Finite Group Databasebeta

← C11×#23899 #14601092

Subgroups — C11×#23899 #14601092

Order 2816.

1672 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1672 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×#3486C212yesmaximal, complemented
2C11×#3020C214yesmaximal, complemented
3C11×#2010C214yesmaximal, complemented
4C11×#1912C214yesmaximal, complemented
5C11×#1784C211yesmaximal, characteristic, complemented
6C2×C11×2−1+4C2212yes—
7C23×Q8×C11C2211yescharacteristic
8C11×#575C2214yes—
9D4×Q8×C11—28no—
10C11×#548—28no—
11C11×#536—24no—
12C11×#536C2214yes—
13C11×#525—24no—
14C11×#525C2214yes—
15C11×#519C2212yes—
16C11×#456—28no—
17C11×#454—28no—
18C11×#421C2218yes—
19C2×C11×#101C2214yes—
20C11×#407C2212yes—
21C11×H(3,ℤ/4)C2214yes—
22C11×2−1+4—28no—
23C11×2−1+4—44no—
24C2×C11×#41—24no—
25C2×C11×#41—24no—
26C2×C11×#41C2314yes—
27C22×Q8×C11—28no—
28C22×Q8×C11—24no—
29C22×Q8×C11—42no—
30C22×Q8×C11D412yes—
31C22×Q8×C11C2312yes—
32C23×C4×C11D412yes—
33C23×C4×C11C2311yescharacteristic
34C11×#137—28no—
35C11×AGL(1,ℤ/8)—28no—
36C11×#135—44no—
37C2×C11×M16C2314yes—
38C11×C4⋊Q8—28no—
39C11×C4⋊Q8D418yescomplemented
40C11×#124—28no—
41C11×#124D418yescomplemented
42C11×#123—28no—
43C11×#123—24no—
44C11×C22⋊Q8—28no—
45C11×C22⋊Q8—216no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—28no—
48C11×#121—28no—
49C11×#121—24no—
50C11×#120—24no—
51C4×Q8×C11—28no—
52C4×D4×C11—216no—
53C4×D4×C11—28no—
54C11×#117—24no—
55C11×#117C2314yes—
56C11×#104—216no—
57C11×#101—28no—
58C11×C22⋊C8—42no—
59#23899C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11C2×D411yescharacteristic
61C11×#41—28no—
62C11×#41—28no—
63C11×#41—48no—
64C11×#41—416no—
65C11×#41—48no—
66C2×Q8×C11—24no—
67C2×Q8×C11—28no—
68C2×Q8×C11—24no—
69C2×Q8×C11—24no—
70C2×Q8×C11—42no—
71C2×Q8×C11—416no—
72C2×Q8×C11—416no—
73C2×Q8×C11C2×D414yes—
74C2×Q8×C11C2×D418yes—
75C2×D4×C11—28no—
76C2×D4×C11—24no—
77C2×D4×C11—24no—
78C2×D4×C11C2×D414yes—
79C22×C4×C11—28no—
80C22×C4×C11—28no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—22no—
84C22×C4×C11—42no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D414yes—
87C22×C4×C11C2411yescharacteristic
88C11×Q16—44no—
89C11×SD16—48no—
90C11×D8—44no—
91C11×M16—28no—
92C2×C8×C11—24no—
93C11×C4⋊C4—28no—
94C11×C4⋊C4—28no—
95C11×C4⋊C4—216no—
96C11×C4⋊C4—24no—
97C11×C22⋊C4—28no—
98C11×C22⋊C4—28no—
99C11×C22⋊C4—24no—
100C11×C22⋊C4—216no—
101C42×C11—28no—
102C42×C11C2×D418yes—
103#3486C2×C1112yescomplemented
104#3020C2×C1114yescomplemented
105#2010C2×C1114yescomplemented
106#1912C2×C1114yescomplemented
107#1784C2×C1111yescharacteristic, complemented
108C23×C11—22no—
109C23×C11—21no—
110C23×C11—24no—
111C23×C11—42no—
112C23×C11C22×D411yescharacteristic
113Q8×C11—216no—
114Q8×C11—28no—
115Q8×C11—48no—
116Q8×C11—48no—
117D4×C11—28no—
118D4×C11—48no—
119D4×C11—416no—
120D4×C11—44no—
121D4×C11—44no—
122C2×C4×C11—24no—
123C2×C4×C11—24no—
124C2×C4×C11—28no—
125C2×C4×C11—22no—
126C2×C4×C11—24no—
127C2×C4×C11—21no—
128C2×C4×C11—48no—
129C2×C4×C11—416no—
130C2×C4×C11—44no—
131C2×C4×C11—48no—
132C2×C4×C11#12018yes—
133C2×C4×C11C22×D414yes—
134C2×C4×C11H(5,𝔽2)12yes—
135C8×C11—44no—
136C2×2−1+4C22×C1112yes—
137C23×Q8C22×C1111yescharacteristic
138#575C22×C1114yes—
139D4×Q8—28no—
140#548—28no—
141#536—24no—
142#536C22×C1114yes—
143#525—24no—
144#525C22×C1114yes—
