Finite Group Databasebeta

← C11×#9411 #14586604

Subgroups — C11×#9411 #14586604

Order 2816.

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

normal subgroups only

This group has 606 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×#2561C211yesmaximal, characteristic
2C11×#2312C211yesmaximal, characteristic
3C11×#1508C212yesmaximal, complemented
4C11×#1462C211yesmaximal, characteristic
5C11×#1297C212yesmaximal, complemented
6C2×C11×C22⋊Q8C2211yescharacteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C11×#407C2212yes—
9C11×#397C412yescomplemented
10C11×#393C412yescomplemented
11C11×#388—22no—
12C11×#388—24no—
13C11×#381—21no—
14C11×#380—21no—
15C11×#379—21no—
16C11×#379—21no—
17C4×C11×C22⋊C4C2211yescharacteristic
18C4×C11×C22⋊C4C2212yes—
19C11×#328—24no—
20C11×#323—22no—
21C25×C11D411yescharacteristic
22C22×Q8×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C2×C11×M16—22no—
26C11×C22⋊Q8—22no—
27C11×C22⋊Q8—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4C2×C412yes—
41C2×C11×C22⋊C4D412yes—
42C2×C42×C11—21no—
43C2×C42×C11—22no—
44C11×C22⋊C8—22no—
45C11×C22⋊C8—22no—
46C11×#95—22no—
47C11×#95—22no—
48C11×#95—22no—
49C11×#95C2×C412yes—
50C11×#95D414yes—
51#9411C1111yesmaximal, characteristic, direct product factor, Sylow
52C24×C11—21no—
53C24×C11—21no—
54C24×C11—42no—
55C24×C11—42no—
56C24×C11—81no—
57C24×C11C22⋊C412yes—
58C24×C11C2×D411yescharacteristic
59C2×Q8×C11—22no—
60C2×Q8×C11—81no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—24no—
67C22×C4×C11—42no—
68C22×C4×C11—81no—
69C22×C4×C11C22⋊C412yes—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4112yes—
74C11×M16—82no—
75C2×C8×C11—42no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—82no—
79C11×C22⋊C4—24no—
80C11×C22⋊C4—24no—
81C11×C22⋊C4—44no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—44no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—82no—
87C11×C22⋊C4—82no—
88C11×C22⋊C4—82no—
89C42×C11—82no—
90C42×C11—81no—
91#2561C2×C1111yescharacteristic
92#2312C2×C1111yescharacteristic
93#1508C2×C1112yescomplemented
94#1462C2×C1111yescharacteristic
95#1297C2×C1112yescomplemented
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—41no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11—42no—
108C23×C11—81no—
109C23×C11—81no—
110C23×C11—88no—
111C23×C11C2×C22⋊C411yescharacteristic
112C23×C11#12011yescharacteristic
113C23×C11#12311yescharacteristic
114Q8×C11—82no—
115C2×C4×C11—22no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—44no—
124C2×C4×C11—42no—
125C2×C4×C11—44no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—44no—
132C2×C4×C11—81no—
133C2×C4×C11C4×D412yes—
134C2×C4×C11#12112yes—
135C8×C11—82no—
136C2×C22⋊Q8C22×C1111yescharacteristic
137C22×C22⋊C4C22×C1111yescharacteristic
138#407C22×C1112yes—
139#397C4×C1112yescomplemented
140#393C4×C1112yescomplemented
141#388—22no—
142#388—24no—
143#381—21no—
144#380—21no—
145#379—21no—
146#379—21no—
147C4×C22⋊C4C22×C1111yescharacteristic
148C4×C22⋊C4C22×C1112yes—
149#328—24no—
150#323—22no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—44no—
159C22×C11—44no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11—82no—
164C22×C11—84no—
165C22×C11—84no—
166C22×C11#38611yescharacteristic
167C22×C11#42112yes—
168C22×C11#45512yes—
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—42no—
172C4×C11—84no—
173C4×C11—82no—
174C4×C11—81no—
175C4×C11—81no—
176C25D4×C1111yescharacteristic
177C22×Q8C2×C4×C1111yescharacteristic
178C23×C4D4×C1111yescharacteristic
179C23×C4C23×C1111yescharacteristic
180C2×M16—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4C2×C4×C1111yescharacteristic
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—21no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4C2×C4×C1112yes—
196C2×C22⋊C4D4×C1112yes—
197C2×C42—21no—
198C2×C42—22no—
199C22⋊C8—22no—
200C22⋊C8—22no—
201#95—22no—
202#95—22no—
203#95—22no—
204#95C2×C4×C1112yes—
205#95D4×C1114yes—
206C2×C11—22no—
207C2×C11—22no—
208C2×C11—41no—
209C2×C11—82no—
210C2×C11#188511yescharacteristic
211C2×C11#189711yescharacteristic
212C2×C11#191311yescharacteristic
213C24—21no—
214C24—21no—
215C24—42no—
216C24—42no—
217C24—81no—
218C24C11×C22⋊C412yes—
219C24C2×D4×C1111yescharacteristic
220C2×Q8—22no—
221C2×Q8—81no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—24no—
228C22×C4—42no—
229C22×C4—81no—
230C22×C4C11×C22⋊C412yes—
231C22×C4C22×C4×C1111yescharacteristic
232C22×C4C2×D4×C1112yes—
233C22×C4C2×D4×C1111yescharacteristic
234C22×C4C11×#4112yes—
235M16—82no—
236C2×C8—42no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C4⋊C4—82no—
240C22⋊C4—24no—
241C22⋊C4—24no—
242C22⋊C4—44no—
243C22⋊C4—42no—
244C22⋊C4—44no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—82no—
248C22⋊C4—82no—
249C22⋊C4—82no—
250C42—81no—
251C42—82no—
252C11#941111yescharacteristic, direct product factor, Sylow
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—41no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—81no—
266C23—81no—
267C23—88no—
268C23C2×C11×C22⋊C411yescharacteristic
269C23C11×#12011yescharacteristic
270C23C11×#12311yescharacteristic
271Q8—82no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—44no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—81no—
290C2×C4C4×D4×C1112yes—
291C2×C4C11×#12112yes—
292C8—82no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—44no—
301C22—44no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—82no—
306C22—84no—
307C22—84no—
308C22C11×#38611yescharacteristic
309C22C11×#42112yes—
310C22C11×#45512yes—
311C4—22no—
312C4—22no—
313C4—42no—
314C4—84no—
315C4—82no—
316C4—81no—
317C4—81no—
318C2—22no—
319C2—22no—
320C2—41no—
321C2—82no—
322C2C11×#188511yescharacteristic
323C2C11×#189711yescharacteristic
324C2C11×#191311yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC25×C11D4
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
3. C11×#1508C2semidirect
5. C11×#1297C2semidirect
9. C11×#397C4semidirect
10. C11×#393C4semidirect
51. #9411C11direct (N × H)
93. #1508C2×C11semidirect
95. #1297C2×C11semidirect
139. #397C4×C11semidirect
140. #393C4×C11semidirect
252. C11#9411direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25612
C11×#23122
C11×#15082
C11×#14622
C11×#12972
#941111