Finite Group Databasebeta

← C11×#2411 #13065249

Subgroups — C11×#2411 #13065249

Order 1408.

786 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#123C211yesmaximal, characteristic, complemented
2C2×C11×#120C211yesmaximal, characteristic
3C2×C11×#117C211yesmaximal, characteristic, complemented
4C22×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C11×#396C212yesmaximal, complemented
6C11×#394C212yesmaximal, complemented
7C11×#390C212yesmaximal, complemented
8C11×#388C212yesmaximal, complemented
9C11×#386C211yesmaximal, characteristic, complemented
10C11×#385C211yesmaximal, characteristic, complemented
11C11×#379C211yesmaximal, characteristic, complemented
12C25×C11C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C22×D4×C11C2212yes—
15C23×C4×C11C2211yescharacteristic
16C23×C4×C11C2211yescharacteristic
17C11×#123—24no—
18C11×#120—24no—
19C11×#117—24no—
20C2×C11×C4⋊C4C2212yescomplemented
21C2×C11×C4⋊C4C2211yescharacteristic, complemented
22C2×C11×C4⋊C4C2211yescharacteristic, complemented
23C2×C11×C4⋊C4C2212yescomplemented
24C2×C11×C22⋊C4—24no—
25C2×C11×C22⋊C4C2212yes—
26C2×C11×C22⋊C4C2212yes—
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2212yes—
30C2×C11×C22⋊C4C2212yes—
31C2×C11×C22⋊C4C2212yes—
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic, complemented
34C2×C11×C22⋊C4C2211yescharacteristic, complemented
35C2×C11×C22⋊C4C2212yescomplemented
36C2×C42×C11C2212yescomplemented
37C11×#95C2212yescomplemented
38C11×#95C2212yescomplemented
39C24×C11—22no—
40C24×C11—24no—
41C24×C11—22no—
42C24×C11—22no—
43C24×C11—42no—
44C24×C11C2311yescharacteristic
45C24×C11C2312yes—
46C24×C11C2311yescharacteristic
47C2×D4×C11—22no—
48C2×D4×C11—22no—
49C2×D4×C11—24no—
50C2×D4×C11—22no—
51C2×D4×C11—24no—
52C2×D4×C11—42no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—42no—
57C22×C4×C11D414yescomplemented
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2312yes—
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2312yes—
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2312yes—
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C11×C4⋊C4—24no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—22no—
69C11×C4⋊C4—42no—
70C11×C22⋊C4—22no—
71C11×C22⋊C4—22no—
72C11×C22⋊C4—24no—
73C11×C22⋊C4—24no—
74C11×C22⋊C4—24no—
75C11×C22⋊C4—24no—
76C11×C22⋊C4—22no—
77C11×C22⋊C4—22no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4D414yes—
81C42×C11—24no—
82#2411C1111yesmaximal, characteristic, direct product factor, Sylow
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—28no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—22no—
96C23×C11—22no—
97C23×C11—48no—
98C23×C11—48no—
99C23×C11—44no—
100C23×C11—44no—
101C23×C11C2×D412yes—
102C23×C11C2×D412yes—
103C23×C11#4114yes—
104C23×C11#4112yes—
105C23×C11C2411yescharacteristic
106D4×C11—48no—
107D4×C11—44no—
108C2×C4×C11—28no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—21no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—44no—
129C2×C4×C11C2×D414yes—
130C2×C4×C11C2×D412yes—
131C2×C4×C11C2×D412yes—
132C2×#123C2×C1111yescharacteristic, complemented
133C2×#120C2×C1111yescharacteristic
134C2×#117C2×C1111yescharacteristic, complemented
135C22×C22⋊C4C2×C1111yescharacteristic, complemented
136#396C2×C1112yescomplemented
137#394C2×C1112yescomplemented
138#390C2×C1112yescomplemented
139#388C2×C1112yescomplemented
140#386C2×C1111yescharacteristic, complemented
141#385C2×C1111yescharacteristic, complemented
142#379C2×C1111yescharacteristic, complemented
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—24no—
146C22×C11—24no—
147C22×C11—24no—
148C22×C11—24no—
149C22×C11—24no—
150C22×C11—416no—
151C22×C11—42no—
152C22×C11—42no—
153C22×C11—42no—
154C22×C11—42no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11#12114yes—
161C22×C11C22×D411yescharacteristic
162C22×C11C22×D411yescharacteristic
163C22×C11C2×#4111yescharacteristic
164C22×C11C2×#4112yes—
165C22×C11H(5,𝔽2)12yes—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—24no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—42no—
173C4×C11—42no—
174C25C22×C1111yescharacteristic
175C22×D4C22×C1111yescharacteristic
176C22×D4C22×C1112yes—
177C23×C4C22×C1111yescharacteristic
178C23×C4C22×C1111yescharacteristic
179#123—24no—
180#120—24no—
181#117—24no—
182C2×C4⋊C4C22×C1112yescomplemented
