Finite Group Databasebeta

← C2×#19448 #6354502

Subgroups — C2×#19448 #6354502

Order 512.

1800 conjugacy classes of subgroups.

The subgroup lattice has 740 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×#3106C211yesmaximal, characteristic, complemented
4C2×#2989C211yesmaximal, characteristic, complemented
5#19448C2116yesmaximal, direct product factor
6C2×#1704C211yesmaximal, characteristic, complemented
7C2×#1698C211yesmaximal, characteristic, complemented
8C2×#1688C211yesmaximal, characteristic, complemented
9C2×#1686C211yesmaximal, characteristic, complemented
10C2×#1703C211yesmaximal, characteristic, complemented
11C2×#1697C211yesmaximal, characteristic, complemented
12C2×#1687C211yesmaximal, characteristic, complemented
13C2×#1685C211yesmaximal, characteristic, complemented
14C2×#1572C211yesmaximal, characteristic, complemented
15C2×#1551C211yesmaximal, characteristic, complemented
16C2×#1540C211yesmaximal, characteristic, complemented
17C2×#532C2211yescharacteristic
18C2×#532C2211yescharacteristic
19C2×C4×#41C2211yescharacteristic
20#3207—24no—
21#3207C2218yescomplemented
22C2×#493C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#487C2211yescharacteristic
25C2×#486C2211yescharacteristic
26#3115—24no—
27#3115C2218yescomplemented
28#3106—24no—
29#3106C2218yescomplemented
30C2×#482—21no—
31C2×#482—21no—
32C2×#477C2211yescharacteristic
33C2×#475C2211yescharacteristic
34C2×#476C2211yescharacteristic
35C2×#474C2211yescharacteristic
36C2×#460C2211yescharacteristic
37C2×#460C2211yescharacteristic
38C2×#463—21no—
39C2×#463—21no—
40C2×#459C2211yescharacteristic
41C2×#459C2211yescharacteristic
42C2×#449—21no—
43C2×#449—21no—
44C2×#449—21no—
45C2×#449—21no—
46#2989—24no—
47#2989C2218yescomplemented
48C2×#446C2211yescharacteristic
49C2×#446C2211yescharacteristic
50C2×#442—21no—
51C2×#440—21no—
52C2×C4×SD16—21no—
53C2×C4×D8—21no—
54C2×#436C2211yescharacteristic
55C2×#436C2211yescharacteristic
56C2×#435—21no—
57C2×#435—21no—
58C2×#432—21no—
59C2×#432C2211yescharacteristic
60C2×#431C2211yescharacteristic
61C2×#431C2211yescharacteristic
62C2×#423—21no—
63C22×C4⋊C8C2211yescharacteristic
64#1704C2218yescomplemented
65#1703C2218yescomplemented
66#1698C2218yescomplemented
67#1697C2218yescomplemented
68#1688C2218yescomplemented
69#1687C2218yescomplemented
70#1686C2218yescomplemented
71#1685C2218yescomplemented
72#1572C2218yescomplemented
73C2×#335C2211yescharacteristic
74C2×#335C2211yescharacteristic
75C2×#334C2211yescharacteristic
76C2×#334C2211yescharacteristic
77#1551C2218yescomplemented
78C2×#333C2211yescharacteristic
79C2×#333C2211yescharacteristic
80#1540C2218yescomplemented
81C2×#332C2211yescharacteristic
82C2×#332C2211yescharacteristic
83C2×#331C2211yescharacteristic
84C2×#331C2211yescharacteristic
85C2×#331C2211yescharacteristic
86C2×#331C2211yescharacteristic
87C22×#41—21no—
88C22×#41—21no—
89C22×#41D411yescharacteristic
90C22×SD16—21no—
91C22×SD16—21no—
92C22×SD16—21no—
93C22×SD16—21no—
94C22×D8—21no—
95C22×D8—21no—
96C22×D8—21no—
97C22×D8—21no—
98C22×M16—21no—
99C22×M16—21no—
100C23×C8—21no—
101#532—22no—
102#532—22no—
103#532—22no—
104#532—22no—
105#532—22no—
106#532—22no—
107#532C2314yes—
108#532C2314yes—
109C2×C4⋊Q8C2311yescharacteristic
110C2×C4⋊Q8C2311yescharacteristic
111C2×#127C2311yescharacteristic
112C2×#127C2311yescharacteristic
113C2×#124—21no—
