Finite Group Databasebeta

← C41×#19872 #23796073

Subgroups — C41×#19872 #23796073

Order 10496.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3398C211yesmaximal, characteristic, complemented
2C41×#3394C211yesmaximal, characteristic
3C41×#3365C211yesmaximal, characteristic, complemented
4C41×#3342C211yesmaximal, characteristic, complemented
5C41×#1722C211yesmaximal, characteristic, complemented
6C41×#1686C211yesmaximal, characteristic, complemented
7C41×#1681C211yesmaximal, characteristic
8C41×#1674C211yesmaximal, characteristic, complemented
9C41×#1670C211yesmaximal, characteristic, complemented
10C41×#1650C211yesmaximal, characteristic, complemented
11C41×#1648C211yesmaximal, characteristic, complemented
12C41×#1640C211yesmaximal, characteristic, complemented
13C41×#1628C211yesmaximal, characteristic
14C41×#1584C211yesmaximal, characteristic, complemented
15C41×SD16⋊C8C211yesmaximal, characteristic, complemented
16C41×#559C2211yescharacteristic
17C41×#557C2211yescharacteristic
18C41×#556C2211yescharacteristic
19C41×#556C2211yescharacteristic
20C41×#500C2211yescharacteristic
21C41×#500C2211yescharacteristic
22C41×#497—21no—
23C41×#495—21no—
24C41×#494C2211yescharacteristic
25C41×#492C2211yescharacteristic
26C41×#488—21no—
27C41×#486C2211yescharacteristic
28C41×#486C2211yescharacteristic
29C41×#485—21no—
30C41×#485—21no—
31C41×#478—21no—
32C41×#475C2211yescharacteristic
33C41×#475C2211yescharacteristic
34C41×#475C2211yescharacteristic
35C41×#467—21no—
36C41×#464—21no—
37C41×#464—21no—
38C41×#464—21no—
39C41×#463—21no—
40C41×#462—21no—
41C41×#462C2211yescharacteristic
42C41×#462C2211yescharacteristic
43C41×#461C2211yescharacteristic
44C41×#460C2211yescharacteristic
45C41×#459C2211yescharacteristic
46C41×#446C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C8×Q8×C41C2211yescharacteristic
49C41×#441—21no—
50C4×Q16×C41C2211yescharacteristic
51C4×SD16×C41—21no—
52C4×SD16×C41—21no—
53C4×SD16×C41C2211yescharacteristic
54C8×D4×C41C2211yescharacteristic
55C41×#427—21no—
56C41×#335C2211yescharacteristic
57C41×#335C2211yescharacteristic
58C41×#332C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×Q8⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C41×#322C2211yescharacteristic
67C2×Q16×C41—21no—
68C2×Q16×C41—21no—
69C2×Q16×C41—21no—
70C2×Q16×C41—21no—
71C2×Q16×C41D411yescharacteristic
72C2×SD16×C41—21no—
73C2×SD16×C41—21no—
74C2×SD16×C41—21no—
75C2×SD16×C41—21no—
76C2×SD16×C41D411yescharacteristic
77C2×D8×C41—21no—
78C22×C8×C41—21no—
79C4⋊Q8×C41—21no—
80C4⋊Q8×C41C2311yescharacteristic
81C4⋊Q8×C41C2311yescharacteristic
82C4⋊Q8×C41C2311yescharacteristic
83#127×C41C2311yescharacteristic
84#126×C41—41no—
85#126×C41—41no—
86#125×C41—21no—
87#125×C41—41no—
88#124×C41—21no—
89#124×C41—21no—
90#124×C41—21no—
91#124×C41—21no—
92#123×C41—41no—
93C22⋊Q8×C41—21no—
94C22⋊Q8×C41—21no—
95C4×Q8×C41—21no—
96C4×Q8×C41—21no—
97C4×Q8×C41—21no—
98C4×Q8×C41—21no—
99C4×Q8×C41C2311yescharacteristic
100C4×Q8×C41C2311yescharacteristic
101C4×Q8×C41C2311yescharacteristic
102C4×D4×C41—21no—
103C4×D4×C41—21no—
104C4×D4×C41C2311yescharacteristic
105#117×C41—21no—
106#117×C41—21no—
107#107×C41—21no—
108#107×C41—21no—
109#107×C41—41no—
110#107×C41D411yescharacteristic
111#106×C41—21no—
112#106×C41—21no—
113#106×C41—21no—
114#106×C41D411yescharacteristic
