Finite Group Databasebeta

← C11×#60176 #14637369

Subgroups — C11×#60176 #14637369

Order 2816.

2818 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#576C211yesmaximal, characteristic
2C4×C11×H(5,𝔽2)C212yesmaximal, complemented
3C11×#2952C213yesmaximal, complemented
4C11×#2948C213yesmaximal, complemented
5C11×#2946C216yesmaximal, complemented
6C4×C11×AGL(1,ℤ/8)C216yesmaximal, complemented
7C11×#2943C213yesmaximal, complemented
8C2×C11×#442C213yesmaximal, complemented
9C11×#2912C211yesmaximal, characteristic, complemented
10C11×#2897C212yesmaximal, complemented
11C11×#2875C211yesmaximal, characteristic, complemented
12C2×C11×H(5,𝔽2)C2212yes—
13C11×#576C4116yescomplemented
14C2×C11×AGL(1,ℤ/8)C2216yes—
15C2×C11×#135C2213yes—
16C22×C11×D8C2213yes—
17C2×C11×#131C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C11×#520—22no—
20C11×#520C2212yes—
21C11×#520C2216yescomplemented
22C11×#518—26no—
23C11×#518C2216yescomplemented
24C4×C11×#41—22no—
25C4×C11×#41C2211yescharacteristic
26C4×C11×#41C2216yescomplemented
27C2×C4×D4×C11—26no—
28C2×C4×D4×C11C2216yescomplemented
29C11×#442C2213yescomplemented
30C11×#442C2216yescomplemented
31C11×#442C2216yescomplemented
32C11×#442C2216yescomplemented
33C11×#442C2213yescomplemented
34C11×#441C2211yescharacteristic, complemented
35C11×#441C2213yescomplemented
36C11×#440C2216yescomplemented
37C11×#440C2216yescomplemented
38C4×C11×SD16C22112yescomplemented
39C4×C11×D8C22112yescomplemented
40C11×#428C2216yescomplemented
41C11×#427C2213yescomplemented
42C2×C11×#106C2213yescomplemented
43C11×#418C2216yescomplemented
44C11×#417C2216yescomplemented
45C11×#416C2216yescomplemented
46C2×C11×#102C2216yescomplemented
47C11×#405C2213yescomplemented
48C11×#405C2213yescomplemented
49C4×C11×M16C2213yescomplemented
50C2×C11×#97C2213yescomplemented
51C11×H(5,𝔽2)—28no—
52C11×H(5,𝔽2)C2×C4116yescomplemented
53C2×C11×#41—22no—
54C2×C11×#41C2316yes—
55C2×C11×#41C2311yescharacteristic
56C22×D4×C11—26no—
57C22×D4×C11C2316yes—
58C23×C4×C11—26no—
59C11×AGL(1,ℤ/8)C2×C4148yescomplemented
60C11×#135C2×C4124yescomplemented
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16C2316yes—
63C2×C11×D8C2×C4124yescomplemented
64C2×C11×D8C2313yes—
65C2×C11×D8C2316yes—
66C11×#131—24no—
67C11×#131C2×C418yescomplemented
68C2×C11×M16C2313yes—
69C2×C11×M16C2313yes—
70C22×C8×C11C2313yes—
71C22×C8×C11C2313yes—
72C4×Q8×C11—22no—
73C4×Q8×C11D412yes—
74C4×Q8×C11C2312yes—
75C4×Q8×C11C2316yes—
76C4×D4×C11—26no—
77C4×D4×C11—26no—
78C4×D4×C11—26no—
79C4×D4×C11—26no—
80C4×D4×C11—26no—
81C4×D4×C11—212no—
82C4×D4×C11—26no—
83C4×D4×C11—26no—
84C4×D4×C11D416yes—
85C4×D4×C11C2316yes—
86C4×D4×C11C23112yes—
87C4×D4×C11C2316yes—
88C11×#117—26no—
89C11×#117—26no—
90C11×#117C2316yes—
91C11×#117C2313yes—
92C2×C11×C4⋊C4—26no—
93C2×C11×C4⋊C4C2316yes—
