Finite Group Databasebeta

← C41×#20284 #23796485

Subgroups — C41×#20284 #23796485

Order 10496.

584 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×#3400C211yesmaximal, characteristic, complemented
2C41×#3396C211yesmaximal, characteristic
3C41×#3387C211yesmaximal, characteristic, complemented
4C41×#3375C211yesmaximal, characteristic, complemented
5C41×#1715C211yesmaximal, characteristic
6C41×#1698C211yesmaximal, characteristic, complemented
7C41×#1688C211yesmaximal, characteristic
8C41×#1686C211yesmaximal, characteristic, complemented
9C41×#1672C211yesmaximal, characteristic, complemented
10C41×#1640C211yesmaximal, characteristic, complemented
11C41×#1630C211yesmaximal, characteristic, complemented
12C41×#1626C211yesmaximal, characteristic, complemented
13C41×#1623C211yesmaximal, characteristic, complemented
14C41×#1593C211yesmaximal, characteristic, complemented
15C41×#1584C211yesmaximal, characteristic, complemented
16C41×#559C2211yescharacteristic
17C41×#559C2211yescharacteristic
18Q82×C41C2211yescharacteristic
19C41×#557C2211yescharacteristic
20C41×#501—21no—
21C41×#498C2211yescharacteristic
22C41×#497—21no—
23C41×#495—21no—
24C41×#493C2211yescharacteristic
25C41×#492C2211yescharacteristic
26C41×#492C2211yescharacteristic
27C41×#489—21no—
28C41×#486C2211yescharacteristic
29C41×#486C2211yescharacteristic
30C41×#479—21no—
31C41×#477C2211yescharacteristic
32C41×#477C2211yescharacteristic
33C41×#475—21no—
34C41×#475C2211yescharacteristic
35C41×#474—21no—
36C41×#464—21no—
37C41×#464—21no—
38C41×#463—21no—
39C41×#463—21no—
40C41×#462C2211yescharacteristic
41C41×#461—21no—
42C41×#460C2211yescharacteristic
43C41×#460C2211yescharacteristic
44C41×#460C2211yescharacteristic
45C41×#460C2211yescharacteristic
46C41×#446C2211yescharacteristic
47C41×#446C2211yescharacteristic
48C41×#446C2211yescharacteristic
49C8×Q8×C41C2211yescharacteristic
50C41×#441—21no—
51C41×#440—21no—
52C41×#440—21no—
53C4×Q16×C41C2211yescharacteristic
54C4×Q16×C41C2211yescharacteristic
55C4×D8×C41—21no—
56C41×#335C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#331C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×Q8⋊C8C2211yescharacteristic
65C41×Q8⋊C8C2211yescharacteristic
66C41×#322C2211yescharacteristic
67C2×Q16×C41—21no—
68C2×Q16×C41D411yescharacteristic
69C2×Q16×C41D411yescharacteristic
70C2×SD16×C41—21no—
71C2×SD16×C41—21no—
72C2×SD16×C41—21no—
73C2×SD16×C41—21no—
74C2×SD16×C41—21no—
75C2×SD16×C41—21no—
76C2×SD16×C41—41no—
77C2×D8×C41—21no—
78C2×D8×C41—21no—
79C4⋊Q8×C41—21no—
80C4⋊Q8×C41—21no—
81C4⋊Q8×C41—21no—
82C4⋊Q8×C41—41no—
83C4⋊Q8×C41C2311yescharacteristic
84C4⋊Q8×C41C2311yescharacteristic
85#127×C41C2311yescharacteristic
86#127×C41C2311yescharacteristic
87#125×C41—21no—
88#125×C41—41no—
89#124×C41—21no—
90#124×C41—21no—
91#124×C41—21no—
92#124×C41—21no—
93#123×C41—41no—
94#123×C41—41no—
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×Q8×C41C2311yescharacteristic
103C4×D4×C41—21no—
104C4×D4×C41—21no—
105C4×D4×C41—21no—
106C4×D4×C41—21no—
107#107×C41—21no—
108#107×C41—21no—
109#107×C41D411yescharacteristic
110#107×C41D411yescharacteristic
111#106×C41—21no—
112#106×C41—21no—
