Finite Group Databasebeta

← C4×#19127990 #35411975

Subgroups — C4×#19127990 #35411975

Order 21248.

1000 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127990C211yesmaximal, characteristic
2C4×#14581791C211yesmaximal, characteristic, complemented
3C4×#14581754C211yesmaximal, characteristic
4#24908409C211yesmaximal, characteristic, complemented
5#24908223C211yesmaximal, characteristic, complemented
6#24908050C211yesmaximal, characteristic, complemented
7#24908046C211yesmaximal, characteristic, complemented
8#24907725C211yesmaximal, characteristic
9#24907721C211yesmaximal, characteristic
10#24907462C211yesmaximal, characteristic
11C4×#14581723C211yesmaximal, characteristic, complemented
12C4×Dic83⋊C8C211yesmaximal, characteristic, complemented
13C4×#14581712C211yesmaximal, characteristic
14C4×#14581714C211yesmaximal, characteristic
15C4×#106×C83C211yesmaximal, characteristic, complemented
16C2×#14581791C2211yescharacteristic
17C2×C4×Dic166—21no—
18C2×C4×D332C2211yescharacteristic
19C2×#14581754C2211yescharacteristic
20C2×#14581754C2211yescharacteristic
21C2×C42×D83—21no—
22#19127990C418yesdirect product factor
23C2×#14581723C2211yescharacteristic
24C2×#14581723C2211yescharacteristic
25C2×Dic83⋊C8C2211yescharacteristic
26C2×Dic83⋊C8C2211yescharacteristic
27C2×#14581714C2211yescharacteristic
28C2×#14581714C2211yescharacteristic
29C2×#14581712C2211yescharacteristic
30C2×#14581712C2211yescharacteristic
31C2×C4×C83⋊C8C2211yescharacteristic
32#19127605—21no—
33#19127600C2211yescharacteristic
34#19127598—21no—
35#19127597C2211yescharacteristic
36#19127570C2211yescharacteristic
37C4⋊C4×Dic83C2211yescharacteristic
38C4⋊C4×Dic83C2211yescharacteristic
39C4×Dic83⋊C4—21no—
40C4×C4⋊Dic83C2211yescharacteristic
41C4×(C2×D83)⋊C4—21no—
42#19127548—21no—
43#19127548—21no—
44C42×Dic83C2211yescharacteristic
45#19127464C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53C2×#106×C83C2211yescharacteristic
54C2×#106×C83C2211yescharacteristic
55C2×C4×C8×C83C2211yescharacteristic
56C4×C4⋊C4×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic
60C22×Dic166—21no—
61C22×D332C2311yescharacteristic
62C22×C4×D83—21no—
63C22×C4×D83—21no—
64C22×C4×D83—21no—
65C22×C83⋊C8C2311yescharacteristic
66C22×C83⋊C8C2311yescharacteristic
67#14581791—22no—
68#14581791C2×C414yescomplemented
69C4×Dic166—44no—
70C4×D332—22no—
71C4×D332Q814yescomplemented
72#14581754—22no—
73#14581754—22no—
74#14581754—22no—
75#14581754C2×C414yes—
76C2×C4⋊Dic83—21no—
77C2×C4⋊Dic83C2311yescharacteristic
78C2×C4⋊Dic83C2311yescharacteristic
79C2×C4⋊Dic83C2311yescharacteristic
80C2×Dic83⋊C4—21no—
81C2×Dic83⋊C4—21no—
82C2×Dic83⋊C4—21no—
83C2×Dic83⋊C4—21no—
84C2×(C2×D83)⋊C4—21no—
85C2×(C2×D83)⋊C4—21no—
86C2×(C2×D83)⋊C4—21no—
87C2×C4×Dic83—21no—
88C2×C4×Dic83—21no—
89C2×C4×Dic83—21no—
90C2×C4×Dic83D411yescharacteristic
91C2×C4×Dic83D411yescharacteristic
92C2×C4×Dic83D411yescharacteristic
93C2×C4×Dic83D411yescharacteristic
