Finite Group Databasebeta

← #7785335

Subgroups — #7785335

Order 512.

4560 conjugacy classes of subgroups.

The subgroup lattice has 1261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59923C212yesmaximal, complemented
2#59321C212yesmaximal, complemented
3#51594C214yesmaximal, complemented
4#51594C214yesmaximal, complemented
5#47979C214yesmaximal, complemented
6#47976C214yesmaximal, complemented
7#45099C214yesmaximal, complemented
8#45025C214yesmaximal, complemented
9#43572C214yesmaximal, complemented
10#43141C214yesmaximal, complemented
11#43130C214yesmaximal, complemented
12#39678C212yesmaximal, complemented
13#39677C212yesmaximal, complemented
14#39620C212yesmaximal, complemented
15#37873C212yesmaximal
16#37685C212yesmaximal
17#36750C212yesmaximal
18#36545C212yesmaximal, complemented
19#35839C214yesmaximal
20#35012C211yesmaximal, characteristic
21C2×#2423C211yesmaximal, characteristic
22#34433C212yesmaximal
23#34270C211yesmaximal, characteristic
24C2×#557C2212yescomplemented
25C2×#544C2212yes—
26C2×#543C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29#2857C2212yes—
30#2851C2212yes—
31#2851C2212yes—
32#2848C2212yes—
33#2811C2212yescomplemented
34#2807C2214yes—
35#2806C2212yescomplemented
36#2806C2212yescomplemented
37#2806C2214yescomplemented
38#2806C2214yescomplemented
39#2806C2214yescomplemented
40#2802C2214yescomplemented
41#2802C2214yescomplemented
42#2799C2214yescomplemented
43#2799C2214yescomplemented
44#2792C2214yescomplemented
45#2792C2214yescomplemented
46#2791C2214yescomplemented
47#2791C2214yescomplemented
48#2791C2214yescomplemented
49#2791C2214yescomplemented
50#2791C2214yescomplemented
51#2788C2214yes—
52#2788C2214yes—
53#2774C2214yescomplemented
54#2768C2214yes—
55#2768C2214yes—
56#2763C2214yes—
57#2755C2214yescomplemented
58#2755C2214yescomplemented
59#2755C2214yescomplemented
60#2742C2214yes—
61#2734C2212yescomplemented
62#2734C2214yescomplemented
63#2729C2214yes—
64#2729C2214yes—
65#2726C2214yescomplemented
66#2726C2214yescomplemented
67#2726C2214yescomplemented
68#2720C2214yes—
69#2720C2214yes—
70#2704C2214yes—
71#2704C2214yes—
72#2704C2214yes—
73#2704C2214yes—
74#2677C2214yes—
75#2667C2214yes—
76#2667C2214yes—
77#2659C2212yes—
78#2659C2212yes—
79#2659C2212yes—
80#2659C2211yescharacteristic
81#2659C2211yescharacteristic
82#2646C2212yes—
83#2627C2212yes—
84#2627C2212yes—
85#2626C2212yes—
86#2607C2214yes—
87#2607C2214yes—
88#2590C2214yescomplemented
89#2589C2214yes—
90#2589C2214yes—
91#2588C2214yescomplemented
92#2586C2214yescomplemented
93#2586C2214yescomplemented
94#2586C2214yescomplemented
95#2586C2214yescomplemented
96#2586C2214yescomplemented
97#2585C2214yescomplemented
98#2584C2214yescomplemented
99#2584C2212yescomplemented
100#2584C2214yescomplemented
101#2584C2212yescomplemented
102#2583C2214yes—
103#2582C2212yescomplemented
104#2582C2214yescomplemented
105#2582C2212yescomplemented
106#2581C2212yescomplemented
107#2581C2212yescomplemented
108#2574C2214yes—
109#2565C2214yescomplemented
110#2565C2214yescomplemented
111#2556C2214yes—
112#2556C2214yes—
113#2556C2214yes—
114#2552C2214yescomplemented
115#2552C2212yescomplemented
116#2550C2214yescomplemented
117#2549C2214yes—
