Finite Group Databasebeta

← C41×#19802 #23796003

Subgroups — C41×#19802 #23796003

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×#3394C211yesmaximal, characteristic, complemented
2C41×#3375C211yesmaximal, characteristic, complemented
3C41×#3362C211yesmaximal, characteristic, complemented
4C41×#3304C211yesmaximal, characteristic, complemented
5C41×#1717C211yesmaximal, characteristic, complemented
6C41×#1702C211yesmaximal, characteristic, complemented
7C41×#1678C211yesmaximal, characteristic, complemented
8C41×#1677C211yesmaximal, characteristic, complemented
9C41×#1666C211yesmaximal, characteristic, complemented
10C41×#1645C211yesmaximal, characteristic, complemented
11C41×#1638C211yesmaximal, characteristic, complemented
12C41×#1621C211yesmaximal, characteristic
13C41×#1620C211yesmaximal, characteristic, complemented
14C41×#1582C211yesmaximal, characteristic, complemented
15C41×#1579C211yesmaximal, characteristic, complemented
16C41×#559C2211yescharacteristic
17Q82×C41C2211yescharacteristic
18C41×#556C2211yescharacteristic
19C41×#550C2211yescharacteristic
20C41×#495—21no—
21C41×#493C2211yescharacteristic
22C41×#492C2211yescharacteristic
23C41×#489—21no—
24C41×#487C2211yescharacteristic
25C41×#486—21no—
26C41×#486C2211yescharacteristic
27C41×#486C2211yescharacteristic
28C41×#486C2211yescharacteristic
29C41×#482—21no—
30C41×#477C2211yescharacteristic
31C41×#476—21no—
32C41×#476C2211yescharacteristic
33C41×#475C2211yescharacteristic
34C41×#474—21no—
35C41×#465—21no—
36C41×#464—21no—
37C41×#464—21no—
38C41×#463—21no—
39C41×#462C2211yescharacteristic
40C41×#460—21no—
41C41×#460C2211yescharacteristic
42C41×#460C2211yescharacteristic
43C41×#460C2211yescharacteristic
44C41×#459C2211yescharacteristic
45C41×#452—21no—
46C41×#446C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C8×Q8×C41C2211yescharacteristic
49C41×#440—21no—
50C4×Q16×C41C2211yescharacteristic
51C4×SD16×C41—21no—
52C4×SD16×C41—21no—
53C4×SD16×C41C2211yescharacteristic
54C8×D4×C41C2211yescharacteristic
55C41×#416—21no—
56C41×#334C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#331C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×Q8⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C41×#322C2211yescharacteristic
67C2×#41×C41—21no—
68C2×Q16×C41—21no—
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×C41D411yescharacteristic
76C2×D8×C41—21no—
77C2×D8×C41—41no—
78C22×C8×C41—21no—
79C4⋊Q8×C41—21no—
80C4⋊Q8×C41—21no—
81C4⋊Q8×C41—41no—
82C4⋊Q8×C41C2311yescharacteristic
83C4⋊Q8×C41C2311yescharacteristic
84#127×C41—21no—
85#127×C41C2311yescharacteristic
86#127×C41C2311yescharacteristic
87#126×C41—41no—
88#124×C41—21no—
89#124×C41—21no—
90#124×C41—21no—
91#123×C41—41no—
92C22⋊Q8×C41—21no—
93#121×C41—21no—
94#121×C41—41no—
95C4×Q8×C41—21no—
96C4×Q8×C41—21no—
97C4×Q8×C41—21no—
98C4×Q8×C41C2311yescharacteristic
99C4×Q8×C41C2311yescharacteristic
100C4×Q8×C41C2311yescharacteristic
101C4×D4×C41—21no—
102C4×D4×C41—21no—
103C4×D4×C41—21no—
104C4×D4×C41C2311yescharacteristic
105#117×C41—21no—
106#107×C41—21no—
107#107×C41D411yescharacteristic
108#106×C41—21no—
109#106×C41—21no—
110#106×C41D411yescharacteristic
111C4⋊C8×C41—21no—
112C4⋊C8×C41—21no—
113C4⋊C8×C41—21no—
114C4⋊C8×C41C2311yescharacteristic
