Finite Group Databasebeta

← C2×#19895 #6358262

Subgroups — C2×#19895 #6358262

Order 512.

1796 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3385C211yesmaximal, characteristic, complemented
2C2×Q8×SD16C211yesmaximal, characteristic, complemented
3C2×#3335C211yesmaximal, characteristic
4C2×#3276C211yesmaximal, characteristic
5#19895C2116yesmaximal, direct product factor
6C2×#1707C211yesmaximal, characteristic, complemented
7C2×#1690C211yesmaximal, characteristic, complemented
8C2×#1695C211yesmaximal, characteristic, complemented
9C2×#1672C211yesmaximal, characteristic, complemented
10C2×#1671C211yesmaximal, characteristic, complemented
11C2×#1645C211yesmaximal, characteristic, complemented
12C2×#1637C211yesmaximal, characteristic, complemented
13C2×#1635C211yesmaximal, characteristic
14C2×#1643C211yesmaximal, characteristic, complemented
15C2×#1590C211yesmaximal, characteristic, complemented
16C2×C8×SD16C211yesmaximal, characteristic, complemented
17C22×#137—21no—
18C2×Q82C2211yescharacteristic
19C2×#554C2211yescharacteristic
20C2×D4×Q8C2211yescharacteristic
21C2×#547C2211yescharacteristic
22#3385—24no—
23#3385C2218yescomplemented
24Q8×SD16—24no—
25Q8×SD16C2218yescomplemented
26#3335—24no—
27#3335C2218yes—
28#3276—24no—
29#3276C2218yes—
30C2×#501—21no—
31C2×#500C2211yescharacteristic
32C2×#498—21no—
33C2×#498C2211yescharacteristic
34C2×#498C2211yescharacteristic
35C2×#494C2211yescharacteristic
36C2×#487C2211yescharacteristic
37C2×#487C2211yescharacteristic
38C2×#481—21no—
39C2×#483—21no—
40C2×#479—21no—
41C2×#477C2211yescharacteristic
42C2×#475—21no—
43C2×#475C2211yescharacteristic
44C2×#475C2211yescharacteristic
45C2×#476—21no—
46C2×#476C2211yescharacteristic
47C2×#476C2211yescharacteristic
48C2×#476C2211yescharacteristic
49C2×#474—21no—
50C2×#470—21no—
51C2×#465—21no—
52C2×#462C2211yescharacteristic
53C2×#461C2211yescharacteristic
54C2×#452—21no—
55C2×#451—21no—
56C2×#446C2211yescharacteristic
57C2×C8×Q8C2211yescharacteristic
58C2×#440—21no—
59C2×C4×SD16—21no—
60C2×C4×SD16C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×#436C2211yescharacteristic
63C2×C8×D4C2211yescharacteristic
64C22×#106—21no—
65#1707C2218yescomplemented
66#1695C2218yescomplemented
67#1690C2218yescomplemented
68#1672C2218yescomplemented
69#1671C2218yescomplemented
70#1645C2218yescomplemented
71#1643C2218yescomplemented
72#1637C2218yescomplemented
73#1635C2218yes—
74#1590C2218yescomplemented
75C8×SD16C2218yescomplemented
76C2×#334C2211yescharacteristic
77C2×#334C2211yescharacteristic
78C2×#333C2211yescharacteristic
79C2×#333C2211yescharacteristic
80C2×#332C2211yescharacteristic
81C2×#332C2211yescharacteristic
82C2×Q8⋊C8C2211yescharacteristic
83C2×Q8⋊C8C2211yescharacteristic
84C2×D4⋊C8C2211yescharacteristic
85C2×D4⋊C8C2211yescharacteristic
86C2×C82C2211yescharacteristic
87C22×#41—21no—
88C23×Q8—21no—
89C2×#137—28no—
90C2×#137—48no—
91C22×Q16—21no—
92C22×Q16—21no—
93C22×Q16—21no—
94C22×SD16—21no—
95C22×SD16D411yescharacteristic
96C22×SD16D411yescharacteristic
97C22×M16—21no—
98C23×C8—21no—
99Q82—22no—
100Q82—22no—
101Q82—41no—
102Q82C2314yes—
103#554—22no—
104#554—22no—
105#554—41no—
106#554C2314yes—
107D4×Q8—22no—
108D4×Q8—22no—
