Finite Group Databasebeta

← C11×#9417 #14586610

Subgroups — C11×#9417 #14586610

Order 2816.

442 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3184C211yesmaximal, characteristic
2C11×#2980C211yesmaximal, characteristic, complemented
3C11×#1536C211yesmaximal, characteristic, complemented
4C11×#1514C211yesmaximal, characteristic, complemented
5C11×#1514C211yesmaximal, characteristic, complemented
6C11×#1291C211yesmaximal, characteristic, complemented
7C11×#1288C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C11×#498C411yescharacteristic, complemented
11C11×#493C411yescharacteristic, complemented
12C11×#486C411yescharacteristic, complemented
13C11×#486C411yescharacteristic, complemented
14C11×#469—22no—
15C11×#442—22no—
16C11×#435—22no—
17C11×#435—22no—
18C11×#432C2211yescharacteristic
19C11×#432C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C11×#408—22no—
22C4×C11×M16C2211yescharacteristic
23C11×#383C2211yescharacteristic
24C11×#329—22no—
25C11×#327—22no—
26C11×#327—22no—
27C2×C11×#41—21no—
28C2×C11×#41—21no—
29C2×C11×D8—22no—
30C2×C11×M16—21no—
31C2×C11×M16—22no—
32C22×C8×C11—22no—
33C11×C4⋊Q8C2×C411yescharacteristic
34C11×C4⋊Q8C2×C411yescharacteristic
35C11×#127C2×C411yescharacteristic
36C11×#127C2×C411yescharacteristic
37C11×#124—21no—
38C11×#124—21no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#121D412yes—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11D412yes—
47C2×C42×C11C2311yescharacteristic
48C11×#106—22no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×#102—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#9417C1111yesmaximal, characteristic, direct product factor, Sylow
68C11×#41—81no—
69C11×#41—81no—
70C11×#41—82no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×D4×C11—22no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C2×D4×C11C22⋊C412yes—
81C22×C4×C11—22no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C11×D8—44no—
88C11×M16—42no—
89C11×M16—82no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C2×C8×C11—82no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4C22⋊C412yes—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11C22×C411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108#3184C2×C1111yescharacteristic
109#2980C2×C1111yescharacteristic, complemented
110#1536C2×C1111yescharacteristic, complemented
111#1514C2×C1111yescharacteristic, complemented
112#1514C2×C1111yescharacteristic, complemented
113#1291C2×C1111yescharacteristic, complemented
114#1288C2×C1111yescharacteristic, complemented
115C23×C11—22no—
116C23×C11—41no—
117C23×C11#12111yescharacteristic
118Q8×C11—81no—
119Q8×C11—81no—
120D4×C11—42no—
121D4×C11—42no—
122D4×C11—81no—
123D4×C11—81no—
124D4×C11—81no—
125D4×C11—81no—
126D4×C11—82no—
127D4×C11—82no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—41no—
135C2×C4×C11—82no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11C2×C22⋊C411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C8×C11—22no—
146C8×C11—42no—
147C8×C11—42no—
148C8×C11—41no—
149C8×C11—81no—
150#532C22×C1111yescharacteristic
151#532C22×C1111yescharacteristic
152#498C4×C1111yescharacteristic, complemented
153#493C4×C1111yescharacteristic, complemented
154#486C4×C1111yescharacteristic, complemented
155#486C4×C1111yescharacteristic, complemented
156#469—22no—
157#442—22no—
158#435—22no—
159#435—22no—
160#432C22×C1111yescharacteristic
161#432C22×C1111yescharacteristic
162#432C22×C1111yescharacteristic
163#408—22no—
164C4×M16C22×C1111yescharacteristic
165#383C22×C1111yescharacteristic
166#329—22no—
167#327—22no—
168#327—22no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—81no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11#38611yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11—81no—
187C4×C11—161no—
188C2×#41—21no—
189C2×#41—21no—
190C2×D8—22no—
191C2×M16—21no—
192C2×M16—22no—
193C22×C8—22no—
194C4⋊Q8C2×C4×C1111yescharacteristic
195C4⋊Q8C2×C4×C1111yescharacteristic
196#127C2×C4×C1111yescharacteristic
197#127C2×C4×C1111yescharacteristic
198#124—21no—
199#124—21no—
200#121—21no—
201#121—21no—
202#121—21no—
203#121D4×C1112yes—
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—21no—
207C4×D4D4×C1112yes—
208C2×C42C23×C1111yescharacteristic
209#106—22no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213#102—22no—
214#102—22no—
215C22⋊C8—24no—
216C22⋊C8—21no—
217C22⋊C8—21no—
218C22⋊C8D4×C1112yes—
219#97—21no—
220#97—21no—
221#97—21no—
222#97D4×C1112yes—
223C4×C8C2×C4×C1111yescharacteristic
224C4×C8C2×C4×C1111yescharacteristic
225#95—21no—
226#95—21no—
227#95—21no—
228C2×C11—41no—
229C2×C11—82no—
230C2×C11—161no—
231C2×C11#188411yescharacteristic
232C2×C11#190311yescharacteristic
233C2×C11#190411yescharacteristic
234#41—81no—
235#41—81no—
236#41—82no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—41no—
246C2×D4C11×C22⋊C412yes—
247C22×C4—22no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4C2×D4×C1111yescharacteristic
251C22×C4C2×D4×C1111yescharacteristic
252C22×C4C11×#4111yescharacteristic
253D8—44no—
254M16—42no—
255M16—82no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—82no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4C11×C22⋊C412yes—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C42C22×C4×C1111yescharacteristic
271C42C2×D4×C1111yescharacteristic
272C42C2×D4×C1111yescharacteristic
273C42C11×#4111yescharacteristic
274C11#941711yescharacteristic, direct product factor, Sylow
275C23—22no—
276C23—41no—
277C23C11×#12111yescharacteristic
278Q8—81no—
279Q8—81no—
280D4—42no—
281D4—42no—
282D4—81no—
283D4—81no—
284D4—81no—
285D4—81no—
286D4—82no—
287D4—82no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4C2×C11×C22⋊C411yescharacteristic
300C2×C4C4×D4×C1111yescharacteristic
301C2×C4C4×D4×C1111yescharacteristic
302C2×C4C11×#12011yescharacteristic
303C2×C4C11×#12111yescharacteristic
304C2×C4C11×#12311yescharacteristic
305C8—22no—
306C8—42no—
307C8—42no—
308C8—41no—
309C8—81no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22C11×#38611yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—81no—
328C4—161no—
329C2—41no—
330C2—82no—
331C2—161no—
332C2C11×#188411yescharacteristic
333C2C11×#190311yescharacteristic
334C2C11×#190411yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3184C2
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
2. C11×#2980C2semidirect
3. C11×#1536C2semidirect
4. C11×#1514C2semidirect
5. C11×#1514C2semidirect
6. C11×#1291C2semidirect
7. C11×#1288C2semidirect
10. C11×#498C4semidirect
11. C11×#493C4semidirect
12. C11×#486C4semidirect
13. C11×#486C4semidirect
67. #9417C11direct (N × H)
109. #2980C2×C11semidirect
110. #1536C2×C11semidirect
111. #1514C2×C11semidirect
112. #1514C2×C11semidirect
113. #1291C2×C11semidirect
114. #1288C2×C11semidirect
152. #498C4×C11semidirect
153. #493C4×C11semidirect
154. #486C4×C11semidirect
155. #486C4×C11semidirect
274. C11#9417direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31842
C11×#29802
C11×#15362
C11×#15142
C11×#12912
C11×#12882
#941711