Finite Group Databasebeta

← C41×#19844 #23796045

Subgroups — C41×#19844 #23796045

Order 10496.

590 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Q16×C41C211yesmaximal, characteristic, complemented
2C41×#3369C211yesmaximal, characteristic, complemented
3C41×#3362C211yesmaximal, characteristic
4C41×#3304C211yesmaximal, characteristic
5C41×#1719C211yesmaximal, characteristic, complemented
6C41×#1698C211yesmaximal, characteristic, complemented
7C41×#1684C211yesmaximal, characteristic, complemented
8C41×#1682C211yesmaximal, characteristic, complemented
9C41×#1675C211yesmaximal, characteristic, complemented
10C41×#1645C211yesmaximal, characteristic, complemented
11C41×#1638C211yesmaximal, characteristic, complemented
12C41×#1631C211yesmaximal, characteristic
13C41×#1623C211yesmaximal, characteristic, complemented
14C41×#1584C211yesmaximal, characteristic, complemented
15C41×SD16⋊C8C211yesmaximal, characteristic, complemented
16Q82×C41C2211yescharacteristic
17Q82×C41C2211yescharacteristic
18C41×#556C2211yescharacteristic
19C41×#550C2211yescharacteristic
20C41×#500—21no—
21C41×#500C2211yescharacteristic
22C41×#492C2211yescharacteristic
23C41×#489—21no—
24C41×#487C2211yescharacteristic
25C41×#487C2211yescharacteristic
26C41×#486—21no—
27C41×#486C2211yescharacteristic
28C41×#486C2211yescharacteristic
29C41×#482—21no—
30C41×#477—21no—
31C41×#477—21no—
32C41×#477C2211yescharacteristic
33C41×#477C2211yescharacteristic
34C41×#476—21no—
35C41×#476C2211yescharacteristic
36C41×#476C2211yescharacteristic
37C41×#475—21no—
38C41×#475C2211yescharacteristic
39C41×#465—21no—
40C41×#464—21no—
41C41×#462C2211yescharacteristic
42C41×#460—21no—
43C41×#460C2211yescharacteristic
44C41×#460C2211yescharacteristic
45C41×#452—21no—
46C41×#446C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C8×Q8×C41C2211yescharacteristic
49C41×#441—21no—
50C4×Q16×C41—21no—
51C4×Q16×C41C2211yescharacteristic
52C4×SD16×C41—21no—
53C4×SD16×C41C2211yescharacteristic
54C8×D4×C41C2211yescharacteristic
55C41×#416—21no—
56C41×#335C2211yescharacteristic
57C41×#335C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#333C2211yescharacteristic
60C41×#332C2211yescharacteristic
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—41no—
73C2×SD16×C41D411yescharacteristic
74C22×C8×C41—21no—
75C4⋊Q8×C41—21no—
76C4⋊Q8×C41—21no—
77C4⋊Q8×C41—21no—
78C4⋊Q8×C41—21no—
79C4⋊Q8×C41—41no—
80C4⋊Q8×C41—41no—
81C4⋊Q8×C41C2311yescharacteristic
82C4⋊Q8×C41C2311yescharacteristic
83C4⋊Q8×C41C2311yescharacteristic
84#127×C41—21no—
85#127×C41C2311yescharacteristic
86#126×C41—41no—
87#124×C41—21no—
88C22⋊Q8×C41—21no—
89#121×C41—21no—
90#121×C41—41no—
91C4×Q8×C41—21no—
92C4×Q8×C41—21no—
93C4×Q8×C41—21no—
94C4×Q8×C41—21no—
95C4×Q8×C41—21no—
96C4×Q8×C41C2311yescharacteristic
97C4×Q8×C41C2311yescharacteristic
98C4×Q8×C41C2311yescharacteristic
99C4×D4×C41—21no—
100C4×D4×C41C2311yescharacteristic
101#117×C41—21no—
102#107×C41—21no—
103#107×C41—21no—
104#107×C41—21no—
105#107×C41—21no—
106#107×C41D411yescharacteristic
107#106×C41—21no—
