Finite Group Databasebeta

← C4×#19128003 #35412014

Subgroups — C4×#19128003 #35412014

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×#19128003C211yesmaximal, characteristic
2C4×#14581783C211yesmaximal, characteristic, complemented
3C4×D4×Dic83C211yesmaximal, characteristic
4#24908417C211yesmaximal, characteristic, complemented
5#24908230C211yesmaximal, characteristic, complemented
6#24908058C211yesmaximal, characteristic, complemented
7#24908040C211yesmaximal, characteristic, complemented
8#24907726C211yesmaximal, characteristic
9#24907708C211yesmaximal, characteristic
10#24907471C211yesmaximal, characteristic
11C4×#14581725C211yesmaximal, characteristic, complemented
12C4×#14581724C211yesmaximal, characteristic, complemented
13C4×Dic83⋊C8C211yesmaximal, characteristic, complemented
14C4×#14581713C211yesmaximal, characteristic
15C4×#102×C83C211yesmaximal, characteristic
16C2×#14581783C2211yescharacteristic
17C2×D4×Dic83C2211yescharacteristic
18C2×D4×Dic83C2211yescharacteristic
19C22×C4×Dic83—21no—
20#19128003C418yesdirect product factor
21C2×#14581725C2211yescharacteristic
22C2×#14581725C2211yescharacteristic
23C2×#14581724C2211yescharacteristic
24C2×#14581724C2211yescharacteristic
25C2×Dic83⋊C8C2211yescharacteristic
26C2×Dic83⋊C8C2211yescharacteristic
27C2×#14581713C2211yescharacteristic
28C2×#14581713C2211yescharacteristic
29C2×C4×C83⋊C8C2211yescharacteristic
30#19127600C2211yescharacteristic
31#19127597C2211yescharacteristic
32#19127588—21no—
33#19127584—21no—
34#19127566C2211yescharacteristic
35C4⋊C4×Dic83C2211yescharacteristic
36C4⋊C4×Dic83C2211yescharacteristic
37C4×Dic83⋊C4—21no—
38C4×C4⋊Dic83—21no—
39C4×C4⋊Dic83C2211yescharacteristic
40C4×C4⋊Dic83C2211yescharacteristic
41C22⋊C4×Dic83—21no—
42C22⋊C4×Dic83—21no—
43C4×C22⋊Dic83—21no—
44C42×Dic83C2211yescharacteristic
45#19127464C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53C2×C4×D4×C83C2211yescharacteristic
54C2×#102×C83C2211yescharacteristic
55C2×#102×C83C2211yescharacteristic
56C2×C4×C8×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic
60C23×Dic83—21no—
61C23×Dic83—21no—
62C22×C83⋊C8C2311yescharacteristic
63C22×C83⋊C8C2311yescharacteristic
64#14581783—22no—
65#14581783C2×C414yescomplemented
66D4×Dic83—22no—
67D4×Dic83—22no—
68D4×Dic83—22no—
69D4×Dic83C2×C414yes—
70C2×C4⋊Dic83—21no—
71C2×C4⋊Dic83—21no—
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×C4⋊Dic83C2311yescharacteristic
76C2×Dic83⋊C4—21no—
77C2×Dic83⋊C4—21no—
78C2×C22⋊Dic83—21no—
79C2×C22⋊Dic83—21no—
80C2×C4×Dic83—21no—
81C2×C4×Dic83—21no—
82C2×C4×Dic83—21no—
83C2×C4×Dic83—21no—
84C2×C4×Dic83—44no—
85C2×C4×Dic83D411yescharacteristic
86C2×C4×Dic83D411yescharacteristic
87C2×C4×Dic83D411yescharacteristic
88C2×C4×Dic83D411yescharacteristic
89C2×C4×Dic83C2311yescharacteristic
