Finite Group Databasebeta

← C11×#18368 #14595561

Subgroups — C11×#18368 #14595561

Order 2816.

1168 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic, complemented
2C11×#3213C212yesmaximal, complemented
3C11×#2632C211yesmaximal, characteristic, complemented
4C11×#1604C214yesmaximal, complemented
5C11×#1598C214yesmaximal, complemented
6C11×#1514C212yesmaximal, complemented
7C11×#1467C211yesmaximal, characteristic, complemented
8C2×C11×2−1+4—21no—
9C11×#550—22no—
10D4×Q8×C11—22no—
11C11×#548—24no—
12C11×#537—21no—
13C11×#537C2214yes—
14C11×#532—22no—
15C11×#532C2212yes—
16C2×C11×#124C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#496—22no—
19C11×#489—22no—
20C11×#463—24no—
21C11×#448C2214yes—
22C11×#447C2214yes—
23C11×#432C2212yes—
24C11×#399—21no—
25C11×#395C2212yes—
26C11×#394C2212yes—
27C11×#393—21no—
28C11×#388—22no—
29C11×#383C2211yescharacteristic
30C11×#327C2218yes—
31C11×#324C2214yes—
32C11×2−1+4—48no—
33C2×C11×#41—24no—
34C2×C11×#41—24no—
35C2×C11×#41—22no—
36C22×Q8×C11—24no—
37C22×Q8×C11D411yescharacteristic
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11C2311yescharacteristic
40C2×C11×SD16—24no—
41C2×C11×D8—24no—
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8D412yes—
44C11×#127—22no—
45C11×#127D412yes—
46C11×#124—24no—
47C11×#124—22no—
48C11×#124—22no—
49C11×#124—22no—
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8—28no—
52C11×#121—24no—
53C11×#121—28no—
54C11×#121—22no—
55C11×#121—24no—
56C11×#121C2314yes—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×D4×C11—24no—
60C4×D4×C11—24no—
61C4×D4×C11—22no—
62C4×D4×C11D414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—22no—
70C2×C42×C11D412yes—
71C2×C42×C11C2311yescharacteristic
72C11×C4⋊C8—22no—
73C11×#103—24no—
74C11×#102—24no—
75C11×C22⋊C8C2314yes—
76C11×#97—22no—
77C11×#95—21no—
78C11×#95—21no—
79C11×#95—22no—
80C11×#95C2312yes—
81#18368C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—21no—
83C11×#41—48no—
84C11×#41—48no—
85C11×#41—416no—
86C11×#41—48no—
87C2×Q8×C11—24no—
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—416no—
93C2×Q8×C11—81no—
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—81no—
101C2×D4×C11C2×D414yes—
102C22×C4×C11—28no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C11×SD16—84no—
112C11×D8—84no—
113C2×C8×C11—24no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—82no—
119C11×C4⋊C4C2×D414yes—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—42no—
126C11×C22⋊C4—44no—
127C11×C22⋊C4—82no—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11C2×D412yes—
131C42×C11C2×D412yes—
132#3497C2×C1111yescharacteristic, complemented
133#3213C2×C1112yescomplemented
134#2632C2×C1111yescharacteristic, complemented
135#1604C2×C1114yescomplemented
136#1598C2×C1114yescomplemented
137#1514C2×C1112yescomplemented
138#1467C2×C1111yescharacteristic, complemented
139C23×C11—24no—
140C23×C11—42no—
141C23×C11—42no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11C22×D411yescharacteristic
145Q8×C11—28no—
146Q8×C11—44no—
147Q8×C11—48no—
148Q8×C11—44no—
149D4×C11—44no—
150D4×C11—44no—
151D4×C11—44no—
152D4×C11—48no—
153D4×C11—44no—
154D4×C11—48no—
155D4×C11—84no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—24no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—48no—
164C2×C4×C11—416no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12012yes—
174C2×C4×C11AGL(1,ℤ/8)14yes—
175C2×C4×C11C22×D412yes—
176C8×C11—44no—
177C2×2−1+4—21no—
178#550—22no—
179D4×Q8—22no—
180#548—24no—
181#537—21no—
182#537C22×C1114yes—
183#532—22no—
184#532C22×C1112yes—
185C2×#124C22×C1111yescharacteristic
186C2×C4×Q8C22×C1111yescharacteristic
187#496—22no—
188#489—22no—
189#463—24no—
190#448C22×C1114yes—
191#447C22×C1114yes—
192#432C22×C1112yes—
193#399—21no—
194#395C22×C1112yes—
195#394C22×C1112yes—
196#393—21no—
197#388—22no—
198#383C22×C1111yescharacteristic
199#327C22×C1118yes—