109D4×Q8—41no—
110D4×Q8C2314yes—
111#547—22no—
112#547—22no—
113#547—41no—
114#547C2314yes—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—41no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×#125—21no—
124C2×#123—41no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—41no—
129C2×C22⋊Q8—41no—
130C2×#121—21no—
131C2×C4×Q8—21no—
132C2×C4×Q8—21no—
133C2×C4×Q8C2311yescharacteristic
134C2×C4×Q8C2311yescharacteristic
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4C2311yescharacteristic
138C2×C4×D4C2311yescharacteristic
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141#501—28no—
142#500—22no—
143#500C2314yes—
144#498—28no—
145#498—22no—
146#498—22no—
147#498C2314yes—
148#498C2314yes—
149#494—22no—
150#494C2314yes—
151#487—41no—
152#487—41no—
153#487C2314yes—
154#487C2314yes—
155#483—28no—
156#481—28no—
157#479—28no—
158#477—22no—
159#477C2314yes—
160#476—22no—
161#476—22no—
162#476—22no—
163#476—28no—
164#476C2314yes—
165#476C2314yes—
166#476C2314yes—
167#475—22no—
168#475—22no—
169#475—28no—
170#475C2314yes—
171#475C2314yes—
172#474—28no—
173#470—28no—
174#465—28no—
175#462—22no—
176#462C2314yes—
177#461—22no—
178#461C2314yes—
179#452—28no—
180#451—28no—
181#446—22no—
182#446C2314yes—
183C8×Q8—22no—
184C8×Q8C2314yes—
185#440—28no—
186C4×SD16—28no—
187C4×SD16D414yes—
188C4×SD16D414yes—
189C4×SD16C2314yes—
190C4×SD16C2314yes—
191#436—22no—
192#436C2314yes—
193C8×D4—22no—
194C8×D4C2314yes—
195C2×#107—21no—
196C2×#107—21no—
197C2×#107—21no—
198C2×#106—21no—
199C2×#106—21no—
200C2×#106—21no—
201C2×#106—21no—
202C2×#106—21no—
203C2×#106—21no—
204C2×#106—21no—
205C2×#106—21no—
206C2×#106—21no—
207C2×#106—28no—
208C2×#106D411yescharacteristic
209C2×#106D411yescharacteristic
210C2×C4⋊C8—21no—
211C2×C4⋊C8—21no—
212C2×C4⋊C8C2311yescharacteristic
213C2×C4⋊C8C2311yescharacteristic
214C2×C4⋊C8C2311yescharacteristic
215C2×C4⋊C8C2311yescharacteristic
216C2×#103—21no—
217C2×#103—21no—
218C2×#103—21no—
219C2×#103—21no—
220C2×#103—21no—
221C2×#103—41no—
222C2×#103—41no—
223C2×#103D411yescharacteristic
224C2×#103D411yescharacteristic
225C2×#102—21no—
226C2×#102—21no—
227C2×#102—21no—
228C2×#102D411yescharacteristic
229C2×#102D411yescharacteristic
230C2×C22⋊C8—21no—
231C2×C22⋊C8—21no—
232C2×#97—21no—
233C2×C4×C8—21no—
234C2×C4×C8C2311yescharacteristic
235C2×C4×C8C2311yescharacteristic
236C2×C4×C8C2311yescharacteristic
237#334C2314yes—
238#334C2314yes—
239#333C2314yes—
240#333C2314yes—
241#332C2314yes—
242#332C2314yes—
243Q8⋊C8C2314yes—
244Q8⋊C8C2314yes—
245D4⋊C8C2314yes—
246D4⋊C8C2314yes—
247C82C2314yes—
248C2×#41—24no—
249C2×#41—42no—
250C2×#41—44no—
251C2×#41—82no—
252C22×Q8—24no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—21no—
256C22×Q8—21no—
257C22×Q8—41no—
258C22×Q8—41no—
259C22×Q8—42no—
260C22×Q8—44no—
261C22×Q8—82no—
262C22×Q8C2×D411yescharacteristic
263C22×Q8C2×D411yescharacteristic
264C22×D4—41no—
265C22×D4C2×D411yescharacteristic
266C22×D4C2×D411yescharacteristic
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—41no—
270C23×C4—41no—
271C23×C4—41no—
272#137—432no—
273C2×Q16—24no—
274C2×Q16—24no—
275C2×Q16—24no—
276C2×Q16—44no—
277C2×Q16—44no—
278C2×Q16—82no—
279C2×SD16—24no—
