Finite Group Databasebeta

← C41×#19142 #23795343

Subgroups — C41×#19142 #23795343

Order 10496.

684 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3131C211yesmaximal, characteristic, complemented
2C41×#3101C211yesmaximal, characteristic, complemented
3C41×#3100C211yesmaximal, characteristic
4C2×C41×#436C211yesmaximal, characteristic, complemented
5C41×#1703C212yesmaximal, complemented
6C41×#1701C212yesmaximal, complemented
7C41×#1699C212yesmaximal, complemented
8C41×#1697C212yesmaximal, complemented
9C41×#1564C211yesmaximal, characteristic, complemented
10C41×#1542C211yesmaximal, characteristic, complemented
11C41×#1540C211yesmaximal, characteristic, complemented
12C22×M16×C41—21no—
13C41×#533C2211yescharacteristic
14C41×#532C2211yescharacteristic
15C2×C4×D4×C41C2211yescharacteristic
16C41×#488—21no—
17C41×#488—21no—
18C41×#487C2211yescharacteristic, complemented
19C41×#487C2211yescharacteristic, complemented
20C41×#486C2211yescharacteristic, complemented
21C41×#486C2211yescharacteristic, complemented
22C41×#483—21no—
23C41×#480—21no—
24C41×#476C2212yes—
25C41×#474C2212yes—
26C41×#461C2212yes—
27C41×#459C2212yes—
28C41×#450—21no—
29C41×#447—21no—
30C4×SD16×C41—22no—
31C4×D8×C41—22no—
32C41×#436—21no—
33C41×#436—21no—
34C41×#436C2212yes—
35C41×#436C2212yes—
36C41×#431C2211yescharacteristic
37C41×#431C2211yescharacteristic
38C2×C4⋊C8×C41C2211yescharacteristic
39C41×#416—21no—
40C41×#416—21no—
41C2×C22⋊C8×C41—21no—
42C2×C4×C8×C41C2211yescharacteristic
43C41×#335C2212yescomplemented
44C41×#334C2212yescomplemented
45C41×#333C2212yescomplemented
46C41×#332C2212yescomplemented
47C41×#332C2212yescomplemented
48C41×#331C2212yescomplemented
49C2×#41×C41—21no—
50C22×D4×C41D411yescharacteristic
51C23×C4×C41—21no—
52C2×SD16×C41—22no—
53C2×D8×C41—22no—
54C2×M16×C41—22no—
55C2×M16×C41—22no—
56C2×M16×C41—44no—
57C22×C8×C41—21no—
58C22×C8×C41D411yescharacteristic
59C22×C8×C41D411yescharacteristic
60C4⋊Q8×C41C2311yescharacteristic
61C4⋊Q8×C41C2311yescharacteristic
62C4⋊Q8×C41C2311yescharacteristic
63#127×C41C2311yescharacteristic
64#125×C41—21no—
65#124×C41—21no—
66C22⋊Q8×C41—21no—
67C22⋊Q8×C41—21no—
68#121×C41—21no—
69#121×C41—21no—
70C4×Q8×C41—21no—
71C4×Q8×C41—21no—
72C4×D4×C41—21no—
73C4×D4×C41—21no—
74C4×D4×C41—21no—
75C4×D4×C41—21no—
76C4×D4×C41D412yes—
77C4×D4×C41C2312yes—
78#117×C41—21no—
79C2×C4⋊C4×C41D411yescharacteristic
80C2×C22⋊C4×C41—21no—
81C2×C42×C41C2311yescharacteristic
82#107×C41—22no—
83#106×C41—22no—
84C4⋊C8×C41—21no—
85C4⋊C8×C41C2312yes—
86C4⋊C8×C41C2312yes—
87C4⋊C8×C41C2312yes—
88#103×C41—21no—
89#103×C41—21no—
90#103×C41—21no—
91#103×C41—21no—
92#103×C41—22no—
93#102×C41—22no—
94#102×C41—22no—
95#102×C41—21no—
96#102×C41—21no—
97#102×C41—21no—
98#102×C41—21no—
99#102×C41—22no—
100C22⋊C8×C41—21no—
101C22⋊C8×C41—21no—
102C22⋊C8×C41—22no—
103C22⋊C8×C41—22no—
104C4×C8×C41—21no—
105C4×C8×C41—21no—
106C4×C8×C41D411yescharacteristic
107C4×C8×C41D411yescharacteristic
108C4×C8×C41C2311yescharacteristic
