Finite Group Databasebeta

← C11×#18404 #14595597

Subgroups — C11×#18404 #14595597

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic
2C11×#3209C212yesmaximal
3C11×#2567C211yesmaximal, characteristic
4C11×#1605C218yesmaximal
5C11×#1503C212yesmaximal
6C11×#1461C211yesmaximal, characteristic
7Q82×C11—22no—
8C11×#557—22no—
9C11×#557—24no—
10C11×#544—21no—
11C11×#544C2214yes—
12C11×#533—22no—
13C11×#533C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C11×#519—21no—
16C2×C4×Q8×C11C2211yescharacteristic
17C11×#494—22no—
18C11×#487—22no—
19C11×#462—24no—
20C11×#451C2218yes—
21C11×#431C2212yes—
22C11×#395C2214yes—
23C11×#391—21no—
24C11×#389—22no—
25C11×#384—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#328C2218yes—
28C11×#324C2214yes—
29C22×Q8×C11D411yescharacteristic
30C22×Q8×C11C2312yes—
31C2×C11×Q16—28no—
32C11×C4⋊Q8—22no—
33C11×C4⋊Q8—22no—
34C11×C4⋊Q8—24no—
35C11×C4⋊Q8—28no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D412yes—
40C11×#125—24no—
41C11×#125—24no—
42C11×#125—28no—
43C11×#125—22no—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8C2314yes—
47C4×Q8×C11—24no—
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11D414yes—
55C11×#117—24no—
56C11×#117—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11—21no—
64C2×C42×C11D412yes—
65C2×C42×C11C2311yescharacteristic
66C11×C4⋊C8—22no—
67C11×#103—28no—
68C11×C22⋊C8C2314yes—
69C4×C8×C11—22no—
70C11×#95—24no—
71C11×#95C2312yes—
72#18404C1111yesmaximal, characteristic, direct product factor, Sylow
73C2×Q8×C11—24no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—24no—
78C2×Q8×C11—82no—
79C2×Q8×C11Q1614yescomplemented
80C2×Q8×C11C2×D414yes—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2411yescharacteristic
88C11×Q16—88no—
89C2×C8×C11—24no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—28no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—84no—
106C11×C4⋊C4C2×D414yes—
107C11×C22⋊C4—24no—
108C42×C11—28no—
109C42×C11—22no—
110C42×C11—22no—
111C42×C11—24no—
112C42×C11—42no—
113C42×C11C2×D412yes—
114C42×C11C2×D412yes—
115#3502C2×C1111yescharacteristic
116#3209C2×C1112yes—
117#2567C2×C1111yescharacteristic
118#1605C2×C1118yes—
119#1503C2×C1112yes—
120#1461C2×C1111yescharacteristic
121C23×C11C22×D411yescharacteristic
122Q8×C11—28no—
123Q8×C11—44no—
124Q8×C11—48no—
125Q8×C11—44no—
126Q8×C11—84no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—24no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—44no—
139C2×C4×C11—42no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12012yes—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11C2×Q1614yes—
144C2×C4×C11C2×Q1612yes—
145C2×C4×C11#13712yes—
146C2×C4×C11C22×D412yes—
147C8×C11—44no—
148Q82—22no—
149#557—22no—
150#557—24no—
151#544—21no—
152#544C22×C1114yes—
153#533—22no—
154#533C22×C1112yes—
155C2×C4⋊Q8C22×C1111yescharacteristic
156#519—21no—
157C2×C4×Q8C22×C1111yescharacteristic
158#494—22no—
159#487—22no—
160#462—24no—
161#451C22×C1118yes—
162#431C22×C1112yes—
163#395C22×C1114yes—
164#391—21no—
165#389—22no—
166#384—21no—
167C4×C4⋊C4C22×C1111yescharacteristic