114C2×#124—21no—
115C2×#121—21no—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—21no—
119C4×#41—22no—
120C4×#41—22no—
121C4×#41D414yes—
122C4×#41C2314yes—
123C2×C4×Q8D411yescharacteristic
124C2×C4×Q8C2311yescharacteristic
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4D411yescharacteristic
132C2×C4×D4C2311yescharacteristic
133C2×#117—21no—
134C2×#117D411yescharacteristic
135C22×C42—21no—
136C22×C42C2311yescharacteristic
137#493—22no—
138#493C2314yes—
139#492—22no—
140#492C2314yes—
141#487—22no—
142#487C2314yes—
143#486—22no—
144#486C2314yes—
145#482—28no—
146#482—28no—
147#477—22no—
148#477C2314yes—
149#476—22no—
150#476C2314yes—
151#475—22no—
152#475C2314yes—
153#474—22no—
154#474C2314yes—
155#463—28no—
156#463—28no—
157#460—22no—
158#460—22no—
159#460C2314yes—
160#460C2314yes—
161#459—22no—
162#459—22no—
163#459C2314yes—
164#459C2314yes—
165#449—28no—
166#449—28no—
167#449—28no—
168#449—28no—
169#446—22no—
170#446—22no—
171#446C2314yes—
172#446C2314yes—
173#442—28no—
174#440—28no—
175C4×SD16—28no—
176C4×D8—28no—
177#436—22no—
178#436—22no—
179#436C2314yes—
180#436C2314yes—
181#435—28no—
182#435—28no—
183#432—22no—
184#432—28no—
185#432C2314yes—
186#431—22no—
187#431D414yes—
188#431C2314yes—
189#431C2314yes—
190C2×#107—21no—
191C2×#107—21no—
192C2×#106—21no—
193C2×#106—21no—
194#423—28no—
195C2×C4⋊C8—21no—
196C2×C4⋊C8—21no—
197C2×C4⋊C8—21no—
198C2×C4⋊C8—22no—
199C2×C4⋊C8D411yescharacteristic
200C2×C4⋊C8D411yescharacteristic
201C2×C4⋊C8C2311yescharacteristic
202C2×C4⋊C8C2311yescharacteristic
203C2×C4⋊C8C2311yescharacteristic
204C2×C4⋊C8C2311yescharacteristic
205C2×C4⋊C8C2311yescharacteristic
206C2×C4⋊C8C2311yescharacteristic
207C2×C4⋊C8C2314yes—
208C2×#103—21no—
209C2×#103—21no—
210C2×#103—21no—
211C2×#103—21no—
212C2×#102—21no—
213C2×#102—21no—
214C2×#102—21no—
215C2×#102—21no—
216C2×#102—21no—
217C2×#102—21no—
218C2×#102—21no—
219C2×#102—21no—
220C2×C22⋊C8—21no—
221C2×C22⋊C8—21no—
222C2×C22⋊C8—21no—
223C2×C22⋊C8—21no—
224C2×C22⋊C8D411yescharacteristic
225C2×C22⋊C8D411yescharacteristic
226C2×#97—21no—
227C2×#97—21no—
228C2×#97—21no—
229C2×C4×C8—21no—
230C2×C4×C8C2311yescharacteristic
231C2×C4×C8C2311yescharacteristic
232#335C2314yes—
233#335C2314yes—
234#334C2314yes—
235#334C2314yes—
236#333C2314yes—
237#333C2314yes—
238#332C2314yes—
239#332C2314yes—
240#331C2314yes—
241#331C2314yes—
242#331C2314yes—
243#331C2314yes—
244C2×#41—22no—
245C2×#41—24no—
246C2×#41—24no—
247C2×#41—42no—
248C2×#41—42no—
249C2×#41—42no—
250C2×#41—42no—
251C2×#41—82no—
252C2×#41—82no—
253C2×#41—84no—
254C2×#41C2×D414yes—
255C22×Q8—21no—
256C22×Q8—21no—
257C22×Q8C2×D411yescharacteristic
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—41no—
266C22×D4—41no—
267C22×D4C2×D411yescharacteristic
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—41no—
272C23×C4—41no—
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4#4111yescharacteristic
276C2×SD16—24no—
277C2×SD16—24no—
278C2×SD16—24no—
279C2×SD16—24no—
280C2×SD16—44no—
281C2×SD16—44no—
282C2×SD16—82no—
283C2×SD16—82no—
284C2×D8—24no—
285C2×D8—24no—
286C2×D8—24no—
287C2×D8—24no—
288C2×D8—44no—
289C2×D8—44no—
290C2×D8—82no—
291C2×D8—82no—
292C2×M16—24no—
293C2×M16—24no—
294C2×M16—82no—
295C2×M16—82no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—24no—
303C22×C8—82no—
304C22×C8C2×D411yescharacteristic
305C22×C8C2×D411yescharacteristic