94C2×C11×C22⋊C4—26no—
95C2×C11×C22⋊C4—212no—
96C2×C42×C11—26no—
97C2×C42×C11C2313yes—
98C11×#107C2316yes—
99C11×#106C2313yes—
100C11×#106C2316yes—
101C11×#106C2311yescharacteristic
102C11×#103C2312yes—
103C11×#103C2316yes—
104C11×#102C2316yes—
105C11×#102C23112yes—
106C11×#102C2316yes—
107C11×#97C2311yescharacteristic
108C11×#97C2313yes—
109C11×#97C2313yes—
110C11×#97C2313yes—
111C4×C8×C11C2316yes—
112#60176C1111yesmaximal, characteristic, direct product factor, Sylow
113C24×C11—26no—
114C11×#41—216no—
115C11×#41—212no—
116C11×#41C22×C414yes—
117C11×#41C22×C4124yescomplemented
118C11×#41#4114yes—
119C2×Q8×C11C2×D411yescharacteristic
120C2×Q8×C11C2412yes—
121C2×D4×C11—26no—
122C2×D4×C11—248no—
123C2×D4×C11—26no—
124C2×D4×C11—212no—
125C2×D4×C11C22×C4124yescomplemented
126C2×D4×C11C2×D413yes—
127C2×D4×C11C2416yes—
128C22×C4×C11—26no—
129C22×C4×C11—26no—
130C22×C4×C11—26no—
131C22×C4×C11—26no—
132C22×C4×C11—212no—
133C22×C4×C11—812no—
134C22×C4×C11C2×D416yes—
135C22×C4×C11C2413yes—
136C11×Q16C22×C414yescomplemented
137C11×SD16C22×C4124yescomplemented
138C11×D8C22×C4112yescomplemented
139C11×D8C22×C4124yescomplemented
140C11×M16—26no—
141C11×M16C22×C4112yescomplemented
142C2×C8×C11—26no—
143C2×C8×C11C22×C4112yescomplemented
144C2×C8×C11C2413yes—
145C2×C8×C11C2411yescharacteristic
146C2×C8×C11C2413yes—
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4—26no—
149C11×C4⋊C4—26no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4C2×D416yes—
152C11×C4⋊C4C2416yes—
153C11×C4⋊C4C2412yes—
154C11×C22⋊C4—26no—
155C11×C22⋊C4—26no—
156C11×C22⋊C4—26no—
157C11×C22⋊C4—212no—
158C11×C22⋊C4C2×D416yes—
159C42×C11—22no—
160C42×C11—26no—
161C42×C11—26no—
162C42×C11C2×D416yes—
163C42×C11C2413yes—
164C42×C11C2411yescharacteristic
165C2×#576C2×C1111yescharacteristic
166C4×H(5,𝔽2)C2×C1112yescomplemented
167#2952C2×C1113yescomplemented
168#2948C2×C1113yescomplemented
169#2946C2×C1116yescomplemented
170C4×AGL(1,ℤ/8)C2×C1116yescomplemented
171#2943C2×C1113yescomplemented
172C2×#442C2×C1113yescomplemented
173#2912C2×C1111yescharacteristic, complemented
174#2897C2×C1112yescomplemented
175#2875C2×C1111yescharacteristic, complemented
176C23×C11—26no—
177C23×C11—224no—
178C23×C11—86no—
179C23×C11—86no—
180C23×C11C22×D413yes—
181Q8×C11—22no—
182Q8×C11C4×D414yes—
183Q8×C11C23×C414yes—
184D4×C11—224no—
185D4×C11—224no—
186D4×C11—26no—
187D4×C11C4×D4112yes—
188D4×C11C23×C4112yes—
189C2×C4×C11—22no—
190C2×C4×C11—224no—
191C2×C4×C11—22no—
192C2×C4×C11—26no—
193C2×C4×C11—46no—
194C2×C4×C11—412no—
195C2×C4×C11—86no—
196C2×C4×C11—812no—
197C2×C4×C11—86no—
198C2×C4×C11C23×C416yes—
199C2×C4×C11C22×D412yes—
200C2×C4×C11C22×D416yes—
201C2×C4×C11C22×D413yes—
202C2×C4×C11C2×#4116yes—
203C2×C4×C11C2511yescharacteristic
204C8×C11—21no—
205C8×C11—23no—
206C8×C11C23×C412yes—
