Finite Group Databasebeta

← C41×#20292 #23796493

Subgroups — C41×#20292 #23796493

Order 10496.

608 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3372C211yesmaximal, characteristic, complemented
2C41×#3368C211yesmaximal, characteristic, complemented
3C41×#3332C211yesmaximal, characteristic
4C41×#3331C211yesmaximal, characteristic, complemented
5C41×#1708C211yesmaximal, characteristic, complemented
6C41×#1704C211yesmaximal, characteristic, complemented
7C41×#1703C211yesmaximal, characteristic, complemented
8C41×#1702C211yesmaximal, characteristic, complemented
9C41×#1701C211yesmaximal, characteristic, complemented
10C41×#1654C211yesmaximal, characteristic, complemented
11C41×#1653C211yesmaximal, characteristic, complemented
12C41×#1631C211yesmaximal, characteristic, complemented
13C41×#1622C211yesmaximal, characteristic, complemented
14C41×#1590C211yesmaximal, characteristic, complemented
15C41×#1590C211yesmaximal, characteristic, complemented
16C41×#557C2211yescharacteristic
17C41×#554C2211yescharacteristic
18C41×#550C2211yescharacteristic
19C41×#547C2211yescharacteristic
20C41×#498C2211yescharacteristic
21C41×#492C2211yescharacteristic
22C41×#491—21no—
23C41×#490—21no—
24C41×#487C2211yescharacteristic
25C41×#487C2211yescharacteristic
26C41×#486C2211yescharacteristic
27C41×#486C2211yescharacteristic
28C41×#483—21no—
29C41×#481—21no—
30C41×#479—21no—
31C41×#478—21no—
32C41×#477C2211yescharacteristic
33C41×#476C2211yescharacteristic
34C41×#475C2211yescharacteristic
35C41×#474C2211yescharacteristic
36C41×#470—21no—
37C41×#469—21no—
38C41×#462C2211yescharacteristic
39C41×#461—21no—
40C41×#461C2211yescharacteristic
41C41×#460—21no—
42C41×#460C2211yescharacteristic
43C41×#459C2211yescharacteristic
44C41×#452—21no—
45C41×#449—21no—
46C41×#446C2211yescharacteristic
47C41×#446C2211yescharacteristic
48C41×#440—21no—
49C41×#440—21no—
50C4×SD16×C41C2211yescharacteristic
51C4×SD16×C41C2211yescharacteristic
52C41×#436C2211yescharacteristic
53C41×#436C2211yescharacteristic
54C41×#417—21no—
55C41×#417—21no—
56C41×#334C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C82×C41C2211yescharacteristic
67C2×#41×C41—21no—
68C2×#41×C41—21no—
69C2×Q16×C41—21no—
70C2×SD16×C41—21no—
71C2×SD16×C41—21no—
72C2×SD16×C41—41no—
73C2×SD16×C41D411yescharacteristic
74C2×SD16×C41D411yescharacteristic
75C2×D8×C41—21no—
76C2×M16×C41—21no—
77C2×M16×C41—21no—
78C4⋊Q8×C41—21no—
79C4⋊Q8×C41C2311yescharacteristic
80C4⋊Q8×C41C2311yescharacteristic
81C4⋊Q8×C41C2311yescharacteristic
82#127×C41—21no—
83#127×C41C2311yescharacteristic
84#125×C41—21no—
85#125×C41—21no—
86#125×C41—41no—
87#123×C41—41no—
88C22⋊Q8×C41—21no—
89C22⋊Q8×C41—21no—
90C22⋊Q8×C41—41no—
91#121×C41—21no—
92#121×C41—21no—
93#121×C41—41no—
94C4×Q8×C41—21no—
95C4×Q8×C41—21no—
96C4×Q8×C41C2311yescharacteristic
97C4×Q8×C41C2311yescharacteristic
98C4×D4×C41—21no—
99C4×D4×C41—21no—
100C4×D4×C41C2311yescharacteristic
101C4×D4×C41C2311yescharacteristic
102C2×C4⋊C4×C41—21no—
103C2×C4⋊C4×C41—21no—
104#107×C41—21no—
105#107×C41—21no—
106#106×C41—21no—
107#106×C41—21no—
108#106×C41—41no—
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×C41D411yescharacteristic
126#103×C41D411yescharacteristic
127#102×C41—21no—
128#102×C41—21no—
129#102×C41—21no—
