Finite Group Databasebeta

← C11×#9412 #14586605

Subgroups — C11×#9412 #14586605

Order 2816.

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

normal subgroups only

This group has 526 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
1C11×#2583C211yesmaximal, characteristic
2C11×#2313C211yesmaximal, characteristic
3C11×#1508C212yesmaximal
4C11×#1463C211yesmaximal, characteristic
5C11×#1297C212yesmaximal
6C2×C11×C22⋊Q8C2211yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C11×#407C2212yes—
9C11×#398C412yescomplemented
10C11×#395C412yescomplemented
11C11×#389—22no—
12C11×#387—24no—
13C11×#385—21no—
14C11×#385—21no—
15C11×#381—21no—
16C11×#380—21no—
17C4×C11×C22⋊C4C2211yescharacteristic
18C4×C11×C22⋊C4C2212yes—
19C11×#328—24no—
20C11×#324—22no—
21C22×Q8×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C2×C11×M16—22no—
26C11×C22⋊Q8—22no—
27C11×C22⋊Q8—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C412yes—
36C2×C11×C4⋊C4D412yes—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—22no—
41C2×C42×C11—21no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—22no—
44C11×#95—22no—
45C11×#95—24no—
46C11×#95—22no—
47C11×#95—22no—
48C11×#95C2×C412yes—
49C11×#95D414yes—
50#9412C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11C2×D411yescharacteristic
52C2×Q8×C11—22no—
53C2×Q8×C11—81no—
54C22×C4×C11—22no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—24no—
62C22×C4×C11—42no—
63C22×C4×C11—81no—
64C22×C4×C11—81no—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22⋊C412yes—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4112yes—
71C11×M16—82no—
72C2×C8×C11—42no—
73C11×C4⋊C4—24no—
74C11×C4⋊C4—24no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—44no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—82no—
79C11×C4⋊C4—82no—
80C11×C22⋊C4—24no—
81C11×C22⋊C4—44no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11—81no—
85C42×C11—82no—
86#2583C2×C1111yescharacteristic
87#2313C2×C1111yescharacteristic
88#1508C2×C1112yes—
89#1463C2×C1111yescharacteristic
90#1297C2×C1112yes—
91C23×C11—22no—
92C23×C11—22no—
93C23×C11—41no—
94C23×C11C2×C22⋊C411yescharacteristic
95C23×C11#12011yescharacteristic
96C23×C11#12311yescharacteristic
97Q8×C11—82no—
98C2×C4×C11—24no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—44no—
114C2×C4×C11—44no—
115C2×C4×C11—42no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—44no—
120C2×C4×C11—81no—
121C2×C4×C11C4×D412yes—
122C2×C4×C11#12112yes—
123C8×C11—82no—
124C2×C22⋊Q8C22×C1111yescharacteristic
125C22×C4⋊C4C22×C1111yescharacteristic
126#407C22×C1112yes—
127#398C4×C1112yescomplemented
128#395C4×C1112yescomplemented
129#389—22no—
130#387—24no—
131#385—21no—
132#385—21no—
133#381—21no—
134#380—21no—
135C4×C22⋊C4C22×C1111yescharacteristic
136C4×C22⋊C4C22×C1112yes—
137#328—24no—
138#324—22no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—44no—
147C22×C11#38611yescharacteristic
148C22×C11#42112yes—
149C22×C11#45612yes—
150C4×C11—22no—
151C4×C11—22no—
152C4×C11—44no—
153C4×C11—42no—
154C4×C11—42no—
155C4×C11—84no—
156C4×C11—81no—
157C4×C11—81no—
158C22×Q8C2×C4×C1111yescharacteristic
159C23×C4D4×C1111yescharacteristic
160C23×C4D4×C1111yescharacteristic
161C23×C4C23×C1111yescharacteristic
162C2×M16—22no—
163C22⋊Q8—22no—
164C22⋊Q8—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4C2×C4×C1111yescharacteristic
172C2×C4⋊C4C2×C4×C1112yes—
173C2×C4⋊C4D4×C1112yes—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—21no—
176C2×C22⋊C4—22no—
177C2×C42—22no—
178C2×C42—21no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181#95—22no—
182#95—24no—
183#95—22no—
184#95—22no—
185#95C2×C4×C1112yes—
186#95D4×C1114yes—
187C2×C11—22no—
188C2×C11—22no—
189C2×C11—41no—
190C2×C11#188611yescharacteristic
191C2×C11#189711yescharacteristic
192C2×C11#191311yescharacteristic
193C24C2×D4×C1111yescharacteristic
194C2×Q8—22no—
195C2×Q8—81no—
196C22×C4—22no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—24no—
204C22×C4—42no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4C11×C22⋊C412yes—
208C22×C4C11×C22⋊C412yes—
209C22×C4C22×C4×C1111yescharacteristic
210C22×C4C2×D4×C1112yes—
211C22×C4C2×D4×C1111yescharacteristic
212C22×C4C11×#4112yes—
213M16—82no—
214C2×C8—42no—
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—22no—
218C4⋊C4—44no—
219C4⋊C4—42no—
220C4⋊C4—82no—
221C4⋊C4—82no—
222C22⋊C4—24no—
223C22⋊C4—44no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C42—81no—
227C42—82no—
228C11#941211yescharacteristic, direct product factor, Sylow
229C23—22no—
230C23—22no—
231C23—41no—
232C23C2×C11×C22⋊C411yescharacteristic
233C23C11×#12011yescharacteristic
234C23C11×#12311yescharacteristic
235Q8—82no—
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—44no—
252C2×C4—44no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—44no—
258C2×C4—81no—
259C2×C4C4×D4×C1112yes—
260C2×C4C11×#12112yes—
261C8—82no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—44no—
270C22C11×#38611yescharacteristic
271C22C11×#42112yes—
272C22C11×#45612yes—
273C4—22no—
274C4—22no—
275C4—44no—
276C4—42no—
277C4—42no—
278C4—84no—
279C4—81no—
280C4—81no—
281C2—22no—
282C2—22no—
283C2—41no—
284C2C11×#188611yescharacteristic
285C2C11×#189711yescharacteristic
286C2C11×#191311yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
9. C11×#398C4semidirect
10. C11×#395C4semidirect
50. #9412C11direct (N × H)
127. #398C4×C11semidirect
128. #395C4×C11semidirect
228. C11#9412direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25832
C11×#23132
C11×#15082
C11×#14632
C11×#12972
#941211