Finite Group Databasebeta

← C41×#2505 #19106285

Subgroups — C41×#2505 #19106285

Order 5248.

456 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#400C211yesmaximal, characteristic, complemented
2C41×#400C211yesmaximal, characteristic, complemented
3C41×#400C211yesmaximal, characteristic, complemented
4C41×#398C211yesmaximal, characteristic, complemented
5C41×#389C211yesmaximal, characteristic, complemented
6C41×#387C211yesmaximal, characteristic, complemented
7C41×#387C211yesmaximal, characteristic, complemented
8C41×#385C211yesmaximal, characteristic
9C41×#385C211yesmaximal, characteristic
10C41×#385C211yesmaximal, characteristic
11C41×#385C211yesmaximal, characteristic
12C41×#382C211yesmaximal, characteristic, complemented
13C41×#380C211yesmaximal, characteristic
14C4×C22⋊C4×C41C211yesmaximal, characteristic
15C2×#95×C41C211yesmaximal, characteristic
16C23×C4×C41C2211yescharacteristic
17C23×C4×C41C2211yescharacteristic
18C23×C4×C41C2211yescharacteristic
19C2×C4⋊C4×C41C2211yescharacteristic
20C2×C4⋊C4×C41C2211yescharacteristic
21C2×C4⋊C4×C41C2211yescharacteristic
22C2×C4⋊C4×C41C2211yescharacteristic
23C2×C4⋊C4×C41C2211yescharacteristic
24C2×C4⋊C4×C41C2211yescharacteristic
25C2×C4⋊C4×C41C2211yescharacteristic
26C2×C4⋊C4×C41C2211yescharacteristic
27C2×C4⋊C4×C41C2211yescharacteristic
28C2×C4⋊C4×C41C2211yescharacteristic
29C2×C22⋊C4×C41C2211yescharacteristic
30C2×C22⋊C4×C41C2211yescharacteristic
31C2×C22⋊C4×C41C2211yescharacteristic
32C2×C22⋊C4×C41C2211yescharacteristic
33C2×C42×C41C2211yescharacteristic
34C2×C42×C41C2211yescharacteristic
35#95×C41C2211yescharacteristic
36#95×C41C2211yescharacteristic
37#95×C41C2211yescharacteristic
38#95×C41C2211yescharacteristic
39#95×C41C2211yescharacteristic
40#95×C41C2211yescharacteristic
41#95×C41C2211yescharacteristic
42#95×C41C2211yescharacteristic
43#95×C41C2211yescharacteristic
44#95×C41C2211yescharacteristic
45#95×C41C2211yescharacteristic
46#95×C41C2211yescharacteristic
47#95×C41C2211yescharacteristic
48#95×C41C2211yescharacteristic
49#95×C41C2211yescharacteristic
50#95×C41C2211yescharacteristic
51C24×C41C2311yescharacteristic
52C22×C4×C41—22no—
53C22×C4×C41—22no—
54C22×C4×C41—22no—
55C22×C4×C41—22no—
56C22×C4×C41—22no—
57C22×C4×C41—41no—
58C22×C4×C41—41no—
59C22×C4×C41—41no—
60C22×C4×C41—41no—
61C22×C4×C41C2311yescharacteristic
62C22×C4×C41C2311yescharacteristic
63C22×C4×C41C2311yescharacteristic
64C22×C4×C41C2311yescharacteristic
65C22×C4×C41C2311yescharacteristic
66C22×C4×C41C2311yescharacteristic
67C22×C4×C41C2311yescharacteristic
68C22×C4×C41C2311yescharacteristic
69C22×C4×C41C2311yescharacteristic
70C22×C4×C41C2311yescharacteristic
71C22×C4×C41C2311yescharacteristic
72C22×C4×C41C2311yescharacteristic
73C22×C4×C41C2311yescharacteristic
74C22×C4×C41C2311yescharacteristic
75C4⋊C4×C41—22no—
76C4⋊C4×C41—22no—
77C4⋊C4×C41—22no—
78C4⋊C4×C41—41no—
79C4⋊C4×C41—41no—
80C4⋊C4×C41—41no—
81C4⋊C4×C41—41no—
82C4⋊C4×C41—41no—
83C4⋊C4×C41—41no—
84C4⋊C4×C41—41no—
85C22⋊C4×C41—22no—
86C22⋊C4×C41—22no—
87C22⋊C4×C41—22no—
88C22⋊C4×C41Q814yes—
89C42×C41—22no—
90C42×C41—41no—
