Finite Group Databasebeta

← C11×#11889 #14589082

Subgroups — C11×#11889 #14589082

Order 2816.

412 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 122 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×#467C211yesmaximal, characteristic
2C11×#2112C211yesmaximal, characteristic
3C11×#1807C211yesmaximal, characteristic
4C11×#1348C214yesmaximal, complemented
5C22×C11×Q16C411yescharacteristic, complemented
6C23×C8×C11C2211yescharacteristic
7C2×C11×C22⋊Q8—21no—
8C2×C11×M32—21no—
9C11×#467—21no—
10C11×#467—21no—
11C11×#467C412yescomplemented
12C11×#467C2212yes—
13C2×C11×#107C411yescharacteristic, complemented
14C2×C11×#106—21no—
15C2×C11×#103—21no—
16C11×#380—21no—
17C11×C22⋊C16—21no—
18C11×C22⋊C16C2212yes—
19C11×#340C2212yes—
20C22×Q8×C11—21no—
21C23×C4×C11D411yescharacteristic
22C2×C11×Q16—21no—
23C2×C11×Q16—42no—
24C2×C11×Q16C2×C412yes—
25C22×C8×C11—42no—
26C22×C8×C11C2×C411yescharacteristic
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11C2311yescharacteristic
32C11×C22⋊Q8—22no—
33C11×C22⋊Q8—22no—
34C11×C22⋊Q8—41no—
35C11×C22⋊Q8—41no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—41no—
39C2×C11×C22⋊C4—41no—
40C2×C11×C22⋊C4—41no—
41C11×M32—42no—
42C2×C11×C16—22no—
43C11×#107—21no—
44C11×#107C2×C412yes—
45C11×#106—42no—
46C11×#103—22no—
47C11×#103—22no—
48C11×#95—41no—
49#11889C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11D811yescharacteristic
51C2×Q8×C11—22no—
52C2×Q8×C11—42no—
53C2×Q8×C11—42no—
54C2×Q8×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11—42no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11D811yescharacteristic
63C22×C4×C11SD1611yescharacteristic
64C22×C4×C11SD1611yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C11×Q16—42no—
67C11×Q16—42no—
68C2×C8×C11—22no—
69C2×C8×C11—22no—
70C2×C8×C11—22no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11C22⋊C411yescharacteristic
75C2×C8×C11C22⋊C411yescharacteristic
76C2×C8×C11C22×C411yescharacteristic
77C2×C8×C11C2×D411yescharacteristic
78C11×C4⋊C4—22no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C22⋊C4—42no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—82no—
87C11×C16—42no—
88C2×#467C2×C1111yescharacteristic
89#2112C2×C1111yescharacteristic
90#1807C2×C1111yescharacteristic
91#1348C2×C1114yescomplemented
92C23×C11—22no—
93C23×C11—22no—
94C23×C11—41no—
95C23×C11#10211yescharacteristic
96C23×C11#10211yescharacteristic
97C23×C11C2×D811yescharacteristic
98Q8×C11—42no—
99Q8×C11—42no—
100Q8×C11—82no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—82no—
113C2×C4×C11—82no—
114C2×C4×C11—82no—
115C2×C4×C11—82no—
116C2×C4×C11—82no—
117C2×C4×C11#10211yescharacteristic
118C2×C4×C11#10211yescharacteristic
119C2×C4×C11C2×C22⋊C411yescharacteristic
120C2×C4×C11C2×SD1611yescharacteristic
121C8×C11—21no—
122C8×C11—21no—
123C8×C11—21no—
124C8×C11#9912yes—
125C22×Q16C4×C1111yescharacteristic, complemented
126C23×C8C22×C1111yescharacteristic
127C2×C22⋊Q8—21no—
128C2×M32—21no—
129#467—21no—
130#467—21no—
131#467C4×C1112yescomplemented
132#467C22×C1112yes—
133C2×#107C4×C1111yescharacteristic, complemented
134C2×#106—21no—
135C2×#103—21no—
136#380—21no—
137C22⋊C16—21no—
138C22⋊C16C22×C1112yes—
