Finite Group Databasebeta

← C11×#3343 #13066181

Subgroups — C11×#3343 #13066181

Order 1408.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#552C211yesmaximal, characteristic, complemented
2C11×#547C211yesmaximal, characteristic
3C11×#501C211yesmaximal, characteristic, complemented
4C11×#484C211yesmaximal, characteristic, complemented
5C11×#483C211yesmaximal, characteristic, complemented
6C11×#482C211yesmaximal, characteristic, complemented
7C11×#480C211yesmaximal, characteristic, complemented
8C11×#478C211yesmaximal, characteristic, complemented
9C11×#477C211yesmaximal, characteristic, complemented
10C11×#468C211yesmaximal, characteristic, complemented
11C11×#465C211yesmaximal, characteristic, complemented
12C11×#440C211yesmaximal, characteristic, complemented
13C11×#435C211yesmaximal, characteristic, complemented
14C11×#428C211yesmaximal, characteristic, complemented
15C2×C11×#107C211yesmaximal, characteristic, complemented
16C2×C11×#41—21no—
17C2×C11×SD16C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C22×C8×C11C2211yescharacteristic
20C11×C4⋊Q8C2211yescharacteristic
21C11×#126—21no—
22C11×#125—21no—
23C11×#125C2211yescharacteristic
24C11×#123—21no—
25C11×#123—21no—
26C11×#123—21no—
27C11×C22⋊Q8—21no—
28C11×C22⋊Q8C2211yescharacteristic
29C11×C22⋊Q8C2211yescharacteristic
30C11×#121C2211yescharacteristic
31C11×#121C2211yescharacteristic
32C4×Q8×C11C2211yescharacteristic
33C4×D4×C11C2211yescharacteristic
34C4×D4×C11C2211yescharacteristic
35C11×#117—21no—
36C11×#117C2211yescharacteristic
37C2×C11×C4⋊C4C2211yescharacteristic
38C2×C11×C4⋊C4C2211yescharacteristic
39C2×C11×C4⋊C4C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#107C2211yescharacteristic
45C11×#107C2211yescharacteristic
46C11×#106C2211yescharacteristic
47C11×#106C2211yescharacteristic
48C11×#106C2211yescharacteristic
49C11×C4⋊C8C2211yescharacteristic
50C11×#103C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×#103C2211yescharacteristic
53C11×#102C2211yescharacteristic
54C11×#102C2211yescharacteristic
55C11×#102C2211yescharacteristic
56C11×C22⋊C8C2211yescharacteristic
57C11×C22⋊C8C2211yescharacteristic
58C11×#97C2211yescharacteristic
59C11×#41—44no—
60C2×Q8×C11—21no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11D411yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C11×SD16—22no—
73C11×M16—22no—
74C2×C8×C11—22no—
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
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⋊C4D411yescharacteristic
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C4⋊C4C2311yescharacteristic
93C11×C4⋊C4C2311yescharacteristic
94C11×C4⋊C4C2311yescharacteristic
95C11×C22⋊C4—21no—
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C11×C22⋊C4—21no—
99C11×C22⋊C4—21no—
100C11×C22⋊C4—21no—
101C11×C22⋊C4D411yescharacteristic
102C11×C22⋊C4D411yescharacteristic
103C42×C11—21no—
104C42×C11—21no—
105C42×C11C2311yescharacteristic
106#3343C1111yesmaximal, characteristic, direct product factor, Sylow
107C23×C11—21no—
108C23×C11C2×D411yescharacteristic
109C23×C11C2×D411yescharacteristic
110Q8×C11—21no—
111Q8×C11—21no—
112Q8×C11—42no—
113D4×C11—22no—
114D4×C11—21no—
115D4×C11—21no—
116D4×C11—42no—
117D4×C11—42no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
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—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2411yescharacteristic
138C8×C11—21no—
139C8×C11—21no—
140C8×C11—21no—
141C8×C11#4112yescomplemented
142#552C2×C1111yescharacteristic, complemented
143#547C2×C1111yescharacteristic
144#501C2×C1111yescharacteristic, complemented
145#484C2×C1111yescharacteristic, complemented
146#483C2×C1111yescharacteristic, complemented
147#482C2×C1111yescharacteristic, complemented
148#480C2×C1111yescharacteristic, complemented
149#478C2×C1111yescharacteristic, complemented
150#477C2×C1111yescharacteristic, complemented
151#468C2×C1111yescharacteristic, complemented
152#465C2×C1111yescharacteristic, complemented
153#440C2×C1111yescharacteristic, complemented
154#435C2×C1111yescharacteristic, complemented
155#428C2×C1111yescharacteristic, complemented
156C2×#107C2×C1111yescharacteristic, complemented
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11AGL(1,ℤ/8)12yes—
166C22×C11C22×D411yescharacteristic
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11C2×#4111yescharacteristic
179C4×C112−1+411yescharacteristic
180C2×#41—21no—
181C2×SD16C22×C1111yescharacteristic
182C2×M16C22×C1111yescharacteristic