94C2×C4×Dic83C2311yescharacteristic
95C2×C4×Dic83C2311yescharacteristic
96C42×D83—44no—
97#14581723—22no—
98#14581723C2×C414yescomplemented
99Dic83⋊C8—22no—
100Dic83⋊C8C2×C414yescomplemented
101#14581714—22no—
102#14581714C2×C414yes—
103#14581712—22no—
104#14581712C2×C414yes—
105C4×C83⋊C8—22no—
106C83⋊#95—21no—
107C83⋊#95—21no—
108C83⋊#95—21no—
109C83⋊#95—21no—
110C83⋊#95—21no—
111C22×C8×C83C2311yescharacteristic
112C22×C8×C83C2311yescharacteristic
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C4⋊C4×C83C2311yescharacteristic
116C2×C4⋊C4×C83C2311yescharacteristic
117C2×C42×C83—21no—
118C2×C42×C83—21no—
119C2×C42×C83C2311yescharacteristic
120#106×C83—22no—
121#106×C83C2×C414yescomplemented
122C4×C8×C83—22no—
123#95×C83—21no—
124#95×C83—21no—
125C23×D83—21no—
126C2×Dic166—24no—
127C2×Dic166—42no—
128C2×Dic166—42no—
129C2×D332—21no—
130C2×D332—21no—
131C2×D332—21no—
132C2×D332C22×C412yes—
133C2×D332C2×Q812yes—
134C2×D332#4112yes—
135C22×Dic83—21no—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83C2×D411yescharacteristic
139C22×Dic83C2×D411yescharacteristic
140C22×Dic83C2×D411yescharacteristic
141C22×Dic83C2×D411yescharacteristic
142C2×C4×D83—24no—
143C2×C4×D83—24no—
144C2×C4×D83—24no—
145C2×C4×D83—42no—
146C2×C4×D83—42no—
147C2×C4×D83—42no—
148C2×C4×D83—42no—
149C2×C4×D83—42no—
150C2×C4×D83—42no—
151C2×C83⋊C8—21no—
152C2×C83⋊C8—21no—
153C2×C83⋊C8—21no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8C22×C412yes—
157C4⋊Dic83—21no—
158C4⋊Dic83—21no—
159C4⋊Dic83—21no—
160C4⋊Dic83—21no—
161C4⋊Dic83—42no—
162C4⋊Dic83C22×C412yes—
163C4⋊Dic83C2×Q812yes—
164Dic83⋊C4—24no—
165Dic83⋊C4—42no—
166Dic83⋊C4—42no—
167Dic83⋊C4—42no—
168(C2×D83)⋊C4—24no—
169(C2×D83)⋊C4—24no—
170(C2×D83)⋊C4—24no—
171C4×Dic83—22no—
172C4×Dic83—21no—
173C4×Dic83—21no—
174C4×Dic83—22no—
175C4×Dic83—41no—
176C4×Dic83—42no—
177C4×Dic83—42no—
178C4×Dic83—42no—
179C4×Dic83SD1614yes—
180C4×Dic83C22×C412yes—
181C4×Dic83#4112yes—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—21no—
186C22×C4×C83C2×D411yescharacteristic
187C22×C4×C83C2×D411yescharacteristic
188C22×C4×C83C2411yescharacteristic
189C2×C8×C83—21no—
190C2×C8×C83—21no—
191C2×C8×C83—21no—
192C2×C8×C83—21no—
193C2×C8×C83—21no—
194C2×C8×C83C22×C412yes—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83—21no—
198C4⋊C4×C83—21no—
199C4⋊C4×C83—21no—
200C4⋊C4×C83C22×C412yes—
201C4⋊C4×C83C22×C412yes—
202C4⋊C4×C83#4112yes—
203C42×C83—42no—
204C42×C83—42no—
205C42×C83C2×Q812yes—
206C42×C83#4112yes—
207C23×C83C22×D411yescharacteristic
208C22×D83—22no—
209C22×D83—22no—
210C22×D83—22no—
211C22×D83—41no—
212C22×D83—41no—
213C22×D83—41no—
214C22×D83—41no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—22no—
220C2×C4×C83—41no—
221C2×C4×C83—41no—
222C2×C4×C83—41no—
223C2×C4×C83—41no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83—41no—
227C2×C4×C83—41no—
228C2×C4×C83—41no—
229C2×C4×C83C22⋊Q812yes—
230C2×C4×C83C22⋊Q812yes—
231C2×C4×C83C2×SD1612yes—
