Finite Group Databasebeta

← C41×#20320 #23796521

Subgroups — C41×#20320 #23796521

Order 10496.

560 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3400C211yesmaximal, characteristic
2C41×#3387C211yesmaximal, characteristic, complemented
3C41×#3375C211yesmaximal, characteristic
4C41×#3374C211yesmaximal, characteristic, complemented
5C41×#1708C211yesmaximal, characteristic
6C41×#1700C211yesmaximal, characteristic, complemented
7C41×#1698C211yesmaximal, characteristic
8C41×#1692C211yesmaximal, characteristic, complemented
9C41×#1686C211yesmaximal, characteristic
10C41×#1645C211yesmaximal, characteristic, complemented
11C41×#1640C211yesmaximal, characteristic
12C41×#1636C211yesmaximal, characteristic, complemented
13C41×#1626C211yesmaximal, characteristic
14C41×#1591C211yesmaximal, characteristic, complemented
15C41×#1591C211yesmaximal, characteristic, complemented
16C41×#559C2211yescharacteristic
17Q82×C41C2211yescharacteristic
18C41×#557C2211yescharacteristic
19C41×#557C2211yescharacteristic
20C41×#501—21no—
21C41×#498C2211yescharacteristic
22C41×#497—21no—
23C41×#492C2211yescharacteristic
24C41×#491—21no—
25C41×#489—21no—
26C41×#487C2211yescharacteristic
27C41×#487C2211yescharacteristic
28C41×#486C2211yescharacteristic
29C41×#486C2211yescharacteristic
30C41×#479—21no—
31C41×#479—21no—
32C41×#477C2211yescharacteristic
33C41×#477C2211yescharacteristic
34C41×#475—21no—
35C41×#475C2211yescharacteristic
36C41×#475C2211yescharacteristic
37C41×#474—21no—
38C41×#464—21no—
39C41×#464—21no—
40C41×#462—21no—
41C41×#462C2211yescharacteristic
42C41×#462C2211yescharacteristic
43C41×#461—21no—
44C41×#460C2211yescharacteristic
45C41×#460C2211yescharacteristic
46C41×#446C2211yescharacteristic
47C41×#446C2211yescharacteristic
48C41×#446C2211yescharacteristic
49C41×#446C2211yescharacteristic
50C41×#441—21no—
51C41×#441—21no—
52C41×#440—21no—
53C41×#440—21no—
54C4×Q16×C41C2211yescharacteristic
55C4×Q16×C41C2211yescharacteristic
56C41×#335C2211yescharacteristic
57C41×#335C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×Q8⋊C8C2211yescharacteristic
65C41×Q8⋊C8C2211yescharacteristic
66C82×C41C2211yescharacteristic
67C2×Q16×C41—21no—
68C2×Q16×C41—21no—
69C2×Q16×C41D411yescharacteristic
70C2×Q16×C41D411yescharacteristic
71C2×SD16×C41—21no—
72C2×SD16×C41—21no—
73C2×SD16×C41—21no—
74C2×SD16×C41—21no—
75C4⋊Q8×C41—21no—
76C4⋊Q8×C41—21no—
77C4⋊Q8×C41—21no—
78C4⋊Q8×C41—21no—
79C4⋊Q8×C41—41no—
80C4⋊Q8×C41C2311yescharacteristic
81C4⋊Q8×C41C2311yescharacteristic
82C4⋊Q8×C41C2311yescharacteristic
83#127×C41C2311yescharacteristic
84#125×C41—21no—
85#125×C41—21no—
86#125×C41—41no—
87#125×C41—41no—
88#124×C41—21no—
89#124×C41—21no—
90#123×C41—41no—
91C4×Q8×C41—21no—
92C4×Q8×C41—21no—
93C4×Q8×C41—21no—
94C4×Q8×C41—21no—
95C4×Q8×C41—21no—
96C4×Q8×C41—21no—
97C4×Q8×C41C2311yescharacteristic
98C4×Q8×C41C2311yescharacteristic
99C4×Q8×C41C2311yescharacteristic
100C4×Q8×C41C2311yescharacteristic
101C4×D4×C41—21no—
102C4×D4×C41—21no—
103#107×C41—21no—
104#107×C41—21no—
105#107×C41D411yescharacteristic
106#107×C41D411yescharacteristic
