Finite Group Databasebeta

← C11×#3524 #13066362

Subgroups — C11×#3524 #13066362

Order 1408.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#559C213yesmaximal, complemented
2C11×#557C211yesmaximal, characteristic, complemented
3C11×#555C213yesmaximal, complemented
4C11×#553C213yesmaximal, complemented
5C11×#552C213yesmaximal, complemented
6C11×#550C211yesmaximal, characteristic, complemented
7C11×#548C211yesmaximal, characteristic, complemented
8C11×#548C211yesmaximal, characteristic, complemented
9C11×#542C213yesmaximal, complemented
10C11×#540C213yesmaximal, complemented
11C11×#529C213yesmaximal, complemented
12C11×#529C213yesmaximal, complemented
13C11×#520C211yesmaximal, characteristic, complemented
14C11×#519C211yesmaximal, characteristic, complemented
15C4×C11×#41C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×#41C2211yescharacteristic
18C22×Q8×C11C2211yescharacteristic
19C11×C4⋊Q8C2213yes—
20C11×#127C2213yes—
21C11×#126C2211yescharacteristic
22C11×#126C2213yes—
23C11×#126C2216yes—
24C11×#125C2213yes—
25C11×#125C2213yes—
26C11×#125C2213yes—
27C11×#124C2213yes—
28C11×#124C2213yes—
29C11×#124C2213yes—
30C11×#124C2216yes—
31C11×#123C2216yes—
32C11×#123C2213yes—
33C11×#123C2213yes—
34C11×#123C2216yes—
35C11×C22⋊Q8C2213yes—
36C11×C22⋊Q8C2213yes—
37C11×C22⋊Q8C2213yes—
38C11×#121C2213yes—
39C11×#121C2213yes—
40C11×#121C2213yes—
41C11×#121C2213yes—
42C11×#121C2216yes—
43C11×#121C2213yes—
44C4×Q8×C11C2211yescharacteristic
45C4×Q8×C11C2211yescharacteristic
46C4×Q8×C11C2213yes—
47C4×Q8×C11C2211yescharacteristic
48C4×Q8×C11C2213yes—
49C4×Q8×C11C2211yescharacteristic
50C4×Q8×C11C2213yes—
51C4×D4×C11C2213yes—
52C4×D4×C11C2213yes—
53C4×D4×C11C2213yes—
54C4×D4×C11C2213yes—
55C4×D4×C11C2213yes—
56C4×D4×C11C2213yes—
57C4×D4×C11C2213yes—
58C4×D4×C11C2216yes—
59C11×#117C2213yes—
60C11×#117C2213yes—
61C11×#117C2213yes—
62C11×#117C2213yes—
63C11×#117C2216yes—
64C2×C11×C4⋊C4C2213yes—
65C2×C42×C11C2213yes—
66C11×#41—24no—
67C11×#41—24no—
68C2×Q8×C11—24no—
69C2×Q8×C11C2313yes—
70C2×Q8×C11C2313yes—
71C2×Q8×C11C2311yescharacteristic
72C2×D4×C11C2313yes—
73C2×D4×C11C2313yes—
74C2×D4×C11C2313yes—
75C2×D4×C11C2313yes—
76C2×D4×C11C2316yes—
77C2×D4×C11C2313yes—
78C22×C4×C11C2313yes—
79C22×C4×C11C2313yes—
80C22×C4×C11C2313yes—
81C22×C4×C11C2313yes—
82C22×C4×C11C2313yes—
83C22×C4×C11C2316yes—
84C11×C4⋊C4C2313yes—
85C11×C4⋊C4C2313yes—
86C11×C4⋊C4C2313yes—
87C11×C4⋊C4C2311yescharacteristic
88C11×C4⋊C4C2313yes—
89C11×C4⋊C4C2313yes—
90C11×C4⋊C4C2313yes—
91C11×C4⋊C4C2313yes—
92C11×C4⋊C4C2313yes—
93C11×C4⋊C4C2316yes—
94C11×C4⋊C4C2311yescharacteristic
95C11×C4⋊C4C2313yes—
96C11×C4⋊C4C2313yes—
97C11×C4⋊C4C2311yescharacteristic
98C11×C4⋊C4C2313yes—
99C11×C22⋊C4C2311yescharacteristic
100C11×C22⋊C4C2313yes—
101C11×C22⋊C4C2313yes—
102C11×C22⋊C4C2313yes—
103C11×C22⋊C4C2316yes—
104C11×C22⋊C4C2313yes—
105C11×C22⋊C4C2316yes—
106C11×C22⋊C4C2311yescharacteristic
107C11×C22⋊C4C2313yes—
108C11×C22⋊C4C2311yescharacteristic
109C11×C22⋊C4C2313yes—
110C11×C22⋊C4C2316yes—
111C11×C22⋊C4C2313yes—
112C42×C11C2311yescharacteristic
113C42×C11C2313yes—
114C42×C11C2313yes—
115C42×C11C2313yes—
116C42×C11C2316yes—
117C42×C11C2313yes—
118C42×C11C2313yes—
119#3524C1111yesmaximal, characteristic, direct product factor, Sylow