232C2×C4×C83AGL(1,ℤ/8)12yes—
233C2×C4×C83C23×C411yescharacteristic
234C2×C4×C83C22×Q811yescharacteristic
235C2×C4×C83C2×#4111yescharacteristic
236C2×C4×C83C2×#4111yescharacteristic
237C2×C4×C83C2×#4111yescharacteristic
238C2×C4×C83C2×#4111yescharacteristic
239C2×Dic83—21no—
240C2×Dic83—21no—
241C2×Dic83—21no—
242C2×Dic83—21no—
243C2×Dic83—22no—
244C2×Dic83—22no—
245C2×Dic83—21no—
246C2×Dic83—21no—
247C2×Dic83—21no—
248C2×Dic83—41no—
249C2×Dic83—41no—
250C2×Dic83—41no—
251C2×Dic83—41no—
252C2×Dic83—41no—
253C2×Dic83—41no—
254C2×Dic83—41no—
255C2×Dic83C4×D412yes—
256C2×Dic83C4×D412yes—
257C2×Dic83C2×SD1612yes—
258C2×Dic83C2×SD1612yes—
259C2×Dic83#13512yes—
260D332—22no—
261D332—22no—
262D332—22no—
263D332C4×Q814yescomplemented
264C4×D83—48no—
265C4×D83—48no—
266C4×D83—48no—
267Dic166—48no—
268C8×C83—22no—
269C8×C83—41no—
270C83⋊C8—22no—
271C83⋊C8—41no—
272C22×C83C2×C4×D411yescharacteristic
273C22×C83C2×C22⋊Q811yescharacteristic
274C22×C83#52511yescharacteristic
275C22×C83C22×SD1611yescharacteristic
276C22×C83C2×#13511yescharacteristic
277C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
278C22×C83#57511yescharacteristic
279C2×D83—24no—
280C2×D83—42no—
281C2×D83—42no—
282C2×D83—42no—
283C2×D83—42no—
284C2×D83—42no—
285C2×D83—42no—
286C4×C83—22no—
287C4×C83—42no—
288C4×C83—42no—
289C4×C83—42no—
290C4×C83—81no—
291C4×C83#47614yescomplemented
292C4×C83C2×C4×Q811yescharacteristic
293C4×C83C4×#4111yescharacteristic
294C4×C83#52911yescharacteristic
295C4×C83#53311yescharacteristic
296Dic83—22no—
297Dic83—22no—
298Dic83—41no—
299Dic83—42no—
300Dic83—42no—
301Dic83—81no—
302Dic83C4×SD1614yes—
303C4×#476—831nomaximal, Sylow
304C2×C83C4×C22⋊Q811yescharacteristic
305C2×C83C2×C4×SD1611yescharacteristic
306C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
307C2×C83C2×#47611yescharacteristic
308C2×C83#307611yescharacteristic
309C2×C83#310111yescharacteristic
310C2×C83#310611yescharacteristic
311D83—44no—
312C2×#476—831no—
313C4×C4⋊Q8—831no—
314C42×D4—831no—
315#1987—831no—
316#1948—831no—
317#1920—831no—
318#1920—831no—
319#1864—831no—
320#1864—831no—
321#1802—831no—
322C4×#106—831no—
323C4×#106D8311yescharacteristic, complemented
324C4×C4⋊C8—831no—
325C4×#102—831no—
326C4×#102—831no—
327C83C4×#47611yescharacteristic, complemented, Sylow
328C2×C4⋊Q8—831no—
329C2×C4×Q8—1661no—
330C2×C4×D4—831no—
331C2×C4×D4—831no—
332C2×C4×D4—831no—
333C22×C42—1661no—
334#476—838no—
335C2×#106—831no—
336C2×#106—831no—
337C2×#106C2×D8311yescharacteristic
338C2×#106C2×D8311yescharacteristic
339C2×C4⋊C8—831no—
340C2×C4⋊C8—831no—
341C2×#102—831no—
342C2×#102—831no—
343C2×#102—831no—
344C2×#102—831no—
345C2×C4×C8—831no—
346C2×C4×C8C2×D8311yescharacteristic
347#391—1661no—
348#389—831no—
349#389—831no—
350#389—1661no—
351#384—831no—
352C4×C4⋊C4—831no—
353C4×C4⋊C4—831no—
354C4×C4⋊C4—831no—
355C4×C4⋊C4—1661no—
356C4×C4⋊C4C2×D8311yescharacteristic
357C4×C4⋊C4C2×D8311yescharacteristic
358C4×C22⋊C4—1661no—
359C4×C22⋊C4—1661no—
