Finite Group Databasebeta

← C4×#19128002 #35412012

Subgroups — C4×#19128002 #35412012

Order 21248.

948 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128002C211yesmaximal, characteristic
2C4×#14581784C211yesmaximal, characteristic, complemented
3C42×D332C211yesmaximal, characteristic
4#24908418C211yesmaximal, characteristic, complemented
5#24908233C211yesmaximal, characteristic, complemented
6#24908056C211yesmaximal, characteristic, complemented
7#24908042C211yesmaximal, characteristic, complemented
8#24907727C211yesmaximal, characteristic
9#24907713C211yesmaximal, characteristic
10#24907474C211yesmaximal, characteristic
11C4×#14581726C211yesmaximal, characteristic, complemented
12C4×#14581724C211yesmaximal, characteristic, complemented
13C4×#14581714C211yesmaximal, characteristic
14C4×#14581714C211yesmaximal, characteristic
15C4×C4⋊C8×C83C211yesmaximal, characteristic, complemented
16C2×#14581784C2211yescharacteristic
17C2×C4×D332C2211yescharacteristic
18C2×C4×D332C2211yescharacteristic
19C2×C4×D332C2211yescharacteristic
20C2×C42×D83—21no—
21#19128002C418yesdirect product factor
22C2×#14581726C2211yescharacteristic
23C2×#14581726C2211yescharacteristic
24C2×#14581724C2211yescharacteristic
25C2×#14581724C2211yescharacteristic
26C2×#14581714C2211yescharacteristic
27C2×#14581714C2211yescharacteristic
28C2×#14581714C2211yescharacteristic
29C2×#14581714C2211yescharacteristic
30#19127599C2211yescharacteristic
31#19127599C2211yescharacteristic
32#19127585—21no—
33#19127585—21no—
34#19127567C2211yescharacteristic
35C4×Dic83⋊C4—21no—
36C4×Dic83⋊C4—21no—
37C4×C4⋊Dic83C2211yescharacteristic
38C4×C4⋊Dic83C2211yescharacteristic
39C4×C4⋊Dic83C2211yescharacteristic
40C4×C4⋊Dic83C2211yescharacteristic
41C4×C4⋊Dic83C2211yescharacteristic
42C4×(C2×D83)⋊C4—21no—
43C4×(C2×D83)⋊C4—21no—
44C4×(C2×D83)⋊C4—21no—
45#19127464C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127464C2211yescharacteristic
50#19127464C2211yescharacteristic
51#19127464C2211yescharacteristic
52#19127464C2211yescharacteristic
53C2×C4⋊C8×C83C2211yescharacteristic
54C2×C4⋊C8×C83C2211yescharacteristic
55C2×C4×C8×C83C2211yescharacteristic
56C2×C4×C8×C83C2211yescharacteristic
57C43×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60C22×D332C2311yescharacteristic
61C22×C4×D83—21no—
62C22×C4×D83—21no—
63C22×C4×D83—21no—
64#14581784—22no—
65#14581784C2×C414yescomplemented
66C4×D332—22no—
67C4×D332—22no—
68C4×D332—22no—
69C4×D332—22no—
70C4×D332C2×C414yes—
71C4×D332Q814yes—
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×C4⋊Dic83C2311yescharacteristic
76C2×C4⋊Dic83C2311yescharacteristic
77C2×C4⋊Dic83C2311yescharacteristic
78C2×C4⋊Dic83C2311yescharacteristic
79C2×Dic83⋊C4—21no—
80C2×Dic83⋊C4—21no—
81C2×Dic83⋊C4—21no—
82C2×Dic83⋊C4—21no—
83C2×(C2×D83)⋊C4—21no—
84C2×(C2×D83)⋊C4—21no—
85C2×(C2×D83)⋊C4—21no—
86C2×C4×Dic83—21no—
87C2×C4×Dic83—21no—
