Finite Group Databasebeta

← C41×#19800 #23796001

Subgroups — C41×#19800 #23796001

Order 10496.

598 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3369C211yesmaximal, characteristic, complemented
2C41×#3362C211yesmaximal, characteristic, complemented
3C41×#3340C211yesmaximal, characteristic, complemented
4C41×#3305C211yesmaximal, characteristic
5C41×#1720C211yesmaximal, characteristic, complemented
6C41×#1698C211yesmaximal, characteristic, complemented
7C41×#1683C211yesmaximal, characteristic, complemented
8C41×#1677C211yesmaximal, characteristic, complemented
9C41×#1672C211yesmaximal, characteristic, complemented
10C41×#1641C211yesmaximal, characteristic, complemented
11C41×#1634C211yesmaximal, characteristic, complemented
12C41×#1633C211yesmaximal, characteristic, complemented
13C41×#1628C211yesmaximal, characteristic, complemented
14C41×#1582C211yesmaximal, characteristic, complemented
15C41×SD16⋊C8C211yesmaximal, characteristic, complemented
16Q82×C41C2211yescharacteristic
17C41×#556C2211yescharacteristic
18C41×#555C2211yescharacteristic
19C41×#550C2211yescharacteristic
20C41×#498C2211yescharacteristic
21C41×#494C2211yescharacteristic
22C41×#489—21no—
23C41×#487C2211yescharacteristic
24C41×#486—21no—
25C41×#486C2211yescharacteristic
26C41×#486C2211yescharacteristic
27C41×#486C2211yescharacteristic
28C41×#485—21no—
29C41×#482—21no—
30C41×#482—21no—
31C41×#477C2211yescharacteristic
32C41×#477C2211yescharacteristic
33C41×#476—21no—
34C41×#476C2211yescharacteristic
35C41×#476C2211yescharacteristic
36C41×#475—21no—
37C41×#474C2211yescharacteristic
38C41×#466—21no—
39C41×#465—21no—
40C41×#464—21no—
41C41×#462C2211yescharacteristic
42C41×#460—21no—
43C41×#460C2211yescharacteristic
44C41×#459C2211yescharacteristic
45C41×#449—21no—
46C41×#446C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C41×#441—21no—
49C4×SD16×C41—21no—
50C4×SD16×C41C2211yescharacteristic
51C4×SD16×C41C2211yescharacteristic
52C8×D4×C41C2211yescharacteristic
53C8×D4×C41C2211yescharacteristic
54C41×#427—21no—
55C41×#416—21no—
56C41×#335C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#333C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C41×#322C2211yescharacteristic
67C2×#41×C41—21no—
68C2×Q16×C41—21no—
69C2×Q16×C41—41no—
70C2×SD16×C41—21no—
71C2×SD16×C41D411yescharacteristic
72C2×SD16×C41D411yescharacteristic
73C2×D8×C41—21no—
74C22×C8×C41—21no—
75C22×C8×C41—21no—
76C4⋊Q8×C41—21no—
77C4⋊Q8×C41—21no—
78C4⋊Q8×C41—41no—
79C4⋊Q8×C41C2311yescharacteristic
80C4⋊Q8×C41C2311yescharacteristic
81C4⋊Q8×C41C2311yescharacteristic
82#127×C41—21no—
83#127×C41C2311yescharacteristic
84#126×C41—41no—
85#124×C41—21no—
86#124×C41—41no—
87C22⋊Q8×C41—21no—
88#121×C41—21no—
89#121×C41—21no—
90#121×C41—21no—
91#121×C41—41no—
92C4×Q8×C41—21no—
93C4×Q8×C41—21no—
94C4×Q8×C41—21no—
95C4×Q8×C41C2311yescharacteristic
96C4×Q8×C41C2311yescharacteristic
97C4×D4×C41—21no—
98C4×D4×C41C2311yescharacteristic
99C4×D4×C41C2311yescharacteristic
100#117×C41—21no—
101#117×C41—21no—
102#117×C41—21no—
103#107×C41—21no—
104#107×C41—21no—
105#107×C41—21no—
106#106×C41—21no—