90C2×C4×Dic83C2311yescharacteristic
91#14581725—22no—
92#14581725C2×C414yescomplemented
93#14581724—22no—
94#14581724C2×C414yescomplemented
95Dic83⋊C8—22no—
96Dic83⋊C8C2×C414yescomplemented
97#14581713—22no—
98#14581713C2×C414yes—
99C4×C83⋊C8—22no—
100C83⋊#95—21no—
101C83⋊#95—21no—
102C83⋊#95—21no—
103C83⋊#95—21no—
104C83⋊#95—21no—
105C83⋊#95—21no—
106C83⋊#95—21no—
107C83⋊#95—21no—
108C22×D4×C83C2311yescharacteristic
109C23×C4×C83—21no—
110C22×C8×C83C2311yescharacteristic
111C22×C8×C83C2311yescharacteristic
112C4×D4×C83—22no—
113C4×D4×C83Q814yes—
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C4⋊C4×C83C2311yescharacteristic
116C2×C4⋊C4×C83C2311yescharacteristic
117C2×C22⋊C4×C83—21no—
118C2×C42×C83—21no—
119C2×C42×C83C2311yescharacteristic
120#102×C83—22no—
121#102×C83C2×C414yes—
122C4×C8×C83—22no—
123#95×C83—21no—
124C22×Dic83—24no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—24no—
129C22×Dic83—21no—
130C22×Dic83—42no—
131C22×Dic83—42no—
132C22×Dic83—42no—
133C22×Dic83—42no—
134C22×Dic83C2×D411yescharacteristic
135C22×Dic83C2×D411yescharacteristic
136C22×Dic83C2×D411yescharacteristic
137C22×Dic83C2×D411yescharacteristic
138C2×C83⋊C8—21no—
139C2×C83⋊C8—21no—
140C2×C83⋊C8—21no—
141C2×C83⋊C8—21no—
142C2×C83⋊C8—21no—
143C2×C83⋊C8C22×C412yes—
144C4⋊Dic83—21no—
145C4⋊Dic83—21no—
146C4⋊Dic83—21no—
147C4⋊Dic83—24no—
148C4⋊Dic83—21no—
149C4⋊Dic83—21no—
150C4⋊Dic83—42no—
151C4⋊Dic83C22×C412yes—
152C4⋊Dic83C22×C412yes—
153C4⋊Dic83#4112yes—
154Dic83⋊C4—24no—
155Dic83⋊C4—42no—
156C22⋊Dic83—24no—
157C22⋊Dic83—24no—
158C4×Dic83—22no—
159C4×Dic83—22no—
160C4×Dic83—21no—
161C4×Dic83—21no—
162C4×Dic83—22no—
163C4×Dic83—41no—
164C4×Dic83—42no—
165C4×Dic83—42no—
166C4×Dic83—42no—
167C4×Dic83—42no—
168C4×Dic83C22×C412yes—
169C4×Dic83#4112yes—
170C24×C83—21no—
171C2×D4×C83—21no—
172C2×D4×C83—21no—
173C2×D4×C83—21no—
174C2×D4×C83C22×C412yes—
175C2×D4×C83C2×Q812yes—
176C2×D4×C83#4112yes—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83—24no—
180C22×C4×C83—21no—
181C22×C4×C83—42no—
182C22×C4×C83—42no—
183C22×C4×C83C2×D411yescharacteristic
184C22×C4×C83C2×D411yescharacteristic
185C22×C4×C83C2411yescharacteristic
186C2×C8×C83—21no—
187C2×C8×C83—21no—
188C2×C8×C83—21no—
189C2×C8×C83—21no—
190C2×C8×C83—21no—
191C2×C8×C83C22×C412yes—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83C22×C412yes—
197C4⋊C4×C83C2×Q812yes—
198C22⋊C4×C83—24no—
199C42×C83—42no—
200C42×C83C2×Q812yes—
201C42×C83#4112yes—
202C23×C83—22no—
203C23×C83—22no—
204C23×C83—22no—
205C23×C83—41no—
206C23×C83—41no—
207C23×C83—41no—
208C23×C83—41no—
209C23×C83C22×D411yescharacteristic
210D4×C83—22no—
211D4×C83—22no—
212D4×C83—22no—
213D4×C83C4×Q814yes—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—22no—
217C2×C4×C83—22no—
218C2×C4×C83—41no—