88C2×C4×Dic83—21no—
89C2×C4×Dic83—21no—
90C2×C4×Dic83—21no—
91C42×D83—44no—
92#14581726—22no—
93#14581726C2×C414yescomplemented
94#14581724—22no—
95#14581724C2×C414yescomplemented
96#14581714—22no—
97#14581714—22no—
98#14581714C2×C414yes—
99#14581714C2×C414yes—
100C83⋊#95—21no—
101C83⋊#95—21no—
102C83⋊#95—21no—
103C83⋊#95—21no—
104C83⋊#95—21no—
105C83⋊#95—21no—
106C83⋊#95—21no—
107C83⋊#95—21no—
108C83⋊#95—21no—
109C22×C8×C83C2311yescharacteristic
110C22×C8×C83C2311yescharacteristic
111C22×C8×C83C2311yescharacteristic
112C22×C8×C83C2311yescharacteristic
113C2×C42×C83D411yescharacteristic
114C2×C42×C83D411yescharacteristic
115C2×C42×C83D411yescharacteristic
116C2×C42×C83D411yescharacteristic
117C2×C42×C83C2311yescharacteristic
118C2×C42×C83C2311yescharacteristic
119C2×C42×C83C2311yescharacteristic
120C4⋊C8×C83—22no—
121C4⋊C8×C83C2×C414yescomplemented
122C4×C8×C83—22no—
123C4×C8×C83—22no—
124C23×D83—21no—
125C2×D332—21no—
126C2×D332—21no—
127C2×D332—21no—
128C2×D332C22×C412yes—
129C2×D332C2×Q812yes—
130C2×D332#4112yes—
131C22×Dic83—21no—
132C22×Dic83—21no—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C2×C4×D83—24no—
139C2×C4×D83—24no—
140C2×C4×D83—24no—
141C2×C4×D83—42no—
142C2×C4×D83—42no—
143C2×C4×D83—42no—
144C2×C4×D83—42no—
145C2×C4×D83—42no—
146C2×C4×D83—42no—
147C4⋊Dic83—21no—
148C4⋊Dic83—21no—
149C4⋊Dic83—21no—
150C4⋊Dic83—21no—
151C4⋊Dic83—21no—
152C4⋊Dic83—21no—
153C4⋊Dic83—21no—
154C4⋊Dic83—21no—
155C4⋊Dic83—21no—
156C4⋊Dic83C22×C412yes—
157C4⋊Dic83C22×C412yes—
158C4⋊Dic83C22×C412yes—
159C4⋊Dic83C2×Q812yes—
160C4⋊Dic83#4112yes—
161Dic83⋊C4—24no—
162Dic83⋊C4—24no—
163Dic83⋊C4—42no—
164Dic83⋊C4—42no—
165(C2×D83)⋊C4—24no—
166(C2×D83)⋊C4—24no—
167(C2×D83)⋊C4—24no—
168C4×Dic83—42no—
169C4×Dic83—42no—
170C4×Dic83—42no—
171C4×Dic83—42no—
172C4×Dic83—42no—
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2×D411yescharacteristic
178C22×C4×C83C2×D411yescharacteristic
179C22×C4×C83C2411yescharacteristic
180C2×C8×C83—21no—
181C2×C8×C83—21no—
182C2×C8×C83—21no—
183C2×C8×C83—21no—
184C2×C8×C83—21no—
185C2×C8×C83—21no—
186C2×C8×C83—21no—
187C2×C8×C83—21no—
188C2×C8×C83—21no—
189C2×C8×C83—21no—
190C2×C8×C83C22×C412yes—
191C2×C8×C83C22×C412yes—
192C42×C83—22no—
193C42×C83—22no—
194C42×C83—22no—
195C42×C83—21no—
196C42×C83—21no—
197C42×C83—41no—
198C42×C83C22×C412yes—
199C42×C83C2×Q812yes—
200C42×C83#4112yes—
201C42×C83#4112yes—
202C23×C83C22×D411yescharacteristic
203C22×D83—22no—
204C22×D83—22no—
205C22×D83—22no—
206C22×D83—41no—
207C22×D83—41no—
208C22×D83—41no—
209C22×D83—41no—
210C2×C4×C83—21no—
211C2×C4×C83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83C4×D412yes—
222C2×C4×C83C4×D412yes—
223C2×C4×C83C22⋊Q812yes—
224C2×C4×C83C22⋊Q812yes—
225C2×C4×C83#13512yes—
226C2×C4×C83#13512yes—
227C2×C4×C83AGL(1,ℤ/8)12yes—
228C2×C4×C83C23×C411yescharacteristic
229C2×C4×C83C22×Q811yescharacteristic
230C2×C4×C83C2×#4111yescharacteristic
