Finite Group Databasebeta

← C11×#60037 #14637230

Subgroups — C11×#60037 #14637230

Order 2816.

2228 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2697C213yesmaximal, complemented
2C11×#2679C211yesmaximal, characteristic
3C11×#2576C216yesmaximal, complemented
4C11×#2566C213yesmaximal, complemented
5C11×#2534C213yesmaximal, complemented
6C11×#2460C216yesmaximal, complemented
7C11×#2374C213yesmaximal, complemented
8C11×#2358C213yesmaximal, complemented
9C4×C11×#120C213yesmaximal, complemented
10C24×C4×C11C2211yescharacteristic, complemented
11C2×C11×#125C2213yescomplemented
12C2×C11×#123C2213yes—
13C2×C11×#120C2213yes—
14C2×C11×#120C2213yes—
15C2×C4×D4×C11C2216yes—
16C2×C4×D4×C11C2213yes—
17C22×C11×C22⋊C4C2213yescomplemented
18C11×#401C2212yescomplemented
19C11×#397C2216yescomplemented
20C11×#396C2216yescomplemented
21C11×#396C2216yescomplemented
22C11×#394C2216yes—
23C11×#394C2216yes—
24C11×#390C2213yes—
25C11×#390C2213yes—
26C11×#388C2216yescomplemented
27C11×#388C2216yescomplemented
28C11×#388C2216yescomplemented
29C11×#387C2216yescomplemented
30C11×#387C2216yescomplemented
31C11×#386C2216yes—
32C11×#386C2216yes—
33C11×#386C2213yes—
34C11×#385C2213yescomplemented
35C11×#385C2216yescomplemented
36C11×#385C2216yescomplemented
37C11×#384C2211yescharacteristic, complemented
38C11×#382C2213yescomplemented
39C11×#381C2213yescomplemented
40C11×#380C2213yescomplemented
41C11×#379C2213yescomplemented
42C11×#379C2211yescharacteristic, complemented
43C4×C11×C4⋊C4C2213yescomplemented
44C4×C11×C22⋊C4C2216yescomplemented
45C4×C11×C22⋊C4C2213yescomplemented
46C4×C11×C22⋊C4C2216yescomplemented
47C25×C11C2311yescharacteristic
48C25×C11C2311yescharacteristic
49C22×D4×C11C2316yes—
50C22×D4×C11C2313yes—
51C23×C4×C11—46no—
52C23×C4×C11C2313yes—
53C23×C4×C11C2313yes—
54C23×C4×C11C2313yes—
55C23×C4×C11C2313yes—
56C11×#125—46no—
57C11×#123—212no—
58C11×#120—212no—
59C11×#120—212no—
60C4×D4×C11—46no—
61C4×D4×C11—412no—
62C2×C11×C4⋊C4C2316yes—
63C2×C11×C4⋊C4C2316yes—
64C2×C11×C4⋊C4C2313yes—
65C2×C11×C4⋊C4C2316yes—
66C2×C11×C4⋊C4C2313yes—
67C2×C11×C4⋊C4C2313yes—
68C2×C11×C22⋊C4—46no—
69C2×C11×C22⋊C4C2316yes—
70C2×C11×C22⋊C4C2316yes—
71C2×C11×C22⋊C4C2316yes—
72C2×C11×C22⋊C4C2316yes—
73C2×C11×C22⋊C4C2313yes—
74C2×C11×C22⋊C4C2313yes—
75C2×C11×C22⋊C4C2313yes—
76C2×C11×C22⋊C4C2316yes—
77C2×C11×C22⋊C4C2313yes—
78C2×C11×C22⋊C4C2313yes—
79C2×C11×C22⋊C4C2316yes—
80C2×C11×C22⋊C4C2313yes—
81C2×C42×C11C2313yes—
82C2×C42×C11C2316yes—
83C2×C42×C11C2313yes—
84C2×C42×C11C2311yescharacteristic
85C11×#95C2316yes—
86C11×#95C2316yes—
87C11×#95C2316yes—
88C11×#95C2316yes—
89C11×#95C2316yes—
90C11×#95C2316yes—
91C11×#95C2312yes—
92#60037C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—26no—
94C24×C11—26no—
95C24×C11—43no—
96C24×C11—41no—
97C24×C11—43no—
98C24×C11—41no—
99C24×C11C2413yes—
100C24×C11C2413yes—
101C2×D4×C11—212no—
102C2×D4×C11—212no—
103C2×D4×C11—43no—
104C2×D4×C11—46no—