145#519C22×C1112yes—
146#456—28no—
147#454—28no—
148#421C22×C1118yes—
149C2×#101C22×C1114yes—
150#407C22×C1112yes—
151H(3,ℤ/4)C22×C1114yes—
152C22×C11—24no—
153C22×C11—22no—
154C22×C11—41no—
155C22×C11—42no—
156C22×C11—41no—
157C22×C11—48no—
158C22×C11—41no—
159C22×C11—44no—
160C22×C11C2×#12012yes—
161C22×C11#53411yescharacteristic
162C4×C11—28no—
163C4×C11—48no—
164C4×C11—41no—
165C4×C11—44no—
166C4×C11D4214yes—
1672−1+4—28no—
1682−1+4—44no—
169C2×#41—24no—
170C2×#41—24no—
171C2×#41C23×C1114yes—
172C22×Q8—28no—
173C22×Q8—24no—
174C22×Q8—42no—
175C22×Q8D4×C1112yes—
176C22×Q8C23×C1112yes—
177C23×C4D4×C1112yes—
178C23×C4C23×C1111yescharacteristic
179#137—28no—
180AGL(1,ℤ/8)—28no—
181#135—44no—
182C2×M16C23×C1114yes—
183C4⋊Q8—28no—
184C4⋊Q8D4×C1118yescomplemented
185#124—28no—
186#124D4×C1118yescomplemented
187#123—28no—
188#123—24no—
189C22⋊Q8—28no—
190C22⋊Q8—216no—
191C22⋊Q8—24no—
192C22⋊Q8—28no—
193#121—28no—
194#121—24no—
195#120—24no—
196C4×Q8—28no—
197C4×D4—216no—
198C4×D4—28no—
199#117—24no—
200#117C23×C1114yes—
201#104—216no—
202#101—28no—
203C22⋊C8—42no—
204C2×C11—22no—
205C2×C11—21no—
206C2×C11—42no—
207C2×C11—84no—
208C2×C11#240311yescharacteristic
209C24C2×D4×C1111yescharacteristic
210#41—28no—
211#41—28no—
212#41—48no—
213#41—416no—
214#41—48no—
215C2×Q8—24no—
216C2×Q8—28no—
217C2×Q8—24no—
218C2×Q8—24no—
219C2×Q8—42no—
220C2×Q8—416no—
221C2×Q8—416no—
222C2×Q8C2×D4×C1114yes—
223C2×Q8C2×D4×C1118yes—
224C2×D4—28no—
225C2×D4—24no—
226C2×D4—24no—
227C2×D4C2×D4×C1114yes—
228C22×C4—28no—
229C22×C4—28no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—22no—
233C22×C4—42no—
234C22×C4C2×D4×C1111yescharacteristic
235C22×C4C2×D4×C1114yes—
236C22×C4C24×C1111yescharacteristic
237Q16—44no—
238SD16—48no—
239D8—44no—
240M16—28no—
241C2×C8—24no—
242C4⋊C4—28no—
243C4⋊C4—28no—
244C4⋊C4—216no—
245C4⋊C4—24no—
246C22⋊C4—28no—
247C22⋊C4—28no—
248C22⋊C4—24no—
249C22⋊C4—216no—
250C42—28no—
251C42C2×D4×C1118yes—
252C11#2389911yescharacteristic, direct product factor, Sylow
253C23—22no—
254C23—21no—
255C23—24no—
256C23—42no—
257C23C22×D4×C1111yescharacteristic
258Q8—216no—
259Q8—28no—
260Q8—48no—
261Q8—48no—
262D4—28no—
263D4—48no—
264D4—416no—
265D4—44no—
266D4—44no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—28no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—21no—
273C2×C4—48no—
274C2×C4—416no—
275C2×C4—44no—
276C2×C4—48no—
277C2×C4C11×#12018yes—
278C2×C4C22×D4×C1114yes—
279C2×C4C11×H(5,𝔽2)12yes—
280C8—44no—
281C22—24no—
282C22—22no—
283C22—41no—
284C22—42no—
285C22—41no—
286C22—48no—
287C22—41no—
288C22—44no—
289C22C2×C11×#12012yes—
290C22C11×#53411yescharacteristic
291C4—28no—
292C4—48no—
293C4—41no—
294C4—44no—
295C4D42×C1114yes—
296C2—22no—
297C2—21no—
298C2—42no—
299C2—84no—
300C2C11×#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×#3486C2semidirect
2. C11×#3020C2semidirect
3. C11×#2010C2semidirect
4. C11×#1912C2semidirect
5. C11×#1784C2semidirect
39. C11×C4⋊Q8D4semidirect
41. C11×#124D4semidirect
59. #23899C11direct (N × H)
103. #3486C2×C11semidirect
104. #3020C2×C11semidirect
105. #2010C2×C11semidirect
106. #1912C2×C11semidirect
107. #1784C2×C11semidirect
184. C4⋊Q8D4×C11semidirect
186. #124D4×C11semidirect
252. C11#23899direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34862
C11×#30202
C11×#20102
C11×#19122
C11×#17842
#2389911