231C2×C4×C83C2×#4111yescharacteristic
232C2×C4×C83C2×#4111yescharacteristic
233C2×C4×C83C2×#4111yescharacteristic
234C2×Dic83—22no—
235C2×Dic83—22no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—22no—
239C2×Dic83—41no—
240C2×Dic83—41no—
241C2×Dic83—41no—
242C2×Dic83—41no—
243C2×Dic83—41no—
244C2×Dic83—41no—
245C2×Dic83—41no—
246C2×Dic83—41no—
247C2×Dic83—41no—
248C2×Dic83—41no—
249C2×Dic83—41no—
250C2×Dic83—41no—
251C2×Dic83—41no—
252C2×Dic83—41no—
253C2×Dic83—41no—
254C2×Dic83—41no—
255D332—22no—
256D332—22no—
257D332—22no—
258D332C4×Q814yes—
259C4×D83—48no—
260C4×D83—48no—
261C4×D83—48no—
262C8×C83—22no—
263C8×C83—22no—
264C8×C83—41no—
265C8×C83—41no—
266C22×C83C2×C4×D411yescharacteristic
267C22×C83C2×C22⋊Q811yescharacteristic
268C22×C83#52511yescharacteristic
269C22×C83C2×#13511yescharacteristic
270C22×C83C2×#13511yescharacteristic
271C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C83#57511yescharacteristic
273C2×D83—24no—
274C2×D83—42no—
275C2×D83—42no—
276C2×D83—42no—
277C2×D83—42no—
278C2×D83—42no—
279C2×D83—42no—
280C4×C83—22no—
281C4×C83—22no—
282C4×C83—22no—
283C4×C83—22no—
284C4×C83—41no—
285C4×C83#47814yescomplemented
286C4×C83C2×C4×Q811yescharacteristic
287C4×C83C4×#4111yescharacteristic
288C4×C83#52911yescharacteristic
289C4×C83#53311yescharacteristic
290Dic83—42no—
291Dic83—42no—
292Dic83—42no—
293Dic83—42no—
294Dic83—42no—
295Dic83—81no—
296Dic83—81no—
297C4×#478—831nomaximal, Sylow
298C2×C83C4×C22⋊Q811yescharacteristic
299C2×C83C4×#13511yescharacteristic
300C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
301C2×C83C2×#47811yescharacteristic
302C2×C83#307611yescharacteristic
303C2×C83#310211yescharacteristic
304C2×C83#310511yescharacteristic
305D83—44no—
306C2×#478—831no—
307C4×#125—831no—
308C42×D4—831no—
309#1989—831no—
310#1949—831no—
311#1921—831no—
312#1919—831no—
313#1864—831no—
314#1862—831no—
315#1804—831no—
316C4×#107—831no—
317C4×#106—831no—
318C4×C4⋊C8D8311yescharacteristic, complemented
319C4×#102—831no—
320C4×#102—831no—
321C83C4×#47811yescharacteristic, complemented, Sylow
322C2×#125—831no—
323C2×C4×D4—831no—
324C2×C4×D4—831no—
325C2×C4×D4—831no—
326C22×C42—1661no—
327#478—838no—
328C2×#107—831no—
329C2×#107—831no—
330C2×#106—831no—
331C2×#106—831no—
332C2×C4⋊C8C2×D8311yescharacteristic
333C2×C4⋊C8C2×D8311yescharacteristic
334C2×#102—831no—
335C2×#102—831no—
336C2×#102—831no—
337C2×#102—831no—
338C2×C4×C8C2×D8311yescharacteristic
339C2×C4×C8C2×D8311yescharacteristic
340#389—831no—
341#389—831no—
342#387—1661no—
343#387—1661no—
344#382—831no—
345C4×C4⋊C4—831no—
346C4×C4⋊C4—831no—
347C4×C4⋊C4—831no—
348C4×C4⋊C4—831no—
349C4×C4⋊C4—831no—
350C4×C4⋊C4—1661no—
351C4×C4⋊C4—1661no—
352C4×C22⋊C4—1661no—
353C4×C22⋊C4—1661no—
354C4×C22⋊C4—1661no—
355C43C2×D8311yescharacteristic
356#340—831no—
357#340—831no—
358#340—831no—
359#340—831no—
360#340—831no—
361#340—831no—