306C22×C8C2×D411yescharacteristic
307C22×C8C2×D411yescharacteristic
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8C2412yes—
315C4⋊Q8C2412yes—
316#127—21no—
317#127—21no—
318#127—21no—
319#127—21no—
320#127—21no—
321#127—21no—
322#127C2412yes—
323#127C2412yes—
324#124—24no—
325#124—24no—
326#124—42no—
327#124—42no—
328#121—24no—
329#121—24no—
330#121—24no—
331#121—24no—
332#121—42no—
333#121—42no—
334#121—42no—
335#121—42no—
336C4×Q8—22no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8C2×D414yes—
340C4×Q8C2×D412yes—
341C4×Q8C2412yes—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—24no—
345C4×D4—24no—
346C4×D4—22no—
347C4×D4—21no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—24no—
351C4×D4—21no—
352C4×D4—24no—
353C4×D4—42no—
354C4×D4—42no—
355C4×D4—42no—
356C4×D4—42no—
357C4×D4C2×D414yes—
358C4×D4C2×D412yes—
359C4×D4C2412yes—
360#117—22no—
361#117—24no—
362#117—24no—
363#117C2×D414yes—
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⋊C4C2×D411yescharacteristic
371C2×C4⋊C4C2×D411yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42C2×D411yescharacteristic
385C2×C42C2×D411yescharacteristic
386C2×C42C2×D412yes—
387C2×C42C2×D412yes—
388C2×C42#4111yescharacteristic
389C2×C42#4112yes—
390C2×C42C2411yescharacteristic
391C2×C42C2412yes—
392#107—24no—
393#107—24no—
394#106—24no—
395#106—24no—
396C4⋊C8—24no—
397C4⋊C8—24no—
398C4⋊C8—24no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C2×D414yes—
406C4⋊C8C2×D414yes—
407C4⋊C8C2412yes—
408C4⋊C8C2412yes—
409C4⋊C8C2412yes—
410C4⋊C8C2412yes—
411C4⋊C8C2412yes—
412C4⋊C8C2412yes—
413#103—24no—
414#103—24no—
415#103—24no—
416#103—24no—
417#102—24no—
418#102—24no—
419#102—24no—
420#102—24no—
421#102—24no—
422#102—24no—
423#102—24no—
424#102—24no—
425C22⋊C8—24no—
426C22⋊C8—24no—
427C22⋊C8—24no—
428C22⋊C8—24no—
429C22⋊C8C2×D414yes—
430C22⋊C8C2×D414yes—
431#97—24no—
432#97—24no—
433#97—24no—
434C4×C8—24no—
435C4×C8C2×D412yes—
436C4×C8C2×D412yes—
437C4×C8C2412yes—
438C4×C8C2412yes—
439C24—21no—
440C24—41no—
441C24—41no—
442C24#12111yescharacteristic
443#41—44no—
444#41—44no—
445#41—48no—
446#41—84no—
447#41—84no—
448#41—88no—
449#41—88no—
450#41—88no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—82no—
461C2×Q8C22×D412yes—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—82no—
490C2×D4—82no—
491C2×D4—84no—
492C2×D4—84no—
493C2×D4C22×D412yes—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—42no—
506C22×C4—44no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—82no—
514C22×C4—84no—
515C22×C4—84no—
516C22×C4#12112yes—
517C22×C4#12112yes—
518C22×C4#12111yescharacteristic
519C22×C4#12111yescharacteristic
520C22×C4#12111yescharacteristic
521C22×C4#12112yes—
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C2×#4111yescharacteristic
527C22×C4C2×#4112yes—
528SD16—48no—
529SD16—48no—
530SD16—84no—
531SD16—84no—
532D8—48no—
533D8—48no—
534D8—84no—
535D8—84no—
536M16—84no—
537M16—84no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—42no—
549C2×C8—42no—
550C2×C8—42no—
551C2×C8—42no—
552C2×C8—42no—
553C2×C8—42no—
554C2×C8—84no—
555C2×C8C22×D412yes—
556C2×C8C22×D412yes—
557C2×C8C22×D412yes—
558C2×C8C22×D412yes—
559C4⋊C4—22no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4C22×D412yes—
573C4⋊C4C22×D412yes—
574C22⋊C4—24no—
575C22⋊C4—22no—
576C22⋊C4—24no—
577C22⋊C4—22no—
578C22⋊C4—44no—
