Finite Group Databasebeta

← C11×#23897 #14601090

Subgroups — C11×#23897 #14601090

Order 2816.

1952 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1952 conjugacy classes of subgroups — too many to draw. Only its 282 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3484C212yesmaximal, complemented
2C11×#3019C214yesmaximal, complemented
3C11×#2010C214yesmaximal, complemented
4C11×#1911C214yesmaximal, complemented
5C11×#1783C211yesmaximal, characteristic, complemented
6C2×C11×H(5,𝔽2)C2212yescomplemented
7C23×D4×C11C2211yescharacteristic
8C11×#575C2214yescomplemented
9C11×#546—28no—
10D42×C11—28no—
11C11×#535C2214yes—
12C11×#534—24no—
13C11×#525C2214yescomplemented
14C2×C11×#120—24no—
15C11×#518C2212yescomplemented
16C11×#455—28no—
17C11×#453—28no—
18C11×#421C2218yescomplemented
19C2×C11×#100C2214yescomplemented
20C11×#407C2212yescomplemented
21C11×H(3,ℤ/4)C2214yescomplemented
22C25×C11D412yes—
23C11×H(5,𝔽2)—28no—
24C11×H(5,𝔽2)—44no—
25C2×C11×#41—24no—
26C2×C11×#41C2314yes—
27C22×D4×C11—24no—
28C22×D4×C11—28no—
29C22×D4×C11—28no—
30C22×D4×C11—24no—
31C22×D4×C11—42no—
32C22×D4×C11D412yes—
33C22×D4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C11×#137—28no—
36C11×AGL(1,ℤ/8)—28no—
37C11×#135—44no—
38C2×C11×M16C2314yes—
39C11×#127D418yescomplemented
40C11×#124D418yescomplemented
41C11×#123—28no—
42C11×#123—24no—
43C11×C22⋊Q8—24no—
44C11×#121—216no—
45C11×#121—28no—
46C11×#121—24no—
47C11×#120—216no—
48C11×#120—28no—
49C11×#120—24no—
50C11×#120—28no—
51C4×D4×C11—28no—
52C4×D4×C11—28no—
53C11×#117C2314yes—
54C2×C11×C22⋊C4—28no—
55C2×C11×C22⋊C4—24no—
56C11×#104—216no—
57C11×#100—28no—
58C11×C22⋊C8—42no—
59#23897C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11—24no—
61C24×C11—28no—
62C24×C11—42no—
63C24×C11—84no—
64C24×C11C2×D411yescharacteristic
65C24×C11C2×D414yes—
66C11×#41—28no—
67C11×#41—28no—
68C11×#41—416no—
69C2×Q8×C11C2×D414yescomplemented
70C2×D4×C11—28no—
71C2×D4×C11—28no—
72C2×D4×C11—28no—
73C2×D4×C11—24no—
74C2×D4×C11—216no—
75C2×D4×C11—24no—
76C2×D4×C11—24no—
77C2×D4×C11—42no—
78C2×D4×C11—416no—
79C2×D4×C11—416no—
80C2×D4×C11—48no—
81C2×D4×C11—48no—
82C2×D4×C11—816no—
83C2×D4×C11C2×D418yes—
84C2×D4×C11C2×D414yescomplemented
85C22×C4×C11—24no—
86C22×C4×C11—28no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—22no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2411yescharacteristic
92C11×Q16—44no—
93C11×SD16—48no—
94C11×D8—44no—
95C11×M16—28no—
96C2×C8×C11—24no—
97C11×C4⋊C4—28no—
98C11×C4⋊C4—24no—
99C11×C22⋊C4—28no—
100C11×C22⋊C4—28no—
101C11×C22⋊C4—28no—
102C11×C22⋊C4—216no—
103C11×C22⋊C4—24no—
104C42×C11C2×D418yescomplemented
105#3484C2×C1112yescomplemented
106#3019C2×C1114yescomplemented