105C2×D4×C11—43no—
106C2×D4×C11#41112yes—
107C22×C4×C11—26no—
108C22×C4×C11—212no—
109C22×C4×C11—26no—
110C22×C4×C11—26no—
111C22×C4×C11—43no—
112C22×C4×C11—46no—
113C22×C4×C11—43no—
114C22×C4×C11—46no—
115C22×C4×C11—43no—
116C22×C4×C11—416no—
117C22×C4×C11C2416yes—
118C22×C4×C11C2416yes—
119C22×C4×C11C2411yescharacteristic
120C22×C4×C11C2413yes—
121C22×C4×C11C2413yes—
122C22×C4×C11C2413yes—
123C22×C4×C11C2413yes—
124C11×C4⋊C4—212no—
125C11×C4⋊C4—212no—
126C11×C4⋊C4—43no—
127C11×C4⋊C4—43no—
128C11×C4⋊C4—43no—
129C11×C4⋊C4—46no—
130C11×C22⋊C4—26no—
131C11×C22⋊C4—26no—
132C11×C22⋊C4—26no—
133C11×C22⋊C4—212no—
134C11×C22⋊C4—212no—
135C11×C22⋊C4—212no—
136C11×C22⋊C4—212no—
137C11×C22⋊C4—46no—
138C11×C22⋊C4—43no—
139C11×C22⋊C4—43no—
140C11×C22⋊C4—43no—
141C11×C22⋊C4—46no—
142C42×C11—26no—
143C42×C11—41no—
144C42×C11—43no—
145C42×C11—46no—
146#2697C2×C1113yescomplemented
147#2679C2×C1111yescharacteristic
148#2576C2×C1116yescomplemented
149#2566C2×C1113yescomplemented
150#2534C2×C1113yescomplemented
151#2460C2×C1116yescomplemented
152#2374C2×C1113yescomplemented
153#2358C2×C1113yescomplemented
154C4×#120C2×C1113yescomplemented
155C23×C11—26no—
156C23×C11—26no—
157C23×C11—26no—
158C23×C11—26no—
159C23×C11—23no—
160C23×C11—23no—
161C23×C11—23no—
162C23×C11—23no—
163C23×C11—412no—
164C23×C11—412no—
165C23×C11—412no—
166C23×C11—44no—
167C23×C11—86no—
168C23×C11—82no—
169C23×C11C2×#4116yes—
170C23×C11C2×#4116yes—
171C23×C11C2511yescharacteristic
172D4×C11—412no—
173D4×C11—424no—
174C2×C4×C11—23no—
175C2×C4×C11—26no—
176C2×C4×C11—23no—
177C2×C4×C11—26no—
178C2×C4×C11—26no—
179C2×C4×C11—26no—
180C2×C4×C11—26no—
181C2×C4×C11—23no—
182C2×C4×C11—26no—
183C2×C4×C11—26no—
184C2×C4×C11—23no—
185C2×C4×C11—26no—
186C2×C4×C11—23no—
187C2×C4×C11—26no—
188C2×C4×C11—412no—
189C2×C4×C11—412no—
190C2×C4×C11—86no—
191C2×C4×C11—86no—
192C2×C4×C11C2×#4116yes—
193C2×C4×C11H(5,𝔽2)16yes—
194C24×C4C22×C1111yescharacteristic, complemented
195C2×#125C22×C1113yescomplemented
196C2×#123C22×C1113yes—
197C2×#120C22×C1113yes—
198C2×#120C22×C1113yes—
199C2×C4×D4C22×C1113yes—
200C2×C4×D4C22×C1116yes—
201C22×C22⋊C4C22×C1113yescomplemented
202#401C22×C1112yescomplemented
203#397C22×C1116yescomplemented
204#396C22×C1116yescomplemented
205#396C22×C1116yescomplemented
206#394C22×C1116yes—
207#394C22×C1116yes—
208#390C22×C1113yes—
209#390C22×C1113yes—
210#388C22×C1116yescomplemented
211#388C22×C1116yescomplemented
212#388C22×C1116yescomplemented
213#387C22×C1116yescomplemented
214#387C22×C1116yescomplemented
215#386C22×C1116yes—
216#386C22×C1116yes—
217#386C22×C1113yes—
218#385C22×C1116yescomplemented
219#385C22×C1116yescomplemented
220#385C22×C1113yescomplemented
221#384C22×C1111yescharacteristic, complemented
222#382C22×C1113yescomplemented
223#381C22×C1113yescomplemented
224#380C22×C1113yescomplemented
225#379C22×C1113yescomplemented
226#379C22×C1111yescharacteristic, complemented
