Finite Group Databasebeta

← C41×#19998 #23796199

Subgroups — C41×#19998 #23796199

Order 10496.

604 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3364C211yesmaximal, characteristic, complemented
2C41×#3359C211yesmaximal, characteristic, complemented
3C41×#3302C211yesmaximal, characteristic
4C41×#3298C211yesmaximal, characteristic
5C41×#1710C211yesmaximal, characteristic, complemented
6C41×#1680C211yesmaximal, characteristic, complemented
7C41×#1680C211yesmaximal, characteristic, complemented
8C41×#1679C211yesmaximal, characteristic, complemented
9C41×#1679C211yesmaximal, characteristic, complemented
10C41×#1650C211yesmaximal, characteristic, complemented
11C41×#1649C211yesmaximal, characteristic, complemented
12C41×#1648C211yesmaximal, characteristic, complemented
13C41×#1647C211yesmaximal, characteristic
14C8×SD16×C41C211yesmaximal, characteristic, complemented
15C8×SD16×C41C211yesmaximal, characteristic, complemented
16C41×#557C2211yescharacteristic
17C41×#556C2211yescharacteristic
18D4×Q8×C41C2211yescharacteristic
19C41×#547C2211yescharacteristic
20C41×#500C2211yescharacteristic
21C41×#500C2211yescharacteristic
22C41×#488—21no—
23C41×#487—21no—
24C41×#487C2211yescharacteristic
25C41×#487C2211yescharacteristic
26C41×#487C2211yescharacteristic
27C41×#487C2211yescharacteristic
28C41×#485—21no—
29C41×#483—21no—
30C41×#479—21no—
31C41×#475—21no—
32C41×#475C2211yescharacteristic
33C41×#475C2211yescharacteristic
34C41×#474C2211yescharacteristic
35C41×#474C2211yescharacteristic
36C41×#467—21no—
37C41×#465—21no—
38C41×#464—21no—
39C41×#462C2211yescharacteristic
40C41×#462C2211yescharacteristic
41C41×#461—21no—
42C41×#461C2211yescharacteristic
43C41×#461C2211yescharacteristic
44C41×#452—21no—
45C41×#448—21no—
46C8×Q8×C41C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C4×Q16×C41—21no—
49C4×SD16×C41—21no—
50C4×SD16×C41C2211yescharacteristic
51C4×SD16×C41C2211yescharacteristic
52C8×D4×C41C2211yescharacteristic
53C8×D4×C41C2211yescharacteristic
54C41×#416—21no—
55C2×#103×C41—21no—
56C41×#334C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#332C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#332C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C82×C41C2211yescharacteristic
67C2×#41×C41—21no—
68C22×Q8×C41—21no—
69C2×Q16×C41—21no—
70C2×Q16×C41—21no—
71C2×SD16×C41—21no—
72C2×SD16×C41—21no—
73C2×SD16×C41D411yescharacteristic
74C2×SD16×C41D411yescharacteristic
75C22×C8×C41—21no—
76C22×C8×C41—21no—
77C4⋊Q8×C41—21no—
78C4⋊Q8×C41—21no—
79C4⋊Q8×C41C2311yescharacteristic
80C4⋊Q8×C41C2311yescharacteristic
81C4⋊Q8×C41C2311yescharacteristic
82C4⋊Q8×C41C2311yescharacteristic
83#126×C41—41no—
84#125×C41—21no—
85#125×C41—41no—
86#124×C41—21no—
87#123×C41—41no—
88C22⋊Q8×C41—21no—
89C22⋊Q8×C41—21no—
90C22⋊Q8×C41—21no—
91C22⋊Q8×C41—41no—
92#121×C41—21no—
93C4×Q8×C41—21no—
94C4×Q8×C41—21no—
95C4×Q8×C41—21no—
96C4×Q8×C41C2311yescharacteristic
97C4×Q8×C41C2311yescharacteristic
98C4×D4×C41—21no—
99C4×D4×C41C2311yescharacteristic
100C4×D4×C41C2311yescharacteristic
101#117×C41—21no—
102C2×C4⋊C4×C41—21no—
103#107×C41—21no—
104#107×C41—21no—
105#107×C41—41no—
106#107×C41—41no—
107#106×C41—21no—
108#106×C41—21no—
109#106×C41D411yescharacteristic
110#106×C41D411yescharacteristic
111C4⋊C8×C41—21no—
112C4⋊C8×C41—21no—
113C4⋊C8×C41C2311yescharacteristic
