Finite Group Databasebeta

← C11×#18187 #14595380

Subgroups — C11×#18187 #14595380

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic
2C11×#3112C212yesmaximal, complemented
3C11×#2399C211yesmaximal, characteristic, complemented
4C11×#1610C214yesmaximal, complemented
5C11×#1604C214yesmaximal, 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×Q8×C11C2211yescharacteristic
18C11×#480C2214yes—
19C11×#477—22no—
20C11×#460—22no—
21C11×#448C2214yes—
22C11×#440—24no—
23C11×#432C2212yes—
24C11×#398—21no—
25C11×#398C2212yes—
26C11×#395—21no—
27C11×#395C2212yes—
28C4×C11×C4⋊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×Q8×C11C2311yescharacteristic
39C2×C11×SD16—24no—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8D412yes—
42C11×#127—22no—
43C11×#127D412yes—
44C11×#124—24no—
45C11×#124—22no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—28no—
48C11×#121—24no—
49C11×#121—28no—
50C11×#121—22no—
51C11×#121—24no—
52C11×#121C2314yes—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×D4×C11—24no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11D414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11D412yes—
70C2×C42×C11C2311yescharacteristic
71C11×#107—24no—
72C11×C4⋊C8—22no—
73C11×#103—24no—
74C11×#102—24no—
75C11×C22⋊C8C2314yes—
76C11×#97—22no—
77C11×#95—21no—
78C11×#95—22no—
79C11×#95—22no—
80C11×#95C2312yes—
81#18187C1111yesmaximal, characteristic, direct product factor, Sylow
82C11×#41—48no—
83C11×#41—48no—
84C11×#41—416no—
85C11×#41—48no—
86C2×Q8×C11—24no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—24no—
90C2×Q8×C11—22no—
91C2×Q8×C11—42no—
92C2×Q8×C11—416no—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11C2×D414yes—
99C22×C4×C11—28no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—24no—
103C22×C4×C11—21no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2411yescharacteristic
109C11×SD16—48no—
110C2×C8×C11—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—44no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—44no—
119C11×C4⋊C4C2×D414yes—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C42×C11—24no—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—41no—
127C42×C11—41no—
128C42×C11C2×D412yes—
129C42×C11C2×D412yes—
130#3497C2×C1111yescharacteristic
131#3112C2×C1112yescomplemented
132#2399C2×C1111yescharacteristic, complemented
133#1610C2×C1114yescomplemented
134#1604C2×C1114yescomplemented
135#1505C2×C1112yescomplemented
136#1467C2×C1111yescharacteristic, complemented
137C23×C11—24no—
138C23×C11C22×D411yescharacteristic
139Q8×C11—28no—
140Q8×C11—24no—
141Q8×C11—42no—
142Q8×C11—44no—
143Q8×C11—48no—
144D4×C11—44no—
145D4×C11—44no—
146D4×C11—48no—
147D4×C11—48no—
148D4×C11—44no—
149D4×C11—84no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—41no—
159C2×C4×C11—48no—
160C2×C4×C11—416no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12012yes—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)14yes—
172C2×C4×C11C22×D412yes—
173C8×C11—44no—
174C2×2−1+4—21no—
175#550—22no—
176D4×Q8—22no—
177#548—24no—
178#537—21no—
179#537C22×C1114yes—
180#532—22no—
181#532C22×C1112yes—
182C2×C4×Q8C22×C1111yescharacteristic
183C2×C4×Q8C22×C1111yescharacteristic
184#480C22×C1114yes—
185#477—22no—
186#460—22no—
187#448C22×C1114yes—
188#440—24no—
189#432C22×C1112yes—
190#398—21no—
191#398C22×C1112yes—
192#395—21no—
193#395C22×C1112yes—
194C4×C4⋊C4—22no—
195#376C22×C1111yescharacteristic
196#327C22×C1118yes—
197#324C22×C1114yes—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—44no—
201C22×C11—44no—
202C22×C11—44no—
203C22×C11C2×#12011yescharacteristic