207C8×C11C23×C416yes—
208C2×H(5,𝔽2)C22×C1112yes—
209#576C4×C11116yescomplemented
210C2×AGL(1,ℤ/8)C22×C1116yes—
211C2×#135C22×C1113yes—
212C22×D8C22×C1113yes—
213C2×#131C22×C1111yescharacteristic
214C2×#131C22×C1111yescharacteristic
215#520—22no—
216#520C22×C1112yes—
217#520C22×C1116yescomplemented
218#518—26no—
219#518C22×C1116yescomplemented
220C4×#41—22no—
221C4×#41C22×C1111yescharacteristic
222C4×#41C22×C1116yescomplemented
223C2×C4×D4—26no—
224C2×C4×D4C22×C1116yescomplemented
225#442C22×C1113yescomplemented
226#442C22×C1116yescomplemented
227#442C22×C1116yescomplemented
228#442C22×C1116yescomplemented
229#442C22×C1113yescomplemented
230#441C22×C1111yescharacteristic, complemented
231#441C22×C1113yescomplemented
232#440C22×C1116yescomplemented
233#440C22×C1116yescomplemented
234C4×SD16C22×C11112yescomplemented
235C4×D8C22×C11112yescomplemented
236#428C22×C1116yescomplemented
237#427C22×C1113yescomplemented
238C2×#106C22×C1113yescomplemented
239#418C22×C1116yescomplemented
240#417C22×C1116yescomplemented
241#416C22×C1116yescomplemented
242C2×#102C22×C1116yescomplemented
243#405C22×C1113yescomplemented
244#405C22×C1113yescomplemented
245C4×M16C22×C1113yescomplemented
246C2×#97C22×C1113yescomplemented
247C22×C11—26no—
248C22×C11—212no—
249C22×C11—46no—
250C22×C11—46no—
251C22×C11—824no—
252C22×C11C2×C4×D416yes—
253C22×C11C23×D411yescharacteristic
254C4×C11—22no—
255C4×C11—26no—
256C4×C11—24no—
257C4×C11—46no—
258C4×C11—42no—
259C4×C11C2×C4×D416yes—
260C4×C11C24×C411yescharacteristic
261C4×C11C22×#4111yescharacteristic
262H(5,𝔽2)—28no—
263H(5,𝔽2)C2×C4×C11116yescomplemented
264C2×#41—22no—
265C2×#41C23×C1116yes—
266C2×#41C23×C1111yescharacteristic
267C22×D4—26no—
268C22×D4C23×C1116yes—
269C23×C4—26no—
270AGL(1,ℤ/8)C2×C4×C11148yescomplemented
271#135C2×C4×C11124yescomplemented
272C2×Q16C23×C1111yescharacteristic
273C2×SD16C23×C1116yes—
274C2×D8C2×C4×C11124yescomplemented
275C2×D8C23×C1113yes—
276C2×D8C23×C1116yes—
277#131—24no—
278#131C2×C4×C1118yescomplemented
279C2×M16C23×C1113yes—
280C2×M16C23×C1113yes—
281C22×C8C23×C1113yes—
282C22×C8C23×C1113yes—
283C4×Q8—22no—
284C4×Q8D4×C1112yes—
285C4×Q8C23×C1112yes—
286C4×Q8C23×C1116yes—
287C4×D4—26no—
288C4×D4—26no—
289C4×D4—26no—
290C4×D4—26no—
291C4×D4—26no—
292C4×D4—212no—
293C4×D4—26no—
294C4×D4—26no—
295C4×D4D4×C1116yes—
296C4×D4C23×C1116yes—
297C4×D4C23×C11112yes—
298C4×D4C23×C1116yes—
299#117—26no—
300#117—26no—
301#117C23×C1116yes—
302#117C23×C1113yes—
303C2×C4⋊C4—26no—
304C2×C4⋊C4C23×C1116yes—
305C2×C22⋊C4—26no—
306C2×C22⋊C4—212no—
307C2×C42—26no—
308C2×C42C23×C1113yes—
309#107C23×C1116yes—
310#106C23×C1113yes—
311#106C23×C1116yes—
312#106C23×C1111yescharacteristic
313#103C23×C1112yes—
314#103C23×C1116yes—
315#102C23×C1116yes—
316#102C23×C11112yes—
317#102C23×C1116yes—
