Finite Group Databasebeta

← C11×#18410 #14595603

Subgroups — C11×#18410 #14595603

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic
2C11×#3229C212yesmaximal
3C11×#2546C211yesmaximal, characteristic
4C11×#1611C218yesmaximal
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⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C11×#519—21no—
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#498—22no—
19C11×#487—22no—
20C11×#483C2218yes—
21C11×#475—24no—
22C11×#431C2212yes—
23C11×#398C2214yes—
24C11×#391—21no—
25C11×#389—22no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#328C2218yes—
28C11×#324C2214yes—
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C11×C4⋊Q8—22no—
32C11×C4⋊Q8—22no—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8—28no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8—44no—
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—24no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11—21no—
64C2×C42×C11D412yes—
65C2×C42×C11C2311yescharacteristic
66C11×#106—28no—
67C11×C4⋊C8—22no—
68C11×#103—28no—
69C11×C22⋊C8C2314yes—
70C4×C8×C11—22no—
71C11×#95—24no—
72C11×#95C2312yes—
73#18410C1111yesmaximal, characteristic, direct product factor, Sylow
74C2×Q8×C11—24no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—42no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×Q8×C11SD1614yes—
82C2×Q8×C11C2×D414yes—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2411yescharacteristic
90C2×C8×C11—24no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—28no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—48no—
107C11×C4⋊C4C2×D414yes—
108C11×C22⋊C4—24no—
109C42×C11—28no—
110C42×C11—22no—
111C42×C11—22no—
112C42×C11—24no—
113C42×C11—42no—
114C42×C11C2×D412yes—
115C42×C11C2×D412yes—
116#3502C2×C1111yescharacteristic
117#3229C2×C1112yes—
118#2546C2×C1111yescharacteristic
119#1611C2×C1118yes—
120#1503C2×C1112yes—
121#1461C2×C1111yescharacteristic
122C23×C11C22×D411yescharacteristic
123Q8×C11—28no—
124Q8×C11—44no—
125Q8×C11—44no—
126Q8×C11—84no—
127Q8×C11—84no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12012yes—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11C2×SD1614yes—
146C2×C4×C11C2×SD1612yes—
147C2×C4×C11#13712yes—
148C2×C4×C11C22×D412yes—
149C8×C11—44no—
150Q82—22no—
151#557—22no—
152#557—24no—
153#544—21no—
154#544C22×C1114yes—
155#533—22no—
156#533C22×C1112yes—
157C2×C4⋊Q8—21no—
158C2×C4⋊Q8C22×C1111yescharacteristic
159#519—21no—
160C2×C4×Q8C22×C1111yescharacteristic
161#498—22no—
162#487—22no—
163#483C22×C1118yes—
164#475—24no—
165#431C22×C1112yes—
166#398C22×C1114yes—
167#391—21no—
168#389—22no—
169C4×C4⋊C4C22×C1111yescharacteristic
170#328C22×C1118yes—
171#324C22×C1114yes—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11C2×#12011yescharacteristic
175C22×C11C22×SD1611yescharacteristic
176C22×C11C2×#13711yescharacteristic
177C4×C11—24no—
178C4×C11—21no—
179C4×C11—22no—
180C4×C11—44no—
181C4×C11—44no—
182C4×C11—42no—
183C4×C11—44no—
184C4×C11—82no—
185C4×C11#44814yes—
186C4×C11#45612yes—
187C22×Q8—21no—
188C22×Q8D4×C1111yescharacteristic
189C4⋊Q8—22no—
190C4⋊Q8—22no—
191C4⋊Q8—24no—
192C4⋊Q8—28no—
193C4⋊Q8—22no—
194C4⋊Q8—22no—
195C4⋊Q8—44no—
196C4⋊Q8D4×C1112yes—
197C4⋊Q8D4×C1112yes—
198#125—24no—
199#125—24no—
200#125—28no—
201#125—22no—
202C22⋊Q8—22no—
203C22⋊Q8—24no—
204C22⋊Q8C23×C1114yes—
205C4×Q8—24no—
206C4×Q8—24no—
207C4×Q8—24no—
208C4×Q8—24no—
209C4×Q8—22no—
210C4×Q8—22no—
211C4×Q8—22no—
212C4×Q8D4×C1114yes—
213#117—24no—
214#117—22no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4D4×C1111yescharacteristic
219C2×C4⋊C4C23×C1112yes—
220C2×C4⋊C4C23×C1112yes—
221C2×C42—21no—
222C2×C42D4×C1112yes—
223C2×C42C23×C1111yescharacteristic
224#106—28no—
225C4⋊C8—22no—
226#103—28no—
227C22⋊C8C23×C1114yes—
228C4×C8—22no—
229#95—24no—
230#95C23×C1112yes—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11C2×#44811yescharacteristic
234C2×C11C2×#45611yescharacteristic
235C2×C11#302811yescharacteristic
236C2×Q8—24no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8C11×SD1614yes—
244C2×Q8C2×D4×C1114yes—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4C2×D4×C1111yescharacteristic
248C22×C4C2×D4×C1112yes—
249C22×C4C2×D4×C1112yes—
250C22×C4C2×D4×C1111yescharacteristic
251C22×C4C24×C1111yescharacteristic
252C2×C8—24no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—24no—
257C4⋊C4—28no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—24no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—48no—
269C4⋊C4C2×D4×C1114yes—
270C22⋊C4—24no—
271C42—28no—
272C42—22no—
273C42—22no—
274C42—24no—
275C42—42no—
276C42C2×D4×C1112yes—
277C42C2×D4×C1112yes—
278C11#1841011yescharacteristic, direct product factor, Sylow
279C23C22×D4×C1111yescharacteristic
280Q8—28no—
281Q8—44no—
282Q8—44no—
283Q8—84no—
284Q8—84no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4C11×#12011yescharacteristic
300C2×C4C11×#12012yes—
301C2×C4C11×#12011yescharacteristic
302C2×C4C2×C11×SD1614yes—
303C2×C4C2×C11×SD1612yes—
304C2×C4C11×#13712yes—
305C2×C4C22×D4×C1112yes—
306C8—44no—
307C22—21no—
308C22—21no—
309C22C2×C11×#12011yescharacteristic
310C22C22×C11×SD1611yescharacteristic
311C22C2×C11×#13711yescharacteristic
312C4—24no—
313C4—21no—
314C4—22no—
315C4—44no—
316C4—44no—
317C4—42no—
318C4—44no—
319C4—82no—
320C4C11×#44814yes—
321C4C11×#45612yes—
322C2—21no—
323C2—21no—
324C2C2×C11×#44811yescharacteristic
325C2C2×C11×#45611yescharacteristic
326C2C11×#302811yescharacteristic
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
73. #18410C11direct (N × H)
278. C11#18410direct (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×#32292
C11×#25462
C11×#16112
C11×#15032
C11×#14612
#1841011