Finite Group Databasebeta

← C11×#18401 #14595594

Subgroups — C11×#18401 #14595594

Order 2816.

1262 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic, complemented
2C11×#3205C212yesmaximal, complemented
3C11×#2548C211yesmaximal, characteristic, complemented
4C11×#1598C218yesmaximal, complemented
5C11×#1502C212yesmaximal, complemented
6C11×#1461C211yesmaximal, characteristic, complemented
7C2×C11×2−1+4—21no—
8C11×#550—22no—
9D4×Q8×C11—22no—
10C11×#548—24no—
11C11×#537—21no—
12C11×#537C2214yes—
13C11×#532—22no—
14C11×#532C2212yes—
15C2×C11×#127C2211yescharacteristic
16C2×C11×#124—21no—
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#493—22no—
19C11×#486—22no—
20C11×#459—24no—
21C11×#447C2218yes—
22C11×#431C2212yes—
23C11×#394C2214yes—
24C11×#390—21no—
25C11×#390—22no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#327C2218yes—
28C11×#324C2214yes—
29C11×2−1+4—44no—
30C11×2−1+4—44no—
31C2×C11×#41—24no—
32C2×C11×#41—24no—
33C2×C11×#41—22no—
34C22×Q8×C11—24no—
35C22×Q8×C11D411yescharacteristic
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11C2312yes—
39C2×C11×D8—28no—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8D412yes—
42C11×#127—22no—
43C11×#127—22no—
44C11×#127—22no—
45C11×#127D412yes—
46C11×#124—24no—
47C11×#124—22no—
48C11×#124—44no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—28no—
51C11×#121—24no—
52C11×#121—28no—
53C11×#121—22no—
54C11×#121—24no—
55C11×#121C2314yes—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×D4×C11—24no—
59C4×D4×C11—24no—
60C4×D4×C11—22no—
61C4×D4×C11D414yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C42×C11—21no—
68C2×C42×C11D412yes—
69C2×C42×C11C2311yescharacteristic
70C11×C4⋊C8—22no—
71C11×#102—28no—
72C11×C22⋊C8C2314yes—
73C4×C8×C11—22no—
74C11×#95C2312yes—
75#18401C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—22no—
77C11×#41—48no—
78C11×#41—416no—
79C11×#41—48no—
80C11×#41—44no—
81C11×#41—44no—
82C2×Q8×C11—24no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—416no—
87C2×Q8×C11D814yescomplemented
88C2×D4×C11—24no—
89C2×D4×C11—24no—
90C2×D4×C11—24no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—24no—
94C2×D4×C11—44no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C2×D4×C11—41no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—82no—
101C2×D4×C11C2×D414yes—
102C22×C4×C11—28no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C11×D8—88no—
111C2×C8×C11—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4C2×D414yes—
118C11×C22⋊C4—28no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—48no—
122C11×C22⋊C4—84no—
123C42×C11—22no—
124C42×C11—22no—
125C42×C11—42no—
126C42×C11C2×D412yes—
127C42×C11C2×D412yes—
128#3497C2×C1111yescharacteristic, complemented
129#3205C2×C1112yescomplemented
130#2548C2×C1111yescharacteristic, complemented
131#1598C2×C1118yescomplemented
132#1502C2×C1112yescomplemented
133#1461C2×C1111yescharacteristic, complemented
134C23×C11—24no—
135C23×C11—44no—
136C23×C11—44no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11—42no—
140C23×C11C22×D411yescharacteristic
141Q8×C11—28no—
142Q8×C11—48no—
143Q8×C11—44no—
144D4×C11—44no—
145D4×C11—48no—
146D4×C11—48no—
147D4×C11—44no—
148D4×C11—44no—
149D4×C11—44no—
150D4×C11—44no—
151D4×C11—82no—
152D4×C11—84no—
153D4×C11—84no—
154D4×C11—82no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—41no—
161C2×C4×C11—416no—
162C2×C4×C11—48no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12012yes—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11C2×D814yes—
171C2×C4×C11C2×D812yes—
172C2×C4×C11AGL(1,ℤ/8)12yes—
173C2×C4×C11C22×D412yes—
174C8×C11—44no—
175C2×2−1+4—21no—
176#550—22no—
177D4×Q8—22no—
178#548—24no—
179#537—21no—
180#537C22×C1114yes—
181#532—22no—
182#532C22×C1112yes—
183C2×#127C22×C1111yescharacteristic
184C2×#124—21no—
185C2×C4×Q8C22×C1111yescharacteristic
186#493—22no—
187#486—22no—
188#459—24no—
189#447C22×C1118yes—
190#431C22×C1112yes—
191#394C22×C1114yes—
192#390—21no—
193#390—22no—
194C4×C4⋊C4C22×C1111yescharacteristic
195#327C22×C1118yes—
196#324C22×C1114yes—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—44no—
200C22×C11—44no—
201C22×C11—44no—