107#106×C41—21no—
108#106×C41—21no—
109#106×C41—21no—
110#106×C41—21no—
111C4⋊C8×C41—21no—
112C4⋊C8×C41—21no—
113C4⋊C8×C41—21no—
114C4⋊C8×C41—21no—
115C4⋊C8×C41C2311yescharacteristic
116C4⋊C8×C41C2311yescharacteristic
117C4⋊C8×C41C2311yescharacteristic
118C4⋊C8×C41C2311yescharacteristic
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×C41—21no—
126#103×C41—21no—
127#103×C41—41no—
128#103×C41D411yescharacteristic
129#103×C41D411yescharacteristic
130#103×C41D411yescharacteristic
131#103×C41D411yescharacteristic
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—
140#97×C41—21no—
141C4×C8×C41C2311yescharacteristic
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144C2×Q8×C41—21no—
145C2×Q8×C41—21no—
146C2×Q8×C41—21no—
147C2×Q8×C41—41no—
148C2×Q8×C41C2×D411yescharacteristic
149C2×Q8×C41C2×D411yescharacteristic
150C2×Q8×C41C2×D411yescharacteristic
151C2×Q8×C41C2×D411yescharacteristic
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C22×C4×C41—41no—
156Q16×C41—22no—
157Q16×C41—41no—
158Q16×C41—42no—
159Q16×C41—81no—
160SD16×C41—42no—
161SD16×C41—42no—
162SD16×C41—81no—
163SD16×C41—81no—
164C2×C8×C41—21no—
165C2×C8×C41—21no—
166C2×C8×C41—21no—
167C2×C8×C41—21no—
168C2×C8×C41—21no—
169C2×C8×C41C2×D411yescharacteristic
170C2×C8×C41C2×D411yescharacteristic
171C2×C8×C41C2×D411yescharacteristic
172C2×C8×C41C2×D411yescharacteristic
173C4⋊C4×C41—21no—
174C4⋊C4×C41—21no—
175C4⋊C4×C41—21no—
176C4⋊C4×C41—21no—
177C4⋊C4×C41—21no—
178C4⋊C4×C41—21no—
179C4⋊C4×C41—21no—
180C4⋊C4×C41—21no—
181C4⋊C4×C41—21no—
182C4⋊C4×C41—21no—
183C4⋊C4×C41—41no—
184C4⋊C4×C41—41no—
185C4⋊C4×C41—41no—
186C4⋊C4×C41—41no—
187C4⋊C4×C41—41no—
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—41no—
196C22⋊C4×C41—41no—
197C22⋊C4×C41—41no—
198C42×C41—21no—
199C42×C41—21no—
200C42×C41—21no—
201C42×C41—21no—
202C42×C41—41no—
203C42×C41—41no—
204C42×C41—41no—
205C42×C41C2411yescharacteristic
206C23×C41—41no—
207Q8×C41—21no—
208Q8×C41—21no—
209Q8×C41—21no—
210Q8×C41—21no—
211Q8×C41—21no—
212Q8×C41—21no—
213Q8×C41—21no—
214Q8×C41—21no—
215Q8×C41—41no—
216Q8×C41—41no—
217Q8×C41—41no—
218Q8×C41—41no—
219Q8×C41—81no—
220Q8×C41—161no—
221D4×C41—41no—
222D4×C41—41no—
223D4×C41—41no—
224D4×C41—41no—
225D4×C41—81no—
226C2×C4×C41—21no—
227C2×C4×C41—21no—
228C2×C4×C41—21no—
229C2×C4×C41—21no—
230C2×C4×C41—21no—
231C2×C4×C41—21no—
232C2×C4×C41—21no—
233C2×C4×C41—21no—
234C2×C4×C41—41no—
235C2×C4×C41—41no—
236C2×C4×C41—41no—
237C2×C4×C41—161no—
238C2×C4×C41C22×D411yescharacteristic
239C2×C4×C41C22×D411yescharacteristic
240C2×C4×C41H(5,𝔽2)11yescharacteristic
241C8×C41—21no—
242C8×C41—21no—
243C8×C41—21no—
244C8×C41—41no—
245C8×C41—41no—
246C8×C41—41no—
247C8×C41—41no—
248C8×C41—41no—
249C8×C41#13712yes—
250#20320C4111yesmaximal, characteristic, direct product factor, Sylow
251C22×C41—81no—
252C22×C41—81no—
253C22×C41—81no—
254C22×C41D4211yescharacteristic
255C4×C41—21no—
256C4×C41—41no—
257C4×C41—41no—
258C4×C41—41no—
259C4×C41—41no—
260C4×C41—41no—
261C4×C41—41no—
262C4×C41—41no—
263C4×C41—41no—
264C4×C41—81no—
265C4×C41—81no—
