Finite Group Databasebeta

← C41×#10480 #23786681

Subgroups — C41×#10480 #23786681

Order 10496.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#476C211yesmaximal, characteristic
2C41×#1990C211yesmaximal, characteristic, complemented
3C41×#1954C211yesmaximal, characteristic
4C41×#1802C211yesmaximal, characteristic
5C2×C41×#334C211yesmaximal, characteristic, complemented
6C2×C41×#333C211yesmaximal, characteristic, complemented
7C41×#1296C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C41C2211yescharacteristic
9C2×C4×D4×C41C2211yescharacteristic
10C41×#476—22no—
11C41×#476—22no—
12C2×#106×C41—21no—
13C2×C4⋊C8×C41C2211yescharacteristic
14C2×C4⋊C8×C41C2211yescharacteristic
15C2×C4⋊C8×C41C2211yescharacteristic
16C2×#102×C41—21no—
17C2×#102×C41—21no—
18C2×C22⋊C8×C41—21no—
19C2×C22⋊C8×C41—21no—
20C2×C4×C8×C41C2211yescharacteristic
21C41×#384C2211yescharacteristic
22C41×#340—21no—
23C41×#340—21no—
24C41×#340—21no—
25C41×#334—22no—
26C41×#333—22no—
27C22×Q8×C41—21no—
28C22×D4×C41D411yescharacteristic
29C23×C4×C41—21no—
30C22×C8×C41—21no—
31C22×C8×C41—21no—
32C22×C8×C41—21no—
33C22×C8×C41D411yescharacteristic
34C22×C8×C41D411yescharacteristic
35C4⋊Q8×C41—21no—
36C4⋊Q8×C41—21no—
37C4⋊Q8×C41—21no—
38C4⋊Q8×C41D412yes—
39C4×D4×C41—21no—
40C4×D4×C41—21no—
41C4×D4×C41—21no—
42C4×D4×C41—21no—
43C2×C4⋊C4×C41—21no—
44C2×C4⋊C4×C41—21no—
45C2×C4⋊C4×C41—21no—
46C2×C4⋊C4×C41—21no—
47C2×C4⋊C4×C41—21no—
48C2×C4⋊C4×C41D411yescharacteristic
49C2×C22⋊C4×C41—21no—
50C2×C42×C41C2311yescharacteristic
51#106×C41—24no—
52C4⋊C8×C41—21no—
53C4⋊C8×C41—21no—
54C4⋊C8×C41—21no—
55C4⋊C8×C41—21no—
56C4⋊C8×C41—21no—
57C4⋊C8×C41D412yes—
58#102×C41—24no—
59#102×C41—42no—
60C22⋊C8×C41—42no—
61C22⋊C8×C41—42no—
62C4×C8×C41—21no—
63C4×C8×C41—21no—
64C24×C41—21no—
65C2×Q8×C41—22no—
66C2×Q8×C41—41no—
67C2×Q8×C41—81no—
68C2×Q8×C41—81no—
69C2×D4×C41—21no—
70C2×D4×C41—21no—
71C2×D4×C41—21no—
72C2×D4×C41—21no—
73C2×D4×C41—21no—
74C2×D4×C41SD1612yes—
75C22×C4×C41—21no—
76C22×C4×C41—41no—
77C22×C4×C41—41no—
78C22×C4×C41—41no—
79C22×C4×C41—41no—
80C22×C4×C41—41no—
81C22×C4×C41—41no—
82C22×C4×C41—41no—
83C22×C4×C41—41no—
84C22×C4×C41C2×D411yescharacteristic
85C22×C4×C41C2×D411yescharacteristic
86C22×C4×C41#4111yescharacteristic
87C2×C8×C41—21no—
88C2×C8×C41—21no—
89C2×C8×C41—22no—
90C2×C8×C41—21no—
91C2×C8×C41—21no—
92C2×C8×C41—21no—
93C2×C8×C41—41no—
94C2×C8×C41—41no—
95C2×C8×C41—41no—
96C2×C8×C41—41no—
97C2×C8×C41—41no—
98C2×C8×C41—41no—
99C2×C8×C41—41no—
100C2×C8×C41—41no—
101C2×C8×C41SD1612yes—
102C4⋊C4×C41—22no—
103C4⋊C4×C41—21no—
104C4⋊C4×C41—22no—
105C4⋊C4×C41—21no—
106C4⋊C4×C41—41no—
107C4⋊C4×C41—41no—
108C4⋊C4×C41—41no—
109C4⋊C4×C41—41no—
110C4⋊C4×C41—41no—
111C4⋊C4×C41—41no—
112C4⋊C4×C41—81no—
113C22⋊C4×C41—41no—
114C22⋊C4×C41—41no—
115C42×C41C2×D411yescharacteristic
116C42×C41C2×D411yescharacteristic
117C42×C41#4111yescharacteristic
118C42×C41#4111yescharacteristic
119C23×C41—22no—
120C23×C41—41no—
121C23×C41—41no—
122C23×C41—41no—
123C23×C41—41no—
124C23×C41—41no—
125C23×C41—41no—
126C23×C41#12111yescharacteristic
127Q8×C41—82no—
128Q8×C41—82no—
129D4×C41—22no—
130D4×C41—22no—