115C4⋊C8×C41—21no—
116C4⋊C8×C41—21no—
117C4⋊C8×C41—21no—
118C4⋊C8×C41C2311yescharacteristic
119C4⋊C8×C41C2311yescharacteristic
120C4⋊C8×C41C2311yescharacteristic
121C4⋊C8×C41C2311yescharacteristic
122#103×C41—21no—
123#103×C41—21no—
124#103×C41—21no—
125#103×C41—21no—
126#103×C41—21no—
127#103×C41—21no—
128#103×C41D411yescharacteristic
129#103×C41D411yescharacteristic
130#103×C41D411yescharacteristic
131#102×C41—21no—
132#102×C41—21no—
133#102×C41—21no—
134#102×C41—21no—
135#102×C41—41no—
136#102×C41D411yescharacteristic
137C22⋊C8×C41—21no—
138#97×C41—21no—
139C4×C8×C41—21no—
140C4×C8×C41—21no—
141C4×C8×C41C2311yescharacteristic
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144C2×Q8×C41—21no—
145C2×Q8×C41—21no—
146C2×Q8×C41—21no—
147C2×Q8×C41C2×D411yescharacteristic
148C2×Q8×C41C2×D411yescharacteristic
149C2×Q8×C41C2×D411yescharacteristic
150C2×D4×C41—21no—
151C2×D4×C41—21no—
152C2×D4×C41—21no—
153C2×D4×C41C2×D411yescharacteristic
154C22×C4×C41—21no—
155C22×C4×C41—41no—
156Q16×C41—41no—
157Q16×C41—42no—
158Q16×C41—81no—
159Q16×C41—81no—
160Q16×C41—81no—
161SD16×C41—22no—
162SD16×C41—42no—
163SD16×C41—42no—
164SD16×C41—81no—
165SD16×C41—81no—
166D8×C41—81no—
167C2×C8×C41—21no—
168C2×C8×C41—21no—
169C2×C8×C41—21no—
170C2×C8×C41—21no—
171C2×C8×C41—21no—
172C2×C8×C41—42no—
173C2×C8×C41C2×D411yescharacteristic
174C2×C8×C41C2×D411yescharacteristic
175C2×C8×C41C2×D411yescharacteristic
176C2×C8×C41C2×D411yescharacteristic
177C4⋊C4×C41—21no—
178C4⋊C4×C41—21no—
179C4⋊C4×C41—21no—
180C4⋊C4×C41—21no—
181C4⋊C4×C41—21no—
182C4⋊C4×C41—21no—
183C4⋊C4×C41—21no—
184C4⋊C4×C41—21no—
185C4⋊C4×C41—21no—
186C4⋊C4×C41—41no—
187C4⋊C4×C41—41no—
188C4⋊C4×C41—41no—
189C4⋊C4×C41—41no—
190C4⋊C4×C41—41no—
191C4⋊C4×C41C2×D411yescharacteristic
192C4⋊C4×C41C2×D411yescharacteristic
193C4⋊C4×C41C2×D411yescharacteristic
194C4⋊C4×C41C2×D411yescharacteristic
195C22⋊C4×C41—21no—
196C22⋊C4×C41—41no—
197C22⋊C4×C41—41no—
198C22⋊C4×C41—41no—
199C22⋊C4×C41—41no—
200C22⋊C4×C41—41no—
201C22⋊C4×C41—41no—
202C22⋊C4×C41—41no—
203C42×C41—21no—
204C42×C41—21no—
205C42×C41—21no—
206C42×C41—41no—
207C42×C41—41no—
208C42×C41—41no—
209C42×C41C2411yescharacteristic
210C23×C41—21no—
211C23×C41—41no—
212Q8×C41—21no—
213Q8×C41—21no—
214Q8×C41—21no—
215Q8×C41—21no—
216Q8×C41—21no—
217Q8×C41—21no—
218Q8×C41—41no—
219Q8×C41—41no—
220Q8×C41—41no—
221Q8×C41—41no—
222Q8×C41—41no—
223Q8×C41—41no—
224D4×C41—21no—
225D4×C41—21no—
226D4×C41—41no—
227D4×C41—41no—
228D4×C41—41no—
229D4×C41—41no—
230D4×C41—81no—
231C2×C4×C41—21no—
232C2×C4×C41—21no—
233C2×C4×C41—21no—
234C2×C4×C41—21no—
235C2×C4×C41—21no—
236C2×C4×C41—21no—
237C2×C4×C41—21no—
238C2×C4×C41—41no—
239C2×C4×C41—41no—
240C2×C4×C41—41no—
241C2×C4×C41—41no—
242C2×C4×C41—41no—
243C2×C4×C41—161no—
244C2×C4×C41C22×D411yescharacteristic
245C2×C4×C41C22×D411yescharacteristic
246C2×C4×C41H(5,𝔽2)11yescharacteristic
247C8×C41—21no—
248C8×C41—21no—
249C8×C41—21no—
250C8×C41—41no—
251C8×C41—41no—
252C8×C41—41no—
253C8×C41—41no—
254C8×C41—41no—
255C8×C41#13512yes—
256#19872C4111yesmaximal, characteristic, direct product factor, Sylow
257C22×C41—41no—
258C22×C41—41no—
259C22×C41—41no—
260C22×C41—81no—
261C22×C41—81no—
262C22×C41—81no—
263C22×C41D4211yescharacteristic
264C4×C41—21no—
265C4×C41—41no—
266C4×C41—41no—
267C4×C41—41no—
