Finite Group Databasebeta

← C11×#34529 #14611722

Subgroups — C11×#34529 #14611722

Order 2816.

2488 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×H(3,𝔽4)C211yesmaximal, characteristic
2C11×#2379C213yesmaximal, complemented
3C11×#2367C216yesmaximal, complemented
4C11×#2358C216yesmaximal, complemented
5C11×#2337C216yesmaximal, complemented
6C11×#2321C216yesmaximal, complemented
7C4×C11×#124C213yesmaximal, complemented
8C11×H(3,𝔽4)C4116yescomplemented
9C2×C11×#124C2213yes—
10C2×C11×#124C2216yes—
11C2×C11×#120C2216yes—
12C2×C4×Q8×C11C2213yescomplemented
13C2×C4×D4×C11C2213yes—
14C2×C4×D4×C11C2216yes—
15C22×C11×C22⋊C4C2216yescomplemented
16C11×#391C2216yescomplemented
17C11×#391C2213yescomplemented
18C11×#390C2213yes—
19C11×#390C2216yes—
20C11×#388C2216yescomplemented
21C11×#388C2216yescomplemented
22C11×#388C2216yescomplemented
23C11×#388C2216yescomplemented
24C11×#388C2216yescomplemented
25C11×#388C2216yescomplemented
26C11×#386C2216yes—
27C11×#386C2216yes—
28C11×#386C2216yes—
29C11×#385C2216yescomplemented
30C11×#385C2216yescomplemented
31C11×#385C2216yescomplemented
32C11×#383C2212yescomplemented
33C11×#382C2213yescomplemented
34C11×#379C2212yescomplemented
35C4×C11×C4⋊C4C2216yescomplemented
36C4×C11×C22⋊C4C2216yescomplemented
37C4×C11×C22⋊C4C2216yescomplemented
38C4×C11×C22⋊C4C2216yescomplemented
39C43×C11C2211yescharacteristic, complemented
40C25×C11C2312yes—
41C22×Q8×C11C2313yes—
42C22×D4×C11C2313yes—
43C22×D4×C11C2316yes—
44C23×C4×C11C2316yes—
45C23×C4×C11C2316yes—
46C11×#124C2×C4124yescomplemented
47C11×#124C2×C4148yescomplemented
48C11×#120C2×C4148yescomplemented
49C4×Q8×C11—46no—
50C4×D4×C11—46no—
51C4×D4×C11—412no—
52C2×C11×C4⋊C4C2316yes—
53C2×C11×C4⋊C4C2313yes—
54C2×C11×C4⋊C4C2316yes—
55C2×C11×C4⋊C4C2313yes—
56C2×C11×C22⋊C4—412no—
57C2×C11×C22⋊C4C2316yes—
58C2×C11×C22⋊C4C2316yes—
59C2×C11×C22⋊C4C2316yes—
60C2×C11×C22⋊C4C2316yes—
61C2×C11×C22⋊C4C2316yes—
62C2×C11×C22⋊C4C2316yes—
63C2×C11×C22⋊C4C2316yes—
64C2×C11×C22⋊C4C2316yes—
65C2×C11×C22⋊C4C2316yes—
66C2×C42×C11C2313yes—
67C2×C42×C11C2313yes—
68C2×C42×C11C2316yes—
69C2×C42×C11C2316yes—
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2312yes—
72C11×#95C2316yes—
73C11×#95C2316yes—
74C11×#95C2316yes—
75C11×#95C2316yes—
76C11×#95C2316yes—
77C11×#95C2316yes—
78#34529C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11—46no—
80C24×C11—46no—
81C24×C11C22×C418yes—
82C24×C11C2416yes—
83C2×Q8×C11—43no—
84C2×Q8×C11—43no—
85C2×Q8×C11C22×C4112yes—
86C2×D4×C11—43no—
87C2×D4×C11—46no—
88C2×D4×C11—43no—
89C2×D4×C11—46no—
