Finite Group Databasebeta

← C11×#18388 #14595581

Subgroups — C11×#18388 #14595581

Order 2816.

1258 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic
2C11×#3206C212yesmaximal, complemented
3C11×#2563C211yesmaximal, characteristic, complemented
4C11×#1601C218yesmaximal, complemented
5C11×#1502C212yesmaximal, complemented
6C11×#1460C211yesmaximal, characteristic, complemented
7C2×C11×H(5,𝔽2)—21no—
8C11×#547—22no—
9C11×#546—24no—
10D42×C11—22no—
11C11×#537—21no—
12C11×#534C2214yes—
13C11×#532C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic, complemented
15C2×C11×#121—22no—
16C2×C4×D4×C11C2211yescharacteristic
17C11×#492—22no—
18C11×#487—22no—
19C11×#461—24no—
20C11×#448C2218yescomplemented
21C11×#431C2212yescomplemented
22C11×#393C2214yescomplemented
23C11×#390—21no—
24C11×#382—21no—
25C11×#380—22no—
26C4×C11×C4⋊C4C2211yescharacteristic, complemented
27C11×#327C2218yescomplemented
28C11×#323C2214yescomplemented
29C11×H(5,𝔽2)—44no—
30C11×H(5,𝔽2)—44no—
31C2×C11×#41—24no—
32C2×C11×#41—22no—
33C22×Q8×C11C2312yes—
34C22×D4×C11—24no—
35C22×D4×C11—24no—
36C22×D4×C11—22no—
37C22×D4×C11D411yescharacteristic
38C23×C4×C11D412yes—
39C2×C11×SD16—28no—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8D412yes—
43C11×#127D412yes—
44C11×#124—22no—
45C11×#123—28no—
46C11×C22⋊Q8—24no—
47C11×#121—24no—
48C11×#121—24no—
49C11×#121—24no—
50C11×#121—22no—
51C11×#121—24no—
52C11×#121C2314yes—
53C11×#120—28no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11D414yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4C2312yes—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C11×C4⋊C8—22no—
69C11×#103—28no—
70C11×C22⋊C8C2314yes—
71C4×C8×C11—22no—
72C11×#95—24no—
73C11×#95C2312yes—
74#18388C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11—24no—
76C24×C11C2×D412yes—
77C11×#41—416no—
78C11×#41—44no—
79C11×#41—44no—
80C2×Q8×C11—22no—
81C2×Q8×C11—24no—
82C2×Q8×C11—82no—
83C2×D4×C11—28no—
84C2×D4×C11—24no—
85C2×D4×C11—24no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—416no—
91C2×D4×C11—48no—
92C2×D4×C11—48no—
93C2×D4×C11—84no—
94C2×D4×C11SD1614yescomplemented
95C2×D4×C11C2×D414yes—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—44no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C11×SD16—88no—
108C2×C8×C11—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4C2×D414yes—
117C11×C22⋊C4—28no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—84no—
122C42×C11—42no—
123C42×C11C2×D412yes—
124C42×C11C2×D412yes—
125#3496C2×C1111yescharacteristic
126#3206C2×C1112yescomplemented
127#2563C2×C1111yescharacteristic, complemented
128#1601C2×C1118yescomplemented
129#1502C2×C1112yescomplemented
130#1460C2×C1111yescharacteristic, complemented
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—24no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—48no—
137C23×C11—84no—
138C23×C11—84no—
139C23×C11C2×SD1614yes—
140C23×C11C22×D411yescharacteristic
141Q8×C11—48no—
142Q8×C11—44no—
143D4×C11—28no—
144D4×C11—44no—
145D4×C11—416no—
146D4×C11—44no—
147D4×C11—44no—
148D4×C11—44no—
149D4×C11—44no—
150D4×C11—84no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—41no—
155C2×C4×C11—48no—
156C2×C4×C11—48no—
157C2×C4×C11—44no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—82no—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12012yes—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11C2×SD1612yes—
169C2×C4×C11AGL(1,ℤ/8)12yes—
170C2×C4×C11C22×D412yes—
171C8×C11—44no—
172C2×H(5,𝔽2)—21no—
173#547—22no—
174#546—24no—
175D42—22no—
176#537—21no—
177#534C22×C1114yes—
178#532C22×C1112yes—
179C2×C4⋊Q8C22×C1111yescharacteristic, complemented
180C2×#121—22no—
181C2×C4×D4C22×C1111yescharacteristic
182#492—22no—
183#487—22no—
184#461—24no—
185#448C22×C1118yescomplemented
186#431C22×C1112yescomplemented
187#393C22×C1114yescomplemented
188#390—21no—
189#382—21no—
190#380—22no—
191C4×C4⋊C4C22×C1111yescharacteristic, complemented
192#327C22×C1118yescomplemented
193#323C22×C1114yescomplemented
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—24no—
197C22×C11—44no—
198C22×C11—42no—
199C22×C11—42no—
200C22×C11—44no—
201C22×C11—44no—
202C22×C11—44no—
203C22×C11—82no—
204C22×C11—168no—
205C22×C11C2×#12011yescharacteristic
206C22×C11C22×SD1611yescharacteristic
