Finite Group Databasebeta

← C11×#18188 #14595381

Subgroups — C11×#18188 #14595381

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic, complemented
2C11×#3110C212yesmaximal
3C11×#2398C211yesmaximal, characteristic
4C11×#1617C214yesmaximal, complemented
5C11×#1599C214yesmaximal
6C11×#1506C212yesmaximal, complemented
7C11×#1467C211yesmaximal, characteristic, complemented
8Q82×C11—22no—
9C11×#557—22no—
10C11×#557—24no—
11C11×#544—21no—
12C11×#544C2214yes—
13C11×#533—22no—
14C11×#533C2212yes—
15C11×#519—21no—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#484C2214yes—
19C11×#474—22no—
20C11×#461—22no—
21C11×#450C2214yes—
22C11×#440—24no—
23C11×#432C2212yes—
24C11×#400C2212yes—
25C11×#397—21no—
26C11×#394C2212yes—
27C11×#393—21no—
28C4×C11×C22⋊C4—22no—
29C11×#376C2211yescharacteristic
30C11×#328C2218yes—
31C11×#324C2214yes—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11—21no—
35C2×C11×SD16—24no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8—24no—
39C11×C4⋊Q8—28no—
40C11×C4⋊Q8D412yes—
41C11×C4⋊Q8D412yes—
42C11×#125—24no—
43C11×#125—24no—
44C11×#125—28no—
45C11×#125—22no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8C2314yes—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C4×Q8×C11—24no—
52C4×Q8×C11—24no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11D414yes—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C11×#117—24no—
60C11×#117—22no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—21no—
67C2×C42×C11—21no—
68C2×C42×C11D412yes—
69C2×C42×C11C2311yescharacteristic
70C11×#107—24no—
71C11×C4⋊C8—22no—
72C11×#103—24no—
73C11×#102—24no—
74C11×C22⋊C8C2314yes—
75C11×#97—22no—
76C11×#95—21no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95C2312yes—
80#18188C1111yesmaximal, 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×C11C2×D414yes—
87C2×D4×C11—22no—
88C2×D4×C11—42no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—44no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2411yescharacteristic
99C11×SD16—48no—
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—22no—
113C11×C4⋊C4C2×D414yes—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—44no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—44no—
118C42×C11—28no—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11—24no—
122C42×C11—42no—
123C42×C11C2×D412yes—
124C42×C11C2×D412yes—
125#3502C2×C1111yescharacteristic, complemented
126#3110C2×C1112yes—
127#2398C2×C1111yescharacteristic
128#1617C2×C1114yescomplemented
129#1599C2×C1114yes—
130#1506C2×C1112yescomplemented
131#1467C2×C1111yescharacteristic, complemented
132C23×C11—22no—
133C23×C11—42no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—42no—
137C23×C11C22×D411yescharacteristic
138Q8×C11—28no—
139Q8×C11—44no—
140Q8×C11—44no—
141Q8×C11—84no—
142D4×C11—24no—
143D4×C11—42no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
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—82no—
159C2×C4×C11—82no—
160C2×C4×C11#12012yes—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#13714yes—
164C2×C4×C11C22×D412yes—
165C8×C11—44no—
166Q82—22no—
167#557—22no—
168#557—24no—
169#544—21no—
170#544C22×C1114yes—
171#533—22no—
172#533C22×C1112yes—
173#519—21no—
174C2×C4×Q8C22×C1111yescharacteristic
175C2×C4×D4C22×C1111yescharacteristic
176#484C22×C1114yes—
177#474—22no—
178#461—22no—
179#450C22×C1114yes—
180#440—24no—
181#432C22×C1112yes—