131D4×C41—41no—
132D4×C41—41no—
133C2×C4×C41—21no—
134C2×C4×C41—21no—
135C2×C4×C41—41no—
136C2×C4×C41—42no—
137C2×C4×C41—41no—
138C2×C4×C41—41no—
139C2×C4×C41—81no—
140C2×C4×C41—81no—
141C2×C4×C41—81no—
142C2×C4×C41—81no—
143C2×C4×C41—81no—
144C2×C4×C41—81no—
145C2×C4×C41—81no—
146C2×C4×C41—81no—
147C2×C4×C41—81no—
148C2×C4×C41#12011yescharacteristic
149C2×C4×C41#12111yescharacteristic
150C2×C4×C41#12111yescharacteristic
151C2×C4×C41#12311yescharacteristic
152C2×C4×C41#12311yescharacteristic
153C2×C4×C41#12411yescharacteristic
154C2×C4×C41C2×SD1611yescharacteristic
155C2×C4×C41C2×SD1611yescharacteristic
156C2×C4×C41#13511yescharacteristic
157C2×C4×C41#13511yescharacteristic
158C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C41#13711yescharacteristic
160C2×C4×C41#13711yescharacteristic
161C2×C4×C41#13711yescharacteristic
162C8×C41—22no—
163C8×C41—42no—
164C8×C41—41no—
165C8×C41—81no—
166C8×C41—81no—
167#10480C4111yesmaximal, characteristic, direct product factor, Sylow
168C22×C41—42no—
169C22×C41—42no—
170C22×C41—42no—
171C22×C41—81no—
172C22×C41—81no—
173C22×C41—81no—
174C22×C41—81no—
175C22×C41#39411yescharacteristic
176C22×C41#46111yescharacteristic
177C22×C41#46311yescharacteristic
178C22×C41#46511yescharacteristic
179C22×C41#47011yescharacteristic
180C22×C41#47111yescharacteristic
181C22×C41#47211yescharacteristic
182C4×C41—21no—
183C4×C41—21no—
184C4×C41—82no—
185C4×C41—81no—
186C4×C41—161no—
187C4×C41#44811yescharacteristic
188C4×C41#45211yescharacteristic
189C4×C41#46011yescharacteristic
190C4×C41#46411yescharacteristic
191C4×C41#46511yescharacteristic
192C4×C41#46811yescharacteristic
193C4×C41#48311yescharacteristic
194C4×C41#48511yescharacteristic
195C2×#476C2×C4111yescharacteristic
196#1990C2×C4111yescharacteristic, complemented
197#1954C2×C4111yescharacteristic
198#1802C2×C4111yescharacteristic
199C2×#334C2×C4111yescharacteristic, complemented
200C2×#333C2×C4111yescharacteristic, complemented
201#1296C2×C4111yescharacteristic, complemented
202C2×C41—82no—
203C2×C41#167111yescharacteristic
204C2×C41#167711yescharacteristic
205C2×C41#169511yescharacteristic
206C2×C41#170311yescharacteristic
207C2×C41#203511yescharacteristic
208C2×C41#205111yescharacteristic
209C2×C41#205511yescharacteristic
210C2×C4⋊Q8C22×C4111yescharacteristic
211C2×C4×D4C22×C4111yescharacteristic
212#476—22no—
213#476—22no—
214C2×#106—21no—
215C2×C4⋊C8C22×C4111yescharacteristic
216C2×C4⋊C8C22×C4111yescharacteristic
217C2×C4⋊C8C22×C4111yescharacteristic
218C2×#102—21no—
219C2×#102—21no—
220C2×C22⋊C8—21no—
221C2×C22⋊C8—21no—
222C2×C4×C8C22×C4111yescharacteristic
223#384C22×C4111yescharacteristic
224#340—21no—
225#340—21no—
226#340—21no—
227#334—22no—
228#333—22no—
229C41#1048011yescharacteristic, direct product factor, Sylow
230C22×Q8—21no—
231C22×D4D4×C4111yescharacteristic
232C23×C4—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8D4×C4111yescharacteristic
237C22×C8D4×C4111yescharacteristic
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8D4×C4112yes—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4D4×C4111yescharacteristic
252C2×C22⋊C4—21no—