118#2549C2214yes—
119#2549C2214yes—
120#2546C2212yescomplemented
121#2522C2214yes—
122#2522C2214yes—
123#2522C2214yes—
124#2520C2214yescomplemented
125#2520C2214yescomplemented
126#2511C2214yescomplemented
127#2507C2214yescomplemented
128#2506C2214yescomplemented
129#2506C2214yescomplemented
130#2505C2214yes—
131#2502C2214yes—
132#2473C2214yes—
133#2473C2214yes—
134#2473C2214yes—
135#2473C2214yes—
136#2473C2214yes—
137#2465C2214yes—
138#2462C2214yescomplemented
139#2462C2214yescomplemented
140#2462C2214yescomplemented
141#2462C2214yescomplemented
142#2453C2214yescomplemented
143#2453C2214yescomplemented
144#2451C2214yescomplemented
145#2451C2214yescomplemented
146#2451C2214yescomplemented
147#2446C2214yescomplemented
148#2446C2214yescomplemented
149#2442C2214yes—
150#2442C2214yes—
151#2441C2214yes—
152#2441C2214yes—
153#2440C2214yes—
154#2440C2214yes—
155#2438C2214yes—
156#2438C2214yes—
157#2437C2214yes—
158#2437C2214yes—
159#2434C2214yes—
160#2423C2214yes—
161#2423C2214yes—
162#2423C2214yes—
163#2423C2214yes—
164#2423C2214yes—
165#2423C2214yes—
166#2396C2214yes—
167#2396C2214yes—
168C2×#399C2212yes—
169C2×#398C2212yes—
170#2378C2214yes—
171#2378C2214yes—
172#2369C2214yescomplemented
173#2368C2214yes—
174#2368C2214yes—
175#2368C2214yes—
176#2368C2214yes—
177#2365C2214yescomplemented
178#2362C2214yes—
179#2362C2214yes—
180#2360C2214yes—
181#2360C2214yes—
182#2360C2214yes—
183#2360C2214yes—
184#2360C2214yes—
185#2355C2212yescomplemented
186#2355C2212yescomplemented
187Q8×C4⋊C4C2212yescomplemented
188#2345C2214yes—
189#2342C2214yes—
190#2342C2214yes—
191#2332C2214yes—
192#2332C2214yes—
193#2329C2212yes—
194#2329C2212yes—
195#2329C2212yes—
196#2329C2212yes—
197#2329C2212yes—
198#2329C2212yes—
199#2329C2212yes—
200#2323C2214yes—
201#2323C2214yes—
202#2316C2212yes—
203#2315C2211yescharacteristic
204#2312C2212yes—
205C4×C22⋊Q8C2212yes—
206C4×C22⋊Q8C2212yes—
207C4×C22⋊Q8C2212yes—
208C4×C22⋊Q8C2212yes—
209C4×C22⋊Q8C2212yes—
210C2×#391C2211yescharacteristic
211C2×#389C2211yescharacteristic
212C2×#388C2212yes—
213C2×#387C2212yes—
214C2×#385C2212yes—
215C2×#384C2211yescharacteristic
216C2×#380C2211yescharacteristic
217#2273C2212yes—
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C24×C4C2311yescharacteristic
221#557—48no—
222#544—48no—
223#543Q8116yescomplemented
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2314yes—
227C2×C4⋊Q8C2314yes—
228C2×#125C2314yes—
229C2×#125C2312yes—
230C2×#125C2312yes—
231C2×#125C2314yes—
232C2×#125C2314yes—
233C2×#125C2314yes—
234C2×#125C2314yes—
235C2×#125C2314yes—
236C2×C22⋊Q8—44no—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C4×Q8—44no—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2314yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2312yes—
283C22×C42C2311yescharacteristic
284C22×C42C2312yes—
285C22×C42C2311yescharacteristic
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#399C2314yes—
303#399C2314yes—
304#399C2314yes—
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#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
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#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#393C2314yes—
372#393C2314yes—