120C23×C11C2411yescharacteristic
121C23×C11C2413yes—
122C23×C11C2413yes—
123Q8×C11—26no—
124Q8×C11—43no—
125Q8×C11#4114yes—
126D4×C11—26no—
127D4×C11—26no—
128D4×C11—43no—
129D4×C11—43no—
130D4×C11—43no—
131D4×C11—46no—
132C2×C4×C11—26no—
133C2×C4×C11—26no—
134C2×C4×C11—26no—
135C2×C4×C11—43no—
136C2×C4×C11—46no—
137C2×C4×C11—43no—
138C2×C4×C11C2411yescharacteristic
139C2×C4×C11C2411yescharacteristic
140C2×C4×C11C2411yescharacteristic
141C2×C4×C11C2413yes—
142C2×C4×C11C2411yescharacteristic
143C2×C4×C11C2413yes—
144C2×C4×C11C2411yescharacteristic
145C2×C4×C11C2413yes—
146C2×C4×C11C2413yes—
147C2×C4×C11C2413yes—
148C2×C4×C11C2411yescharacteristic
149C2×C4×C11C2413yes—
150#559C2×C1113yescomplemented
151#557C2×C1111yescharacteristic, complemented
152#555C2×C1113yescomplemented
153#553C2×C1113yescomplemented
154#552C2×C1113yescomplemented
155#550C2×C1111yescharacteristic, complemented
156#548C2×C1111yescharacteristic, complemented
157#548C2×C1111yescharacteristic, complemented
158#542C2×C1113yescomplemented
159#540C2×C1113yescomplemented
160#529C2×C1113yescomplemented
161#529C2×C1113yescomplemented
162#520C2×C1111yescharacteristic, complemented
163#519C2×C1111yescharacteristic, complemented
164C4×#41C2×C1111yescharacteristic, complemented
165C22×C11—21no—
166C22×C11—23no—
167C22×C11—23no—
168C22×C11—23no—
169C22×C11—23no—
170C22×C11—23no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—23no—
174C22×C11C2511yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—23no—
178C4×C11—21no—
179C4×C11—23no—
180C4×C11—21no—
181C4×C11—23no—
182C4×C11—23no—
183C4×C11—21no—
184C4×C11—23no—
185C4×C11—21no—
186C4×C11C2×#4116yes—
187C2×#41C22×C1111yescharacteristic
188C2×#41C22×C1111yescharacteristic
189C22×Q8C22×C1111yescharacteristic
190C4⋊Q8C22×C1113yes—
191#127C22×C1113yes—
192#126C22×C1111yescharacteristic
193#126C22×C1113yes—
194#126C22×C1116yes—
195#125C22×C1113yes—
196#125C22×C1113yes—
197#125C22×C1113yes—
198#124C22×C1113yes—
199#124C22×C1113yes—
200#124C22×C1113yes—
201#124C22×C1116yes—
202#123C22×C1116yes—
203#123C22×C1113yes—
204#123C22×C1113yes—
205#123C22×C1116yes—
206C22⋊Q8C22×C1113yes—
207C22⋊Q8C22×C1113yes—
208C22⋊Q8C22×C1113yes—
209#121C22×C1113yes—
210#121C22×C1113yes—
211#121C22×C1113yes—
212#121C22×C1113yes—
213#121C22×C1116yes—
214#121C22×C1113yes—
215C4×Q8C22×C1111yescharacteristic
216C4×Q8C22×C1111yescharacteristic
217C4×Q8C22×C1113yes—
218C4×Q8C22×C1111yescharacteristic
219C4×Q8C22×C1113yes—
220C4×Q8C22×C1111yescharacteristic
221C4×Q8C22×C1113yes—
222C4×D4C22×C1113yes—
223C4×D4C22×C1113yes—
224C4×D4C22×C1113yes—
225C4×D4C22×C1113yes—
226C4×D4C22×C1113yes—
227C4×D4C22×C1113yes—
228C4×D4C22×C1113yes—
229C4×D4C22×C1116yes—
230#117C22×C1113yes—
231#117C22×C1113yes—
232#117C22×C1113yes—
233#117C22×C1113yes—
234#117C22×C1116yes—
235C2×C4⋊C4C22×C1113yes—
236C2×C42C22×C1113yes—
237C2×C11—41no—
238C2×C11—43no—
239C2×C11—43no—
240C2×C11C22×#4111yescharacteristic
241C2×C11#58511yescharacteristic
242C2×C11#58511yescharacteristic
243#41—24no—
244#41—24no—
245C2×Q8—24no—
246C2×Q8C23×C1113yes—
247C2×Q8C23×C1113yes—
248C2×Q8C23×C1111yescharacteristic
249C2×D4C23×C1113yes—
250C2×D4C23×C1113yes—
251C2×D4C23×C1113yes—
252C2×D4C23×C1113yes—
253C2×D4C23×C1116yes—
254C2×D4C23×C1113yes—
