Finite Group Databasebeta

← C11×#3111 #13065949

Subgroups — C11×#3111 #13065949

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#529C211yesmaximal, characteristic, complemented
2C4×C11×#41C211yesmaximal, characteristic, complemented
3C11×#485C211yesmaximal, characteristic, complemented
4C11×#482C211yesmaximal, characteristic, complemented
5C11×#479C211yesmaximal, characteristic, complemented
6C11×#478C211yesmaximal, characteristic, complemented
7C11×#464C211yesmaximal, characteristic, complemented
8C11×#463C211yesmaximal, characteristic, complemented
9C11×#452C211yesmaximal, characteristic, complemented
10C11×#449C211yesmaximal, characteristic
11C11×#442C211yesmaximal, characteristic, complemented
12C11×#441C211yesmaximal, characteristic, complemented
13C11×#440C211yesmaximal, characteristic, complemented
14C11×#440C211yesmaximal, characteristic, complemented
15C11×#432C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×Q16C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C11×#126—21no—
22C11×#125C2211yescharacteristic
23C11×#124C2211yescharacteristic
24C11×#123—21no—
25C11×C22⋊Q8C2211yescharacteristic
26C11×#121C2211yescharacteristic
27C4×Q8×C11C2211yescharacteristic
28C4×Q8×C11C2211yescharacteristic
29C4×Q8×C11C2211yescharacteristic
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C4×D4×C11C2211yescharacteristic
34C4×D4×C11C2211yescharacteristic
35C4×D4×C11C2211yescharacteristic
36C11×#117—21no—
37C11×#117—21no—
38C11×#117C2211yescharacteristic
39C2×C42×C11—21no—
40C2×C42×C11C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×C4⋊C8C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#103C2211yescharacteristic
49C11×#103C2211yescharacteristic
50C11×#103C2211yescharacteristic
51C11×#102C2211yescharacteristic
52C11×#102C2211yescharacteristic
53C11×#102C2211yescharacteristic
54C11×#102C2211yescharacteristic
55C11×C22⋊C8C2211yescharacteristic
56C11×C22⋊C8C2211yescharacteristic
57C11×#97C2211yescharacteristic
58C11×#97C2211yescharacteristic
59C11×#41—22no—
60C11×#41—22no—
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11C2311yescharacteristic
66C2×D4×C11C2311yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11D411yescharacteristic
72C22×C4×C11D411yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C11×Q16—22no—
75C11×SD16—22no—
76C11×SD16—22no—
77C11×D8—22no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4C2311yescharacteristic
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C11×C22⋊C4—21no—
99C11×C22⋊C4—21no—
100C42×C11—21no—
101C42×C11—21no—
102C42×C11—21no—
103C42×C11—21no—
104C42×C11D411yescharacteristic
105C42×C11D411yescharacteristic
106C42×C11C2311yescharacteristic
107C42×C11C2311yescharacteristic
108#3111C1111yesmaximal, characteristic, direct product factor, Sylow
109C23×C11—21no—
110C23×C11—21no—
111C23×C11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115Q8×C11#4112yes—
116D4×C11—24no—
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—42no—
121D4×C11#4112yes—
122C2×C4×C11—24no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2×D411yescharacteristic
140C2×C4×C11C2×D411yescharacteristic
141C2×C4×C11C2411yescharacteristic
142C8×C11—21no—
143C8×C11—21no—
144C8×C11—21no—
145C8×C11—21no—
146#529C2×C1111yescharacteristic, complemented
147C4×#41C2×C1111yescharacteristic, complemented
148#485C2×C1111yescharacteristic, complemented
149#482C2×C1111yescharacteristic, complemented
150#479C2×C1111yescharacteristic, complemented
151#478C2×C1111yescharacteristic, complemented
152#464C2×C1111yescharacteristic, complemented
153#463C2×C1111yescharacteristic, complemented
154#452C2×C1111yescharacteristic, complemented
155#449C2×C1111yescharacteristic
156#442C2×C1111yescharacteristic, complemented
157#441C2×C1111yescharacteristic, complemented
158#440C2×C1111yescharacteristic, complemented
159#440C2×C1111yescharacteristic, complemented
160#432C2×C1111yescharacteristic, complemented
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11C22×D411yescharacteristic
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11C2×#4111yescharacteristic
183C4×C11C2×#4111yescharacteristic
184C2×#41C22×C1111yescharacteristic
185C2×Q16C22×C1111yescharacteristic
186C2×SD16C22×C1111yescharacteristic
187C2×SD16C22×C1111yescharacteristic