227C4×C4⋊C4C22×C1113yescomplemented
228C4×C22⋊C4C22×C1113yescomplemented
229C4×C22⋊C4C22×C1116yescomplemented
230C4×C22⋊C4C22×C1116yescomplemented
231C22×C11—212no—
232C22×C11—212no—
233C22×C11—26no—
234C22×C11—26no—
235C22×C11—416no—
236C22×C11—43no—
237C22×C11—43no—
238C22×C11—46no—
239C22×C11—46no—
240C22×C11—43no—
241C22×C11—43no—
242C22×C11—88no—
243C22×C11C22×#4113yes—
244C22×C11C2×H(5,𝔽2)13yes—
245C22×C11#58511yescharacteristic
246C4×C11—26no—
247C4×C11—26no—
248C4×C11—43no—
249C4×C11—46no—
250C4×C11—46no—
251C4×C11—41no—
252C4×C11—43no—
253C25C23×C1111yescharacteristic
254C25C23×C1111yescharacteristic
255C22×D4C23×C1116yes—
256C22×D4C23×C1113yes—
257C23×C4—46no—
258C23×C4C23×C1113yes—
259C23×C4C23×C1113yes—
260C23×C4C23×C1113yes—
261C23×C4C23×C1113yes—
262#125—46no—
263#123—212no—
264#120—212no—
265#120—212no—
266C4×D4—46no—
267C4×D4—412no—
268C2×C4⋊C4C23×C1116yes—
269C2×C4⋊C4C23×C1116yes—
270C2×C4⋊C4C23×C1113yes—
271C2×C4⋊C4C23×C1116yes—
272C2×C4⋊C4C23×C1113yes—
273C2×C4⋊C4C23×C1113yes—
274C2×C22⋊C4—46no—
275C2×C22⋊C4C23×C1116yes—
276C2×C22⋊C4C23×C1116yes—
277C2×C22⋊C4C23×C1116yes—
278C2×C22⋊C4C23×C1113yes—
279C2×C22⋊C4C23×C1113yes—
280C2×C22⋊C4C23×C1116yes—
281C2×C22⋊C4C23×C1113yes—
282C2×C22⋊C4C23×C1116yes—
283C2×C22⋊C4C23×C1113yes—
284C2×C22⋊C4C23×C1116yes—
285C2×C22⋊C4C23×C1113yes—
286C2×C22⋊C4C23×C1113yes—
287C2×C42C23×C1113yes—
288C2×C42C23×C1116yes—
289C2×C42C23×C1113yes—
290C2×C42C23×C1111yescharacteristic
291#95C23×C1116yes—
292#95C23×C1116yes—
293#95C23×C1116yes—
294#95C23×C1116yes—
295#95C23×C1116yes—
296#95C23×C1116yes—
297#95C23×C1112yes—
298C2×C11—46no—
299C2×C11—46no—
300C2×C11#348113yes—
301C2×C11#350513yes—
302C2×C11#353211yescharacteristic
303C24—26no—
304C24—26no—
305C24—43no—
306C24—41no—
307C24—43no—
308C24—41no—
309C24C24×C1113yes—
310C24C24×C1113yes—
311C2×D4—212no—
312C2×D4—212no—
313C2×D4—43no—
314C2×D4—46no—
315C2×D4—43no—
316C2×D4C11×#41112yes—
317C22×C4—26no—
318C22×C4—212no—
319C22×C4—26no—
320C22×C4—26no—
321C22×C4—43no—
322C22×C4—46no—
323C22×C4—43no—
324C22×C4—46no—
325C22×C4—43no—
326C22×C4—416no—
327C22×C4C24×C1116yes—
328C22×C4C24×C1116yes—
329C22×C4C24×C1111yescharacteristic
330C22×C4C24×C1113yes—
331C22×C4C24×C1113yes—
332C22×C4C24×C1113yes—
333C22×C4C24×C1113yes—
334C4⋊C4—212no—
335C4⋊C4—212no—
336C4⋊C4—43no—
337C4⋊C4—43no—
338C4⋊C4—43no—
339C4⋊C4—46no—
340C22⋊C4—26no—
341C22⋊C4—26no—
342C22⋊C4—26no—
343C22⋊C4—212no—
344C22⋊C4—212no—
345C22⋊C4—212no—
346C22⋊C4—212no—
347C22⋊C4—46no—
348C22⋊C4—43no—
349C22⋊C4—43no—
350C22⋊C4—46no—
351C22⋊C4—43no—
352C42—26no—
353C42—46no—
354C42—41no—
355C42—43no—
356C11#6003711yescharacteristic, direct product factor, Sylow
357C23—26no—
358C23—26no—
359C23—26no—
360C23—26no—
361C23—23no—
362C23—23no—
363C23—23no—
364C23—23no—
365C23—412no—
366C23—412no—
367C23—412no—
368C23—44no—
369C23—86no—
370C23—82no—
371C23C2×C11×#4116yes—
372C23C2×C11×#4116yes—