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—21no—
122#103×C41—21no—
123#103×C41—21no—
124#103×C41—41no—
125#103×C41D411yescharacteristic
126#103×C41D411yescharacteristic
127#103×C41D411yescharacteristic
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—21no—
149C2×Q8×C41—41no—
150C2×Q8×C41—41no—
151C2×Q8×C41C2×D411yescharacteristic
152C2×Q8×C41C2×D411yescharacteristic
153C2×Q8×C41C2×D411yescharacteristic
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—21no—
157C2×D4×C41—41no—
158C2×D4×C41—41no—
159C2×D4×C41C2×D411yescharacteristic
160C22×C4×C41—21no—
161C22×C4×C41—41no—
162Q16×C41—22no—
163Q16×C41—42no—
164SD16×C41—22no—
165SD16×C41—42no—
166SD16×C41—81no—
167SD16×C41—82no—
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×C41C2×D411yescharacteristic
175C2×C8×C41C2×D411yescharacteristic
176C2×C8×C41C2×D411yescharacteristic
177C2×C8×C41C2×D411yescharacteristic
178C4⋊C4×C41—21no—
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—41no—
188C4⋊C4×C41—41no—
189C4⋊C4×C41—41no—
190C4⋊C4×C41—41no—
191C4⋊C4×C41—41no—
192C4⋊C4×C41C2×D411yescharacteristic
193C4⋊C4×C41C2×D411yescharacteristic
194C4⋊C4×C41C2×D411yescharacteristic
195C4⋊C4×C41C2×D411yescharacteristic
196C22⋊C4×C41—21no—
197C22⋊C4×C41—41no—
198C22⋊C4×C41—41no—
199C22⋊C4×C41—41no—
200C42×C41—21no—
201C42×C41—21no—
202C42×C41—21no—
203C42×C41—41no—
204C42×C41—41no—
205C42×C41—41no—
206C42×C41C2411yescharacteristic
207C23×C41—21no—
208C23×C41—41no—
209Q8×C41—21no—
210Q8×C41—21no—
211Q8×C41—21no—
212Q8×C41—21no—
213Q8×C41—41no—
214Q8×C41—41no—
215Q8×C41—81no—
216Q8×C41—81no—
217Q8×C41—161no—
218Q8×C41—161no—
219Q8×C41#13512yes—
220Q8×C41#13712yes—
221D4×C41—21no—
222D4×C41—21no—
223D4×C41—41no—
224D4×C41—41no—
225D4×C41—41no—
226D4×C41—41no—
227D4×C41—82no—
228D4×C41—81no—
229D4×C41—161no—
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—21no—
237C2×C4×C41—41no—
238C2×C4×C41—41no—
239C2×C4×C41—41no—
240C2×C4×C41—41no—
241C2×C4×C41—41no—
242C2×C4×C41—82no—
243C2×C4×C41C22×D411yescharacteristic
244C2×C4×C41C22×D411yescharacteristic
245C2×C4×C41H(5,𝔽2)11yescharacteristic
246C8×C41—21no—
247C8×C41—21no—
248C8×C41—21no—
249C8×C41—21no—
250C8×C41—41no—
251C8×C41—41no—
252C8×C41—41no—
253C8×C41—41no—
254C8×C41—41no—
255#19844C4111yesmaximal, characteristic, direct product factor, Sylow
256C22×C41—41no—
257C22×C41—41no—
258C22×C41—41no—
259C22×C41—81no—
260C22×C41—81no—
261C22×C41—81no—
262C22×C41D4211yescharacteristic
263C4×C41—22no—
264C4×C41—22no—
265C4×C41—21no—
266C4×C41—41no—
267C4×C41—41no—
268C4×C41—41no—
269C4×C41—41no—
270C4×C41—41no—
271C4×C41—81no—
272C4×C41—81no—
273C4×C41—81no—
274C4×C41C2×#13511yescharacteristic
275C4×C41C2×#13711yescharacteristic
276C4×C41#57711yescharacteristic
277C4×C41#57811yescharacteristic
278Q8×Q16C2×C4111yescharacteristic, complemented
279#3369C2×C4111yescharacteristic, complemented
280#3362C2×C4111yescharacteristic
281#3304C2×C4111yescharacteristic
282#1719C2×C4111yescharacteristic, complemented
283#1698C2×C4111yescharacteristic, complemented
