Finite Group Databasebeta

← C2×C11×#1662 #14596178

Subgroups — C2×C11×#1662 #14596178

Order 2816.

958 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 238 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×#562C211yesmaximal, characteristic
2C2×C11×#491C211yesmaximal, characteristic, complemented
3C2×C11×#489C212yesmaximal, complemented
4C11×#1662C218yesmaximal, direct product factor
5C2×C11×#330C211yesmaximal, characteristic, complemented
6C2×C11×#329C212yesmaximal, complemented
7C11×#562—22no—
8C11×#562—24no—
9C11×#562C2214yes—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#125C2211yescharacteristic
12C2×C11×#124C2212yes—
13C2×C11×#123—22no—
14C2×C11×C22⋊Q8—22no—
15C2×C11×#121—22no—
16C11×#491—22no—
17C11×#491C2214yescomplemented
18C11×#489—24no—
19C11×#489C2218yescomplemented
20C2×C11×#103—22no—
21C2×C11×#103—22no—
22C2×C11×#102—22no—
23C2×C11×#97C2211yescharacteristic
24C2×C11×#97C2212yes—
25C11×#330C2214yescomplemented
26C11×#329C2218yescomplemented
27C22×Q8×C11—21no—
28C22×Q8×C11D412yes—
29C22×D4×C11—22no—
30C22×D4×C11D412yes—
31C23×C4×C11—22no—
32C22×C8×C11—22no—
33C22×C8×C11—21no—
34C11×C4⋊Q8—22no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8C2312yes—
37C11×#125—22no—
38C11×#125D412yes—
39C11×#125C2312yes—
40C11×#124—22no—
41C11×#124—22no—
42C11×#124D414yes—
43C11×#124C2314yes—
44C11×#123—28no—
45C11×#123—28no—
46C11×C22⋊Q8—28no—
47C11×C22⋊Q8—28no—
48C11×#121—28no—
49C11×#121—28no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—22no—
57C2×C42×C11C2311yescharacteristic
58C11×#103—28no—
59C11×#103—28no—
60C11×#102—28no—
61C11×#97—22no—
62C11×#97—21no—
63C11×#97C2314yes—
64C11×#97C2312yes—
65C2×#1662C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—22no—
67C2×Q8×C11—22no—
68C2×Q8×C11—22no—
69C2×Q8×C11—44no—
70C2×Q8×C11—44no—
71C2×Q8×C11—41no—
72C2×Q8×C11C2×D414yes—
73C2×D4×C11—28no—
74C2×D4×C11—22no—
75C2×D4×C11—44no—
76C2×D4×C11—84no—
77C2×D4×C11C2×D414yes—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—28no—
81C22×C4×C11—41no—
82C22×C4×C11—84no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D412yes—
85C2×C8×C11—24no—
86C2×C8×C11—22no—
87C2×C8×C11—42no—
88C2×C8×C11—44no—
89C11×C4⋊C4—28no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4C2×D414yes—
96C11×C22⋊C4—28no—
97C11×C22⋊C4—24no—
98C11×C22⋊C4—24no—
99C11×C22⋊C4—24no—
100C11×C22⋊C4—24no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D412yes—
103C42×C11C2411yescharacteristic
104C2×#562C2×C1111yescharacteristic
105C2×#491C2×C1111yescharacteristic, complemented
106C2×#489C2×C1112yescomplemented
107#1662C2×C1118yesdirect product factor
108C2×#330C2×C1111yescharacteristic, complemented
109C2×#329C2×C1112yescomplemented
110C23×C11—24no—
111C23×C11—44no—
112C23×C11—44no—
113C23×C11—44no—
114C23×C11#12011yescharacteristic
115Q8×C11—44no—
116Q8×C11—44no—
117Q8×C11—82no—
118Q8×C11—82no—
119D4×C11—44no—
120D4×C11—82no—
121D4×C11—88no—
122C2×C4×C11—22no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—24no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11—42no—
129C2×C4×C11—88no—
130C2×C4×C11—82no—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12012yes—
133C2×C4×C11C22×D411yescharacteristic
134C2×C4×C11C22×D412yes—
135C8×C11—44no—
136C8×C11—42no—
137#562—22no—
138#562—24no—
139#562C22×C1114yes—
140C2×C4⋊Q8C22×C1111yescharacteristic
141C2×#125C22×C1111yescharacteristic
142C2×#124C22×C1112yes—
143C2×#123—22no—
144C2×C22⋊Q8—22no—
145C2×#121—22no—
146#491—22no—
147#491C22×C1114yescomplemented
148#489—24no—
149#489C22×C1118yescomplemented
150C2×#103—22no—
151C2×#103—22no—
