Finite Group Databasebeta

← C11×#19003 #14596196

Subgroups — C11×#19003 #14596196

Order 2816.

808 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#564C211yesmaximal, characteristic, complemented
2C11×#3234C212yesmaximal
3C11×#3142C211yesmaximal, characteristic
4C11×#1663C214yesmaximal, complemented
5C11×#1658C214yesmaximal, complemented
6C11×#1534C211yesmaximal, characteristic, complemented
7C11×#1528C212yesmaximal, complemented
8C11×#564—24no—
9C11×#564—22no—
10C11×#564C2214yes—
11C11×#532C2211yescharacteristic
12C2×C11×#125—22no—
13C2×C11×#125—22no—
14C2×C11×#125—22no—
15C2×C11×#125C2212yes—
16C2×C11×#125C2211yescharacteristic
17C11×#501C2214yes—
18C11×#491C2212yes—
19C11×#490C2214yes—
20C11×#490C2212yes—
21C11×#488—22no—
22C11×#481—22no—
23C11×#480—22no—
24C11×#478—24no—
25C11×#432C2212yes—
26C11×#417—22no—
27C4×C11×M16C2211yescharacteristic
28C11×#330C2218yes—
29C11×#330C2214yes—
30C2×C11×#41—21no—
31C2×C11×M16—21no—
32C11×C4⋊Q8C2311yescharacteristic
33C11×#127C2311yescharacteristic
34C11×#125—28no—
35C11×#125—28no—
36C11×#125—28no—
37C11×#125—28no—
38C11×#125—28no—
39C11×#125—28no—
40C11×#125—22no—
41C11×#125—22no—
42C11×#125—22no—
43C11×#125D414yes—
44C11×#125D412yes—
45C11×#125C2312yes—
46C11×#125C2314yes—
47C11×#124—21no—
48C11×#121—22no—
49C4×D4×C11—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C4⋊C4D412yes—
59C2×C42×C11—22no—
60C2×C42×C11C2311yescharacteristic
61C11×#107—24no—
62C11×#106—24no—
63C11×C4⋊C8—22no—
64C11×#103—24no—
65C11×#102—24no—
66C11×#102—24no—
67C11×#102—24no—
68C11×C22⋊C8—22no—
69C11×#97C2312yes—
70C11×#97C2314yes—
71C4×C8×C11—21no—
72#19003C1111yesmaximal, characteristic, direct product factor, Sylow
73C11×#41—44no—
74C2×Q8×C11—21no—
75C2×D4×C11—22no—
76C2×D4×C11—21no—
77C2×D4×C11—41no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D412yes—
84C11×M16—42no—
85C2×C8×C11—22no—
86C2×C8×C11—24no—
87C11×C4⋊C4—28no—
88C11×C4⋊C4—28no—
89C11×C4⋊C4—28no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4C2×D414yes—
101C11×C4⋊C4C2×D414yes—
102C11×C4⋊C4C2×D414yes—
103C11×C22⋊C4—42no—
104C42×C11—28no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D412yes—
107C42×C11C2411yescharacteristic
108C2×#564C2×C1111yescharacteristic, complemented
109#3234C2×C1112yes—
110#3142C2×C1111yescharacteristic
111#1663C2×C1114yescomplemented
112#1658C2×C1114yescomplemented
113#1534C2×C1111yescharacteristic, complemented
114#1528C2×C1112yescomplemented
115C23×C11—41no—
116C23×C11#12011yescharacteristic
117Q8×C11—42no—
118D4×C11—44no—
119D4×C11—42no—
120D4×C11—82no—
121C2×C4×C11—22no—
122C2×C4×C11—24no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—41no—
130C2×C4×C11—82no—
131C2×C4×C11#12012yes—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11C22×D412yes—
134C2×C4×C11C22×D411yescharacteristic
135C8×C11—44no—
136C8×C11—42no—
137#564—24no—
138#564—22no—
139#564C22×C1114yes—
140#532C22×C1111yescharacteristic
141C2×#125—22no—
142C2×#125—22no—
143C2×#125—22no—
144C2×#125C22×C1111yescharacteristic
145C2×#125C22×C1112yes—
146#501C22×C1114yes—