90C2×D4×C11C22×C4112yes—
91C2×D4×C11C22×C4124yes—
92C22×C4×C11—212no—
93C22×C4×C11—46no—
94C22×C4×C11—46no—
95C22×C4×C11—46no—
96C22×C4×C11—46no—
97C22×C4×C11—46no—
98C22×C4×C11C2411yescharacteristic
99C22×C4×C11C2416yes—
100C22×C4×C11C2416yes—
101C22×C4×C11C2413yes—
102C22×C4×C11C2416yes—
103C22×C4×C11C2413yes—
104C11×C4⋊C4—212no—
105C11×C4⋊C4—46no—
106C11×C4⋊C4—43no—
107C11×C4⋊C4—43no—
108C11×C22⋊C4—212no—
109C11×C22⋊C4—212no—
110C11×C22⋊C4—46no—
111C11×C22⋊C4—46no—
112C11×C22⋊C4—46no—
113C11×C22⋊C4—46no—
114C11×C22⋊C4C22×C4124yes—
115C11×C22⋊C4C22×C4124yes—
116C11×C22⋊C4C22×C4124yes—
117C42×C11—26no—
118C42×C11—43no—
119C42×C11—46no—
120C42×C11—46no—
121C42×C11C22×C414yes—
122C42×C11C22×C418yes—
123C2×H(3,𝔽4)C2×C1111yescharacteristic
124#2379C2×C1113yescomplemented
125#2367C2×C1116yescomplemented
126#2358C2×C1116yescomplemented
127#2337C2×C1116yescomplemented
128#2321C2×C1116yescomplemented
129C4×#124C2×C1113yescomplemented
130C23×C11—26no—
131C23×C11—26no—
132C23×C11—26no—
133C23×C11—26no—
134C23×C11—26no—
135C23×C11—26no—
136C23×C11—424no—
137C23×C11—812no—
138C23×C11—84no—
139C23×C11C23×C4112yes—
140C23×C11C2511yescharacteristic
141Q8×C11—412no—
142D4×C11—412no—
143D4×C11—424no—
144C2×C4×C11—23no—
145C2×C4×C11—23no—
146C2×C4×C11—26no—
147C2×C4×C11—23no—
148C2×C4×C11—23no—
149C2×C4×C11—26no—
150C2×C4×C11—26no—
151C2×C4×C11—26no—
152C2×C4×C11—26no—
153C2×C4×C11—26no—
154C2×C4×C11—23no—
155C2×C4×C11—26no—
156C2×C4×C11—26no—
157C2×C4×C11—812no—
158C2×C4×C11—812no—
159C2×C4×C11C23×C416yes—
160C2×C4×C11C23×C4112yes—
161C2×C4×C11H(5,𝔽2)16yes—
162H(3,𝔽4)C4×C11116yescomplemented
163C2×#124C22×C1116yes—
164C2×#124C22×C1113yes—
165C2×#120C22×C1116yes—
166C2×C4×Q8C22×C1113yescomplemented
167C2×C4×D4C22×C1116yes—
168C2×C4×D4C22×C1113yes—
169C22×C22⋊C4C22×C1116yescomplemented
170#391C22×C1113yescomplemented
171#391C22×C1116yescomplemented
172#390C22×C1113yes—
173#390C22×C1116yes—
174#388C22×C1116yescomplemented
175#388C22×C1116yescomplemented
176#388C22×C1116yescomplemented
177#388C22×C1116yescomplemented
178#388C22×C1116yescomplemented
179#388C22×C1116yescomplemented
180#386C22×C1116yes—
181#386C22×C1116yes—
182#386C22×C1116yes—
183#385C22×C1116yescomplemented
184#385C22×C1116yescomplemented
185#385C22×C1116yescomplemented
186#383C22×C1112yescomplemented
187#382C22×C1113yescomplemented
188#379C22×C1112yescomplemented
189C4×C4⋊C4C22×C1116yescomplemented
190C4×C22⋊C4C22×C1116yescomplemented
191C4×C22⋊C4C22×C1116yescomplemented
192C4×C22⋊C4C22×C1116yescomplemented
193C43C22×C1111yescharacteristic, complemented
