Finite Group Databasebeta

← C2×#19480 #6354549

Subgroups — C2×#19480 #6354549

Order 512.

1920 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3207C211yesmaximal, characteristic, complemented
2C2×#3115C211yesmaximal, characteristic, complemented
3C2×#3035C211yesmaximal, characteristic, complemented
4C2×#2990C211yesmaximal, characteristic, complemented
5#19480C2116yesmaximal, direct product factor
6C2×#1702C211yesmaximal, characteristic, complemented
7C2×#1700C211yesmaximal, characteristic, complemented
8C2×#1688C211yesmaximal, characteristic, complemented
9C2×#1686C211yesmaximal, characteristic, complemented
10C2×#1681C211yesmaximal, characteristic, complemented
11C2×#1679C211yesmaximal, characteristic, complemented
12C2×#1667C211yesmaximal, characteristic, complemented
13C2×#1665C211yesmaximal, characteristic, complemented
14C2×#1573C211yesmaximal, characteristic, complemented
15C2×#1557C211yesmaximal, characteristic, complemented
16C2×#1547C211yesmaximal, characteristic, complemented
17C22×#135—21no—
18C2×#532C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×C4×#41C2211yescharacteristic
21#3207—24no—
22#3207C2218yescomplemented
23C2×#493C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#486C2211yescharacteristic
27#3115—24no—
28#3115C2218yescomplemented
29C2×#482—21no—
30C2×#475C2211yescharacteristic
31C2×#474C2211yescharacteristic
32#3035—24no—
33#3035C2218yescomplemented
34C2×#464—21no—
35C2×#462C2211yescharacteristic
36C2×#460C2211yescharacteristic
37C2×#460C2211yescharacteristic
38C2×#463—21no—
39C2×#463—21no—
40C2×#463—21no—
41C2×#461C2211yescharacteristic
42C2×#459C2211yescharacteristic
43C2×#459C2211yescharacteristic
44C2×#449—21no—
45C2×#449—21no—
46C2×#449—21no—
47#2990—24no—
48#2990C2218yescomplemented
49C2×#446C2211yescharacteristic
50C2×#446C2211yescharacteristic
51C2×#442—21no—
52C2×#440—21no—
53C2×#435—21no—
54C2×#435—21no—
55C2×C8×D4C2211yescharacteristic
56C2×C8×D4C2211yescharacteristic
57C2×#432—21no—
58C2×#432C2211yescharacteristic
59C2×#431C2211yescharacteristic
60C2×#423C2211yescharacteristic
61C22×C4⋊C8—21no—
62C22×C4⋊C8C2211yescharacteristic
63C2×#416—21no—
64#1702C2218yescomplemented
65#1700C2218yescomplemented
66#1688C2218yescomplemented
67#1686C2218yescomplemented
68#1681C2218yescomplemented
69#1679C2218yescomplemented
70#1667C2218yescomplemented
71#1665C2218yescomplemented
72#1573C2218yescomplemented
73C2×#335C2211yescharacteristic
74C2×#335C2211yescharacteristic
75C2×#334C2211yescharacteristic
76C2×#334C2211yescharacteristic
77#1557C2218yescomplemented
78#1547C2218yescomplemented
79C2×#332C2211yescharacteristic
80C2×#332C2211yescharacteristic
81C2×#332C2211yescharacteristic
82C2×#332C2211yescharacteristic
83C2×#331C2211yescharacteristic
84C2×#331C2211yescharacteristic
85C2×#331C2211yescharacteristic
86C2×#331C2211yescharacteristic
87C22×#41—21no—
88C22×#41—21no—
89C22×#41D411yescharacteristic
90C2×#135—28no—
91C2×#135—48no—
92C22×Q16—21no—
93C22×SD16—21no—
94C22×SD16—21no—
95C22×SD16—21no—
96C22×SD16—21no—
97C22×SD16—21no—
98C22×D8—21no—
99C22×D8—21no—
100C22×D8—21no—
101C22×D8—21no—
102C22×M16—21no—
103C23×C8—21no—
104C23×C8—21no—
105C23×C8—21no—
106#532—22no—
107#532—22no—
108#532—22no—
109#532—22no—
110#532—22no—
111#532—22no—
112#532C2314yes—
113#532C2314yes—
114C2×C4⋊Q8C2311yescharacteristic
115C2×C4⋊Q8C2311yescharacteristic
116C2×#127C2311yescharacteristic
