Finite Group Databasebeta

← C4×#19127851 #35409982

Subgroups — C4×#19127851 #35409982

Order 21248.

1880 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D332C211yesmaximal, characteristic
2C2×#19127851C211yesmaximal, characteristic
3C2×C4×#13050577C212yesmaximal, complemented
4#24907800C212yesmaximal, complemented
5#24907771C211yesmaximal, characteristic, complemented
6#24907723C212yesmaximal, complemented
7#24907655C211yesmaximal, characteristic, complemented
8#24907393C211yesmaximal, characteristic
9C4×#14581712C212yesmaximal, complemented
10C4×C22⋊(C83⋊C8)C211yesmaximal, characteristic, complemented
11C4×C22⋊Q8×C83C211yesmaximal, characteristic, complemented
12C23×D332C2211yescharacteristic
13C23×C4×D83—21no—
14C22×#13050577C2212yes—
15C2×C4×D332—28no—
16C2×C4×D332—21no—
17C2×C4×D332—21no—
18C2×C4×D332C2212yes—
19C2×C4×D332C2212yes—
20C22×C4⋊Dic83C2211yescharacteristic
21C22×(C2×D83)⋊C4—21no—
22#19127851C418yesdirect product factor
23C4×#13050577—28no—
24C2×#14581723C2212yescomplemented
25C2×#14581716C2212yescomplemented
26C2×#14581712C2212yes—
27C2×#14581712C2212yes—
28C2×#14581712C2212yes—
29C2×C22⋊(C83⋊C8)C2211yescharacteristic
30C2×C22⋊(C83⋊C8)C2211yescharacteristic
31C2×C4×C83⋊C8C2212yescomplemented
32#19127463C2212yescomplemented
33#19127463C2212yescomplemented
34#19127456C2212yescomplemented
35C2×C22⋊Q8×C83C2211yescharacteristic
36C2×C4×Q8×C83C2211yescharacteristic, complemented
37C22×C42×C83C2211yescharacteristic
38#391×C83C2211yescharacteristic, complemented
39#389×C83C2211yescharacteristic, complemented
40#387×C83—21no—
41#385×C83—21no—
42#380×C83C2211yescharacteristic
43C4×C4⋊C4×C83—21no—
44C4×C4⋊C4×C83C2211yescharacteristic, complemented
45C4×C22⋊C4×C83—21no—
46C24×D83—21no—
47C22×D332—24no—
48C22×D332—24no—
49C22×D332—21no—
50C22×D332—22no—
51C22×D332C2×C414yes—
52C22×D332C2312yes—
53C23×Dic83—21no—
54C22×C4×D83—28no—
55C22×C4×D83—22no—
56C22×C4×D83—22no—
57C22×C4×D83—44no—
58C22×C4×D83—44no—
59C2×#13050577—24no—
60C2×#13050577—24no—
61C2×#13050577C2×C418yescomplemented
62C22×C83⋊C8C2312yes—
63C22×C83⋊C8C2312yes—
64C4×D332—28no—
65C4×D332—28no—
66C4×D332—24no—
67C4×D332—24no—
68C4×D332—24no—
69C4×D332D418yes—
70C2×C4⋊Dic83—24no—
71C2×C4⋊Dic83—21no—
72C2×C4⋊Dic83C2312yes—
73C2×(C2×D83)⋊C4—28no—
74C2×(C2×D83)⋊C4—22no—
75C2×(C2×D83)⋊C4—22no—
76#14581723—24no—
77#14581716—24no—
78#14581712—24no—
79#14581712—24no—
80#14581712C2×C418yescomplemented
81C22⋊(C83⋊C8)—22no—
82C22⋊(C83⋊C8)C2×C414yescomplemented
83C4×C83⋊C8—24no—
84C22×Q8×C83C2311yescharacteristic
85C23×C4×C83D411yescharacteristic
86C23×C4×C83D411yescharacteristic
87C23×C4×C83C2311yescharacteristic
88C22⋊Q8×C83—22no—
89C22⋊Q8×C83C2×C414yescomplemented
90C4×Q8×C83—24no—
91C2×C4⋊C4×C83—21no—
92C2×C4⋊C4×C83—21no—
93C2×C4⋊C4×C83—21no—
94C2×C4⋊C4×C83C2311yescharacteristic
95C2×C4⋊C4×C83C2311yescharacteristic
96C2×C4⋊C4×C83C2311yescharacteristic
97C2×C22⋊C4×C83—21no—