147#491C22×C1112yes—
148#490C22×C1112yes—
149#490C22×C1114yes—
150#488—22no—
151#481—22no—
152#480—22no—
153#478—24no—
154#432C22×C1112yes—
155#417—22no—
156C4×M16C22×C1111yescharacteristic
157#330C22×C1118yes—
158#330C22×C1114yes—
159C22×C11—22no—
160C22×C11—81no—
161C22×C11—82no—
162C22×C11#45412yes—
163C22×C11C2×#12011yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—44no—
169C4×C11—44no—
170C4×C11—44no—
171C4×C11—81no—
172C2×#41—21no—
173C2×M16—21no—
174C4⋊Q8C23×C1111yescharacteristic
175#127C23×C1111yescharacteristic
176#125—28no—
177#125—28no—
178#125—28no—
179#125—28no—
180#125—28no—
181#125—28no—
182#125—22no—
183#125—22no—
184#125—22no—
185#125D4×C1114yes—
186#125D4×C1112yes—
187#125C23×C1112yes—
188#125C23×C1114yes—
189#124—21no—
190#121—22no—
191C4×D4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4D4×C1112yes—
199C2×C4⋊C4D4×C1112yes—
200C2×C4⋊C4D4×C1112yes—
201C2×C42—22no—
202C2×C42C23×C1111yescharacteristic
203#107—24no—
204#106—24no—
205C4⋊C8—22no—
206#103—24no—
207#102—24no—
208#102—24no—
209#102—24no—
210C22⋊C8—22no—
211#97C23×C1112yes—
212#97C23×C1114yes—
213C4×C8—21no—
214C2×C11—22no—
215C2×C11—161no—
216C2×C11C2×#45411yescharacteristic
217C2×C11#302012yes—
218#41—44no—
219C2×Q8—21no—
220C2×D4—22no—
221C2×D4—21no—
222C2×D4—41no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4C2×D4×C1111yescharacteristic
228C22×C4C2×D4×C1112yes—
229M16—42no—
230C2×C8—22no—
231C2×C8—24no—
232C4⋊C4—28no—
233C4⋊C4—28no—
234C4⋊C4—28no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—24no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—22no—
245C4⋊C4C2×D4×C1114yes—
246C4⋊C4C2×D4×C1114yes—
247C4⋊C4C2×D4×C1114yes—
248C22⋊C4—42no—
249C42—28no—
250C42C2×D4×C1111yescharacteristic
251C42C2×D4×C1112yes—
252C42C24×C1111yescharacteristic
253C11#1900311yescharacteristic, direct product factor, Sylow
254C23—41no—
255C23C11×#12011yescharacteristic
256Q8—42no—
257D4—44no—
258D4—42no—
259D4—82no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—42no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—44no—
268C2×C4—41no—
269C2×C4—82no—
270C2×C4C11×#12012yes—
271C2×C4C11×#12011yescharacteristic
272C2×C4C22×D4×C1112yes—
273C2×C4C22×D4×C1111yescharacteristic
274C8—42no—
275C8—44no—
276C22—22no—
277C22—81no—
278C22—82no—
279C22C11×#45412yes—
280C22C2×C11×#12011yescharacteristic
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—44no—
286C4—44no—
287C4—44no—
288C4—81no—
289C2—22no—
290C2—161no—
291C2C2×C11×#45411yescharacteristic
292C2C11×#302012yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
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×#564C2semidirect
4. C11×#1663C2semidirect
5. C11×#1658C2semidirect
6. C11×#1534C2semidirect
7. C11×#1528C2semidirect
72. #19003C11direct (N × H)
108. C2×#564C2×C11semidirect
111. #1663C2×C11semidirect
112. #1658C2×C11semidirect
113. #1534C2×C11semidirect
114. #1528C2×C11semidirect
253. C11#19003direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5642
C11×#32342
C11×#31422
C11×#16632
C11×#16582
C11×#15342
C11×#15282
#1900311