204C22×C11C2×AGL(1,ℤ/8)12yes—
205C4×C11—22no—
206C4×C11—24no—
207C4×C11—21no—
208C4×C11—22no—
209C4×C11—44no—
210C4×C11—44no—
211C4×C11—42no—
212C4×C11—42no—
213C4×C11—81no—
214C4×C11#45612yes—
2152−1+4—48no—
216C2×#41—24no—
217C2×#41—24no—
218C2×#41—22no—
219C22×Q8—24no—
220C22×Q8D4×C1111yescharacteristic
221C22×Q8C23×C1111yescharacteristic
222C2×SD16—24no—
223C4⋊Q8—22no—
224C4⋊Q8D4×C1112yes—
225#127—22no—
226#127D4×C1112yes—
227#124—24no—
228#124—22no—
229C22⋊Q8—24no—
230C22⋊Q8—28no—
231#121—24no—
232#121—28no—
233#121—22no—
234#121—24no—
235#121C23×C1114yes—
236C4×Q8—22no—
237C4×Q8—22no—
238C4×Q8—22no—
239C4×Q8—22no—
240C4×D4—24no—
241C4×D4—24no—
242C4×D4—22no—
243C4×D4D4×C1114yes—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4D4×C1111yescharacteristic
248C2×C4⋊C4C23×C1111yescharacteristic
249C2×C4⋊C4C23×C1112yes—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42D4×C1112yes—
253C2×C42C23×C1111yescharacteristic
254#107—24no—
255C4⋊C8—22no—
256#103—24no—
257#102—24no—
258C22⋊C8C23×C1114yes—
259#97—22no—
260#95—21no—
261#95—22no—
262#95—22no—
263#95C23×C1112yes—
264C2×C11—22no—
265C2×C11—84no—
266C2×C11#300311yescharacteristic
267C2×C11C2×#45611yescharacteristic
268C2×C11#302511yescharacteristic
269#41—48no—
270#41—48no—
271#41—416no—
272#41—48no—
273C2×Q8—24no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—24no—
277C2×Q8—22no—
278C2×Q8—42no—
279C2×Q8—416no—
280C2×D4—24no—
281C2×D4—24no—
282C2×D4—24no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4C2×D4×C1114yes—
286C22×C4—28no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—24no—
290C22×C4—21no—
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C2×D4×C1112yes—
294C22×C4C2×D4×C1112yes—
295C22×C4C24×C1111yescharacteristic
296SD16—48no—
297C2×C8—24no—
298C4⋊C4—24no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—24no—
302C4⋊C4—22no—
303C4⋊C4—44no—
304C4⋊C4—42no—
305C4⋊C4—44no—
306C4⋊C4C2×D4×C1114yes—
307C22⋊C4—28no—
308C22⋊C4—24no—
309C22⋊C4—24no—
310C42—24no—
311C42—22no—
312C42—22no—
313C42—41no—
314C42—41no—
315C42C2×D4×C1112yes—
316C42C2×D4×C1112yes—
317C11#1818711yescharacteristic, direct product factor, Sylow
318C23—24no—
319C23C22×D4×C1111yescharacteristic
320Q8—28no—
321Q8—24no—
322Q8—42no—
323Q8—44no—
324Q8—48no—
325D4—44no—
326D4—44no—
327D4—48no—
328D4—48no—
329D4—44no—
330D4—84no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—41no—
340C2×C4—48no—
341C2×C4—416no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4C11×#12011yescharacteristic
350C2×C4C11×#12012yes—
351C2×C4C11×#12011yescharacteristic
352C2×C4C11×AGL(1,ℤ/8)14yes—
353C2×C4C22×D4×C1112yes—
354C8—44no—
355C22—21no—
356C22—21no—
357C22—44no—
358C22—44no—
359C22—44no—
360C22C2×C11×#12011yescharacteristic
361C22C2×C11×AGL(1,ℤ/8)12yes—
362C4—22no—
363C4—24no—
364C4—21no—
365C4—22no—
366C4—44no—
367C4—44no—
368C4—42no—
369C4—42no—
370C4—81no—
371C4C11×#45612yes—
372C2—22no—
373C2—84no—
374C2C11×#300311yescharacteristic
375C2C2×C11×#45611yescharacteristic
376C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3497C2
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×#3112C2semidirect
3. C11×#2399C2semidirect
4. C11×#1610C2semidirect
5. C11×#1604C2semidirect
6. C11×#1505C2semidirect
7. C11×#1467C2semidirect
81. #18187C11direct (N × H)
131. #3112C2×C11semidirect
132. #2399C2×C11semidirect
133. #1610C2×C11semidirect
134. #1604C2×C11semidirect
135. #1505C2×C11semidirect
136. #1467C2×C11semidirect
317. C11#18187direct (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×#31122
C11×#23992
C11×#16102
C11×#16042
C11×#15052
C11×#14672
#1818711