Finite Group Databasebeta

← C11×#11893 #14589086

Subgroups — C11×#11893 #14589086

Order 2816.

400 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×#3050C211yesmaximal, characteristic
2C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
3C11×#1810C211yesmaximal, characteristic, complemented
4C11×#1350C212yesmaximal, complemented
5C11×#1349C212yesmaximal, complemented
6C2×C11×#135C411yescharacteristic
7C23×C8×C11C2211yescharacteristic
8C11×#525—21no—
9C22×C11×C16—21no—
10C11×#467C411yescharacteristic
11C11×#467C2211yescharacteristic
12C11×#466C411yescharacteristic
13C11×#466C2211yescharacteristic
14C11×#465—21no—
15C11×#465—21no—
16C2×C11×#108—21no—
17C11×#427C411yescharacteristic
18C11×#416—21no—
19C11×#407—21no—
20C11×C22⋊C16—21no—
21C11×C22⋊C16C2212yes—
22C11×#341C2212yes—
23C2×C11×#41—21no—
24C23×C4×C11D411yescharacteristic
25C11×#135—42no—
26C2×C11×Q16C2×C411yescharacteristic
27C2×C11×SD16—21no—
28C2×C11×D8C2×C411yescharacteristic
29C2×C11×M16—22no—
30C22×C8×C11—42no—
31C22×C8×C11C2×C411yescharacteristic
32C22×C8×C11C2×C411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C22×C8×C11D411yescharacteristic
35C22×C8×C11D411yescharacteristic
36C22×C8×C11C2311yescharacteristic
37C11×#123—41no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#120—41no—
43C4×D4×C11—41no—
44C4×D4×C11—41no—
45C11×#117—21no—
46C2×C11×C16—22no—
47C2×C11×C16—42no—
48C11×#108—42no—
49C11×#107C2×C411yescharacteristic
50C11×#107C2×C411yescharacteristic
51C11×#106—21no—
52C11×#103—21no—
53C11×#103—21no—
54C11×#102—21no—
55C11×#102—21no—
56C11×C22⋊C8—41no—
57C11×C22⋊C8—41no—
58#11893C1111yesmaximal, characteristic, direct product factor, Sylow
59C24×C11SD1611yescharacteristic
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×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11D811yescharacteristic
73C22×C4×C11D811yescharacteristic
74C22×C4×C11SD1611yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C11×Q16—41no—
77C11×SD16—42no—
78C11×D8—41no—
79C11×M16—42no—
80C11×M16—42no—
81C2×C8×C11—22no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—42no—
88C2×C8×C11C22⋊C411yescharacteristic
89C2×C8×C11C22⋊C411yescharacteristic
90C2×C8×C11C22×C411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
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—
101C42×C11—41no—
102C11×C16—42no—
103#3050C2×C1111yescharacteristic
104C2×C22⋊C16C2×C1111yescharacteristic, complemented
105#1810C2×C1111yescharacteristic, complemented
106#1350C2×C1112yescomplemented
107#1349C2×C1112yescomplemented
108C23×C11—22no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11#10211yescharacteristic
113C23×C11#10211yescharacteristic
114C23×C11C2×SD1611yescharacteristic
115Q8×C11—41no—
116Q8×C11—41no—
117D4×C11—41no—
118D4×C11—41no—
119D4×C11—82no—
120D4×C11—82no—
121D4×C11—82no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—82no—
135C2×C4×C11#10211yescharacteristic
136C2×C4×C11#10211yescharacteristic
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C8×C11—21no—
140C8×C11—21no—
141C8×C11—21no—
142C8×C11—82no—
143C8×C11#9912yes—
144C2×#135C4×C1111yescharacteristic
145C23×C8C22×C1111yescharacteristic
146#525—21no—
147C22×C16—21no—
148#467C4×C1111yescharacteristic
149#467C22×C1111yescharacteristic
150#466C4×C1111yescharacteristic
151#466C22×C1111yescharacteristic
152#465—21no—
153#465—21no—
154C2×#108—21no—
155#427C4×C1111yescharacteristic
156#416—21no—
157#407—21no—
