Finite Group Databasebeta

← C11×#19080 #14596273

Subgroups — C11×#19080 #14596273

Order 2816.

936 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3548C211yesmaximal, characteristic
2C11×#3141C212yesmaximal, complemented
3C11×#3139C211yesmaximal, characteristic, complemented
4C11×#1662C218yesmaximal, complemented
5C11×#1526C211yesmaximal, characteristic, complemented
6C11×#1525C212yesmaximal, complemented
7C11×#562C2214yes—
8C11×#554—22no—
9C11×#550—22no—
10C11×#547—22no—
11C11×#540—22no—
12C11×#537—24no—
13C11×#533C2211yescharacteristic
14C11×#532C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C11×#491C2214yes—
17C11×#489C2218yes—
18C11×#487—22no—
19C11×#487—22no—
20C11×#486—22no—
21C11×#419—22no—
22C11×#417—24no—
23C4×C11×M16C2211yescharacteristic
24C4×C11×M16C2212yes—
25C11×#330C2214yes—
26C11×#329C2218yes—
27C2×C11×#41—24no—
28C2×C11×#41D414yes—
29C22×Q8×C11—21no—
30C2×C11×M16—22no—
31C2×C11×M16—21no—
32C11×C4⋊Q8—22no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8D412yes—
35C11×C4⋊Q8D412yes—
36C11×C4⋊Q8C2312yes—
37C11×#127—22no—
38C11×#127D412yes—
39C11×#125—22no—
40C11×#125C2312yes—
41C11×#124C2314yes—
42C11×#123—28no—
43C11×C22⋊Q8—24no—
44C11×C22⋊Q8—28no—
45C11×C22⋊Q8—22no—
46C11×#121—28no—
47C11×#121—24no—
48C11×#121—28no—
49C11×#121—22no—
50C11×#121—22no—
51C4×Q8×C11—22no—
52C4×D4×C11—24no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C11×#117D412yes—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—22no—
58C2×C42×C11C2311yescharacteristic
59C11×#103—28no—
60C11×#103—28no—
61C11×#102—28no—
62C11×#97C2314yes—
63C11×#97C2312yes—
64C4×C8×C11—22no—
65C4×C8×C11—21no—
66#19080C1111yesmaximal, characteristic, direct product factor, Sylow
67C11×#41—48no—
68C11×#41—88no—
69C2×Q8×C11—22no—
70C2×Q8×C11—22no—
71C2×Q8×C11—44no—
72C2×Q8×C11—41no—
73C2×Q8×C11C2×D414yes—
74C2×D4×C11—28no—
75C2×D4×C11—24no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11C2×D414yes—
79C22×C4×C11—28no—
80C22×C4×C11—24no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D411yescharacteristic
84C11×M16—42no—
85C11×M16—44no—
86C2×C8×C11—24no—
87C2×C8×C11—22no—
88C11×C4⋊C4—28no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4C2×D414yes—
96C11×C22⋊C4—28no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—24no—
99C11×C22⋊C4—24no—
100C42×C11—22no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D412yes—
103C42×C11C2411yescharacteristic
104#3548C2×C1111yescharacteristic
105#3141C2×C1112yescomplemented
106#3139C2×C1111yescharacteristic, complemented
107#1662C2×C1118yescomplemented
108#1526C2×C1111yescharacteristic, complemented
109#1525C2×C1112yescomplemented
110C23×C11—24no—
111C23×C11#12011yescharacteristic
112Q8×C11—44no—
113Q8×C11—44no—
114Q8×C11—44no—
115Q8×C11—82no—
116D4×C11—44no—
117D4×C11—44no—
118D4×C11—44no—
119D4×C11—84no—
120D4×C11—88no—
121C2×C4×C11—22no—
122C2×C4×C11—24no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—48no—
126C2×C4×C11—42no—
127C2×C4×C11—88no—
128C2×C4×C11—82no—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12012yes—
131C2×C4×C11C22×D411yescharacteristic
132C2×C4×C11C22×D412yes—
133C8×C11—44no—
134C8×C11—42no—
135#562C22×C1114yes—
136#554—22no—
137#550—22no—
138#547—22no—
139#540—22no—
140#537—24no—
141#533C22×C1111yescharacteristic
