Finite Group Databasebeta

← C11×#9415 #14586608

Subgroups — C11×#9415 #14586608

Order 2816.

420 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3182C211yesmaximal, characteristic
2C11×#2980C211yesmaximal, characteristic
3C11×#1537C211yesmaximal, characteristic, complemented
4C11×#1515C211yesmaximal, characteristic, complemented
5C11×#1514C211yesmaximal, characteristic
6C11×#1291C211yesmaximal, characteristic, complemented
7C11×#1288C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C11×#500C411yescharacteristic, complemented
11C11×#492C411yescharacteristic, complemented
12C11×#487C411yescharacteristic, complemented
13C11×#486C411yescharacteristic, complemented
14C11×#468—22no—
15C11×#440—22no—
16C11×#435—22no—
17C11×#435—22no—
18C11×#432C2211yescharacteristic
19C11×#432C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C11×#408—22no—
22C4×C11×M16C2211yescharacteristic
23C11×#383C2211yescharacteristic
24C11×#330—22no—
25C11×#328—22no—
26C11×#327—22no—
27C2×C11×#41—21no—
28C2×C11×SD16—22no—
29C2×C11×M16—21no—
30C2×C11×M16—22no—
31C22×C8×C11—22no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×C4⋊Q8C2×C411yescharacteristic
34C11×C4⋊Q8C2×C411yescharacteristic
35C11×#127C2×C411yescharacteristic
36C11×#125—21no—
37C11×#124—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×#121—21no—
41C11×#121D412yes—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11D412yes—
46C11×#117—21no—
47C2×C42×C11C2311yescharacteristic
48C11×#107—22no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×#103—22no—
53C11×#102—22no—
54C11×C22⋊C8—24no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8D412yes—
58C11×#97—21no—
59C11×#97—21no—
60C11×#97—21no—
61C11×#97D412yes—
62C4×C8×C11C2×C411yescharacteristic
63C4×C8×C11C2×C411yescharacteristic
64C11×#95—21no—
65C11×#95—21no—
66C11×#95—21no—
67#9415C1111yesmaximal, characteristic, direct product factor, Sylow
68C11×#41—81no—
69C11×#41—81no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×D4×C11—22no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11C22⋊C412yes—
77C22×C4×C11—22no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C11×SD16—44no—
83C11×M16—42no—
84C11×M16—82no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—41no—
90C2×C8×C11—82no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4C22⋊C412yes—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—41no—
102C42×C11—41no—
103C42×C11C22×C411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107#3182C2×C1111yescharacteristic
108#2980C2×C1111yescharacteristic
109#1537C2×C1111yescharacteristic, complemented
110#1515C2×C1111yescharacteristic, complemented
111#1514C2×C1111yescharacteristic
112#1291C2×C1111yescharacteristic, complemented
113#1288C2×C1111yescharacteristic, complemented
114C23×C11—22no—
115C23×C11#12111yescharacteristic
116Q8×C11—42no—
117Q8×C11—81no—
118Q8×C11—81no—
119D4×C11—42no—
120D4×C11—81no—
121D4×C11—81no—
122D4×C11—82no—
123C2×C4×C11—22no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11C2×C22⋊C411yescharacteristic
135C2×C4×C11C4×D411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12311yescharacteristic
140C8×C11—22no—
141C8×C11—42no—
142C8×C11—42no—
143C8×C11—41no—
144C8×C11—81no—
145#533C22×C1111yescharacteristic
146#532C22×C1111yescharacteristic
147#500C4×C1111yescharacteristic, complemented
148#492C4×C1111yescharacteristic, complemented
149#487C4×C1111yescharacteristic, complemented
150#486C4×C1111yescharacteristic, complemented
151#468—22no—
152#440—22no—
153#435—22no—
154#435—22no—
155#432C22×C1111yescharacteristic