253C2×C42C23×C4111yescharacteristic
254#106—24no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8D4×C4112yes—
261#102—24no—
262#102—42no—
263C22⋊C8—42no—
264C22⋊C8—42no—
265C4×C8—21no—
266C4×C8—21no—
267C24—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—81no—
271C2×Q8—81no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4SD16×C4112yes—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4C2×D4×C4111yescharacteristic
288C22×C4C2×D4×C4111yescharacteristic
289C22×C4#41×C4111yescharacteristic
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—22no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8SD16×C4112yes—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—81no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C42C2×D4×C4111yescharacteristic
319C42C2×D4×C4111yescharacteristic
320C42#41×C4111yescharacteristic
321C42#41×C4111yescharacteristic
322C23—22no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23#121×C4111yescharacteristic
330Q8—82no—
331Q8—82no—
332D4—22no—
333D4—22no—
334D4—41no—
335D4—41no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4#120×C4111yescharacteristic
352C2×C4#121×C4111yescharacteristic
353C2×C4#121×C4111yescharacteristic
354C2×C4#123×C4111yescharacteristic
355C2×C4#123×C4111yescharacteristic
356C2×C4#124×C4111yescharacteristic
357C2×C4C2×SD16×C4111yescharacteristic
358C2×C4C2×SD16×C4111yescharacteristic
359C2×C4#135×C4111yescharacteristic
360C2×C4#135×C4111yescharacteristic
361C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
362C2×C4#137×C4111yescharacteristic
363C2×C4#137×C4111yescharacteristic
364C2×C4#137×C4111yescharacteristic
365C8—22no—
366C8—42no—
367C8—41no—
368C8—81no—
369C8—81no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22C41×#39411yescharacteristic
378C22C41×#46111yescharacteristic
379C22C41×#46311yescharacteristic
380C22C41×#46511yescharacteristic
381C22C41×#47011yescharacteristic
382C22C41×#47111yescharacteristic
383C22C41×#47211yescharacteristic
384C4—21no—
385C4—21no—
386C4—82no—
387C4—81no—
388C4—161no—
389C4C41×#44811yescharacteristic
390C4C41×#45211yescharacteristic
391C4C41×#46011yescharacteristic
392C4C41×#46411yescharacteristic
393C4C41×#46511yescharacteristic
394C4C41×#46811yescharacteristic
395C4C41×#48311yescharacteristic
396C4C41×#48511yescharacteristic
397C2—82no—
398C2C41×#167111yescharacteristic
399C2C41×#167711yescharacteristic
400C2C41×#169511yescharacteristic
401C2C41×#170311yescharacteristic
402C2C41×#203511yescharacteristic
403C2C41×#205111yescharacteristic
404C2C41×#205511yescharacteristic
subgroupG/H
center, socleC23×C41#121
commutator, Frattini, cosocleC2×C42C23×C41
prime radicalC22×D4×C41D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#1990C2semidirect
5. C2×C41×#334C2semidirect
6. C2×C41×#333C2semidirect
7. C41×#1296C2semidirect
167. #10480C41direct (N × H)
196. #1990C2×C41semidirect
199. C2×#334C2×C41semidirect
200. C2×#333C2×C41semidirect
201. #1296C2×C41semidirect
229. C41#10480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4762
C41×#19902
C41×#19542
C41×#18022
C2×C41×#3342
C2×C41×#3332
C41×#12962
#1048041