158C22⋊C16—21no—
159C22⋊C16C22×C1112yes—
160#341C22×C1112yes—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—44no—
170C22×C11—81no—
171C22×C11—81no—
172C22×C11—81no—
173C22×C11#35912yes—
174C22×C11C2×#10211yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11—81no—
181C4×C11C2×#9911yescharacteristic
182C4×C11#42111yescharacteristic
183C2×#41—21no—
184C23×C4D4×C1111yescharacteristic
185#135—42no—
186C2×Q16C2×C4×C1111yescharacteristic
187C2×SD16—21no—
188C2×D8C2×C4×C1111yescharacteristic
189C2×M16—22no—
190C22×C8—42no—
191C22×C8C2×C4×C1111yescharacteristic
192C22×C8C2×C4×C1111yescharacteristic
193C22×C8D4×C1111yescharacteristic
194C22×C8D4×C1111yescharacteristic
195C22×C8D4×C1111yescharacteristic
196C22×C8C23×C1111yescharacteristic
197#123—41no—
198C22⋊Q8—21no—
199C22⋊Q8—21no—
200#121—21no—
201#121—21no—
202#120—41no—
203C4×D4—41no—
204C4×D4—41no—
205#117—21no—
206C2×C16—22no—
207C2×C16—42no—
208#108—42no—
209#107C2×C4×C1111yescharacteristic
210#107C2×C4×C1111yescharacteristic
211#106—21no—
212#103—21no—
213#103—21no—
214#102—21no—
215#102—21no—
216C22⋊C8—41no—
217C22⋊C8—41no—
218C2×C11—22no—
219C2×C11—41no—
220C2×C11—41no—
221C2×C11—161no—
222C2×C11#151911yescharacteristic
223C2×C11C2×#35911yescharacteristic
224C2×C11#214811yescharacteristic
225C24C11×SD1611yescharacteristic
226#41—42no—
227#41—42no—
228C2×Q8—21no—
229C2×D4—21no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4C11×C22⋊C411yescharacteristic
237C22×C4C11×C22⋊C411yescharacteristic
238C22×C4C11×D811yescharacteristic
239C22×C4C11×D811yescharacteristic
240C22×C4C11×SD1611yescharacteristic
241C22×C4C2×D4×C1111yescharacteristic
242Q16—41no—
243SD16—42no—
244D8—41no—
245M16—42no—
246M16—42no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—42no—
254C2×C8C11×C22⋊C411yescharacteristic
255C2×C8C11×C22⋊C411yescharacteristic
256C2×C8C22×C4×C1111yescharacteristic
257C2×C8C2×D4×C1111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C42—41no—
268C16—42no—
269C11#1189311yescharacteristic, direct product factor, Sylow
270C23—22no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23C11×#10211yescharacteristic
275C23C11×#10211yescharacteristic
276C23C2×C11×SD1611yescharacteristic
277Q8—41no—
278Q8—41no—
279D4—41no—
280D4—41no—
281D4—82no—
282D4—82no—
283D4—82no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—82no—
297C2×C4C11×#10211yescharacteristic
298C2×C4C11×#10211yescharacteristic
299C2×C4C2×C11×C22⋊C411yescharacteristic
300C2×C4C2×C11×D811yescharacteristic
301C8—21no—
302C8—21no—
303C8—21no—
304C8—82no—
305C8C11×#9912yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—44no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22C11×#35912yes—
319C22C2×C11×#10211yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—81no—
326C4C2×C11×#9911yescharacteristic
327C4C11×#42111yescharacteristic
328C2—22no—
329C2—41no—
330C2—41no—
331C2—161no—
332C2C11×#151911yescharacteristic
333C2C2×C11×#35911yescharacteristic
334C2C11×#214811yescharacteristic
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. C2×C11×C22⋊C16C2semidirect
3. C11×#1810C2semidirect
4. C11×#1350C2semidirect
5. C11×#1349C2semidirect
58. #11893C11direct (N × H)
104. C2×C22⋊C16C2×C11semidirect
105. #1810C2×C11semidirect
106. #1350C2×C11semidirect
107. #1349C2×C11semidirect
269. C11#11893direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30502
C2×C11×C22⋊C162
C11×#18102
C11×#13502
C11×#13492
#1189311