Finite Group Databasebeta

← C11×#8959 #14586152

Subgroups — C11×#8959 #14586152

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2972C211yesmaximal, characteristic, complemented
2C4×C11×#127C211yesmaximal, characteristic
3C11×#1478C212yesmaximal, complemented
4C11×#1460C211yesmaximal, characteristic, complemented
5C11×#1276C212yesmaximal, complemented
6C2×C11×#127C411yescharacteristic
7C2×C4×D4×C11—22no—
8C2×C4×D4×C11C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C8×D4×C11—24no—
11C11×#431C2212yes—
12C11×#431C2212yes—
13C2×C11×C22⋊C8—22no—
14C11×#390—22no—
15C11×#390C411yescharacteristic
16C11×#390C411yescharacteristic
17C11×#384C411yescharacteristic
18C43×C11C2211yescharacteristic
19C11×D4⋊C8—24no—
20C11×#323—22no—
21C22×D4×C11—22no—
22C22×D4×C11C2×C411yescharacteristic
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11—21no—
25C23×C4×C11D412yes—
26C22×C8×C11—24no—
27C11×#127—22no—
28C11×#127C814yescomplemented
29C4×D4×C11—22no—
30C4×D4×C11—22no—
31C4×D4×C11—22no—
32C4×D4×C11—22no—
33C4×D4×C11—48no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4D412yes—
41C2×C42×C11—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2×C411yescharacteristic
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C11×C4⋊C8—22no—
47C11×C4⋊C8D414yescomplemented
48C11×C22⋊C8—24no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—22no—
51C4×C8×C11—22no—
52C4×C8×C11—22no—
53#8959C1111yesmaximal, characteristic, direct product factor, Sylow
54C24×C11—21no—
55C24×C11C22⋊C412yes—
56C2×D4×C11—28no—
57C2×D4×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—21no—
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—44no—
63C2×D4×C11—44no—
64C2×D4×C11C2×C812yes—
65C2×D4×C11C2×C812yescomplemented
66C2×D4×C11M1612yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—44no—
73C22×C4×C11—44no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C22⋊C412yes—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C2×C8×C11—24no—
81C2×C8×C11—42no—
82C2×C8×C11—84no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—44no—
86C11×C22⋊C4—24no—
87C11×C22⋊C4—44no—
88C11×C22⋊C4—44no—
89C11×C22⋊C4—42no—
90C42×C11—24no—
91C42×C11—21no—
92C42×C11—22no—
93C42×C11—42no—
94C42×C11C2×C812yescomplemented
95C42×C11C2×D412yes—
96C42×C11#4112yes—
97#2972C2×C1111yescharacteristic, complemented
98C4×#127C2×C1111yescharacteristic
99#1478C2×C1112yescomplemented
100#1460C2×C1111yescharacteristic, complemented
101#1276C2×C1112yescomplemented
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—22no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11—42no—
108C23×C11—42no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11C22⋊C814yes—
112C23×C11C2×C22⋊C411yescharacteristic
113D4×C11—24no—
114D4×C11—24no—
115D4×C11—24no—
116D4×C11—416no—
117D4×C11—42no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—44no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—82no—
132C2×C4×C11—82no—
133C2×C4×C11—82no—
134C2×C4×C11C4×D412yes—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12112yes—
137C2×C4×C11#12311yescharacteristic
138C2×C4×C11C22×C811yescharacteristic
139C2×C4×C11C2×M1611yescharacteristic
140C2×C4×C11#13112yes—
141C8×C11—44no—
142C8×C11—82no—
143C2×#127C4×C1111yescharacteristic
144C2×C4×D4—22no—
145C2×C4×D4C22×C1111yescharacteristic
146C2×C4×D4C22×C1111yescharacteristic
147C8×D4—24no—
148#431C22×C1112yes—
149#431C22×C1112yes—
150C2×C22⋊C8—22no—
151#390—22no—
152#390C4×C1111yescharacteristic
153#390C4×C1111yescharacteristic
154#384C4×C1111yescharacteristic
155C43C22×C1111yescharacteristic
156D4⋊C8—24no—
157#323—22no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—24no—
161C22×C11—44no—
162C22×C11—44no—
163C22×C11—42no—
164C22×C11—42no—
165C22×C11—42no—
166C22×C11—82no—
167C22×C11—82no—
168C22×C11—81no—
169C22×C11—81no—
170C22×C11#38611yescharacteristic