266C4×C41—81no—
267C4×C41C2×#13711yescharacteristic
268C4×C41#57511yescharacteristic
269C4×C41#57711yescharacteristic
270C4×C41#57811yescharacteristic
271#3400C2×C4111yescharacteristic
272#3387C2×C4111yescharacteristic, complemented
273#3375C2×C4111yescharacteristic
274#3374C2×C4111yescharacteristic, complemented
275#1708C2×C4111yescharacteristic
276#1700C2×C4111yescharacteristic, complemented
277#1698C2×C4111yescharacteristic
278#1692C2×C4111yescharacteristic, complemented
279#1686C2×C4111yescharacteristic
280#1645C2×C4111yescharacteristic, complemented
281#1640C2×C4111yescharacteristic
282#1636C2×C4111yescharacteristic, complemented
283#1626C2×C4111yescharacteristic
284#1591C2×C4111yescharacteristic, complemented
285#1591C2×C4111yescharacteristic, complemented
286C2×C41—161no—
287C2×C41#327711yescharacteristic
288C2×C41#327811yescharacteristic
289C2×C41#329011yescharacteristic
290#559C22×C4111yescharacteristic
291Q82C22×C4111yescharacteristic
292#557C22×C4111yescharacteristic
293#557C22×C4111yescharacteristic
294#501—21no—
295#498C22×C4111yescharacteristic
296#497—21no—
297#492C22×C4111yescharacteristic
298#491—21no—
299#489—21no—
300#487C22×C4111yescharacteristic
301#487C22×C4111yescharacteristic
302#486C22×C4111yescharacteristic
303#486C22×C4111yescharacteristic
304#479—21no—
305#479—21no—
306#477C22×C4111yescharacteristic
307#477C22×C4111yescharacteristic
308#475—21no—
309#475C22×C4111yescharacteristic
310#475C22×C4111yescharacteristic
311#474—21no—
312#464—21no—
313#464—21no—
314#462—21no—
315#462C22×C4111yescharacteristic
316#462C22×C4111yescharacteristic
317#461—21no—
318#460C22×C4111yescharacteristic
319#460C22×C4111yescharacteristic
320#446C22×C4111yescharacteristic
321#446C22×C4111yescharacteristic
322#446C22×C4111yescharacteristic
323#446C22×C4111yescharacteristic
324#441—21no—
325#441—21no—
326#440—21no—
327#440—21no—
328C4×Q16C22×C4111yescharacteristic
329C4×Q16C22×C4111yescharacteristic
330#335C22×C4111yescharacteristic
331#335C22×C4111yescharacteristic
332#333C22×C4111yescharacteristic
333#332C22×C4111yescharacteristic
334#332C22×C4111yescharacteristic
335#331C22×C4111yescharacteristic
336Q8⋊C8C22×C4111yescharacteristic
337Q8⋊C8C22×C4111yescharacteristic
338Q8⋊C8C22×C4111yescharacteristic
339Q8⋊C8C22×C4111yescharacteristic
340C82C22×C4111yescharacteristic
341C41#2032011yescharacteristic, direct product factor, Sylow
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16D4×C4111yescharacteristic
345C2×Q16D4×C4111yescharacteristic
346C2×SD16—21no—
347C2×SD16—21no—
348C2×SD16—21no—
349C2×SD16—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—41no—
355C4⋊Q8C23×C4111yescharacteristic
356C4⋊Q8C23×C4111yescharacteristic
357C4⋊Q8C23×C4111yescharacteristic
358#127C23×C4111yescharacteristic
359#125—21no—
360#125—21no—
361#125—41no—
362#125—41no—
363#124—21no—
364#124—21no—
365#123—41no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C23×C4111yescharacteristic
373C4×Q8C23×C4111yescharacteristic
374C4×Q8C23×C4111yescharacteristic
375C4×Q8C23×C4111yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378#107—21no—
