Finite Group Databasebeta

← C11×#18999 #14596192

Subgroups — C11×#18999 #14596192

Order 2816.

850 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#563C211yesmaximal, characteristic
2C11×#3236C212yesmaximal, complemented
3C11×#3140C211yesmaximal, characteristic
4C11×#1664C218yesmaximal, complemented
5C11×#1533C211yesmaximal, characteristic
6C11×#1528C212yesmaximal, complemented
7C11×#563—24no—
8C11×#563—22no—
9C11×#563C2214yes—
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8—21no—
12C2×C11×#126—22no—
13C2×C11×#125C2212yes—
14C2×C11×#124C2211yescharacteristic
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8—22no—
17C11×#501C2214yescomplemented
18C11×#491C2214yescomplemented
19C11×#489C2214yes—
20C11×#488—22no—
21C11×#484—22no—
22C11×#483—22no—
23C11×#479—24no—
24C11×#432C2212yes—
25C11×#419—21no—
26C11×#418—21no—
27C4×C11×M16C2211yescharacteristic
28C11×#330C2218yescomplemented
29C11×#329C2214yes—
30C22×Q8×C11—21no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×C11×M16—21no—
35C11×C4⋊Q8—24no—
36C11×C4⋊Q8—24no—
37C11×C4⋊Q8C2312yes—
38C11×#126—28no—
39C11×#126—28no—
40C11×#125—22no—
41C11×#125—22no—
42C11×#125—21no—
43C11×#125D414yes—
44C11×#125C2314yes—
45C11×#124—22no—
46C11×#124D412yes—
47C11×#124C2312yes—
48C11×#123—24no—
49C11×#123—24no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8—28no—
52C11×C22⋊Q8—22no—
53C4×Q8×C11—22no—
54C11×#117—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4D412yes—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C11×#107—24no—
66C11×#106—24no—
67C11×C4⋊C8—22no—
68C11×#103—24no—
69C11×#103—24no—
70C11×#103—24no—
71C11×#102—24no—
72C11×C22⋊C8—22no—
73C11×#97C2312yes—
74C11×#97C2314yes—
75C4×C8×C11—21no—
76#18999C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11—21no—
78C2×Q8×C11—24no—
79C2×Q8×C11—21no—
80C2×Q8×C11—22no—
81C2×Q8×C11—42no—
82C2×Q8×C11—82no—
83C2×Q8×C11C2×D412yes—
84C2×D4×C11—21no—
85C2×D4×C11—42no—
86C2×D4×C11C2×D412yes—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—24no—
91C22×C4×C11—82no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D412yes—
94C11×M16—42no—
95C2×C8×C11—22no—
96C2×C8×C11—24no—
97C11×C4⋊C4—28no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4C2×D414yes—
108C11×C4⋊C4C2×D414yes—
109C11×C22⋊C4—28no—
110C11×C22⋊C4—24no—
111C11×C22⋊C4—24no—
112C11×C22⋊C4—24no—
113C11×C22⋊C4—41no—
114C42×C11—24no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D412yes—
118C42×C11C2411yescharacteristic
119C2×#563C2×C1111yescharacteristic
120#3236C2×C1112yescomplemented
121#3140C2×C1111yescharacteristic
122#1664C2×C1118yescomplemented
123#1533C2×C1111yescharacteristic
124#1528C2×C1112yescomplemented
125C23×C11—22no—
126C23×C11—44no—
127C23×C11—42no—
128C23×C11#12011yescharacteristic
129Q8×C11—42no—
130Q8×C11—44no—
131Q8×C11—81no—
132Q8×C11—84no—
133D4×C11—42no—
134D4×C11—81no—
135C2×C4×C11—22no—
136C2×C4×C11—24no—
137C2×C4×C11—22no—
138C2×C4×C11—24no—
139C2×C4×C11—42no—
140C2×C4×C11—44no—
141C2×C4×C11—44no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—84no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12012yes—
147C2×C4×C11C22×D412yes—
148C2×C4×C11C22×D411yescharacteristic
149C8×C11—44no—
150C8×C11—42no—
151#563—24no—
152#563—22no—
153#563C22×C1114yes—
154#533C22×C1111yescharacteristic
155C2×C4⋊Q8—21no—
156C2×#126—22no—
157C2×#125C22×C1112yes—
158C2×#124C22×C1111yescharacteristic
159C2×#123—21no—
