Finite Group Databasebeta

← C11×#18403 #14595596

Subgroups — C11×#18403 #14595596

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic, complemented
2C11×#3208C212yesmaximal
3C11×#2548C211yesmaximal, characteristic
4C11×#1599C218yesmaximal, complemented
5C11×#1503C212yesmaximal, complemented
6C11×#1461C211yesmaximal, characteristic, complemented
7Q82×C11—22no—
8C11×#557—22no—
9C11×#557—24no—
10C11×#544—21no—
11C11×#544C2214yes—
12C11×#533—22no—
13C11×#533C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124—21no—
16C11×#519—21no—
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#492—22no—
19C11×#486—22no—
20C11×#460—24no—
21C11×#450C2218yes—
22C11×#431C2212yes—
23C11×#394C2214yes—
24C11×#390—21no—
25C11×#390—22no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#328C2218yes—
28C11×#324C2214yes—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11C2312yes—
33C2×C11×SD16—28no—
34C11×C4⋊Q8—22no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—24no—
37C11×C4⋊Q8—28no—
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D412yes—
40C11×#127—22no—
41C11×#127—22no—
42C11×#125—24no—
43C11×#125—24no—
44C11×#125—28no—
45C11×#125—22no—
46C11×#124—44no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8C2314yes—
50C4×Q8×C11—24no—
51C4×Q8×C11—24no—
52C4×Q8×C11—24no—
53C4×Q8×C11—24no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11D414yes—
58C11×#117—24no—
59C11×#117—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C42×C11—21no—
66C2×C42×C11D412yes—
67C2×C42×C11C2311yescharacteristic
68C11×C4⋊C8—22no—
69C11×#102—28no—
70C11×C22⋊C8C2314yes—
71C4×C8×C11—22no—
72C11×#95C2312yes—
73#18403C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11—22no—
75C2×Q8×C11—24no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—22no—
79C2×Q8×C11SD1614yescomplemented
80C2×Q8×C11C2×D414yes—
81C2×D4×C11—24no—
82C2×D4×C11—44no—
83C2×D4×C11—41no—
84C2×D4×C11—42no—
85C2×D4×C11—41no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11—82no—
89C22×C4×C11—22no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2411yescharacteristic
95C11×SD16—88no—
96C2×C8×C11—24no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—28no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4C2×D414yes—
110C11×C22⋊C4—24no—
111C11×C22⋊C4—48no—
112C11×C22⋊C4—84no—
113C42×C11—28no—
114C42×C11—22no—
115C42×C11—22no—
116C42×C11—24no—
117C42×C11—42no—
118C42×C11C2×D412yes—
119C42×C11C2×D412yes—
120#3502C2×C1111yescharacteristic, complemented
121#3208C2×C1112yes—
122#2548C2×C1111yescharacteristic
123#1599C2×C1118yescomplemented
124#1503C2×C1112yescomplemented
125#1461C2×C1111yescharacteristic, complemented
126C23×C11—44no—
127C23×C11—44no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11C22×D411yescharacteristic
132Q8×C11—28no—
133Q8×C11—44no—
134Q8×C11—44no—
135Q8×C11—84no—
136D4×C11—48no—
137D4×C11—82no—
138D4×C11—84no—
139D4×C11—82no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12012yes—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11C2×SD1614yes—
155C2×C4×C11C2×SD1612yes—
156C2×C4×C11#13712yes—
157C2×C4×C11C22×D412yes—
158C8×C11—44no—
159Q82—22no—
160#557—22no—
161#557—24no—
162#544—21no—
163#544C22×C1114yes—
164#533—22no—
165#533C22×C1112yes—
166C2×#127C22×C1111yescharacteristic
167C2×#124—21no—
168#519—21no—
169C2×C4×Q8C22×C1111yescharacteristic
170#492—22no—
171#486—22no—
172#460—24no—
173#450C22×C1118yes—
174#431C22×C1112yes—
175#394C22×C1114yes—
176#390—21no—
177#390—22no—
178C4×C4⋊C4C22×C1111yescharacteristic
179#328C22×C1118yes—
180#324C22×C1114yes—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—84no—