98C2×C22⋊C4×C83—21no—
99C2×C42×C83—24no—
100C2×C42×C83—21no—
101C2×C42×C83—21no—
102C2×C42×C83D411yescharacteristic
103C2×C42×C83D411yescharacteristic
104C2×C42×C83C2311yescharacteristic
105C2×C42×C83C2311yescharacteristic
106#95×C83—21no—
107#95×C83—21no—
108#95×C83—21no—
109#95×C83—21no—
110#95×C83—21no—
111C23×D83—24no—
112C23×D83—24no—
113C23×D83—24no—
114C23×D83—22no—
115C23×D83—42no—
116C23×D83—42no—
117C23×D83—42no—
118C23×D83—42no—
119C2×D332—24no—
120C2×D332—216no—
121C2×D332—24no—
122C2×D332—24no—
123C2×D332—22no—
124C2×D332—22no—
125C2×D332—22no—
126C2×D332—216no—
127C2×D332C22×C414yes—
128C2×D332C2×D414yes—
129C2×D332#4114yes—
130C22×Dic83—24no—
131C22×Dic83—22no—
132C22×Dic83—42no—
133C22×Dic83—42no—
134C2×C4×D83—28no—
135C2×C4×D83—28no—
136C2×C4×D83—44no—
137C2×C4×D83—432no—
138C2×C4×D83—44no—
139C2×C4×D83—44no—
140C2×C4×D83—44no—
141#13050577—216no—
142C2×C83⋊C8—22no—
143C2×C83⋊C8—22no—
144C2×C83⋊C8—22no—
145C2×C83⋊C8—22no—
146C2×C83⋊C8—22no—
147C2×C83⋊C8C22×C414yescomplemented
148C4⋊Dic83—24no—
149C4⋊Dic83—22no—
150C4⋊Dic83C2×D414yes—
151(C2×D83)⋊C4—28no—
152(C2×D83)⋊C4—28no—
153C24×C83C2×D411yescharacteristic
154C2×Q8×C83—21no—
155C2×Q8×C83—22no—
156C2×Q8×C83—22no—
157C2×Q8×C83C22×C412yescomplemented
158C22×C4×C83—22no—
159C22×C4×C83—22no—
160C22×C4×C83—22no—
161C22×C4×C83—22no—
162C22×C4×C83—22no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—22no—
166C22×C4×C83—21no—
167C22×C4×C83—21no—
168C22×C4×C83—41no—
169C22×C4×C83SD1614yescomplemented
170C22×C4×C83C22×C412yes—
171C22×C4×C83C2×D411yescharacteristic
172C22×C4×C83C2×D411yescharacteristic
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83#4112yes—
177C22×C4×C83C2411yescharacteristic
178C4⋊C4×C83—24no—
179C4⋊C4×C83—21no—
180C4⋊C4×C83—22no—
181C4⋊C4×C83—22no—
182C4⋊C4×C83—42no—
183C4⋊C4×C83—42no—
184C4⋊C4×C83C22×C412yescomplemented
185C22⋊C4×C83—24no—
186C22⋊C4×C83—42no—
187C42×C83—22no—
188C42×C83—22no—
189C42×C83—22no—
190C42×C83—42no—
191C42×C83—42no—
192C42×C83C2×D414yes—
193C23×C83—21no—
194C23×C83—21no—
195C23×C83—21no—
196C23×C83—21no—
197C23×C83C4×D412yes—
198C23×C83C2×SD1612yes—
199C23×C83#13512yes—
200C23×C83C22×D411yescharacteristic
201C22×D83—216no—
202C22×D83—24no—
203C22×D83—24no—
204C22×D83—24no—
205C22×D83—48no—
206C22×D83—48no—
207C22×D83—48no—
208C22×D83—48no—
209C22×D83—48no—
210C22×D83—42no—
211C22×D83—42no—
212C22×D83—42no—
213C22×D83—42no—
214C22×D83—48no—
215Q8×C83—24no—
216Q8×C83—42no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—24no—
224C2×C4×C83—24no—
225C2×C4×C83—28no—
226C2×C4×C83—22no—
227C2×C4×C83—22no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—44no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83C4×D412yes—
243C2×C4×C83#12012yes—
244C2×C4×C83#12012yes—
245C2×C4×C83C2×SD1612yes—
246C2×C4×C83C2×SD1612yes—
247C2×C4×C83AGL(1,ℤ/8)12yes—
248C2×C4×C83C23×C411yescharacteristic
249C2×C4×C83C22×D412yes—
250C2×C4×C83C2×#4112yes—
