Finite Group Databasebeta

← C11×#60624 #14637817

Subgroups — C11×#60624 #14637817

Order 2816.

2038 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3504C211yesmaximal, characteristic, complemented
2C11×#3500C211yesmaximal, characteristic
3C11×#3142C213yesmaximal, complemented
4C11×#3140C213yesmaximal, complemented
5C11×#3137C216yesmaximal, complemented
6C11×#3136C216yesmaximal, complemented
7C11×#3131C213yesmaximal, complemented
8C2×C11×#488C213yesmaximal, complemented
9C11×#2898C212yesmaximal, complemented
10C11×#2897C212yesmaximal, complemented
11C4×C11×#131C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13C2×C11×H(5,𝔽2)C2211yescharacteristic
14C2×C11×#131C2212yes—
15C11×#557—22no—
16C11×#554—26no—
17C11×#548—22no—
18C11×#546—26no—
19C11×#544C2216yescomplemented
20C11×#536C2213yes—
21C11×#535C2213yes—
22C11×#533C2213yescomplemented
23C11×#532C2213yes—
24C2×C11×#125C2213yescomplemented
25C2×C11×#124C2213yes—
26C11×#520C2212yes—
27C4×C11×#41C2211yescharacteristic
28C11×#491C2216yescomplemented
29C11×#490C2216yescomplemented
30C11×#489C22112yescomplemented
31C11×#488C2213yescomplemented
32C11×#488C22112yescomplemented
33C11×#488C2216yescomplemented
34C11×#488C2211yescharacteristic, complemented
35C11×#488C2213yescomplemented
36C11×#488C2213yescomplemented
37C11×#487C2216yescomplemented
38C11×#486C2216yescomplemented
39C11×#419C2216yescomplemented
40C11×#418C2216yes—
41C11×#417C2216yes—
42C11×#417C2216yescomplemented
43C11×#416C2216yes—
44C11×#416C2216yescomplemented
45C2×C11×#103C2216yescomplemented
46C2×C11×#102C2216yes—
47C11×#405C2216yescomplemented
48C4×C11×M16C2213yescomplemented
49C2×C4×C8×C11C2213yescomplemented
50C11×2−1+4—28no—
51C11×H(5,𝔽2)—28no—
52C2×C11×#41—21no—
53C2×C11×#41—23no—
54C2×C11×#41C2313yes—
55C2×C11×#41C2313yes—
56C2×C11×#41C2311yescharacteristic
57C22×Q8×C11—21no—
58C22×Q8×C11C2313yes—
59C22×D4×C11—23no—
60C22×D4×C11C2313yes—
61C11×#131—28no—
62C2×C11×M16C2316yes—
63C22×C8×C11C2316yes—
64C11×C4⋊Q8—26no—
65C11×C4⋊Q8C2313yes—
66C11×C4⋊Q8C2316yes—
67C11×#127C2313yes—
68C11×#125—26no—
69C11×#125—26no—
70C11×#125C2316yes—
71C11×#125C2313yes—
72C11×#125C2311yescharacteristic
73C11×#124—26no—
74C11×#124C2316yes—
75C11×#124C2313yes—
76C11×#124C2311yescharacteristic
77C11×#123—26no—
78C11×C22⋊Q8—26no—
79C11×C22⋊Q8—26no—
80C11×C22⋊Q8—212no—
81C11×#121—26no—
82C11×#121—26no—
83C11×#120—26no—
84C4×Q8×C11—22no—
85C4×Q8×C11—26no—
86C4×Q8×C11D412yes—
87C4×D4×C11—26no—
88C4×D4×C11—26no—
89C4×D4×C11D416yes—
90C11×#117C2316yes—
91C11×#117C2313yes—
92C2×C11×C4⋊C4—26no—
93C2×C11×C4⋊C4C2316yes—
94C2×C11×C22⋊C4—26no—
95C2×C42×C11C2313yes—
96C11×#103C2316yes—
97C11×#103C23112yes—
98C11×#103C2316yes—
99C11×#103C2316yes—
100C11×#103C2312yes—
101C11×#102C2316yes—
102C11×#102C23112yes—
103C11×#102C2316yes—
104C11×#102C2316yes—
105C11×#102C2312yes—
106C11×#97C2316yes—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2313yes—
109C4×C8×C11C2316yes—