114C4⋊C8×C41C2311yescharacteristic
115C4⋊C8×C41C2311yescharacteristic
116C4⋊C8×C41C2311yescharacteristic
117#103×C41—21no—
118#103×C41—21no—
119#103×C41—21no—
120#103×C41—21no—
121#103×C41—21no—
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×C41—21no—
129#103×C41—21no—
130#103×C41—21no—
131#103×C41D411yescharacteristic
132#103×C41D411yescharacteristic
133#102×C41—21no—
134#102×C41—21no—
135#102×C41D411yescharacteristic
136#102×C41D411yescharacteristic
137C22⋊C8×C41—21no—
138C22⋊C8×C41—21no—
139C4×C8×C41—21no—
140C4×C8×C41—21no—
141C4×C8×C41C2311yescharacteristic
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144#41×C41—42no—
145#41×C41—81no—
146C2×Q8×C41—21no—
147C2×Q8×C41—21no—
148C2×Q8×C41—21no—
149C2×Q8×C41—21no—
150C2×Q8×C41—41no—
151C2×Q8×C41—42no—
152C2×Q8×C41—81no—
153C2×Q8×C41C2×D411yescharacteristic
154C2×Q8×C41C2×D411yescharacteristic
155C2×D4×C41—41no—
156C2×D4×C41C2×D411yescharacteristic
157C2×D4×C41C2×D411yescharacteristic
158C22×C4×C41—21no—
159C22×C4×C41—21no—
160C22×C4×C41—41no—
161C22×C4×C41—41no—
162Q16×C41—42no—
163Q16×C41—81no—
164SD16×C41—22no—
165SD16×C41—22no—
166SD16×C41—42no—
167SD16×C41—81no—
168C2×C8×C41—21no—
169C2×C8×C41—21no—
170C2×C8×C41—21no—
171C2×C8×C41—21no—
172C2×C8×C41—21no—
173C2×C8×C41—81no—
174C2×C8×C41—81no—
175C2×C8×C41C2×D411yescharacteristic
176C2×C8×C41C2×D411yescharacteristic
177C2×C8×C41C2×D411yescharacteristic
178C2×C8×C41C2×D411yescharacteristic
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—21no—
187C4⋊C4×C41—21no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—41no—
190C4⋊C4×C41—41no—
191C4⋊C4×C41—41no—
192C4⋊C4×C41—41no—
193C4⋊C4×C41—41no—
194C4⋊C4×C41—41no—
195C4⋊C4×C41C2×D411yescharacteristic
196C4⋊C4×C41C2×D411yescharacteristic
197C4⋊C4×C41C2×D411yescharacteristic
198C4⋊C4×C41C2×D411yescharacteristic
199C22⋊C4×C41—21no—
200C22⋊C4×C41—21no—
201C22⋊C4×C41—41no—
202C22⋊C4×C41—41no—
203C22⋊C4×C41—41no—
204C22⋊C4×C41—41no—
205C42×C41—21no—
206C42×C41—21no—
207C42×C41—41no—
208C42×C41—41no—
209C42×C41C2411yescharacteristic
210C23×C41—21no—
211C23×C41—21no—
212Q8×C41—21no—
213Q8×C41—21no—
214Q8×C41—21no—
215Q8×C41—41no—
216Q8×C41—41no—
217Q8×C41—41no—
218Q8×C41—41no—
219Q8×C41—41no—
220Q8×C41—41no—
221Q8×C41—41no—
222Q8×C41—41no—
223Q8×C41—82no—
224Q8×C41#13512yes—
225D4×C41—21no—
226D4×C41—21no—
227D4×C41—21no—
228D4×C41—82no—
229D4×C41#13512yes—
230C2×C4×C41—21no—
231C2×C4×C41—21no—
232C2×C4×C41—21no—
233C2×C4×C41—21no—
234C2×C4×C41—21no—
235C2×C4×C41—21no—
236C2×C4×C41—41no—
237C2×C4×C41—41no—
238C2×C4×C41—41no—
239C2×C4×C41—41no—
240C2×C4×C41—41no—
241C2×C4×C41—41no—
242C2×C4×C41—41no—
243C2×C4×C41—41no—
244C2×C4×C41—82no—
245C2×C4×C41—82no—
246C2×C4×C41C22×D411yescharacteristic
247C2×C4×C41C22×D411yescharacteristic
248C2×C4×C41H(5,𝔽2)11yescharacteristic
249C8×C41—22no—
250C8×C41—21no—
251C8×C41—21no—
252C8×C41—21no—
253C8×C41—21no—
254C8×C41—41no—
255C8×C41—41no—
256C8×C41—41no—
257C8×C41—41no—
258#19998C4111yesmaximal, characteristic, direct product factor, Sylow
259C22×C41—22no—
260C22×C41—41no—
261C22×C41—41no—
262C22×C41—41no—
263C22×C41—41no—
264C22×C41—41no—
265C22×C41D4211yescharacteristic
266C4×C41—22no—
267C4×C41—21no—
268C4×C41—41no—
269C4×C41—41no—
270C4×C41—41no—
271C4×C41—41no—
272C4×C41—41no—
273C4×C41—81no—
274C4×C41—81no—