142#532C22×C1112yes—
143C2×C4⋊Q8C22×C1111yescharacteristic
144#491C22×C1114yes—
145#489C22×C1118yes—
146#487—22no—
147#487—22no—
148#486—22no—
149#419—22no—
150#417—24no—
151C4×M16C22×C1111yescharacteristic
152C4×M16C22×C1112yes—
153#330C22×C1114yes—
154#329C22×C1118yes—
155C22×C11—22no—
156C22×C11—21no—
157C22×C11—44no—
158C22×C11—44no—
159C22×C11—44no—
160C22×C11C2×#12011yescharacteristic
161C4×C11—22no—
162C4×C11—21no—
163C4×C11—44no—
164C4×C11—44no—
165C4×C11—82no—
166C4×C11#45412yes—
167C4×C11#45514yes—
168C2×#41—24no—
169C2×#41D4×C1114yes—
170C22×Q8—21no—
171C2×M16—22no—
172C2×M16—21no—
173C4⋊Q8—22no—
174C4⋊Q8—21no—
175C4⋊Q8D4×C1112yes—
176C4⋊Q8D4×C1112yes—
177C4⋊Q8C23×C1112yes—
178#127—22no—
179#127D4×C1112yes—
180#125—22no—
181#125C23×C1112yes—
182#124C23×C1114yes—
183#123—28no—
184C22⋊Q8—24no—
185C22⋊Q8—28no—
186C22⋊Q8—22no—
187#121—28no—
188#121—24no—
189#121—28no—
190#121—22no—
191#121—22no—
192C4×Q8—22no—
193C4×D4—24no—
194C4×D4—22no—
195C4×D4—22no—
196#117D4×C1112yes—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—22no—
199C2×C42C23×C1111yescharacteristic
200#103—28no—
201#103—28no—
202#102—28no—
203#97C23×C1112yes—
204#97C23×C1114yes—
205C4×C8—22no—
206C4×C8—21no—
207C2×C11—41no—
208C2×C11—84no—
209C2×C11C2×#45512yes—
210C2×C11C2×#45411yescharacteristic
211#41—48no—
212#41—88no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—44no—
216C2×Q8—41no—
217C2×Q8C2×D4×C1114yes—
218C2×D4—28no—
219C2×D4—24no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4C2×D4×C1114yes—
223C22×C4—28no—
224C22×C4—24no—
225C22×C4—41no—
226C22×C4C2×D4×C1112yes—
227C22×C4C2×D4×C1111yescharacteristic
228M16—42no—
229M16—44no—
230C2×C8—24no—
231C2×C8—22no—
232C4⋊C4—28no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—24no—
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4C2×D4×C1114yes—
240C22⋊C4—28no—
241C22⋊C4—22no—
242C22⋊C4—24no—
243C22⋊C4—24no—
244C42—22no—
245C42C2×D4×C1111yescharacteristic
246C42C2×D4×C1112yes—
247C42C24×C1111yescharacteristic
248C11#1908011yescharacteristic, direct product factor, Sylow
249C23—24no—
250C23C11×#12011yescharacteristic
251Q8—44no—
252Q8—44no—
253Q8—44no—
254Q8—82no—
255D4—44no—
256D4—44no—
257D4—44no—
258D4—84no—
259D4—88no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—48no—
265C2×C4—42no—
266C2×C4—88no—
267C2×C4—82no—
268C2×C4C11×#12011yescharacteristic
269C2×C4C11×#12012yes—
270C2×C4C22×D4×C1111yescharacteristic
271C2×C4C22×D4×C1112yes—
272C8—44no—
273C8—42no—
274C22—22no—
275C22—21no—
276C22—44no—
277C22—44no—
278C22—44no—
279C22C2×C11×#12011yescharacteristic
280C4—22no—
281C4—21no—
282C4—44no—
283C4—44no—
284C4—82no—
285C4C11×#45412yes—
286C4C11×#45514yes—
287C2—41no—
288C2—84no—
289C2C2×C11×#45512yes—
290C2C2×C11×#45411yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3548C2
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
2. C11×#3141C2semidirect
3. C11×#3139C2semidirect
4. C11×#1662C2semidirect
5. C11×#1526C2semidirect
6. C11×#1525C2semidirect
66. #19080C11direct (N × H)
105. #3141C2×C11semidirect
106. #3139C2×C11semidirect
107. #1662C2×C11semidirect
108. #1526C2×C11semidirect
109. #1525C2×C11semidirect
248. C11#19080direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#31412
C11×#31392
C11×#16622
C11×#15262
C11×#15252
#1908011