Finite Group Databasebeta

← C41×#19813 #23796014

Subgroups — C41×#19813 #23796014

Order 10496.

580 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3385C211yesmaximal, characteristic
2Q8×Q16×C41C211yesmaximal, characteristic, complemented
3Q8×SD16×C41C211yesmaximal, characteristic
4C41×#3299C211yesmaximal, characteristic
5C41×#1723C211yesmaximal, characteristic, complemented
6C41×#1692C211yesmaximal, characteristic, complemented
7C41×#1684C211yesmaximal, characteristic, complemented
8C41×#1676C211yesmaximal, characteristic, complemented
9C41×#1675C211yesmaximal, characteristic
10C41×#1645C211yesmaximal, characteristic, complemented
11C41×#1637C211yesmaximal, characteristic
12C41×#1633C211yesmaximal, characteristic, complemented
13C41×#1632C211yesmaximal, characteristic
14C41×#1584C211yesmaximal, characteristic, complemented
15C41×SD16⋊C8C211yesmaximal, characteristic
16Q82×C41C2211yescharacteristic
17Q82×C41C2211yescharacteristic
18C41×#554C2211yescharacteristic
19D4×Q8×C41C2211yescharacteristic
20C41×#501—21no—
21C41×#500—21no—
22C41×#500C2211yescharacteristic
23C41×#500C2211yescharacteristic
24C41×#498—21no—
25C41×#498C2211yescharacteristic
26C41×#494C2211yescharacteristic
27C41×#487C2211yescharacteristic
28C41×#487C2211yescharacteristic
29C41×#484—21no—
30C41×#479—21no—
31C41×#477—21no—
32C41×#477—21no—
33C41×#477C2211yescharacteristic
34C41×#477C2211yescharacteristic
35C41×#477C2211yescharacteristic
36C41×#477C2211yescharacteristic
37C41×#476—21no—
38C41×#476C2211yescharacteristic
39C41×#476C2211yescharacteristic
40C41×#475—21no—
41C41×#475C2211yescharacteristic
42C41×#474—21no—
43C41×#467—21no—
44C41×#462C2211yescharacteristic
45C41×#451—21no—
46C41×#446C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C8×Q8×C41C2211yescharacteristic
49C41×#440—21no—
50C4×Q16×C41—21no—
51C4×Q16×C41C2211yescharacteristic
52C4×SD16×C41—21no—
53C4×SD16×C41C2211yescharacteristic
54C8×D4×C41C2211yescharacteristic
55C2×#103×C41—21no—
56C41×#335C2211yescharacteristic
57C41×#335C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#333C2211yescharacteristic
60C41×#333C2211yescharacteristic
61C41×#332C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×Q8⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C41×#322C2211yescharacteristic
67C22×Q8×C41—21no—
68C2×Q16×C41—21no—
69C2×Q16×C41—41no—
70C2×Q16×C41D411yescharacteristic
71C2×SD16×C41D411yescharacteristic
72C22×C8×C41—21no—
73C4⋊Q8×C41—21no—
74C4⋊Q8×C41—21no—
75C4⋊Q8×C41—21no—
76C4⋊Q8×C41—21no—
77C4⋊Q8×C41—21no—
78C4⋊Q8×C41—41no—
79C4⋊Q8×C41—41no—
80C4⋊Q8×C41C2311yescharacteristic
81C4⋊Q8×C41C2311yescharacteristic
82C4⋊Q8×C41C2311yescharacteristic
83C4⋊Q8×C41C2311yescharacteristic
84#125×C41—21no—
85C22⋊Q8×C41—21no—
86C22⋊Q8×C41—21no—
87C22⋊Q8×C41—41no—
88C22⋊Q8×C41—41no—
89C4×Q8×C41—21no—
90C4×Q8×C41—21no—
91C4×Q8×C41—21no—
92C4×Q8×C41—21no—
93C4×Q8×C41C2311yescharacteristic
94C4×Q8×C41C2311yescharacteristic
95C4×Q8×C41C2311yescharacteristic
96C4×D4×C41—21no—
97C4×D4×C41—21no—
98C4×D4×C41C2311yescharacteristic
99C2×C4⋊C4×C41—21no—
100#107×C41—21no—