275C4×C41—81no—
276C4×C41—81no—
277C4×C41C2×#13511yescharacteristic
278C4×C41C2×#13511yescharacteristic
279C4×C41#57711yescharacteristic
280C4×C41#57711yescharacteristic
281#3364C2×C4111yescharacteristic, complemented
282#3359C2×C4111yescharacteristic, complemented
283#3302C2×C4111yescharacteristic
284#3298C2×C4111yescharacteristic
285#1710C2×C4111yescharacteristic, complemented
286#1680C2×C4111yescharacteristic, complemented
287#1680C2×C4111yescharacteristic, complemented
288#1679C2×C4111yescharacteristic, complemented
289#1679C2×C4111yescharacteristic, complemented
290#1650C2×C4111yescharacteristic, complemented
291#1649C2×C4111yescharacteristic, complemented
292#1648C2×C4111yescharacteristic, complemented
293#1647C2×C4111yescharacteristic
294C8×SD16C2×C4111yescharacteristic, complemented
295C8×SD16C2×C4111yescharacteristic, complemented
296C2×C41—42no—
297C2×C41—81no—
298C2×C41#328211yescharacteristic
299C2×C41#328211yescharacteristic
300C2×C41#329311yescharacteristic
301#557C22×C4111yescharacteristic
302#556C22×C4111yescharacteristic
303D4×Q8C22×C4111yescharacteristic
304#547C22×C4111yescharacteristic
305#500C22×C4111yescharacteristic
306#500C22×C4111yescharacteristic
307#488—21no—
308#487—21no—
309#487C22×C4111yescharacteristic
310#487C22×C4111yescharacteristic
311#487C22×C4111yescharacteristic
312#487C22×C4111yescharacteristic
313#485—21no—
314#483—21no—
315#479—21no—
316#475—21no—
317#475C22×C4111yescharacteristic
318#475C22×C4111yescharacteristic
319#474C22×C4111yescharacteristic
320#474C22×C4111yescharacteristic
321#467—21no—
322#465—21no—
323#464—21no—
324#462C22×C4111yescharacteristic
325#462C22×C4111yescharacteristic
326#461—21no—
327#461C22×C4111yescharacteristic
328#461C22×C4111yescharacteristic
329#452—21no—
330#448—21no—
331C8×Q8C22×C4111yescharacteristic
332C8×Q8C22×C4111yescharacteristic
333C4×Q16—21no—
334C4×SD16—21no—
335C4×SD16C22×C4111yescharacteristic
336C4×SD16C22×C4111yescharacteristic
337C8×D4C22×C4111yescharacteristic
338C8×D4C22×C4111yescharacteristic
339#416—21no—
340C2×#103—21no—
341#334C22×C4111yescharacteristic
342#334C22×C4111yescharacteristic
343#332C22×C4111yescharacteristic
344#332C22×C4111yescharacteristic
345#332C22×C4111yescharacteristic
346#332C22×C4111yescharacteristic
347Q8⋊C8C22×C4111yescharacteristic
348Q8⋊C8C22×C4111yescharacteristic
349D4⋊C8C22×C4111yescharacteristic
350D4⋊C8C22×C4111yescharacteristic
351C82C22×C4111yescharacteristic
352C41#1999811yescharacteristic, direct product factor, Sylow
353C2×#41—21no—
354C22×Q8—21no—
355C2×Q16—21no—
356C2×Q16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16D4×C4111yescharacteristic
360C2×SD16D4×C4111yescharacteristic
361C22×C8—21no—
362C22×C8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8C23×C4111yescharacteristic
366C4⋊Q8C23×C4111yescharacteristic
367C4⋊Q8C23×C4111yescharacteristic
368C4⋊Q8C23×C4111yescharacteristic
369#126—41no—
370#125—21no—
371#125—41no—
372#124—21no—
373#123—41no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—41no—
378#121—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8C23×C4111yescharacteristic
383C4×Q8C23×C4111yescharacteristic
384C4×D4—21no—
385C4×D4C23×C4111yescharacteristic
386C4×D4C23×C4111yescharacteristic
387#117—21no—
388C2×C4⋊C4—21no—
389#107—21no—
390#107—21no—
391#107—41no—
392#107—41no—