188C2×D8C22×C1111yescharacteristic
189#126—21no—
190#125C22×C1111yescharacteristic
191#124C22×C1111yescharacteristic
192#123—21no—
193C22⋊Q8C22×C1111yescharacteristic
194#121C22×C1111yescharacteristic
195C4×Q8C22×C1111yescharacteristic
196C4×Q8C22×C1111yescharacteristic
197C4×Q8C22×C1111yescharacteristic
198C4×D4—21no—
199C4×D4—21no—
200C4×D4—21no—
201C4×D4C22×C1111yescharacteristic
202C4×D4C22×C1111yescharacteristic
203C4×D4C22×C1111yescharacteristic
204#117—21no—
205#117—21no—
206#117C22×C1111yescharacteristic
207C2×C42—21no—
208C2×C42C22×C1111yescharacteristic
209#107C22×C1111yescharacteristic
210#107C22×C1111yescharacteristic
211#106C22×C1111yescharacteristic
212#106C22×C1111yescharacteristic
213C4⋊C8C22×C1111yescharacteristic
214C4⋊C8C22×C1111yescharacteristic
215#103C22×C1111yescharacteristic
216#103C22×C1111yescharacteristic
217#103C22×C1111yescharacteristic
218#103C22×C1111yescharacteristic
219#102C22×C1111yescharacteristic
220#102C22×C1111yescharacteristic
221#102C22×C1111yescharacteristic
222#102C22×C1111yescharacteristic
223C22⋊C8C22×C1111yescharacteristic
224C22⋊C8C22×C1111yescharacteristic
225#97C22×C1111yescharacteristic
226#97C22×C1111yescharacteristic
227C2×C11—41no—
228C2×C11—42no—
229C2×C11—81no—
230C2×C11#52511yescharacteristic
231C2×C11#57511yescharacteristic
232C2×C11#57511yescharacteristic
233#41—22no—
234#41—22no—
235C2×Q8C23×C1111yescharacteristic
236C2×Q8C23×C1111yescharacteristic
237C2×D4—21no—
238C2×D4—21no—
239C2×D4C23×C1111yescharacteristic
240C2×D4C23×C1111yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4D4×C1111yescharacteristic
246C22×C4D4×C1111yescharacteristic
247C22×C4C23×C1111yescharacteristic
248Q16—22no—
249SD16—22no—
250SD16—22no—
251D8—22no—
252C2×C8C23×C1111yescharacteristic
253C2×C8C23×C1111yescharacteristic
254C2×C8C23×C1111yescharacteristic
255C2×C8C23×C1111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4C23×C1111yescharacteristic
263C4⋊C4C23×C1111yescharacteristic
264C4⋊C4C23×C1111yescharacteristic
265C4⋊C4C23×C1111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C42—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42D4×C1111yescharacteristic
279C42D4×C1111yescharacteristic
280C42C23×C1111yescharacteristic
281C42C23×C1111yescharacteristic
282C11#311111yescharacteristic, direct product factor, Sylow
283C23—21no—
284C23—21no—
285C23C2×D4×C1111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8C11×#4112yes—
290D4—24no—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—42no—
295D4C11×#4112yes—
296C2×C4—24no—
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—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4C2×D4×C1111yescharacteristic
311C2×C4C2×D4×C1111yescharacteristic
312C2×C4C2×D4×C1111yescharacteristic
313C2×C4C2×D4×C1111yescharacteristic
314C2×C4C2×D4×C1111yescharacteristic
315C2×C4C24×C1111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C22×D4×C1111yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4C2×C11×#4111yescharacteristic
342C4C2×C11×#4111yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2C11×#52511yescharacteristic
347C2C11×#57511yescharacteristic
348C2C11×#57511yescharacteristic
subgroupG/H
center, socleC22×C11C22×D4
commutator, Frattini, cosocleC2×C4C24×C11
prime radicalC11×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#529C2semidirect
2. C4×C11×#41C2semidirect
3. C11×#485C2semidirect
4. C11×#482C2semidirect
5. C11×#479C2semidirect
6. C11×#478C2semidirect
7. C11×#464C2semidirect
8. C11×#463C2semidirect
9. C11×#452C2semidirect
11. C11×#442C2semidirect
12. C11×#441C2semidirect
13. C11×#440C2semidirect
14. C11×#440C2semidirect
15. C11×#432C2semidirect
108. #3111C11direct (N × H)
146. #529C2×C11semidirect
147. C4×#41C2×C11semidirect
148. #485C2×C11semidirect
149. #482C2×C11semidirect
150. #479C2×C11semidirect
151. #478C2×C11semidirect
152. #464C2×C11semidirect
153. #463C2×C11semidirect
154. #452C2×C11semidirect
156. #442C2×C11semidirect
157. #441C2×C11semidirect
158. #440C2×C11semidirect
159. #440C2×C11semidirect
160. #432C2×C11semidirect
282. C11#3111direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5292
C4×C11×#412
C11×#4852
C11×#4822
C11×#4792
C11×#4782
C11×#4642
C11×#4632
C11×#4522
C11×#4492
C11×#4422
C11×#4412
C11×#4402
C11×#4322
#311111