109C4×C8×C41C2311yescharacteristic
110C24×C41—21no—
111#41×C41—42no—
112#41×C41—42no—
113C2×Q8×C41—21no—
114C2×Q8×C41—21no—
115C2×Q8×C41—21no—
116C2×D4×C41—21no—
117C2×D4×C41—21no—
118C2×D4×C41—21no—
119C2×D4×C41—21no—
120C2×D4×C41—42no—
121C2×D4×C41—41no—
122C2×D4×C41C2×D412yes—
123C22×C4×C41—21no—
124C22×C4×C41—22no—
125C22×C4×C41—22no—
126C22×C4×C41—42no—
127C22×C4×C41—42no—
128C22×C4×C41—41no—
129C22×C4×C41C2×D411yescharacteristic
130C22×C4×C41C2×D411yescharacteristic
131C22×C4×C41#4111yescharacteristic
132SD16×C41—44no—
133D8×C41—44no—
134M16×C41—44no—
135M16×C41—44no—
136C2×C8×C41—22no—
137C2×C8×C41—22no—
138C2×C8×C41—22no—
139C2×C8×C41—22no—
140C2×C8×C41—22no—
141C2×C8×C41—42no—
142C2×C8×C41C2×D411yescharacteristic
143C2×C8×C41C2×D411yescharacteristic
144C2×C8×C41C2×D411yescharacteristic
145C2×C8×C41C2×D411yescharacteristic
146C4⋊C4×C41—21no—
147C4⋊C4×C41—21no—
148C4⋊C4×C41—21no—
149C4⋊C4×C41—21no—
150C4⋊C4×C41—21no—
151C4⋊C4×C41—21no—
152C4⋊C4×C41—21no—
153C4⋊C4×C41—41no—
154C4⋊C4×C41—41no—
155C4⋊C4×C41C2×D412yes—
156C22⋊C4×C41—22no—
157C22⋊C4×C41—22no—
158C22⋊C4×C41—41no—
159C22⋊C4×C41—41no—
160C22⋊C4×C41—41no—
161C42×C41—41no—
162C42×C41C2×D411yescharacteristic
163C42×C41C2×D411yescharacteristic
164C42×C41#4111yescharacteristic
165C42×C41C2411yescharacteristic
166C23×C41—22no—
167C23×C41—42no—
168C23×C41—42no—
169C23×C41—42no—
170C23×C41—41no—
171C23×C41#12111yescharacteristic
172Q8×C41—41no—
173Q8×C41—41no—
174Q8×C41—42no—
175Q8×C41—81no—
176D4×C41—22no—
177D4×C41—22no—
178D4×C41—42no—
179D4×C41—41no—
180D4×C41—41no—
181D4×C41—42no—
182D4×C41—81no—
183D4×C41—82no—
184C2×C4×C41—22no—
185C2×C4×C41—22no—
186C2×C4×C41—41no—
187C2×C4×C41—42no—
188C2×C4×C41—42no—
189C2×C4×C41—42no—
190C2×C4×C41—44no—
191C2×C4×C41—41no—
192C2×C4×C41—41no—
193C2×C4×C41—41no—
194C2×C4×C41—82no—
195C2×C4×C41#12111yescharacteristic
196C2×C4×C41#12111yescharacteristic
197C2×C4×C41#12111yescharacteristic
198C2×C4×C41#13512yes—
199C2×C4×C41AGL(1,ℤ/8)12yes—
200C2×C4×C41C22×D411yescharacteristic
201C2×C4×C41C22×D411yescharacteristic
202C2×C4×C41C2×#4111yescharacteristic
203C8×C41—21no—
204C8×C41—21no—
205C8×C41—21no—
206C8×C41—21no—
207C8×C41—42no—
208C8×C41—42no—
209C8×C41—42no—
210#19142C4111yesmaximal, characteristic, direct product factor, Sylow
211C22×C41—21no—
212C22×C41—21no—
213C22×C41—42no—
214C22×C41—42no—
215C22×C41—42no—
216C22×C41—84no—
217C22×C41—81no—
218C22×C41—81no—
219C22×C41—81no—
220C22×C41#46312yes—
221C22×C41C2×#12111yescharacteristic
222C4×C41—21no—
223C4×C41—21no—
224C4×C41—21no—
225C4×C41—42no—
226C4×C41—81no—
227C4×C41—81no—
228C4×C41—81no—
229C4×C41#46312yes—
230C4×C41C2×#13511yescharacteristic
231C4×C41C2×AGL(1,ℤ/8)11yescharacteristic
232C4×C41#57512yes—
233#3131C2×C4111yescharacteristic, complemented
234#3101C2×C4111yescharacteristic, complemented
235#3100C2×C4111yescharacteristic
236C2×#436C2×C4111yescharacteristic, complemented
237#1703C2×C4112yescomplemented
238#1701C2×C4112yescomplemented