373#393C2314yes—
374#391C2312yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2312yes—
379#391C2314yes—
380#391C2314yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2312yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2312yes—
404#391C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2312yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2314yes—
420#389C2312yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
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#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#384C2314yes—
547#384C2314yes—
548#384C2312yes—
549#384C2312yes—
550#384C2314yes—
551#384C2312yes—
552#384C2314yes—
553#382C2314yes—
554#382C2314yes—
555#382C2312yes—
556#382C2312yes—
557#381C2314yes—
558#381C2314yes—
559#380C2312yes—
560#380C2312yes—
561#380C2312yes—
562#380C2312yes—
563#380C2312yes—
564#380C2312yes—
565#380C2314yes—
566#380C2312yes—
567#380C2314yes—
568#380C2314yes—
569#380C2312yes—
570#380C2312yes—
571#380C2314yes—
572#380C2314yes—
573#380C2312yes—
574#380C2314yes—
575#380C2314yes—
576#379C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2312yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C2×#95C2311yescharacteristic
612C2×#95C2312yes—
613C2×#95C2311yescharacteristic
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C25C2411yescharacteristic
620C22×Q8—24no—
621C22×Q8—42no—
622C22×Q8—42no—
623C22×Q8C2412yes—
624C22×Q8C2411yescharacteristic
625C22×Q8C2414yes—
626C22×Q8C2412yes—
627C22×Q8C2414yes—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×Q8C2411yescharacteristic
632C23×C4—42no—
633C23×C4—42no—
634C23×C4—42no—
635C23×C4C2411yescharacteristic
636C23×C4C2412yes—
637C23×C4C2412yes—
638C23×C4C2411yescharacteristic
639C23×C4C2412yes—
640C23×C4C2412yes—
641C23×C4C2411yescharacteristic
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2411yescharacteristic
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2411yescharacteristic
650C23×C4C2411yescharacteristic
651C4⋊Q8—216no—
652C4⋊Q8—44no—
653C4⋊Q8—48no—
654C4⋊Q8—48no—
655#125—48no—
656#125—44no—
657#125—44no—
658#125—48no—
659#125—48no—
660#125—48no—
661#125—84no—
662#125—84no—
663C22⋊Q8—28no—
664C22⋊Q8—28no—
665C22⋊Q8—48no—
666C22⋊Q8—48no—
667C22⋊Q8—44no—
668C22⋊Q8—48no—
669C22⋊Q8—48no—
670C22⋊Q8—44no—
671C22⋊Q8—44no—
672C22⋊Q8—44no—
673C22⋊Q8—84no—
674C22⋊Q8C2×Q8116yes—
675C22⋊Q8C2×Q8116yes—
676C22⋊Q8C2×Q8132yescomplemented
677C22⋊Q8C2×Q8132yescomplemented
678C4×Q8—28no—
679C4×Q8—44no—
680C4×Q8—44no—
681C4×Q8—44no—
682C4×Q8—44no—
683C4×Q8—44no—
684C4×Q8—44no—
685C4×Q8—44no—
686C4×Q8—44no—
687C4×Q8—48no—
688C4×Q8—84no—
689C4×Q8—84no—
690#117—48no—
691#117—84no—
692C2×C4⋊C4—28no—
693C2×C4⋊C4—44no—
694C2×C4⋊C4—44no—
695C2×C4⋊C4—42no—
696C2×C4⋊C4—42no—
697C2×C4⋊C4—44no—
698C2×C4⋊C4—44no—
699C2×C4⋊C4—42no—
700C2×C4⋊C4—82no—
701C2×C4⋊C4—82no—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C22⋊C4—24no—
776C2×C22⋊C4—44no—
777C2×C22⋊C4—44no—
778C2×C22⋊C4—82no—
779C2×C22⋊C4C2×Q8116yes—
780C2×C22⋊C4C2×Q818yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
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×C42—42no—
798C2×C42—44no—
799C2×C42—42no—
800C2×C42C2414yes—
801C2×C42C2412yes—
