Finite Group Databasebeta

← C11×#11505 #14588698

Subgroups — C11×#11505 #14588698

Order 2816.

814 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 118 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×#390C211yesmaximal, characteristic
2C11×#1463C212yesmaximal, complemented
3C11×#1318C214yesmaximal, complemented
4C23×D4×C11C411yescharacteristic
5C22×C11×C4⋊C4C2211yescharacteristic
6C22×C11×C22⋊C4—22no—
7C22×C42×C11C411yescharacteristic
8C11×#407—22no—
9C11×#390—22no—
10C11×#390C412yes—
11C11×#390C2212yes—
12C11×#324—22no—
13C11×#324C2214yescomplemented
14C25×C11—21no—
15C22×D4×C11—24no—
16C22×D4×C11—21no—
17C22×D4×C11—41no—
18C22×D4×C11—41no—
19C22×D4×C11—42no—
20C22×D4×C11C2×C412yes—
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D412yes—
24C2×C11×M16—42no—
25C2×C11×C4⋊C4—41no—
26C2×C11×C4⋊C4—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D412yes—
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C11×C22⋊C4—24no—
31C2×C11×C22⋊C4—24no—
32C2×C11×C22⋊C4—48no—
33C2×C42×C11—21no—
34C2×C42×C11—42no—
35C2×C42×C11C2×C412yes—
36C11×C22⋊C8—24no—
37C11×C22⋊C8—42no—
38#11505C1111yesmaximal, characteristic, direct product factor, Sylow
39C24×C11—24no—
40C24×C11—22no—
41C24×C11—44no—
42C24×C11—42no—
43C24×C11—44no—
44C24×C11—41no—
45C24×C11—41no—
46C24×C11C22⋊C411yescharacteristic
47C2×D4×C11—24no—
48C2×D4×C11—22no—
49C2×D4×C11—48no—
50C2×D4×C11—48no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—42no—
54C2×D4×C11—42no—
55C2×D4×C11M1614yescomplemented
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—24no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—44no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C412yes—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D412yes—
71C11×M16—84no—
72C2×C8×C11—44no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—41no—
76C11×C22⋊C4—48no—
77C11×C22⋊C4—48no—
78C42×C11—42no—
79C42×C11—42no—
80C2×#390C2×C1111yescharacteristic
81#1463C2×C1112yescomplemented
82#1318C2×C1114yescomplemented
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—24no—
88C23×C11—44no—
89C23×C11—44no—
90C23×C11—44no—
91C23×C11—416no—
92C23×C11—44no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—88no—
96C23×C11—82no—
97C23×C11—82no—
98C23×C11—82no—
99C23×C11—82no—
100C23×C11#9911yescharacteristic
101C23×C11#9911yescharacteristic
102C23×C11C2×C22⋊C411yescharacteristic
103D4×C11—44no—
104D4×C11—48no—
105D4×C11—44no—
106C2×C4×C11—24no—
107C2×C4×C11—24no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—24no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—48no—
116C2×C4×C11—42no—
117C2×C4×C11—44no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—82no—
122C2×C4×C11#10012yes—
123C2×C4×C11C2×M1612yes—
124C8×C11—84no—
125C23×D4C4×C1111yescharacteristic
126C22×C4⋊C4C22×C1111yescharacteristic
127C22×C22⋊C4—22no—
128C22×C42C4×C1111yescharacteristic
129#407—22no—
130#390—22no—
131#390C4×C1112yes—
132#390C22×C1112yes—
133#324—22no—
134#324C22×C1114yescomplemented
135C22×C11—24no—
136C22×C11—24no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—48no—
144C22×C11—44no—
145C22×C11—84no—
146C22×C11—88no—
147C22×C11—88no—
148C22×C11—82no—
149C22×C11—82no—
150C22×C11#35312yes—
151C22×C11#35512yes—
152C22×C11#40711yescharacteristic
153C22×C11C2×#9911yescharacteristic
154C22×C11C2×#10011yescharacteristic
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—44no—
158C4×C11—42no—
159C4×C11—42no—
160C25—21no—
161C22×D4—24no—
162C22×D4—21no—
163C22×D4—41no—
164C22×D4—41no—
165C22×D4—42no—
166C22×D4C2×C4×C1112yes—
167C23×C4—21no—
168C23×C4C2×C4×C1111yescharacteristic
169C23×C4D4×C1112yes—
170C2×M16—42no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4C2×C4×C1111yescharacteristic
174C2×C4⋊C4D4×C1112yes—
175C2×C4⋊C4C23×C1111yescharacteristic
176C2×C22⋊C4—24no—
177C2×C22⋊C4—24no—
178C2×C22⋊C4—48no—
179C2×C42—21no—
180C2×C42—42no—
181C2×C42C2×C4×C1112yes—
182C22⋊C8—24no—
183C22⋊C8—42no—
184C2×C11—21no—
185C2×C11—21no—
186C2×C11—22no—
187C2×C11—22no—
188C2×C11—84no—
189C2×C11#146211yescharacteristic
190C2×C11C2×#35311yescharacteristic
191C2×C11C2×#35511yescharacteristic
192C24—24no—
193C24—22no—
194C24—44no—
195C24—42no—
196C24—44no—
197C24—41no—
198C24—41no—
199C24C11×C22⋊C411yescharacteristic
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—48no—
205C2×D4—48no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4C11×M1614yescomplemented
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—44no—
220C22×C4C11×C22⋊C411yescharacteristic
221C22×C4C11×C22⋊C412yes—
222C22×C4C22×C4×C1111yescharacteristic
223C22×C4C2×D4×C1112yes—
224M16—84no—
225C2×C8—44no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C22⋊C4—48no—
230C22⋊C4—48no—
231C42—42no—
232C42—42no—
233C11#1150511yescharacteristic, direct product factor, Sylow
234C23—22no—
235C23—22no—
236C23—21no—
237C23—21no—
238C23—24no—
239C23—44no—
240C23—44no—
241C23—44no—
242C23—416no—
243C23—44no—
244C23—42no—
245C23—42no—
246C23—88no—
247C23—82no—
248C23—82no—
249C23—82no—
250C23—82no—
251C23C11×#9911yescharacteristic
252C23C11×#9911yescharacteristic
253C23C2×C11×C22⋊C411yescharacteristic
254D4—44no—
255D4—48no—
256D4—44no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—48no—
267C2×C4—42no—
268C2×C4—44no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—82no—
273C2×C4C11×#10012yes—
274C2×C4C2×C11×M1612yes—
275C8—84no—
276C22—24no—
277C22—24no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—48no—
285C22—44no—
286C22—84no—
287C22—88no—
288C22—88no—
289C22—82no—
290C22—82no—
291C22C11×#35312yes—
292C22C11×#35512yes—
293C22C11×#40711yescharacteristic
294C22C2×C11×#9911yescharacteristic
295C22C2×C11×#10011yescharacteristic
296C4—22no—
297C4—22no—
298C4—44no—
299C4—42no—
300C4—42no—
301C2—21no—
302C2—21no—
303C2—22no—
304C2—22no—
305C2—84no—
306C2C11×#146211yescharacteristic
307C2C2×C11×#35311yescharacteristic
308C2C2×C11×#35511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC23×D4×C11C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1463C2semidirect
3. C11×#1318C2semidirect
13. C11×#324C22semidirect
38. #11505C11direct (N × H)
55. C2×D4×C11M16semidirect
81. #1463C2×C11semidirect
82. #1318C2×C11semidirect
134. #324C22×C11semidirect
208. C2×D4C11×M16semidirect
233. C11#11505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3902
C11×#14632
C11×#13182
#1150511