107#2010C2×C1114yescomplemented
108#1911C2×C1114yescomplemented
109#1783C2×C1111yescharacteristic, complemented
110C23×C11—22no—
111C23×C11—24no—
112C23×C11—21no—
113C23×C11—24no—
114C23×C11—24no—
115C23×C11—42no—
116C23×C11—48no—
117C23×C11—416no—
118C23×C11—48no—
119C23×C11—84no—
120C23×C11—84no—
121C23×C11—88no—
122C23×C11—88no—
123C23×C11—84no—
124C23×C11#12018yes—
125C23×C11C22×D411yescharacteristic
126Q8×C11—28no—
127D4×C11—216no—
128D4×C11—28no—
129D4×C11—48no—
130D4×C11—416no—
131D4×C11—416no—
132D4×C11—44no—
133D4×C11—44no—
134D4×C11—816no—
135C2×C4×C11—28no—
136C2×C4×C11—24no—
137C2×C4×C11—22no—
138C2×C4×C11—21no—
139C2×C4×C11—48no—
140C2×C4×C11—44no—
141C2×C4×C11—48no—
142C2×C4×C11—88no—
143C2×C4×C11C22×D414yes—
144C2×C4×C11H(5,𝔽2)12yes—
145C8×C11—44no—
146C2×H(5,𝔽2)C22×C1112yescomplemented
147C23×D4C22×C1111yescharacteristic
148#575C22×C1114yescomplemented
149#546—28no—
150D42—28no—
151#535C22×C1114yes—
152#534—24no—
153#525C22×C1114yescomplemented
154C2×#120—24no—
155#518C22×C1112yescomplemented
156#455—28no—
157#453—28no—
158#421C22×C1118yescomplemented
159C2×#100C22×C1114yescomplemented
160#407C22×C1112yescomplemented
161H(3,ℤ/4)C22×C1114yescomplemented
162C22×C11—24no—
163C22×C11—22no—
164C22×C11—28no—
165C22×C11—41no—
166C22×C11—48no—
167C22×C11—48no—
168C22×C11—42no—
169C22×C11—41no—
170C22×C11—48no—
171C22×C11—41no—
172C22×C11—44no—
173C22×C11—84no—
174C22×C11—816no—
175C22×C11—168no—
176C22×C11C2×#12012yes—
177C22×C11#53411yescharacteristic
178C4×C11—48no—
179C4×C11—41no—
180C4×C11—44no—
181C4×C11D4214yes—
182C25D4×C1112yes—
183H(5,𝔽2)—28no—
184H(5,𝔽2)—44no—
185C2×#41—24no—
186C2×#41C23×C1114yes—
187C22×D4—24no—
188C22×D4—28no—
189C22×D4—28no—
190C22×D4—24no—
191C22×D4—42no—
192C22×D4D4×C1112yes—
193C22×D4C23×C1112yes—
194C23×C4C23×C1111yescharacteristic
195#137—28no—
196AGL(1,ℤ/8)—28no—
197#135—44no—
198C2×M16C23×C1114yes—
199#127D4×C1118yescomplemented
200#124D4×C1118yescomplemented
201#123—28no—
202#123—24no—
203C22⋊Q8—24no—
204#121—216no—
205#121—28no—
206#121—24no—
207#120—216no—
208#120—28no—
209#120—24no—
210#120—28no—
211C4×D4—28no—
212C4×D4—28no—
213#117C23×C1114yes—
214C2×C22⋊C4—28no—
215C2×C22⋊C4—24no—
216#104—216no—
217#100—28no—
218C22⋊C8—42no—
219C2×C11—22no—
220C2×C11—21no—
221C2×C11—42no—
222C2×C11—48no—
223C2×C11—84no—
224C2×C11#240311yescharacteristic
225C24—24no—
226C24—28no—
227C24—42no—
228C24—84no—
229C24C2×D4×C1111yescharacteristic
230C24C2×D4×C1114yes—
231#41—28no—
232#41—28no—
233#41—416no—
234C2×Q8C2×D4×C1114yescomplemented
235C2×D4—28no—
236C2×D4—28no—
237C2×D4—28no—
238C2×D4—24no—
239C2×D4—216no—
240C2×D4—24no—
241C2×D4—24no—
242C2×D4—42no—
243C2×D4—416no—
244C2×D4—416no—
245C2×D4—48no—
