Finite Group Databasebeta

← C4×#2063 #359394

Subgroups — C4×#2063 #359394

Order 512.

1218 conjugacy classes of subgroups.

The subgroup lattice has 737 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2063C211yesmaximal, characteristic
2C2×C4×#108C211yesmaximal, characteristic, complemented
3C4×#428C211yesmaximal, characteristic, complemented
4C4×#424C211yesmaximal, characteristic, complemented
5C4×#418C211yesmaximal, characteristic
6C2×C4×#102C211yesmaximal, characteristic
7C2×C4×#100C211yesmaximal, characteristic
8#11303C211yesmaximal, characteristic, complemented
9#11249C211yesmaximal, characteristic, complemented
10#11242C211yesmaximal, characteristic, complemented
11#11216C211yesmaximal, characteristic, complemented
12#11144C211yesmaximal, characteristic
13#11127C211yesmaximal, characteristic
14#11061C211yesmaximal, characteristic
15C4×#343C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C22×#108C2211yescharacteristic
18C22×#108C2211yescharacteristic
19C2×#428C2211yescharacteristic
20C2×#428C2211yescharacteristic
21C2×#424C2211yescharacteristic
22C2×#424C2211yescharacteristic
23C2×#418C2211yescharacteristic
24C2×#418C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#100C2211yescharacteristic
28C22×#100C2211yescharacteristic
29C2×C4×M16C2211yescharacteristic
30C2×C4×M16C2211yescharacteristic
31C2×C4×M16C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33C4×#117C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35#2063C418yesdirect product factor
36C4×#108—24no—
37#1776—21no—
38#1776—21no—
39C4×#107—21no—
40C4×#106—21no—
41#1768—22no—
42C4×C4⋊C8—22no—
43#1762—21no—
44#1762—21no—
45C4×#102—22no—
46C4×#102—22no—
47C4×#102—21no—
48C4×#102—21no—
49C4×#100—24no—
50C2×#343C2211yescharacteristic
51C2×#343C2211yescharacteristic
52C2×#343C2211yescharacteristic
53C2×#343C2211yescharacteristic
54C2×#343C2211yescharacteristic
55C2×#343C2211yescharacteristic
56C2×#341C2211yescharacteristic
57C2×#341C2211yescharacteristic
58#1736C2211yescharacteristic
59#1736C2211yescharacteristic
60#1736C2211yescharacteristic
61#1736C2211yescharacteristic
62C2×#340C2211yescharacteristic
63C2×#340C2211yescharacteristic
64#1729C2211yescharacteristic
65#1729C2211yescharacteristic
66C23×D4C2311yescharacteristic
67C24×C4—21no—
68C22×M16C2311yescharacteristic
69C22×M16C2311yescharacteristic
70C22×M16C2311yescharacteristic
71C22×M16C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C2×C4×D4—22no—
77C2×C4×D4—21no—
78C2×C4×D4—21no—
79C2×C4×D4—21no—
80C2×C4×D4—21no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4Q814yes—
84C2×#117C2311yescharacteristic
85C2×#117C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C22⋊C4—21no—
90C22×C42—21no—
91C22×C42C2311yescharacteristic
92C2×#108—22no—
93C2×#108—22no—
94C2×#108—22no—
95C2×#108—22no—
96C2×#108—22no—
97C2×#108C2×C414yescomplemented
98#428—22no—
99#428—22no—
100#428—22no—
101#428C2×C414yescomplemented
102C2×#107—21no—
103C2×#107—21no—
104C2×#106—21no—
105C2×#106—21no—
106#424—22no—
107#424—22no—
108#424—22no—
109#424C2×C414yescomplemented