251C2×C4×C83C2×#4111yescharacteristic
252C2×Dic83—24no—
253C2×Dic83—48no—
254C2×Dic83—42no—
255C2×Dic83—42no—
256D332—216no—
257D332—24no—
258D332—24no—
259D332—24no—
260D332C4×D418yes—
261C4×D83—416no—
262C4×D83—416no—
263C83⋊C8—24no—
264C83⋊C8—42no—
265C22×C83—22no—
266C22×C83—22no—
267C22×C83—22no—
268C22×C83—22no—
269C22×C83—22no—
270C22×C83—22no—
271C22×C83C4×SD1614yescomplemented
272C22×C83C2×C4×D411yescharacteristic
273C22×C83C2×#12011yescharacteristic
274C22×C83#52511yescharacteristic
275C22×C83C22×SD1611yescharacteristic
276C22×C83C2×#13511yescharacteristic
277C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
278C22×C83#57511yescharacteristic
279C2×D83—28no—
280C2×D83—432no—
281C2×D83—44no—
282C2×D83—44no—
283C2×D83—44no—
284C2×D83—44no—
285C2×D83—44no—
286C2×D83—44no—
287C4×C83—22no—
288C4×C83—22no—
289C4×C83—22no—
290C4×C83—42no—
291C4×C83—41no—
292C4×C83—42no—
293C4×C83—81no—
294C4×C83—81no—
295C4×C83#45014yescomplemented
296C4×C83C2×C4×D412yes—
297C4×C83#52512yes—
298Dic83—44no—
299C4×#450—831nomaximal, Sylow
300C2×C83—24no—
301C2×C83C4×#12011yescharacteristic
302C2×C83C2×C4×SD1611yescharacteristic
303C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
304C2×C83C2×#45011yescharacteristic
305C2×C83#300211yescharacteristic
306C2×C83#310111yescharacteristic
307C2×C83#310511yescharacteristic
308D83—48no—
309C22×C4×D4—831no—
310C2×#450—831no—
311C2×C4×SD16—832no—
312C4×C22⋊Q8D8311yescharacteristic, complemented
313#1877—832no—
314#1872—831no—
315#1864—832no—
316#1853—831no—
317#1786—831no—
318C4×#102—832no—
319C4×C22⋊C8—831no—
320C83C4×#45011yescharacteristic, complemented, Sylow
321C23×D4—831no—
322C24×C4—1661no—
323C22×SD16—832no—
324C2×C22⋊Q8C2×D8311yescharacteristic
325C2×C4×Q8C2×D8311yescharacteristic, complemented
326C2×C4×D4—832no—
327C2×C4×D4—832no—
328C2×C4×D4—1668no—
329C2×C4×D4—1661no—
330C2×C4×D4—1661no—
331C22×C4⋊C4—831no—
332C22×C22⋊C4—1661no—
333C22×C42C2×D8311yescharacteristic
334#450—838no—
335C4×SD16—1668no—
336C2×#106—832no—
337C2×#103—832no—
338C2×#102—832no—
339C2×#102—832no—
340C2×#102—832no—
341C2×C22⋊C8—831no—
342C2×C22⋊C8—831no—
343C2×C4×C8—832no—
344#391C2×D8311yescharacteristic, complemented
345#389C2×D8311yescharacteristic, complemented
346#387—21no—
347#385—21no—
348#380C2×D8311yescharacteristic
349C4×C4⋊C4—21no—
350C4×C4⋊C4C2×D8311yescharacteristic, complemented
351C4×C22⋊C4—21no—
352#340—832no—
353#340—832no—
354#336—832no—
355C25—1661no—
356C22×Q8C22×D8311yescharacteristic
357C22×D4—834no—
358C22×D4—832no—
359C22×D4—1664no—
360C22×D4—1664no—
361C22×D4—1661no—
362C22×D4—1662no—
363C23×C4—3324no—
364C23×C4—3324no—
365C23×C4—1668no—
366C23×C4—1661no—
367C23×C4—1662no—
368C23×C4—1662no—
369C23×C4C22⋊D8311yescharacteristic
370C23×C4C22⋊D8311yescharacteristic
371C23×C4C22×D8311yescharacteristic
372C2×SD16—838no—
373C2×SD16—1664no—
374C2×SD16—1664no—
375C22×C8—832no—
376C22×C8—832no—
377C22⋊Q8—22no—