219C2×C4×C83—41no—
220C2×C4×C83—41no—
221C2×C4×C83—41no—
222C2×C4×C83—48no—
223C2×C4×C83—41no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83C22⋊Q812yes—
227C2×C4×C83C22⋊Q812yes—
228C2×C4×C83#13512yes—
229C2×C4×C83AGL(1,ℤ/8)12yes—
230C2×C4×C83C23×C411yescharacteristic
231C2×C4×C83C22×Q811yescharacteristic
232C2×C4×C83C2×#4111yescharacteristic
233C2×C4×C83C2×#4111yescharacteristic
234C2×C4×C83C2×#4111yescharacteristic
235C2×C4×C83C2×#4111yescharacteristic
236C2×Dic83—21no—
237C2×Dic83—21no—
238C2×Dic83—21no—
239C2×Dic83—21no—
240C2×Dic83—21no—
241C2×Dic83—21no—
242C2×Dic83—22no—
243C2×Dic83—22no—
244C2×Dic83—21no—
245C2×Dic83—22no—
246C2×Dic83—21no—
247C2×Dic83—21no—
248C2×Dic83—48no—
249C2×Dic83—48no—
250C2×Dic83—41no—
251C2×Dic83—41no—
252C2×Dic83—41no—
253C2×Dic83—41no—
254C2×Dic83—41no—
255C2×Dic83—41no—
256C2×Dic83—41no—
257C2×Dic83—41no—
258C2×Dic83—41no—
259C2×Dic83C4×D412yes—
260C2×Dic83C4×D412yes—
261C2×Dic83#13512yes—
262C8×C83—22no—
263C8×C83—41no—
264C83⋊C8—22no—
265C83⋊C8—41no—
266C22×C83—24no—
267C22×C83—42no—
268C22×C83—42no—
269C22×C83—42no—
270C22×C83—42no—
271C22×C83—42no—
272C22×C83—42no—
273C22×C83C2×C4×D411yescharacteristic
274C22×C83C2×C22⋊Q811yescharacteristic
275C22×C83#52511yescharacteristic
276C22×C83C2×#13511yescharacteristic
277C22×C83C2×#13511yescharacteristic
278C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C83#57511yescharacteristic
280C4×C83—22no—
281C4×C83—42no—
282C4×C83—42no—
283C4×C83—81no—
284C4×C83#47814yescomplemented
285C4×C83C2×C4×Q811yescharacteristic
286C4×C83C4×#4111yescharacteristic
287C4×C83#52911yescharacteristic
288C4×C83#53311yescharacteristic
289Dic83—22no—
290Dic83—22no—
291Dic83—22no—
292Dic83—41no—
293Dic83—42no—
294Dic83—42no—
295Dic83—42no—
296Dic83—81no—
297C4×#478—831nomaximal, Sylow
298C2×C83—44no—
299C2×C83C4×C22⋊Q811yescharacteristic
300C2×C83C4×#13511yescharacteristic
301C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
302C2×C83C2×#47811yescharacteristic
303C2×C83#307611yescharacteristic
304C2×C83#310211yescharacteristic
305C2×C83#310511yescharacteristic
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⋊C8—831no—
319C4×#102—831no—
320C4×#102D8311yescharacteristic
321C83C4×#47811yescharacteristic, complemented, Sylow
322C2×#125—831no—
323C2×C4×D4—831no—
324C2×C4×D4—831no—
325C2×C4×D4C2×D8311yescharacteristic
326C22×C42—1661no—
327#478—838no—
328C2×#107—831no—
329C2×#107—831no—
330C2×#106—831no—
331C2×#106—831no—
332C2×C4⋊C8—831no—
333C2×C4⋊C8—831no—
334C2×#102—831no—
335C2×#102—831no—
336C2×#102C2×D8311yescharacteristic
337C2×#102C2×D8311yescharacteristic
338C2×C4×C8—831no—
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—1661no—
350C4×C4⋊C4—1661no—
351C4×C4⋊C4C2×D8311yescharacteristic
352C4×C22⋊C4—1661no—
353C4×C22⋊C4—1661no—