110C2×C4⋊C8—22no—
111C2×C4⋊C8—22no—
112#418—22no—
113#418—22no—
114#418—22no—
115#418C2×C414yes—
116C2×#102—22no—
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—21no—
121C2×#102—21no—
122C2×#102—21no—
123C2×#102—21no—
124C2×#102—22no—
125C2×#102C2×C414yes—
126C2×#100—22no—
127C2×#100—22no—
128C2×#100—22no—
129C2×#100—22no—
130C2×#100—22no—
131C2×#100C2×C414yes—
132C4×M16—22no—
133C4×M16—22no—
134C4×M16—22no—
135C4×M16—22no—
136C4×M16—22no—
137C4×M16D414yes—
138C2×#97—21no—
139C2×#97—21no—
140C2×#97—21no—
141C2×C4×C8—22no—
142C2×C4×C8—21no—
143C2×C4×C8—22no—
144C2×C4×C8—21no—
145C2×C4×C8—21no—
146C2×C4×C8D412yes—
147C2×C4×C8D412yes—
148C4×C4⋊C4—21no—
149C4×C4⋊C4—21no—
150C4×C4⋊C4—21no—
151C4×C4⋊C4—21no—
152C4×C4⋊C4D411yescharacteristic
153C4×C4⋊C4D411yescharacteristic
154C4×C4⋊C4D411yescharacteristic
155C4×C4⋊C4D411yescharacteristic
156C4×C22⋊C4—21no—
157C4×C22⋊C4—21no—
158#376—21no—
159C2×#95—21no—
160C43—21no—
161#343—22no—
162#343—22no—
163#343—22no—
164#343—22no—
165#343—22no—
166#343C2×C414yescomplemented
167#341—22no—
168#341—22no—
169#340—22no—
170#340—22no—
171#340—21no—
172#340—21no—
173#340—21no—
174#340—21no—
175#340—21no—
176#340—21no—
177#340—21no—
178#340—21no—
179#336—22no—
180#336—22no—
181C25—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4C22×C412yes—
194C22×D4C2×Q812yes—
195C22×D4#4112yes—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—24no—
200C23×C4—41no—
201C23×C4—41no—
202C23×C4—42no—
203C23×C4—82no—
204C23×C4—82no—
205C23×C4#4111yescharacteristic
206C23×C4#4111yescharacteristic
207C23×C4C2411yescharacteristic
208C2×M16—21no—
209C2×M16—21no—
210C2×M16—21no—
211C2×M16—21no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16C22×C412yes—
237C2×M16C22×C412yes—
238C2×M16C22×C412yes—
239C2×M16C2×D412yes—
240C2×M16C2×D412yes—
241C2×M16#4112yes—
242C2×M16#4112yes—
243C2×M16#4112yes—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8C22×C412yes—
261C22×C8C2×D412yes—
262C22×C8C2×D412yes—
263C22×C8#4112yes—
264C4×D4—24no—
265C4×D4—24no—
266C4×D4—24no—
267C4×D4—24no—
268C4×D4—42no—
269C4×D4—42no—
270C4×D4—42no—
271C4×D4—42no—
272#117—21no—
273#117—21no—
274#117—21no—
275#117—21no—
276#117—21no—
277#117—21no—
278#117C22×C412yes—
279#117#4112yes—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4C22×C412yes—
296C2×C4⋊C4C2×D411yescharacteristic
297C2×C4⋊C4C2×D411yescharacteristic
298C2×C4⋊C4C2×D411yescharacteristic
299C2×C4⋊C4C2×D411yescharacteristic
300C2×C4⋊C4C2×Q812yes—
301C2×C4⋊C4#4112yes—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—41no—
306C2×C22⋊C4—41no—
307C2×C22⋊C4—42no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—41no—
315C2×C42—41no—
316C2×C42—82no—
317C2×C42C2×D412yes—
318C2×C42C2×D411yescharacteristic
319C2×C42C2×D411yescharacteristic
320C2×C42C2×D411yescharacteristic
321C2×C42C2×D411yescharacteristic
322C2×C42C2×Q812yes—
323C2×C42#4112yes—
324C2×C42#4112yes—
325#108—28no—
326#108—28no—
327#107—24no—
328#107—24no—
329#106—24no—
330#106—24no—
331C4⋊C8—28no—
332C4⋊C8—28no—
333#102—28no—
334#102—24no—