91C23×C41—21no—
92C23×C41—21no—
93C23×C41—21no—
94C23×C41—21no—
95C23×C41C2×Q812yes—
96C23×C41#4112yes—
97C23×C41#4112yes—
98C23×C41C2411yescharacteristic
99C2×C4×C41—21no—
100C2×C4×C41—21no—
101C2×C4×C41—21no—
102C2×C4×C41—21no—
103C2×C4×C41—21no—
104C2×C4×C41—21no—
105C2×C4×C41—21no—
106C2×C4×C41—21no—
107C2×C4×C41—21no—
108C2×C4×C41—21no—
109C2×C4×C41—21no—
110C2×C4×C41—21no—
111C2×C4×C41—21no—
112C2×C4×C41—21no—
113C2×C4×C41—21no—
114C2×C4×C41—21no—
115C2×C4×C41—21no—
116C2×C4×C41—21no—
117C2×C4×C41—21no—
118C2×C4×C41—21no—
119C2×C4×C41—21no—
120C2×C4×C41—21no—
121C2×C4×C41—21no—
122C2×C4×C41—21no—
123C2×C4×C41—21no—
124C2×C4×C41—21no—
125C2×C4×C41—21no—
126C2×C4×C41—21no—
127C2×C4×C41—21no—
128C2×C4×C41—21no—
129C2×C4×C41—21no—
130C2×C4×C41—21no—
131C2×C4×C41—21no—
132C2×C4×C41—21no—
133C2×C4×C41—21no—
134C2×C4×C41—21no—
135C2×C4×C41—21no—
136C2×C4×C41—21no—
137C2×C4×C41—44no—
138C2×C4×C41—44no—
139C2×C4×C41—44no—
140C2×C4×C41C2×Q812yes—
141C2×C4×C41C2×Q812yes—
142C2×C4×C41#4112yes—
143C2×C4×C41#4112yes—
144C22×C41—22no—
145C22×C41—22no—
146C22×C41—22no—
147C22×C41—22no—
148C22×C41—22no—
149C22×C41—22no—
150C22×C41#12514yes—
151C22×C41C22×Q811yescharacteristic
152C22×C41C2×#4111yescharacteristic
153C22×C41C2×#4111yescharacteristic
154C22×C41C2×#4111yescharacteristic
155C22×C41C2×#4111yescharacteristic
156C22×C41H(5,𝔽2)11yescharacteristic
157C22×C41H(5,𝔽2)11yescharacteristic
158C4×C41—22no—
159C4×C41—22no—
160C4×C41—22no—
161C4×C41—22no—
162C4×C41—41no—
163C4×C41—41no—
164C4×C41—41no—
165C4×C41—41no—
166C4×C41—41no—
167C4×C41—41no—
168C4×C41—41no—
169C4×C41—41no—
170C4×C41—41no—
171C4×C41—41no—
172#2505C4111yesmaximal, characteristic, direct product factor, Sylow
173C2×C41—24no—
174C2×C41C2×#12511yescharacteristic
175C2×C41#52911yescharacteristic
176C2×C41#53811yescharacteristic
177C2×C41#55111yescharacteristic
178C2×C41#55111yescharacteristic
179C2×C41#55411yescharacteristic
180C2×C41#55411yescharacteristic
181#400C2×C4111yescharacteristic, complemented
182#400C2×C4111yescharacteristic, complemented
183#400C2×C4111yescharacteristic, complemented
184#398C2×C4111yescharacteristic, complemented
185#389C2×C4111yescharacteristic, complemented
186#387C2×C4111yescharacteristic, complemented
187#387C2×C4111yescharacteristic, complemented
188#385C2×C4111yescharacteristic
189#385C2×C4111yescharacteristic
190#385C2×C4111yescharacteristic
191#385C2×C4111yescharacteristic
192#382C2×C4111yescharacteristic, complemented
193#380C2×C4111yescharacteristic
194C4×C22⋊C4C2×C4111yescharacteristic
195C2×#95C2×C4111yescharacteristic
196C41#250511yescharacteristic, direct product factor, Sylow
197C23×C4C22×C4111yescharacteristic
198C23×C4C22×C4111yescharacteristic
199C23×C4C22×C4111yescharacteristic
200C2×C4⋊C4C22×C4111yescharacteristic
201C2×C4⋊C4C22×C4111yescharacteristic
202C2×C4⋊C4C22×C4111yescharacteristic
203C2×C4⋊C4C22×C4111yescharacteristic
204C2×C4⋊C4C22×C4111yescharacteristic
205C2×C4⋊C4C22×C4111yescharacteristic
206C2×C4⋊C4C22×C4111yescharacteristic
207C2×C4⋊C4C22×C4111yescharacteristic