117C2×#127C2311yescharacteristic
118C2×#124—21no—
119C2×#124—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C4×#41—22no—
125C4×#41—22no—
126C4×#41D414yes—
127C4×#41C2314yes—
128C2×C4×Q8D411yescharacteristic
129C2×C4×Q8C2311yescharacteristic
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4D411yescharacteristic
137C2×C4×D4C2311yescharacteristic
138C2×#117—21no—
139C2×#117D411yescharacteristic
140C22×C42—21no—
141C22×C42C2311yescharacteristic
142#493—22no—
143#493C2314yes—
144#492—22no—
145#492C2314yes—
146#487—22no—
147#487C2314yes—
148#486—22no—
149#486C2314yes—
150#482—28no—
151#475—22no—
152#475C2314yes—
153#474—22no—
154#474C2314yes—
155#464—28no—
156#463—28no—
157#463—28no—
158#463—28no—
159#462—22no—
160#462C2314yes—
161#461—22no—
162#461C2314yes—
163#460—22no—
164#460—22no—
165#460C2314yes—
166#460C2314yes—
167#459—22no—
168#459—22no—
169#459C2314yes—
170#459C2314yes—
171#449—28no—
172#449—28no—
173#449—28no—
174#446—22no—
175#446—22no—
176#446C2314yes—
177#446C2314yes—
178#442—28no—
179#440—28no—
180#435—28no—
181#435—28no—
182C8×D4—22no—
183C8×D4—22no—
184C8×D4C2314yes—
185C8×D4C2314yes—
186#432—22no—
187#432—28no—
188#432C2314yes—
189#431D414yes—
190#431C2314yes—
191C2×#107—21no—
192C2×#106—21no—
193#423—22no—
194#423C2314yes—
195C2×C4⋊C8—21no—
196C2×C4⋊C8—21no—
197C2×C4⋊C8—21no—
198C2×C4⋊C8—21no—
199C2×C4⋊C8—22no—
200C2×C4⋊C8—28no—
201C2×C4⋊C8D411yescharacteristic
202C2×C4⋊C8D411yescharacteristic
203C2×C4⋊C8C2311yescharacteristic
204C2×C4⋊C8C2311yescharacteristic
205C2×C4⋊C8C2311yescharacteristic
206C2×C4⋊C8C2311yescharacteristic
207C2×C4⋊C8C2311yescharacteristic
208C2×C4⋊C8C2311yescharacteristic
209C2×C4⋊C8C2314yes—
210#416—28no—
211C2×#103—21no—
212C2×#103—21no—
213C2×#103—21no—
214C2×#103—21no—
215C2×#103—21no—
216C2×#102—21no—
217C2×#102—21no—
218C2×#102—21no—
219C2×#102—21no—
220C2×#102—21no—
221C2×#102—21no—
222C2×#102—21no—
223C2×C22⋊C8—21no—
224C2×C22⋊C8—21no—
225C2×C22⋊C8—21no—
226C2×C22⋊C8D411yescharacteristic
227C2×C22⋊C8D411yescharacteristic
228C2×#97—21no—
229C2×#97—21no—
230C2×#97—21no—
231C2×C4×C8C2311yescharacteristic
232C2×C4×C8C2311yescharacteristic
233#335C2314yes—
234#335C2314yes—
235#334C2314yes—
236#334C2314yes—
237#332C2314yes—
238#332C2314yes—
239#332C2314yes—
240#332C2314yes—
241#331C2314yes—
242#331C2314yes—
243#331C2314yes—
244#331C2314yes—
245C2×#41—22no—
246C2×#41—24no—
247C2×#41—24no—
248C2×#41—24no—
249C2×#41—42no—
250C2×#41—44no—
251C2×#41—44no—
252C2×#41—42no—
253C2×#41—42no—
254C2×#41—82no—
255C2×#41—82no—
256C2×#41C2×D414yes—
257C22×Q8—21no—
258C22×Q8—21no—
259C22×Q8C2×D411yescharacteristic
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4—41no—
268C22×D4—41no—
269C22×D4C2×D411yescharacteristic
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—41no—
274C23×C4—41no—
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4#4111yescharacteristic
278#135—432no—
279C2×Q16—24no—
280C2×Q16—44no—
281C2×SD16—24no—
282C2×SD16—24no—
283C2×SD16—24no—
284C2×SD16—24no—
285C2×SD16—24no—
286C2×SD16—44no—
287C2×SD16—44no—
288C2×SD16—44no—
289C2×SD16—82no—
290C2×SD16—82no—
291C2×D8—24no—
292C2×D8—24no—
293C2×D8—24no—
294C2×D8—24no—
295C2×D8—44no—
296C2×D8—44no—
297C2×D8—82no—
298C2×D8—82no—
299C2×M16—24no—
300C2×M16—82no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—24no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—24no—
309C22×C8—24no—
310C22×C8—44no—
311C22×C8—82no—
