Finite Group Databasebeta

← C41×#19895 #23796096

Subgroups — C41×#19895 #23796096

Order 10496.

624 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3385C211yesmaximal, characteristic, complemented
2Q8×SD16×C41C211yesmaximal, characteristic, complemented
3C41×#3335C211yesmaximal, characteristic
4C41×#3276C211yesmaximal, characteristic
5C41×#1707C211yesmaximal, characteristic, complemented
6C41×#1695C211yesmaximal, characteristic, complemented
7C41×#1690C211yesmaximal, characteristic, complemented
8C41×#1672C211yesmaximal, characteristic, complemented
9C41×#1671C211yesmaximal, characteristic, complemented
10C41×#1645C211yesmaximal, characteristic, complemented
11C41×#1643C211yesmaximal, characteristic, complemented
12C41×#1637C211yesmaximal, characteristic, complemented
13C41×#1635C211yesmaximal, characteristic
14C41×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C41C211yesmaximal, characteristic, complemented
16C2×#137×C41—21no—
17Q82×C41C2211yescharacteristic
18C41×#554C2211yescharacteristic
19D4×Q8×C41C2211yescharacteristic
20C41×#547C2211yescharacteristic
21C41×#501—21no—
22C41×#500C2211yescharacteristic
23C41×#498—21no—
24C41×#498C2211yescharacteristic
25C41×#498C2211yescharacteristic
26C41×#494C2211yescharacteristic
27C41×#487C2211yescharacteristic
28C41×#487C2211yescharacteristic
29C41×#483—21no—
30C41×#481—21no—
31C41×#479—21no—
32C41×#477C2211yescharacteristic
33C41×#476—21no—
34C41×#476C2211yescharacteristic
35C41×#476C2211yescharacteristic
36C41×#476C2211yescharacteristic
37C41×#475—21no—
38C41×#475C2211yescharacteristic
39C41×#475C2211yescharacteristic
40C41×#474—21no—
41C41×#470—21no—
42C41×#465—21no—
43C41×#462C2211yescharacteristic
44C41×#461C2211yescharacteristic
45C41×#452—21no—
46C41×#451—21no—
47C41×#446C2211yescharacteristic
48C8×Q8×C41C2211yescharacteristic
49C41×#440—21no—
50C4×SD16×C41—21no—
51C4×SD16×C41C2211yescharacteristic
52C4×SD16×C41C2211yescharacteristic
53C41×#436C2211yescharacteristic
54C8×D4×C41C2211yescharacteristic
55C2×#106×C41—21no—
56C41×#334C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#333C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#332C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C82×C41C2211yescharacteristic
67C2×#41×C41—21no—
68C22×Q8×C41—21no—
69#137×C41—44no—
70C2×Q16×C41—21no—
71C2×Q16×C41—21no—
72C2×Q16×C41—21no—
73C2×SD16×C41—21no—
74C2×SD16×C41D411yescharacteristic
75C2×SD16×C41D411yescharacteristic
76C2×M16×C41—21no—
77C22×C8×C41—21no—
78C4⋊Q8×C41—21no—
79C4⋊Q8×C41—21no—
80C4⋊Q8×C41—21no—
81C4⋊Q8×C41—41no—
82C4⋊Q8×C41C2311yescharacteristic
83C4⋊Q8×C41C2311yescharacteristic
84C4⋊Q8×C41C2311yescharacteristic
85C4⋊Q8×C41C2311yescharacteristic
86#125×C41—21no—
87#123×C41—41no—
88C22⋊Q8×C41—21no—
89C22⋊Q8×C41—21no—
90C22⋊Q8×C41—21no—
91C22⋊Q8×C41—41no—
92C22⋊Q8×C41—41no—
93#121×C41—21no—
94C4×Q8×C41—21no—
95C4×Q8×C41—21no—
96C4×Q8×C41C2311yescharacteristic
97C4×Q8×C41C2311yescharacteristic
98C4×D4×C41—21no—
99C4×D4×C41—21no—
100C4×D4×C41C2311yescharacteristic
101C4×D4×C41C2311yescharacteristic
102C2×C4⋊C4×C41—21no—
103C2×C4⋊C4×C41—21no—
104#107×C41—21no—
105#107×C41—21no—
106#107×C41—21no—
107#106×C41—21no—
108#106×C41—21no—
109#106×C41—21no—
110#106×C41—21no—
111#106×C41—21no—
112#106×C41—21no—
113#106×C41—21no—
114#106×C41—21no—
115#106×C41—21no—
116#106×C41D411yescharacteristic