183C22×C8C22×C1111yescharacteristic
184C4⋊Q8C22×C1111yescharacteristic
185#126—21no—
186#125—21no—
187#125C22×C1111yescharacteristic
188#123—21no—
189#123—21no—
190#123—21no—
191C22⋊Q8—21no—
192C22⋊Q8C22×C1111yescharacteristic
193C22⋊Q8C22×C1111yescharacteristic
194#121C22×C1111yescharacteristic
195#121C22×C1111yescharacteristic
196C4×Q8C22×C1111yescharacteristic
197C4×D4C22×C1111yescharacteristic
198C4×D4C22×C1111yescharacteristic
199#117—21no—
200#117C22×C1111yescharacteristic
201C2×C4⋊C4C22×C1111yescharacteristic
202C2×C4⋊C4C22×C1111yescharacteristic
203C2×C4⋊C4C22×C1111yescharacteristic
204#107C22×C1111yescharacteristic
205#107C22×C1111yescharacteristic
206#107C22×C1111yescharacteristic
207#107C22×C1111yescharacteristic
208#107C22×C1111yescharacteristic
209#107C22×C1111yescharacteristic
210#106C22×C1111yescharacteristic
211#106C22×C1111yescharacteristic
212#106C22×C1111yescharacteristic
213C4⋊C8C22×C1111yescharacteristic
214#103C22×C1111yescharacteristic
215#103C22×C1111yescharacteristic
216#103C22×C1111yescharacteristic
217#102C22×C1111yescharacteristic
218#102C22×C1111yescharacteristic
219#102C22×C1111yescharacteristic
220C22⋊C8C22×C1111yescharacteristic
221C22⋊C8C22×C1111yescharacteristic
222#97C22×C1111yescharacteristic
223C2×C11—22no—
224C2×C11—41no—
225C2×C11—81no—
226C2×C11#54711yescharacteristic
227C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
228C2×C11#57811yescharacteristic
229#41—44no—
230C2×Q8—21no—
231C2×Q8C23×C1111yescharacteristic
232C2×D4—21no—
233C2×D4—21no—
234C2×D4D4×C1111yescharacteristic
235C2×D4C23×C1111yescharacteristic
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4C23×C1111yescharacteristic
241C22×C4C23×C1111yescharacteristic
242SD16—22no—
243M16—22no—
244C2×C8—22no—
245C2×C8C23×C1111yescharacteristic
246C2×C8C23×C1111yescharacteristic
247C2×C8C23×C1111yescharacteristic
248C2×C8C23×C1111yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4D4×C1111yescharacteristic
259C4⋊C4C23×C1111yescharacteristic
260C4⋊C4C23×C1111yescharacteristic
261C4⋊C4C23×C1111yescharacteristic
262C4⋊C4C23×C1111yescharacteristic
263C4⋊C4C23×C1111yescharacteristic
264C4⋊C4C23×C1111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4D4×C1111yescharacteristic
272C22⋊C4D4×C1111yescharacteristic
273C42—21no—
274C42—21no—
275C42C23×C1111yescharacteristic
276C11#334311yescharacteristic, direct product factor, Sylow
277C23—21no—
278C23C2×D4×C1111yescharacteristic
279C23C2×D4×C1111yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—42no—
283D4—22no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—42no—
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—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×D4×C1111yescharacteristic
304C2×C4C2×D4×C1111yescharacteristic
305C2×C4C2×D4×C1111yescharacteristic
306C2×C4C2×D4×C1111yescharacteristic
307C2×C4C24×C1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8C11×#4112yescomplemented
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22C11×AGL(1,ℤ/8)12yes—
321C22C22×D4×C1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4C2×C11×#4111yescharacteristic
334C4C11×2−1+411yescharacteristic
335C2—22no—
336C2—41no—
337C2—81no—
338C2C11×#54711yescharacteristic
339C2C2×C11×AGL(1,ℤ/8)11yescharacteristic
340C2C11×#57811yescharacteristic
subgroupG/H
center, socleC22×C11C22×D4
commutator, Frattini, cosocleC2×C4C24×C11
prime radicalC11×#547C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#552C2semidirect
3. C11×#501C2semidirect
4. C11×#484C2semidirect
5. C11×#483C2semidirect
6. C11×#482C2semidirect
7. C11×#480C2semidirect
8. C11×#478C2semidirect
9. C11×#477C2semidirect
10. C11×#468C2semidirect
11. C11×#465C2semidirect
12. C11×#440C2semidirect
13. C11×#435C2semidirect
14. C11×#428C2semidirect
15. C2×C11×#107C2semidirect
106. #3343C11direct (N × H)
141. C8×C11#41semidirect
142. #552C2×C11semidirect
144. #501C2×C11semidirect
145. #484C2×C11semidirect
146. #483C2×C11semidirect
147. #482C2×C11semidirect
148. #480C2×C11semidirect
149. #478C2×C11semidirect
150. #477C2×C11semidirect
151. #468C2×C11semidirect
152. #465C2×C11semidirect
153. #440C2×C11semidirect
154. #435C2×C11semidirect
155. #428C2×C11semidirect
156. C2×#107C2×C11semidirect
276. C11#3343direct (N × H)
311. C8C11×#41semidirect

Maximal subgroups

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

subgroupindex
C11×#5522
C11×#5472
C11×#5012
C11×#4842
C11×#4832
C11×#4822
C11×#4802
C11×#4782
C11×#4772
C11×#4682
C11×#4652
C11×#4402
C11×#4352
C11×#4282
C2×C11×#1072
#334311