280C2×SD16—24no—
281C2×SD16—44no—
282C2×SD16SD1618yescomplemented
283C2×SD16C2×D414yes—
284C2×SD16C2×D414yes—
285C2×M16—24no—
286C2×M16—44no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—24no—
293C22×C8—44no—
294C22×C8C2×D411yescharacteristic
295C22×C8C2×D411yescharacteristic
296C22×C8C2×D411yescharacteristic
297C22×C8C2×D411yescharacteristic
298C4⋊Q8—24no—
299C4⋊Q8—24no—
300C4⋊Q8—24no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—42no—
314C4⋊Q8—42no—
315C4⋊Q8—42no—
316C4⋊Q8—44no—
317C4⋊Q8—44no—
318C4⋊Q8C2412yes—
319C4⋊Q8C2412yes—
320C4⋊Q8C2412yes—
321C4⋊Q8C2412yes—
322#125—24no—
323#125—42no—
324#123—44no—
325#123—44no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329C22⋊Q8—44no—
330C22⋊Q8—44no—
331C22⋊Q8—44no—
332C22⋊Q8—44no—
333C22⋊Q8—42no—
334C22⋊Q8—42no—
335C22⋊Q8—42no—
336#121—24no—
337#121—42no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—24no—
343C4×Q8—24no—
344C4×Q8—42no—
345C4×Q8—42no—
346C4×Q8C2×D412yes—
347C4×Q8C2×D412yes—
348C4×Q8C2412yes—
349C4×Q8C2412yes—
350C4×D4—24no—
351C4×D4—24no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—42no—
357C4×D4—42no—
358C4×D4C2×D412yes—
359C4×D4C2×D412yes—
360C4×D4C2412yes—
361C4×D4C2412yes—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—41no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—41no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—41no—
394C2×C42C2411yescharacteristic
395#107—24no—
396#107—24no—
397#107—24no—
398#106—24no—
399#106—24no—
400#106—24no—
401#106—24no—
402#106—24no—
403#106—24no—
404#106—24no—
405#106—24no—
406#106—24no—
407#106C2×D414yes—
408#106C2×D414yes—
409C4⋊C8—24no—
410C4⋊C8—24no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C2412yes—
416C4⋊C8C2412yes—
417C4⋊C8C2412yes—
418C4⋊C8C2412yes—
419#103—24no—
420#103—24no—
421#103—24no—
422#103—24no—
423#103—24no—
424#103—44no—
425#103—44no—
426#103C2×D414yes—
427#103C2×D414yes—
428#102—24no—
429#102—24no—
430#102—24no—
431#102C2×D414yes—
432#102C2×D414yes—
433C22⋊C8—24no—
434C22⋊C8—24no—
435#97—24no—
436C4×C8—24no—
437C4×C8—21no—
438C4×C8C2×D412yes—
439C4×C8C2×D412yes—
440C4×C8C2412yes—
441C4×C8C2412yes—
442C4×C8C2412yes—
443C24—21no—
444C24—21no—
445#41—48no—
446#41—84no—
447#41—88no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—41no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×Q8—41no—
463C2×Q8—48no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—84no—
469C2×Q8—82no—
470C2×Q8—82no—
471C2×Q8—84no—
472C2×Q8—88no—
473C2×Q8—162no—
474C2×Q8C2×SD1614yes—
475C2×Q8C22×D412yes—
476C2×Q8C22×D412yes—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—44no—
483C2×D4—84no—
484C2×D4C2×SD1614yes—
485C2×D4C22×D412yes—
486C2×D4C22×D412yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—84no—
509C22×C4—84no—
510C22×C4—162no—
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4H(5,𝔽2)11yescharacteristic
514Q16—48no—
515Q16—48no—
516Q16—84no—
517SD16—28no—
518SD16—48no—
519SD16C2×SD16116yescomplemented
520M16—48no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—42no—
529C2×C8—42no—
530C2×C8—42no—
531C2×C8—42no—
532C2×C8—42no—
533C2×C8—48no—
534C2×C8C2×SD1614yes—
535C2×C8#13714yescomplemented
536C2×C8C22×D412yes—