117#106×C41D411yescharacteristic
118C4⋊C8×C41—21no—
119C4⋊C8×C41—21no—
120C4⋊C8×C41C2311yescharacteristic
121C4⋊C8×C41C2311yescharacteristic
122C4⋊C8×C41C2311yescharacteristic
123C4⋊C8×C41C2311yescharacteristic
124#103×C41—21no—
125#103×C41—21no—
126#103×C41—21no—
127#103×C41—21no—
128#103×C41—21no—
129#103×C41—41no—
130#103×C41—41no—
131#103×C41D411yescharacteristic
132#103×C41D411yescharacteristic
133#102×C41—21no—
134#102×C41—21no—
135#102×C41—21no—
136#102×C41D411yescharacteristic
137#102×C41D411yescharacteristic
138C22⋊C8×C41—21no—
139C22⋊C8×C41—21no—
140#97×C41—21no—
141C4×C8×C41—21no—
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144C4×C8×C41C2311yescharacteristic
145#41×C41—42no—
146#41×C41—81no—
147C2×Q8×C41—21no—
148C2×Q8×C41—21no—
149C2×Q8×C41—21no—
150C2×Q8×C41—21no—
151C2×Q8×C41—41no—
152C2×Q8×C41—41no—
153C2×Q8×C41—42no—
154C2×Q8×C41—81no—
155C2×Q8×C41C2×D411yescharacteristic
156C2×Q8×C41C2×D411yescharacteristic
157C2×D4×C41—41no—
158C2×D4×C41C2×D411yescharacteristic
159C2×D4×C41C2×D411yescharacteristic
160C22×C4×C41—21no—
161C22×C4×C41—21no—
162C22×C4×C41—41no—
163C22×C4×C41—41no—
164C22×C4×C41—41no—
165Q16×C41—42no—
166Q16×C41—42no—
167Q16×C41—81no—
168SD16×C41—22no—
169SD16×C41—42no—
170SD16×C41SD1614yescomplemented
171M16×C41—42no—
172C2×C8×C41—21no—
173C2×C8×C41—21no—
174C2×C8×C41—21no—
175C2×C8×C41—21no—
176C2×C8×C41—21no—
177C2×C8×C41—42no—
178C2×C8×C41C2×D411yescharacteristic
179C2×C8×C41C2×D411yescharacteristic
180C2×C8×C41C2×D411yescharacteristic
181C2×C8×C41C2×D411yescharacteristic
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—21no—
189C4⋊C4×C41—21no—
190C4⋊C4×C41—21no—
191C4⋊C4×C41—21no—
192C4⋊C4×C41—41no—
193C4⋊C4×C41—41no—
194C4⋊C4×C41—41no—
195C4⋊C4×C41—41no—
196C4⋊C4×C41—41no—
197C4⋊C4×C41—41no—
198C4⋊C4×C41C2×D411yescharacteristic
199C4⋊C4×C41C2×D411yescharacteristic
200C4⋊C4×C41C2×D411yescharacteristic
201C4⋊C4×C41C2×D411yescharacteristic
202C22⋊C4×C41—21no—
203C22⋊C4×C41—21no—
204C22⋊C4×C41—41no—
205C22⋊C4×C41—41no—
206C22⋊C4×C41—41no—
207C42×C41—21no—
208C42×C41—21no—
209C42×C41—41no—
210C42×C41C2411yescharacteristic
211C23×C41—21no—
212C23×C41—21no—
213Q8×C41—21no—
214Q8×C41—21no—
215Q8×C41—21no—
216Q8×C41—41no—
217Q8×C41—41no—
218Q8×C41—41no—
219Q8×C41—41no—
220Q8×C41—82no—
221Q8×C41—81no—
222Q8×C41—81no—
223Q8×C41—161no—
224Q8×C41C2×SD1612yes—
225D4×C41—21no—
226D4×C41—21no—
227D4×C41—21no—
228D4×C41—82no—
229D4×C41C2×SD1612yes—
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—41no—
237C2×C4×C41—41no—
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—82no—
245C2×C4×C41—82no—
246C2×C4×C41—161no—
247C2×C4×C41C22×D411yescharacteristic
248C2×C4×C41C22×D411yescharacteristic
249C2×C4×C41H(5,𝔽2)11yescharacteristic
250C8×C41—21no—
251C8×C41—21no—
252C8×C41—41no—
253C8×C41—41no—
254C8×C41—41no—
255C8×C41—41no—
256C8×C41—41no—
257C8×C41C2×SD1612yes—
258C8×C41#13712yescomplemented
259#19895C4111yesmaximal, characteristic, direct product factor, Sylow
260C22×C41—22no—
261C22×C41—41no—
262C22×C41—41no—
263C22×C41—41no—
264C22×C41—41no—
265C22×C41—41no—
266C22×C41D4211yescharacteristic
267C4×C41—22no—
268C4×C41—21no—
269C4×C41—41no—
270C4×C41—41no—
271C4×C41—41no—
272C4×C41—41no—
273C4×C41—41no—
274C4×C41—81no—
275C4×C41—81no—
276C4×C41—81no—
277C4×C41—81no—
278C4×C41C22×SD1611yescharacteristic
279C4×C41C2×#13711yescharacteristic