130#102×C41—21no—
131#102×C41—21no—
132#102×C41—21no—
133#102×C41—21no—
134#102×C41—21no—
135#102×C41D411yescharacteristic
136#102×C41D411yescharacteristic
137C22⋊C8×C41—21no—
138C22⋊C8×C41—21no—
139#97×C41—21no—
140#97×C41—21no—
141C4×C8×C41C2311yescharacteristic
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144#41×C41—42no—
145#41×C41—42no—
146#41×C41—81no—
147#41×C41—81no—
148C2×Q8×C41—21no—
149C2×Q8×C41—21no—
150C2×Q8×C41—21no—
151C2×Q8×C41C2×D411yescharacteristic
152C2×Q8×C41C2×D411yescharacteristic
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—41no—
157C2×D4×C41—41no—
158C2×D4×C41—41no—
159C2×D4×C41C2×D411yescharacteristic
160C2×D4×C41C2×D411yescharacteristic
161C22×C4×C41—21no—
162C22×C4×C41—21no—
163C22×C4×C41—41no—
164C22×C4×C41—41no—
165C22×C4×C41—41no—
166Q16×C41—81no—
167SD16×C41—41no—
168SD16×C41—41no—
169SD16×C41—42no—
170SD16×C41—42no—
171SD16×C41—82no—
172D8×C41—81no—
173M16×C41—81no—
174M16×C41—81no—
175C2×C8×C41—21no—
176C2×C8×C41—21no—
177C2×C8×C41—21no—
178C2×C8×C41—21no—
179C2×C8×C41—21no—
180C2×C8×C41C2×D411yescharacteristic
181C2×C8×C41C2×D411yescharacteristic
182C2×C8×C41C2×D411yescharacteristic
183C2×C8×C41C2×D411yescharacteristic
184C4⋊C4×C41—21no—
185C4⋊C4×C41—21no—
186C4⋊C4×C41—21no—
187C4⋊C4×C41—21no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—21no—
190C4⋊C4×C41—21no—
191C4⋊C4×C41—21no—
192C4⋊C4×C41—41no—
193C4⋊C4×C41—41no—
194C4⋊C4×C41—41no—
195C4⋊C4×C41—41no—
196C4⋊C4×C41—41no—
197C4⋊C4×C41—41no—
198C4⋊C4×C41C2×D411yescharacteristic
199C4⋊C4×C41C2×D411yescharacteristic
200C4⋊C4×C41C2×D411yescharacteristic
201C4⋊C4×C41C2×D411yescharacteristic
202C22⋊C4×C41—21no—
203C22⋊C4×C41—21no—
204C22⋊C4×C41—41no—
205C22⋊C4×C41—41no—
206C22⋊C4×C41—41no—
207C42×C41—21no—
208C42×C41—21no—
209C42×C41—41no—
210C42×C41C2411yescharacteristic
211C23×C41—21no—
212C23×C41—21no—
213C23×C41—41no—
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—81no—
223D4×C41—21no—
224D4×C41—21no—
225D4×C41—21no—
226D4×C41—21no—
227D4×C41—41no—
228D4×C41—41no—
229D4×C41—41no—
230D4×C41—41no—
231D4×C41—81no—
232D4×C41—82no—
233D4×C41—82no—
234D4×C41—161no—
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—41no—
242C2×C4×C41—41no—
243C2×C4×C41—41no—
244C2×C4×C41—41no—
245C2×C4×C41—41no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—82no—
249C2×C4×C41—82no—
250C2×C4×C41—161no—
251C2×C4×C41C22×D411yescharacteristic
252C2×C4×C41C22×D411yescharacteristic
253C2×C4×C41H(5,𝔽2)11yescharacteristic
254C8×C41—22no—
255C8×C41—21no—
256C8×C41—21no—
257C8×C41—21no—
258C8×C41—21no—
259C8×C41—41no—
260C8×C41—41no—
261C8×C41—41no—
262C8×C41—41no—
263#20292C4111yesmaximal, characteristic, direct product factor, Sylow
264C22×C41—41no—
265C22×C41—41no—
266C22×C41—41no—
267C22×C41—41no—
268C22×C41—41no—
269C22×C41—41no—
270C22×C41—81no—
271C22×C41—81no—
272C22×C41—81no—
273C22×C41D4211yescharacteristic
274C4×C41—21no—
275C4×C41—41no—
276C4×C41—41no—
277C4×C41—41no—
278C4×C41—41no—
279C4×C41—41no—
280C4×C41—41no—
281C4×C41—81no—
282C4×C41—81no—
283C4×C41—81no—
284C4×C41#57511yescharacteristic
285C4×C41#57511yescharacteristic
286C4×C41#57711yescharacteristic
287C4×C41#57711yescharacteristic
288#3372C2×C4111yescharacteristic, complemented