335#102—24no—
336#102—28no—
337#102—24no—
338#102—24no—
339#100—28no—
340#100—28no—
341#97—24no—
342#97—42no—
343#97—42no—
344C4×C8—24no—
345C4×C8—24no—
346C4×C8—24no—
347C4×C8—42no—
348C4×C8—42no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—41no—
354#95—41no—
355C24—22no—
356C24—22no—
357C24—22no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—81no—
363C24—81no—
364C24—81no—
365C24—81no—
366C24C2×#4111yescharacteristic
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4C4×Q814yes—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—82no—
415C22×C4—82no—
416C22×C4—88no—
417C22×C4—88no—
418C22×C4—82no—
419C22×C4—82no—
420C22×C4—81no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—81no—
424C22×C4—81no—
425C22×C4—81no—
426C22×C4#12111yescharacteristic
427C22×C4#12111yescharacteristic
428C22×C4#12111yescharacteristic
429C22×C4#12111yescharacteristic
430C22×C4C22⋊Q812yes—
431C22×C4C22⋊Q812yes—
432C22×C4#12612yes—
433C22×C4#12612yes—
434C22×C4C23×C411yescharacteristic
435C22×C4C22×D411yescharacteristic
436C22×C4C22×D411yescharacteristic
437C22×C4C22×D411yescharacteristic
438C22×C4C22×Q811yescharacteristic
439C22×C4C2×#4111yescharacteristic
440C22×C4C2×#4111yescharacteristic
441C22×C4C2×#4111yescharacteristic
442C22×C4C2×#4111yescharacteristic
443C22×C4C2×#4111yescharacteristic
444C22×C4C2×#4111yescharacteristic
445C22×C4C2×#4111yescharacteristic
446C22×C4C2×#4111yescharacteristic
447C22×C4C2×#4111yescharacteristic
448M16—22no—
449M16—22no—
450M16—22no—
451M16—22no—
452M16—22no—
453M16—22no—
454M16—22no—
455M16—22no—
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—41no—
462M16—41no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16C4×D414yes—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8C4×D414yes—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4C4×D412yes—
523C4⋊C4C4×D412yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—44no—
529C22⋊C4—44no—
530C42—22no—
531C42—22no—
532C42—42no—
533C42—42no—
534C42—41no—
535C42—41no—
536C42—42no—
537C42—42no—
538C42—82no—
539C42—82no—
540C42#12112yes—
541C42#12112yes—
542C42#12112yes—
543C42#12112yes—
544C42C22⋊Q812yes—
545C42C22⋊Q812yes—
546C42C22⋊Q812yes—
547C42C22⋊Q812yes—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—24no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—82no—
560C23—82no—
561C23—82no—
562C23—82no—
563C23—82no—
564C23—82no—
565C23—82no—
566C23—82no—
567C23—82no—
568C23—82no—
569C23—82no—
570C23—82no—
571C23—81no—
572C23—81no—
573C23—81no—
574C23—81no—
575C23C4×#4111yescharacteristic
576C23C2×#12111yescharacteristic
577C23C2×C22⋊Q811yescharacteristic
578C23C2×#12611yescharacteristic
579C23#52911yescharacteristic
580C23#52911yescharacteristic
581C23#52911yescharacteristic
582D4—24no—
583D4—24no—
584D4—42no—
585D4—42no—
586D4—42no—
587D4—42no—
588D4—42no—
589D4—42no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—88no—
616C2×C4—82no—
617C2×C4—82no—
618C2×C4—82no—
619C2×C4—81no—
620C2×C4—81no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4—88no—
626C2×C4—82no—
