Finite Group Databasebeta

← C11×#11890 #14589083

Subgroups — C11×#11890 #14589083

Order 2816.

416 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3050C211yesmaximal, characteristic
2C11×#2112C211yesmaximal, characteristic, complemented
3C11×#1808C211yesmaximal, characteristic, complemented
4C11×#1348C212yesmaximal, complemented
5C11×#1347C212yesmaximal, complemented
6C2×C11×#135C411yescharacteristic, complemented
7C23×C8×C11C2211yescharacteristic
8C11×#525—21no—
9C2×C11×M32—21no—
10C11×#467C411yescharacteristic, complemented
11C11×#467C2211yescharacteristic
12C11×#466C411yescharacteristic, complemented
13C11×#466C2211yescharacteristic
14C11×#465—21no—
15C11×#465—21no—
16C11×#427C411yescharacteristic, complemented
17C2×C11×#107—21no—
18C11×#416—21no—
19C11×#380—21no—
20C11×C22⋊C16—21no—
21C11×C22⋊C16C2212yes—
22C11×#340C2212yes—
23C2×C11×#41—21no—
24C23×C4×C11D411yescharacteristic
25C11×#135—42no—
26C2×C11×Q16C2×C411yescharacteristic
27C2×C11×SD16—21no—
28C2×C11×D8C2×C411yescharacteristic
29C22×C8×C11—42no—
30C22×C8×C11C2×C411yescharacteristic
31C22×C8×C11C2×C411yescharacteristic
32C22×C8×C11D411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C22×C8×C11D411yescharacteristic
35C22×C8×C11C2311yescharacteristic
36C11×#123—41no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#120—41no—
42C4×D4×C11—41no—
43C4×D4×C11—41no—
44C11×#117—21no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C22⋊C4—41no—
47C11×M32—42no—
48C2×C11×C16—22no—
49C11×#107—42no—
50C11×#107C2×C411yescharacteristic
51C11×#107C2×C411yescharacteristic
52C11×#106—21no—
53C11×#103—21no—
54C11×#103—21no—
55C11×#102—21no—
56C11×#102—21no—
57C11×#95—41no—
58#11890C1111yesmaximal, characteristic, direct product factor, Sylow
59C24×C11D811yescharacteristic
60C11×#41—42no—
61C11×#41—42no—
62C2×Q8×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—42no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11D811yescharacteristic
74C22×C4×C11SD1611yescharacteristic
75C22×C4×C11SD1611yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C11×Q16—41no—
78C11×SD16—42no—
79C11×D8—41no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11C22⋊C411yescharacteristic
87C2×C8×C11C22⋊C411yescharacteristic
88C2×C8×C11C22×C411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—42no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—82no—
102C42×C11—41no—
103C11×C16—42no—
104#3050C2×C1111yescharacteristic
105#2112C2×C1111yescharacteristic, complemented
106#1808C2×C1111yescharacteristic, complemented
107#1348C2×C1112yescomplemented
108#1347C2×C1112yescomplemented
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11#10211yescharacteristic
115C23×C11#10211yescharacteristic
116C23×C11C2×D811yescharacteristic
117Q8×C11—41no—
118Q8×C11—41no—
119D4×C11—41no—
120D4×C11—41no—
121D4×C11—82no—
122D4×C11—82no—
123D4×C11—81no—
124D4×C11—81no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—82no—
138C2×C4×C11—82no—
139C2×C4×C11—82no—
140C2×C4×C11—82no—
141C2×C4×C11#10211yescharacteristic
142C2×C4×C11#10211yescharacteristic
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C8×C11—21no—
146C8×C11—21no—
147C8×C11—21no—
148C8×C11#9912yes—
149C2×#135C4×C1111yescharacteristic, complemented
150C23×C8C22×C1111yescharacteristic
151#525—21no—
152C2×M32—21no—
153#467C4×C1111yescharacteristic, complemented
154#467C22×C1111yescharacteristic
155#466C4×C1111yescharacteristic, complemented
156#466C22×C1111yescharacteristic
157#465—21no—
158#465—21no—
159#427C4×C1111yescharacteristic, complemented
160C2×#107—21no—
161#416—21no—
162#380—21no—
163C22⋊C16—21no—
164C22⋊C16C22×C1112yes—