115C4⋊C8×C41C2311yescharacteristic
116C4⋊C8×C41C2311yescharacteristic
117C4⋊C8×C41C2311yescharacteristic
118#103×C41—21no—
119#103×C41—21no—
120#103×C41—21no—
121#103×C41—41no—
122#103×C41D411yescharacteristic
123#103×C41D411yescharacteristic
124#103×C41D411yescharacteristic
125#102×C41—21no—
126#102×C41—21no—
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×C41—21no—
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
144#41×C41—42no—
145#41×C41—81no—
146C2×Q8×C41—21no—
147C2×Q8×C41—21no—
148C2×Q8×C41—41no—
149C2×Q8×C41C2×D411yescharacteristic
150C2×Q8×C41C2×D411yescharacteristic
151C2×Q8×C41C2×D411yescharacteristic
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—21no—
157C2×D4×C41—21no—
158C2×D4×C41—41no—
159C2×D4×C41—41no—
160C2×D4×C41C2×D411yescharacteristic
161C22×C4×C41—21no—
162C22×C4×C41—41no—
163C22×C4×C41—41no—
164Q16×C41—22no—
165Q16×C41—81no—
166SD16×C41—41no—
167SD16×C41—42no—
168SD16×C41—42no—
169SD16×C41—42no—
170SD16×C41—81no—
171SD16×C41—81no—
172D8×C41—81no—
173D8×C41—82no—
174C2×C8×C41—21no—
175C2×C8×C41—21no—
176C2×C8×C41—21no—
177C2×C8×C41—21no—
178C2×C8×C41—21no—
179C2×C8×C41—81no—
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—41no—
192C4⋊C4×C41—41no—
193C4⋊C4×C41—41no—
194C4⋊C4×C41C2×D411yescharacteristic
195C4⋊C4×C41C2×D411yescharacteristic
196C4⋊C4×C41C2×D411yescharacteristic
197C4⋊C4×C41C2×D411yescharacteristic
198C22⋊C4×C41—21no—
199C22⋊C4×C41—41no—
200C22⋊C4×C41—41no—
201C22⋊C4×C41—41no—
202C22⋊C4×C41—41no—
203C22⋊C4×C41—41no—
204C22⋊C4×C41—41no—
205C42×C41—21no—
206C42×C41—21no—
207C42×C41—21no—
208C42×C41—41no—
209C42×C41—41no—
210C42×C41C2411yescharacteristic
211C23×C41—21no—
212C23×C41—41no—
213C23×C41—41no—
214Q8×C41—21no—
215Q8×C41—21no—
216Q8×C41—21no—
217Q8×C41—21no—
218Q8×C41—21no—
219Q8×C41—41no—
220Q8×C41—41no—
221Q8×C41—81no—
222Q8×C41—161no—
223Q8×C41#13512yes—
224D4×C41—21no—
225D4×C41—21no—
226D4×C41—41no—
227D4×C41—41no—
228D4×C41—41no—
229D4×C41—41no—
230D4×C41—41no—
231D4×C41—41no—
232D4×C41—41no—
233D4×C41—41no—
234D4×C41—82no—
235D4×C41—81no—
236D4×C41—81no—
237D4×C41—161no—
238C2×C4×C41—21no—
239C2×C4×C41—21no—
240C2×C4×C41—21no—
241C2×C4×C41—21no—
242C2×C4×C41—21no—
243C2×C4×C41—21no—
244C2×C4×C41—21no—
245C2×C4×C41—41no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—41no—
249C2×C4×C41—82no—
250C2×C4×C41—161no—
251C2×C4×C41C22×D411yescharacteristic
252C2×C4×C41C22×D411yescharacteristic
253C2×C4×C41H(5,𝔽2)11yescharacteristic
254C8×C41—21no—
255C8×C41—21no—
256C8×C41—21no—
257C8×C41—21no—
258C8×C41—41no—
259C8×C41—41no—
260C8×C41—41no—
261C8×C41—41no—
262C8×C41—41no—
263#19802C4111yesmaximal, characteristic, direct product factor, Sylow
264C22×C41—41no—
265C22×C41—41no—
266C22×C41—41no—
267C22×C41—81no—
268C22×C41—81no—
269C22×C41—81no—
270C22×C41—81no—
271C22×C41—81no—
272C22×C41—81no—
273C22×C41D4211yescharacteristic
274C4×C41—22no—
275C4×C41—21no—
276C4×C41—41no—
277C4×C41—41no—
278C4×C41—41no—
279C4×C41—41no—
280C4×C41—41no—
281C4×C41—41no—
282C4×C41—81no—
283C4×C41—81no—
284C4×C41C2×#13511yescharacteristic
285C4×C41#57511yescharacteristic
286C4×C41#57711yescharacteristic
287C4×C41#57711yescharacteristic
288#3394C2×C4111yescharacteristic, complemented