156#432C22×C1111yescharacteristic
157#432C22×C1111yescharacteristic
158#408—22no—
159C4×M16C22×C1111yescharacteristic
160#383C22×C1111yescharacteristic
161#330—22no—
162#328—22no—
163#327—22no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—42no—
168C22×C11—42no—
169C22×C11—42no—
170C22×C11#38611yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—42no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11—161no—
181C2×#41—21no—
182C2×SD16—22no—
183C2×M16—21no—
184C2×M16—22no—
185C22×C8—22no—
186C4⋊Q8C2×C4×C1111yescharacteristic
187C4⋊Q8C2×C4×C1111yescharacteristic
188C4⋊Q8C2×C4×C1111yescharacteristic
189#127C2×C4×C1111yescharacteristic
190#125—21no—
191#124—21no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194#121—21no—
195#121D4×C1112yes—
196C4×Q8—21no—
197C4×Q8—21no—
198C4×D4—21no—
199C4×D4D4×C1112yes—
200#117—21no—
201C2×C42C23×C1111yescharacteristic
202#107—22no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206#103—22no—
207#102—22no—
208C22⋊C8—24no—
209C22⋊C8—21no—
210C22⋊C8—21no—
211C22⋊C8D4×C1112yes—
212#97—21no—
213#97—21no—
214#97—21no—
215#97D4×C1112yes—
216C4×C8C2×C4×C1111yescharacteristic
217C4×C8C2×C4×C1111yescharacteristic
218#95—21no—
219#95—21no—
220#95—21no—
221C2×C11—41no—
222C2×C11—82no—
223C2×C11#188411yescharacteristic
224C2×C11#190211yescharacteristic
225C2×C11#190411yescharacteristic
226#41—81no—
227#41—81no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×D4—22no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4C11×C22⋊C412yes—
235C22×C4—22no—
236C22×C4—41no—
237C22×C4C2×D4×C1111yescharacteristic
238C22×C4C2×D4×C1111yescharacteristic
239C22×C4C11×#4111yescharacteristic
240SD16—44no—
241M16—42no—
242M16—82no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—22no—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—82no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4C11×C22⋊C412yes—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—41no—
260C42—41no—
261C42C22×C4×C1111yescharacteristic
262C42C2×D4×C1111yescharacteristic
263C42C2×D4×C1111yescharacteristic
264C42C11×#4111yescharacteristic
265C11#941511yescharacteristic, direct product factor, Sylow
266C23—22no—
267C23C11×#12111yescharacteristic
268Q8—42no—
269Q8—81no—
270Q8—81no—
271D4—42no—
272D4—81no—
273D4—81no—
274D4—82no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4C2×C11×C22⋊C411yescharacteristic
287C2×C4C4×D4×C1111yescharacteristic
288C2×C4C4×D4×C1111yescharacteristic
289C2×C4C11×#12011yescharacteristic
290C2×C4C11×#12111yescharacteristic
291C2×C4C11×#12311yescharacteristic
292C8—22no—
293C8—42no—
294C8—42no—
295C8—41no—
296C8—81no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22C11×#38611yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—42no—
311C4—81no—
312C4—81no—
313C4—161no—
314C2—41no—
315C2—82no—
316C2C11×#188411yescharacteristic
317C2C11×#190211yescharacteristic
318C2C11×#190411yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
3. C11×#1537C2semidirect
4. C11×#1515C2semidirect
6. C11×#1291C2semidirect
7. C11×#1288C2semidirect
10. C11×#500C4semidirect
11. C11×#492C4semidirect
12. C11×#487C4semidirect
13. C11×#486C4semidirect
67. #9415C11direct (N × H)
109. #1537C2×C11semidirect
110. #1515C2×C11semidirect
112. #1291C2×C11semidirect
113. #1288C2×C11semidirect
147. #500C4×C11semidirect
148. #492C4×C11semidirect
149. #487C4×C11semidirect
150. #486C4×C11semidirect
265. C11#9415direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31822
C11×#29802
C11×#15372
C11×#15152
C11×#15142
C11×#12912
C11×#12882
#941511