289#3368C2×C4111yescharacteristic, complemented
290#3332C2×C4111yescharacteristic
291#3331C2×C4111yescharacteristic, complemented
292#1708C2×C4111yescharacteristic, complemented
293#1704C2×C4111yescharacteristic, complemented
294#1703C2×C4111yescharacteristic, complemented
295#1702C2×C4111yescharacteristic, complemented
296#1701C2×C4111yescharacteristic, complemented
297#1654C2×C4111yescharacteristic, complemented
298#1653C2×C4111yescharacteristic, complemented
299#1631C2×C4111yescharacteristic, complemented
300#1622C2×C4111yescharacteristic, complemented
301#1590C2×C4111yescharacteristic, complemented
302#1590C2×C4111yescharacteristic, complemented
303C2×C41—81no—
304C2×C41—81no—
305C2×C41—161no—
306C2×C41#327511yescharacteristic
307C2×C41#327511yescharacteristic
308C2×C41#329111yescharacteristic
309#557C22×C4111yescharacteristic
310#554C22×C4111yescharacteristic
311#550C22×C4111yescharacteristic
312#547C22×C4111yescharacteristic
313#498C22×C4111yescharacteristic
314#492C22×C4111yescharacteristic
315#491—21no—
316#490—21no—
317#487C22×C4111yescharacteristic
318#487C22×C4111yescharacteristic
319#486C22×C4111yescharacteristic
320#486C22×C4111yescharacteristic
321#483—21no—
322#481—21no—
323#479—21no—
324#478—21no—
325#477C22×C4111yescharacteristic
326#476C22×C4111yescharacteristic
327#475C22×C4111yescharacteristic
328#474C22×C4111yescharacteristic
329#470—21no—
330#469—21no—
331#462C22×C4111yescharacteristic
332#461—21no—
333#461C22×C4111yescharacteristic
334#460—21no—
335#460C22×C4111yescharacteristic
336#459C22×C4111yescharacteristic
337#452—21no—
338#449—21no—
339#446C22×C4111yescharacteristic
340#446C22×C4111yescharacteristic
341#440—21no—
342#440—21no—
343C4×SD16C22×C4111yescharacteristic
344C4×SD16C22×C4111yescharacteristic
345#436C22×C4111yescharacteristic
346#436C22×C4111yescharacteristic
347#417—21no—
348#417—21no—
349#334C22×C4111yescharacteristic
350#334C22×C4111yescharacteristic
351#333C22×C4111yescharacteristic
352#332C22×C4111yescharacteristic
353#332C22×C4111yescharacteristic
354#331C22×C4111yescharacteristic
355Q8⋊C8C22×C4111yescharacteristic
356Q8⋊C8C22×C4111yescharacteristic
357D4⋊C8C22×C4111yescharacteristic
358D4⋊C8C22×C4111yescharacteristic
359C82C22×C4111yescharacteristic
360C41#2029211yescharacteristic, direct product factor, Sylow
361C2×#41—21no—
362C2×#41—21no—
363C2×Q16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—41no—
367C2×SD16D4×C4111yescharacteristic
368C2×SD16D4×C4111yescharacteristic
369C2×D8—21no—
370C2×M16—21no—
371C2×M16—21no—
372C4⋊Q8—21no—
373C4⋊Q8C23×C4111yescharacteristic
374C4⋊Q8C23×C4111yescharacteristic
375C4⋊Q8C23×C4111yescharacteristic
376#127—21no—
377#127C23×C4111yescharacteristic
378#125—21no—
379#125—21no—
380#125—41no—
381#123—41no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—41no—
385#121—21no—
386#121—21no—
387#121—41no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8C23×C4111yescharacteristic
391C4×Q8C23×C4111yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C23×C4111yescharacteristic
395C4×D4C23×C4111yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398#107—21no—
399#107—21no—
400#106—21no—
401#106—21no—
402#106—41no—
403#106D4×C4111yescharacteristic
404#106D4×C4111yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C4111yescharacteristic
