Finite Group Databasebeta

← C11×#18409 #14595602

Subgroups — C11×#18409 #14595602

Order 2816.

1134 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic
2C11×#3227C212yesmaximal, complemented
3C11×#2568C211yesmaximal, characteristic, complemented
4C11×#1616C218yesmaximal, complemented
5C11×#1502C212yesmaximal, complemented
6C11×#1461C211yesmaximal, characteristic, complemented
7C2×C11×2−1+4—21no—
8C11×#550—22no—
9D4×Q8×C11—22no—
10C11×#548—24no—
11C11×#537—21no—
12C11×#537C2214yes—
13C11×#532—22no—
14C11×#532C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C11×#498—22no—
18C11×#486—22no—
19C11×#481C2218yes—
20C11×#476—24no—
21C11×#431C2212yes—
22C11×#400C2214yes—
23C11×#391—21no—
24C11×#391—22no—
25C11×#382—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#327C2218yes—
28C11×#324C2214yes—
29C11×2−1+4—44no—
30C11×2−1+4—44no—
31C2×C11×#41—24no—
32C2×C11×#41—24no—
33C2×C11×#41—22no—
34C22×Q8×C11—24no—
35C22×Q8×C11—21no—
36C22×Q8×C11D411yescharacteristic
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8D412yes—
41C11×#127—22no—
42C11×#127D412yes—
43C11×#124—24no—
44C11×#124—22no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—28no—
47C11×#121—24no—
48C11×#121—28no—
49C11×#121—22no—
50C11×#121—24no—
51C11×#121C2314yes—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×D4×C11—24no—
55C4×D4×C11—24no—
56C4×D4×C11—22no—
57C4×D4×C11D414yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11—21no—
64C2×C42×C11D412yes—
65C2×C42×C11C2311yescharacteristic
66C11×#106—28no—
67C11×C4⋊C8—22no—
68C11×#102—28no—
69C11×C22⋊C8C2314yes—
70C4×C8×C11—22no—
71C11×#95—24no—
72C11×#95—24no—
73C11×#95C2312yes—
74#18409C1111yesmaximal, characteristic, direct product factor, Sylow
75C11×#41—48no—
76C11×#41—416no—
77C11×#41—48no—
78C11×#41—44no—
79C11×#41—44no—
80C2×Q8×C11—24no—
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—44no—
85C2×Q8×C11—416no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11SD1614yes—
89C2×D4×C11—24no—
90C2×D4×C11—24no—
91C2×D4×C11—24no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11C2×D414yes—
95C22×C4×C11—28no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C2×C8×C11—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4C2×D414yes—
113C11×C22⋊C4—28no—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—24no—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11—42no—
119C42×C11C2×D412yes—
120C42×C11C2×D412yes—
121#3497C2×C1111yescharacteristic
122#3227C2×C1112yescomplemented
123#2568C2×C1111yescharacteristic, complemented
124#1616C2×C1118yescomplemented
125#1502C2×C1112yescomplemented
126#1461C2×C1111yescharacteristic, complemented
127C23×C11—24no—
128C23×C11C22×D411yescharacteristic
129Q8×C11—28no—
130Q8×C11—48no—
131Q8×C11—44no—
132Q8×C11—82no—
133Q8×C11—82no—
134D4×C11—44no—
135D4×C11—48no—
136D4×C11—44no—
137D4×C11—44no—
138D4×C11—44no—
139D4×C11—44no—
140D4×C11—84no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—41no—
147C2×C4×C11—416no—
148C2×C4×C11—48no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—44no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12012yes—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11C2×SD1614yes—
159C2×C4×C11C2×SD1612yes—
160C2×C4×C11AGL(1,ℤ/8)12yes—
161C2×C4×C11C22×D412yes—
162C8×C11—44no—
163C2×2−1+4—21no—
164#550—22no—
165D4×Q8—22no—
166#548—24no—
167#537—21no—
168#537C22×C1114yes—
169#532—22no—
170#532C22×C1112yes—
171C2×C4⋊Q8C22×C1111yescharacteristic
172C2×C4×Q8C22×C1111yescharacteristic
173#498—22no—
174#486—22no—
175#481C22×C1118yes—
176#476—24no—
177#431C22×C1112yes—
178#400C22×C1114yes—
179#391—21no—
180#391—22no—
181#382—21no—
182C4×C4⋊C4C22×C1111yescharacteristic
183#327C22×C1118yes—
184#324C22×C1114yes—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—44no—