318#97C23×C1111yescharacteristic
319#97C23×C1113yes—
320#97C23×C1113yes—
321#97C23×C1113yes—
322C4×C8C23×C1116yes—
323C2×C11—26no—
324C2×C11—412no—
325C2×C11C22×C4×D411yescharacteristic
326C2×C11#358512yes—
327C24—26no—
328#41—216no—
329#41—212no—
330#41C22×C4×C1114yes—
331#41C22×C4×C11124yescomplemented
332#41C11×#4114yes—
333C2×Q8C2×D4×C1111yescharacteristic
334C2×Q8C24×C1112yes—
335C2×D4—26no—
336C2×D4—248no—
337C2×D4—26no—
338C2×D4—212no—
339C2×D4C22×C4×C11124yescomplemented
340C2×D4C2×D4×C1113yes—
341C2×D4C24×C1116yes—
342C22×C4—26no—
343C22×C4—26no—
344C22×C4—26no—
345C22×C4—26no—
346C22×C4—212no—
347C22×C4—812no—
348C22×C4C2×D4×C1116yes—
349C22×C4C24×C1113yes—
350Q16C22×C4×C1114yescomplemented
351SD16C22×C4×C11124yescomplemented
352D8C22×C4×C11112yescomplemented
353D8C22×C4×C11124yescomplemented
354M16—26no—
355M16C22×C4×C11112yescomplemented
356C2×C8—26no—
357C2×C8C22×C4×C11112yescomplemented
358C2×C8C24×C1113yes—
359C2×C8C24×C1111yescharacteristic
360C2×C8C24×C1113yes—
361C2×C8C24×C1111yescharacteristic
362C4⋊C4—26no—
363C4⋊C4—26no—
364C4⋊C4—22no—
365C4⋊C4C2×D4×C1116yes—
366C4⋊C4C24×C1116yes—
367C4⋊C4C24×C1112yes—
368C22⋊C4—26no—
369C22⋊C4—26no—
370C22⋊C4—26no—
371C22⋊C4—212no—
372C22⋊C4C2×D4×C1116yes—
373C42—22no—
374C42—26no—
375C42—26no—
376C42C2×D4×C1116yes—
377C42C24×C1113yes—
378C42C24×C1111yescharacteristic
379C11#6017611yescharacteristic, direct product factor, Sylow
380C23—26no—
381C23—224no—
382C23—86no—
383C23—86no—
384C23C22×D4×C1113yes—
385Q8—22no—
386Q8C4×D4×C1114yes—
387Q8C23×C4×C1114yes—
388D4—224no—
389D4—224no—
390D4—26no—
391D4C4×D4×C11112yes—
392D4C23×C4×C11112yes—
393C2×C4—22no—
394C2×C4—224no—
395C2×C4—22no—
396C2×C4—26no—
397C2×C4—46no—
398C2×C4—412no—
399C2×C4—86no—
400C2×C4—812no—
401C2×C4—86no—
402C2×C4C23×C4×C1116yes—
403C2×C4C22×D4×C1112yes—
404C2×C4C22×D4×C1116yes—
405C2×C4C22×D4×C1113yes—
406C2×C4C2×C11×#4116yes—
407C2×C4C25×C1111yescharacteristic
408C8—21no—
409C8—23no—
410C8C23×C4×C1112yes—
411C8C23×C4×C1116yes—
412C22—26no—
413C22—212no—
414C22—46no—
415C22—46no—
416C22—824no—
417C22C2×C4×D4×C1116yes—
418C22C23×D4×C1111yescharacteristic
419C4—24no—
420C4—22no—
421C4—26no—
422C4—46no—
423C4—42no—
424C4C2×C4×D4×C1116yes—
425C4C24×C4×C1111yescharacteristic
426C4C22×C11×#4111yescharacteristic
427C2—26no—
428C2—412no—
429C2C22×C4×D4×C1111yescharacteristic
430C2C11×#358512yes—
subgroupG/H
center, socleC22×C11C23×D4
commutatorC4C24×C4×C11
Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#576C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×H(5,𝔽2)C2semidirect
3. C11×#2952C2semidirect
4. C11×#2948C2semidirect
5. C11×#2946C2semidirect
6. C4×C11×AGL(1,ℤ/8)C2semidirect
7. C11×#2943C2semidirect
8. C2×C11×#442C2semidirect
9. C11×#2912C2semidirect
10. C11×#2897C2semidirect
11. C11×#2875C2semidirect