168#328C22×C1118yes—
169#324C22×C1114yes—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11C2×#12011yescharacteristic
173C22×C11C22×Q1611yescharacteristic
174C22×C11C2×#13711yescharacteristic
175C4×C11—24no—
176C4×C11—21no—
177C4×C11—22no—
178C4×C11—44no—
179C4×C11—44no—
180C4×C11—42no—
181C4×C11—44no—
182C4×C11—82no—
183C4×C11#45114yes—
184C4×C11#45612yes—
185C22×Q8D4×C1111yescharacteristic
186C22×Q8C23×C1112yes—
187C2×Q16—28no—
188C4⋊Q8—22no—
189C4⋊Q8—22no—
190C4⋊Q8—24no—
191C4⋊Q8—28no—
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C4⋊Q8D4×C1112yes—
195C4⋊Q8D4×C1112yes—
196#125—24no—
197#125—24no—
198#125—28no—
199#125—22no—
200C22⋊Q8—22no—
201C22⋊Q8—24no—
202C22⋊Q8C23×C1114yes—
203C4×Q8—24no—
204C4×Q8—24no—
205C4×Q8—24no—
206C4×Q8—24no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×Q8—22no—
210C4×Q8D4×C1114yes—
211#117—24no—
212#117—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4D4×C1111yescharacteristic
218C2×C4⋊C4C23×C1112yes—
219C2×C42—21no—
220C2×C42D4×C1112yes—
221C2×C42C23×C1111yescharacteristic
222C4⋊C8—22no—
223#103—28no—
224C22⋊C8C23×C1114yes—
225C4×C8—22no—
226#95—24no—
227#95C23×C1112yes—
228C2×C11—21no—
229C2×C11—21no—
230C2×C11C2×#45111yescharacteristic
231C2×C11C2×#45611yescharacteristic
232C2×C11#302711yescharacteristic
233C2×Q8—24no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—24no—
238C2×Q8—82no—
239C2×Q8C11×Q1614yescomplemented
240C2×Q8C2×D4×C1114yes—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4C2×D4×C1111yescharacteristic
244C22×C4C2×D4×C1112yes—
245C22×C4C2×D4×C1112yes—
246C22×C4C2×D4×C1111yescharacteristic
247C22×C4C24×C1111yescharacteristic
248Q16—88no—
249C2×C8—24no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—28no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—84no—
266C4⋊C4C2×D4×C1114yes—
267C22⋊C4—24no—
268C42—28no—
269C42—22no—
270C42—22no—
271C42—24no—
272C42—42no—
273C42C2×D4×C1112yes—
274C42C2×D4×C1112yes—
275C11#1840411yescharacteristic, direct product factor, Sylow
276C23C22×D4×C1111yescharacteristic
277Q8—28no—
278Q8—44no—
279Q8—48no—
280Q8—44no—
281Q8—84no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4C11×#12011yescharacteristic
296C2×C4C11×#12012yes—
297C2×C4C11×#12011yescharacteristic
298C2×C4C2×C11×Q1614yes—
299C2×C4C2×C11×Q1612yes—
300C2×C4C11×#13712yes—
301C2×C4C22×D4×C1112yes—
302C8—44no—
303C22—21no—
304C22—21no—
305C22C2×C11×#12011yescharacteristic
306C22C22×C11×Q1611yescharacteristic
307C22C2×C11×#13711yescharacteristic
308C4—24no—
309C4—21no—
310C4—22no—
311C4—44no—
312C4—44no—
313C4—42no—
314C4—44no—
315C4—82no—
316C4C11×#45114yes—
317C4C11×#45612yes—
318C2—21no—
319C2—21no—
320C2C2×C11×#45111yescharacteristic
321C2C2×C11×#45611yescharacteristic
322C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×C11C22×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
72. #18404C11direct (N × H)
79. C2×Q8×C11Q16semidirect
239. C2×Q8C11×Q16semidirect
275. C11#18404direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35022
C11×#32092
C11×#25672
C11×#16052
C11×#15032
C11×#14612
#1840411