160C2×C22⋊Q8—22no—
161#501C22×C1114yescomplemented
162#491C22×C1114yescomplemented
163#489C22×C1114yes—
164#488—22no—
165#484—22no—
166#483—22no—
167#479—24no—
168#432C22×C1112yes—
169#419—21no—
170#418—21no—
171C4×M16C22×C1111yescharacteristic
172#330C22×C1118yescomplemented
173#329C22×C1114yes—
174C22×C11—22no—
175C22×C11—42no—
176C22×C11—44no—
177C22×C11—84no—
178C22×C11#45512yes—
179C22×C11C2×#12011yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—22no—
183C4×C11—22no—
184C4×C11—44no—
185C4×C11—42no—
186C4×C11—44no—
187C4×C11—82no—
188C22×Q8—21no—
189C22×Q8D4×C1111yescharacteristic
190C22×D4D4×C1111yescharacteristic
191C23×C4—21no—
192C2×M16—21no—
193C4⋊Q8—24no—
194C4⋊Q8—24no—
195C4⋊Q8C23×C1112yes—
196#126—28no—
197#126—28no—
198#125—22no—
199#125—22no—
200#125—21no—
201#125D4×C1114yes—
202#125C23×C1114yes—
203#124—22no—
204#124D4×C1112yes—
205#124C23×C1112yes—
206#123—24no—
207#123—24no—
208C22⋊Q8—28no—
209C22⋊Q8—28no—
210C22⋊Q8—22no—
211C4×Q8—22no—
212#117—21no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4D4×C1112yes—
217C2×C4⋊C4D4×C1112yes—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—22no—
221C2×C42—21no—
222C2×C42C23×C1111yescharacteristic
223#107—24no—
224#106—24no—
225C4⋊C8—22no—
226#103—24no—
227#103—24no—
228#103—24no—
229#102—24no—
230C22⋊C8—22no—
231#97C23×C1114yes—
232#97C23×C1112yes—
233C4×C8—21no—
234C2×C11—22no—
235C2×C11—82no—
236C2×C11C2×#45511yescharacteristic
237C2×C11#302012yes—
238C24—21no—
239C2×Q8—24no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—42no—
243C2×Q8—82no—
244C2×Q8C2×D4×C1112yes—
245C2×D4—21no—
246C2×D4—42no—
247C2×D4C2×D4×C1112yes—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—82no—
253C22×C4C2×D4×C1111yescharacteristic
254C22×C4C2×D4×C1112yes—
255M16—42no—
256C2×C8—22no—
257C2×C8—24no—
258C4⋊C4—28no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4C2×D4×C1114yes—
269C4⋊C4C2×D4×C1114yes—
270C22⋊C4—28no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—24no—
274C22⋊C4—41no—
275C42—24no—
276C42—41no—
277C42C2×D4×C1111yescharacteristic
278C42C2×D4×C1112yes—
279C42C24×C1111yescharacteristic
280C11#1899911yescharacteristic, direct product factor, Sylow
281C23—22no—
282C23—44no—
283C23—42no—
284C23C11×#12011yescharacteristic
285Q8—42no—
286Q8—44no—
287Q8—81no—
288Q8—84no—
289D4—42no—
290D4—81no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—84no—
301C2×C4C11×#12011yescharacteristic
302C2×C4C11×#12012yes—
303C2×C4C22×D4×C1112yes—
304C2×C4C22×D4×C1111yescharacteristic
305C8—42no—
306C8—44no—
307C22—22no—
308C22—42no—
309C22—44no—
310C22—84no—
311C22C11×#45512yes—
312C22C2×C11×#12011yescharacteristic
313C4—21no—
314C4—21no—
315C4—22no—
316C4—22no—
317C4—44no—
318C4—42no—
319C4—44no—
320C4—82no—
321C2—22no—
322C2—82no—
323C2C2×C11×#45511yescharacteristic
324C2C11×#302012yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
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
2. C11×#3236C2semidirect
4. C11×#1664C2semidirect
6. C11×#1528C2semidirect
17. C11×#501C22semidirect
18. C11×#491C22semidirect
28. C11×#330C22semidirect
76. #18999C11direct (N × H)
120. #3236C2×C11semidirect
122. #1664C2×C11semidirect
124. #1528C2×C11semidirect
161. #501C22×C11semidirect
162. #491C22×C11semidirect
172. #330C22×C11semidirect
280. C11#18999direct (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×#32362
C11×#31402
C11×#16642
C11×#15332
C11×#15282
#1899911