280C4×C41#57711yescharacteristic
281C4×C41#57811yescharacteristic
282#3385C2×C4111yescharacteristic, complemented
283Q8×SD16C2×C4111yescharacteristic, complemented
284#3335C2×C4111yescharacteristic
285#3276C2×C4111yescharacteristic
286#1707C2×C4111yescharacteristic, complemented
287#1695C2×C4111yescharacteristic, complemented
288#1690C2×C4111yescharacteristic, complemented
289#1672C2×C4111yescharacteristic, complemented
290#1671C2×C4111yescharacteristic, complemented
291#1645C2×C4111yescharacteristic, complemented
292#1643C2×C4111yescharacteristic, complemented
293#1637C2×C4111yescharacteristic, complemented
294#1635C2×C4111yescharacteristic
295#1590C2×C4111yescharacteristic, complemented
296C8×SD16C2×C4111yescharacteristic, complemented
297C2×C41—42no—
298C2×C41—81no—
299C2×C41#327611yescharacteristic
300C2×C41D4×SD1611yescharacteristic
301C2×C41#329011yescharacteristic
302C2×#137—21no—
303Q82C22×C4111yescharacteristic
304#554C22×C4111yescharacteristic
305D4×Q8C22×C4111yescharacteristic
306#547C22×C4111yescharacteristic
307#501—21no—
308#500C22×C4111yescharacteristic
309#498—21no—
310#498C22×C4111yescharacteristic
311#498C22×C4111yescharacteristic
312#494C22×C4111yescharacteristic
313#487C22×C4111yescharacteristic
314#487C22×C4111yescharacteristic
315#483—21no—
316#481—21no—
317#479—21no—
318#477C22×C4111yescharacteristic
319#476—21no—
320#476C22×C4111yescharacteristic
321#476C22×C4111yescharacteristic
322#476C22×C4111yescharacteristic
323#475—21no—
324#475C22×C4111yescharacteristic
325#475C22×C4111yescharacteristic
326#474—21no—
327#470—21no—
328#465—21no—
329#462C22×C4111yescharacteristic
330#461C22×C4111yescharacteristic
331#452—21no—
332#451—21no—
333#446C22×C4111yescharacteristic
334C8×Q8C22×C4111yescharacteristic
335#440—21no—
336C4×SD16—21no—
337C4×SD16C22×C4111yescharacteristic
338C4×SD16C22×C4111yescharacteristic
339#436C22×C4111yescharacteristic
340C8×D4C22×C4111yescharacteristic
341C2×#106—21no—
342#334C22×C4111yescharacteristic
343#334C22×C4111yescharacteristic
344#333C22×C4111yescharacteristic
345#333C22×C4111yescharacteristic
346#332C22×C4111yescharacteristic
347#332C22×C4111yescharacteristic
348Q8⋊C8C22×C4111yescharacteristic
349Q8⋊C8C22×C4111yescharacteristic
350D4⋊C8C22×C4111yescharacteristic
351D4⋊C8C22×C4111yescharacteristic
352C82C22×C4111yescharacteristic
353C41#1989511yescharacteristic, direct product factor, Sylow
354C2×#41—21no—
355C22×Q8—21no—
356#137—44no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×SD16—21no—
361C2×SD16D4×C4111yescharacteristic
362C2×SD16D4×C4111yescharacteristic
363C2×M16—21no—
364C22×C8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—41no—
369C4⋊Q8C23×C4111yescharacteristic
370C4⋊Q8C23×C4111yescharacteristic
371C4⋊Q8C23×C4111yescharacteristic
372C4⋊Q8C23×C4111yescharacteristic
373#125—21no—
374#123—41no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—41no—
379C22⋊Q8—41no—
380#121—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8C23×C4111yescharacteristic
384C4×Q8C23×C4111yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C4111yescharacteristic
388C4×D4C23×C4111yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391#107—21no—
392#107—21no—
393#107—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106D4×C4111yescharacteristic
404#106D4×C4111yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C4111yescharacteristic