110#60624C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—23no—
112C11×#41—212no—
113C11×#41—212no—
114C11×#41—44no—
115C11×#41—412no—
116C11×#41#4118yes—
117C2×Q8×C11—23no—
118C2×Q8×C11—26no—
119C2×Q8×C11—212no—
120C2×Q8×C11—44no—
121C2×Q8×C11C2×D411yescharacteristic
122C2×Q8×C11C2413yes—
123C2×Q8×C11C2411yescharacteristic
124C2×D4×C11—23no—
125C2×D4×C11—23no—
126C2×D4×C11—23no—
127C2×D4×C11—26no—
128C2×D4×C11—212no—
129C2×D4×C11—412no—
130C2×D4×C11C2×D413yes—
131C2×D4×C11C2413yes—
132C2×D4×C11C2411yescharacteristic
133C22×C4×C11—23no—
134C22×C4×C11—26no—
135C22×C4×C11—23no—
136C22×C4×C11—23no—
137C22×C4×C11C2×D416yes—
138C22×C4×C11C2413yes—
139C11×M16—212no—
140C2×C8×C11—212no—
141C2×C8×C11C2412yes—
142C2×C8×C11C2416yes—
143C11×C4⋊C4—26no—
144C11×C4⋊C4—212no—
145C11×C4⋊C4—26no—
146C11×C4⋊C4—26no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—26no—
149C11×C4⋊C4C2×D416yes—
150C11×C4⋊C4C2416yes—
151C11×C4⋊C4C2412yes—
152C11×C22⋊C4—26no—
153C11×C22⋊C4—26no—
154C11×C22⋊C4—212no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4C2×D416yes—
157C42×C11—26no—
158C42×C11C2×D416yes—
159C42×C11C2411yescharacteristic
160C42×C11C2413yes—
161#3504C2×C1111yescharacteristic, complemented
162#3500C2×C1111yescharacteristic
163#3142C2×C1113yescomplemented
164#3140C2×C1113yescomplemented
165#3137C2×C1116yescomplemented
166#3136C2×C1116yescomplemented
167#3131C2×C1113yescomplemented
168C2×#488C2×C1113yescomplemented
169#2898C2×C1112yescomplemented
170#2897C2×C1112yescomplemented
171C4×#131C2×C1111yescharacteristic, complemented
172C23×C11—23no—
173C23×C11—21no—
174C23×C11—46no—
175C23×C11—86no—
176C23×C11C22×D413yes—
177Q8×C11—26no—
178Q8×C11—22no—
179Q8×C11—46no—
180Q8×C11—86no—
181Q8×C11#12414yes—
182D4×C11—26no—
183D4×C11—22no—
184D4×C11—46no—
185D4×C11—46no—
186D4×C11—46no—
187D4×C11—86no—
188D4×C11#124112yes—
189C2×C4×C11—22no—
190C2×C4×C11—26no—
191C2×C4×C11—23no—
192C2×C4×C11—21no—
193C2×C4×C11—46no—
194C2×C4×C11—46no—
195C2×C4×C11—46no—
196C2×C4×C11—46no—
197C2×C4×C11—86no—
198C2×C4×C11C22×D412yes—
199C2×C4×C11C22×D416yes—
200C2×C4×C11C22×D413yes—
201C2×C4×C11C2×#41112yes—
202C2×C4×C11C2511yescharacteristic
203C8×C11—22no—
204C8×C11—26no—
205C2×2−1+4C22×C1111yescharacteristic
206C2×H(5,𝔽2)C22×C1111yescharacteristic
207C2×#131C22×C1112yes—
208#557—22no—
209#554—26no—
210#548—22no—
211#546—26no—
212#544C22×C1116yescomplemented
213#536C22×C1113yes—
214#535C22×C1113yes—
215#533C22×C1113yescomplemented
216#532C22×C1113yes—
217C2×#125C22×C1113yescomplemented
218C2×#124C22×C1113yes—
219#520C22×C1112yes—
220C4×#41C22×C1111yescharacteristic
221#491C22×C1116yescomplemented
222#490C22×C1116yescomplemented
223#489C22×C11112yescomplemented
224#488C22×C1113yescomplemented
225#488C22×C11112yescomplemented
226#488C22×C1116yescomplemented
227#488C22×C1111yescharacteristic, complemented
228#488C22×C1113yescomplemented
229#488C22×C1113yescomplemented
230#487C22×C1116yescomplemented