362#340—831no—
363#340—831no—
364#336C2×D8311yescharacteristic
365#336C2×D8311yescharacteristic
366C22×D4—831no—
367C23×C4—1661no—
368C23×C4—1661no—
369C23×C4—1661no—
370C22×C8C22×D8311yescharacteristic
371C22×C8C22×D8311yescharacteristic
372C22×C8C22×D8311yescharacteristic
373C22×C8C22×D8311yescharacteristic
374#125—834no—
375#125—1662no—
376C4×D4—834no—
377C4×D4—834no—
378C4×D4—1662no—
379C4×D4—1662no—
380C4×D4—1662no—
381C4×D4—1662no—
382C2×C4⋊C4—831no—
383C2×C4⋊C4—831no—
384C2×C4⋊C4—831no—
385C2×C4⋊C4—831no—
386C2×C4⋊C4—831no—
387C2×C4⋊C4—831no—
388C2×C4⋊C4—831no—
389C2×C4⋊C4—1661no—
390C2×C4⋊C4—1661no—
391C2×C4⋊C4—1661no—
392C2×C4⋊C4—1661no—
393C2×C22⋊C4—1661no—
394C2×C22⋊C4—1661no—
395C2×C22⋊C4—1661no—
396C2×C42—3324no—
397C2×C42—1661no—
398C2×C42—1661no—
399C2×C42—1661no—
400C2×C42—1661no—
401C2×C42—1661no—
402C2×C42D33211yescharacteristic
403C2×C42D33211yescharacteristic
404C2×C42D33211yescharacteristic
405C2×C42D33211yescharacteristic
406C2×C42C22×D8311yescharacteristic
407C2×C42C22×D8311yescharacteristic
408C2×C42C22×D8311yescharacteristic
409#107—834no—
410#107—1662no—
411#106—834no—
412#106—1662no—
413C4⋊C8—22no—
414C4⋊C8C4×D8314yescomplemented
415#102—834no—
416#102—834no—
417#102—1662no—
418#102—1662no—
419C4×C8—22no—
420C4×C8—22no—
421#95—1661no—
422#95—1661no—
423#95—1661no—
424#95—1661no—
425#95—1661no—
426#95—1661no—
427#95—1661no—
428#95—1661no—
429#95—1661no—
430C24—1661no—
431C2×D4—832no—
432C2×D4—832no—
433C2×D4—832no—
434C2×D4—1661no—
435C2×D4—1661no—
436C2×D4—1661no—
437C22×C4—3322no—
438C22×C4—3322no—
439C22×C4—3322no—
440C22×C4—3322no—
441C22×C4—3322no—
442C22×C4—3322no—
443C22×C4—1664no—
444C22×C4—1661no—
445C22×C4—1661no—
446C22×C4—1661no—
447C22×C4—1661no—
448C22×C4—1661no—
449C22×C4—1661no—
450C22×C4—1661no—
451C22×C4—1664no—
452C22×C4—1664no—
453C22×C4C2×D33211yescharacteristic
454C22×C4C2×D33211yescharacteristic
455C22×C4C2×D33211yescharacteristic
456C22×C4C2×D33211yescharacteristic
457C22×C4C2×D33211yescharacteristic
458C22×C4C2×D33211yescharacteristic
459C22×C4C23×D8311yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×C4×D8312yes—
471C2×C8C2×C4×D8312yes—
472C4⋊C4—3322no—
473C4⋊C4—3322no—
474C4⋊C4—832no—
475C4⋊C4—832no—
476C4⋊C4—832no—
477C4⋊C4—832no—
478C4⋊C4—832no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4—1661no—
482C4⋊C4—1661no—
483C4⋊C4—1661no—
484C4⋊C4—1661no—
485C4⋊C4—1661no—
486C4⋊C4—1661no—
487C4⋊C4—1661no—
488C4⋊C4—1664no—
489C4⋊C4—1664no—
490C22⋊C4—1664no—
491C22⋊C4—1664no—
492C22⋊C4—1664no—
493C42—22no—
494C42—22no—
495C42—22no—
496C42—21no—
497C42—21no—
498C42—41no—
499C42—3322no—
500C42—3322no—
501C42—3322no—
502C42—3322no—
503C42—3322no—
504C42C2×C4×D8312yes—
505C42Q8×D8312yes—
506C42#1305058912yes—
507C42#1305059012yes—
508C23—3321no—
509C23—3321no—
510C23—3321no—
511C23—3321no—
512C23—1662no—
513C23—1662no—
514C23—1662no—
515C23C22×D33211yescharacteristic
