Finite Group Databasebeta

← C11×#19061 #14596254

Subgroups — C11×#19061 #14596254

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3548C211yesmaximal, characteristic, complemented
2C11×#3214C212yesmaximal, complemented
3C11×#3135C211yesmaximal, characteristic, complemented
4C11×#1662C214yesmaximal, complemented
5C11×#1656C214yesmaximal, complemented
6C11×#1537C211yesmaximal, characteristic, complemented
7C11×#1530C212yesmaximal, complemented
8C11×#562C2214yes—
9C11×#554—22no—
10C11×#550—22no—
11C11×#547—22no—
12C11×#540—22no—
13C11×#537—24no—
14C11×#533C2211yescharacteristic
15C11×#532C2211yescharacteristic
16C11×#532C2212yes—
17C11×#496C2214yes—
18C11×#491C2212yes—
19C11×#490C2212yes—
20C11×#489—22no—
21C11×#489C2214yes—
22C11×#461—22no—
23C11×#459—22no—
24C11×#449—24no—
25C11×#432C2212yes—
26C11×#416—22no—
27C2×C11×#97C2211yescharacteristic
28C11×#330C2214yes—
29C11×#329C2218yes—
30C2×C11×#41—24no—
31C2×C11×#41—21no—
32C2×C11×#41D414yes—
33C2×C11×SD16—24no—
34C2×C11×D8—24no—
35C22×C8×C11—21no—
36C11×C4⋊Q8D412yes—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8C2311yescharacteristic
39C11×#127—22no—
40C11×#127D412yes—
41C11×#127C2311yescharacteristic
42C11×#125—22no—
43C11×#125C2312yes—
44C11×#124—21no—
45C11×#124C2314yes—
46C11×#123—28no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—28no—
49C11×C22⋊Q8—22no—
50C11×#121—28no—
51C11×#121—24no—
52C11×#121—28no—
53C11×#121—22no—
54C11×#121—22no—
55C11×#121—22no—
56C4×Q8×C11—22no—
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C11×#117D412yes—
62C2×C11×C4⋊C4—24no—
63C2×C42×C11C2311yescharacteristic
64C11×C4⋊C8—22no—
65C11×#103—24no—
66C11×#103—24no—
67C11×#102—24no—
68C11×#102—24no—
69C11×C22⋊C8—22no—
70C11×#97—21no—
71C11×#97C2314yes—
72C11×#97C2312yes—
73#19061C1111yesmaximal, characteristic, direct product factor, Sylow
74C11×#41—44no—
75C11×#41—84no—
76C11×#41—88no—
77C2×Q8×C11—22no—
78C2×Q8×C11—21no—
79C2×Q8×C11C2×D414yes—
80C2×D4×C11—28no—
81C2×D4×C11—24no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—21no—
85C2×D4×C11—22no—
86C2×D4×C11—41no—
87C2×D4×C11C2×D414yes—
88C22×C4×C11—28no—
89C22×C4×C11—24no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D412yes—
93C11×SD16—84no—
94C11×D8—84no—
95C2×C8×C11—22no—
96C2×C8×C11—24no—
97C2×C8×C11—42no—
98C11×C4⋊C4—28no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4C2×D414yes—
105C11×C22⋊C4—28no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—42no—
110C42×C11—22no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D412yes—
113C42×C11C2411yescharacteristic
114#3548C2×C1111yescharacteristic, complemented
115#3214C2×C1112yescomplemented
116#3135C2×C1111yescharacteristic, complemented
117#1662C2×C1114yescomplemented
118#1656C2×C1114yescomplemented
119#1537C2×C1111yescharacteristic, complemented
120#1530C2×C1112yescomplemented
121C23×C11—24no—
122C23×C11—41no—
123C23×C11#12011yescharacteristic
124Q8×C11—44no—
125Q8×C11—44no—
126Q8×C11—42no—
127D4×C11—44no—
128D4×C11—44no—
129D4×C11—42no—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—44no—
133D4×C11—84no—
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—48no—
141C2×C4×C11—41no—
142C2×C4×C11—88no—
143C2×C4×C11—82no—
144C2×C4×C11#12012yes—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C22×D412yes—
148C8×C11—42no—
149C8×C11—44no—
150#562C22×C1114yes—
151#554—22no—
152#550—22no—
153#547—22no—
154#540—22no—
155#537—24no—
156#533C22×C1111yescharacteristic
157#532C22×C1111yescharacteristic
158#532C22×C1112yes—
159#496C22×C1114yes—
