Finite Group Databasebeta

← C11×#3201 #13066039

Subgroups — C11×#3201 #13066039

Order 1408.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#537C211yesmaximal, characteristic
2C11×#536C211yesmaximal, characteristic, complemented
3C11×#485C211yesmaximal, characteristic, complemented
4C11×#484C211yesmaximal, characteristic, complemented
5C11×#483C211yesmaximal, characteristic, complemented
6C11×#482C211yesmaximal, characteristic, complemented
7C11×#470C211yesmaximal, characteristic, complemented
8C11×#468C211yesmaximal, characteristic, complemented
9C11×#467C211yesmaximal, characteristic, complemented
10C11×#465C211yesmaximal, characteristic, complemented
11C11×#452C211yesmaximal, characteristic, complemented
12C11×#452C211yesmaximal, characteristic, complemented
13C11×#451C211yesmaximal, characteristic, complemented
14C11×#448C211yesmaximal, characteristic, complemented
15C11×#408C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×#41C2211yescharacteristic
18C22×Q8×C11C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C2×C11×Q16C2211yescharacteristic
21C2×C11×SD16C2211yescharacteristic
22C2×C11×SD16C2211yescharacteristic
23C2×C11×M16C2211yescharacteristic
24C22×C8×C11C2211yescharacteristic
25C11×C4⋊Q8—21no—
26C11×#124—21no—
27C11×#123—21no—
28C11×#123—21no—
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8C2211yescharacteristic
31C11×C22⋊Q8C2211yescharacteristic
32C11×C22⋊Q8C2211yescharacteristic
33C11×C22⋊Q8C2211yescharacteristic
34C11×C22⋊Q8C2211yescharacteristic
35C11×C22⋊Q8C2211yescharacteristic
36C11×#121—21no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121C2211yescharacteristic
40C11×#121C2211yescharacteristic
41C11×#117C2211yescharacteristic
42C2×C11×C4⋊C4C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#107C2211yescharacteristic
45C11×#106C2211yescharacteristic
46C11×#106C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#103C2211yescharacteristic
49C11×#103C2211yescharacteristic
50C11×#103C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×#103C2211yescharacteristic
53C11×#102C2211yescharacteristic
54C11×#102C2211yescharacteristic
55C11×C22⋊C8C2211yescharacteristic
56C11×C22⋊C8C2211yescharacteristic
57C11×C22⋊C8C2211yescharacteristic
58C11×C22⋊C8C2211yescharacteristic
59C11×#41—41no—
60C11×#41—41no—
61C11×#41—41no—
62C11×#41—41no—
63C2×Q8×C11—21no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C2×Q8×C11D411yescharacteristic
67C2×Q8×C11C2311yescharacteristic
68C2×Q8×C11C2311yescharacteristic
69C2×Q8×C11C2311yescharacteristic
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11D411yescharacteristic
74C2×D4×C11D411yescharacteristic
75C2×D4×C11D411yescharacteristic
76C2×D4×C11C2311yescharacteristic
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11C2311yescharacteristic
81C22×C4×C11C2311yescharacteristic
82C22×C4×C11C2311yescharacteristic
83C11×Q16—41no—
84C11×Q16—41no—
85C11×SD16—41no—
86C11×SD16—41no—
87C11×M16—41no—
88C2×C8×C11—41no—
89C2×C8×C11C2311yescharacteristic
90C2×C8×C11C2311yescharacteristic
91C2×C8×C11C2311yescharacteristic
92C2×C8×C11C2311yescharacteristic
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4C2311yescharacteristic
101C11×C4⋊C4C2311yescharacteristic
102C11×C4⋊C4C2311yescharacteristic
103C11×C4⋊C4C2311yescharacteristic
104C11×C22⋊C4—21no—
105C11×C22⋊C4—21no—
106C11×C22⋊C4—21no—
107C11×C22⋊C4—21no—
108C11×C22⋊C4—21no—
109C11×C22⋊C4—21no—
110C11×C22⋊C4—21no—
111C11×C22⋊C4—21no—
112C11×C22⋊C4—21no—
113C42×C11—21no—
114#3201C1111yesmaximal, characteristic, direct product factor, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C23×C11C2×D411yescharacteristic
118C23×C11C2×D411yescharacteristic
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122Q8×C11—21no—
123Q8×C11—21no—
124Q8×C11—21no—
125Q8×C11—41no—
126Q8×C11—42no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—41no—
130D4×C11—41no—
131D4×C11—41no—
132D4×C11—42no—
133D4×C11—81no—
134D4×C11—81no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—81no—
151C2×C4×C11C2×D411yescharacteristic
152C2×C4×C11C2×D411yescharacteristic
153C2×C4×C11C2×D411yescharacteristic
154C2×C4×C11C2411yescharacteristic
155C8×C11—21no—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11—21no—
159#537C2×C1111yescharacteristic
160#536C2×C1111yescharacteristic, complemented
161#485C2×C1111yescharacteristic, complemented
162#484C2×C1111yescharacteristic, complemented
163#483C2×C1111yescharacteristic, complemented
164#482C2×C1111yescharacteristic, complemented
165#470C2×C1111yescharacteristic, complemented
166#468C2×C1111yescharacteristic, complemented
167#467C2×C1111yescharacteristic, complemented
168#465C2×C1111yescharacteristic, complemented
169#452C2×C1111yescharacteristic, complemented
170#452C2×C1111yescharacteristic, complemented
