Finite Group Databasebeta

← C11×#9416 #14586609

Subgroups — C11×#9416 #14586609

Order 2816.

380 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3185C211yesmaximal, characteristic
2C11×#2987C211yesmaximal, characteristic
3C11×#1537C211yesmaximal, characteristic
4C11×#1515C211yesmaximal, characteristic
5C11×#1515C211yesmaximal, characteristic
6C11×#1291C211yesmaximal, characteristic
7C11×#1288C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#533C2211yescharacteristic
10C11×#498C411yescharacteristic, complemented
11C11×#494C411yescharacteristic, complemented
12C11×#487C411yescharacteristic, complemented
13C11×#487C411yescharacteristic, complemented
14C11×#470—22no—
15C11×#446—22no—
16C11×#446—22no—
17C11×#441—22no—
18C11×#433—22no—
19C11×#432C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C11×#432C2211yescharacteristic
22C4×C11×M16C2211yescharacteristic
23C11×#383C2211yescharacteristic
24C11×#330—22no—
25C11×#328—22no—
26C11×#328—22no—
27C2×C11×Q16—22no—
28C2×C11×M16—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#125—21no—
34C11×#125—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8D412yes—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11D412yes—
43C11×#117—21no—
44C11×#117—21no—
45C2×C42×C11C2311yescharacteristic
46C11×#106—22no—
47C11×C4⋊C8—24no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×#103—22no—
52C11×#103—22no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8D412yes—
56C11×#97—22no—
57C11×#97—21no—
58C11×#97—21no—
59C11×#97—21no—
60C11×#97D412yes—
61C4×C8×C11—22no—
62C4×C8×C11C2×C411yescharacteristic
63C4×C8×C11C2×C411yescharacteristic
64C11×#95—21no—
65C11×#95—21no—
66C11×#95—21no—
67#9416C1111yesmaximal, characteristic, direct product factor, Sylow
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11C22⋊C412yes—
72C22×C4×C11—41no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C11×Q16—44no—
77C11×M16—42no—
78C2×C8×C11—21no—
79C2×C8×C11—21no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—41no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4C22⋊C412yes—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—41no—
97C42×C11—22no—
98C42×C11—41no—
99C42×C11C22×C411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103#3185C2×C1111yescharacteristic
104#2987C2×C1111yescharacteristic
105#1537C2×C1111yescharacteristic
106#1515C2×C1111yescharacteristic
107#1515C2×C1111yescharacteristic
108#1291C2×C1111yescharacteristic
109#1288C2×C1111yescharacteristic
110C23×C11#12111yescharacteristic
111Q8×C11—42no—
112Q8×C11—42no—
113Q8×C11—81no—
114Q8×C11—81no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11C2×C22⋊C411yescharacteristic
126C2×C4×C11C4×D411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C8×C11—22no—
132C8×C11—42no—
133C8×C11—42no—
134C8×C11—41no—
135C8×C11—81no—
136#533C22×C1111yescharacteristic
137#533C22×C1111yescharacteristic
138#498C4×C1111yescharacteristic, complemented
139#494C4×C1111yescharacteristic, complemented
140#487C4×C1111yescharacteristic, complemented
141#487C4×C1111yescharacteristic, complemented
142#470—22no—
143#446—22no—
144#446—22no—
145#441—22no—
146#433—22no—
147#432C22×C1111yescharacteristic
148#432C22×C1111yescharacteristic
149#432C22×C1111yescharacteristic
150C4×M16C22×C1111yescharacteristic
151#383C22×C1111yescharacteristic
152#330—22no—
153#328—22no—
154#328—22no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11#38611yescharacteristic
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—42no—
166C4×C11—42no—
167C4×C11—81no—
168C4×C11—81no—
169C4×C11—161no—
170C2×Q16—22no—
171C2×M16—21no—
172C4⋊Q8C2×C4×C1111yescharacteristic
173C4⋊Q8C2×C4×C1111yescharacteristic
174C4⋊Q8C2×C4×C1111yescharacteristic
175C4⋊Q8C2×C4×C1111yescharacteristic
176#125—21no—
177#125—21no—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C22⋊Q8—21no—
181C22⋊Q8D4×C1112yes—
182C4×Q8—21no—
183C4×Q8—21no—
184C4×Q8—21no—
185C4×Q8D4×C1112yes—
186#117—21no—
187#117—21no—
188C2×C42C23×C1111yescharacteristic
189#106—22no—
190C4⋊C8—24no—
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—21no—
194#103—22no—
195#103—22no—
196C22⋊C8—21no—
197C22⋊C8—21no—
198C22⋊C8D4×C1112yes—
199#97—22no—
200#97—21no—
201#97—21no—
202#97—21no—
203#97D4×C1112yes—
204C4×C8—22no—
205C4×C8C2×C4×C1111yescharacteristic
206C4×C8C2×C4×C1111yescharacteristic
207#95—21no—
208#95—21no—
209#95—21no—
210C2×C11—41no—
211C2×C11#188411yescharacteristic
212C2×C11#190211yescharacteristic
213C2×C11#190511yescharacteristic
214C2×Q8—21no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8C11×C22⋊C412yes—
218C22×C4—41no—
219C22×C4C2×D4×C1111yescharacteristic
220C22×C4C2×D4×C1111yescharacteristic
221C22×C4C11×#4111yescharacteristic
222Q16—44no—
223M16—42no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—22no—
227C2×C8—22no—
228C2×C8—41no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4C11×C22⋊C412yes—
241C22⋊C4—22no—
242C22⋊C4—41no—
243C42—22no—
244C42—41no—
245C42C22×C4×C1111yescharacteristic
246C42C2×D4×C1111yescharacteristic
247C42C2×D4×C1111yescharacteristic
248C42C11×#4111yescharacteristic
249C11#941611yescharacteristic, direct product factor, Sylow
250C23C11×#12111yescharacteristic
251Q8—42no—
252Q8—42no—
253Q8—81no—
254Q8—81no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4C2×C11×C22⋊C411yescharacteristic
266C2×C4C4×D4×C1111yescharacteristic
267C2×C4C4×D4×C1111yescharacteristic
268C2×C4C11×#12011yescharacteristic
269C2×C4C11×#12111yescharacteristic
270C2×C4C11×#12311yescharacteristic
271C8—22no—
272C8—41no—
273C8—42no—
274C8—42no—
275C8—81no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22C11×#38611yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—42no—
287C4—42no—
288C4—81no—
289C4—81no—
290C4—161no—
291C2—41no—
292C2C11×#188411yescharacteristic
293C2C11×#190211yescharacteristic
294C2C11×#190511yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
10. C11×#498C4semidirect
11. C11×#494C4semidirect
12. C11×#487C4semidirect
13. C11×#487C4semidirect
67. #9416C11direct (N × H)
138. #498C4×C11semidirect
139. #494C4×C11semidirect
140. #487C4×C11semidirect
141. #487C4×C11semidirect
249. C11#9416direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31852
C11×#29872
C11×#15372
C11×#15152
C11×#12912
C11×#12882
#941611