Finite Group Databasebeta

← C11×#19001 #14596194

Subgroups — C11×#19001 #14596194

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#562C211yesmaximal, characteristic, complemented
2C11×#3213C212yesmaximal, complemented
3C11×#3142C211yesmaximal, characteristic, complemented
4C11×#1662C214yesmaximal, complemented
5C11×#1656C214yesmaximal, complemented
6C11×#1534C211yesmaximal, characteristic, complemented
7C11×#1527C212yesmaximal, complemented
8C11×#562—22no—
9C11×#562—24no—
10C11×#562C2214yes—
11C11×#532C2211yescharacteristic
12C2×C11×#125C2211yescharacteristic
13C2×C11×#124C2212yes—
14C2×C11×#123—22no—
15C2×C11×C22⋊Q8—22no—
16C2×C11×#121—22no—
17C11×#496C2214yescomplemented
18C11×#491C2212yescomplemented
19C11×#490C2212yescomplemented
20C11×#489C2214yescomplemented
21C11×#488—22no—
22C11×#463—24no—
23C11×#448—22no—
24C11×#447—22no—
25C11×#432C2212yes—
26C11×#417—22no—
27C4×C11×M16C2211yescharacteristic
28C11×#330C2214yescomplemented
29C11×#329C2218yescomplemented
30C2×C11×#41—21no—
31C22×Q8×C11D412yes—
32C22×D4×C11—22no—
33C22×D4×C11D412yes—
34C23×C4×C11—22no—
35C2×C11×SD16—24no—
36C2×C11×D8—24no—
37C2×C11×M16—21no—
38C11×C4⋊Q8C2311yescharacteristic
39C11×#127C2311yescharacteristic
40C11×#125—22no—
41C11×#125D412yes—
42C11×#125C2312yes—
43C11×#124—22no—
44C11×#124—22no—
45C11×#124—21no—
46C11×#124D414yes—
47C11×#124C2314yes—
48C11×#123—28no—
49C11×#123—28no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8—28no—
52C11×#121—28no—
53C11×#121—28no—
54C11×#121—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4D412yes—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11C2311yescharacteristic
63C11×C4⋊C8—22no—
64C11×#103—24no—
65C11×#103—24no—
66C11×#102—24no—
67C11×#102—24no—
68C11×C22⋊C8—22no—
69C11×#97C2314yes—
70C11×#97C2312yes—
71C4×C8×C11—21no—
72#19001C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—22no—
74C11×#41—44no—
75C2×Q8×C11—22no—
76C2×Q8×C11—21no—
77C2×Q8×C11—82no—
78C2×Q8×C11C2×D414yes—
79C2×D4×C11—28no—
80C2×D4×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—41no—
84C2×D4×C11—82no—
85C2×D4×C11—84no—
86C2×D4×C11C2×D414yes—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—28no—
90C22×C4×C11—41no—
91C22×C4×C11—84no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D412yes—
94C11×SD16—84no—
95C11×D8—84no—
96C11×M16—42no—
97C2×C8×C11—22no—
98C2×C8×C11—24no—
99C11×C4⋊C4—28no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4C2×D414yes—
105C11×C22⋊C4—28no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—24no—
110C11×C22⋊C4—42no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D412yes—
113C42×C11C2411yescharacteristic
114C2×#562C2×C1111yescharacteristic, complemented
115#3213C2×C1112yescomplemented
116#3142C2×C1111yescharacteristic, complemented
117#1662C2×C1114yescomplemented
118#1656C2×C1114yescomplemented
119#1534C2×C1111yescharacteristic, complemented
120#1527C2×C1112yescomplemented
121C23×C11—24no—
122C23×C11—44no—
123C23×C11—44no—
124C23×C11—44no—
125C23×C11—41no—
126C23×C11#12011yescharacteristic
127Q8×C11—44no—
128Q8×C11—42no—
129Q8×C11—82no—
130D4×C11—44no—
131D4×C11—44no—
132D4×C11—42no—
133D4×C11—82no—
134D4×C11—88no—
135D4×C11—82no—
136C2×C4×C11—22no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—42no—
140C2×C4×C11—44no—
141C2×C4×C11—44no—
142C2×C4×C11—41no—
143C2×C4×C11—82no—
144C2×C4×C11—88no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12012yes—
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C22×D412yes—
149C8×C11—42no—
150C8×C11—44no—
151#562—22no—
152#562—24no—
153#562C22×C1114yes—
154#532C22×C1111yescharacteristic
155C2×#125C22×C1111yescharacteristic
156C2×#124C22×C1112yes—
157C2×#123—22no—
158C2×C22⋊Q8—22no—
159C2×#121—22no—
160#496C22×C1114yescomplemented
161#491C22×C1112yescomplemented
162#490C22×C1112yescomplemented
163#489C22×C1114yescomplemented