360C4×C22⋊C4—1661no—
361C43—831no—
362#340—831no—
363#340—831no—
364#340—831no—
365#340—831no—
366#340—831no—
367#340—831no—
368#340C2×D8311yescharacteristic
369#340C2×D8311yescharacteristic
370#336—831no—
371#336—831no—
372C22×Q8—1661no—
373C22×D4—831no—
374C23×C4—1661no—
375C23×C4—1661no—
376C23×C4—1661no—
377C22×C8—831no—
378C22×C8—831no—
379C22×C8C22×D8311yescharacteristic
380C22×C8C22×D8311yescharacteristic
381C4⋊Q8—834no—
382C4⋊Q8—1662no—
383C4×Q8—3324no—
384C4×D4—834no—
385C4×D4—834no—
386C4×D4—1662no—
387C4×D4—1662no—
388C4×D4—1662no—
389C4×D4—1662no—
390C2×C4⋊C4—831no—
391C2×C4⋊C4—831no—
392C2×C4⋊C4—831no—
393C2×C4⋊C4—1661no—
394C2×C4⋊C4—1661no—
395C2×C4⋊C4—1661no—
396C2×C4⋊C4—1661no—
397C2×C4⋊C4—1661no—
398C2×C4⋊C4C22×D8311yescharacteristic
399C2×C4⋊C4C22×D8311yescharacteristic
400C2×C4⋊C4C22×D8311yescharacteristic
401C2×C4⋊C4C22×D8311yescharacteristic
402C2×C22⋊C4—1661no—
403C2×C22⋊C4—1661no—
404C2×C22⋊C4—1661no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—3324no—
408C2×C42—831no—
409C2×C42—831no—
410C2×C42—831no—
411C2×C42—831no—
412C2×C42—831no—
413C2×C42—831no—
414C2×C42—1661no—
415C2×C42—1661no—
416C2×C42—1661no—
417C2×C42C22×D8311yescharacteristic
418#106—22no—
419#106—834no—
420#106—1662no—
421#106C4×D8314yescomplemented
422C4⋊C8—834no—
423C4⋊C8—1662no—
424#102—834no—
425#102—834no—
426#102—1662no—
427#102—1662no—
428C4×C8—22no—
429C4×C8—1662no—
430#95—21no—
431#95—21no—
432#95—1661no—
433#95—1661no—
434#95—1661no—
435#95—1661no—
436#95—1661no—
437C24—1661no—
438C2×Q8—3322no—
439C2×Q8—3322no—
440C2×Q8—1664no—
441C2×D4—832no—
442C2×D4—832no—
443C2×D4—832no—
444C2×D4—1661no—
445C2×D4—1661no—
446C2×D4—1661no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—3322no—
452C22×C4—3322no—
453C22×C4—3322no—
454C22×C4—3322no—
455C22×C4—3322no—
456C22×C4—3322no—
457C22×C4—831no—
458C22×C4—831no—
459C22×C4—831no—
460C22×C4—831no—
461C22×C4—1664no—
462C22×C4—1664no—
463C22×C4—1661no—
464C22×C4—1661no—
465C22×C4—1661no—
466C22×C4—1664no—
467C22×C4D4×D8311yescharacteristic
468C22×C4D4×D8311yescharacteristic
469C22×C4C23×D8311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—832no—
476C2×C8—1661no—
477C2×C8—1661no—
478C2×C8—1661no—
479C2×C8—1661no—
480C2×C8—1661no—
481C2×C8C2×C4×D8312yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—3322no—
488C4⋊C4—3322no—
489C4⋊C4—3322no—
490C4⋊C4—3322no—
491C4⋊C4—832no—
492C4⋊C4—832no—
493C4⋊C4—1664no—
494C4⋊C4—1661no—
495C4⋊C4—1661no—
496C4⋊C4—1661no—
497C4⋊C4—1661no—
498C4⋊C4C2×C4×D8312yes—
499C4⋊C4C2×C4×D8312yes—
500C4⋊C4#1305059012yes—
501C22⋊C4—1664no—
502C22⋊C4—1664no—
503C22⋊C4—1664no—
504C42—42no—
505C42—42no—
506C42—3321no—
507C42—3322no—
508C42—3322no—
509C42—3322no—
510C42—834no—
511C42—832no—
512C42—832no—
513C42—1662no—
514C42—1662no—
515C42—1661no—
516C42—1661no—
517C42Q8×D8312yes—
518C42#1305059012yes—
519C23—3321no—
520C23—3321no—
521C23—3321no—
522C23—3321no—
523C23—1662no—
524C23—1662no—
525C23—1662no—