312C22×C8—82no—
313C22×C8C2×D411yescharacteristic
314C22×C8C2×D411yescharacteristic
315C22×C8C2×D411yescharacteristic
316C22×C8C2×D411yescharacteristic
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8C2412yes—
324C4⋊Q8C2412yes—
325#127—21no—
326#127—21no—
327#127—21no—
328#127—21no—
329#127—21no—
330#127—21no—
331#127C2412yes—
332#127C2412yes—
333#124—24no—
334#124—24no—
335#124—42no—
336#124—42no—
337#121—24no—
338#121—24no—
339#121—24no—
340#121—24no—
341#121—42no—
342#121—42no—
343#121—42no—
344#121—42no—
345C4×Q8—22no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8C2×D414yes—
349C4×Q8C2×D412yes—
350C4×Q8C2412yes—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4—24no—
354C4×D4—24no—
355C4×D4—22no—
356C4×D4—21no—
357C4×D4—24no—
358C4×D4—24no—
359C4×D4—21no—
360C4×D4—24no—
361C4×D4—24no—
362C4×D4—42no—
363C4×D4—42no—
364C4×D4—42no—
365C4×D4—42no—
366C4×D4C2×D414yes—
367C4×D4C2×D412yes—
368C4×D4C2412yes—
369#117—22no—
370#117—24no—
371#117—24no—
372#117C2×D414yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4—41no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D412yes—
396C2×C42C2×D412yes—
397C2×C42#4111yescharacteristic
398C2×C42#4112yes—
399C2×C42C2411yescharacteristic
400C2×C42C2412yes—
401#107—24no—
402#106—24no—
403C4⋊C8—24no—
404C4⋊C8—24no—
405C4⋊C8—24no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—24no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8C2×D414yes—
414C4⋊C8C2×D414yes—
415C4⋊C8C2412yes—
416C4⋊C8C2412yes—
417C4⋊C8C2412yes—
418C4⋊C8C2412yes—
419C4⋊C8C2412yes—
420C4⋊C8C2412yes—
421#103—24no—
422#103—24no—
423#103—24no—
424#103—24no—
425#103—24no—
426#102—24no—
427#102—24no—
428#102—24no—
429#102—24no—
430#102—24no—
431#102—24no—
432#102—24no—
433C22⋊C8—24no—
434C22⋊C8—24no—
435C22⋊C8—24no—
436C22⋊C8C2×D414yes—
437C22⋊C8C2×D414yes—
438#97—24no—
439#97—24no—
440#97—24no—
441C4×C8C2×D412yes—
442C4×C8C2×D412yes—
443C4×C8C2412yes—
444C4×C8C2412yes—
445C24—21no—
446C24—41no—
447C24—41no—
448C24#12111yescharacteristic
449#41—28no—
450#41—44no—
451#41—48no—
452#41—48no—
453#41—48no—
454#41—84no—
455#41—84no—
456#41—88no—
457#41—88no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—41no—
464C2×Q8—41no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8C22×D412yes—
470C2×D4—24no—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—82no—
497C2×D4—82no—
498C2×D4—84no—
499C2×D4—84no—
500C2×D4AGL(1,ℤ/8)14yes—
501C2×D4C22×D412yes—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—84no—
523C22×C4—84no—
524C22×C4#12112yes—
525C22×C4#12112yes—
526C22×C4#12111yescharacteristic
527C22×C4#12111yescharacteristic
528C22×C4#12111yescharacteristic
529C22×C4#12112yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C22×C4C2×#4112yes—
536Q16—48no—
537SD16—48no—
538SD16—48no—
539SD16—48no—
540SD16—84no—
541SD16—84no—
542D8—48no—
543D8—48no—
544D8—84no—
545D8—84no—
546M16—84no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—48no—
558C2×C8—42no—
559C2×C8—42no—
560C2×C8—42no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—42no—
564C2×C8—84no—
565C2×C8—84no—
566C2×C8C22×D412yes—
567C2×C8C22×D412yes—
568C2×C8C22×D412yes—
569C2×C8C22×D412yes—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4C22×D412yes—
584C4⋊C4C22×D412yes—
585C22⋊C4—24no—
586C22⋊C4—22no—
587C22⋊C4—24no—
588C22⋊C4—22no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C42—24no—
594C42—24no—
595C42—22no—
