Finite Group Databasebeta

← C11×#3275 #13066113

Subgroups — C11×#3275 #13066113

Order 1408.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#137C211yesmaximal, characteristic, complemented
2C2×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C11×#548C211yesmaximal, characteristic, complemented
4C11×#546C211yesmaximal, characteristic, complemented
5C11×#495C211yesmaximal, characteristic, complemented
6C11×#470C211yesmaximal, characteristic, complemented
7C11×#469C211yesmaximal, characteristic, complemented
8C11×#464C211yesmaximal, characteristic, complemented
9C11×#463C211yesmaximal, characteristic, complemented
10C11×#452C211yesmaximal, characteristic, complemented
11C11×#450C211yesmaximal, characteristic, complemented
12C11×#449C211yesmaximal, characteristic, complemented
13C11×#448C211yesmaximal, characteristic, complemented
14C4×C11×SD16C211yesmaximal, characteristic, complemented
15C11×#436C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×#41C2211yescharacteristic
18C22×Q8×C11C2211yescharacteristic, complemented
19C22×D4×C11C2211yescharacteristic
20C11×#137—24no—
21C11×AGL(1,ℤ/8)—24no—
22C2×C11×Q16C2211yescharacteristic, complemented
23C2×C11×Q16C2211yescharacteristic, complemented
24C2×C11×SD16C2211yescharacteristic
25C2×C11×SD16C2211yescharacteristic
26C2×C11×SD16C2211yescharacteristic
27C2×C11×SD16C2211yescharacteristic
28C2×C11×SD16C2211yescharacteristic, complemented
29C2×C11×D8C2211yescharacteristic
30C2×C11×D8C2211yescharacteristic
31C2×C11×M16C2211yescharacteristic
32C2×C11×M16C2211yescharacteristic, complemented
33C11×#124—21no—
34C11×#124C2211yescharacteristic
35C11×#124C2211yescharacteristic, complemented
36C11×#123—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8C2211yescharacteristic
39C11×C22⋊Q8C2211yescharacteristic
40C11×#121—21no—
41C11×#121—21no—
42C11×#121C2211yescharacteristic
43C11×#121C2211yescharacteristic, complemented
44C11×#120—21no—
45C4×Q8×C11C2211yescharacteristic, complemented
46C4×D4×C11—21no—
47C4×D4×C11C2211yescharacteristic
48C4×D4×C11C2211yescharacteristic
49C2×C11×C22⋊C4—21no—
50C11×#106C2211yescharacteristic, complemented
51C11×C4⋊C8C2211yescharacteristic, complemented
52C11×#103C2211yescharacteristic, complemented
53C11×#103C2211yescharacteristic, complemented
54C11×#103C2211yescharacteristic, complemented
55C11×#102C2211yescharacteristic
56C11×#102C2211yescharacteristic
57C11×#102C2211yescharacteristic, complemented
58C11×C22⋊C8C2211yescharacteristic
59C11×C22⋊C8C2211yescharacteristic, complemented
60C4×C8×C11C2211yescharacteristic, complemented
61C24×C11—21no—
62C11×#41—22no—
63C11×#41—22no—
64C11×#41—41no—
65C11×#41—41no—
66C2×Q8×C11—21no—
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C2×Q8×C11C2311yescharacteristic
70C2×Q8×C11C2311yescharacteristic
71C2×Q8×C11C2311yescharacteristic
72C2×D4×C11—22no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C2×D4×C11D411yescharacteristic
80C2×D4×C11C2311yescharacteristic
81C2×D4×C11C2311yescharacteristic
82C2×D4×C11C2311yescharacteristic
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11C2311yescharacteristic
88C22×C4×C11C2311yescharacteristic
89C11×Q16—22no—
90C11×Q16—22no—
91C11×SD16—22no—
92C11×SD16—22no—
93C11×SD16—41no—
94C11×SD16—41no—
95C11×SD16D414yescomplemented
96C11×D8—22no—
97C11×D8—22no—
98C11×M16—22no—
99C11×M16—22no—
100C2×C8×C11C2311yescharacteristic
101C2×C8×C11C2311yescharacteristic
102C2×C8×C11C2311yescharacteristic
103C2×C8×C11C2311yescharacteristic
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4D411yescharacteristic
108C11×C4⋊C4C2311yescharacteristic
109C11×C4⋊C4C2311yescharacteristic
110C11×C22⋊C4—21no—
111C11×C22⋊C4—21no—
112C11×C22⋊C4—21no—
113C11×C22⋊C4—21no—
114C11×C22⋊C4—21no—
115C11×C22⋊C4—21no—
116C11×C22⋊C4—21no—
117C11×C22⋊C4—21no—
118C11×C22⋊C4—21no—
119C11×C22⋊C4D411yescharacteristic
120C11×C22⋊C4D411yescharacteristic
121C42×C11—21no—
122C42×C11C2311yescharacteristic
