Finite Group Databasebeta

← C11×#18219 #14595412

Subgroups — C11×#18219 #14595412

Order 2816.

1154 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×#3497C211yesmaximal, characteristic
2C11×#3103C212yesmaximal, complemented
3C11×#2581C211yesmaximal, characteristic, complemented
4C11×#1616C214yesmaximal, complemented
5C11×#1604C214yesmaximal, complemented
6C11×#1517C212yesmaximal, complemented
7C11×#1461C211yesmaximal, 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×#481C2214yes—
19C11×#475—22no—
20C11×#460—22no—
21C11×#448C2214yes—
22C4×C11×SD16—24no—
23C11×#431C2212yes—
24C11×#400C2212yes—
25C11×#395C2212yes—
26C11×#391—21no—
27C11×#389—21no—
28C11×#387—22no—
29C11×#382C2211yescharacteristic
30C11×#327C2218yes—
31C11×#324C2214yes—
32C11×2−1+4—44no—
33C11×2−1+4—44no—
34C2×C11×#41—24no—
35C2×C11×#41—24no—
36C2×C11×#41—22no—
37C22×Q8×C11—24no—
38C22×Q8×C11D411yescharacteristic
39C22×Q8×C11C2311yescharacteristic
40C2×C11×SD16—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×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⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C42×C11—21no—
69C2×C42×C11D412yes—
70C2×C42×C11C2311yescharacteristic
71C11×#106—24no—
72C11×C4⋊C8—22no—
73C11×#103—24no—
74C11×#102—24no—
75C11×C22⋊C8C2314yes—
76C4×C8×C11—22no—
77C11×#95—21no—
78C11×#95—22no—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95C2312yes—
82#18219C1111yesmaximal, characteristic, direct product factor, Sylow
83C11×#41—48no—
84C11×#41—416no—
85C11×#41—48no—
86C11×#41—44no—
87C11×#41—44no—
88C2×Q8×C11—24no—
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—42no—
94C2×Q8×C11—416no—
95C2×Q8×C11SD1614yescomplemented
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11C2×D414yes—
102C22×C4×C11—28no—
103C22×C4×C11—21no—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C11×SD16—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⋊C4—44no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4C2×D414yes—
124C11×C22⋊C4—28no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C42×C11—22no—
128C42×C11—22no—
129C42×C11—42no—
130C42×C11C2×D412yes—
131C42×C11C2×D412yes—
132#3497C2×C1111yescharacteristic
133#3103C2×C1112yescomplemented
134#2581C2×C1111yescharacteristic, complemented
135#1616C2×C1114yescomplemented
136#1604C2×C1114yescomplemented
137#1517C2×C1112yescomplemented
138#1461C2×C1111yescharacteristic, complemented
139C23×C11—24no—
140C23×C11C22×D411yescharacteristic
141Q8×C11—28no—
142Q8×C11—24no—
143Q8×C11—42no—
144Q8×C11—48no—
145Q8×C11—44no—
146D4×C11—44no—
147D4×C11—44no—
148D4×C11—48no—
149D4×C11—44no—
150D4×C11—44no—
151D4×C11—44no—
152D4×C11—84no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—416no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—48no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12012yes—
173C2×C4×C11C2×SD1614yes—
174C2×C4×C11C2×SD1612yes—
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C2×C4×C11C22×D412yes—
177C8×C11—44no—
178C2×2−1+4—21no—
179#550—22no—
180D4×Q8—22no—
181#548—24no—
182#537—21no—
183#537C22×C1114yes—
184#532—22no—
185#532C22×C1112yes—
186C2×C4×Q8C22×C1111yescharacteristic
187C2×C4×Q8C22×C1111yescharacteristic
188#481C22×C1114yes—
189#475—22no—
190#460—22no—
191#448C22×C1114yes—
192C4×SD16—24no—
193#431C22×C1112yes—
194#400C22×C1112yes—
195#395C22×C1112yes—
196#391—21no—
197#389—21no—
198#387—22no—
199#382C22×C1111yescharacteristic
200#327C22×C1118yes—
201#324C22×C1114yes—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—44no—
205C22×C11—44no—
206C22×C11—44no—
207C22×C11C2×#12011yescharacteristic
208C22×C11C22×SD1611yescharacteristic
209C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
210C4×C11—24no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—22no—
214C4×C11—44no—