13. C11×#576C4semidirect
21. C11×#520C22semidirect
23. C11×#518C22semidirect
26. C4×C11×#41C22semidirect
28. C2×C4×D4×C11C22semidirect
29. C11×#442C22semidirect
30. C11×#442C22semidirect
31. C11×#442C22semidirect
32. C11×#442C22semidirect
33. C11×#442C22semidirect
34. C11×#441C22semidirect
35. C11×#441C22semidirect
36. C11×#440C22semidirect
37. C11×#440C22semidirect
38. C4×C11×SD16C22semidirect
39. C4×C11×D8C22semidirect
40. C11×#428C22semidirect
41. C11×#427C22semidirect
42. C2×C11×#106C22semidirect
43. C11×#418C22semidirect
44. C11×#417C22semidirect
45. C11×#416C22semidirect
46. C2×C11×#102C22semidirect
47. C11×#405C22semidirect
48. C11×#405C22semidirect
49. C4×C11×M16C22semidirect
50. C2×C11×#97C22semidirect
52. C11×H(5,𝔽2)C2×C4semidirect
59. C11×AGL(1,ℤ/8)C2×C4semidirect
60. C11×#135C2×C4semidirect
63. C2×C11×D8C2×C4semidirect
67. C11×#131C2×C4semidirect
112. #60176C11direct (N × H)
117. C11×#41C22×C4semidirect
125. C2×D4×C11C22×C4semidirect
136. C11×Q16C22×C4semidirect
137. C11×SD16C22×C4semidirect
138. C11×D8C22×C4semidirect
139. C11×D8C22×C4semidirect
141. C11×M16C22×C4semidirect
143. C2×C8×C11C22×C4semidirect
166. C4×H(5,𝔽2)C2×C11semidirect
167. #2952C2×C11semidirect
168. #2948C2×C11semidirect
169. #2946C2×C11semidirect
170. C4×AGL(1,ℤ/8)C2×C11semidirect
171. #2943C2×C11semidirect
172. C2×#442C2×C11semidirect
173. #2912C2×C11semidirect
174. #2897C2×C11semidirect
175. #2875C2×C11semidirect
209. #576C4×C11semidirect
217. #520C22×C11semidirect
219. #518C22×C11semidirect
222. C4×#41C22×C11semidirect
224. C2×C4×D4C22×C11semidirect
225. #442C22×C11semidirect
226. #442C22×C11semidirect
227. #442C22×C11semidirect
228. #442C22×C11semidirect
229. #442C22×C11semidirect
230. #441C22×C11semidirect
231. #441C22×C11semidirect
232. #440C22×C11semidirect
233. #440C22×C11semidirect
234. C4×SD16C22×C11semidirect
235. C4×D8C22×C11semidirect
236. #428C22×C11semidirect
237. #427C22×C11semidirect
238. C2×#106C22×C11semidirect
239. #418C22×C11semidirect
240. #417C22×C11semidirect
241. #416C22×C11semidirect
242. C2×#102C22×C11semidirect
243. #405C22×C11semidirect
244. #405C22×C11semidirect
245. C4×M16C22×C11semidirect
246. C2×#97C22×C11semidirect
263. H(5,𝔽2)C2×C4×C11semidirect
270. AGL(1,ℤ/8)C2×C4×C11semidirect
271. #135C2×C4×C11semidirect
274. C2×D8C2×C4×C11semidirect
278. #131C2×C4×C11semidirect
331. #41C22×C4×C11semidirect
339. C2×D4C22×C4×C11semidirect
350. Q16C22×C4×C11semidirect
351. SD16C22×C4×C11semidirect
352. D8C22×C4×C11semidirect
353. D8C22×C4×C11semidirect
355. M16C22×C4×C11semidirect
357. C2×C8C22×C4×C11semidirect
379. C11#60176direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5762
C4×C11×H(5,𝔽2)2
C11×#29522
C11×#29482
C11×#29462
C4×C11×AGL(1,ℤ/8)2
C11×#29432
C2×C11×#4422
C11×#29122
C11×#28972
C11×#28752
#6017611