. #2569C22semidirect
124. #2556C22semidirect
125. #2556C22semidirect
126. #2550C22semidirect
132. #2549C22semidirect
133. #2522C22semidirect
134. #2522C22semidirect
135. #2520C22semidirect
136. #2520C22semidirect
137. #2511C22semidirect
138. #2507C22semidirect
139. #2497C22semidirect
140. #2492C22semidirect
141. #2465C22semidirect
142. #2465C22semidirect
143. #2462C22semidirect
144. #2462C22semidirect
145. #2451C22semidirect
146. #2446C22semidirect
148. #2442C22semidirect
149. #2442C22semidirect
150. #2441C22semidirect
151. #2441C22semidirect
153. #2440C22semidirect
154. #2440C22semidirect
155. #2439C22semidirect
156. #2439C22semidirect
157. #2438C22semidirect
158. #2438C22semidirect
159. #2438C22semidirect
160. #2438C22semidirect
169. #2429C22semidirect
170. #2423C22semidirect
171. #2396C22semidirect
172. #2396C22semidirect
185. #2331C22semidirect
186. #2330C22semidirect
189. #2329C22semidirect
190. #2329C22semidirect
204. C4×C22⋊Q8C22semidirect
205. C4×C22⋊Q8C22semidirect
250. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#406372
#406362
#406332
#406322
#399672
#399662
#399652
#399642
#376092
#374782
#371342
#367502
#367492
#354022
#352352
#350792
#350652
#350152
#350132
#349582
#341852
C2×#23572
#340572