516D4—834no—
517D4—1662no—
518D4—1662no—
519D4—1662no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—3328no—
532C2×C4—3328no—
533C2×C4—3321no—
534C2×C4—3321no—
535C2×C4—3321no—
536C2×C4—3321no—
537C2×C4—3321no—
538C2×C4—3321no—
539C2×C4—3321no—
540C2×C4—3321no—
541C2×C4—3321no—
542C2×C4—3321no—
543C2×C4—3328no—
544C2×C4—3321no—
545C2×C4—3321no—
546C2×C4—3321no—
547C2×C4—3321no—
548C2×C4—3321no—
549C2×C4—3321no—
550C2×C4—1662no—
551C2×C4—1662no—
552C2×C4—1662no—
553C2×C4—1662no—
554C2×C4—1662no—
555C2×C4C4×D33212yes—
556C2×C4C4×D33212yes—
557C2×C4#1458177212yes—
558C2×C4#1458177212yes—
559C2×C4#1458181412yes—
560C2×C4#1458181412yes—
561C2×C4#1458182012yes—
562C2×C4C22×C4×D8311yescharacteristic
563C2×C4C2×Q8×D8311yescharacteristic
564C2×C4#41×D8311yescharacteristic
565C2×C4#41×D8311yescharacteristic
566C2×C4C2×#1305058911yescharacteristic
567C2×C4C2×#1305059011yescharacteristic
568C8—22no—
569C8—22no—
570C8—41no—
571C8—41no—
572C22—3322no—
573C22—3322no—
574C22—3322no—
575C22—3322no—
576C22—3322no—
577C22—3322no—
578C22—1664no—
579C22C2×C4×D33211yescharacteristic
580C22C2×#1458177211yescharacteristic
581C22#1912821311yescharacteristic
582C22C2×#1458181411yescharacteristic
583C22C2×#1458181411yescharacteristic
584C22C2×#1458182011yescharacteristic
585C22#1912850111yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—41no—
591C4—3322no—
592C4—3322no—
593C4—3322no—
594C4—3322no—
595C4—3322no—
596C4—6641no—
597C4—6641no—
598C4#1912800214yesdirect product factor
599C4C4×Q8×D8311yescharacteristic
600C4C4×#1305058911yescharacteristic
601C4#1912823311yescharacteristic
602C4#1912825511yescharacteristic
603C2—3324no—
604C2C4×#1458177211yescharacteristic
605C2C4×#1458181411yescharacteristic
606C2C4×#1458182011yescharacteristic
607C2C2×#1912800211yescharacteristic
608C2#2491725311yescharacteristic
609C2#2491748311yescharacteristic
610C2#2491751211yescharacteristic
subgroupG/H
centerC22×C4C2×D332
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC4×C4⋊C8×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
cosocleC22×C4×C83C24
hypercenterC4×C4⋊C8D83
hypocenterC83C4×#478
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#14581784C2semidirect
4. #24908418C2semidirect
5. #24908233C2semidirect
6. #24908056C2semidirect
7. #24908042C2semidirect
11. C4×#14581726C2semidirect
12. C4×#14581724C2semidirect
15. C4×C4⋊C8×C83C2semidirect
21. #19128002C4direct (N × H)
65. #14581784C2×C4semidirect
93. #14581726C2×C4semidirect
95. #14581724C2×C4semidirect
121. C4⋊C8×C83C2×C4semidirect
285. C4×C83#478semidirect
318. C4×C4⋊C8D83semidirect
321. C83C4×#478semidirect
414. C4⋊C8C4×D83semidirect
598. C4#19128002direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191280022
C4×#145817842
C42×D3322
#249084182
#249082332
#249080562
#249080422
#249077272
#249077132
#249074742
C4×#145817262
C4×#145817242
C4×#145817142
C4×C4⋊C8×C832
C4×#47883