596C42—22no—
597C42#12112yes—
598C42#12112yes—
599C42#12112yes—
600C42C22×D411yescharacteristic
601C42C22×D412yes—
602C42C22×D411yescharacteristic
603C42C22×D412yes—
604C42C2×#4112yes—
605C42C2×#4111yescharacteristic
606C42C2511yescharacteristic
607C23—22no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—22no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23—82no—
620C23—82no—
621C23—82no—
622C23C2×#12112yes—
623C23C2×#12111yescharacteristic
624Q8—22no—
625Q8—22no—
626Q8—42no—
627Q8—42no—
628Q8—42no—
629Q8—42no—
630Q8—42no—
631Q8—82no—
632Q8—82no—
633D4—24no—
634D4—22no—
635D4—48no—
636D4—42no—
637D4—42no—
638D4—42no—
639D4—42no—
640D4—42no—
641D4—42no—
642D4—42no—
643D4—42no—
644D4—82no—
645D4—82no—
646D4—82no—
647D4—82no—
648D4—88no—
649D4—88no—
650D4—82no—
651D4—82no—
652D4—82no—
653D4—82no—
654D4C2×AGL(1,ℤ/8)14yes—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—48no—
671C2×C4—48no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—44no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—88no—
681C2×C4—88no—
682C2×C4—82no—
683C2×C4—82no—
684C2×C4C2×#12112yes—
685C2×C4C2×#12112yes—
686C2×C4C2×#12111yescharacteristic
687C2×C4C2×#12112yes—
688C2×C4C2×#12111yescharacteristic
689C2×C4C2×#12111yescharacteristic
690C2×C4C2×AGL(1,ℤ/8)12yes—
691C2×C4#57512yes—
692C2×C4#57612yes—
693C2×C4#57712yes—
694C2×C4C23×D411yescharacteristic
695C2×C4C23×D411yescharacteristic
696C2×C4C22×#4111yescharacteristic
697C8—22no—
698C8—22no—
699C8—22no—
700C8—22no—
701C8—42no—
702C8—42no—
703C8—42no—
704C8—42no—
705C8—42no—
706C8—42no—
707C22—22no—
708C22—22no—
709C22—24no—
710C22—22no—
711C22—42no—
712C22—44no—
713C22—48no—
714C22—42no—
715C22—82no—
716C22—82no—
717C22—82no—
718C22—82no—
719C22—82no—
720C22—82no—
721C22—164no—
722C22—164no—
723C22#304512yes—
724C22#305512yes—
725C22#306712yes—
726C22C22×#12111yescharacteristic
727C4—22no—
728C4—22no—
729C4—22no—
730C4—21no—
731C4—21no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—82no—
736C4—82no—
737C4#304512yes—
738C4#305512yes—
739C4C22×AGL(1,ℤ/8)11yescharacteristic
740C4C2×#57511yescharacteristic
741C4C2×#57611yescharacteristic
742C4C2×#57711yescharacteristic
743C2—42no—
744C2—44no—
745C2—162no—
746C2—162no—
747C2#1948014yesdirect product factor
748C2C2×#304511yescharacteristic
749C2C2×#305511yescharacteristic
750C2C2×#306711yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC42C25
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3207C2semidirect
2. C2×#3115C2semidirect
3. C2×#3035C2semidirect
4. C2×#2990C2semidirect
5. #19480C2direct (N × H)
6. C2×#1702C2semidirect
7. C2×#1700C2semidirect
8. C2×#1688C2semidirect
9. C2×#1686C2semidirect
10. C2×#1681C2semidirect
11. C2×#1679C2semidirect
12. C2×#1667C2semidirect
13. C2×#1665C2semidirect
14. C2×#1573C2semidirect
15. C2×#1557C2semidirect
16. C2×#1547C2semidirect
22. #3207C22semidirect
28. #3115C22semidirect
33. #3035C22semidirect
48. #2990C22semidirect
64. #1702C22semidirect
65. #1700C22semidirect
66. #1688C22semidirect
67. #1686C22semidirect
68. #1681C22semidirect
69. #1679C22semidirect
70. #1667C22semidirect
71. #1665C22semidirect
72. #1573C22semidirect
77. #1557C22semidirect
78. #1547C22semidirect
747. C2#19480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32072
C2×#31152
C2×#30352
C2×#29902
#194802
C2×#17022
C2×#17002
C2×#16882
C2×#16862
C2×#16812
C2×#16792
C2×#16672
C2×#16652
C2×#15732
C2×#15572
C2×#15472