Finite Group Databasebeta

← C11×#11891 #14589084

Subgroups — C11×#11891 #14589084

Order 2816.

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

normal subgroups only

This group has 448 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×#466C211yesmaximal, characteristic
2C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
3C11×#1810C211yesmaximal, characteristic, complemented
4C11×#1349C214yesmaximal, complemented
5C22×C11×D8C411yescharacteristic
6C23×C8×C11C2211yescharacteristic
7C2×C11×#121—21no—
8C22×C11×C16—21no—
9C11×#466—21no—
10C11×#466—21no—
11C11×#466C412yes—
12C11×#466C2212yes—
13C2×C11×#108—21no—
14C2×C11×#107C411yescharacteristic
15C2×C11×#102—21no—
16C11×#407—21no—
17C11×C22⋊C16—21no—
18C11×C22⋊C16C2212yescomplemented
19C11×#341C2212yescomplemented
20C22×D4×C11—21no—
21C22×D4×C11—41no—
22C23×C4×C11D411yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—42no—
25C2×C11×D8C2×C412yes—
26C2×C11×M16—22no—
27C22×C8×C11—42no—
28C22×C8×C11C2×C411yescharacteristic
29C22×C8×C11C2×C411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C22×C8×C11D411yescharacteristic
33C22×C8×C11C2311yescharacteristic
34C11×#121—22no—
35C11×#121—22no—
36C11×#121—41no—
37C11×#121—41no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C22⋊C4—41no—
40C2×C11×C16—22no—
41C2×C11×C16—42no—
42C11×#108—42no—
43C11×#107—21no—
44C11×#107C2×C412yes—
45C11×#102—22no—
46C11×#102—22no—
47C11×C22⋊C8—41no—
48C11×C22⋊C8—41no—
49#11891C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11—41no—
51C24×C11SD1611yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—42no—
54C2×D4×C11—42no—
55C2×D4×C11—42no—
56C2×D4×C11—42no—
57C2×D4×C11—41no—
58C2×D4×C11—84no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11D811yescharacteristic
65C22×C4×C11D811yescharacteristic
66C22×C4×C11SD1611yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C11×D8—42no—
69C11×D8—42no—
70C11×M16—42no—
71C11×M16—42no—
72C2×C8×C11—22no—
73C2×C8×C11—22no—
74C2×C8×C11—22no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—42no—
79C2×C8×C11C22⋊C411yescharacteristic
80C2×C8×C11C22⋊C411yescharacteristic
81C2×C8×C11C22×C411yescharacteristic
82C2×C8×C11C2×D411yescharacteristic
83C11×C4⋊C4—22no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87C11×C16—42no—
88C2×#466C2×C1111yescharacteristic
89C2×C22⋊C16C2×C1111yescharacteristic, complemented
90#1810C2×C1111yescharacteristic, complemented
91#1349C2×C1114yescomplemented
92C23×C11—22no—
93C23×C11—22no—
94C23×C11—41no—
95C23×C11—42no—
96C23×C11—82no—
97C23×C11—82no—
98C23×C11—82no—
99C23×C11#10211yescharacteristic
100C23×C11#10211yescharacteristic
101C23×C11C2×SD1611yescharacteristic
102D4×C11—42no—
103D4×C11—42no—
104D4×C11—82no—
105D4×C11—84no—
106D4×C11—84no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—82no—
118C2×C4×C11#10211yescharacteristic
119C2×C4×C11#10211yescharacteristic
120C2×C4×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11C2×D811yescharacteristic
122C8×C11—21no—
123C8×C11—21no—
124C8×C11—21no—
125C8×C11—82no—
126C8×C11#9912yes—
127C22×D8C4×C1111yescharacteristic
128C23×C8C22×C1111yescharacteristic
129C2×#121—21no—
130C22×C16—21no—
131#466—21no—
132#466—21no—
133#466C4×C1112yes—
134#466C22×C1112yes—
135C2×#108—21no—
136C2×#107C4×C1111yescharacteristic
137C2×#102—21no—
138#407—21no—
139C22⋊C16—21no—
140C22⋊C16C22×C1112yescomplemented
141#341C22×C1112yescomplemented
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—44no—
150C22×C11—82no—