182#400C22×C1112yes—
183#397—21no—
184#394C22×C1112yes—
185#393—21no—
186C4×C22⋊C4—22no—
187#376C22×C1111yescharacteristic
188#328C22×C1118yes—
189#324C22×C1114yes—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—44no—
193C22×C11—42no—
194C22×C11—82no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11C2×#12011yescharacteristic
198C22×C11C2×#13712yes—
199C4×C11—22no—
200C4×C11—24no—
201C4×C11—21no—
202C4×C11—22no—
203C4×C11—44no—
204C4×C11—42no—
205C4×C11—44no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11#45412yes—
209C22×Q8D4×C1111yescharacteristic
210C22×D4C23×C1111yescharacteristic
211C23×C4—21no—
212C2×SD16—24no—
213C4⋊Q8—22no—
214C4⋊Q8—22no—
215C4⋊Q8—24no—
216C4⋊Q8—28no—
217C4⋊Q8D4×C1112yes—
218C4⋊Q8D4×C1112yes—
219#125—24no—
220#125—24no—
221#125—28no—
222#125—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—
234C4×D4—22no—
235C4×D4—22no—
236#117—24no—
237#117—22no—
238C2×C4⋊C4D4×C1111yescharacteristic
239C2×C4⋊C4C23×C1111yescharacteristic
240C2×C4⋊C4C23×C1112yes—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C42—21no—
245C2×C42D4×C1112yes—
246C2×C42C23×C1111yescharacteristic
247#107—24no—
248C4⋊C8—22no—
249#103—24no—
250#102—24no—
251C22⋊C8C23×C1114yes—
252#97—22no—
253#95—21no—
254#95—22no—
255#95—22no—
256#95C23×C1112yes—
257C2×C11—22no—
258C2×C11—82no—
259C2×C11#300411yescharacteristic
260C2×C11C2×#45411yescharacteristic
261C2×C11#302511yescharacteristic
262C24—21no—
263C2×Q8—24no—
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—24no—
267C2×Q8C2×D4×C1114yes—
268C2×D4—22no—
269C2×D4—42no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—44no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C2×D4×C1111yescharacteristic
277C22×C4C2×D4×C1112yes—
278C22×C4C2×D4×C1112yes—
279C22×C4C24×C1111yescharacteristic
280SD16—48no—
281C2×C8—24no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—28no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—22no—
294C4⋊C4C2×D4×C1114yes—
295C22⋊C4—24no—
296C22⋊C4—44no—
297C22⋊C4—42no—
298C22⋊C4—44no—
299C42—28no—
300C42—22no—
301C42—22no—
302C42—24no—
303C42—42no—
304C42C2×D4×C1112yes—
305C42C2×D4×C1112yes—
306C11#1818811yescharacteristic, direct product factor, Sylow
307C23—22no—
308C23—42no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23C22×D4×C1111yescharacteristic
313Q8—28no—
314Q8—44no—
315Q8—44no—
316Q8—84no—
317D4—24no—
318D4—42no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4C11×#12012yes—
336C2×C4C11×#12011yescharacteristic
337C2×C4C11×#12011yescharacteristic
338C2×C4C11×#13714yes—
339C2×C4C22×D4×C1112yes—
340C8—44no—
341C22—21no—
342C22—21no—
343C22—44no—
344C22—42no—
345C22—82no—
346C22—81no—
347C22—81no—
348C22C2×C11×#12011yescharacteristic
349C22C2×C11×#13712yes—
350C4—22no—
351C4—24no—
352C4—21no—
353C4—22no—
354C4—44no—
355C4—42no—
356C4—44no—
357C4—82no—
358C4—81no—
359C4C11×#45412yes—
360C2—22no—
361C2—82no—
362C2C11×#300411yescharacteristic
363C2C2×C11×#45411yescharacteristic
364C2C11×#302511yescharacteristic
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×#1617C2semidirect
6. C11×#1506C2semidirect
7. C11×#1467C2semidirect
80. #18188C11direct (N × H)
125. #3502C2×C11semidirect
128. #1617C2×C11semidirect
130. #1506C2×C11semidirect
131. #1467C2×C11semidirect
306. C11#18188direct (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×#31102
C11×#23982
C11×#16172
C11×#15992
C11×#15062
C11×#14672
#1818811