194C22×C11—212no—
195C22×C11—212no—
196C22×C11—212no—
197C22×C11—46no—
198C22×C11—46no—
199C22×C11—46no—
200C22×C11—46no—
201C22×C11—816no—
202C22×C11C24×C411yescharacteristic
203C22×C11C2×H(5,𝔽2)13yes—
204C22×C11#58513yes—
205C4×C11—26no—
206C4×C11—212no—
207C4×C11—26no—
208C4×C11—46no—
209C4×C11—46no—
210C4×C11—41no—
211C25C23×C1112yes—
212C22×Q8C23×C1113yes—
213C22×D4C23×C1116yes—
214C22×D4C23×C1113yes—
215C23×C4C23×C1116yes—
216C23×C4C23×C1116yes—
217#124C2×C4×C11148yescomplemented
218#124C2×C4×C11124yescomplemented
219#120C2×C4×C11148yescomplemented
220C4×Q8—46no—
221C4×D4—46no—
222C4×D4—412no—
223C2×C4⋊C4C23×C1116yes—
224C2×C4⋊C4C23×C1113yes—
225C2×C4⋊C4C23×C1113yes—
226C2×C4⋊C4C23×C1116yes—
227C2×C22⋊C4—412no—
228C2×C22⋊C4C23×C1116yes—
229C2×C22⋊C4C23×C1116yes—
230C2×C22⋊C4C23×C1116yes—
231C2×C22⋊C4C23×C1116yes—
232C2×C22⋊C4C23×C1116yes—
233C2×C22⋊C4C23×C1116yes—
234C2×C22⋊C4C23×C1116yes—
235C2×C22⋊C4C23×C1116yes—
236C2×C22⋊C4C23×C1116yes—
237C2×C42C23×C1113yes—
238C2×C42C23×C1116yes—
239C2×C42C23×C1116yes—
240C2×C42C23×C1113yes—
241C2×C42C23×C1111yescharacteristic
242C2×C42C23×C1112yes—
243#95C23×C1116yes—
244#95C23×C1116yes—
245#95C23×C1116yes—
246#95C23×C1116yes—
247#95C23×C1116yes—
248#95C23×C1116yes—
249C2×C11—412no—
250C2×C11C4×H(5,𝔽2)13yes—
251C2×C11#355813yes—
252C2×C11#356811yescharacteristic
253C24—46no—
254C24—46no—
255C24C22×C4×C1118yes—
256C24C24×C1116yes—
257C2×Q8—43no—
258C2×Q8—43no—
259C2×Q8C22×C4×C11112yes—
260C2×D4—43no—
261C2×D4—46no—
262C2×D4—43no—
263C2×D4—46no—
264C2×D4C22×C4×C11124yes—
265C2×D4C22×C4×C11112yes—
266C22×C4—212no—
267C22×C4—46no—
268C22×C4—46no—
269C22×C4—46no—
270C22×C4—46no—
271C22×C4—46no—
272C22×C4C24×C1111yescharacteristic
273C22×C4C24×C1116yes—
274C22×C4C24×C1116yes—
275C22×C4C24×C1113yes—
276C22×C4C24×C1116yes—
277C22×C4C24×C1113yes—
278C4⋊C4—212no—
279C4⋊C4—43no—
280C4⋊C4—43no—
281C4⋊C4—46no—
282C22⋊C4—212no—
283C22⋊C4—212no—
284C22⋊C4—46no—
285C22⋊C4—46no—
286C22⋊C4—46no—
287C22⋊C4—46no—
288C22⋊C4C22×C4×C11124yes—
289C22⋊C4C22×C4×C11124yes—
290C22⋊C4C22×C4×C11124yes—
291C42—26no—
292C42—46no—
293C42—46no—
294C42—43no—
295C42C22×C4×C1114yes—
296C42C22×C4×C1118yes—
297C11#3452911yescharacteristic, direct product factor, Sylow
298C23—26no—
299C23—26no—
300C23—26no—
301C23—26no—
302C23—26no—
303C23—26no—
304C23—424no—
305C23—812no—
306C23—84no—
307C23C23×C4×C11112yes—
308C23C25×C1111yescharacteristic
309Q8—412no—
310D4—412no—
311D4—424no—
312C2×C4—23no—
313C2×C4—23no—
314C2×C4—26no—
315C2×C4—23no—
316C2×C4—23no—
317C2×C4—26no—
318C2×C4—26no—