164#488—22no—
165#463—24no—
166#448—22no—
167#447—22no—
168#432C22×C1112yes—
169#417—22no—
170C4×M16C22×C1111yescharacteristic
171#330C22×C1114yescomplemented
172#329C22×C1118yescomplemented
173C22×C11—22no—
174C22×C11—44no—
175C22×C11—44no—
176C22×C11—44no—
177C22×C11—88no—
178C22×C11—81no—
179C22×C11—82no—
180C22×C11#45412yes—
181C22×C11C2×#12011yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—44no—
187C4×C11—44no—
188C4×C11—81no—
189C2×#41—21no—
190C22×Q8D4×C1112yes—
191C22×D4—22no—
192C22×D4D4×C1112yes—
193C23×C4—22no—
194C2×SD16—24no—
195C2×D8—24no—
196C2×M16—21no—
197C4⋊Q8C23×C1111yescharacteristic
198#127C23×C1111yescharacteristic
199#125—22no—
200#125D4×C1112yes—
201#125C23×C1112yes—
202#124—22no—
203#124—22no—
204#124—21no—
205#124D4×C1114yes—
206#124C23×C1114yes—
207#123—28no—
208#123—28no—
209C22⋊Q8—28no—
210C22⋊Q8—28no—
211#121—28no—
212#121—28no—
213#121—22no—
214C4×D4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4D4×C1112yes—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C42C23×C1111yescharacteristic
222C4⋊C8—22no—
223#103—24no—
224#103—24no—
225#102—24no—
226#102—24no—
227C22⋊C8—22no—
228#97C23×C1112yes—
229#97C23×C1114yes—
230C4×C8—21no—
231C2×C11—22no—
232C2×C11—84no—
233C2×C11—161no—
234C2×C11C2×#45411yescharacteristic
235C2×C11#301912yes—
236C24—22no—
237#41—44no—
238C2×Q8—22no—
239C2×Q8—21no—
240C2×Q8—82no—
241C2×Q8C2×D4×C1114yes—
242C2×D4—28no—
243C2×D4—22no—
244C2×D4—21no—
245C2×D4—22no—
246C2×D4—41no—
247C2×D4—82no—
248C2×D4—84no—
249C2×D4C2×D4×C1114yes—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—28no—
253C22×C4—41no—
254C22×C4—84no—
255C22×C4C2×D4×C1111yescharacteristic
256C22×C4C2×D4×C1112yes—
257SD16—84no—
258D8—84no—
259M16—42no—
260C2×C8—22no—
261C2×C8—24no—
262C4⋊C4—28no—
263C4⋊C4—24no—
264C4⋊C4—22no—
265C4⋊C4—24no—
266C4⋊C4—22no—
267C4⋊C4C2×D4×C1114yes—
268C22⋊C4—28no—
269C22⋊C4—24no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—42no—
274C42C2×D4×C1111yescharacteristic
275C42C2×D4×C1112yes—
276C42C24×C1111yescharacteristic
277C11#1900111yescharacteristic, direct product factor, Sylow
278C23—24no—
279C23—44no—
280C23—44no—
281C23—44no—
282C23—41no—
283C23C11×#12011yescharacteristic
284Q8—44no—
285Q8—42no—
286Q8—82no—
287D4—44no—
288D4—44no—
289D4—42no—
290D4—82no—
291D4—88no—
292D4—82no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—42no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—41no—
300C2×C4—82no—
301C2×C4—88no—
302C2×C4C11×#12011yescharacteristic
303C2×C4C11×#12012yes—
304C2×C4C22×D4×C1111yescharacteristic
305C2×C4C22×D4×C1112yes—
306C8—42no—
307C8—44no—
308C22—22no—
309C22—44no—
310C22—44no—
311C22—44no—
312C22—88no—
313C22—81no—
314C22—82no—
315C22C11×#45412yes—
316C22C2×C11×#12011yescharacteristic
317C4—21no—
318C4—21no—
319C4—22no—
320C4—22no—
321C4—44no—
322C4—44no—
323C4—81no—
324C2—22no—
325C2—84no—
326C2—161no—
327C2C2×C11×#45411yescharacteristic
328C2C11×#301912yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#562C2semidirect
2. C11×#3213C2semidirect
3. C11×#3142C2semidirect
4. C11×#1662C2semidirect
5. C11×#1656C2semidirect
6. C11×#1534C2semidirect
7. C11×#1527C2semidirect
17. C11×#496C22semidirect
18. C11×#491C22semidirect
19. C11×#490C22semidirect
20. C11×#489C22semidirect
28. C11×#330C22semidirect
29. C11×#329C22semidirect
72. #19001C11direct (N × H)
114. C2×#562C2×C11semidirect
115. #3213C2×C11semidirect
116. #3142C2×C11semidirect
117. #1662C2×C11semidirect
118. #1656C2×C11semidirect
119. #1534C2×C11semidirect
120. #1527C2×C11semidirect
160. #496C22×C11semidirect
161. #491C22×C11semidirect
162. #490C22×C11semidirect
163. #489C22×C11semidirect
171. #330C22×C11semidirect
172. #329C22×C11semidirect
277. C11#19001direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5622
C11×#32132
C11×#31422
C11×#16622
C11×#16562
C11×#15342
C11×#15272
#1900111