Finite Group Databasebeta

← C11×#18186 #14595379

Subgroups — C11×#18186 #14595379

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic, complemented
2C11×#3109C212yesmaximal, complemented
3C11×#2398C211yesmaximal, characteristic, complemented
4C11×#1616C214yesmaximal, complemented
5C11×#1598C214yesmaximal, complemented
6C11×#1505C212yesmaximal, 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×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#481C2214yes—
19C11×#476—22no—
20C11×#459—22no—
21C11×#447C2214yes—
22C11×#442—24no—
23C11×#432C2212yes—
24C11×#400C2212yes—
25C11×#397—21no—
26C11×#394C2212yes—
27C11×#393—21no—
28C4×C11×C22⋊C4—22no—
29C11×#376C2211yescharacteristic
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×D4×C11C2311yescharacteristic
39C23×C4×C11—21no—
40C2×C11×D8—24no—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8D412yes—
43C11×#127—22no—
44C11×#127D412yes—
45C11×#124—24no—
46C11×#124—22no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—28no—
49C11×#121—24no—
50C11×#121—28no—
51C11×#121—22no—
52C11×#121—24no—
53C11×#121C2314yes—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×D4×C11—24no—
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11D414yes—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—21no—
68C2×C42×C11—21no—
69C2×C42×C11D412yes—
70C2×C42×C11C2311yescharacteristic
71C11×#106—24no—
72C11×C4⋊C8—22no—
73C11×#102—24no—
74C11×#102—24no—
75C11×C22⋊C8C2314yes—
76C11×#97—22no—
77C11×#95—21no—
78C11×#95—22no—
79C11×#95—22no—
80C11×#95C2312yes—
81#18186C1111yesmaximal, 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—416no—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11C2×D414yes—
100C22×C4×C11—28no—
101C22×C4×C11—24no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—44no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2411yescharacteristic
112C11×D8—48no—
113C2×C8×C11—24no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4C2×D414yes—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—44no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—44no—
126C42×C11—22no—
127C42×C11—22no—
128C42×C11—42no—
129C42×C11C2×D412yes—
130C42×C11C2×D412yes—
131#3497C2×C1111yescharacteristic, complemented
132#3109C2×C1112yescomplemented
133#2398C2×C1111yescharacteristic, complemented
134#1616C2×C1114yescomplemented
135#1598C2×C1114yescomplemented
136#1505C2×C1112yescomplemented
137#1467C2×C1111yescharacteristic, complemented
138C23×C11—22no—
139C23×C11—24no—
140C23×C11—42no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11C22×D411yescharacteristic
145Q8×C11—28no—
146Q8×C11—44no—
147Q8×C11—48no—
148D4×C11—24no—
149D4×C11—44no—
150D4×C11—42no—
151D4×C11—44no—
152D4×C11—48no—
153D4×C11—48no—
154D4×C11—44no—
155D4×C11—84no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
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—82no—
172C2×C4×C11—82no—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12012yes—
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)14yes—
177C2×C4×C11C22×D412yes—
178C8×C11—44no—
179C2×2−1+4—21no—
180#550—22no—
181D4×Q8—22no—
182#548—24no—
183#537—21no—
184#537C22×C1114yes—
185#532—22no—
186#532C22×C1112yes—
187C2×C4×Q8C22×C1111yescharacteristic
188C2×C4×D4C22×C1111yescharacteristic
189#481C22×C1114yes—
190#476—22no—
191#459—22no—
192#447C22×C1114yes—
193#442—24no—
194#432C22×C1112yes—
195#400C22×C1112yes—
196#397—21no—
197#394C22×C1112yes—
198#393—21no—
199C4×C22⋊C4—22no—
200#376C22×C1111yescharacteristic
201#327C22×C1118yes—
202#324C22×C1114yes—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—44no—
206C22×C11—44no—
207C22×C11—44no—
208C22×C11—42no—
209C22×C11—44no—