160#491C22×C1112yes—
161#490C22×C1112yes—
162#489—22no—
163#489C22×C1114yes—
164#461—22no—
165#459—22no—
166#449—24no—
167#432C22×C1112yes—
168#416—22no—
169C2×#97C22×C1111yescharacteristic
170#330C22×C1114yes—
171#329C22×C1118yes—
172C22×C11—21no—
173C22×C11—22no—
174C22×C11—44no—
175C22×C11—44no—
176C22×C11—44no—
177C22×C11—81no—
178C22×C11—82no—
179C22×C11C2×#12011yescharacteristic
180C4×C11—21no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11—44no—
184C4×C11—44no—
185C4×C11—81no—
186C4×C11#45412yes—
187C2×#41—24no—
188C2×#41—21no—
189C2×#41D4×C1114yes—
190C2×SD16—24no—
191C2×D8—24no—
192C22×C8—21no—
193C4⋊Q8D4×C1112yes—
194C4⋊Q8D4×C1112yes—
195C4⋊Q8C23×C1111yescharacteristic
196#127—22no—
197#127D4×C1112yes—
198#127C23×C1111yescharacteristic
199#125—22no—
200#125C23×C1112yes—
201#124—21no—
202#124C23×C1114yes—
203#123—28no—
204C22⋊Q8—24no—
205C22⋊Q8—28no—
206C22⋊Q8—22no—
207#121—28no—
208#121—24no—
209#121—28no—
210#121—22no—
211#121—22no—
212#121—22no—
213C4×Q8—22no—
214C4×D4—24no—
215C4×D4—22no—
216C4×D4—22no—
217C4×D4—22no—
218#117D4×C1112yes—
219C2×C4⋊C4—24no—
220C2×C42C23×C1111yescharacteristic
221C4⋊C8—22no—
222#103—24no—
223#103—24no—
224#102—24no—
225#102—24no—
226C22⋊C8—22no—
227#97—21no—
228#97C23×C1112yes—
229#97C23×C1114yes—
230C2×C11—41no—
231C2×C11—84no—
232C2×C11—161no—
233C2×C11C2×#45411yescharacteristic
234C2×C11#301912yes—
235#41—44no—
236#41—84no—
237#41—88no—
238C2×Q8—22no—
239C2×Q8—21no—
240C2×Q8C2×D4×C1114yes—
241C2×D4—28no—
242C2×D4—24no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—21no—
246C2×D4—22no—
247C2×D4—41no—
248C2×D4C2×D4×C1114yes—
249C22×C4—28no—
250C22×C4—24no—
251C22×C4—41no—
252C22×C4C2×D4×C1111yescharacteristic
253C22×C4C2×D4×C1112yes—
254SD16—84no—
255D8—84no—
256C2×C8—22no—
257C2×C8—24no—
258C2×C8—42no—
259C4⋊C4—28no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—24no—
264C4⋊C4—22no—
265C4⋊C4C2×D4×C1114yes—
266C22⋊C4—28no—
267C22⋊C4—22no—
268C22⋊C4—24no—
269C22⋊C4—24no—
270C22⋊C4—42no—
271C42—22no—
272C42C2×D4×C1111yescharacteristic
273C42C2×D4×C1112yes—
274C42C24×C1111yescharacteristic
275C11#1906111yescharacteristic, direct product factor, Sylow
276C23—24no—
277C23—41no—
278C23C11×#12011yescharacteristic
279Q8—44no—
280Q8—44no—
281Q8—42no—
282D4—44no—
283D4—44no—
284D4—42no—
285D4—42no—
286D4—42no—
287D4—44no—
288D4—84no—
289D4—88no—
290D4—82no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—42no—
295C2×C4—48no—
296C2×C4—41no—
297C2×C4—88no—
298C2×C4—82no—
299C2×C4C11×#12012yes—
300C2×C4C11×#12011yescharacteristic
301C2×C4C22×D4×C1111yescharacteristic
302C2×C4C22×D4×C1112yes—
303C8—42no—
304C8—44no—
305C22—21no—
306C22—22no—
307C22—44no—
308C22—44no—
309C22—44no—
310C22—81no—
311C22—82no—
312C22C2×C11×#12011yescharacteristic
313C4—21no—
314C4—22no—
315C4—22no—
316C4—44no—
317C4—44no—
318C4—81no—
319C4C11×#45412yes—
320C2—41no—
321C2—84no—
322C2—161no—
323C2C2×C11×#45411yescharacteristic
324C2C11×#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. C11×#3548C2semidirect
2. C11×#3214C2semidirect
3. C11×#3135C2semidirect
4. C11×#1662C2semidirect
5. C11×#1656C2semidirect
6. C11×#1537C2semidirect
7. C11×#1530C2semidirect
73. #19061C11direct (N × H)
114. #3548C2×C11semidirect
115. #3214C2×C11semidirect
116. #3135C2×C11semidirect
117. #1662C2×C11semidirect
118. #1656C2×C11semidirect
119. #1537C2×C11semidirect
120. #1530C2×C11semidirect
275. C11#19061direct (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×#32142
C11×#31352
C11×#16622
C11×#16562
C11×#15372
C11×#15302
#1906111