Finite Group Databasebeta

← C11×#18402 #14595595

Subgroups — C11×#18402 #14595595

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic
2C11×#3206C212yesmaximal, complemented
3C11×#2567C211yesmaximal, characteristic, complemented
4C11×#1604C218yesmaximal, 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×#492—22no—
18C11×#487—22no—
19C11×#461—24no—
20C11×#448C2218yes—
21C11×#431C2212yes—
22C11×#395C2214yes—
23C11×#391—21no—
24C11×#389—22no—
25C11×#384—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×C11D411yescharacteristic
36C22×Q8×C11C2312yes—
37C2×C11×SD16—28no—
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8—22no—
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×D4×C11—24no—
56C4×D4×C11—24no—
57C4×D4×C11—22no—
58C4×D4×C11D414yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C42×C11—21no—
66C2×C42×C11D412yes—
67C2×C42×C11C2311yescharacteristic
68C11×C4⋊C8—22no—
69C11×#103—28no—
70C11×C22⋊C8C2314yes—
71C4×C8×C11—22no—
72C11×#95—24no—
73C11×#95C2312yes—
74#18402C1111yesmaximal, 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—24no—
85C2×Q8×C11—416no—
86C2×Q8×C11—82no—
87C2×Q8×C11SD1614yescomplemented
88C2×D4×C11—24no—
89C2×D4×C11—24no—
90C2×D4×C11—24no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11C2×D414yes—
94C22×C4×C11—28no—
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C11×SD16—88no—
104C2×C8×C11—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—84no—
114C11×C4⋊C4C2×D414yes—
115C11×C22⋊C4—28no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—24no—
118C42×C11—22no—
119C42×C11—22no—
120C42×C11—42no—
121C42×C11C2×D412yes—
122C42×C11C2×D412yes—
123#3497C2×C1111yescharacteristic
124#3206C2×C1112yescomplemented
125#2567C2×C1111yescharacteristic, complemented
126#1604C2×C1118yescomplemented
127#1502C2×C1112yescomplemented
128#1461C2×C1111yescharacteristic, complemented
129C23×C11—24no—
130C23×C11C22×D411yescharacteristic
131Q8×C11—28no—
132Q8×C11—48no—
133Q8×C11—48no—
134Q8×C11—44no—
135D4×C11—44no—
136D4×C11—48no—
137D4×C11—44no—
138D4×C11—44no—
139D4×C11—44no—
140D4×C11—44no—
141D4×C11—84no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—41no—
149C2×C4×C11—416no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—48no—
153C2×C4×C11—42no—
154C2×C4×C11—44no—
155C2×C4×C11—42no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12012yes—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11C2×SD1614yes—
160C2×C4×C11C2×SD1612yes—
161C2×C4×C11AGL(1,ℤ/8)12yes—
162C2×C4×C11C22×D412yes—
163C8×C11—44no—
164C2×2−1+4—21no—
165#550—22no—
166D4×Q8—22no—
167#548—24no—
168#537—21no—
169#537C22×C1114yes—
170#532—22no—
171#532C22×C1112yes—
172C2×C4⋊Q8C22×C1111yescharacteristic
173C2×C4×Q8C22×C1111yescharacteristic
174#492—22no—
175#487—22no—
176#461—24no—
177#448C22×C1118yes—
178#431C22×C1112yes—
179#395C22×C1114yes—
180#391—21no—
181#389—22no—
182#384—21no—
183C4×C4⋊C4C22×C1111yescharacteristic
184#327C22×C1118yes—
185#324C22×C1114yes—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—44no—
189C22×C11—44no—
190C22×C11—44no—
191C22×C11C2×#12011yescharacteristic
192C22×C11C22×SD1611yescharacteristic
193C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
194C4×C11—24no—
195C4×C11—21no—
196C4×C11—22no—
197C4×C11—44no—
198C4×C11—44no—
199C4×C11—42no—
200C4×C11—82no—
201C4×C11#45014yes—
202C4×C11#45612yes—
2032−1+4—44no—
2042−1+4—44no—
205C2×#41—24no—