284#1684C2×C4111yescharacteristic, complemented
285#1682C2×C4111yescharacteristic, complemented
286#1675C2×C4111yescharacteristic, complemented
287#1645C2×C4111yescharacteristic, complemented
288#1638C2×C4111yescharacteristic, complemented
289#1631C2×C4111yescharacteristic
290#1623C2×C4111yescharacteristic, complemented
291#1584C2×C4111yescharacteristic, complemented
292SD16⋊C8C2×C4111yescharacteristic, complemented
293C2×C41—81no—
294C2×C41—161no—
295C2×C41#326611yescharacteristic
296C2×C41#328511yescharacteristic
297C2×C41#328811yescharacteristic
298Q82C22×C4111yescharacteristic
299Q82C22×C4111yescharacteristic
300#556C22×C4111yescharacteristic
301#550C22×C4111yescharacteristic
302#500—21no—
303#500C22×C4111yescharacteristic
304#492C22×C4111yescharacteristic
305#489—21no—
306#487C22×C4111yescharacteristic
307#487C22×C4111yescharacteristic
308#486—21no—
309#486C22×C4111yescharacteristic
310#486C22×C4111yescharacteristic
311#482—21no—
312#477—21no—
313#477—21no—
314#477C22×C4111yescharacteristic
315#477C22×C4111yescharacteristic
316#476—21no—
317#476C22×C4111yescharacteristic
318#476C22×C4111yescharacteristic
319#475—21no—
320#475C22×C4111yescharacteristic
321#465—21no—
322#464—21no—
323#462C22×C4111yescharacteristic
324#460—21no—
325#460C22×C4111yescharacteristic
326#460C22×C4111yescharacteristic
327#452—21no—
328#446C22×C4111yescharacteristic
329C8×Q8C22×C4111yescharacteristic
330C8×Q8C22×C4111yescharacteristic
331#441—21no—
332C4×Q16—21no—
333C4×Q16C22×C4111yescharacteristic
334C4×SD16—21no—
335C4×SD16C22×C4111yescharacteristic
336C8×D4C22×C4111yescharacteristic
337#416—21no—
338#335C22×C4111yescharacteristic
339#335C22×C4111yescharacteristic
340#333C22×C4111yescharacteristic
341#333C22×C4111yescharacteristic
342#332C22×C4111yescharacteristic
343#331C22×C4111yescharacteristic
344Q8⋊C8C22×C4111yescharacteristic
345Q8⋊C8C22×C4111yescharacteristic
346Q8⋊C8C22×C4111yescharacteristic
347D4⋊C8C22×C4111yescharacteristic
348#322C22×C4111yescharacteristic
349C41#1984411yescharacteristic, direct product factor, Sylow
350C2×#41—21no—
351C2×Q16—21no—
352C2×Q16D4×C4111yescharacteristic
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—41no—
356C2×SD16D4×C4111yescharacteristic
357C22×C8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—41no—
363C4⋊Q8—41no—
364C4⋊Q8C23×C4111yescharacteristic
365C4⋊Q8C23×C4111yescharacteristic
366C4⋊Q8C23×C4111yescharacteristic
367#127—21no—
368#127C23×C4111yescharacteristic
369#126—41no—
370#124—21no—
371C22⋊Q8—21no—
372#121—21no—
373#121—41no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C23×C4111yescharacteristic
380C4×Q8C23×C4111yescharacteristic
381C4×Q8C23×C4111yescharacteristic
382C4×D4—21no—
383C4×D4C23×C4111yescharacteristic
384#117—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107D4×C4111yescharacteristic
390#106—21no—
391#106—21no—
392#106—21no—
393#106D4×C4111yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C4111yescharacteristic
398C4⋊C8C23×C4111yescharacteristic
399C4⋊C8C23×C4111yescharacteristic