113#106×C41—21no—
114C4⋊C8×C41—21no—
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×C41D411yescharacteristic
127#103×C41D411yescharacteristic
128#103×C41D411yescharacteristic
129#103×C41D411yescharacteristic
130#102×C41—21no—
131#102×C41—21no—
132#102×C41—21no—
133#102×C41—21no—
134#102×C41—21no—
135#102×C41—21no—
136#102×C41—41no—
137#97×C41—21no—
138#97×C41—21no—
139#97×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—41no—
147C2×Q8×C41C2×D411yescharacteristic
148C2×Q8×C41C2×D411yescharacteristic
149C2×Q8×C41C2×D411yescharacteristic
150C2×Q8×C41C2×D411yescharacteristic
151C2×D4×C41—21no—
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—21no—
157C22×C4×C41—41no—
158C22×C4×C41—41no—
159Q16×C41—22no—
160Q16×C41—41no—
161Q16×C41—81no—
162SD16×C41—42no—
163SD16×C41—42no—
164SD16×C41—81no—
165SD16×C41—81no—
166SD16×C41—81no—
167SD16×C41—81no—
168SD16×C41—82no—
169D8×C41—42no—
170D8×C41—81no—
171C2×C8×C41—21no—
172C2×C8×C41—21no—
173C2×C8×C41—21no—
174C2×C8×C41—21no—
175C2×C8×C41—21no—
176C2×C8×C41C2×D411yescharacteristic
177C2×C8×C41C2×D411yescharacteristic
178C2×C8×C41C2×D411yescharacteristic
179C2×C8×C41C2×D411yescharacteristic
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—41no—
189C4⋊C4×C41—41no—
190C4⋊C4×C41—41no—
191C4⋊C4×C41—41no—
192C4⋊C4×C41—41no—
193C4⋊C4×C41C2×D411yescharacteristic
194C4⋊C4×C41C2×D411yescharacteristic
195C4⋊C4×C41C2×D411yescharacteristic
196C4⋊C4×C41C2×D411yescharacteristic
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—21no—
207C42×C41—41no—
208C42×C41—41no—
209C42×C41C2411yescharacteristic
210C23×C41—41no—
211C23×C41—41no—
212Q8×C41—21no—
213Q8×C41—21no—
214Q8×C41—21no—
215Q8×C41—21no—
216Q8×C41—21no—
217Q8×C41—21no—
218Q8×C41—21no—
219Q8×C41—21no—
220Q8×C41—41no—
221Q8×C41—41no—
222Q8×C41—81no—
223Q8×C41—161no—
224D4×C41—41no—
225D4×C41—41no—
226D4×C41—41no—
227D4×C41—41no—
228D4×C41—41no—
229D4×C41—41no—
230D4×C41—41no—
231D4×C41—41no—
232D4×C41—81no—
233D4×C41—81no—
234C2×C4×C41—21no—
235C2×C4×C41—21no—
236C2×C4×C41—21no—
237C2×C4×C41—21no—
238C2×C4×C41—21no—
239C2×C4×C41—21no—
240C2×C4×C41—21no—
241C2×C4×C41—21no—
242C2×C4×C41—41no—
243C2×C4×C41—41no—
244C2×C4×C41—161no—
245C2×C4×C41—161no—
246C2×C4×C41C22×D411yescharacteristic
247C2×C4×C41C22×D411yescharacteristic
248C2×C4×C41H(5,𝔽2)11yescharacteristic
249C8×C41—21no—
250C8×C41—21no—
251C8×C41—21no—
252C8×C41—41no—
253C8×C41—41no—
254C8×C41—41no—
255C8×C41—41no—
256C8×C41—41no—
257C8×C41#13712yes—
258#20284C4111yesmaximal, characteristic, direct product factor, Sylow
259C22×C41—81no—
260C22×C41—81no—
261C22×C41—81no—
262C22×C41—81no—
263C22×C41—81no—
264C22×C41—81no—
265C22×C41D4211yescharacteristic
266C4×C41—21no—
267C4×C41—41no—
268C4×C41—41no—
269C4×C41—41no—
270C4×C41—41no—
271C4×C41—41no—
272C4×C41—41no—
273C4×C41—41no—
274C4×C41—41no—
275C4×C41—81no—
276C4×C41—81no—
277C4×C41C2×#13711yescharacteristic
278C4×C41#57511yescharacteristic
279C4×C41#57711yescharacteristic
280C4×C41#57711yescharacteristic
281#3400C2×C4111yescharacteristic, complemented
282#3396C2×C4111yescharacteristic
283#3387C2×C4111yescharacteristic, complemented
284#3375C2×C4111yescharacteristic, complemented