152C2×#102—22no—
153C2×#97C22×C1112yes—
154C2×#97C22×C1111yescharacteristic
155#330C22×C1114yescomplemented
156#329C22×C1118yescomplemented
157C22×C11—44no—
158C22×C11—44no—
159C22×C11—44no—
160C22×C11—88no—
161C22×C11#45412yes—
162C22×C11#45514yes—
163C22×C11C2×#12011yescharacteristic
164C4×C11—22no—
165C4×C11—22no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—44no—
169C4×C11—44no—
170C4×C11—82no—
171C22×Q8—21no—
172C22×Q8D4×C1112yes—
173C22×D4—22no—
174C22×D4D4×C1112yes—
175C23×C4—22no—
176C22×C8—22no—
177C22×C8—21no—
178C4⋊Q8—22no—
179C4⋊Q8—21no—
180C4⋊Q8C23×C1112yes—
181#125—22no—
182#125D4×C1112yes—
183#125C23×C1112yes—
184#124—22no—
185#124—22no—
186#124D4×C1114yes—
187#124C23×C1114yes—
188#123—28no—
189#123—28no—
190C22⋊Q8—28no—
191C22⋊Q8—28no—
192#121—28no—
193#121—28no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4D4×C1112yes—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C42C23×C1111yescharacteristic
202#103—28no—
203#103—28no—
204#102—28no—
205#97—22no—
206#97—21no—
207#97C23×C1112yes—
208#97C23×C1114yes—
209C2×C11—84no—
210C2×C11#166214yesdirect product factor
211C2×C11C2×#45512yes—
212C2×C11C2×#45411yescharacteristic
213C24—22no—
214C2×Q8—22no—
215C2×Q8—22no—
216C2×Q8—44no—
217C2×Q8—44no—
218C2×Q8—41no—
219C2×Q8C2×D4×C1114yes—
220C2×D4—28no—
221C2×D4—22no—
222C2×D4—44no—
223C2×D4—84no—
224C2×D4C2×D4×C1114yes—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—28no—
228C22×C4—41no—
229C22×C4—84no—
230C22×C4C2×D4×C1111yescharacteristic
231C22×C4C2×D4×C1112yes—
232C2×C8—24no—
233C2×C8—22no—
234C2×C8—42no—
235C2×C8—44no—
236C4⋊C4—28no—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4—24no—
240C4⋊C4—24no—
241C4⋊C4—42no—
242C4⋊C4C2×D4×C1114yes—
243C22⋊C4—28no—
244C22⋊C4—24no—
245C22⋊C4—24no—
246C22⋊C4—24no—
247C22⋊C4—24no—
248C42C2×D4×C1111yescharacteristic
249C42C2×D4×C1112yes—
250C42C24×C1111yescharacteristic
251C11C2×#166211yescharacteristic, direct product factor, Sylow
252C23—24no—
253C23—44no—
254C23—44no—
255C23—44no—
256C23C11×#12011yescharacteristic
257Q8—44no—
258Q8—44no—
259Q8—82no—
260Q8—82no—
261D4—44no—
262D4—82no—
263D4—88no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—24no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—42no—
271C2×C4—88no—
272C2×C4—82no—
273C2×C4C11×#12011yescharacteristic
274C2×C4C11×#12012yes—
275C2×C4C22×D4×C1111yescharacteristic
276C2×C4C22×D4×C1112yes—
277C8—44no—
278C8—42no—
279C22—44no—
280C22—44no—
281C22—44no—
282C22—88no—
283C22C11×#45412yes—
284C22C11×#45514yes—
285C22C2×C11×#12011yescharacteristic
286C4—22no—
287C4—22no—
288C4—21no—
289C4—21no—
290C4—44no—
291C4—44no—
292C4—82no—
293C2—84no—
294C2C11×#166214yesdirect product factor
295C2C2×C11×#45512yes—
296C2C2×C11×#45411yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#562C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#491C2semidirect
3. C2×C11×#489C2semidirect
4. C11×#1662C2direct (N × H)
5. C2×C11×#330C2semidirect
6. C2×C11×#329C2semidirect
17. C11×#491C22semidirect
19. C11×#489C22semidirect
25. C11×#330C22semidirect
26. C11×#329C22semidirect
65. C2×#1662C11direct (N × H)
105. C2×#491C2×C11semidirect
106. C2×#489C2×C11semidirect
107. #1662C2×C11direct (N × H)
108. C2×#330C2×C11semidirect
109. C2×#329C2×C11semidirect
147. #491C22×C11semidirect
149. #489C22×C11semidirect
155. #330C22×C11semidirect
156. #329C22×C11semidirect
210. C2×C11#1662direct (N × H)
251. C11C2×#1662direct (N × H)
294. C2C11×#1662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5622
C2×C11×#4912
C2×C11×#4892
C11×#16622
C2×C11×#3302
C2×C11×#3292
C2×#166211