802C2×C42C2412yes—
803C2×C42C2412yes—
804C2×C42C2412yes—
805C2×C42C2414yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
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#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
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—
880C24—22no—
881C24—22no—
882C24—41no—
883C24—41no—
884C24—41no—
885C24—41no—
886C24C22×Q814yes—
887C24C2512yes—
888C24C2511yescharacteristic
889C2×Q8—24no—
890C2×Q8—22no—
891C2×Q8—28no—
892C2×Q8—24no—
893C2×Q8—24no—
894C2×Q8—42no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—41no—
898C2×Q8—41no—
899C2×Q8—41no—
900C2×Q8—42no—
901C2×Q8—41no—
902C2×Q8—42no—
903C2×Q8—42no—
904C2×Q8—44no—
905C2×Q8—44no—
906C2×Q8—44no—
907C2×Q8—44no—
908C2×Q8—42no—
909C2×Q8—44no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—416no—
914C2×Q8C22×Q818yes—
915C2×Q8C22×Q818yes—
916C2×Q8H(5,𝔽2)14yes—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—24no—
921C22×C4—22no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—22no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—41no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—42no—
940C22×C4—41no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—41no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—88no—
961C22×C4C22×Q814yes—
962C22×C4C22×Q814yes—
963C22×C4C22×Q818yes—
964C22×C4C22×Q818yes—
965C22×C42−1+414yes—
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2514yes—
969C22×C4C2512yes—
970C22×C4C2514yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2514yes—
975C22×C4C2512yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2512yes—
980C22×C4C2514yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2511yescharacteristic
985C22×C4C2512yes—
986C22×C4C2511yescharacteristic
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—44no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—44no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4C22×Q818yes—
1057C4⋊C4C22×Q8116yes—
1058C4⋊C4C22×Q8116yes—
1059C4⋊C4C22×Q818yes—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4C22×Q8116yes—
1074C22⋊C4C22×Q8116yes—
1075C22⋊C4C22×Q8116yes—
1076C42—24no—
1077C42—24no—
1078C42—24no—
1079C42—28no—
1080C42—24no—
1081C42—42no—
1082C42—42no—
1083C42—42no—
1084C42—42no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—28no—
1109C23—44no—
1110C23—44no—
1111C23—82no—
1112C23—82no—
1113C23—82no—
1114C23—82no—
1115C23C23×Q814yes—
1116C23C23×Q812yes—
1117C23C2×2−1+412yes—
1118C23#58512yes—
1119C23C2611yescharacteristic
1120Q8—44no—
1121Q8—48no—
1122Q8—48no—
1123Q8—48no—
1124Q8—44no—
1125Q8—88no—
1126Q8—84no—
1127Q8—88no—
1128Q8—162no—
1129C2×C4—28no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—44no—
1186C2×C4—48no—
1187C2×C4—44no—
1188C2×C4—48no—
1189C2×C4—44no—
1190C2×C4—48no—
1191C2×C4—84no—
1192C2×C4—84no—
1193C2×C4—84no—
1194C2×C4—82no—
1195C2×C4—84no—
1196C2×C4—84no—
1197C2×C4—82no—
1198C2×C4—162no—
1199C2×C4—162no—
1200C2×C4C23×Q818yes—
1201C2×C4C23×Q814yes—
1202C2×C4C23×Q818yes—
1203C2×C4C23×Q814yes—
1204C2×C4C2×H(5,𝔽2)14yes—
1205C2×C4C2×H(5,𝔽2)12yes—
1206C2×C4C2×2−1+414yes—
1207C2×C4#58512yes—
1208C22—22no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—88no—