107#106×C41—21no—
108#106×C41—21no—
109#106×C41—21no—
110#106×C41D411yescharacteristic
111#106×C41D411yescharacteristic
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—21no—
122#103×C41—21no—
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—41no—
135#102×C41D411yescharacteristic
136#102×C41D411yescharacteristic
137C22⋊C8×C41—21no—
138C22⋊C8×C41—21no—
139#97×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—41no—
150C2×Q8×C41C2×D411yescharacteristic
151C2×Q8×C41C2×D411yescharacteristic
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41—41no—
156C2×D4×C41—41no—
157C2×D4×C41—41no—
158C2×D4×C41C2×D411yescharacteristic
159C2×D4×C41C2×D411yescharacteristic
160C22×C4×C41—21no—
161C22×C4×C41—21no—
162C22×C4×C41—41no—
163Q16×C41—42no—
164Q16×C41—82no—
165SD16×C41—22no—
166SD16×C41—41no—
167SD16×C41—42no—
168D8×C41—81no—
169C2×C8×C41—21no—
170C2×C8×C41—21no—
171C2×C8×C41—21no—
172C2×C8×C41—21no—
173C2×C8×C41—21no—
174C2×C8×C41—42no—
175C2×C8×C41—81no—
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×C41C2×D411yescharacteristic
192C4⋊C4×C41C2×D411yescharacteristic
193C4⋊C4×C41C2×D411yescharacteristic
194C4⋊C4×C41C2×D411yescharacteristic
195C22⋊C4×C41—21no—
196C22⋊C4×C41—21no—
197C22⋊C4×C41—41no—
198C22⋊C4×C41—41no—
199C22⋊C4×C41—41no—
200C22⋊C4×C41—41no—
201C22⋊C4×C41—41no—
202C42×C41—21no—
203C42×C41—21no—
204C42×C41—41no—
205C42×C41—41no—
206C42×C41—41no—
207C42×C41C2411yescharacteristic
208C23×C41—21no—
209C23×C41—21no—
210C23×C41—41no—
211Q8×C41—21no—
212Q8×C41—21no—
213Q8×C41—21no—
214Q8×C41—41no—
215Q8×C41—41no—
216Q8×C41—81no—
217Q8×C41—81no—
218Q8×C41—161no—
219Q8×C41#13512yes—
220D4×C41—21no—
221D4×C41—21no—
222D4×C41—21no—
223D4×C41—21no—
224D4×C41—41no—
225D4×C41—41no—
226D4×C41—41no—
227D4×C41—41no—
228D4×C41—82no—
229D4×C41—81no—
230D4×C41—161no—
231D4×C41—161no—
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—41no—
244C2×C4×C41—41no—
245C2×C4×C41—82no—
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—21no—
253C8×C41—41no—
254C8×C41—41no—
255C8×C41—41no—
256C8×C41—41no—
257C8×C41—41no—
258#19800C4111yesmaximal, characteristic, direct product factor, Sylow
259C22×C41—41no—
260C22×C41—41no—
261C22×C41—41no—
262C22×C41—41no—
263C22×C41—41no—
264C22×C41—41no—
265C22×C41—81no—
266C22×C41—81no—
267C22×C41—81no—
268C22×C41D4211yescharacteristic
269C4×C41—22no—
270C4×C41—21no—
271C4×C41—41no—
272C4×C41—41no—
273C4×C41—41no—
274C4×C41—41no—
275C4×C41—41no—
276C4×C41—81no—
277C4×C41—81no—
278C4×C41—81no—
279C4×C41C2×#13511yescharacteristic
280C4×C41#57511yescharacteristic
281C4×C41#57711yescharacteristic
282C4×C41#57811yescharacteristic
283#3369C2×C4111yescharacteristic, complemented
284#3362C2×C4111yescharacteristic, complemented
285#3340C2×C4111yescharacteristic, complemented
286#3305C2×C4111yescharacteristic
287#1720C2×C4111yescharacteristic, complemented
288#1698C2×C4111yescharacteristic, complemented
289#1683C2×C4111yescharacteristic, complemented
290#1677C2×C4111yescharacteristic, complemented
291#1672C2×C4111yescharacteristic, complemented
292#1641C2×C4111yescharacteristic, complemented