200#324C22×C1114yes—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—44no—
204C22×C11—44no—
205C22×C11—44no—
206C22×C11—84no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11C2×#12011yescharacteristic
211C22×C11C2×AGL(1,ℤ/8)12yes—
212C4×C11—22no—
213C4×C11—24no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—22no—
217C4×C11—44no—
218C4×C11—42no—
219C4×C11—82no—
220C4×C11—81no—
2212−1+4—48no—
222C2×#41—24no—
223C2×#41—24no—
224C2×#41—22no—
225C22×Q8—24no—
226C22×Q8D4×C1111yescharacteristic
227C22×Q8C23×C1111yescharacteristic
228C22×D4C23×C1111yescharacteristic
229C2×SD16—24no—
230C2×D8—24no—
231C4⋊Q8—22no—
232C4⋊Q8D4×C1112yes—
233#127—22no—
234#127D4×C1112yes—
235#124—24no—
236#124—22no—
237#124—22no—
238#124—22no—
239C22⋊Q8—24no—
240C22⋊Q8—28no—
241#121—24no—
242#121—28no—
243#121—22no—
244#121—24no—
245#121C23×C1114yes—
246C4×Q8—22no—
247C4×Q8—22no—
248C4×D4—24no—
249C4×D4—24no—
250C4×D4—22no—
251C4×D4D4×C1114yes—
252C2×C4⋊C4—22no—
253C2×C4⋊C4D4×C1111yescharacteristic
254C2×C4⋊C4C23×C1112yes—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C42D4×C1112yes—
260C2×C42C23×C1111yescharacteristic
261C4⋊C8—22no—
262#103—24no—
263#102—24no—
264C22⋊C8C23×C1114yes—
265#97—22no—
266#95—21no—
267#95—21no—
268#95—22no—
269#95C23×C1112yes—
270C2×C11—22no—
271C2×C11—84no—
272C2×C11—161no—
273C2×C11#300311yescharacteristic
274C2×C11#302011yescharacteristic
275C2×C11#302711yescharacteristic
276C24—21no—
277#41—48no—
278#41—48no—
279#41—416no—
280#41—48no—
281C2×Q8—24no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—24no—
285C2×Q8—22no—
286C2×Q8—416no—
287C2×Q8—81no—
288C2×D4—24no—
289C2×D4—24no—
290C2×D4—24no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—81no—
295C2×D4C2×D4×C1114yes—
296C22×C4—28no—
297C22×C4—24no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4C2×D4×C1111yescharacteristic
301C22×C4C2×D4×C1112yes—
302C22×C4C2×D4×C1112yes—
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C24×C1111yescharacteristic
305SD16—84no—
306D8—84no—
307C2×C8—24no—
308C4⋊C4—24no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—24no—
312C4⋊C4—82no—
313C4⋊C4C2×D4×C1114yes—
314C22⋊C4—28no—
315C22⋊C4—24no—
316C22⋊C4—24no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—42no—
320C22⋊C4—44no—
321C22⋊C4—82no—
322C42—22no—
323C42—22no—
324C42C2×D4×C1112yes—
325C42C2×D4×C1112yes—
326C11#1836811yescharacteristic, direct product factor, Sylow
327C23—24no—
328C23—42no—
329C23—42no—
330C23—41no—
331C23—42no—
332C23C22×D4×C1111yescharacteristic
333Q8—28no—
334Q8—44no—
335Q8—48no—
336Q8—44no—
337D4—44no—
338D4—44no—
339D4—44no—
340D4—48no—
341D4—44no—
342D4—48no—
343D4—84no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—48no—
352C2×C4—416no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4C11×#12011yescharacteristic
360C2×C4C11×#12011yescharacteristic
361C2×C4C11×#12012yes—
362C2×C4C11×AGL(1,ℤ/8)14yes—
363C2×C4C22×D4×C1112yes—
364C8—44no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—84no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22C2×C11×#12011yescharacteristic
375C22C2×C11×AGL(1,ℤ/8)12yes—
376C4—22no—
377C4—24no—
378C4—21no—
379C4—21no—
380C4—22no—
381C4—44no—
382C4—42no—
383C4—82no—
384C4—81no—
385C2—22no—
386C2—84no—
387C2—161no—
388C2C11×#300311yescharacteristic
389C2C11×#302011yescharacteristic
390C2C11×#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×#3213C2semidirect
3. C11×#2632C2semidirect
4. C11×#1604C2semidirect
5. C11×#1598C2semidirect
6. C11×#1514C2semidirect
7. C11×#1467C2semidirect
81. #18368C11direct (N × H)
132. #3497C2×C11semidirect
133. #3213C2×C11semidirect
134. #2632C2×C11semidirect
135. #1604C2×C11semidirect
136. #1598C2×C11semidirect
137. #1514C2×C11semidirect
138. #1467C2×C11semidirect
326. C11#18368direct (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×#32132
C11×#26322
C11×#16042
C11×#15982
C11×#15142
C11×#14672
#1836811