289#3375C2×C4111yescharacteristic, complemented
290#3362C2×C4111yescharacteristic, complemented
291#3304C2×C4111yescharacteristic, complemented
292#1717C2×C4111yescharacteristic, complemented
293#1702C2×C4111yescharacteristic, complemented
294#1678C2×C4111yescharacteristic, complemented
295#1677C2×C4111yescharacteristic, complemented
296#1666C2×C4111yescharacteristic, complemented
297#1645C2×C4111yescharacteristic, complemented
298#1638C2×C4111yescharacteristic, complemented
299#1621C2×C4111yescharacteristic
300#1620C2×C4111yescharacteristic, complemented
301#1582C2×C4111yescharacteristic, complemented
302#1579C2×C4111yescharacteristic, complemented
303C2×C41—81no—
304C2×C41—161no—
305C2×C41—161no—
306C2×C41#327111yescharacteristic
307C2×C41#328211yescharacteristic
308C2×C41#328811yescharacteristic
309#559C22×C4111yescharacteristic
310Q82C22×C4111yescharacteristic
311#556C22×C4111yescharacteristic
312#550C22×C4111yescharacteristic
313#495—21no—
314#493C22×C4111yescharacteristic
315#492C22×C4111yescharacteristic
316#489—21no—
317#487C22×C4111yescharacteristic
318#486—21no—
319#486C22×C4111yescharacteristic
320#486C22×C4111yescharacteristic
321#486C22×C4111yescharacteristic
322#482—21no—
323#477C22×C4111yescharacteristic
324#476—21no—
325#476C22×C4111yescharacteristic
326#475C22×C4111yescharacteristic
327#474—21no—
328#465—21no—
329#464—21no—
330#464—21no—
331#463—21no—
332#462C22×C4111yescharacteristic
333#460—21no—
334#460C22×C4111yescharacteristic
335#460C22×C4111yescharacteristic
336#460C22×C4111yescharacteristic
337#459C22×C4111yescharacteristic
338#452—21no—
339#446C22×C4111yescharacteristic
340C8×Q8C22×C4111yescharacteristic
341C8×Q8C22×C4111yescharacteristic
342#440—21no—
343C4×Q16C22×C4111yescharacteristic
344C4×SD16—21no—
345C4×SD16—21no—
346C4×SD16C22×C4111yescharacteristic
347C8×D4C22×C4111yescharacteristic
348#416—21no—
349#334C22×C4111yescharacteristic
350#334C22×C4111yescharacteristic
351#333C22×C4111yescharacteristic
352#332C22×C4111yescharacteristic
353#331C22×C4111yescharacteristic
354#331C22×C4111yescharacteristic
355Q8⋊C8C22×C4111yescharacteristic
356Q8⋊C8C22×C4111yescharacteristic
357Q8⋊C8C22×C4111yescharacteristic
358D4⋊C8C22×C4111yescharacteristic
359#322C22×C4111yescharacteristic
360C41#1980211yescharacteristic, direct product factor, Sylow
361C2×#41—21no—
362C2×Q16—21no—
363C2×Q16D4×C4111yescharacteristic
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16D4×C4111yescharacteristic
370C2×D8—21no—
371C2×D8—41no—
372C22×C8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—41no—
376C4⋊Q8C23×C4111yescharacteristic
377C4⋊Q8C23×C4111yescharacteristic
378#127—21no—
379#127C23×C4111yescharacteristic
380#127C23×C4111yescharacteristic
381#126—41no—
382#124—21no—
383#124—21no—
384#124—21no—
385#123—41no—
386C22⋊Q8—21no—
387#121—21no—
388#121—41no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C23×C4111yescharacteristic
393C4×Q8C23×C4111yescharacteristic
394C4×Q8C23×C4111yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C4111yescharacteristic
399#117—21no—
400#107—21no—
401#107D4×C4111yescharacteristic
402#106—21no—
403#106—21no—
404#106D4×C4111yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8C23×C4111yescharacteristic
409C4⋊C8C23×C4111yescharacteristic