171#451C2×C1111yescharacteristic, complemented
172#448C2×C1111yescharacteristic, complemented
173#408C2×C1111yescharacteristic, complemented
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11C22×D411yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11H(5,𝔽2)11yescharacteristic
198C4×C11H(5,𝔽2)11yescharacteristic
199C2×#41C22×C1111yescharacteristic
200C2×#41C22×C1111yescharacteristic
201C22×Q8C22×C1111yescharacteristic
202C2×Q16C22×C1111yescharacteristic
203C2×Q16C22×C1111yescharacteristic
204C2×SD16C22×C1111yescharacteristic
205C2×SD16C22×C1111yescharacteristic
206C2×M16C22×C1111yescharacteristic
207C22×C8C22×C1111yescharacteristic
208C4⋊Q8—21no—
209#124—21no—
210#123—21no—
211#123—21no—
212C22⋊Q8—21no—
213C22⋊Q8C22×C1111yescharacteristic
214C22⋊Q8C22×C1111yescharacteristic
215C22⋊Q8C22×C1111yescharacteristic
216C22⋊Q8C22×C1111yescharacteristic
217C22⋊Q8C22×C1111yescharacteristic
218C22⋊Q8C22×C1111yescharacteristic
219#121—21no—
220#121—21no—
221#121—21no—
222#121C22×C1111yescharacteristic
223#121C22×C1111yescharacteristic
224#117C22×C1111yescharacteristic
225C2×C4⋊C4C22×C1111yescharacteristic
226#107C22×C1111yescharacteristic
227#107C22×C1111yescharacteristic
228#106C22×C1111yescharacteristic
229#106C22×C1111yescharacteristic
230#103C22×C1111yescharacteristic
231#103C22×C1111yescharacteristic
232#103C22×C1111yescharacteristic
233#103C22×C1111yescharacteristic
234#103C22×C1111yescharacteristic
235#103C22×C1111yescharacteristic
236#102C22×C1111yescharacteristic
237#102C22×C1111yescharacteristic
238C22⋊C8C22×C1111yescharacteristic
239C22⋊C8C22×C1111yescharacteristic
240C22⋊C8C22×C1111yescharacteristic
241C22⋊C8C22×C1111yescharacteristic
242C2×C11—41no—
243C2×C11—41no—
244C2×C11—41no—
245C2×C11—81no—
246C2×C11#53411yescharacteristic
247C2×C11#57711yescharacteristic
248C2×C11#57811yescharacteristic
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—21no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8D4×C1111yescharacteristic
257C2×Q8C23×C1111yescharacteristic
258C2×Q8C23×C1111yescharacteristic
259C2×Q8C23×C1111yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4D4×C1111yescharacteristic
264C2×D4D4×C1111yescharacteristic
265C2×D4D4×C1111yescharacteristic
266C2×D4C23×C1111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4C23×C1111yescharacteristic
271C22×C4C23×C1111yescharacteristic
272C22×C4C23×C1111yescharacteristic
273Q16—41no—
274Q16—41no—
275SD16—41no—
276SD16—41no—
277M16—41no—
278C2×C8—41no—
279C2×C8C23×C1111yescharacteristic
280C2×C8C23×C1111yescharacteristic
281C2×C8C23×C1111yescharacteristic
282C2×C8C23×C1111yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4C23×C1111yescharacteristic
291C4⋊C4C23×C1111yescharacteristic
292C4⋊C4C23×C1111yescharacteristic
293C4⋊C4C23×C1111yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C42—21no—
304C11#320111yescharacteristic, direct product factor, Sylow
305C23—21no—
306C23C2×D4×C1111yescharacteristic
307C23C2×D4×C1111yescharacteristic
308C23C2×D4×C1111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—41no—
316Q8—42no—
317D4—21no—
318D4—21no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—42no—
323D4—81no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4C2×D4×C1111yescharacteristic
342C2×C4C2×D4×C1111yescharacteristic
343C2×C4C2×D4×C1111yescharacteristic
344C2×C4C24×C1111yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C22×D4×C1111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4C11×H(5,𝔽2)11yescharacteristic
373C4C11×H(5,𝔽2)11yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—81no—
378C2C11×#53411yescharacteristic
379C2C11×#57711yescharacteristic
380C2C11×#57811yescharacteristic
subgroupG/H
center, socleC22×C11C22×D4
commutator, Frattini, cosocleC2×C4C24×C11
prime radicalC11×#537C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#536C2semidirect
3. C11×#485C2semidirect
4. C11×#484C2semidirect
5. C11×#483C2semidirect
6. C11×#482C2semidirect
7. C11×#470C2semidirect
8. C11×#468C2semidirect
9. C11×#467C2semidirect
10. C11×#465C2semidirect
11. C11×#452C2semidirect
12. C11×#452C2semidirect
13. C11×#451C2semidirect
14. C11×#448C2semidirect
15. C11×#408C2semidirect
114. #3201C11direct (N × H)
160. #536C2×C11semidirect
161. #485C2×C11semidirect
162. #484C2×C11semidirect
163. #483C2×C11semidirect
164. #482C2×C11semidirect
165. #470C2×C11semidirect
166. #468C2×C11semidirect
167. #467C2×C11semidirect
168. #465C2×C11semidirect
169. #452C2×C11semidirect
170. #452C2×C11semidirect
171. #451C2×C11semidirect
172. #448C2×C11semidirect
173. #408C2×C11semidirect
304. C11#3201direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5372
C11×#5362
C11×#4852
C11×#4842
C11×#4832
C11×#4822
C11×#4702
C11×#4682
C11×#4672
C11×#4652
C11×#4522
C11×#4512
C11×#4482
C11×#4082
#320111