537C2×C8C22×D412yes—
538C2×C8C22×D412yes—
539C2×C8C22×D412yes—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4C22×D412yes—
571C4⋊C4C22×D412yes—
572C4⋊C4C22×D412yes—
573C4⋊C4C22×D412yes—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—44no—
579C22⋊C4—44no—
580C22⋊C4—44no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—44no—
586C42C22×D411yescharacteristic
587C42C22×D411yescharacteristic
588C42H(5,𝔽2)11yescharacteristic
589C42C2511yescharacteristic
590C23—22no—
591C23—24no—
592C23—22no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23D4211yescharacteristic
599Q8—24no—
600Q8—22no—
601Q8—22no—
602Q8—22no—
603Q8—42no—
604Q8—42no—
605Q8—42no—
606Q8—42no—
607Q8—42no—
608Q8—88no—
609Q8—82no—
610Q8—82no—
611Q8—82no—
612Q8—82no—
613Q8—161no—
614Q8—161no—
615Q8—164no—
616Q8C22×SD1614yes—
617D4—24no—
618D4—22no—
619D4—22no—
620D4—22no—
621D4—42no—
622D4—88no—
623D4C22×SD1614yes—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—88no—
648C2×C4—88no—
649C2×C4—82no—
650C2×C4—82no—
651C2×C4—82no—
652C2×C4—82no—
653C2×C4—164no—
654C2×C4D4211yescharacteristic
655C2×C4D4211yescharacteristic
656C2×C4D4211yescharacteristic
657C2×C4C22×SD1612yes—
658C2×C4C2×#13712yes—
659C2×C4#57712yes—
660C2×C4#57812yes—
661C2×C4C23×D411yescharacteristic
662C2×C4C23×D411yescharacteristic
663C2×C4C2×H(5,𝔽2)11yescharacteristic
664C8—22no—
665C8—22no—
666C8—42no—
667C8—42no—
668C8—42no—
669C8—42no—
670C8—42no—
671C8C22×SD1614yes—
672C8C2×#13714yescomplemented
673C22—24no—
674C22—42no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—84no—
681C22#327612yes—
682C22D4×SD1612yes—
683C22#329012yes—
684C22C2×D4211yescharacteristic
685C4—24no—
686C4—21no—
687C4—21no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—82no—
694C4—82no—
695C4—82no—
696C4—82no—
697C4#327612yes—
698C4D4×SD1612yes—
699C4C23×SD1611yescharacteristic
700C4C22×#13711yescharacteristic
701C4C2×#57711yescharacteristic
702C4C2×#57811yescharacteristic
703C2—44no—
704C2—82no—
705C2#1989514yesdirect product factor
706C2C2×#327611yescharacteristic
707C2C2×D4×SD1611yescharacteristic
708C2C2×#329011yescharacteristic
subgroupG/H
center, socleC23D42
commutator, Frattini, cosocleC42C25
prime radicalC2×#547C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3385C2semidirect
2. C2×Q8×SD16C2semidirect
5. #19895C2direct (N × H)
6. C2×#1707C2semidirect
7. C2×#1690C2semidirect
8. C2×#1695C2semidirect
9. C2×#1672C2semidirect
10. C2×#1671C2semidirect
11. C2×#1645C2semidirect
12. C2×#1637C2semidirect
14. C2×#1643C2semidirect
15. C2×#1590C2semidirect
16. C2×C8×SD16C2semidirect
23. #3385C22semidirect
25. Q8×SD16C22semidirect
65. #1707C22semidirect
66. #1695C22semidirect
67. #1690C22semidirect
68. #1672C22semidirect
69. #1671C22semidirect
70. #1645C22semidirect
71. #1643C22semidirect
72. #1637C22semidirect
74. #1590C22semidirect
75. C8×SD16C22semidirect
282. C2×SD16SD16semidirect
519. SD16C2×SD16semidirect
535. C2×C8#137semidirect
672. C8C2×#137semidirect
705. C2#19895direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#33852
C2×Q8×SD162
C2×#33352
C2×#32762
#198952
C2×#17072
C2×#16902
C2×#16952
C2×#16722
C2×#16712
C2×#16452
C2×#16372
C2×#16352
C2×#16432
C2×#15902
C2×C8×SD162