171C22×C11C2×C22⋊C811yescharacteristic
172C22×C11#40811yescharacteristic
173C4×C11—24no—
174C4×C11—22no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—42no—
178C4×C11—81no—
179C4×C11C8×D412yes—
180C4×C11#43512yes—
181C4×C11#45312yes—
182C22×D4—22no—
183C22×D4C2×C4×C1111yescharacteristic
184C22×D4C2×C4×C1111yescharacteristic
185C23×C4—21no—
186C23×C4D4×C1112yes—
187C22×C8—24no—
188#127—22no—
189#127C8×C1114yescomplemented
190C4×D4—22no—
191C4×D4—22no—
192C4×D4—22no—
193C4×D4—22no—
194C4×D4—48no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4C2×C4×C1111yescharacteristic
197C2×C4⋊C4C2×C4×C1111yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4D4×C1112yes—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42C2×C4×C1111yescharacteristic
205C2×C42C2×C4×C1111yescharacteristic
206C2×C42C23×C1111yescharacteristic
207C4⋊C8—22no—
208C4⋊C8D4×C1114yescomplemented
209C22⋊C8—24no—
210C22⋊C8—22no—
211C22⋊C8—22no—
212C4×C8—22no—
213C4×C8—22no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—44no—
217C2×C11—82no—
218C2×C11#186911yescharacteristic
219C2×C11#188411yescharacteristic
220C2×C11#188711yescharacteristic
221C24—21no—
222C24C11×C22⋊C412yes—
223C2×D4—28no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—21no—
227C2×D4—22no—
228C2×D4—22no—
229C2×D4—44no—
230C2×D4—44no—
231C2×D4C2×C8×C1112yes—
232C2×D4C2×C8×C1112yescomplemented
233C2×D4C11×M1612yes—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—44no—
240C22×C4—44no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C11×C22⋊C412yes—
244C22×C4C22×C4×C1111yescharacteristic
245C22×C4C2×D4×C1111yescharacteristic
246C22×C4C2×D4×C1111yescharacteristic
247C2×C8—24no—
248C2×C8—42no—
249C2×C8—84no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—44no—
253C22⋊C4—24no—
254C22⋊C4—44no—
255C22⋊C4—44no—
256C22⋊C4—42no—
257C42—24no—
258C42—21no—
259C42—22no—
260C42—42no—
261C42C2×C8×C1112yescomplemented
262C42C2×D4×C1112yes—
263C42C11×#4112yes—
264C11#895911yescharacteristic, direct product factor, Sylow
265C23—22no—
266C23—22no—
267C23—22no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—41no—
273C23—41no—
274C23C11×C22⋊C814yes—
275C23C2×C11×C22⋊C411yescharacteristic
276D4—24no—
277D4—24no—
278D4—24no—
279D4—416no—
280D4—42no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4C4×D4×C1112yes—
298C2×C4C11×#12011yescharacteristic
299C2×C4C11×#12112yes—
300C2×C4C11×#12311yescharacteristic
301C2×C4C22×C8×C1111yescharacteristic
302C2×C4C2×C11×M1611yescharacteristic
303C2×C4C11×#13112yes—
304C8—44no—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—24no—
309C22—44no—
310C22—44no—
311C22—42no—
312C22—42no—
313C22—42no—
314C22—82no—
315C22—82no—
316C22—81no—
317C22—81no—
318C22C11×#38611yescharacteristic
319C22C2×C11×C22⋊C811yescharacteristic
320C22C11×#40811yescharacteristic
321C4—24no—
322C4—22no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—81no—
327C4C8×D4×C1112yes—
328C4C11×#43512yes—
329C4C11×#45312yes—
330C2—21no—
331C2—21no—
332C2—44no—
333C2—82no—
334C2C11×#186911yescharacteristic
335C2C11×#188411yescharacteristic
336C2C11×#188711yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutatorC2×C4C22×C8×C11
Frattini, cosocleC2×C42C23×C11
socleC22×C11#386
prime radicalC2×C11×#127C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2972C2semidirect
3. C11×#1478C2semidirect
4. C11×#1460C2semidirect
5. C11×#1276C2semidirect
28. C11×#127C8semidirect
47. C11×C4⋊C8D4semidirect
53. #8959C11direct (N × H)
65. C2×D4×C11C2×C8semidirect
94. C42×C11C2×C8semidirect
97. #2972C2×C11semidirect
99. #1478C2×C11semidirect
100. #1460C2×C11semidirect
101. #1276C2×C11semidirect
189. #127C8×C11semidirect
208. C4⋊C8D4×C11semidirect
232. C2×D4C2×C8×C11semidirect
261. C42C2×C8×C11semidirect
264. C11#8959direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29722
C4×C11×#1272
C11×#14782
C11×#14602
C11×#12762
#895911