206C2×#41—24no—
207C2×#41—22no—
208C22×Q8—24no—
209C22×Q8D4×C1111yescharacteristic
210C22×Q8C23×C1112yes—
211C2×SD16—28no—
212C4⋊Q8—22no—
213C4⋊Q8—22no—
214C4⋊Q8—22no—
215C4⋊Q8D4×C1112yes—
216#127—22no—
217#127D4×C1112yes—
218#124—24no—
219#124—22no—
220C22⋊Q8—24no—
221C22⋊Q8—28no—
222#121—24no—
223#121—28no—
224#121—22no—
225#121—24no—
226#121C23×C1114yes—
227C4×Q8—22no—
228C4×Q8—22no—
229C4×D4—24no—
230C4×D4—24no—
231C4×D4—22no—
232C4×D4D4×C1114yes—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4D4×C1111yescharacteristic
238C2×C4⋊C4C23×C1112yes—
239C2×C42—21no—
240C2×C42D4×C1112yes—
241C2×C42C23×C1111yescharacteristic
242C4⋊C8—22no—
243#103—28no—
244C22⋊C8C23×C1114yes—
245C4×C8—22no—
246#95—24no—
247#95C23×C1112yes—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—84no—
251C2×C11C2×#45011yescharacteristic
252C2×C11C2×#45611yescharacteristic
253C2×C11#302711yescharacteristic
254#41—48no—
255#41—416no—
256#41—48no—
257#41—44no—
258#41—44no—
259C2×Q8—24no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—24no—
264C2×Q8—416no—
265C2×Q8—82no—
266C2×Q8C11×SD1614yescomplemented
267C2×D4—24no—
268C2×D4—24no—
269C2×D4—24no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4C2×D4×C1114yes—
273C22×C4—28no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—22no—
277C22×C4C2×D4×C1111yescharacteristic
278C22×C4C2×D4×C1112yes—
279C22×C4C2×D4×C1112yes—
280C22×C4C2×D4×C1111yescharacteristic
281C22×C4C24×C1111yescharacteristic
282SD16—88no—
283C2×C8—24no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—24no—
289C4⋊C4—41no—
290C4⋊C4—42no—
291C4⋊C4—41no—
292C4⋊C4—84no—
293C4⋊C4C2×D4×C1114yes—
294C22⋊C4—28no—
295C22⋊C4—24no—
296C22⋊C4—24no—
297C42—22no—
298C42—22no—
299C42—42no—
300C42C2×D4×C1112yes—
301C42C2×D4×C1112yes—
302C11#1840211yescharacteristic, direct product factor, Sylow
303C23—24no—
304C23C22×D4×C1111yescharacteristic
305Q8—28no—
306Q8—48no—
307Q8—48no—
308Q8—44no—
309D4—44no—
310D4—48no—
311D4—44no—
312D4—44no—
313D4—44no—
314D4—44no—
315D4—84no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—41no—
323C2×C4—416no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—48no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4C11×#12011yescharacteristic
331C2×C4C11×#12012yes—
332C2×C4C11×#12011yescharacteristic
333C2×C4C2×C11×SD1614yes—
334C2×C4C2×C11×SD1612yes—
335C2×C4C11×AGL(1,ℤ/8)12yes—
336C2×C4C22×D4×C1112yes—
337C8—44no—
338C22—21no—
339C22—21no—
340C22—44no—
341C22—44no—
342C22—44no—
343C22C2×C11×#12011yescharacteristic
344C22C22×C11×SD1611yescharacteristic
345C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
346C4—24no—
347C4—21no—
348C4—22no—
349C4—44no—
350C4—44no—
351C4—42no—
352C4—82no—
353C4C11×#45014yes—
354C4C11×#45612yes—
355C2—21no—
356C2—21no—
357C2—84no—
358C2C2×C11×#45011yescharacteristic
359C2C2×C11×#45611yescharacteristic
360C2C11×#302711yescharacteristic
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×#3206C2semidirect
3. C11×#2567C2semidirect
4. C11×#1604C2semidirect
5. C11×#1502C2semidirect
6. C11×#1461C2semidirect
74. #18402C11direct (N × H)
87. C2×Q8×C11SD16semidirect
124. #3206C2×C11semidirect
125. #2567C2×C11semidirect
126. #1604C2×C11semidirect
127. #1502C2×C11semidirect
128. #1461C2×C11semidirect
266. C2×Q8C11×SD16semidirect
302. C11#18402direct (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×#32062
C11×#25672
C11×#16042
C11×#15022
C11×#14612
#1840211