210C22×C11—82no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11C2×#12011yescharacteristic
214C22×C11C2×AGL(1,ℤ/8)12yes—
215C4×C11—22no—
216C4×C11—24no—
217C4×C11—21no—
218C4×C11—22no—
219C4×C11—44no—
220C4×C11—42no—
221C4×C11—82no—
222C4×C11—81no—
223C4×C11#45412yes—
2242−1+4—48no—
225C2×#41—24no—
226C2×#41—24no—
227C2×#41—22no—
228C22×Q8—24no—
229C22×Q8D4×C1111yescharacteristic
230C22×D4C23×C1111yescharacteristic
231C23×C4—21no—
232C2×D8—24no—
233C4⋊Q8—22no—
234C4⋊Q8D4×C1112yes—
235#127—22no—
236#127D4×C1112yes—
237#124—24no—
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×D4—22no—
252C4×D4—22no—
253C4×D4D4×C1114yes—
254C2×C4⋊C4D4×C1111yescharacteristic
255C2×C4⋊C4C23×C1111yescharacteristic
256C2×C4⋊C4C23×C1112yes—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260C2×C42—21no—
261C2×C42D4×C1112yes—
262C2×C42C23×C1111yescharacteristic
263#106—24no—
264C4⋊C8—22no—
265#102—24no—
266#102—24no—
267C22⋊C8C23×C1114yes—
268#97—22no—
269#95—21no—
270#95—22no—
271#95—22no—
272#95C23×C1112yes—
273C2×C11—22no—
274C2×C11—84no—
275C2×C11—82no—
276C2×C11#300311yescharacteristic
277C2×C11C2×#45411yescharacteristic
278C2×C11#302511yescharacteristic
279C24—21no—
280#41—48no—
281#41—48no—
282#41—416no—
283#41—48no—
284C2×Q8—24no—
285C2×Q8—22no—
286C2×Q8—22no—
287C2×Q8—24no—
288C2×Q8—416no—
289C2×D4—24no—
290C2×D4—24no—
291C2×D4—24no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—42no—
296C2×D4C2×D4×C1114yes—
297C22×C4—28no—
298C22×C4—24no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—44no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4C2×D4×C1111yescharacteristic
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C2×D4×C1112yes—
307C22×C4C2×D4×C1112yes—
308C22×C4C24×C1111yescharacteristic
309D8—48no—
310C2×C8—24no—
311C4⋊C4—24no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4C2×D4×C1114yes—
317C22⋊C4—28no—
318C22⋊C4—24no—
319C22⋊C4—24no—
320C22⋊C4—44no—
321C22⋊C4—42no—
322C22⋊C4—44no—
323C42—22no—
324C42—22no—
325C42—42no—
326C42C2×D4×C1112yes—
327C42C2×D4×C1112yes—
328C11#1818611yescharacteristic, direct product factor, Sylow
329C23—22no—
330C23—24no—
331C23—42no—
332C23—41no—
333C23—41no—
334C23—42no—
335C23C22×D4×C1111yescharacteristic
336Q8—28no—
337Q8—44no—
338Q8—48no—
339D4—24no—
340D4—44no—
341D4—42no—
342D4—44no—
343D4—48no—
344D4—48no—
345D4—44no—
346D4—84no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—41no—
354C2×C4—48no—
355C2×C4—416no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4C11×#12011yescharacteristic
365C2×C4C11×#12012yes—
366C2×C4C11×#12011yescharacteristic
367C2×C4C11×AGL(1,ℤ/8)14yes—
368C2×C4C22×D4×C1112yes—
369C8—44no—
370C22—21no—
371C22—21no—
372C22—44no—
373C22—44no—
374C22—44no—
375C22—42no—
376C22—44no—
377C22—82no—
378C22—81no—
379C22—81no—
380C22C2×C11×#12011yescharacteristic
381C22C2×C11×AGL(1,ℤ/8)12yes—
382C4—22no—
383C4—24no—
384C4—21no—
385C4—22no—
386C4—44no—
387C4—42no—
388C4—82no—
389C4—81no—
390C4C11×#45412yes—
391C2—22no—
392C2—82no—
393C2—84no—
394C2C11×#300311yescharacteristic
395C2C2×C11×#45411yescharacteristic
396C2C11×#302511yescharacteristic
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×#3109C2semidirect
3. C11×#2398C2semidirect
4. C11×#1616C2semidirect
5. C11×#1598C2semidirect
6. C11×#1505C2semidirect
7. C11×#1467C2semidirect
81. #18186C11direct (N × H)
131. #3497C2×C11semidirect
132. #3109C2×C11semidirect
133. #2398C2×C11semidirect
134. #1616C2×C11semidirect
135. #1598C2×C11semidirect
136. #1505C2×C11semidirect
137. #1467C2×C11semidirect
328. C11#18186direct (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×#31092
C11×#23982
C11×#16162
C11×#15982
C11×#15052
C11×#14672
#1818611