410C4⋊C8C23×C4111yescharacteristic
411C4⋊C8C23×C4111yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—41no—
416#103D4×C4111yescharacteristic
417#103D4×C4111yescharacteristic
418#103D4×C4111yescharacteristic
419#102—21no—
420#102—21no—
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#102—21no—
430#102D4×C4111yescharacteristic
431C22⋊C8—21no—
432#97—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C4111yescharacteristic
436C4×C8C23×C4111yescharacteristic
437C4×C8C23×C4111yescharacteristic
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8C2×D4×C4111yescharacteristic
444C2×Q8C2×D4×C4111yescharacteristic
445C2×Q8C2×D4×C4111yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×D4×C4111yescharacteristic
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458Q16—22no—
459Q16—81no—
460SD16—41no—
461SD16—42no—
462SD16—42no—
463SD16—42no—
464SD16—81no—
465SD16—81no—
466D8—81no—
467D8—82no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—81no—
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—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C4111yescharacteristic
489C4⋊C4C2×D4×C4111yescharacteristic
490C4⋊C4C2×D4×C4111yescharacteristic
491C4⋊C4C2×D4×C4111yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42—41no—
504C42C24×C4111yescharacteristic
505C23—21no—
506C23—41no—
507C23—41no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—41no—
514Q8—41no—
515Q8—81no—
516Q8—161no—
517Q8#135×C4112yes—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—82no—
529D4—81no—
530D4—81no—
531D4—161no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—161no—
545C2×C4C22×D4×C4111yescharacteristic
546C2×C4C22×D4×C4111yescharacteristic
547C2×C4H(5,𝔽2)×C4111yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22D42×C4111yescharacteristic
567C4—22no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4C2×#135×C4111yescharacteristic
578C4C41×#57511yescharacteristic
579C4C41×#57711yescharacteristic
580C4C41×#57711yescharacteristic
581C2—81no—
582C2—161no—
583C2—161no—
584C2C41×#327111yescharacteristic
585C2C41×#328211yescharacteristic
586C2C41×#328811yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#1621C2
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×#3394C2semidirect
2. C41×#3375C2semidirect
3. C41×#3362C2semidirect
4. C41×#3304C2semidirect
5. C41×#1717C2semidirect
6. C41×#1702C2semidirect
7. C41×#1678C2semidirect
8. C41×#1677C2semidirect
9. C41×#1666C2semidirect
10. C41×#1645C2semidirect
11. C41×#1638C2semidirect
13. C41×#1620C2semidirect
14. C41×#1582C2semidirect
15. C41×#1579C2semidirect
263. #19802C41direct (N × H)
288. #3394C2×C41semidirect
289. #3375C2×C41semidirect
290. #3362C2×C41semidirect
291. #3304C2×C41semidirect
292. #1717C2×C41semidirect
293. #1702C2×C41semidirect
294. #1678C2×C41semidirect
295. #1677C2×C41semidirect
296. #1666C2×C41semidirect
297. #1645C2×C41semidirect
298. #1638C2×C41semidirect
300. #1620C2×C41semidirect
301. #1582C2×C41semidirect
302. #1579C2×C41semidirect
360. C41#19802direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33942
C41×#33752
C41×#33622
C41×#33042
C41×#17172
C41×#17022
C41×#16782
C41×#16772
C41×#16662
C41×#16452
C41×#16382
C41×#16212
C41×#16202
C41×#15822
C41×#15792
#1980241