408C4⋊C8C23×C4111yescharacteristic
409C4⋊C8C23×C4111yescharacteristic
410C4⋊C8C23×C4111yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—41no—
417#103—41no—
418#103D4×C4111yescharacteristic
419#103D4×C4111yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102D4×C4111yescharacteristic
424#102D4×C4111yescharacteristic
425C22⋊C8—21no—
426C22⋊C8—21no—
427#97—21no—
428C4×C8—21no—
429C4×C8C23×C4111yescharacteristic
430C4×C8C23×C4111yescharacteristic
431C4×C8C23×C4111yescharacteristic
432#41—42no—
433#41—81no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8C2×D4×C4111yescharacteristic
443C2×Q8C2×D4×C4111yescharacteristic
444C2×D4—41no—
445C2×D4C2×D4×C4111yescharacteristic
446C2×D4C2×D4×C4111yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—42no—
453Q16—42no—
454Q16—81no—
455SD16—22no—
456SD16—42no—
457SD16SD16×C4114yescomplemented
458M16—42no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—42no—
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—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4C2×D4×C4111yescharacteristic
486C4⋊C4C2×D4×C4111yescharacteristic
487C4⋊C4C2×D4×C4111yescharacteristic
488C4⋊C4C2×D4×C4111yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—21no—
496C42—41no—
497C42C24×C4111yescharacteristic
498C23—21no—
499C23—21no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—82no—
508Q8—81no—
509Q8—81no—
510Q8—161no—
511Q8C2×SD16×C4112yes—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—82no—
516D4C2×SD16×C4112yes—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—161no—
534C2×C4C22×D4×C4111yescharacteristic
535C2×C4C22×D4×C4111yescharacteristic
536C2×C4H(5,𝔽2)×C4111yescharacteristic
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8C2×SD16×C4112yes—
545C8#137×C4112yescomplemented
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22D42×C4111yescharacteristic
553C4—22no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4C22×SD16×C4111yescharacteristic
565C4C2×#137×C4111yescharacteristic
566C4C41×#57711yescharacteristic
567C4C41×#57811yescharacteristic
568C2—42no—
569C2—81no—
570C2C41×#327611yescharacteristic
571C2D4×SD16×C4111yescharacteristic
572C2C41×#329011yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#547C22
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×#3385C2semidirect
2. Q8×SD16×C41C2semidirect
5. C41×#1707C2semidirect
6. C41×#1695C2semidirect
7. C41×#1690C2semidirect
8. C41×#1672C2semidirect
9. C41×#1671C2semidirect
10. C41×#1645C2semidirect
11. C41×#1643C2semidirect
12. C41×#1637C2semidirect
14. C41×#1590C2semidirect
15. C8×SD16×C41C2semidirect
170. SD16×C41SD16semidirect
258. C8×C41#137semidirect
259. #19895C41direct (N × H)
282. #3385C2×C41semidirect
283. Q8×SD16C2×C41semidirect
286. #1707C2×C41semidirect
287. #1695C2×C41semidirect
288. #1690C2×C41semidirect
289. #1672C2×C41semidirect
290. #1671C2×C41semidirect
291. #1645C2×C41semidirect
292. #1643C2×C41semidirect
293. #1637C2×C41semidirect
295. #1590C2×C41semidirect
296. C8×SD16C2×C41semidirect
353. C41#19895direct (N × H)
457. SD16SD16×C41semidirect
545. C8#137×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#33852
Q8×SD16×C412
C41×#33352
C41×#32762
C41×#17072
C41×#16952
C41×#16902
C41×#16722
C41×#16712
C41×#16452
C41×#16432
C41×#16372
C41×#16352
C41×#15902
C8×SD16×C412
#1989541