293#1634C2×C4111yescharacteristic, complemented
294#1633C2×C4111yescharacteristic, complemented
295#1628C2×C4111yescharacteristic, complemented
296#1582C2×C4111yescharacteristic, complemented
297SD16⋊C8C2×C4111yescharacteristic, complemented
298C2×C41—81no—
299C2×C41—81no—
300C2×C41—161no—
301C2×C41#326911yescharacteristic
302C2×C41#328211yescharacteristic
303C2×C41#328811yescharacteristic
304Q82C22×C4111yescharacteristic
305#556C22×C4111yescharacteristic
306#555C22×C4111yescharacteristic
307#550C22×C4111yescharacteristic
308#498C22×C4111yescharacteristic
309#494C22×C4111yescharacteristic
310#489—21no—
311#487C22×C4111yescharacteristic
312#486—21no—
313#486C22×C4111yescharacteristic
314#486C22×C4111yescharacteristic
315#486C22×C4111yescharacteristic
316#485—21no—
317#482—21no—
318#482—21no—
319#477C22×C4111yescharacteristic
320#477C22×C4111yescharacteristic
321#476—21no—
322#476C22×C4111yescharacteristic
323#476C22×C4111yescharacteristic
324#475—21no—
325#474C22×C4111yescharacteristic
326#466—21no—
327#465—21no—
328#464—21no—
329#462C22×C4111yescharacteristic
330#460—21no—
331#460C22×C4111yescharacteristic
332#459C22×C4111yescharacteristic
333#449—21no—
334#446C22×C4111yescharacteristic
335C8×Q8C22×C4111yescharacteristic
336#441—21no—
337C4×SD16—21no—
338C4×SD16C22×C4111yescharacteristic
339C4×SD16C22×C4111yescharacteristic
340C8×D4C22×C4111yescharacteristic
341C8×D4C22×C4111yescharacteristic
342#427—21no—
343#416—21no—
344#335C22×C4111yescharacteristic
345#334C22×C4111yescharacteristic
346#333C22×C4111yescharacteristic
347#333C22×C4111yescharacteristic
348#332C22×C4111yescharacteristic
349#331C22×C4111yescharacteristic
350Q8⋊C8C22×C4111yescharacteristic
351Q8⋊C8C22×C4111yescharacteristic
352D4⋊C8C22×C4111yescharacteristic
353D4⋊C8C22×C4111yescharacteristic
354#322C22×C4111yescharacteristic
355C41#1980011yescharacteristic, direct product factor, Sylow
356C2×#41—21no—
357C2×Q16—21no—
358C2×Q16—41no—
359C2×SD16—21no—
360C2×SD16D4×C4111yescharacteristic
361C2×SD16D4×C4111yescharacteristic
362C2×D8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—41no—
368C4⋊Q8C23×C4111yescharacteristic
369C4⋊Q8C23×C4111yescharacteristic
370C4⋊Q8C23×C4111yescharacteristic
371#127—21no—
372#127C23×C4111yescharacteristic
373#126—41no—
374#124—21no—
375#124—41no—
376C22⋊Q8—21no—
377#121—21no—
378#121—21no—
379#121—21no—
380#121—41no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8C23×C4111yescharacteristic
385C4×Q8C23×C4111yescharacteristic
386C4×D4—21no—
387C4×D4C23×C4111yescharacteristic
388C4×D4C23×C4111yescharacteristic
389#117—21no—
390#117—21no—
391#117—21no—
392#107—21no—
393#107—21no—
394#107—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106D4×C4111yescharacteristic
400#106D4×C4111yescharacteristic
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8C23×C4111yescharacteristic
404C4⋊C8C23×C4111yescharacteristic
405C4⋊C8C23×C4111yescharacteristic
406C4⋊C8C23×C4111yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103D4×C4111yescharacteristic
413#103D4×C4111yescharacteristic
