Finite Group Databasebeta

← C11×#18994 #14596187

Subgroups — C11×#18994 #14596187

Order 2816.

936 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#563C211yesmaximal, characteristic, complemented
2C11×#3234C212yesmaximal, complemented
3C11×#3153C211yesmaximal, characteristic
4C11×#1660C214yesmaximal, complemented
5C11×#1657C214yesmaximal, complemented
6C11×#1533C211yesmaximal, characteristic, complemented
7C11×#1528C212yesmaximal, complemented
8C2×C11×#137—21no—
9C2×C11×AGL(1,ℤ/8)—21no—
10C11×#563—24no—
11C11×#563—22no—
12C11×#563C2214yes—
13C11×#532C2211yescharacteristic
14C2×C11×C4⋊Q8—21no—
15C2×C11×#126—22no—
16C2×C11×#125C2212yes—
17C2×C11×#124C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8—22no—
20C11×#501C2214yescomplemented
21C11×#497C2212yes—
22C11×#496C2212yes—
23C11×#495—22no—
24C11×#490C2214yescomplemented
25C11×#481—22no—
26C11×#480—22no—
27C11×#478—24no—
28C11×#432C2212yes—
29C4×C11×M16C2211yescharacteristic
30C11×#330C2218yescomplemented
31C11×#329C2214yes—
32C2×C11×#41—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11D411yescharacteristic
35C22×D4×C11D411yescharacteristic
36C23×C4×C11—21no—
37C11×#137—44no—
38C11×AGL(1,ℤ/8)—44no—
39C2×C11×Q16—22no—
40C2×C11×SD16—22no—
41C2×C11×SD16—22no—
42C2×C11×D8—22no—
43C2×C11×M16—21no—
44C11×C4⋊Q8—24no—
45C11×C4⋊Q8—24no—
46C11×C4⋊Q8C2311yescharacteristic
47C11×#127C2311yescharacteristic
48C11×#126—28no—
49C11×#126—28no—
50C11×#125—22no—
51C11×#125—22no—
52C11×#125D414yes—
53C11×#125C2314yes—
54C11×#124—22no—
55C11×#124—21no—
56C11×#124D412yes—
57C11×#124C2312yes—
58C11×#123—24no—
59C11×#123—24no—
60C11×C22⋊Q8—28no—
61C11×C22⋊Q8—28no—
62C11×#121—22no—
63C4×D4×C11—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C11×#107—24no—
75C11×#106—24no—
76C11×C4⋊C8—22no—
77C11×#102—24no—
78C11×#102—24no—
79C11×C22⋊C8—22no—
80C11×#97C2314yes—
81C11×#97C2312yes—
82C4×C8×C11—21no—
83#18994C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—21no—
85C11×#41—42no—
86C11×#41—42no—
87C2×Q8×C11—24no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—42no—
91C2×Q8×C11—82no—
92C2×Q8×C11C2×D412yes—
93C2×D4×C11—21no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11—42no—
97C2×D4×C11—41no—
98C2×D4×C11C2×D412yes—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—24no—
103C22×C4×C11—41no—
104C22×C4×C11—82no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C11×Q16—44no—
108C11×SD16—44no—
109C11×SD16—44no—
110C11×D8—44no—
111C11×M16—24no—
112C2×C8×C11—22no—
113C2×C8×C11—24no—
114C11×C4⋊C4—28no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4C2×D414yes—
123C11×C4⋊C4C2×D414yes—
124C11×C22⋊C4—28no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—42no—
129C42×C11—24no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D412yes—
132C42×C11C2411yescharacteristic
133C2×#563C2×C1111yescharacteristic, complemented
134#3234C2×C1112yescomplemented
135#3153C2×C1111yescharacteristic
136#1660C2×C1114yescomplemented
137#1657C2×C1114yescomplemented
138#1533C2×C1111yescharacteristic, complemented
139#1528C2×C1112yescomplemented
140C23×C11—22no—
141C23×C11—44no—
142C23×C11—42no—
143C23×C11—41no—
144C23×C11#12011yescharacteristic
145Q8×C11—42no—
146Q8×C11—41no—
147Q8×C11—41no—
148Q8×C11—81no—
149Q8×C11—84no—
150D4×C11—42no—
151D4×C11—41no—
152D4×C11—41no—
153D4×C11—44no—
154D4×C11—81no—
155D4×C11—82no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—42no—
161C2×C4×C11—44no—
162C2×C4×C11—44no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—82no—
166C2×C4×C11—84no—
167C2×C4×C11#12012yes—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11C22×D412yes—
170C2×C4×C11C22×D411yescharacteristic
171C8×C11—24no—
172C8×C11—44no—
173C2×#137—21no—
174C2×AGL(1,ℤ/8)—21no—
175#563—24no—
176#563—22no—
177#563C22×C1114yes—
178#532C22×C1111yescharacteristic
179C2×C4⋊Q8—21no—
180C2×#126—22no—
181C2×#125C22×C1112yes—
182C2×#124C22×C1111yescharacteristic
183C2×#123—21no—
184C2×C22⋊Q8—22no—
185#501C22×C1114yescomplemented