231#486C22×C1116yescomplemented
232#419C22×C1116yescomplemented
233#418C22×C1116yes—
234#417C22×C1116yes—
235#417C22×C1116yescomplemented
236#416C22×C1116yes—
237#416C22×C1116yescomplemented
238C2×#103C22×C1116yescomplemented
239C2×#102C22×C1116yes—
240#405C22×C1116yescomplemented
241C4×M16C22×C1113yescomplemented
242C2×C4×C8C22×C1113yescomplemented
243C22×C11—26no—
244C22×C11—42no—
245C22×C11—46no—
246C22×C11—41no—
247C22×C11—43no—
248C22×C11—166no—
249C22×C11C2×#12416yes—
250C22×C11C23×D411yescharacteristic
251C4×C11—22no—
252C4×C11—26no—
253C4×C11—46no—
254C4×C11—42no—
255C4×C11—41no—
256C4×C11—43no—
257C4×C11C2×#12416yes—
258C4×C11C22×#4112yes—
2592−1+4—28no—
260H(5,𝔽2)—28no—
261C2×#41—21no—
262C2×#41—23no—
263C2×#41C23×C1113yes—
264C2×#41C23×C1113yes—
265C2×#41C23×C1111yescharacteristic
266C22×Q8—21no—
267C22×Q8C23×C1113yes—
268C22×D4—23no—
269C22×D4C23×C1113yes—
270#131—28no—
271C2×M16C23×C1116yes—
272C22×C8C23×C1116yes—
273C4⋊Q8—26no—
274C4⋊Q8C23×C1113yes—
275C4⋊Q8C23×C1116yes—
276#127C23×C1113yes—
277#125—26no—
278#125—26no—
279#125C23×C1113yes—
280#125C23×C1116yes—
281#125C23×C1111yescharacteristic
282#124—26no—
283#124C23×C1113yes—
284#124C23×C1116yes—
285#124C23×C1111yescharacteristic
286#123—26no—
287C22⋊Q8—26no—
288C22⋊Q8—26no—
289C22⋊Q8—212no—
290#121—26no—
291#121—26no—
292#120—26no—
293C4×Q8—22no—
294C4×Q8—26no—
295C4×Q8D4×C1112yes—
296C4×D4—26no—
297C4×D4—26no—
298C4×D4D4×C1116yes—
299#117C23×C1116yes—
300#117C23×C1113yes—
301C2×C4⋊C4—26no—
302C2×C4⋊C4C23×C1116yes—
303C2×C22⋊C4—26no—
304C2×C42C23×C1113yes—
305#103C23×C1116yes—
306#103C23×C11112yes—
307#103C23×C1112yes—
308#103C23×C1116yes—
309#103C23×C1116yes—
310#102C23×C1116yes—
311#102C23×C11112yes—
312#102C23×C1116yes—
313#102C23×C1112yes—
314#102C23×C1116yes—
315#97C23×C1116yes—
316C4×C8C23×C1111yescharacteristic
317C4×C8C23×C1113yes—
318C4×C8C23×C1116yes—
319C2×C11—26no—
320C2×C11—81no—
321C2×C11—83no—
322C2×C11C22×#12411yescharacteristic
323C2×C11#358412yes—
324C24—23no—
325#41—212no—
326#41—212no—
327#41—44no—
328#41—412no—
329#41C11×#4118yes—
330C2×Q8—23no—
331C2×Q8—26no—
332C2×Q8—212no—
333C2×Q8—44no—
334C2×Q8C2×D4×C1111yescharacteristic
335C2×Q8C24×C1113yes—
336C2×Q8C24×C1111yescharacteristic
337C2×D4—23no—
338C2×D4—23no—
339C2×D4—23no—
340C2×D4—26no—
341C2×D4—212no—
342C2×D4—412no—
343C2×D4C2×D4×C1113yes—
344C2×D4C24×C1113yes—
345C2×D4C24×C1111yescharacteristic
346C22×C4—23no—
347C22×C4—26no—
348C22×C4—23no—
349C22×C4—23no—
350C22×C4C2×D4×C1116yes—
351C22×C4C24×C1113yes—
352M16—212no—
353C2×C8—212no—
354C2×C8C24×C1112yes—
355C2×C8C24×C1116yes—
356C4⋊C4—26no—
357C4⋊C4—212no—
358C4⋊C4—26no—
359C4⋊C4—26no—
360C4⋊C4—22no—
361C4⋊C4—26no—
362C4⋊C4C2×D4×C1116yes—
363C4⋊C4C24×C1116yes—
364C4⋊C4C24×C1112yes—
365C22⋊C4—26no—
366C22⋊C4—26no—
367C22⋊C4—212no—
368C22⋊C4—22no—
369C22⋊C4C2×D4×C1116yes—
370C42—26no—
371C42C2×D4×C1116yes—
372C42C24×C1111yescharacteristic
373C42C24×C1113yes—