101#107×C41—21no—
102#107×C41—21no—
103#107×C41—21no—
104#107×C41—21no—
105#107×C41—21no—
106#107×C41—21no—
107#107×C41—21no—
108#107×C41D411yescharacteristic
109#106×C41—21no—
110#106×C41—21no—
111#106×C41—21no—
112#106×C41—21no—
113#106×C41—21no—
114#106×C41D411yescharacteristic
115C4⋊C8×C41—21no—
116C4⋊C8×C41—21no—
117C4⋊C8×C41—21no—
118C4⋊C8×C41C2311yescharacteristic
119C4⋊C8×C41C2311yescharacteristic
120C4⋊C8×C41C2311yescharacteristic
121C4⋊C8×C41C2311yescharacteristic
122#103×C41—21no—
123#103×C41—21no—
124#103×C41—21no—
125#103×C41—21no—
126#103×C41—21no—
127#103×C41—21no—
128#103×C41—21no—
129#103×C41—21no—
130#103×C41—41no—
131#103×C41D411yescharacteristic
132#103×C41D411yescharacteristic
133#103×C41D411yescharacteristic
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
144C2×Q8×C41—21no—
145C2×Q8×C41—21no—
146C2×Q8×C41—21no—
147C2×Q8×C41—21no—
148C2×Q8×C41—41no—
149C2×Q8×C41—41no—
150C2×Q8×C41—41no—
151C2×Q8×C41—42no—
152C2×Q8×C41—81no—
153C2×Q8×C41C2×D411yescharacteristic
154C2×Q8×C41C2×D411yescharacteristic
155C2×Q8×C41C2×D411yescharacteristic
156C2×D4×C41C2×D411yescharacteristic
157C22×C4×C41—21no—
158C22×C4×C41—41no—
159C22×C4×C41—41no—
160Q16×C41—22no—
161Q16×C41—81no—
162Q16×C41—82no—
163SD16×C41Q1614yescomplemented
164C2×C8×C41—21no—
165C2×C8×C41—21no—
166C2×C8×C41—21no—
167C2×C8×C41—21no—
168C2×C8×C41—21no—
169C2×C8×C41—81no—
170C2×C8×C41C2×D411yescharacteristic
171C2×C8×C41C2×D411yescharacteristic
172C2×C8×C41C2×D411yescharacteristic
173C2×C8×C41C2×D411yescharacteristic
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—21no—
184C4⋊C4×C41—21no—
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×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—
199C42×C41—21no—
200C42×C41—21no—
201C42×C41—21no—
202C42×C41—41no—
203C42×C41—41no—
204C42×C41C2411yescharacteristic
205C23×C41—21no—
206Q8×C41—21no—
207Q8×C41—21no—
208Q8×C41—21no—
209Q8×C41—21no—
210Q8×C41—41no—
211Q8×C41—41no—
212Q8×C41—82no—
213Q8×C41—81no—
214Q8×C41—81no—
215Q8×C41—81no—
216Q8×C41—161no—
217Q8×C41—161no—
218Q8×C41C2×Q1612yes—
219Q8×C41#13712yes—
220D4×C41—21no—
221D4×C41C2×Q1612yes—
222C2×C4×C41—21no—
223C2×C4×C41—21no—
224C2×C4×C41—21no—
225C2×C4×C41—21no—
226C2×C4×C41—21no—
227C2×C4×C41—21no—
228C2×C4×C41—21no—
229C2×C4×C41—41no—
230C2×C4×C41—41no—
231C2×C4×C41—41no—
232C2×C4×C41—41no—
233C2×C4×C41—41no—
234C2×C4×C41—41no—
235C2×C4×C41—82no—
236C2×C4×C41—161no—
237C2×C4×C41C22×D411yescharacteristic
238C2×C4×C41C22×D411yescharacteristic
239C2×C4×C41H(5,𝔽2)11yescharacteristic
240C8×C41—21no—
241C8×C41—21no—
242C8×C41—21no—
243C8×C41—41no—
244C8×C41—41no—
245C8×C41—41no—
246C8×C41—41no—
247C8×C41—41no—
248C8×C41C2×Q1612yes—
249#19813C4111yesmaximal, characteristic, direct product factor, Sylow
250C22×C41—22no—
251C22×C41—41no—
252C22×C41—41no—
253C22×C41D4211yescharacteristic
254C4×C41—22no—
255C4×C41—22no—
256C4×C41—21no—
257C4×C41—41no—
258C4×C41—41no—
259C4×C41—41no—
260C4×C41—41no—
261C4×C41—41no—
262C4×C41—81no—
263C4×C41—81no—
264C4×C41—81no—
265C4×C41—81no—
266C4×C41C22×Q1611yescharacteristic