268C4×C41—41no—
269C4×C41—41no—
270C4×C41—41no—
271C4×C41—41no—
272C4×C41—81no—
273C4×C41—81no—
274C4×C41—81no—
275C4×C41C2×#13511yescharacteristic
276C4×C41#57511yescharacteristic
277C4×C41#57611yescharacteristic
278C4×C41#57811yescharacteristic
279#3398C2×C4111yescharacteristic, complemented
280#3394C2×C4111yescharacteristic
281#3365C2×C4111yescharacteristic, complemented
282#3342C2×C4111yescharacteristic, complemented
283#1722C2×C4111yescharacteristic, complemented
284#1686C2×C4111yescharacteristic, complemented
285#1681C2×C4111yescharacteristic
286#1674C2×C4111yescharacteristic, complemented
287#1670C2×C4111yescharacteristic, complemented
288#1650C2×C4111yescharacteristic, complemented
289#1648C2×C4111yescharacteristic, complemented
290#1640C2×C4111yescharacteristic, complemented
291#1628C2×C4111yescharacteristic
292#1584C2×C4111yescharacteristic, complemented
293SD16⋊C8C2×C4111yescharacteristic, complemented
294C2×C41—81no—
295C2×C41—161no—
296C2×C41#326911yescharacteristic
297C2×C41#328711yescharacteristic
298C2×C41#328911yescharacteristic
299#559C22×C4111yescharacteristic
300#557C22×C4111yescharacteristic
301#556C22×C4111yescharacteristic
302#556C22×C4111yescharacteristic
303#500C22×C4111yescharacteristic
304#500C22×C4111yescharacteristic
305#497—21no—
306#495—21no—
307#494C22×C4111yescharacteristic
308#492C22×C4111yescharacteristic
309#488—21no—
310#486C22×C4111yescharacteristic
311#486C22×C4111yescharacteristic
312#485—21no—
313#485—21no—
314#478—21no—
315#475C22×C4111yescharacteristic
316#475C22×C4111yescharacteristic
317#475C22×C4111yescharacteristic
318#467—21no—
319#464—21no—
320#464—21no—
321#464—21no—
322#463—21no—
323#462—21no—
324#462C22×C4111yescharacteristic
325#462C22×C4111yescharacteristic
326#461C22×C4111yescharacteristic
327#460C22×C4111yescharacteristic
328#459C22×C4111yescharacteristic
329#446C22×C4111yescharacteristic
330C8×Q8C22×C4111yescharacteristic
331C8×Q8C22×C4111yescharacteristic
332#441—21no—
333C4×Q16C22×C4111yescharacteristic
334C4×SD16—21no—
335C4×SD16—21no—
336C4×SD16C22×C4111yescharacteristic
337C8×D4C22×C4111yescharacteristic
338#427—21no—
339#335C22×C4111yescharacteristic
340#335C22×C4111yescharacteristic
341#332C22×C4111yescharacteristic
342#332C22×C4111yescharacteristic
343#332C22×C4111yescharacteristic
344#331C22×C4111yescharacteristic
345Q8⋊C8C22×C4111yescharacteristic
346Q8⋊C8C22×C4111yescharacteristic
347Q8⋊C8C22×C4111yescharacteristic
348D4⋊C8C22×C4111yescharacteristic
349#322C22×C4111yescharacteristic
350C41#1987211yescharacteristic, direct product factor, Sylow
351C2×Q16—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×Q16—21no—
355C2×Q16D4×C4111yescharacteristic
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16D4×C4111yescharacteristic
361C2×D8—21no—
362C22×C8—21no—
363C4⋊Q8—21no—
364C4⋊Q8C23×C4111yescharacteristic
365C4⋊Q8C23×C4111yescharacteristic
366C4⋊Q8C23×C4111yescharacteristic
367#127C23×C4111yescharacteristic
368#126—41no—
369#126—41no—
370#125—21no—
371#125—41no—
372#124—21no—
373#124—21no—
374#124—21no—
375#124—21no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8C23×C4111yescharacteristic
384C4×Q8C23×C4111yescharacteristic
385C4×Q8C23×C4111yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
388C4×D4C23×C4111yescharacteristic
389#117—21no—