378C22⋊Q8C4×D8314yescomplemented
379C4×Q8—24no—
380C4×D4—838no—
381C4×D4—1664no—
382C4×D4—1664no—
383C4×D4—1668no—
384C4×D4—1668no—
385C4×D4—1664no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—832no—
390C2×C4⋊C4—1664no—
391C2×C4⋊C4—1661no—
392C2×C4⋊C4C22×D8311yescharacteristic
393C2×C4⋊C4C22×D8311yescharacteristic
394C2×C4⋊C4C22×D8311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—1668no—
398C2×C22⋊C4—1662no—
399C2×C22⋊C4—1662no—
400C2×C42—24no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42C22⋊D8311yescharacteristic
404C2×C42C22⋊D8311yescharacteristic
405C2×C42C22×D8311yescharacteristic
406C2×C42C22×D8311yescharacteristic
407#106—1664no—
408#103—1664no—
409#102—838no—
410#102—1664no—
411#102—1664no—
412C22⋊C8—834no—
413C22⋊C8—1662no—
414C4×C8—1664no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420C24—3322no—
421C24—3322no—
422C24—3322no—
423C24—3322no—
424C24—1664no—
425C24—1664no—
426C24—1662no—
427C24—1664no—
428C24C2×C22⋊D8311yescharacteristic
429C2×Q8—21no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8C2×C4×D8312yescomplemented
433C2×D4—834no—
434C2×D4—834no—
435C2×D4—834no—
436C2×D4—16616no—
437C2×D4—1664no—
438C2×D4—1664no—
439C2×D4—16616no—
440C2×D4—1662no—
441C2×D4—1662no—
442C2×D4—1662no—
443C2×D4—1664no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—3324no—
456C22×C4—33232no—
457C22×C4—3322no—
458C22×C4—3322no—
459C22×C4—3324no—
460C22×C4—3324no—
461C22×C4—3324no—
462C22×C4—1668no—
463C22×C4—1664no—
464C22×C4—1662no—
465C22×C4—1668no—
466C22×C4#1305057714yescomplemented
467C22×C4C2×C4×D8312yes—
468C22×C4C2×C22⋊D8311yescharacteristic
469C22×C4C2×C22⋊D8311yescharacteristic
470C22×C4C2×C22⋊D8311yescharacteristic
471C22×C4C2×C22⋊D8311yescharacteristic
472C22×C4C2×C22⋊D8311yescharacteristic
473C22×C4#1305059012yes—
474C22×C4C23×D8311yescharacteristic
475SD16—16616no—
476C2×C8—834no—
477C2×C8—1662no—
478C2×C8—1662no—
479C2×C8—1662no—
480C2×C8—1662no—
481C2×C8—1662no—
482C4⋊C4—21no—
483C4⋊C4—24no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—834no—
489C4⋊C4—1664no—
490C4⋊C4—1662no—
491C4⋊C4C2×C4×D8312yescomplemented
492C22⋊C4—24no—
493C22⋊C4—42no—
494C22⋊C4—1668no—
495C22⋊C4—1668no—
496C42—22no—
497C42—22no—
498C42—22no—
499C42—42no—
500C42—42no—
501C42D4×D8314yes—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—3328no—
507C23—3328no—
508C23—3328no—
509C23—3328no—
510C23—3328no—
511C23—3322no—
512C23—3322no—
513C23—3322no—
514C23—3322no—
515C23—3328no—
516C23—16616no—
517C23—1664no—
518C23—1664no—
519C23—1664no—
520C23C4×C22⋊D8312yes—
521C23C2×#1305057712yes—
522C23#1458181212yes—
523C23C22×C22⋊D8311yescharacteristic
524Q8—24no—
525Q8—42no—
526D4—838no—
527D4—16616no—
528D4—1664no—
529D4—1664no—
530D4—1664no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—28no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—44no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—33216no—
557C2×C4—3328no—