408C4⋊C8C23×C4111yescharacteristic
409C4⋊C8C23×C4111yescharacteristic
410C4⋊C8C23×C4111yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103D4×C4111yescharacteristic
420#103D4×C4111yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102D4×C4111yescharacteristic
430#102D4×C4111yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433#97—21no—
434#97—21no—
435C4×C8C23×C4111yescharacteristic
436C4×C8C23×C4111yescharacteristic
437C4×C8C23×C4111yescharacteristic
438#41—42no—
439#41—42no—
440#41—81no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×D4×C4111yescharacteristic
446C2×Q8C2×D4×C4111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×D4×C4111yescharacteristic
454C2×D4C2×D4×C4111yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460Q16—81no—
461SD16—41no—
462SD16—41no—
463SD16—42no—
464SD16—42no—
465SD16—82no—
466D8—81no—
467M16—81no—
468M16—81no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8C2×D4×C4111yescharacteristic
475C2×C8C2×D4×C4111yescharacteristic
476C2×C8C2×D4×C4111yescharacteristic
477C2×C8C2×D4×C4111yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C4111yescharacteristic
493C4⋊C4C2×D4×C4111yescharacteristic
494C4⋊C4C2×D4×C4111yescharacteristic
495C4⋊C4C2×D4×C4111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—21no—
502C42—21no—
503C42—41no—
504C42C24×C4111yescharacteristic
505C23—21no—
506C23—21no—
507C23—41no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—21no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—81no—
526D4—82no—
527D4—82no—
528D4—161no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—161no—
545C2×C4C22×D4×C4111yescharacteristic
546C2×C4C22×D4×C4111yescharacteristic
547C2×C4H(5,𝔽2)×C4111yescharacteristic
548C8—22no—
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22D42×C4111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C41×#57511yescharacteristic
578C4C41×#57511yescharacteristic
579C4C41×#57711yescharacteristic
580C4C41×#57711yescharacteristic
581C2—81no—
582C2—81no—
583C2—161no—
584C2C41×#327511yescharacteristic
585C2C41×#327511yescharacteristic
586C2C41×#329111yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3332C2
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×#3372C2semidirect
2. C41×#3368C2semidirect
4. C41×#3331C2semidirect
5. C41×#1708C2semidirect
6. C41×#1704C2semidirect
7. C41×#1703C2semidirect
8. C41×#1702C2semidirect
9. C41×#1701C2semidirect
10. C41×#1654C2semidirect
11. C41×#1653C2semidirect
12. C41×#1631C2semidirect
13. C41×#1622C2semidirect
14. C41×#1590C2semidirect
15. C41×#1590C2semidirect
263. #20292C41direct (N × H)
288. #3372C2×C41semidirect
289. #3368C2×C41semidirect
291. #3331C2×C41semidirect
292. #1708C2×C41semidirect
293. #1704C2×C41semidirect
294. #1703C2×C41semidirect
295. #1702C2×C41semidirect
296. #1701C2×C41semidirect
297. #1654C2×C41semidirect
298. #1653C2×C41semidirect
299. #1631C2×C41semidirect
300. #1622C2×C41semidirect
301. #1590C2×C41semidirect
302. #1590C2×C41semidirect
360. C41#20292direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33722
C41×#33682
C41×#33322
C41×#33312
C41×#17082
C41×#17042
C41×#17032
C41×#17022
C41×#17012
C41×#16542
C41×#16532
C41×#16312
C41×#16222
C41×#15902
#2029241