390#117—21no—
391#107—21no—
392#107—21no—
393#107—41no—
394#107D4×C4111yescharacteristic
395#106—21no—
396#106—21no—
397#106—21no—
398#106D4×C4111yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8C23×C4111yescharacteristic
403C4⋊C8C23×C4111yescharacteristic
404C4⋊C8C23×C4111yescharacteristic
405C4⋊C8C23×C4111yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103D4×C4111yescharacteristic
413#103D4×C4111yescharacteristic
414#103D4×C4111yescharacteristic
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—41no—
420#102D4×C4111yescharacteristic
421C22⋊C8—21no—
422#97—21no—
423C4×C8—21no—
424C4×C8—21no—
425C4×C8C23×C4111yescharacteristic
426C4×C8C23×C4111yescharacteristic
427C4×C8C23×C4111yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C2×D4×C4111yescharacteristic
432C2×Q8C2×D4×C4111yescharacteristic
433C2×Q8C2×D4×C4111yescharacteristic
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4C2×D4×C4111yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440Q16—41no—
441Q16—42no—
442Q16—81no—
443Q16—81no—
444Q16—81no—
445SD16—22no—
446SD16—42no—
447SD16—42no—
448SD16—81no—
449SD16—81no—
450D8—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—42no—
457C2×C8C2×D4×C4111yescharacteristic
458C2×C8C2×D4×C4111yescharacteristic
459C2×C8C2×D4×C4111yescharacteristic
460C2×C8C2×D4×C4111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C4111yescharacteristic
476C4⋊C4C2×D4×C4111yescharacteristic
477C4⋊C4C2×D4×C4111yescharacteristic
478C4⋊C4C2×D4×C4111yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—41no—
491C42—41no—
492C42—41no—
493C42C24×C4111yescharacteristic
494C23—21no—
495C23—41no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508D4—21no—
509D4—21no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—161no—
528C2×C4C22×D4×C4111yescharacteristic
529C2×C4C22×D4×C4111yescharacteristic
530C2×C4H(5,𝔽2)×C4111yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8#135×C4112yes—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22D42×C4111yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C2×#135×C4111yescharacteristic
559C4C41×#57511yescharacteristic
560C4C41×#57611yescharacteristic
561C4C41×#57811yescharacteristic
562C2—81no—
563C2—161no—
564C2C41×#326911yescharacteristic
565C2C41×#328711yescharacteristic
566C2C41×#328911yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#459C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3398C2semidirect
3. C41×#3365C2semidirect
4. C41×#3342C2semidirect
5. C41×#1722C2semidirect
6. C41×#1686C2semidirect
8. C41×#1674C2semidirect
9. C41×#1670C2semidirect
10. C41×#1650C2semidirect
11. C41×#1648C2semidirect
12. C41×#1640C2semidirect
14. C41×#1584C2semidirect
15. C41×SD16⋊C8C2semidirect
256. #19872C41direct (N × H)
279. #3398C2×C41semidirect
281. #3365C2×C41semidirect
282. #3342C2×C41semidirect
283. #1722C2×C41semidirect
284. #1686C2×C41semidirect
286. #1674C2×C41semidirect
287. #1670C2×C41semidirect
288. #1650C2×C41semidirect
289. #1648C2×C41semidirect
290. #1640C2×C41semidirect
292. #1584C2×C41semidirect
293. SD16⋊C8C2×C41semidirect
350. C41#19872direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33982
C41×#33942
C41×#33652
C41×#33422
C41×#17222
C41×#16862
C41×#16812
C41×#16742
C41×#16702
C41×#16502
C41×#16482
C41×#16402
C41×#16282
C41×#15842
C41×SD16⋊C82
#1987241