379#107—21no—
380#107D4×C4111yescharacteristic
381#107D4×C4111yescharacteristic
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8C23×C4111yescharacteristic
391C4⋊C8C23×C4111yescharacteristic
392C4⋊C8C23×C4111yescharacteristic
393C4⋊C8C23×C4111yescharacteristic
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—41no—
403#103D4×C4111yescharacteristic
404#103D4×C4111yescharacteristic
405#103D4×C4111yescharacteristic
406#103D4×C4111yescharacteristic
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—41no—
412#97—21no—
413#97—21no—
414#97—21no—
415#97—21no—
416C4×C8C23×C4111yescharacteristic
417C4×C8C23×C4111yescharacteristic
418C4×C8C23×C4111yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—41no—
423C2×Q8C2×D4×C4111yescharacteristic
424C2×Q8C2×D4×C4111yescharacteristic
425C2×Q8C2×D4×C4111yescharacteristic
426C2×Q8C2×D4×C4111yescharacteristic
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C22×C4—41no—
431Q16—22no—
432Q16—41no—
433Q16—42no—
434Q16—81no—
435SD16—42no—
436SD16—42no—
437SD16—81no—
438SD16—81no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8C2×D4×C4111yescharacteristic
445C2×C8C2×D4×C4111yescharacteristic
446C2×C8C2×D4×C4111yescharacteristic
447C2×C8C2×D4×C4111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×D4×C4111yescharacteristic
467C4⋊C4C2×D4×C4111yescharacteristic
468C4⋊C4C2×D4×C4111yescharacteristic
469C4⋊C4C2×D4×C4111yescharacteristic
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42—41no—
480C42C24×C4111yescharacteristic
481C23—41no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—161no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—161no—
513C2×C4C22×D4×C4111yescharacteristic
514C2×C4C22×D4×C4111yescharacteristic
515C2×C4H(5,𝔽2)×C4111yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8#137×C4112yes—
525C22—81no—
526C22—81no—
527C22—81no—
528C22D42×C4111yescharacteristic
529C4—21no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4C2×#137×C4111yescharacteristic
542C4C41×#57511yescharacteristic
543C4C41×#57711yescharacteristic
544C4C41×#57811yescharacteristic
545C2—161no—
546C2C41×#327711yescharacteristic
547C2C41×#327811yescharacteristic
548C2C41×#329011yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radical#127×C41C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C42×C41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C41×#3387C2semidirect
4. C41×#3374C2semidirect
6. C41×#1700C2semidirect
8. C41×#1692C2semidirect
10. C41×#1645C2semidirect
12. C41×#1636C2semidirect
14. C41×#1591C2semidirect
15. C41×#1591C2semidirect
250. #20320C41direct (N × H)
272. #3387C2×C41semidirect
274. #3374C2×C41semidirect
276. #1700C2×C41semidirect
278. #1692C2×C41semidirect
280. #1645C2×C41semidirect
282. #1636C2×C41semidirect
284. #1591C2×C41semidirect
285. #1591C2×C41semidirect
341. C41#20320direct (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×#33872
C41×#33752
C41×#33742
C41×#17082
C41×#17002
C41×#16982
C41×#16922
C41×#16862
C41×#16452
C41×#16402
C41×#16362
C41×#16262
C41×#15912
#2032041