246C2×D4—48no—
247C2×D4—816no—
248C2×D4C2×D4×C1118yes—
249C2×D4C2×D4×C1114yescomplemented
250C22×C4—24no—
251C22×C4—28no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—22no—
255C22×C4C2×D4×C1111yescharacteristic
256C22×C4C24×C1111yescharacteristic
257Q16—44no—
258SD16—48no—
259D8—44no—
260M16—28no—
261C2×C8—24no—
262C4⋊C4—28no—
263C4⋊C4—24no—
264C22⋊C4—28no—
265C22⋊C4—28no—
266C22⋊C4—28no—
267C22⋊C4—216no—
268C22⋊C4—24no—
269C42C2×D4×C1118yescomplemented
270C11#2389711yescharacteristic, direct product factor, Sylow
271C23—22no—
272C23—24no—
273C23—21no—
274C23—24no—
275C23—24no—
276C23—42no—
277C23—48no—
278C23—416no—
279C23—48no—
280C23—84no—
281C23—84no—
282C23—88no—
283C23—88no—
284C23—84no—
285C23C11×#12018yes—
286C23C22×D4×C1111yescharacteristic
287Q8—28no—
288D4—216no—
289D4—28no—
290D4—48no—
291D4—416no—
292D4—416no—
293D4—44no—
294D4—44no—
295D4—816no—
296C2×C4—28no—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—48no—
301C2×C4—44no—
302C2×C4—48no—
303C2×C4—88no—
304C2×C4C22×D4×C1114yes—
305C2×C4C11×H(5,𝔽2)12yes—
306C8—44no—
307C22—24no—
308C22—22no—
309C22—28no—
310C22—41no—
311C22—48no—
312C22—48no—
313C22—42no—
314C22—41no—
315C22—48no—
316C22—41no—
317C22—44no—
318C22—84no—
319C22—816no—
320C22—168no—
321C22C2×C11×#12012yes—
322C22C11×#53411yescharacteristic
323C4—48no—
324C4—41no—
325C4—44no—
326C4D42×C1114yes—
327C2—22no—
328C2—21no—
329C2—42no—
330C2—48no—
331C2—84no—
332C2C11×#240311yescharacteristic
subgroupG/H
center, socleC2×C11#2403
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3484C2semidirect
2. C11×#3019C2semidirect
3. C11×#2010C2semidirect
4. C11×#1911C2semidirect
5. C11×#1783C2semidirect
6. C2×C11×H(5,𝔽2)C22semidirect
8. C11×#575C22semidirect
13. C11×#525C22semidirect
15. C11×#518C22semidirect
18. C11×#421C22semidirect
19. C2×C11×#100C22semidirect
20. C11×#407C22semidirect
21. C11×H(3,ℤ/4)C22semidirect
39. C11×#127D4semidirect
40. C11×#124D4semidirect
59. #23897C11direct (N × H)
69. C2×Q8×C11C2×D4semidirect
84. C2×D4×C11C2×D4semidirect
104. C42×C11C2×D4semidirect
105. #3484C2×C11semidirect
106. #3019C2×C11semidirect
107. #2010C2×C11semidirect
108. #1911C2×C11semidirect
109. #1783C2×C11semidirect
146. C2×H(5,𝔽2)C22×C11semidirect
148. #575C22×C11semidirect
153. #525C22×C11semidirect
155. #518C22×C11semidirect
158. #421C22×C11semidirect
159. C2×#100C22×C11semidirect
160. #407C22×C11semidirect
161. H(3,ℤ/4)C22×C11semidirect
199. #127D4×C11semidirect
200. #124D4×C11semidirect
234. C2×Q8C2×D4×C11semidirect
249. C2×D4C2×D4×C11semidirect
269. C42C2×D4×C11semidirect
270. C11#23897direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34842
C11×#30192
C11×#20102
C11×#19112
C11×#17832
#2389711