208C2×C4⋊C4C22×C4111yescharacteristic
209C2×C4⋊C4C22×C4111yescharacteristic
210C2×C22⋊C4C22×C4111yescharacteristic
211C2×C22⋊C4C22×C4111yescharacteristic
212C2×C22⋊C4C22×C4111yescharacteristic
213C2×C22⋊C4C22×C4111yescharacteristic
214C2×C42C22×C4111yescharacteristic
215C2×C42C22×C4111yescharacteristic
216#95C22×C4111yescharacteristic
217#95C22×C4111yescharacteristic
218#95C22×C4111yescharacteristic
219#95C22×C4111yescharacteristic
220#95C22×C4111yescharacteristic
221#95C22×C4111yescharacteristic
222#95C22×C4111yescharacteristic
223#95C22×C4111yescharacteristic
224#95C22×C4111yescharacteristic
225#95C22×C4111yescharacteristic
226#95C22×C4111yescharacteristic
227#95C22×C4111yescharacteristic
228#95C22×C4111yescharacteristic
229#95C22×C4111yescharacteristic
230#95C22×C4111yescharacteristic
231#95C22×C4111yescharacteristic
232C24C23×C4111yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C23×C4111yescharacteristic
243C22×C4C23×C4111yescharacteristic
244C22×C4C23×C4111yescharacteristic
245C22×C4C23×C4111yescharacteristic
246C22×C4C23×C4111yescharacteristic
247C22×C4C23×C4111yescharacteristic
248C22×C4C23×C4111yescharacteristic
249C22×C4C23×C4111yescharacteristic
250C22×C4C23×C4111yescharacteristic
251C22×C4C23×C4111yescharacteristic
252C22×C4C23×C4111yescharacteristic
253C22×C4C23×C4111yescharacteristic
254C22×C4C23×C4111yescharacteristic
255C22×C4C23×C4111yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4Q8×C4114yes—
270C42—22no—
271C42—41no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23C2×Q8×C4112yes—
277C23#41×C4112yes—
278C23#41×C4112yes—
279C23C24×C4111yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4C2×Q8×C4112yes—
322C2×C4C2×Q8×C4112yes—
323C2×C4#41×C4112yes—
324C2×C4#41×C4112yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22#125×C4114yes—
332C22C22×Q8×C4111yescharacteristic
333C22C2×#41×C4111yescharacteristic
334C22C2×#41×C4111yescharacteristic
335C22C2×#41×C4111yescharacteristic
336C22C2×#41×C4111yescharacteristic
337C22H(5,𝔽2)×C4111yescharacteristic
338C22H(5,𝔽2)×C4111yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C2—24no—
354C2C2×#125×C4111yescharacteristic
355C2C41×#52911yescharacteristic
356C2C41×#53811yescharacteristic
357C2C41×#55111yescharacteristic
358C2C41×#55111yescharacteristic
359C2C41×#55411yescharacteristic
360C2C41×#55411yescharacteristic
subgroupG/H
center, socleC23×C41C24
commutator, Frattini, cosocleC23C24×C41
prime radicalC24×C41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#400C2semidirect
2. C41×#400C2semidirect
3. C41×#400C2semidirect
4. C41×#398C2semidirect
5. C41×#389C2semidirect
6. C41×#387C2semidirect
7. C41×#387C2semidirect
12. C41×#382C2semidirect
172. #2505C41direct (N × H)
181. #400C2×C41semidirect
182. #400C2×C41semidirect
183. #400C2×C41semidirect
184. #398C2×C41semidirect
185. #389C2×C41semidirect
186. #387C2×C41semidirect
187. #387C2×C41semidirect
192. #382C2×C41semidirect
196. C41#2505direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#4002
C41×#3982
C41×#3892
C41×#3872
C41×#3852
C41×#3822
C41×#3802
C4×C22⋊C4×C412
C2×#95×C412
#250541