Finite Group Databasebeta

← C11×#18369 #14595562

Subgroups — C11×#18369 #14595562

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic, complemented
2C11×#3215C212yesmaximal
3C11×#2632C211yesmaximal, characteristic
4C11×#1605C214yesmaximal, complemented
5C11×#1599C214yesmaximal
6C11×#1515C212yesmaximal, complemented
7C11×#1467C211yesmaximal, characteristic, complemented
8Q82×C11—22no—
9C11×#557—22no—
10C11×#557—24no—
11C11×#544—21no—
12C11×#544C2214yes—
13C11×#533—22no—
14C11×#533C2212yes—
15C2×C11×#124C2211yescharacteristic
16C11×#519—21no—
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#497—22no—
19C11×#489—22no—
20C11×#464—24no—
21C11×#451C2214yes—
22C11×#450C2214yes—
23C11×#432C2212yes—
24C11×#399—21no—
25C11×#395C2212yes—
26C11×#394C2212yes—
27C11×#393—21no—
28C11×#388—22no—
29C11×#383C2211yescharacteristic
30C11×#328C2218yes—
31C11×#324C2214yes—
32C22×Q8×C11D411yescharacteristic
33C22×Q8×C11C2311yescharacteristic
34C22×D4×C11C2311yescharacteristic
35C2×C11×Q16—24no—
36C2×C11×SD16—24no—
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8—24no—
40C11×C4⋊Q8—28no—
41C11×C4⋊Q8D412yes—
42C11×C4⋊Q8D412yes—
43C11×#125—24no—
44C11×#125—24no—
45C11×#125—28no—
46C11×#125—22no—
47C11×#124—22no—
48C11×#124—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8C2314yes—
52C4×Q8×C11—24no—
53C4×Q8×C11—24no—
54C4×Q8×C11—24no—
55C4×Q8×C11—24no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11D414yes—
60C11×#117—24no—
61C11×#117—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11D412yes—
70C2×C42×C11C2311yescharacteristic
71C11×C4⋊C8—22no—
72C11×#103—24no—
73C11×#102—24no—
74C11×C22⋊C8C2314yes—
75C11×#97—22no—
76C11×#95—21no—
77C11×#95—21no—
78C11×#95—22no—
79C11×#95C2312yes—
80#18369C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11—21no—
82C2×Q8×C11—24no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—24no—
86C2×Q8×C11—22no—
87C2×Q8×C11—81no—
88C2×Q8×C11C2×D414yes—
89C2×D4×C11—22no—
90C2×D4×C11—81no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C11×Q16—84no—
99C11×SD16—84no—
100C2×C8×C11—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—82no—
113C11×C4⋊C4C2×D414yes—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—44no—
119C11×C22⋊C4—82no—
120C42×C11—28no—
121C42×C11—22no—
122C42×C11—22no—
123C42×C11—24no—
124C42×C11C2×D412yes—
125C42×C11C2×D412yes—
126#3502C2×C1111yescharacteristic, complemented
127#3215C2×C1112yes—
128#2632C2×C1111yescharacteristic
129#1605C2×C1114yescomplemented
130#1599C2×C1114yes—
131#1515C2×C1112yescomplemented
132#1467C2×C1111yescharacteristic, complemented
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—41no—
136C23×C11—42no—
137C23×C11C22×D411yescharacteristic
138Q8×C11—28no—
139Q8×C11—44no—
140Q8×C11—44no—
141Q8×C11—44no—
142Q8×C11—84no—
143D4×C11—44no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12012yes—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#13714yes—
162C2×C4×C11C22×D412yes—
163C8×C11—44no—
164Q82—22no—
165#557—22no—
166#557—24no—
167#544—21no—
168#544C22×C1114yes—
169#533—22no—
170#533C22×C1112yes—
171C2×#124C22×C1111yescharacteristic
172#519—21no—
173C2×C4×Q8C22×C1111yescharacteristic
174#497—22no—
175#489—22no—
176#464—24no—
177#451C22×C1114yes—
178#450C22×C1114yes—
179#432C22×C1112yes—
180#399—21no—
181#395C22×C1112yes—
182#394C22×C1112yes—
183#393—21no—
184#388—22no—
185#383C22×C1111yescharacteristic
186#328C22×C1118yes—