186#497C22×C1112yes—
187#496C22×C1112yes—
188#495—22no—
189#490C22×C1114yescomplemented
190#481—22no—
191#480—22no—
192#478—24no—
193#432C22×C1112yes—
194C4×M16C22×C1111yescharacteristic
195#330C22×C1118yescomplemented
196#329C22×C1114yes—
197C22×C11—22no—
198C22×C11—42no—
199C22×C11—44no—
200C22×C11—84no—
201C22×C11—81no—
202C22×C11—82no—
203C22×C11#45312yes—
204C22×C11C2×#12011yescharacteristic
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—22no—
208C4×C11—22no—
209C4×C11—44no—
210C4×C11—42no—
211C4×C11—44no—
212C4×C11—81no—
213C2×#41—21no—
214C22×Q8—21no—
215C22×Q8D4×C1111yescharacteristic
216C22×D4D4×C1111yescharacteristic
217C23×C4—21no—
218#137—44no—
219AGL(1,ℤ/8)—44no—
220C2×Q16—22no—
221C2×SD16—22no—
222C2×SD16—22no—
223C2×D8—22no—
224C2×M16—21no—
225C4⋊Q8—24no—
226C4⋊Q8—24no—
227C4⋊Q8C23×C1111yescharacteristic
228#127C23×C1111yescharacteristic
229#126—28no—
230#126—28no—
231#125—22no—
232#125—22no—
233#125D4×C1114yes—
234#125C23×C1114yes—
235#124—22no—
236#124—21no—
237#124D4×C1112yes—
238#124C23×C1112yes—
239#123—24no—
240#123—24no—
241C22⋊Q8—28no—
242C22⋊Q8—28no—
243#121—22no—
244C4×D4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4D4×C1112yes—
249C2×C4⋊C4D4×C1112yes—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—22no—
253C2×C42—21no—
254C2×C42C23×C1111yescharacteristic
255#107—24no—
256#106—24no—
257C4⋊C8—22no—
258#102—24no—
259#102—24no—
260C22⋊C8—22no—
261#97C23×C1114yes—
262#97C23×C1112yes—
263C4×C8—21no—
264C2×C11—22no—
265C2×C11—82no—
266C2×C11—161no—
267C2×C11C2×#45311yescharacteristic
268C2×C11#302012yes—
269C24—21no—
270#41—42no—
271#41—42no—
272C2×Q8—24no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—42no—
276C2×Q8—82no—
277C2×Q8C2×D4×C1112yes—
278C2×D4—21no—
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—42no—
282C2×D4—41no—
283C2×D4C2×D4×C1112yes—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—41no—
289C22×C4—82no—
290C22×C4C2×D4×C1111yescharacteristic
291C22×C4C2×D4×C1112yes—
292Q16—44no—
293SD16—44no—
294SD16—44no—
295D8—44no—
296M16—24no—
297C2×C8—22no—
298C2×C8—24no—
299C4⋊C4—28no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—22no—
307C4⋊C4C2×D4×C1114yes—
308C4⋊C4C2×D4×C1114yes—
309C22⋊C4—28no—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C22⋊C4—42no—
314C42—24no—
315C42C2×D4×C1111yescharacteristic
316C42C2×D4×C1112yes—
317C42C24×C1111yescharacteristic
318C11#1899411yescharacteristic, direct product factor, Sylow
319C23—22no—
320C23—44no—
321C23—42no—
322C23—41no—
323C23C11×#12011yescharacteristic
324Q8—42no—
325Q8—41no—
326Q8—41no—
327Q8—81no—
328Q8—84no—
329D4—42no—
330D4—41no—
331D4—41no—
332D4—44no—
333D4—81no—
334D4—82no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—84no—
346C2×C4C11×#12012yes—
347C2×C4C11×#12011yescharacteristic
348C2×C4C22×D4×C1112yes—
349C2×C4C22×D4×C1111yescharacteristic
350C8—24no—
351C8—44no—
352C22—22no—
353C22—42no—
354C22—44no—
355C22—84no—
356C22—81no—
357C22—82no—
358C22C11×#45312yes—
359C22C2×C11×#12011yescharacteristic
360C4—21no—
361C4—21no—
362C4—22no—
363C4—22no—
364C4—44no—
365C4—42no—
366C4—44no—
367C4—81no—
368C2—22no—
369C2—82no—
370C2—161no—
371C2C2×C11×#45311yescharacteristic
372C2C11×#302012yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3153C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C11×#563C2semidirect
2. C11×#3234C2semidirect
4. C11×#1660C2semidirect
5. C11×#1657C2semidirect
6. C11×#1533C2semidirect
7. C11×#1528C2semidirect
20. C11×#501C22semidirect
24. C11×#490C22semidirect
30. C11×#330C22semidirect
83. #18994C11direct (N × H)
133. C2×#563C2×C11semidirect
134. #3234C2×C11semidirect
136. #1660C2×C11semidirect
137. #1657C2×C11semidirect
138. #1533C2×C11semidirect
139. #1528C2×C11semidirect
185. #501C22×C11semidirect
189. #490C22×C11semidirect
195. #330C22×C11semidirect
318. C11#18994direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5632
C11×#32342
C11×#31532
C11×#16602
C11×#16572
C11×#15332
C11×#15282
#1899411