255C22×C4C23×C1113yes—
256C22×C4C23×C1113yes—
257C22×C4C23×C1113yes—
258C22×C4C23×C1113yes—
259C22×C4C23×C1113yes—
260C22×C4C23×C1116yes—
261C4⋊C4C23×C1113yes—
262C4⋊C4C23×C1113yes—
263C4⋊C4C23×C1113yes—
264C4⋊C4C23×C1111yescharacteristic
265C4⋊C4C23×C1113yes—
266C4⋊C4C23×C1113yes—
267C4⋊C4C23×C1113yes—
268C4⋊C4C23×C1113yes—
269C4⋊C4C23×C1113yes—
270C4⋊C4C23×C1116yes—
271C4⋊C4C23×C1111yescharacteristic
272C4⋊C4C23×C1113yes—
273C4⋊C4C23×C1113yes—
274C4⋊C4C23×C1111yescharacteristic
275C4⋊C4C23×C1113yes—
276C22⋊C4C23×C1111yescharacteristic
277C22⋊C4C23×C1113yes—
278C22⋊C4C23×C1113yes—
279C22⋊C4C23×C1113yes—
280C22⋊C4C23×C1116yes—
281C22⋊C4C23×C1113yes—
282C22⋊C4C23×C1116yes—
283C22⋊C4C23×C1111yescharacteristic
284C22⋊C4C23×C1113yes—
285C22⋊C4C23×C1111yescharacteristic
286C22⋊C4C23×C1113yes—
287C22⋊C4C23×C1116yes—
288C22⋊C4C23×C1113yes—
289C42C23×C1111yescharacteristic
290C42C23×C1113yes—
291C42C23×C1113yes—
292C42C23×C1113yes—
293C42C23×C1116yes—
294C42C23×C1113yes—
295C42C23×C1113yes—
296C11#352411yescharacteristic, direct product factor, Sylow
297C23C24×C1111yescharacteristic
298C23C24×C1113yes—
299C23C24×C1113yes—
300Q8—26no—
301Q8—43no—
302Q8C11×#4114yes—
303D4—26no—
304D4—26no—
305D4—43no—
306D4—43no—
307D4—43no—
308D4—46no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—26no—
312C2×C4—43no—
313C2×C4—46no—
314C2×C4—43no—
315C2×C4C24×C1111yescharacteristic
316C2×C4C24×C1111yescharacteristic
317C2×C4C24×C1111yescharacteristic
318C2×C4C24×C1113yes—
319C2×C4C24×C1111yescharacteristic
320C2×C4C24×C1113yes—
321C2×C4C24×C1111yescharacteristic
322C2×C4C24×C1113yes—
323C2×C4C24×C1113yes—
324C2×C4C24×C1113yes—
325C2×C4C24×C1111yescharacteristic
326C2×C4C24×C1113yes—
327C22—21no—
328C22—23no—
329C22—23no—
330C22—23no—
331C22—23no—
332C22—23no—
333C22—21no—
334C22—21no—
335C22—23no—
336C22C25×C1111yescharacteristic
337C4—21no—
338C4—21no—
339C4—23no—
340C4—21no—
341C4—23no—
342C4—21no—
343C4—23no—
344C4—23no—
345C4—21no—
346C4—23no—
347C4—21no—
348C4C2×C11×#4116yes—
349C2—41no—
350C2—43no—
351C2—43no—
352C2C22×C11×#4111yescharacteristic
353C2C11×#58511yescharacteristic
354C2C11×#58511yescharacteristic
subgroupG/H
center, socleC22×C11C25
commutator, Frattini, cosocleC22C25×C11
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#559C2semidirect
2. C11×#557C2semidirect
3. C11×#555C2semidirect
4. C11×#553C2semidirect
5. C11×#552C2semidirect
6. C11×#550C2semidirect
7. C11×#548C2semidirect
8. C11×#548C2semidirect
9. C11×#542C2semidirect
10. C11×#540C2semidirect
11. C11×#529C2semidirect
12. C11×#529C2semidirect
13. C11×#520C2semidirect
14. C11×#519C2semidirect
15. C4×C11×#41C2semidirect
119. #3524C11direct (N × H)
150. #559C2×C11semidirect
151. #557C2×C11semidirect
152. #555C2×C11semidirect
153. #553C2×C11semidirect
154. #552C2×C11semidirect
155. #550C2×C11semidirect
156. #548C2×C11semidirect
157. #548C2×C11semidirect
158. #542C2×C11semidirect
159. #540C2×C11semidirect
160. #529C2×C11semidirect
161. #529C2×C11semidirect
162. #520C2×C11semidirect
163. #519C2×C11semidirect
164. C4×#41C2×C11semidirect
296. C11#3524direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5592
C11×#5572
C11×#5552
C11×#5532
C11×#5522
C11×#5502
C11×#5482
C11×#5422
C11×#5402
C11×#5292
C11×#5202
C11×#5192
C4×C11×#412
#352411