267C4×C41C2×#13711yescharacteristic
268C4×C41#57711yescharacteristic
269C4×C41#57811yescharacteristic
270#3385C2×C4111yescharacteristic
271Q8×Q16C2×C4111yescharacteristic, complemented
272Q8×SD16C2×C4111yescharacteristic
273#3299C2×C4111yescharacteristic
274#1723C2×C4111yescharacteristic, complemented
275#1692C2×C4111yescharacteristic, complemented
276#1684C2×C4111yescharacteristic, complemented
277#1676C2×C4111yescharacteristic, complemented
278#1675C2×C4111yescharacteristic
279#1645C2×C4111yescharacteristic, complemented
280#1637C2×C4111yescharacteristic
281#1633C2×C4111yescharacteristic, complemented
282#1632C2×C4111yescharacteristic
283#1584C2×C4111yescharacteristic, complemented
284SD16⋊C8C2×C4111yescharacteristic
285C2×C41—42no—
286C2×C41#326611yescharacteristic
287C2×C41D4×Q1611yescharacteristic
288C2×C41#328811yescharacteristic
289Q82C22×C4111yescharacteristic
290Q82C22×C4111yescharacteristic
291#554C22×C4111yescharacteristic
292D4×Q8C22×C4111yescharacteristic
293#501—21no—
294#500—21no—
295#500C22×C4111yescharacteristic
296#500C22×C4111yescharacteristic
297#498—21no—
298#498C22×C4111yescharacteristic
299#494C22×C4111yescharacteristic
300#487C22×C4111yescharacteristic
301#487C22×C4111yescharacteristic
302#484—21no—
303#479—21no—
304#477—21no—
305#477—21no—
306#477C22×C4111yescharacteristic
307#477C22×C4111yescharacteristic
308#477C22×C4111yescharacteristic
309#477C22×C4111yescharacteristic
310#476—21no—
311#476C22×C4111yescharacteristic
312#476C22×C4111yescharacteristic
313#475—21no—
314#475C22×C4111yescharacteristic
315#474—21no—
316#467—21no—
317#462C22×C4111yescharacteristic
318#451—21no—
319#446C22×C4111yescharacteristic
320C8×Q8C22×C4111yescharacteristic
321C8×Q8C22×C4111yescharacteristic
322#440—21no—
323C4×Q16—21no—
324C4×Q16C22×C4111yescharacteristic
325C4×SD16—21no—
326C4×SD16C22×C4111yescharacteristic
327C8×D4C22×C4111yescharacteristic
328C2×#103—21no—
329#335C22×C4111yescharacteristic
330#335C22×C4111yescharacteristic
331#333C22×C4111yescharacteristic
332#333C22×C4111yescharacteristic
333#333C22×C4111yescharacteristic
334#332C22×C4111yescharacteristic
335Q8⋊C8C22×C4111yescharacteristic
336Q8⋊C8C22×C4111yescharacteristic
337Q8⋊C8C22×C4111yescharacteristic
338D4⋊C8C22×C4111yescharacteristic
339#322C22×C4111yescharacteristic
340C41#1981311yescharacteristic, direct product factor, Sylow
341C22×Q8—21no—
342C2×Q16—21no—
343C2×Q16—41no—
344C2×Q16D4×C4111yescharacteristic
345C2×SD16D4×C4111yescharacteristic
346C22×C8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—41no—
353C4⋊Q8—41no—
354C4⋊Q8C23×C4111yescharacteristic
355C4⋊Q8C23×C4111yescharacteristic
356C4⋊Q8C23×C4111yescharacteristic
357C4⋊Q8C23×C4111yescharacteristic
358#125—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—41no—
362C22⋊Q8—41no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C23×C4111yescharacteristic
368C4×Q8C23×C4111yescharacteristic
369C4×Q8C23×C4111yescharacteristic
370C4×D4—21no—
371C4×D4—21no—
372C4×D4C23×C4111yescharacteristic
373C2×C4⋊C4—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107D4×C4111yescharacteristic