123#3275C1111yesmaximal, characteristic, direct product factor, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—81no—
130C23×C11C2×D411yescharacteristic
131C23×C11C2×D411yescharacteristic
132Q8×C11—21no—
133Q8×C11—21no—
134Q8×C11—21no—
135Q8×C11—21no—
136Q8×C11—21no—
137Q8×C11—42no—
138Q8×C11C2×D412yes—
139D4×C11—21no—
140D4×C11—21no—
141D4×C11—21no—
142D4×C11—21no—
143D4×C11—21no—
144D4×C11—41no—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11—42no—
148D4×C11—42no—
149D4×C11—81no—
150D4×C11C2×D412yes—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—81no—
164C2×C4×C11C2×D411yescharacteristic
165C2×C4×C11C2×D411yescharacteristic
166C2×C4×C11C2×D411yescharacteristic
167C2×C4×C11C2×D411yescharacteristic
168C2×C4×C11C2411yescharacteristic
169C8×C11—21no—
170C8×C11—21no—
171C8×C11—21no—
172C8×C11C2×D412yes—
173C2×#137C2×C1111yescharacteristic, complemented
174C2×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
175#548C2×C1111yescharacteristic, complemented
176#546C2×C1111yescharacteristic, complemented
177#495C2×C1111yescharacteristic, complemented
178#470C2×C1111yescharacteristic, complemented
179#469C2×C1111yescharacteristic, complemented
180#464C2×C1111yescharacteristic, complemented
181#463C2×C1111yescharacteristic, complemented
182#452C2×C1111yescharacteristic, complemented
183#450C2×C1111yescharacteristic, complemented
184#449C2×C1111yescharacteristic, complemented
185#448C2×C1111yescharacteristic, complemented
186C4×SD16C2×C1111yescharacteristic, complemented
187#436C2×C1111yescharacteristic, complemented
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—22no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—84no—
204C22×C11C22×D411yescharacteristic
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—22no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11C22×D411yescharacteristic
215C4×C11H(5,𝔽2)11yescharacteristic
216C2×#41C22×C1111yescharacteristic
217C2×#41C22×C1111yescharacteristic
218C22×Q8C22×C1111yescharacteristic, complemented
219C22×D4C22×C1111yescharacteristic
220#137—24no—
221AGL(1,ℤ/8)—24no—
222C2×Q16C22×C1111yescharacteristic, complemented
223C2×Q16C22×C1111yescharacteristic, complemented
224C2×SD16C22×C1111yescharacteristic
225C2×SD16C22×C1111yescharacteristic
226C2×SD16C22×C1111yescharacteristic
227C2×SD16C22×C1111yescharacteristic
228C2×SD16C22×C1111yescharacteristic, complemented
229C2×D8C22×C1111yescharacteristic
230C2×D8C22×C1111yescharacteristic
231C2×M16C22×C1111yescharacteristic
232C2×M16C22×C1111yescharacteristic, complemented
233#124—21no—
234#124C22×C1111yescharacteristic
235#124C22×C1111yescharacteristic, complemented
236#123—21no—
237C22⋊Q8—21no—
238C22⋊Q8C22×C1111yescharacteristic
239C22⋊Q8C22×C1111yescharacteristic
240#121—21no—
241#121—21no—
242#121C22×C1111yescharacteristic
243#121C22×C1111yescharacteristic, complemented
244#120—21no—
245C4×Q8C22×C1111yescharacteristic, complemented
246C4×D4—21no—
247C4×D4C22×C1111yescharacteristic
248C4×D4C22×C1111yescharacteristic
249C2×C22⋊C4—21no—
250#106C22×C1111yescharacteristic, complemented
251C4⋊C8C22×C1111yescharacteristic, complemented
252#103C22×C1111yescharacteristic, complemented
253#103C22×C1111yescharacteristic, complemented
254#103C22×C1111yescharacteristic, complemented
255#102C22×C1111yescharacteristic
256#102C22×C1111yescharacteristic
257#102C22×C1111yescharacteristic, complemented
258C22⋊C8C22×C1111yescharacteristic
259C22⋊C8C22×C1111yescharacteristic, complemented
260C4×C8C22×C1111yescharacteristic, complemented
261C2×C11—41no—
262C2×C11—41no—
263C2×C11—42no—
264C2×C11—81no—
265C2×C11—81no—
266C2×C11D4211yescharacteristic
267C2×C11#57511yescharacteristic
268C2×C11#57711yescharacteristic
269C24—21no—
270#41—22no—
271#41—22no—
272#41—41no—
273#41—41no—
274C2×Q8—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8C23×C1111yescharacteristic
278C2×Q8C23×C1111yescharacteristic
279C2×Q8C23×C1111yescharacteristic
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C2×D4D4×C1111yescharacteristic
288C2×D4C23×C1111yescharacteristic