558C2×C4—3322no—
559C2×C4—3322no—
560C2×C4—33216no—
561C2×C4—1664no—
562C2×C4C4×C22⋊D8312yes—
563C2×C4#1458176012yes—
564C2×C4#1458176012yes—
565C2×C4C2×#1305057712yes—
566C2×C4C2×#1305057712yes—
567C2×C4#1458181712yes—
568C2×C4C22×C4×D8311yescharacteristic
569C2×C4C2×D4×D8312yes—
570C2×C4#41×D8312yes—
571C2×C4C2×#1305059011yescharacteristic
572C8—3322no—
573C8—1664no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—33232no—
581C22—3324no—
582C22—3324no—
583C22—3324no—
584C22—3324no—
585C22—3324no—
586C22—3324no—
587C22—1668no—
588C22C4×#1305057714yescomplemented
589C22C2×C4×C22⋊D8311yescharacteristic
590C22C2×#1458176011yescharacteristic
591C22#1912820811yescharacteristic
592C22C22×#1305057711yescharacteristic
593C22C2×#1458181211yescharacteristic
594C22C2×#1458181711yescharacteristic
595C22#1912849911yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—42no—
600C4—42no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4—3324no—
605C4#1912785114yesdirect product factor
606C4C4×D4×D8312yes—
607C4#1912821012yes—
608C2—24no—
609C2—3328no—
610C2C4×#1458176011yescharacteristic
611C2C2×C4×#1305057711yescharacteristic
612C2C4×#1458181711yescharacteristic
613C2C2×#1912785111yescharacteristic
614C2#2491667911yescharacteristic
615C2#2491746711yescharacteristic
616C2#2491750611yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC4×C22⋊Q8×C83C2
socleC23×C83C22×D4
prime radicalC23×D332C22
cosocleC22×C4×C83C24
hypercenterC4×C22⋊Q8D83
hypocenterC83C4×#450
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×C4×#13050577C2semidirect
4. #24907800C2semidirect
5. #24907771C2semidirect
6. #24907723C2semidirect
7. #24907655C2semidirect
9. C4×#14581712C2semidirect
10. C4×C22⋊(C83⋊C8)C2semidirect
11. C4×C22⋊Q8×C83C2semidirect
22. #19127851C4direct (N × H)
24. C2×#14581723C22semidirect
25. C2×#14581716C22semidirect
31. C2×C4×C83⋊C8C22semidirect
32. #19127463C22semidirect
33. #19127463C22semidirect
34. #19127456C22semidirect
36. C2×C4×Q8×C83C22semidirect
38. #391×C83C22semidirect
39. #389×C83C22semidirect
44. C4×C4⋊C4×C83C22semidirect
61. C2×#13050577C2×C4semidirect
80. #14581712C2×C4semidirect
82. C22⋊(C83⋊C8)C2×C4semidirect
89. C22⋊Q8×C83C2×C4semidirect
147. C2×C83⋊C8C22×C4semidirect
157. C2×Q8×C83C22×C4semidirect
169. C22×C4×C83SD16semidirect
184. C4⋊C4×C83C22×C4semidirect
271. C22×C83C4×SD16semidirect
295. C4×C83#450semidirect
312. C4×C22⋊Q8D83semidirect
320. C83C4×#450semidirect
325. C2×C4×Q8C2×D83semidirect
344. #391C2×D83semidirect
345. #389C2×D83semidirect
350. C4×C4⋊C4C2×D83semidirect
378. C22⋊Q8C4×D83semidirect
432. C2×Q8C2×C4×D83semidirect
466. C22×C4#13050577semidirect
491. C4⋊C4C2×C4×D83semidirect
588. C22C4×#13050577semidirect
605. C4#19127851direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D3322
C2×#191278512
C2×C4×#130505772
#249078002
#249077712
#249077232
#249076552
#249073932
C4×#145817122
C4×C22⋊(C83⋊C8)2
C4×C22⋊Q8×C832
C4×#45083