526C23C2×D4×D8311yescharacteristic
527Q8—3328no—
528D4—834no—
529D4—1662no—
530D4—1662no—
531D4—1662no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—3328no—
547C2×C4—3328no—
548C2×C4—3321no—
549C2×C4—3321no—
550C2×C4—3321no—
551C2×C4—3321no—
552C2×C4—3328no—
553C2×C4—3321no—
554C2×C4—3321no—
555C2×C4—3321no—
556C2×C4—832no—
557C2×C4—832no—
558C2×C4—832no—
559C2×C4—832no—
560C2×C4—832no—
561C2×C4—1662no—
562C2×C4—1662no—
563C2×C4—1661no—
564C2×C4—1661no—
565C2×C4—1661no—
566C2×C4—1661no—
567C2×C4—1661no—
568C2×C4—1661no—
569C2×C4—1661no—
570C2×C4#1458177012yes—
571C2×C4#1458177012yes—
572C2×C4SD16×D8312yes—
573C2×C4#1458181912yes—
574C2×C4C22×C4×D8311yescharacteristic
575C2×C4C2×Q8×D8311yescharacteristic
576C2×C4#41×D8311yescharacteristic
577C2×C4#41×D8311yescharacteristic
578C2×C4C2×#1305059011yescharacteristic
579C2×C4C2×#1305059011yescharacteristic
580C8—22no—
581C8—41no—
582C8—3321no—
583C8—1662no—
584C22—3322no—
585C22—3322no—
586C22—3322no—
587C22—3322no—
588C22—3322no—
589C22—3322no—
590C22—1664no—
591C22C4×D4×D8311yescharacteristic
592C22C2×#1458177011yescharacteristic
593C22#1912821011yescharacteristic
594C22C2×SD16×D8311yescharacteristic
595C22#135×D8311yescharacteristic
596C22C2×#1458181911yescharacteristic
597C22#1912849811yescharacteristic
598C4—22no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—81no—
603C4—3321no—
604C4—3322no—
605C4—3322no—
606C4—834no—
607C4—6641no—
608C4—1662no—
609C4—1662no—
610C4#1912799014yesdirect product factor
611C4C4×Q8×D8311yescharacteristic
612C4C4×#1305059011yescharacteristic
613C4#1912822911yescharacteristic
614C4#1912825511yescharacteristic
615C2—3324no—
616C2C4×#1458177011yescharacteristic
617C2C4×SD16×D8311yescharacteristic
618C2C4×#1458181911yescharacteristic
619C2C2×#1912799011yescharacteristic
620C2#2491724911yescharacteristic
621C2#2491746911yescharacteristic
622C2#2491752111yescharacteristic
subgroupG/H
centerC22×C4D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC4×#106×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
cosocleC22×C4×C83C24
hypercenterC4×#106D83
hypocenterC83C4×#476
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
2. C4×#14581791C2semidirect
4. #24908409C2semidirect
5. #24908223C2semidirect
6. #24908050C2semidirect
7. #24908046C2semidirect
11. C4×#14581723C2semidirect
12. C4×Dic83⋊C8C2semidirect
15. C4×#106×C83C2semidirect
22. #19127990C4direct (N × H)
68. #14581791C2×C4semidirect
71. C4×D332Q8semidirect
98. #14581723C2×C4semidirect
100. Dic83⋊C8C2×C4semidirect
121. #106×C83C2×C4semidirect
263. D332C4×Q8semidirect
291. C4×C83#476semidirect
323. C4×#106D83semidirect
327. C83C4×#476semidirect
421. #106C4×D83semidirect
610. C4#19127990direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191279902
C4×#145817912
C4×#145817542
#249084092
#249082232
#249080502
#249080462
#249077252
#249077212
#249074622
C4×#145817232
C4×Dic83⋊C82
C4×#145817122
C4×#145817142
C4×#106×C832
C4×#47683