215C4×C11—42no—
216C4×C11—42no—
217C4×C11—82no—
218C4×C11—81no—
219C4×C11#45014yes—
2202−1+4—44no—
2212−1+4—44no—
222C2×#41—24no—
223C2×#41—24no—
224C2×#41—22no—
225C22×Q8—24no—
226C22×Q8D4×C1111yescharacteristic
227C22×Q8C23×C1111yescharacteristic
228C2×SD16—24no—
229C4⋊Q8—22no—
230C4⋊Q8D4×C1112yes—
231#127—22no—
232#127D4×C1112yes—
233#124—24no—
234#124—22no—
235C22⋊Q8—24no—
236C22⋊Q8—28no—
237#121—24no—
238#121—28no—
239#121—22no—
240#121—24no—
241#121C23×C1114yes—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×Q8—22no—
245C4×Q8—22no—
246C4×D4—24no—
247C4×D4—24no—
248C4×D4—22no—
249C4×D4D4×C1114yes—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4D4×C1111yescharacteristic
254C2×C4⋊C4C23×C1111yescharacteristic
255C2×C4⋊C4C23×C1112yes—
256C2×C42—21no—
257C2×C42D4×C1112yes—
258C2×C42C23×C1111yescharacteristic
259#106—24no—
260C4⋊C8—22no—
261#103—24no—
262#102—24no—
263C22⋊C8C23×C1114yes—
264C4×C8—22no—
265#95—21no—
266#95—22no—
267#95—22no—
268#95—22no—
269#95C23×C1112yes—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—84no—
273C2×C11C2×#45011yescharacteristic
274C2×C11#302011yescharacteristic
275C2×C11#302511yescharacteristic
276#41—48no—
277#41—416no—
278#41—48no—
279#41—44no—
280#41—44no—
281C2×Q8—24no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—22no—
285C2×Q8—22no—
286C2×Q8—42no—
287C2×Q8—416no—
288C2×Q8C11×SD1614yescomplemented
289C2×D4—24no—
290C2×D4—24no—
291C2×D4—24no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4C2×D4×C1114yes—
295C22×C4—28no—
296C22×C4—21no—
297C22×C4—24no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4C2×D4×C1112yes—
301C22×C4C2×D4×C1112yes—
302C22×C4C2×D4×C1111yescharacteristic
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C24×C1111yescharacteristic
305SD16—48no—
306C2×C8—24no—
307C4⋊C4—24no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—24no—
311C4⋊C4—22no—
312C4⋊C4—44no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—42no—
316C4⋊C4C2×D4×C1114yes—
317C22⋊C4—28no—
318C22⋊C4—24no—
319C22⋊C4—24no—
320C42—22no—
321C42—22no—
322C42—42no—
323C42C2×D4×C1112yes—
324C42C2×D4×C1112yes—
325C11#1821911yescharacteristic, direct product factor, Sylow
326C23—24no—
327C23C22×D4×C1111yescharacteristic
328Q8—28no—
329Q8—24no—
330Q8—42no—
331Q8—48no—
332Q8—44no—
333D4—44no—
334D4—44no—
335D4—48no—
336D4—44no—
337D4—44no—
338D4—44no—
339D4—84no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—416no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—48no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4C11×#12011yescharacteristic
358C2×C4C11×#12011yescharacteristic
359C2×C4C11×#12012yes—
360C2×C4C2×C11×SD1614yes—
361C2×C4C2×C11×SD1612yes—
362C2×C4C11×AGL(1,ℤ/8)12yes—
363C2×C4C22×D4×C1112yes—
364C8—44no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22C2×C11×#12011yescharacteristic
371C22C22×C11×SD1611yescharacteristic
372C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
373C4—24no—
374C4—21no—
375C4—21no—
376C4—22no—
377C4—44no—
378C4—42no—
379C4—42no—
380C4—82no—
381C4—81no—
382C4C11×#45014yes—
383C2—21no—
384C2—21no—
385C2—84no—
386C2C2×C11×#45011yescharacteristic
387C2C11×#302011yescharacteristic
388C2C11×#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×#3103C2semidirect
3. C11×#2581C2semidirect
4. C11×#1616C2semidirect
5. C11×#1604C2semidirect
6. C11×#1517C2semidirect
7. C11×#1461C2semidirect
82. #18219C11direct (N × H)
95. C2×Q8×C11SD16semidirect
133. #3103C2×C11semidirect
134. #2581C2×C11semidirect
135. #1616C2×C11semidirect
136. #1604C2×C11semidirect
137. #1517C2×C11semidirect
138. #1461C2×C11semidirect
288. C2×Q8C11×SD16semidirect
325. C11#18219direct (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×#31032
C11×#25812
C11×#16162
C11×#16042
C11×#15172
C11×#14612
#1821911