202C22×C11—84no—
203C22×C11—84no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11—82no—
207C22×C11C2×#12011yescharacteristic
208C22×C11C22×D811yescharacteristic
209C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
210C4×C11—24no—
211C4×C11—21no—
212C4×C11—22no—
213C4×C11—44no—
214C4×C11—42no—
215C4×C11—82no—
216C4×C11#44714yes—
217C4×C11#45412yes—
2182−1+4—44no—
2192−1+4—44no—
220C2×#41—24no—
221C2×#41—24no—
222C2×#41—22no—
223C22×Q8—24no—
224C22×Q8D4×C1111yescharacteristic
225C22×D4—21no—
226C22×D4—21no—
227C22×D4C23×C1112yes—
228C2×D8—28no—
229C4⋊Q8—22no—
230C4⋊Q8D4×C1112yes—
231#127—22no—
232#127—22no—
233#127—22no—
234#127D4×C1112yes—
235#124—24no—
236#124—22no—
237#124—44no—
238C22⋊Q8—24no—
239C22⋊Q8—28no—
240#121—24no—
241#121—28no—
242#121—22no—
243#121—24no—
244#121C23×C1114yes—
245C4×Q8—22no—
246C4×Q8—22no—
247C4×D4—24no—
248C4×D4—24no—
249C4×D4—22no—
250C4×D4D4×C1114yes—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C1111yescharacteristic
253C2×C4⋊C4C23×C1112yes—
254C2×C22⋊C4—24no—
255C2×C22⋊C4—24no—
256C2×C42—21no—
257C2×C42D4×C1112yes—
258C2×C42C23×C1111yescharacteristic
259C4⋊C8—22no—
260#102—28no—
261C22⋊C8C23×C1114yes—
262C4×C8—22no—
263#95C23×C1112yes—
264C2×C11—21no—
265C2×C11—21no—
266C2×C11—84no—
267C2×C11—162no—
268C2×C11C2×#44711yescharacteristic
269C2×C11C2×#45411yescharacteristic
270C2×C11#302711yescharacteristic
271C24—22no—
272#41—48no—
273#41—416no—
274#41—48no—
275#41—44no—
276#41—44no—
277C2×Q8—24no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8—22no—
281C2×Q8—416no—
282C2×Q8C11×D814yescomplemented
283C2×D4—24no—
284C2×D4—24no—
285C2×D4—24no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—24no—
289C2×D4—44no—
290C2×D4—41no—
291C2×D4—42no—
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—82no—
296C2×D4C2×D4×C1114yes—
297C22×C4—28no—
298C22×C4—24no—
299C22×C4—22no—
300C22×C4C2×D4×C1111yescharacteristic
301C22×C4C2×D4×C1112yes—
302C22×C4C2×D4×C1112yes—
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C24×C1111yescharacteristic
305D8—88no—
306C2×C8—24no—
307C4⋊C4—24no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—24no—
311C4⋊C4—42no—
312C4⋊C4C2×D4×C1114yes—
313C22⋊C4—28no—
314C22⋊C4—24no—
315C22⋊C4—24no—
316C22⋊C4—48no—
317C22⋊C4—84no—
318C42—22no—
319C42—22no—
320C42—42no—
321C42C2×D4×C1112yes—
322C42C2×D4×C1112yes—
323C11#1840111yescharacteristic, direct product factor, Sylow
324C23—24no—
325C23—44no—
326C23—44no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23C22×D4×C1111yescharacteristic
331Q8—28no—
332Q8—48no—
333Q8—44no—
334D4—44no—
335D4—48no—
336D4—48no—
337D4—44no—
338D4—44no—
339D4—44no—
340D4—44no—
341D4—82no—
342D4—84no—
343D4—84no—
344D4—82no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—41no—
351C2×C4—416no—
352C2×C4—48no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4C11×#12011yescharacteristic
358C2×C4C11×#12012yes—
359C2×C4C11×#12011yescharacteristic
360C2×C4C2×C11×D814yes—
361C2×C4C2×C11×D812yes—
362C2×C4C11×AGL(1,ℤ/8)12yes—
363C2×C4C22×D4×C1112yes—
364C8—44no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—84no—
371C22—84no—
372C22—82no—
373C22—82no—
374C22—82no—
375C22C2×C11×#12011yescharacteristic
376C22C22×C11×D811yescharacteristic
377C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
378C4—24no—
379C4—21no—
380C4—22no—
381C4—44no—
382C4—42no—
383C4—82no—
384C4C11×#44714yes—
385C4C11×#45412yes—
386C2—21no—
387C2—21no—
388C2—84no—
389C2—162no—
390C2C2×C11×#44711yescharacteristic
391C2C2×C11×#45411yescharacteristic
392C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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×#3497C2semidirect
2. C11×#3205C2semidirect
3. C11×#2548C2semidirect
4. C11×#1598C2semidirect
5. C11×#1502C2semidirect
6. C11×#1461C2semidirect
75. #18401C11direct (N × H)
87. C2×Q8×C11D8semidirect
128. #3497C2×C11semidirect
129. #3205C2×C11semidirect
130. #2548C2×C11semidirect
131. #1598C2×C11semidirect
132. #1502C2×C11semidirect
133. #1461C2×C11semidirect
282. C2×Q8C11×D8semidirect
323. C11#18401direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34972
C11×#32052
C11×#25482
C11×#15982
C11×#15022
C11×#14612
#1840111