188C22×C11—44no—
189C22×C11—44no—
190C22×C11C2×#12011yescharacteristic
191C22×C11C22×SD1611yescharacteristic
192C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
193C4×C11—24no—
194C4×C11—21no—
195C4×C11—22no—
196C4×C11—44no—
197C4×C11—42no—
198C4×C11—82no—
199C4×C11—82no—
200C4×C11#45014yes—
201C4×C11#45412yes—
2022−1+4—44no—
2032−1+4—44no—
204C2×#41—24no—
205C2×#41—24no—
206C2×#41—22no—
207C22×Q8—24no—
208C22×Q8—21no—
209C22×Q8D4×C1111yescharacteristic
210C4⋊Q8—22no—
211C4⋊Q8—22no—
212C4⋊Q8—22no—
213C4⋊Q8D4×C1112yes—
214#127—22no—
215#127D4×C1112yes—
216#124—24no—
217#124—22no—
218C22⋊Q8—24no—
219C22⋊Q8—28no—
220#121—24no—
221#121—28no—
222#121—22no—
223#121—24no—
224#121C23×C1114yes—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×D4—24no—
228C4×D4—24no—
229C4×D4—22no—
230C4×D4D4×C1114yes—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4D4×C1111yescharacteristic
234C2×C4⋊C4C23×C1112yes—
235C2×C4⋊C4C23×C1112yes—
236C2×C42—21no—
237C2×C42D4×C1112yes—
238C2×C42C23×C1111yescharacteristic
239#106—28no—
240C4⋊C8—22no—
241#102—28no—
242C22⋊C8C23×C1114yes—
243C4×C8—22no—
244#95—24no—
245#95—24no—
246#95C23×C1112yes—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—84no—
250C2×C11C2×#45011yescharacteristic
251C2×C11C2×#45411yescharacteristic
252C2×C11#302811yescharacteristic
253#41—48no—
254#41—416no—
255#41—48no—
256#41—44no—
257#41—44no—
258C2×Q8—24no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—44no—
263C2×Q8—416no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8C11×SD1614yes—
267C2×D4—24no—
268C2×D4—24no—
269C2×D4—24no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4C2×D4×C1114yes—
273C22×C4—28no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4C2×D4×C1111yescharacteristic
278C22×C4C2×D4×C1112yes—
279C22×C4C2×D4×C1112yes—
280C22×C4C2×D4×C1111yescharacteristic
281C22×C4C24×C1111yescharacteristic
282C2×C8—24no—
283C4⋊C4—24no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—24no—
287C4⋊C4—24no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4C2×D4×C1114yes—
291C22⋊C4—28no—
292C22⋊C4—24no—
293C22⋊C4—24no—
294C42—22no—
295C42—22no—
296C42—42no—
297C42C2×D4×C1112yes—
298C42C2×D4×C1112yes—
299C11#1840911yescharacteristic, direct product factor, Sylow
300C23—24no—
301C23C22×D4×C1111yescharacteristic
302Q8—28no—
303Q8—48no—
304Q8—44no—
305Q8—82no—
306Q8—82no—
307D4—44no—
308D4—48no—
309D4—44no—
310D4—44no—
311D4—44no—
312D4—44no—
313D4—84no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—41no—
320C2×C4—416no—
321C2×C4—48no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4C11×#12011yescharacteristic
329C2×C4C11×#12012yes—
330C2×C4C11×#12011yescharacteristic
331C2×C4C2×C11×SD1614yes—
332C2×C4C2×C11×SD1612yes—
333C2×C4C11×AGL(1,ℤ/8)12yes—
334C2×C4C22×D4×C1112yes—
335C8—44no—
336C22—21no—
337C22—21no—
338C22—44no—
339C22—44no—
340C22—44no—
341C22C2×C11×#12011yescharacteristic
342C22C22×C11×SD1611yescharacteristic
343C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
344C4—24no—
345C4—21no—
346C4—22no—
347C4—44no—
348C4—42no—
349C4—82no—
350C4—82no—
351C4C11×#45014yes—
352C4C11×#45412yes—
353C2—21no—
354C2—21no—
355C2—84no—
356C2C2×C11×#45011yescharacteristic
357C2C2×C11×#45411yescharacteristic
358C2C11×#302811yescharacteristic
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×#3227C2semidirect
3. C11×#2568C2semidirect
4. C11×#1616C2semidirect
5. C11×#1502C2semidirect
6. C11×#1461C2semidirect
74. #18409C11direct (N × H)
122. #3227C2×C11semidirect
123. #2568C2×C11semidirect
124. #1616C2×C11semidirect
125. #1502C2×C11semidirect
126. #1461C2×C11semidirect
299. C11#18409direct (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×#32272
C11×#25682
C11×#16162
C11×#15022
C11×#14612
#1840911