289C2×D4C23×C1111yescharacteristic
290C2×D4C23×C1111yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4C23×C1111yescharacteristic
296C22×C4C23×C1111yescharacteristic
297Q16—22no—
298Q16—22no—
299SD16—22no—
300SD16—22no—
301SD16—41no—
302SD16—41no—
303SD16D4×C1114yescomplemented
304D8—22no—
305D8—22no—
306M16—22no—
307M16—22no—
308C2×C8C23×C1111yescharacteristic
309C2×C8C23×C1111yescharacteristic
310C2×C8C23×C1111yescharacteristic
311C2×C8C23×C1111yescharacteristic
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4D4×C1111yescharacteristic
316C4⋊C4C23×C1111yescharacteristic
317C4⋊C4C23×C1111yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4D4×C1111yescharacteristic
328C22⋊C4D4×C1111yescharacteristic
329C42—21no—
330C42C23×C1111yescharacteristic
331C11#327511yescharacteristic, direct product factor, Sylow
332C23—21no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23C2×D4×C1111yescharacteristic
339C23C2×D4×C1111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8C2×D4×C1112yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—41no—
353D4—42no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—81no—
358D4C2×D4×C1112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—81no—
372C2×C4C2×D4×C1111yescharacteristic
373C2×C4C2×D4×C1111yescharacteristic
374C2×C4C2×D4×C1111yescharacteristic
375C2×C4C2×D4×C1111yescharacteristic
376C2×C4C24×C1111yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8C2×D4×C1112yes—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—84no—
397C22C22×D4×C1111yescharacteristic
398C4—21no—
399C4—21no—
400C4—22no—
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4C22×D4×C1111yescharacteristic
408C4C11×H(5,𝔽2)11yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—81no—
413C2—81no—
414C2D42×C1111yescharacteristic
415C2C11×#57511yescharacteristic
416C2C11×#57711yescharacteristic
subgroupG/H
center, socleC22×C11C22×D4
commutator, Frattini, cosocleC2×C4C24×C11
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. C2×C11×#137C2semidirect
2. C2×C11×AGL(1,ℤ/8)C2semidirect
3. C11×#548C2semidirect
4. C11×#546C2semidirect
5. C11×#495C2semidirect
6. C11×#470C2semidirect
7. C11×#469C2semidirect
8. C11×#464C2semidirect
9. C11×#463C2semidirect
10. C11×#452C2semidirect
11. C11×#450C2semidirect
12. C11×#449C2semidirect
13. C11×#448C2semidirect
14. C4×C11×SD16C2semidirect
15. C11×#436C2semidirect
18. C22×Q8×C11C22semidirect
22. C2×C11×Q16C22semidirect
23. C2×C11×Q16C22semidirect
28. C2×C11×SD16C22semidirect
32. C2×C11×M16C22semidirect
35. C11×#124C22semidirect
43. C11×#121C22semidirect
45. C4×Q8×C11C22semidirect
50. C11×#106C22semidirect
51. C11×C4⋊C8C22semidirect
52. C11×#103C22semidirect
53. C11×#103C22semidirect
54. C11×#103C22semidirect
57. C11×#102C22semidirect
59. C11×C22⋊C8C22semidirect
60. C4×C8×C11C22semidirect
95. C11×SD16D4semidirect
123. #3275C11direct (N × H)
173. C2×#137C2×C11semidirect
174. C2×AGL(1,ℤ/8)C2×C11semidirect
175. #548C2×C11semidirect
176. #546C2×C11semidirect
177. #495C2×C11semidirect
178. #470C2×C11semidirect
179. #469C2×C11semidirect
180. #464C2×C11semidirect
181. #463C2×C11semidirect
182. #452C2×C11semidirect
183. #450C2×C11semidirect
184. #449C2×C11semidirect
185. #448C2×C11semidirect
186. C4×SD16C2×C11semidirect
187. #436C2×C11semidirect
218. C22×Q8C22×C11semidirect
222. C2×Q16C22×C11semidirect
223. C2×Q16C22×C11semidirect
228. C2×SD16C22×C11semidirect
232. C2×M16C22×C11semidirect
235. #124C22×C11semidirect
243. #121C22×C11semidirect
245. C4×Q8C22×C11semidirect
250. #106C22×C11semidirect
251. C4⋊C8C22×C11semidirect
252. #103C22×C11semidirect
253. #103C22×C11semidirect
254. #103C22×C11semidirect
257. #102C22×C11semidirect
259. C22⋊C8C22×C11semidirect
260. C4×C8C22×C11semidirect
303. SD16D4×C11semidirect
331. C11#3275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1372
C2×C11×AGL(1,ℤ/8)2
C11×#5482
C11×#5462
C11×#4952
C11×#4702
C11×#4692
C11×#4642
C11×#4632
C11×#4522
C11×#4502
C11×#4492
C11×#4482
C4×C11×SD162
C11×#4362
#327511