373C23C25×C1111yescharacteristic
374D4—412no—
375D4—424no—
376C2×C4—23no—
377C2×C4—26no—
378C2×C4—23no—
379C2×C4—26no—
380C2×C4—26no—
381C2×C4—26no—
382C2×C4—26no—
383C2×C4—23no—
384C2×C4—26no—
385C2×C4—26no—
386C2×C4—23no—
387C2×C4—26no—
388C2×C4—23no—
389C2×C4—26no—
390C2×C4—412no—
391C2×C4—412no—
392C2×C4—86no—
393C2×C4—86no—
394C2×C4C2×C11×#4116yes—
395C2×C4C11×H(5,𝔽2)16yes—
396C22—212no—
397C22—212no—
398C22—26no—
399C22—26no—
400C22—416no—
401C22—43no—
402C22—43no—
403C22—46no—
404C22—46no—
405C22—43no—
406C22—43no—
407C22—88no—
408C22C22×C11×#4113yes—
409C22C2×C11×H(5,𝔽2)13yes—
410C22C11×#58511yescharacteristic
411C4—26no—
412C4—26no—
413C4—46no—
414C4—43no—
415C4—46no—
416C4—41no—
417C4—43no—
418C2—46no—
419C2—46no—
420C2C11×#348113yes—
421C2C11×#350513yes—
422C2C11×#353211yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC11×#2679C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2697C2semidirect
3. C11×#2576C2semidirect
4. C11×#2566C2semidirect
5. C11×#2534C2semidirect
6. C11×#2460C2semidirect
7. C11×#2374C2semidirect
8. C11×#2358C2semidirect
9. C4×C11×#120C2semidirect
10. C24×C4×C11C22semidirect
11. C2×C11×#125C22semidirect
17. C22×C11×C22⋊C4C22semidirect
18. C11×#401C22semidirect
19. C11×#397C22semidirect
20. C11×#396C22semidirect
21. C11×#396C22semidirect
26. C11×#388C22semidirect
27. C11×#388C22semidirect
28. C11×#388C22semidirect
29. C11×#387C22semidirect
30. C11×#387C22semidirect
34. C11×#385C22semidirect
35. C11×#385C22semidirect
36. C11×#385C22semidirect
37. C11×#384C22semidirect
38. C11×#382C22semidirect
39. C11×#381C22semidirect
40. C11×#380C22semidirect
41. C11×#379C22semidirect
42. C11×#379C22semidirect
43. C4×C11×C4⋊C4C22semidirect
44. C4×C11×C22⋊C4C22semidirect
45. C4×C11×C22⋊C4C22semidirect
46. C4×C11×C22⋊C4C22semidirect
92. #60037C11direct (N × H)
146. #2697C2×C11semidirect
148. #2576C2×C11semidirect
149. #2566C2×C11semidirect
150. #2534C2×C11semidirect
151. #2460C2×C11semidirect
152. #2374C2×C11semidirect
153. #2358C2×C11semidirect
154. C4×#120C2×C11semidirect
194. C24×C4C22×C11semidirect
195. C2×#125C22×C11semidirect
201. C22×C22⋊C4C22×C11semidirect
202. #401C22×C11semidirect
203. #397C22×C11semidirect
204. #396C22×C11semidirect
205. #396C22×C11semidirect
210. #388C22×C11semidirect
211. #388C22×C11semidirect
212. #388C22×C11semidirect
213. #387C22×C11semidirect
214. #387C22×C11semidirect
218. #385C22×C11semidirect
219. #385C22×C11semidirect
220. #385C22×C11semidirect
221. #384C22×C11semidirect
222. #382C22×C11semidirect
223. #381C22×C11semidirect
224. #380C22×C11semidirect
225. #379C22×C11semidirect
226. #379C22×C11semidirect
227. C4×C4⋊C4C22×C11semidirect
228. C4×C22⋊C4C22×C11semidirect
229. C4×C22⋊C4C22×C11semidirect
230. C4×C22⋊C4C22×C11semidirect
356. C11#60037direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26972
C11×#26792
C11×#25762
C11×#25662
C11×#25342
C11×#24602
C11×#23742
C11×#23582
C4×C11×#1202
#6003711