354C4×C22⋊C4—1661no—
355C43—831no—
356#340—831no—
357#340—831no—
358#340—831no—
359#340—831no—
360#340—831no—
361#340—831no—
362#340C2×D8311yescharacteristic
363#340C2×D8311yescharacteristic
364#336—831no—
365#336—831no—
366C22×D4C22×D8311yescharacteristic
367C23×C4—21no—
368C23×C4—1661no—
369C23×C4—1661no—
370C22×C8—831no—
371C22×C8—831no—
372C22×C8C22×D8311yescharacteristic
373C22×C8C22×D8311yescharacteristic
374#125—834no—
375#125—1662no—
376C4×D4—22no—
377C4×D4—834no—
378C4×D4—1662no—
379C4×D4—1662no—
380C4×D4—1662no—
381C4×D4Dic16614yes—
382C2×C4⋊C4—831no—
383C2×C4⋊C4—831no—
384C2×C4⋊C4—831no—
385C2×C4⋊C4—831no—
386C2×C4⋊C4—1661no—
387C2×C4⋊C4—1661no—
388C2×C4⋊C4—1661no—
389C2×C4⋊C4—1661no—
390C2×C4⋊C4C22×D8311yescharacteristic
391C2×C4⋊C4C22×D8311yescharacteristic
392C2×C4⋊C4C22×D8311yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—1661no—
395C2×C22⋊C4—1661no—
396C2×C42—21no—
397C2×C42—3324no—
398C2×C42—831no—
399C2×C42—831no—
400C2×C42—831no—
401C2×C42—831no—
402C2×C42—831no—
403C2×C42—831no—
404C2×C42—1661no—
405C2×C42—1661no—
406C2×C42—1661no—
407C2×C42—1661no—
408C2×C42C22×D8311yescharacteristic
409#107—834no—
410#107—1662no—
411#106—834no—
412#106—1662no—
413C4⋊C8—834no—
414C4⋊C8—1662no—
415#102—22no—
416#102—834no—
417#102—1662no—
418#102C4×D8314yes—
419C4×C8—22no—
420C4×C8—1662no—
421#95—21no—
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—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C2×C4×D8312yes—
435C2×D4C2×Dic16612yes—
436C2×D4#1305059012yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—3322no—
444C22×C4—3322no—
445C22×C4—3322no—
446C22×C4—3322no—
447C22×C4—831no—
448C22×C4—831no—
449C22×C4—831no—
450C22×C4—831no—
451C22×C4—1661no—
452C22×C4—1664no—
453C22×C4—1664no—
454C22×C4—1661no—
455C22×C4—1661no—
456C22×C4—1661no—
457C22×C4D4×D8311yescharacteristic
458C22×C4D4×D8311yescharacteristic
459C22×C4C23×D8311yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—832no—
466C2×C8—1661no—
467C2×C8—1661no—
468C2×C8—1661no—
469C2×C8—1661no—
470C2×C8—1661no—
471C2×C8C2×C4×D8312yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—3322no—
477C4⋊C4—3322no—
478C4⋊C4—832no—
479C4⋊C4—832no—
480C4⋊C4—832no—
481C4⋊C4—1664no—
482C4⋊C4—1664no—
483C4⋊C4—1661no—
484C4⋊C4—1661no—
485C4⋊C4—1661no—
486C4⋊C4—1661no—
487C4⋊C4—1661no—
488C4⋊C4C2×C4×D8312yes—
489C4⋊C4C2×Dic16612yes—
490C22⋊C4—24no—
491C22⋊C4—1664no—
492C22⋊C4—1664no—
493C42—42no—
494C42—3321no—
495C42—3322no—
496C42—3322no—
497C42—3322no—
498C42—3322no—
499C42—832no—
500C42—832no—
501C42—1662no—
502C42—1662no—
503C42—1662no—
504C42—1661no—
505C42—1661no—
506C42C2×Dic16612yes—
507C42#1305058912yes—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C2×D4×D8311yescharacteristic
516D4—22no—
517D4—22no—
518D4—22no—