285#1715C2×C4111yescharacteristic
286#1698C2×C4111yescharacteristic, complemented
287#1688C2×C4111yescharacteristic
288#1686C2×C4111yescharacteristic, complemented
289#1672C2×C4111yescharacteristic, complemented
290#1640C2×C4111yescharacteristic, complemented
291#1630C2×C4111yescharacteristic, complemented
292#1626C2×C4111yescharacteristic, complemented
293#1623C2×C4111yescharacteristic, complemented
294#1593C2×C4111yescharacteristic, complemented
295#1584C2×C4111yescharacteristic, complemented
296C2×C41—161no—
297C2×C41—161no—
298C2×C41#327111yescharacteristic
299C2×C41#327811yescharacteristic
300C2×C41#328811yescharacteristic
301#559C22×C4111yescharacteristic
302#559C22×C4111yescharacteristic
303Q82C22×C4111yescharacteristic
304#557C22×C4111yescharacteristic
305#501—21no—
306#498C22×C4111yescharacteristic
307#497—21no—
308#495—21no—
309#493C22×C4111yescharacteristic
310#492C22×C4111yescharacteristic
311#492C22×C4111yescharacteristic
312#489—21no—
313#486C22×C4111yescharacteristic
314#486C22×C4111yescharacteristic
315#479—21no—
316#477C22×C4111yescharacteristic
317#477C22×C4111yescharacteristic
318#475—21no—
319#475C22×C4111yescharacteristic
320#474—21no—
321#464—21no—
322#464—21no—
323#463—21no—
324#463—21no—
325#462C22×C4111yescharacteristic
326#461—21no—
327#460C22×C4111yescharacteristic
328#460C22×C4111yescharacteristic
329#460C22×C4111yescharacteristic
330#460C22×C4111yescharacteristic
331#446C22×C4111yescharacteristic
332#446C22×C4111yescharacteristic
333#446C22×C4111yescharacteristic
334C8×Q8C22×C4111yescharacteristic
335#441—21no—
336#440—21no—
337#440—21no—
338C4×Q16C22×C4111yescharacteristic
339C4×Q16C22×C4111yescharacteristic
340C4×D8—21no—
341#335C22×C4111yescharacteristic
342#334C22×C4111yescharacteristic
343#333C22×C4111yescharacteristic
344#332C22×C4111yescharacteristic
345#331C22×C4111yescharacteristic
346#331C22×C4111yescharacteristic
347Q8⋊C8C22×C4111yescharacteristic
348Q8⋊C8C22×C4111yescharacteristic
349Q8⋊C8C22×C4111yescharacteristic
350Q8⋊C8C22×C4111yescharacteristic
351#322C22×C4111yescharacteristic
352C41#2028411yescharacteristic, direct product factor, Sylow
353C2×Q16—21no—
354C2×Q16D4×C4111yescharacteristic
355C2×Q16D4×C4111yescharacteristic
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—41no—
363C2×D8—21no—
364C2×D8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—41no—
369C4⋊Q8C23×C4111yescharacteristic
370C4⋊Q8C23×C4111yescharacteristic
371#127C23×C4111yescharacteristic
372#127C23×C4111yescharacteristic
373#125—21no—
374#125—41no—
375#124—21no—
376#124—21no—
377#124—21no—
378#124—21no—
379#123—41no—
380#123—41no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C4111yescharacteristic
386C4×Q8C23×C4111yescharacteristic
387C4×Q8C23×C4111yescharacteristic
388C4×Q8C23×C4111yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393#107—21no—
394#107—21no—
395#107D4×C4111yescharacteristic
396#107D4×C4111yescharacteristic
397#106—21no—
398#106—21no—
399#106—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C4111yescharacteristic
405C4⋊C8C23×C4111yescharacteristic
406C4⋊C8C23×C4111yescharacteristic