374C11#6062411yescharacteristic, direct product factor, Sylow
375C23—23no—
376C23—21no—
377C23—46no—
378C23—86no—
379C23C22×D4×C1113yes—
380Q8—26no—
381Q8—22no—
382Q8—46no—
383Q8—86no—
384Q8C11×#12414yes—
385D4—26no—
386D4—22no—
387D4—46no—
388D4—46no—
389D4—46no—
390D4—86no—
391D4C11×#124112yes—
392C2×C4—22no—
393C2×C4—26no—
394C2×C4—23no—
395C2×C4—21no—
396C2×C4—46no—
397C2×C4—46no—
398C2×C4—46no—
399C2×C4—46no—
400C2×C4—86no—
401C2×C4C22×D4×C1112yes—
402C2×C4C22×D4×C1116yes—
403C2×C4C22×D4×C1113yes—
404C2×C4C2×C11×#41112yes—
405C2×C4C25×C1111yescharacteristic
406C8—22no—
407C8—26no—
408C22—26no—
409C22—41no—
410C22—43no—
411C22—42no—
412C22—46no—
413C22—166no—
414C22C2×C11×#12416yes—
415C22C23×D4×C1111yescharacteristic
416C4—22no—
417C4—26no—
418C4—41no—
419C4—43no—
420C4—46no—
421C4—42no—
422C4C2×C11×#12416yes—
423C4C22×C11×#4112yes—
424C2—26no—
425C2—83no—
426C2—81no—
427C2C22×C11×#12411yescharacteristic
428C2C11×#358412yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3500C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3504C2semidirect
3. C11×#3142C2semidirect
4. C11×#3140C2semidirect
5. C11×#3137C2semidirect
6. C11×#3136C2semidirect
7. C11×#3131C2semidirect
8. C2×C11×#488C2semidirect
9. C11×#2898C2semidirect
10. C11×#2897C2semidirect
11. C4×C11×#131C2semidirect
19. C11×#544C22semidirect
22. C11×#533C22semidirect
24. C2×C11×#125C22semidirect
28. C11×#491C22semidirect
29. C11×#490C22semidirect
30. C11×#489C22semidirect
31. C11×#488C22semidirect
32. C11×#488C22semidirect
33. C11×#488C22semidirect
34. C11×#488C22semidirect
35. C11×#488C22semidirect
36. C11×#488C22semidirect
37. C11×#487C22semidirect
38. C11×#486C22semidirect
39. C11×#419C22semidirect
42. C11×#417C22semidirect
44. C11×#416C22semidirect
45. C2×C11×#103C22semidirect
47. C11×#405C22semidirect
48. C4×C11×M16C22semidirect
49. C2×C4×C8×C11C22semidirect
110. #60624C11direct (N × H)
161. #3504C2×C11semidirect
163. #3142C2×C11semidirect
164. #3140C2×C11semidirect
165. #3137C2×C11semidirect
166. #3136C2×C11semidirect
167. #3131C2×C11semidirect
168. C2×#488C2×C11semidirect
169. #2898C2×C11semidirect
170. #2897C2×C11semidirect
171. C4×#131C2×C11semidirect
212. #544C22×C11semidirect
215. #533C22×C11semidirect
217. C2×#125C22×C11semidirect
221. #491C22×C11semidirect
222. #490C22×C11semidirect
223. #489C22×C11semidirect
224. #488C22×C11semidirect
225. #488C22×C11semidirect
226. #488C22×C11semidirect
227. #488C22×C11semidirect
228. #488C22×C11semidirect
229. #488C22×C11semidirect
230. #487C22×C11semidirect
231. #486C22×C11semidirect
232. #419C22×C11semidirect
235. #417C22×C11semidirect
237. #416C22×C11semidirect
238. C2×#103C22×C11semidirect
240. #405C22×C11semidirect
241. C4×M16C22×C11semidirect
242. C2×C4×C8C22×C11semidirect
374. C11#60624direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35042
C11×#35002
C11×#31422
C11×#31402
C11×#31372
C11×#31362
C11×#31312
C2×C11×#4882
C11×#28982
C11×#28972
C4×C11×#1312
#6062411