319C2×C4—26no—
320C2×C4—26no—
321C2×C4—26no—
322C2×C4—23no—
323C2×C4—26no—
324C2×C4—26no—
325C2×C4—812no—
326C2×C4—812no—
327C2×C4C23×C4×C1116yes—
328C2×C4C23×C4×C11112yes—
329C2×C4C11×H(5,𝔽2)16yes—
330C22—212no—
331C22—212no—
332C22—212no—
333C22—46no—
334C22—46no—
335C22—46no—
336C22—46no—
337C22—816no—
338C22C24×C4×C1111yescharacteristic
339C22C2×C11×H(5,𝔽2)13yes—
340C22C11×#58513yes—
341C4—26no—
342C4—212no—
343C4—26no—
344C4—46no—
345C4—46no—
346C4—41no—
347C2—412no—
348C2C4×C11×H(5,𝔽2)13yes—
349C2C11×#355813yes—
350C2C11×#356811yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×H(3,𝔽4)C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2379C2semidirect
3. C11×#2367C2semidirect
4. C11×#2358C2semidirect
5. C11×#2337C2semidirect
6. C11×#2321C2semidirect
7. C4×C11×#124C2semidirect
8. C11×H(3,𝔽4)C4semidirect
12. C2×C4×Q8×C11C22semidirect
15. C22×C11×C22⋊C4C22semidirect
16. C11×#391C22semidirect
17. C11×#391C22semidirect
20. C11×#388C22semidirect
21. C11×#388C22semidirect
22. C11×#388C22semidirect
23. C11×#388C22semidirect
24. C11×#388C22semidirect
25. C11×#388C22semidirect
29. C11×#385C22semidirect
30. C11×#385C22semidirect
31. C11×#385C22semidirect
32. C11×#383C22semidirect
33. C11×#382C22semidirect
34. C11×#379C22semidirect
35. C4×C11×C4⋊C4C22semidirect
36. C4×C11×C22⋊C4C22semidirect
37. C4×C11×C22⋊C4C22semidirect
38. C4×C11×C22⋊C4C22semidirect
39. C43×C11C22semidirect
46. C11×#124C2×C4semidirect
47. C11×#124C2×C4semidirect
48. C11×#120C2×C4semidirect
78. #34529C11direct (N × H)
124. #2379C2×C11semidirect
125. #2367C2×C11semidirect
126. #2358C2×C11semidirect
127. #2337C2×C11semidirect
128. #2321C2×C11semidirect
129. C4×#124C2×C11semidirect
162. H(3,𝔽4)C4×C11semidirect
166. C2×C4×Q8C22×C11semidirect
169. C22×C22⋊C4C22×C11semidirect
170. #391C22×C11semidirect
171. #391C22×C11semidirect
174. #388C22×C11semidirect
175. #388C22×C11semidirect
176. #388C22×C11semidirect
177. #388C22×C11semidirect
178. #388C22×C11semidirect
179. #388C22×C11semidirect
183. #385C22×C11semidirect
184. #385C22×C11semidirect
185. #385C22×C11semidirect
186. #383C22×C11semidirect
187. #382C22×C11semidirect
188. #379C22×C11semidirect
189. C4×C4⋊C4C22×C11semidirect
190. C4×C22⋊C4C22×C11semidirect
191. C4×C22⋊C4C22×C11semidirect
192. C4×C22⋊C4C22×C11semidirect
193. C43C22×C11semidirect
217. #124C2×C4×C11semidirect
218. #124C2×C4×C11semidirect
219. #120C2×C4×C11semidirect
297. C11#34529direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×H(3,𝔽4)2
C11×#23792
C11×#23672
C11×#23582
C11×#23372
C11×#23212
C4×C11×#1242
#3452911