165#340C22×C1112yes—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11C2×#10211yescharacteristic
180C22×C11#50911yescharacteristic
181C22×C11#51011yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11—162no—
189C4×C11C2×#9911yescharacteristic
190C4×C11#42111yescharacteristic
191C2×#41—21no—
192C23×C4D4×C1111yescharacteristic
193#135—42no—
194C2×Q16C2×C4×C1111yescharacteristic
195C2×SD16—21no—
196C2×D8C2×C4×C1111yescharacteristic
197C22×C8—42no—
198C22×C8C2×C4×C1111yescharacteristic
199C22×C8C2×C4×C1111yescharacteristic
200C22×C8D4×C1111yescharacteristic
201C22×C8D4×C1111yescharacteristic
202C22×C8D4×C1111yescharacteristic
203C22×C8C23×C1111yescharacteristic
204#123—41no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207#121—21no—
208#121—21no—
209#120—41no—
210C4×D4—41no—
211C4×D4—41no—
212#117—21no—
213C2×C4⋊C4—22no—
214C2×C22⋊C4—41no—
215M32—42no—
216C2×C16—22no—
217#107—42no—
218#107C2×C4×C1111yescharacteristic
219#107C2×C4×C1111yescharacteristic
220#106—21no—
221#103—21no—
222#103—21no—
223#102—21no—
224#102—21no—
225#95—41no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11—41no—
229C2×C11—41no—
230C2×C11—161no—
231C2×C11#151911yescharacteristic
232C2×C11#213911yescharacteristic
233C2×C11#214511yescharacteristic
234C24C11×D811yescharacteristic
235#41—42no—
236#41—42no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—42no—
246C22×C4C11×C22⋊C411yescharacteristic
247C22×C4C11×C22⋊C411yescharacteristic
248C22×C4C11×D811yescharacteristic
249C22×C4C11×SD1611yescharacteristic
250C22×C4C11×SD1611yescharacteristic
251C22×C4C2×D4×C1111yescharacteristic
252Q16—41no—
253SD16—42no—
254D8—41no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8C11×C22⋊C411yescharacteristic
262C2×C8C11×C22⋊C411yescharacteristic
263C2×C8C22×C4×C1111yescharacteristic
264C2×C8C2×D4×C1111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—82no—
277C42—41no—
278C16—42no—
279C11#1189011yescharacteristic, direct product factor, Sylow
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23C11×#10211yescharacteristic
286C23C11×#10211yescharacteristic
287C23C2×C11×D811yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—41no—
291D4—41no—
292D4—82no—
293D4—82no—
294D4—81no—
295D4—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4C11×#10211yescharacteristic
313C2×C4C11×#10211yescharacteristic
314C2×C4C2×C11×C22⋊C411yescharacteristic
315C2×C4C2×C11×SD1611yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8C11×#9912yes—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C2×C11×#10211yescharacteristic
334C22C11×#50911yescharacteristic
335C22C11×#51011yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—162no—
343C4C2×C11×#9911yescharacteristic
344C4C11×#42111yescharacteristic
345C2—21no—
346C2—21no—
347C2—41no—
348C2—41no—
349C2—161no—
350C2C11×#151911yescharacteristic
351C2C11×#213911yescharacteristic
352C2C11×#214511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#102
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC11×#3050C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2112C2semidirect
3. C11×#1808C2semidirect
4. C11×#1348C2semidirect
5. C11×#1347C2semidirect
6. C2×C11×#135C4semidirect
10. C11×#467C4semidirect
12. C11×#466C4semidirect
16. C11×#427C4semidirect
58. #11890C11direct (N × H)
105. #2112C2×C11semidirect
106. #1808C2×C11semidirect
107. #1348C2×C11semidirect
108. #1347C2×C11semidirect
149. C2×#135C4×C11semidirect
153. #467C4×C11semidirect
155. #466C4×C11semidirect
159. #427C4×C11semidirect
279. C11#11890direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30502
C11×#21122
C11×#18082
C11×#13482
C11×#13472
#1189011