239#1699C2×C4112yescomplemented
240#1697C2×C4112yescomplemented
241#1564C2×C4111yescharacteristic, complemented
242#1542C2×C4111yescharacteristic, complemented
243#1540C2×C4111yescharacteristic, complemented
244C2×C41—22no—
245C2×C41—82no—
246C2×C41—161no—
247C2×C41C2×#46311yescharacteristic
248C2×C41#305411yescharacteristic
249C2×C41#306711yescharacteristic
250C22×M16—21no—
251#533C22×C4111yescharacteristic
252#532C22×C4111yescharacteristic
253C2×C4×D4C22×C4111yescharacteristic
254#488—21no—
255#488—21no—
256#487C22×C4111yescharacteristic, complemented
257#487C22×C4111yescharacteristic, complemented
258#486C22×C4111yescharacteristic, complemented
259#486C22×C4111yescharacteristic, complemented
260#483—21no—
261#480—21no—
262#476C22×C4112yes—
263#474C22×C4112yes—
264#461C22×C4112yes—
265#459C22×C4112yes—
266#450—21no—
267#447—21no—
268C4×SD16—22no—
269C4×D8—22no—
270#436—21no—
271#436—21no—
272#436C22×C4112yes—
273#436C22×C4112yes—
274#431C22×C4111yescharacteristic
275#431C22×C4111yescharacteristic
276C2×C4⋊C8C22×C4111yescharacteristic
277#416—21no—
278#416—21no—
279C2×C22⋊C8—21no—
280C2×C4×C8C22×C4111yescharacteristic
281#335C22×C4112yescomplemented
282#334C22×C4112yescomplemented
283#333C22×C4112yescomplemented
284#332C22×C4112yescomplemented
285#332C22×C4112yescomplemented
286#331C22×C4112yescomplemented
287C41#1914211yescharacteristic, direct product factor, Sylow
288C2×#41—21no—
289C22×D4D4×C4111yescharacteristic
290C23×C4—21no—
291C2×SD16—22no—
292C2×D8—22no—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—44no—
296C22×C8—21no—
297C22×C8D4×C4111yescharacteristic
298C22×C8D4×C4111yescharacteristic
299C4⋊Q8C23×C4111yescharacteristic
300C4⋊Q8C23×C4111yescharacteristic
301C4⋊Q8C23×C4111yescharacteristic
302#127C23×C4111yescharacteristic
303#125—21no—
304#124—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307#121—21no—
308#121—21no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4D4×C4112yes—
316C4×D4C23×C4112yes—
317#117—21no—
318C2×C4⋊C4D4×C4111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C42C23×C4111yescharacteristic
321#107—22no—
322#106—22no—
323C4⋊C8—21no—
324C4⋊C8C23×C4112yes—
325C4⋊C8C23×C4112yes—
326C4⋊C8C23×C4112yes—
327#103—21no—
328#103—21no—
329#103—21no—
330#103—21no—
331#103—22no—
332#102—22no—
333#102—22no—
334#102—21no—
335#102—21no—
336#102—21no—
337#102—21no—
338#102—22no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—22no—
342C22⋊C8—22no—
343C4×C8—21no—
344C4×C8—21no—
345C4×C8D4×C4111yescharacteristic
346C4×C8D4×C4111yescharacteristic
347C4×C8C23×C4111yescharacteristic
348C4×C8C23×C4111yescharacteristic
349C24—21no—
350#41—42no—
351#41—42no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—42no—
360C2×D4—41no—
361C2×D4C2×D4×C4112yes—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—41no—
368C22×C4C2×D4×C4111yescharacteristic
369C22×C4C2×D4×C4111yescharacteristic
370C22×C4#41×C4111yescharacteristic
371SD16—44no—
372D8—44no—
373M16—44no—