579C22⋊C4—44no—
580C22⋊C4—44no—
581C22⋊C4—44no—
582C42—24no—
583C42—24no—
584C42—22no—
585C42—22no—
586C42#12112yes—
587C42#12112yes—
588C42#12112yes—
589C42C22×D412yes—
590C42C22×D411yescharacteristic
591C42C22×D411yescharacteristic
592C42C22×D412yes—
593C42C2×#4112yes—
594C42C2×#4111yescharacteristic
595C42C2511yescharacteristic
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—82no—
606C23—82no—
607C23—82no—
608C23—82no—
609C23—82no—
610C23—82no—
611C23C2×#12112yes—
612C23C2×#12111yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—42no—
616Q8—42no—
617Q8—42no—
618Q8—82no—
619Q8—82no—
620Q8—82no—
621D4—22no—
622D4—22no—
623D4—48no—
624D4—42no—
625D4—42no—
626D4—42no—
627D4—42no—
628D4—42no—
629D4—42no—
630D4—42no—
631D4—42no—
632D4—42no—
633D4—82no—
634D4—82no—
635D4—82no—
636D4—82no—
637D4—88no—
638D4—88no—
639D4—82no—
640D4—82no—
641D4—82no—
642D4—82no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—48no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—44no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—84no—
668C2×C4—88no—
669C2×C4—88no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4C2×#12112yes—
673C2×C4C2×#12112yes—
674C2×C4C2×#12111yescharacteristic
675C2×C4C2×#12112yes—
676C2×C4C2×#12111yescharacteristic
677C2×C4C2×#12111yescharacteristic
678C2×C4#57512yes—
679C2×C4#57512yes—
680C2×C4#57612yes—
681C2×C4#57712yes—
682C2×C4C23×D411yescharacteristic
683C2×C4C23×D411yescharacteristic
684C2×C4C22×#4111yescharacteristic
685C8—22no—
686C8—22no—
687C8—22no—
688C8—22no—
689C8—42no—
690C8—42no—
691C8—42no—
692C8—42no—
693C8—42no—
694C8—42no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—44no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—84no—
703C22—82no—
704C22—82no—
705C22—82no—
706C22—82no—
707C22—82no—
708C22—82no—
709C22—164no—
710C22—164no—
711C22#304512yes—
712C22#305412yes—
713C22#306812yes—
714C22C22×#12111yescharacteristic
715C4—22no—
716C4—22no—
717C4—22no—
718C4—21no—
719C4—21no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—82no—
724C4—82no—
725C4#304512yes—
726C4#305412yes—
727C4C2×#57511yescharacteristic
728C4C2×#57511yescharacteristic
729C4C2×#57611yescharacteristic
730C4C2×#57711yescharacteristic
731C2—42no—
732C2—82no—
733C2—162no—
734C2—162no—
735C2#1944814yesdirect product factor
736C2C2×#304511yescharacteristic
737C2C2×#305411yescharacteristic
738C2C2×#306811yescharacteristic
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×#3106C2semidirect
4. C2×#2989C2semidirect
5. #19448C2direct (N × H)
6. C2×#1704C2semidirect
7. C2×#1698C2semidirect
8. C2×#1688C2semidirect
9. C2×#1686C2semidirect
10. C2×#1703C2semidirect
11. C2×#1697C2semidirect
12. C2×#1687C2semidirect
13. C2×#1685C2semidirect
14. C2×#1572C2semidirect
15. C2×#1551C2semidirect
16. C2×#1540C2semidirect
21. #3207C22semidirect
27. #3115C22semidirect
29. #3106C22semidirect
47. #2989C22semidirect
64. #1704C22semidirect
65. #1703C22semidirect
66. #1698C22semidirect
67. #1697C22semidirect
68. #1688C22semidirect
69. #1687C22semidirect
70. #1686C22semidirect
71. #1685C22semidirect
72. #1572C22semidirect
77. #1551C22semidirect
80. #1540C22semidirect
735. C2#19448direct (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×#31062
C2×#29892
#194482
C2×#17042
C2×#16982
C2×#16882
C2×#16862
C2×#17032
C2×#16972
C2×#16872
C2×#16852
C2×#15722
C2×#15512
C2×#15402