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—41no—
424#102D4×C4111yescharacteristic
425#102D4×C4111yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428#97—21no—
429C4×C8—21no—
430C4×C8C23×C4111yescharacteristic
431C4×C8C23×C4111yescharacteristic
432C4×C8C23×C4111yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—41no—
439C2×Q8C2×D4×C4111yescharacteristic
440C2×Q8C2×D4×C4111yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4C2×D4×C4111yescharacteristic
448C2×D4C2×D4×C4111yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452Q16—42no—
453Q16—82no—
454SD16—22no—
455SD16—41no—
456SD16—42no—
457D8—81no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—42no—
464C2×C8—81no—
465C2×C8C2×D4×C4111yescharacteristic
466C2×C8C2×D4×C4111yescharacteristic
467C2×C8C2×D4×C4111yescharacteristic
468C2×C8C2×D4×C4111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C4111yescharacteristic
481C4⋊C4C2×D4×C4111yescharacteristic
482C4⋊C4C2×D4×C4111yescharacteristic
483C4⋊C4C2×D4×C4111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—21no—
492C42—21no—
493C42—41no—
494C42—41no—
495C42—41no—
496C42C24×C4111yescharacteristic
497C23—21no—
498C23—21no—
499C23—41no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—81no—
507Q8—161no—
508Q8#135×C4112yes—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—21no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—82no—
518D4—81no—
519D4—161no—
520D4—161no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4C22×D4×C4111yescharacteristic
536C2×C4C22×D4×C4111yescharacteristic
537C2×C4H(5,𝔽2)×C4111yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22D42×C4111yescharacteristic
557C4—22no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C2×#135×C4111yescharacteristic
568C4C41×#57511yescharacteristic
569C4C41×#57711yescharacteristic
570C4C41×#57811yescharacteristic
571C2—81no—
572C2—81no—
573C2—161no—
574C2C41×#326911yescharacteristic
575C2C41×#328211yescharacteristic
576C2C41×#328811yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3305C2
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×#3369C2semidirect
2. C41×#3362C2semidirect
3. C41×#3340C2semidirect
5. C41×#1720C2semidirect
6. C41×#1698C2semidirect
7. C41×#1683C2semidirect
8. C41×#1677C2semidirect
9. C41×#1672C2semidirect
10. C41×#1641C2semidirect
11. C41×#1634C2semidirect
12. C41×#1633C2semidirect
13. C41×#1628C2semidirect
14. C41×#1582C2semidirect
15. C41×SD16⋊C8C2semidirect
258. #19800C41direct (N × H)
283. #3369C2×C41semidirect
284. #3362C2×C41semidirect
285. #3340C2×C41semidirect
287. #1720C2×C41semidirect
288. #1698C2×C41semidirect
289. #1683C2×C41semidirect
290. #1677C2×C41semidirect
291. #1672C2×C41semidirect
292. #1641C2×C41semidirect
293. #1634C2×C41semidirect
294. #1633C2×C41semidirect
295. #1628C2×C41semidirect
296. #1582C2×C41semidirect
297. SD16⋊C8C2×C41semidirect
355. C41#19800direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33692
C41×#33622
C41×#33402
C41×#33052
C41×#17202
C41×#16982
C41×#16832
C41×#16772
C41×#16722
C41×#16412
C41×#16342
C41×#16332
C41×#16282
C41×#15822
C41×SD16⋊C82
#1980041