151C22×C11—82no—
152C22×C11—82no—
153C22×C11—164no—
154C22×C11#35912yes—
155C22×C11#36112yes—
156C22×C11C2×#10211yescharacteristic
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—82no—
161C4×C11C2×#9911yescharacteristic
162C4×C11#42111yescharacteristic
163C22×D4—21no—
164C22×D4—41no—
165C23×C4D4×C1111yescharacteristic
166C2×D8—21no—
167C2×D8—42no—
168C2×D8C2×C4×C1112yes—
169C2×M16—22no—
170C22×C8—42no—
171C22×C8C2×C4×C1111yescharacteristic
172C22×C8C2×C4×C1111yescharacteristic
173C22×C8D4×C1111yescharacteristic
174C22×C8D4×C1111yescharacteristic
175C22×C8D4×C1111yescharacteristic
176C22×C8C23×C1111yescharacteristic
177#121—22no—
178#121—22no—
179#121—41no—
180#121—41no—
181C2×C4⋊C4—21no—
182C2×C22⋊C4—41no—
183C2×C16—22no—
184C2×C16—42no—
185#108—42no—
186#107—21no—
187#107C2×C4×C1112yes—
188#102—22no—
189#102—22no—
190C22⋊C8—41no—
191C22⋊C8—41no—
192C2×C11—22no—
193C2×C11—22no—
194C2×C11—41no—
195C2×C11—162no—
196C2×C11#151911yescharacteristic
197C2×C11C2×#35911yescharacteristic
198C2×C11C2×#36111yescharacteristic
199C24—41no—
200C24C11×SD1611yescharacteristic
201C2×D4—22no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—41no—
207C2×D4—84no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4C11×C22⋊C411yescharacteristic
212C22×C4C11×C22⋊C411yescharacteristic
213C22×C4C11×D811yescharacteristic
214C22×C4C11×D811yescharacteristic
215C22×C4C11×SD1611yescharacteristic
216C22×C4C2×D4×C1111yescharacteristic
217D8—42no—
218D8—42no—
219M16—42no—
220M16—42no—
221C2×C8—22no—
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—42no—
228C2×C8C11×C22⋊C411yescharacteristic
229C2×C8C11×C22⋊C411yescharacteristic
230C2×C8C22×C4×C1111yescharacteristic
231C2×C8C2×D4×C1111yescharacteristic
232C4⋊C4—22no—
233C4⋊C4—41no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C16—42no—
237C11#1189111yescharacteristic, direct product factor, Sylow
238C23—22no—
239C23—22no—
240C23—41no—
241C23—42no—
242C23—82no—
243C23—82no—
244C23—82no—
245C23C11×#10211yescharacteristic
246C23C11×#10211yescharacteristic
247C23C2×C11×SD1611yescharacteristic
248D4—42no—
249D4—42no—
250D4—82no—
251D4—84no—
252D4—84no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—82no—
264C2×C4C11×#10211yescharacteristic
265C2×C4C11×#10211yescharacteristic
266C2×C4C2×C11×C22⋊C411yescharacteristic
267C2×C4C2×C11×D811yescharacteristic
268C8—21no—
269C8—21no—
270C8—21no—
271C8—82no—
272C8C11×#9912yes—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—44no—
281C22—82no—
282C22—82no—
283C22—82no—
284C22—164no—
285C22C11×#35912yes—
286C22C11×#36112yes—
287C22C2×C11×#10211yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—82no—
292C4C2×C11×#9911yescharacteristic
293C4C11×#42111yescharacteristic
294C2—22no—
295C2—22no—
296C2—41no—
297C2—162no—
298C2C11×#151911yescharacteristic
299C2C2×C11×#35911yescharacteristic
300C2C2×C11×#36111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#102
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#466C2
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
2. C2×C11×C22⋊C16C2semidirect
3. C11×#1810C2semidirect
4. C11×#1349C2semidirect
18. C11×C22⋊C16C22semidirect
19. C11×#341C22semidirect
49. #11891C11direct (N × H)
89. C2×C22⋊C16C2×C11semidirect
90. #1810C2×C11semidirect
91. #1349C2×C11semidirect
140. C22⋊C16C22×C11semidirect
141. #341C22×C11semidirect
237. C11#11891direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4662
C2×C11×C22⋊C162
C11×#18102
C11×#13492
#1189111