407C4⋊C8C23×C4111yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103D4×C4111yescharacteristic
413#103D4×C4111yescharacteristic
414#103D4×C4111yescharacteristic
415#103D4×C4111yescharacteristic
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—41no—
423#97—21no—
424#97—21no—
425#97—21no—
426C4×C8—21no—
427C4×C8C23×C4111yescharacteristic
428C4×C8C23×C4111yescharacteristic
429C4×C8C23×C4111yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8C2×D4×C4111yescharacteristic
434C2×Q8C2×D4×C4111yescharacteristic
435C2×Q8C2×D4×C4111yescharacteristic
436C2×Q8C2×D4×C4111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C22×C4—41no—
444C22×C4—41no—
445Q16—22no—
446Q16—41no—
447Q16—81no—
448SD16—42no—
449SD16—42no—
450SD16—81no—
451SD16—81no—
452SD16—81no—
453SD16—81no—
454SD16—82no—
455D8—42no—
456D8—81no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8C2×D4×C4111yescharacteristic
463C2×C8C2×D4×C4111yescharacteristic
464C2×C8C2×D4×C4111yescharacteristic
465C2×C8C2×D4×C4111yescharacteristic
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—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C4111yescharacteristic
480C4⋊C4C2×D4×C4111yescharacteristic
481C4⋊C4C2×D4×C4111yescharacteristic
482C4⋊C4C2×D4×C4111yescharacteristic
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—41no—
494C42—41no—
495C42C24×C4111yescharacteristic
496C23—41no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—81no—
509Q8—161no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—41no—
518D4—81no—
519D4—81no—
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—41no—
529C2×C4—41no—
530C2×C4—161no—
531C2×C4—161no—
532C2×C4C22×D4×C4111yescharacteristic
533C2×C4C22×D4×C4111yescharacteristic
534C2×C4H(5,𝔽2)×C4111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8#137×C4112yes—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22D42×C4111yescharacteristic
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4C2×#137×C4111yescharacteristic
563C4C41×#57511yescharacteristic
564C4C41×#57711yescharacteristic
565C4C41×#57711yescharacteristic
566C2—161no—
567C2—161no—
568C2C41×#327111yescharacteristic
569C2C41×#327811yescharacteristic
570C2C41×#328811yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#493C22
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×#3400C2semidirect
3. C41×#3387C2semidirect
4. C41×#3375C2semidirect
6. C41×#1698C2semidirect
8. C41×#1686C2semidirect
9. C41×#1672C2semidirect
10. C41×#1640C2semidirect
11. C41×#1630C2semidirect
12. C41×#1626C2semidirect
13. C41×#1623C2semidirect
14. C41×#1593C2semidirect
15. C41×#1584C2semidirect
258. #20284C41direct (N × H)
281. #3400C2×C41semidirect
283. #3387C2×C41semidirect
284. #3375C2×C41semidirect
286. #1698C2×C41semidirect
288. #1686C2×C41semidirect
289. #1672C2×C41semidirect
290. #1640C2×C41semidirect
291. #1630C2×C41semidirect
292. #1626C2×C41semidirect
293. #1623C2×C41semidirect
294. #1593C2×C41semidirect
295. #1584C2×C41semidirect
352. C41#20284direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#34002
C41×#33962
C41×#33872
C41×#33752
C41×#17152
C41×#16982
C41×#16882
C41×#16862
C41×#16722
C41×#16402
C41×#16302
C41×#16262
C41×#16232
C41×#15932
C41×#15842
#2028441