207C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
208C4×C11—21no—
209C4×C11—22no—
210C4×C11—44no—
211C4×C11—42no—
212C4×C11—82no—
213C4×C11—82no—
214C4×C11#45014yes—
215C4×C11#45512yes—
216H(5,𝔽2)—44no—
217H(5,𝔽2)—44no—
218C2×#41—24no—
219C2×#41—22no—
220C22×Q8C23×C1112yes—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—22no—
224C22×D4D4×C1111yescharacteristic
225C23×C4D4×C1112yes—
226C2×SD16—28no—
227C4⋊Q8—22no—
228C4⋊Q8—22no—
229C4⋊Q8D4×C1112yes—
230#127D4×C1112yes—
231#124—22no—
232#123—28no—
233C22⋊Q8—24no—
234#121—24no—
235#121—24no—
236#121—24no—
237#121—22no—
238#121—24no—
239#121C23×C1114yes—
240#120—28no—
241C4×D4—22no—
242C4×D4—22no—
243C4×D4—22no—
244C4×D4D4×C1114yes—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4D4×C1111yescharacteristic
250C2×C22⋊C4—24no—
251C2×C22⋊C4—24no—
252C2×C22⋊C4C23×C1112yes—
253C2×C42—21no—
254C2×C42C23×C1111yescharacteristic
255C4⋊C8—22no—
256#103—28no—
257C22⋊C8C23×C1114yes—
258C4×C8—22no—
259#95—24no—
260#95C23×C1112yes—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—44no—
264C2×C11—84no—
265C2×C11C2×#45011yescharacteristic
266C2×C11C2×#45511yescharacteristic
267C2×C11#302711yescharacteristic
268C24—24no—
269C24C2×D4×C1112yes—
270#41—416no—
271#41—44no—
272#41—44no—
273C2×Q8—22no—
274C2×Q8—24no—
275C2×Q8—82no—
276C2×D4—28no—
277C2×D4—24no—
278C2×D4—24no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—416no—
284C2×D4—48no—
285C2×D4—48no—
286C2×D4—84no—
287C2×D4C11×SD1614yescomplemented
288C2×D4C2×D4×C1114yes—
289C22×C4—24no—
290C22×C4—22no—
291C22×C4—24no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—44no—
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C2×D4×C1112yes—
298C22×C4C2×D4×C1111yescharacteristic
299C22×C4C24×C1111yescharacteristic
300SD16—88no—
301C2×C8—24no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—42no—
306C4⋊C4—41no—
307C4⋊C4—42no—
308C4⋊C4—41no—
309C4⋊C4C2×D4×C1114yes—
310C22⋊C4—28no—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C22⋊C4—24no—
314C22⋊C4—84no—
315C42—42no—
316C42C2×D4×C1112yes—
317C42C2×D4×C1112yes—
318C11#1838811yescharacteristic, direct product factor, Sylow
319C23—22no—
320C23—22no—
321C23—24no—
322C23—42no—
323C23—42no—
324C23—48no—
325C23—84no—
326C23—84no—
327C23C2×C11×SD1614yes—
328C23C22×D4×C1111yescharacteristic
329Q8—48no—
330Q8—44no—
331D4—28no—
332D4—44no—
333D4—416no—
334D4—44no—
335D4—44no—
336D4—44no—
337D4—44no—
338D4—84no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—41no—
343C2×C4—48no—
344C2×C4—48no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4C11×#12011yescharacteristic
354C2×C4C11×#12012yes—
355C2×C4C11×#12011yescharacteristic
356C2×C4C2×C11×SD1612yes—
357C2×C4C11×AGL(1,ℤ/8)12yes—
358C2×C4C22×D4×C1112yes—
359C8—44no—
360C22—21no—
361C22—21no—
362C22—24no—
363C22—44no—
364C22—42no—
365C22—42no—
366C22—44no—
367C22—44no—
368C22—44no—
369C22—82no—
370C22—168no—
371C22C2×C11×#12011yescharacteristic
372C22C22×C11×SD1611yescharacteristic
373C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
374C4—21no—
375C4—22no—
376C4—44no—
377C4—42no—
378C4—82no—
379C4—82no—
380C4C11×#45014yes—
381C4C11×#45512yes—
382C2—21no—
383C2—21no—
384C2—44no—
385C2—84no—
386C2C2×C11×#45011yescharacteristic
387C2C2×C11×#45511yescharacteristic
388C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3496C2
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
2. C11×#3206C2semidirect
3. C11×#2563C2semidirect
4. C11×#1601C2semidirect
5. C11×#1502C2semidirect
6. C11×#1460C2semidirect
14. C2×C11×C4⋊Q8C22semidirect
20. C11×#448C22semidirect
21. C11×#431C22semidirect
22. C11×#393C22semidirect
26. C4×C11×C4⋊C4C22semidirect
27. C11×#327C22semidirect
28. C11×#323C22semidirect
74. #18388C11direct (N × H)
94. C2×D4×C11SD16semidirect
126. #3206C2×C11semidirect
127. #2563C2×C11semidirect
128. #1601C2×C11semidirect
129. #1502C2×C11semidirect
130. #1460C2×C11semidirect
179. C2×C4⋊Q8C22×C11semidirect
185. #448C22×C11semidirect
186. #431C22×C11semidirect
187. #393C22×C11semidirect
191. C4×C4⋊C4C22×C11semidirect
192. #327C22×C11semidirect
193. #323C22×C11semidirect
287. C2×D4C11×SD16semidirect
318. C11#18388direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C11×#32062
C11×#25632
C11×#16012
C11×#15022
C11×#14602
#1838811