183C2×C4⋊C4C22×C1111yescharacteristic, complemented
184C2×C4⋊C4C22×C1111yescharacteristic, complemented
185C2×C4⋊C4C22×C1112yescomplemented
186C2×C22⋊C4—24no—
187C2×C22⋊C4C22×C1112yes—
188C2×C22⋊C4C22×C1112yes—
189C2×C22⋊C4C22×C1111yescharacteristic
190C2×C22⋊C4C22×C1112yes—
191C2×C22⋊C4C22×C1111yescharacteristic
192C2×C22⋊C4C22×C1112yes—
193C2×C22⋊C4C22×C1112yes—
194C2×C22⋊C4C22×C1111yescharacteristic
195C2×C22⋊C4C22×C1111yescharacteristic, complemented
196C2×C22⋊C4C22×C1111yescharacteristic, complemented
197C2×C22⋊C4C22×C1112yescomplemented
198C2×C42C22×C1112yescomplemented
199#95C22×C1112yescomplemented
200#95C22×C1112yescomplemented
201C2×C11—24no—
202C2×C11—44no—
203C2×C11—81no—
204C2×C11C2×#12111yescharacteristic
205C2×C11#52511yescharacteristic
206C2×C11#53511yescharacteristic
207C2×C11#54612yes—
208C2×C11#55112yes—
209C24—22no—
210C24—24no—
211C24—22no—
212C24—22no—
213C24—42no—
214C24C23×C1111yescharacteristic
215C24C23×C1112yes—
216C24C23×C1111yescharacteristic
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—24no—
220C2×D4—22no—
221C2×D4—24no—
222C2×D4—42no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—42no—
227C22×C4D4×C1114yescomplemented
228C22×C4C23×C1111yescharacteristic
229C22×C4C23×C1112yes—
230C22×C4C23×C1111yescharacteristic
231C22×C4C23×C1112yes—
232C22×C4C23×C1111yescharacteristic
233C22×C4C23×C1112yes—
234C22×C4C23×C1111yescharacteristic
235C22×C4C23×C1111yescharacteristic
236C4⋊C4—24no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C22⋊C4—24no—
243C22⋊C4—24no—
244C22⋊C4—24no—
245C22⋊C4—24no—
246C22⋊C4—22no—
247C22⋊C4—22no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4D4×C1114yes—
251C42—24no—
252C11#241111yescharacteristic, direct product factor, Sylow
253C23—22no—
254C23—22no—
255C23—28no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—22no—
266C23—22no—
267C23—48no—
268C23—48no—
269C23—44no—
270C23—44no—
271C23C2×D4×C1112yes—
272C23C2×D4×C1112yes—
273C23C11×#4114yes—
274C23C11×#4112yes—
275C23C24×C1111yescharacteristic
276D4—48no—
277D4—44no—
278C2×C4—28no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—44no—
299C2×C4C2×D4×C1114yes—
300C2×C4C2×D4×C1112yes—
301C2×C4C2×D4×C1112yes—
302C22—22no—
303C22—22no—
304C22—24no—
305C22—24no—
306C22—24no—
307C22—24no—
308C22—24no—
309C22—416no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—42no—
318C22—42no—
319C22C11×#12114yes—
320C22C22×D4×C1111yescharacteristic
321C22C22×D4×C1111yescharacteristic
322C22C2×C11×#4111yescharacteristic
323C22C2×C11×#4112yes—
324C22C11×H(5,𝔽2)12yes—
325C4—22no—
326C4—22no—
327C4—24no—
328C4—41no—
329C4—41no—
330C4—42no—
331C4—41no—
332C4—42no—
333C2—24no—
334C2—44no—
335C2—81no—
336C2C2×C11×#12111yescharacteristic
337C2C11×#52511yescharacteristic
338C2C11×#53511yescharacteristic
339C2C11×#54612yes—
340C2C11×#55112yes—
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC2×C11×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#123C2semidirect
3. C2×C11×#117C2semidirect
4. C22×C11×C22⋊C4C2semidirect
5. C11×#396C2semidirect
6. C11×#394C2semidirect
7. C11×#390C2semidirect
8. C11×#388C2semidirect
9. C11×#386C2semidirect
10. C11×#385C2semidirect
11. C11×#379C2semidirect
20. C2×C11×C4⋊C4C22semidirect
21. C2×C11×C4⋊C4C22semidirect
22. C2×C11×C4⋊C4C22semidirect
23. C2×C11×C4⋊C4C22semidirect
33. C2×C11×C22⋊C4C22semidirect
34. C2×C11×C22⋊C4C22semidirect
35. C2×C11×C22⋊C4C22semidirect
36. C2×C42×C11C22semidirect
37. C11×#95C22semidirect
38. C11×#95C22semidirect
57. C22×C4×C11D4semidirect
82. #2411C11direct (N × H)
132. C2×#123C2×C11semidirect
134. C2×#117C2×C11semidirect
135. C22×C22⋊C4C2×C11semidirect
136. #396C2×C11semidirect
137. #394C2×C11semidirect
138. #390C2×C11semidirect
139. #388C2×C11semidirect
140. #386C2×C11semidirect
141. #385C2×C11semidirect
142. #379C2×C11semidirect
182. C2×C4⋊C4C22×C11semidirect
183. C2×C4⋊C4C22×C11semidirect
184. C2×C4⋊C4C22×C11semidirect
185. C2×C4⋊C4C22×C11semidirect
195. C2×C22⋊C4C22×C11semidirect
196. C2×C22⋊C4C22×C11semidirect
197. C2×C22⋊C4C22×C11semidirect
198. C2×C42C22×C11semidirect
199. #95C22×C11semidirect
200. #95C22×C11semidirect
227. C22×C4D4×C11semidirect
252. C11#2411direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×C11×#1202
C2×C11×#1172
C22×C11×C22⋊C42
C11×#3962
C11×#3942
C11×#3902
C11×#3882
C11×#3862
C11×#3852
C11×#3792
#241111