519D4C4×Dic16614yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—48no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—3321no—
533C2×C4—3321no—
534C2×C4—3321no—
535C2×C4—3321no—
536C2×C4—3321no—
537C2×C4—3321no—
538C2×C4—3328no—
539C2×C4—3328no—
540C2×C4—3321no—
541C2×C4—3321no—
542C2×C4—3321no—
543C2×C4—832no—
544C2×C4—832no—
545C2×C4—832no—
546C2×C4—1662no—
547C2×C4—1662no—
548C2×C4—1661no—
549C2×C4—1662no—
550C2×C4—1661no—
551C2×C4—1661no—
552C2×C4—1661no—
553C2×C4—1661no—
554C2×C4—1661no—
555C2×C4—1661no—
556C2×C4—1661no—
557C2×C4—1661no—
558C2×C4#1458176912yes—
559C2×C4#1458176912yes—
560C2×C4#1458181312yes—
561C2×C4#1458181612yes—
562C2×C4C22×C4×D8311yescharacteristic
563C2×C4C22×Dic16611yescharacteristic
564C2×C4#41×D8311yescharacteristic
565C2×C4#41×D8311yescharacteristic
566C2×C4C2×#1305058911yescharacteristic
567C2×C4C2×#1305059011yescharacteristic
568C8—22no—
569C8—41no—
570C8—3321no—
571C8—1662no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C4×D4×D8311yescharacteristic
580C22C2×#1458176911yescharacteristic
581C22#1912821011yescharacteristic
582C22#135×D8311yescharacteristic
583C22C2×#1458181311yescharacteristic
584C22C2×#1458181611yescharacteristic
585C22#1912849811yescharacteristic
586C4—22no—
587C4—42no—
588C4—42no—
589C4—81no—
590C4—3322no—
591C4—3322no—
592C4—3322no—
593C4—3321no—
594C4—6641no—
595C4—1662no—
596C4—1662no—
597C4—1662no—
598C4#1912800314yesdirect product factor
599C4C2×C4×Dic16611yescharacteristic
600C4C4×#1305058911yescharacteristic
601C4#1912823111yescharacteristic
602C4#1912825411yescharacteristic
603C2—44no—
604C2C4×#1458176911yescharacteristic
605C2C4×#1458181311yescharacteristic
606C2C4×#1458181611yescharacteristic
607C2C2×#1912800311yescharacteristic
608C2#2491724711yescharacteristic
609C2#2491748511yescharacteristic
610C2#2491750811yescharacteristic
subgroupG/H
centerC22×C4D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC4×#102×C83C2
socleC23×C83C22×D4
prime radicalC22×D4×C83C23
cosocleC22×C4×C83C24
hypercenterC4×#102D83
hypocenterC83C4×#478
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C4×#14581783C2semidirect
4. #24908417C2semidirect
5. #24908230C2semidirect
6. #24908058C2semidirect
7. #24908040C2semidirect
11. C4×#14581725C2semidirect
12. C4×#14581724C2semidirect
13. C4×Dic83⋊C8C2semidirect
20. #19128003C4direct (N × H)
65. #14581783C2×C4semidirect
92. #14581725C2×C4semidirect
94. #14581724C2×C4semidirect
96. Dic83⋊C8C2×C4semidirect
284. C4×C83#478semidirect
321. C83C4×#478semidirect
598. C4#19128003direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191280032
C4×#145817832
C4×D4×Dic832
#249084172
#249082302
#249080582
#249080402
#249077262
#249077082
#249074712
C4×#145817252
C4×#145817242
C4×Dic83⋊C82
C4×#145817132
C4×#102×C832
C4×#47883