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106D4×C4111yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8C23×C4111yescharacteristic
393C4⋊C8C23×C4111yescharacteristic
394C4⋊C8C23×C4111yescharacteristic
395C4⋊C8C23×C4111yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—41no—
405#103D4×C4111yescharacteristic
406#103D4×C4111yescharacteristic
407#103D4×C4111yescharacteristic
408#102—21no—
409#102—21no—
410#102D4×C4111yescharacteristic
411C22⋊C8—21no—
412#97—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8C23×C4111yescharacteristic
416C4×C8C23×C4111yescharacteristic
417C4×C8C23×C4111yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—42no—
426C2×Q8—81no—
427C2×Q8C2×D4×C4111yescharacteristic
428C2×Q8C2×D4×C4111yescharacteristic
429C2×Q8C2×D4×C4111yescharacteristic
430C2×D4C2×D4×C4111yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433C22×C4—41no—
434Q16—22no—
435Q16—81no—
436Q16—82no—
437SD16Q16×C4114yescomplemented
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—81no—
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—21no—
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—21no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—41no—
477C42—41no—
478C42C24×C4111yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—41no—
485Q8—41no—
486Q8—82no—
487Q8—81no—
488Q8—81no—
489Q8—81no—
490Q8—161no—
491Q8—161no—
492Q8C2×Q16×C4112yes—
493Q8#137×C4112yes—
494D4—21no—
495D4C2×Q16×C4112yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—82no—
510C2×C4—161no—
511C2×C4C22×D4×C4111yescharacteristic
512C2×C4C22×D4×C4111yescharacteristic
513C2×C4H(5,𝔽2)×C4111yescharacteristic
514C8—21no—
515C8—21no—
516C8—21no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8C2×Q16×C4112yes—
523C22—22no—
524C22—41no—
525C22—41no—
526C22D42×C4111yescharacteristic
527C4—22no—
528C4—22no—
529C4—21no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—81no—
539C4C22×Q16×C4111yescharacteristic
540C4C2×#137×C4111yescharacteristic
541C4C41×#57711yescharacteristic
542C4C41×#57811yescharacteristic
543C2—42no—
544C2C41×#326611yescharacteristic
545C2D4×Q16×C4111yescharacteristic
546C2C41×#328811yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC2×D4×C41C2×D4
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. Q8×Q16×C41C2semidirect
5. C41×#1723C2semidirect
6. C41×#1692C2semidirect
7. C41×#1684C2semidirect
8. C41×#1676C2semidirect
10. C41×#1645C2semidirect
12. C41×#1633C2semidirect
14. C41×#1584C2semidirect
163. SD16×C41Q16semidirect
249. #19813C41direct (N × H)
271. Q8×Q16C2×C41semidirect
274. #1723C2×C41semidirect
275. #1692C2×C41semidirect
276. #1684C2×C41semidirect
277. #1676C2×C41semidirect
279. #1645C2×C41semidirect
281. #1633C2×C41semidirect
283. #1584C2×C41semidirect
340. C41#19813direct (N × H)
437. SD16Q16×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#33852
Q8×Q16×C412
Q8×SD16×C412
C41×#32992
C41×#17232
C41×#16922
C41×#16842
C41×#16762
C41×#16752
C41×#16452
C41×#16372
C41×#16332
C41×#16322
C41×#15842
C41×SD16⋊C82
#1981341