184C22×C11—84no—
185C22×C11—82no—
186C22×C11—82no—
187C22×C11—82no—
188C22×C11C2×#12011yescharacteristic
189C22×C11C22×SD1611yescharacteristic
190C22×C11C2×#13711yescharacteristic
191C4×C11—24no—
192C4×C11—21no—
193C4×C11—22no—
194C4×C11—44no—
195C4×C11—42no—
196C4×C11—44no—
197C4×C11—82no—
198C4×C11#44814yes—
199C4×C11#45412yes—
200C22×Q8D4×C1111yescharacteristic
201C22×D4—21no—
202C22×D4—21no—
203C22×D4C23×C1112yes—
204C2×SD16—28no—
205C4⋊Q8—22no—
206C4⋊Q8—22no—
207C4⋊Q8—24no—
208C4⋊Q8—28no—
209C4⋊Q8D4×C1112yes—
210C4⋊Q8D4×C1112yes—
211#127—22no—
212#127—22no—
213#125—24no—
214#125—24no—
215#125—28no—
216#125—22no—
217#124—44no—
218C22⋊Q8—22no—
219C22⋊Q8—24no—
220C22⋊Q8C23×C1114yes—
221C4×Q8—24no—
222C4×Q8—24no—
223C4×Q8—24no—
224C4×Q8—24no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×Q8D4×C1114yes—
229#117—24no—
230#117—22no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4D4×C1111yescharacteristic
233C2×C4⋊C4C23×C1112yes—
234C2×C22⋊C4—24no—
235C2×C22⋊C4—24no—
236C2×C42—21no—
237C2×C42D4×C1112yes—
238C2×C42C23×C1111yescharacteristic
239C4⋊C8—22no—
240#102—28no—
241C22⋊C8C23×C1114yes—
242C4×C8—22no—
243#95C23×C1112yes—
244C2×C11—21no—
245C2×C11—21no—
246C2×C11—162no—
247C2×C11C2×#44811yescharacteristic
248C2×C11C2×#45411yescharacteristic
249C2×C11#302711yescharacteristic
250C24—22no—
251C2×Q8—24no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8C11×SD1614yescomplemented
256C2×Q8C2×D4×C1114yes—
257C2×D4—24no—
258C2×D4—44no—
259C2×D4—41no—
260C2×D4—42no—
261C2×D4—41no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—82no—
265C22×C4—22no—
266C22×C4C2×D4×C1111yescharacteristic
267C22×C4C2×D4×C1112yes—
268C22×C4C2×D4×C1112yes—
269C22×C4C2×D4×C1111yescharacteristic
270C22×C4C24×C1111yescharacteristic
271SD16—88no—
272C2×C8—24no—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—28no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—42no—
285C4⋊C4C2×D4×C1114yes—
286C22⋊C4—24no—
287C22⋊C4—48no—
288C22⋊C4—84no—
289C42—28no—
290C42—22no—
291C42—22no—
292C42—24no—
293C42—42no—
294C42C2×D4×C1112yes—
295C42C2×D4×C1112yes—
296C11#1840311yescharacteristic, direct product factor, Sylow
297C23—44no—
298C23—44no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23C22×D4×C1111yescharacteristic
303Q8—28no—
304Q8—44no—
305Q8—44no—
306Q8—84no—
307D4—48no—
308D4—82no—
309D4—84no—
310D4—82no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4C11×#12011yescharacteristic
323C2×C4C11×#12012yes—
324C2×C4C11×#12011yescharacteristic
325C2×C4C2×C11×SD1614yes—
326C2×C4C2×C11×SD1612yes—
327C2×C4C11×#13712yes—
328C2×C4C22×D4×C1112yes—
329C8—44no—
330C22—21no—
331C22—21no—
332C22—84no—
333C22—84no—
334C22—82no—
335C22—82no—
336C22—82no—
337C22C2×C11×#12011yescharacteristic
338C22C22×C11×SD1611yescharacteristic
339C22C2×C11×#13711yescharacteristic
340C4—24no—
341C4—21no—
342C4—22no—
343C4—44no—
344C4—42no—
345C4—44no—
346C4—82no—
347C4C11×#44814yes—
348C4C11×#45412yes—
349C2—21no—
350C2—21no—
351C2—162no—
352C2C2×C11×#44811yescharacteristic
353C2C2×C11×#45411yescharacteristic
354C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
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
1. C11×#3502C2semidirect
4. C11×#1599C2semidirect
5. C11×#1503C2semidirect
6. C11×#1461C2semidirect
73. #18403C11direct (N × H)
79. C2×Q8×C11SD16semidirect
120. #3502C2×C11semidirect
123. #1599C2×C11semidirect
124. #1503C2×C11semidirect
125. #1461C2×C11semidirect
255. C2×Q8C11×SD16semidirect
296. C11#18403direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35022
C11×#32082
C11×#25482
C11×#15992
C11×#15032
C11×#14612
#1840311