400C4⋊C8C23×C4111yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—41no—
408#103D4×C4111yescharacteristic
409#103D4×C4111yescharacteristic
410#103D4×C4111yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102D4×C4111yescharacteristic
420C22⋊C8—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8C23×C4111yescharacteristic
425C4×C8C23×C4111yescharacteristic
426C4×C8C23×C4111yescharacteristic
427#41—42no—
428#41—81no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8C2×D4×C4111yescharacteristic
435C2×Q8C2×D4×C4111yescharacteristic
436C2×Q8C2×D4×C4111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4C2×D4×C4111yescharacteristic
443C22×C4—21no—
444C22×C4—41no—
445Q16—22no—
446Q16—42no—
447SD16—22no—
448SD16—42no—
449SD16—81no—
450SD16—82no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—81no—
457C2×C8C2×D4×C4111yescharacteristic
458C2×C8C2×D4×C4111yescharacteristic
459C2×C8C2×D4×C4111yescharacteristic
460C2×C8C2×D4×C4111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C4111yescharacteristic
476C4⋊C4C2×D4×C4111yescharacteristic
477C4⋊C4C2×D4×C4111yescharacteristic
478C4⋊C4C2×D4×C4111yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—41no—
487C42—41no—
488C42—41no—
489C42C24×C4111yescharacteristic
490C23—21no—
491C23—41no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500Q8—161no—
501Q8—161no—
502Q8#135×C4112yes—
503Q8#137×C4112yes—
504D4—21no—
505D4—21no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—82no—
511D4—81no—
512D4—161no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4C22×D4×C4111yescharacteristic
527C2×C4C22×D4×C4111yescharacteristic
528C2×C4H(5,𝔽2)×C4111yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22D42×C4111yescharacteristic
545C4—22no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4C2×#135×C4111yescharacteristic
557C4C2×#137×C4111yescharacteristic
558C4C41×#57711yescharacteristic
559C4C41×#57811yescharacteristic
560C2—81no—
561C2—161no—
562C2C41×#326611yescharacteristic
563C2C41×#328511yescharacteristic
564C2C41×#328811yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#550C22
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. Q8×Q16×C41C2semidirect
2. C41×#3369C2semidirect
5. C41×#1719C2semidirect
6. C41×#1698C2semidirect
7. C41×#1684C2semidirect
8. C41×#1682C2semidirect
9. C41×#1675C2semidirect
10. C41×#1645C2semidirect
11. C41×#1638C2semidirect
13. C41×#1623C2semidirect
14. C41×#1584C2semidirect
15. C41×SD16⋊C8C2semidirect
255. #19844C41direct (N × H)
278. Q8×Q16C2×C41semidirect
279. #3369C2×C41semidirect
282. #1719C2×C41semidirect
283. #1698C2×C41semidirect
284. #1684C2×C41semidirect
285. #1682C2×C41semidirect
286. #1675C2×C41semidirect
287. #1645C2×C41semidirect
288. #1638C2×C41semidirect
290. #1623C2×C41semidirect
291. #1584C2×C41semidirect
292. SD16⋊C8C2×C41semidirect
349. C41#19844direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×Q16×C412
C41×#33692
C41×#33622
C41×#33042
C41×#17192
C41×#16982
C41×#16842
C41×#16822
C41×#16752
C41×#16452
C41×#16382
C41×#16312
C41×#16232
C41×#15842
C41×SD16⋊C82
#1984441