187#324C22×C1114yes—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—84no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11C2×#12011yescharacteristic
195C22×C11C2×#13712yes—
196C4×C11—22no—
197C4×C11—24no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—22no—
201C4×C11—44no—
202C4×C11—42no—
203C4×C11—44no—
204C4×C11—82no—
205C4×C11—81no—
206C22×Q8D4×C1111yescharacteristic
207C22×Q8C23×C1111yescharacteristic
208C22×D4C23×C1111yescharacteristic
209C2×Q16—24no—
210C2×SD16—24no—
211C4⋊Q8—22no—
212C4⋊Q8—22no—
213C4⋊Q8—24no—
214C4⋊Q8—28no—
215C4⋊Q8D4×C1112yes—
216C4⋊Q8D4×C1112yes—
217#125—24no—
218#125—24no—
219#125—28no—
220#125—22no—
221#124—22no—
222#124—22no—
223C22⋊Q8—22no—
224C22⋊Q8—24no—
225C22⋊Q8C23×C1114yes—
226C4×Q8—24no—
227C4×Q8—24no—
228C4×Q8—24no—
229C4×Q8—24no—
230C4×Q8—22no—
231C4×Q8—22no—
232C4×Q8—22no—
233C4×Q8D4×C1114yes—
234#117—24no—
235#117—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4D4×C1111yescharacteristic
238C2×C4⋊C4C23×C1112yes—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C42D4×C1112yes—
244C2×C42C23×C1111yescharacteristic
245C4⋊C8—22no—
246#103—24no—
247#102—24no—
248C22⋊C8C23×C1114yes—
249#97—22no—
250#95—21no—
251#95—21no—
252#95—22no—
253#95C23×C1112yes—
254C2×C11—22no—
255C2×C11—161no—
256C2×C11#300411yescharacteristic
257C2×C11#302011yescharacteristic
258C2×C11#302711yescharacteristic
259C24—21no—
260C2×Q8—24no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—24no—
264C2×Q8—22no—
265C2×Q8—81no—
266C2×Q8C2×D4×C1114yes—
267C2×D4—22no—
268C2×D4—81no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4C2×D4×C1111yescharacteristic
272C22×C4C2×D4×C1112yes—
273C22×C4C2×D4×C1112yes—
274C22×C4C2×D4×C1111yescharacteristic
275C22×C4C24×C1111yescharacteristic
276Q16—84no—
277SD16—84no—
278C2×C8—24no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—28no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—24no—
290C4⋊C4—82no—
291C4⋊C4C2×D4×C1114yes—
292C22⋊C4—24no—
293C22⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—41no—
296C22⋊C4—44no—
297C22⋊C4—82no—
298C42—28no—
299C42—22no—
300C42—22no—
301C42—24no—
302C42C2×D4×C1112yes—
303C42C2×D4×C1112yes—
304C11#1836911yescharacteristic, direct product factor, Sylow
305C23—42no—
306C23—42no—
307C23—41no—
308C23—42no—
309C23C22×D4×C1111yescharacteristic
310Q8—28no—
311Q8—44no—
312Q8—44no—
313Q8—44no—
314Q8—84no—
315D4—44no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4C11×#12011yescharacteristic
331C2×C4C11×#12012yes—
332C2×C4C11×#12011yescharacteristic
333C2×C4C11×#13714yes—
334C2×C4C22×D4×C1112yes—
335C8—44no—
336C22—21no—
337C22—21no—
338C22—84no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22C2×C11×#12011yescharacteristic
343C22C2×C11×#13712yes—
344C4—22no—
345C4—24no—
346C4—21no—
347C4—21no—
348C4—22no—
349C4—44no—
350C4—42no—
351C4—44no—
352C4—82no—
353C4—81no—
354C2—22no—
355C2—161no—
356C2C11×#300411yescharacteristic
357C2C11×#302011yescharacteristic
358C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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
1. C11×#3502C2semidirect
4. C11×#1605C2semidirect
6. C11×#1515C2semidirect
7. C11×#1467C2semidirect
80. #18369C11direct (N × H)
126. #3502C2×C11semidirect
129. #1605C2×C11semidirect
131. #1515C2×C11semidirect
132. #1467C2×C11semidirect
304. C11#18369direct (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×#32152
C11×#26322
C11×#16052
C11×#15992
C11×#15152
C11×#14672
#1836911