139#340C22×C1112yes—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—44no—
148C22×C11#36012yes—
149C22×C11C2×#10211yescharacteristic
150C22×C11#51012yes—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—82no—
155C4×C11—82no—
156C4×C11—162no—
157C4×C11C2×#9911yescharacteristic
158C4×C11#42111yescharacteristic
159C22×Q8—21no—
160C23×C4D4×C1111yescharacteristic
161C2×Q16—21no—
162C2×Q16—42no—
163C2×Q16C2×C4×C1112yes—
164C22×C8—42no—
165C22×C8C2×C4×C1111yescharacteristic
166C22×C8C2×C4×C1111yescharacteristic
167C22×C8D4×C1111yescharacteristic
168C22×C8D4×C1111yescharacteristic
169C22×C8D4×C1111yescharacteristic
170C22×C8C23×C1111yescharacteristic
171C22⋊Q8—22no—
172C22⋊Q8—22no—
173C22⋊Q8—41no—
174C22⋊Q8—41no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—41no—
178C2×C22⋊C4—41no—
179C2×C22⋊C4—41no—
180M32—42no—
181C2×C16—22no—
182#107—21no—
183#107C2×C4×C1112yes—
184#106—42no—
185#103—22no—
186#103—22no—
187#95—41no—
188C2×C11—22no—
189C2×C11—22no—
190C2×C11—41no—
191C2×C11#151911yescharacteristic
192C2×C11#214111yescharacteristic
193C2×C11C2×#36011yescharacteristic
194C24C11×D811yescharacteristic
195C2×Q8—22no—
196C2×Q8—42no—
197C2×Q8—42no—
198C2×Q8—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—42no—
204C22×C4C11×C22⋊C411yescharacteristic
205C22×C4C11×C22⋊C411yescharacteristic
206C22×C4C11×D811yescharacteristic
207C22×C4C11×SD1611yescharacteristic
208C22×C4C11×SD1611yescharacteristic
209C22×C4C2×D4×C1111yescharacteristic
210Q16—42no—
211Q16—42no—
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8C11×C22⋊C411yescharacteristic
219C2×C8C11×C22⋊C411yescharacteristic
220C2×C8C22×C4×C1111yescharacteristic
221C2×C8C2×D4×C1111yescharacteristic
222C4⋊C4—22no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C22⋊C4—82no—
231C16—42no—
232C11#1188911yescharacteristic, direct product factor, Sylow
233C23—22no—
234C23—22no—
235C23—41no—
236C23C11×#10211yescharacteristic
237C23C11×#10211yescharacteristic
238C23C2×C11×D811yescharacteristic
239Q8—42no—
240Q8—42no—
241Q8—82no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4C11×#10211yescharacteristic
259C2×C4C11×#10211yescharacteristic
260C2×C4C2×C11×C22⋊C411yescharacteristic
261C2×C4C2×C11×SD1611yescharacteristic
262C8—21no—
263C8—21no—
264C8—21no—
265C8C11×#9912yes—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—44no—
274C22C11×#36012yes—
275C22C2×C11×#10211yescharacteristic
276C22C11×#51012yes—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—82no—
281C4—82no—
282C4—162no—
283C4C2×C11×#9911yescharacteristic
284C4C11×#42111yescharacteristic
285C2—22no—
286C2—22no—
287C2—41no—
288C2C11×#151911yescharacteristic
289C2C11×#214111yescharacteristic
290C2C2×C11×#36011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#102
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC24×C11D8
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1348C2semidirect
5. C22×C11×Q16C4semidirect
11. C11×#467C4semidirect
13. C2×C11×#107C4semidirect
49. #11889C11direct (N × H)
91. #1348C2×C11semidirect
125. C22×Q16C4×C11semidirect
131. #467C4×C11semidirect
133. C2×#107C4×C11semidirect
232. C11#11889direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C11×#21122
C11×#18072
C11×#13482
#1188911