374M16—44no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—42no—
381C2×C8C2×D4×C4111yescharacteristic
382C2×C8C2×D4×C4111yescharacteristic
383C2×C8C2×D4×C4111yescharacteristic
384C2×C8C2×D4×C4111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4C2×D4×C4112yes—
395C22⋊C4—22no—
396C22⋊C4—22no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C42—41no—
401C42C2×D4×C4111yescharacteristic
402C42C2×D4×C4111yescharacteristic
403C42#41×C4111yescharacteristic
404C42C24×C4111yescharacteristic
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23#121×C4111yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—42no—
414Q8—81no—
415D4—22no—
416D4—22no—
417D4—42no—
418D4—41no—
419D4—41no—
420D4—42no—
421D4—81no—
422D4—82no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—82no—
434C2×C4#121×C4111yescharacteristic
435C2×C4#121×C4111yescharacteristic
436C2×C4#121×C4111yescharacteristic
437C2×C4#135×C4112yes—
438C2×C4AGL(1,ℤ/8)×C4112yes—
439C2×C4C22×D4×C4111yescharacteristic
440C2×C4C22×D4×C4111yescharacteristic
441C2×C4C2×#41×C4111yescharacteristic
442C8—21no—
443C8—21no—
444C8—21no—
445C8—21no—
446C8—42no—
447C8—42no—
448C8—42no—
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22C41×#46312yes—
459C22C2×#121×C4111yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4C41×#46312yes—
468C4C2×#135×C4111yescharacteristic
469C4C2×AGL(1,ℤ/8)×C4111yescharacteristic
470C4C41×#57512yes—
471C2—22no—
472C2—82no—
473C2—161no—
474C2C2×C41×#46311yescharacteristic
475C2C41×#305411yescharacteristic
476C2C41×#306711yescharacteristic
subgroupG/H
centerC2×C4×C41#121
commutator, Frattini, cosocleC42C24×C41
socleC22×C41C2×#121
prime radicalC41×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3131C2semidirect
2. C41×#3101C2semidirect
4. C2×C41×#436C2semidirect
5. C41×#1703C2semidirect
6. C41×#1701C2semidirect
7. C41×#1699C2semidirect
8. C41×#1697C2semidirect
9. C41×#1564C2semidirect
10. C41×#1542C2semidirect
11. C41×#1540C2semidirect
18. C41×#487C22semidirect
19. C41×#487C22semidirect
20. C41×#486C22semidirect
21. C41×#486C22semidirect
43. C41×#335C22semidirect
44. C41×#334C22semidirect
45. C41×#333C22semidirect
46. C41×#332C22semidirect
47. C41×#332C22semidirect
48. C41×#331C22semidirect
210. #19142C41direct (N × H)
233. #3131C2×C41semidirect
234. #3101C2×C41semidirect
236. C2×#436C2×C41semidirect
237. #1703C2×C41semidirect
238. #1701C2×C41semidirect
239. #1699C2×C41semidirect
240. #1697C2×C41semidirect
241. #1564C2×C41semidirect
242. #1542C2×C41semidirect
243. #1540C2×C41semidirect
256. #487C22×C41semidirect
257. #487C22×C41semidirect
258. #486C22×C41semidirect
259. #486C22×C41semidirect
281. #335C22×C41semidirect
282. #334C22×C41semidirect
283. #333C22×C41semidirect
284. #332C22×C41semidirect
285. #332C22×C41semidirect
286. #331C22×C41semidirect
287. C41#19142direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31312
C41×#31012
C41×#31002
C2×C41×#4362
C41×#17032
C41×#17012
C41×#16992
C41×#16972
C41×#15642
C41×#15422
C41×#15402
#1914241