393#106—21no—
394#106—21no—
395#106D4×C4111yescharacteristic
396#106D4×C4111yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C4111yescharacteristic
400C4⋊C8C23×C4111yescharacteristic
401C4⋊C8C23×C4111yescharacteristic
402C4⋊C8C23×C4111yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103D4×C4111yescharacteristic
418#103D4×C4111yescharacteristic
419#102—21no—
420#102—21no—
421#102D4×C4111yescharacteristic
422#102D4×C4111yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—21no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8C23×C4111yescharacteristic
428C4×C8C23×C4111yescharacteristic
429C4×C8C23×C4111yescharacteristic
430#41—42no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—42no—
438C2×Q8—81no—
439C2×Q8C2×D4×C4111yescharacteristic
440C2×Q8C2×D4×C4111yescharacteristic
441C2×D4—41no—
442C2×D4C2×D4×C4111yescharacteristic
443C2×D4C2×D4×C4111yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—41no—
448Q16—42no—
449Q16—81no—
450SD16—22no—
451SD16—22no—
452SD16—42no—
453SD16—81no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8—81no—
461C2×C8C2×D4×C4111yescharacteristic
462C2×C8C2×D4×C4111yescharacteristic
463C2×C8C2×D4×C4111yescharacteristic
464C2×C8C2×D4×C4111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C4111yescharacteristic
482C4⋊C4C2×D4×C4111yescharacteristic
483C4⋊C4C2×D4×C4111yescharacteristic
484C4⋊C4C2×D4×C4111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—21no—
492C42—21no—
493C42—41no—
494C42—41no—
495C42C24×C4111yescharacteristic
496C23—21no—
497C23—21no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—82no—
510Q8#135×C4112yes—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—82no—
515D4#135×C4112yes—
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—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4C22×D4×C4111yescharacteristic
533C2×C4C22×D4×C4111yescharacteristic
534C2×C4H(5,𝔽2)×C4111yescharacteristic
535C8—22no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22D42×C4111yescharacteristic
551C4—21no—
552C4—22no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4C2×#135×C4111yescharacteristic
563C4C2×#135×C4111yescharacteristic
564C4C41×#57711yescharacteristic
565C4C41×#57711yescharacteristic
566C2—42no—
567C2—81no—
568C2C41×#328211yescharacteristic
569C2C41×#328211yescharacteristic
570C2C41×#329311yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#547C22
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×#3364C2semidirect
2. C41×#3359C2semidirect
5. C41×#1710C2semidirect
6. C41×#1680C2semidirect
7. C41×#1680C2semidirect
8. C41×#1679C2semidirect
9. C41×#1679C2semidirect
10. C41×#1650C2semidirect
11. C41×#1649C2semidirect
12. C41×#1648C2semidirect
14. C8×SD16×C41C2semidirect
15. C8×SD16×C41C2semidirect
258. #19998C41direct (N × H)
281. #3364C2×C41semidirect
282. #3359C2×C41semidirect
285. #1710C2×C41semidirect
286. #1680C2×C41semidirect
287. #1680C2×C41semidirect
288. #1679C2×C41semidirect
289. #1679C2×C41semidirect
290. #1650C2×C41semidirect
291. #1649C2×C41semidirect
292. #1648C2×C41semidirect
294. C8×SD16C2×C41semidirect
295. C8×SD16C2×C41semidirect
352. C41#19998direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33642
C41×#33592
C41×#33022
C41×#32982
C41×#17102
C41×#16802
C41×#16792
C41×#16502
C41×#16492
C41×#16482
C41×#16472
C8×SD16×C412
#1999841