627C2×C4—82no—
628C2×C4—82no—
629C2×C4#39612yes—
630C2×C4#39612yes—
631C2×C4#39612yes—
632C2×C4#39612yes—
633C2×C4#47112yes—
634C2×C4#47212yes—
635C2×C4C2×C4×D411yescharacteristic
636C2×C4C2×C4×D411yescharacteristic
637C2×C4C2×C4×D411yescharacteristic
638C2×C4C2×C4×Q811yescharacteristic
639C2×C4C4×#4111yescharacteristic
640C2×C4C4×#4111yescharacteristic
641C2×C4C2×#12111yescharacteristic
642C2×C4C2×#12111yescharacteristic
643C2×C4C2×C22⋊Q811yescharacteristic
644C2×C4C2×C22⋊Q811yescharacteristic
645C2×C4#52511yescharacteristic
646C2×C4#52511yescharacteristic
647C2×C4#52511yescharacteristic
648C2×C4#52511yescharacteristic
649C2×C4#52511yescharacteristic
650C2×C4#52511yescharacteristic
651C2×C4#52911yescharacteristic
652C2×C4#52911yescharacteristic
653C2×C4#52911yescharacteristic
654C2×C4#52911yescharacteristic
655C2×C4#52911yescharacteristic
656C2×C4#52911yescharacteristic
657C2×C4#53211yescharacteristic
658C2×C4#53211yescharacteristic
659C2×C4#53211yescharacteristic
660C2×C4#53311yescharacteristic
661C2×C4#53311yescharacteristic
662C2×C4#53311yescharacteristic
663C8—24no—
664C8—24no—
665C8—42no—
666C8—42no—
667C8—42no—
668C8—42no—
669C8—42no—
670C8—42no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—21no—
682C22—21no—
683C22—44no—
684C22—84no—
685C22—84no—
686C22—84no—
687C22—84no—
688C22—82no—
689C22—82no—
690C22—82no—
691C22—82no—
692C22—82no—
693C22—82no—
694C22C4×#12111yescharacteristic
695C22C4×C22⋊Q811yescharacteristic
696C22C4×#12611yescharacteristic
697C22C2×#39611yescharacteristic
698C22#239211yescharacteristic
699C22#239611yescharacteristic
700C22#240111yescharacteristic
701C22C2×#47111yescharacteristic
702C22C2×#47211yescharacteristic
703C22#306711yescharacteristic
704C22#306711yescharacteristic
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—82no—
711C4—82no—
712C4—81no—
713C4—82no—
714C4—81no—
715C4#206314yesdirect product factor
716C4C4×#12111yescharacteristic
717C4C4×#12111yescharacteristic
718C4C4×C22⋊Q811yescharacteristic
719C4C4×C22⋊Q811yescharacteristic
720C4#239211yescharacteristic
721C4#239211yescharacteristic
722C4#239611yescharacteristic
723C4#239611yescharacteristic
724C2—21no—
725C2—21no—
726C2—21no—
727C2—21no—
728C2—84no—
729C2C4×#39611yescharacteristic
730C2C4×#47111yescharacteristic
731C2C4×#47211yescharacteristic
732C2C2×#206311yescharacteristic
733C2#2360111yescharacteristic
734C2#2371611yescharacteristic
735C2#2371811yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×#121
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×#108C2semidirect
3. C4×#428C2semidirect
4. C4×#424C2semidirect
8. #11303C2semidirect
9. #11249C2semidirect
10. #11242C2semidirect
11. #11216C2semidirect
15. C4×#343C2semidirect
35. #2063C4direct (N × H)
97. C2×#108C2×C4semidirect
101. #428C2×C4semidirect
109. #424C2×C4semidirect
166. #343C2×C4semidirect
715. C4#2063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#20632
C2×C4×#1082
C4×#4282
C4×#4242
C4×#4182
C2×C4×#1022
C2×C4×#1002
#113032
#112492
#112422
#112162
#111442
#111272
#110612
C4×#3432