1222C22#350214yes—
1223C22C24×Q811yescharacteristic
1224C22C22×H(5,𝔽2)11yescharacteristic
1225C22C22×2−1+411yescharacteristic
1226C22C2×#58511yescharacteristic
1227C22C2×#58511yescharacteristic
1228C22H(7,𝔽2)11yescharacteristic
1229C222−1+611yescharacteristic
1230C4—24no—
1231C4—28no—
1232C4—24no—
1233C4—28no—
1234C4—22no—
1235C4—22no—
1236C4—24no—
1237C4—24no—
1238C4—42no—
1239C4—42no—
1240C4—44no—
1241C4—44no—
1242C4—44no—
1243C4—44no—
1244C4—44no—
1245C4—44no—
1246C4—44no—
1247C4—42no—
1248C4—42no—
1249C4—42no—
1250C4—44no—
1251C2—24no—
1252C2—44no—
1253C2C2×#350211yescharacteristic
1254C2#6282011yescharacteristic
1255C2#6286911yescharacteristic
1256C2#6290411yescharacteristic
1257C2#6291711yescharacteristic
1258C2Q8×H(5,𝔽2)11yescharacteristic
1259C2#6298911yescharacteristic
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. #59923C2semidirect
2. #59321C2semidirect
3. #51594C2semidirect
4. #51594C2semidirect
5. #47979C2semidirect
6. #47976C2semidirect
7. #45099C2semidirect
8. #45025C2semidirect
9. #43572C2semidirect
10. #43141C2semidirect
11. #43130C2semidirect
12. #39678C2semidirect
13. #39677C2semidirect
14. #39620C2semidirect
18. #36545C2semidirect
24. C2×#557C22semidirect
33. #2811C22semidirect
35. #2806C22semidirect
36. #2806C22semidirect
37. #2806C22semidirect
38. #2806C22semidirect
39. #2806C22semidirect
40. #2802C22semidirect
41. #2802C22semidirect
42. #2799C22semidirect
43. #2799C22semidirect
44. #2792C22semidirect
45. #2792C22semidirect
46. #2791C22semidirect
47. #2791C22semidirect
48. #2791C22semidirect
49. #2791C22semidirect
50. #2791C22semidirect
53. #2774C22semidirect
57. #2755C22semidirect
58. #2755C22semidirect
59. #2755C22semidirect
61. #2734C22semidirect
62. #2734C22semidirect
65. #2726C22semidirect
66. #2726C22semidirect
67. #2726C22semidirect
88. #2590C22semidirect
91. #2588C22semidirect
92. #2586C22semidirect
93. #2586C22semidirect
94. #2586C22semidirect
95. #2586C22semidirect
96. #2586C22semidirect
97. #2585C22semidirect
98. #2584C22semidirect
99. #2584C22semidirect
100. #2584C22semidirect
101. #2584C22semidirect
103. #2582C22semidirect
104. #2582C22semidirect
105. #2582C22semidirect
106. #2581C22semidirect
107. #2581C22semidirect
109. #2565C22semidirect
110. #2565C22semidirect
114. #2552C22semidirect
115. #2552C22semidirect
116. #2550C22semidirect
120. #2546C22semidirect
124. #2520C22semidirect
125. #2520C22semidirect
126. #2511C22semidirect
127. #2507C22semidirect
128. #2506C22semidirect
129. #2506C22semidirect
138. #2462C22semidirect
139. #2462C22semidirect
140. #2462C22semidirect
141. #2462C22semidirect
142. #2453C22semidirect
143. #2453C22semidirect
144. #2451C22semidirect
145. #2451C22semidirect
146. #2451C22semidirect
147. #2446C22semidirect
148. #2446C22semidirect
172. #2369C22semidirect
177. #2365C22semidirect
185. #2355C22semidirect
186. #2355C22semidirect
187. Q8×C4⋊C4C22semidirect
223. #543Q8semidirect
676. C22⋊Q8C2×Q8semidirect
677. C22⋊Q8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599232
#593212
#515942
#479792
#479762
#450992
#450252
#435722
#431412
#431302
#396782
#396772
#396202
#378732
#376852
#367502
#365452
#358392
#350122
C2×#24232
#344332
#342702