Finite Group Databasebeta

← C11×#2788 #13065626

Subgroups — C11×#2788 #13065626

Order 1408.

416 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#400C211yesmaximal, characteristic, complemented
2C11×#400C211yesmaximal, characteristic, complemented
3C11×#398C211yesmaximal, characteristic, complemented
4C11×#396C211yesmaximal, characteristic
5C11×#395C211yesmaximal, characteristic, complemented
6C11×#393C211yesmaximal, characteristic
7C11×#391C211yesmaximal, characteristic, complemented
8C11×#389C211yesmaximal, characteristic, complemented
9C11×#389C211yesmaximal, characteristic, complemented
10C11×#388C211yesmaximal, characteristic
11C11×#388C211yesmaximal, characteristic
12C11×#387C211yesmaximal, characteristic, complemented
13C11×#385C211yesmaximal, characteristic
14C11×#385C211yesmaximal, characteristic
15C11×#380C211yesmaximal, characteristic
16C22×Q8×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C42×C11C2211yescharacteristic
36C2×C42×C11C2211yescharacteristic
37C11×#95C2211yescharacteristic
38C11×#95C2211yescharacteristic
39C11×#95C2211yescharacteristic
40C11×#95C2211yescharacteristic
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11×#95C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C24×C11C2311yescharacteristic
52C2×Q8×C11—22no—
53C2×Q8×C11—41no—
54C2×Q8×C11—41no—
55C22×C4×C11—22no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4Q814yescomplemented
89C42×C11—41no—
90C42×C11—41no—
91#2788C1111yesmaximal, characteristic, direct product factor, Sylow
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11C2×Q812yes—
99C23×C11C2411yescharacteristic
100Q8×C11—44no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
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—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—44no—
140C2×C4×C11C2×Q812yes—
141C2×C4×C11C2×Q812yes—
142C2×C4×C11#4112yes—
143C2×C4×C11#4112yes—
144#400C2×C1111yescharacteristic, complemented
145#400C2×C1111yescharacteristic, complemented
146#398C2×C1111yescharacteristic, complemented
147#396C2×C1111yescharacteristic
148#395C2×C1111yescharacteristic, complemented
149#393C2×C1111yescharacteristic
150#391C2×C1111yescharacteristic, complemented
151#389C2×C1111yescharacteristic, complemented
152#389C2×C1111yescharacteristic, complemented
153#388C2×C1111yescharacteristic
154#388C2×C1111yescharacteristic
155#387C2×C1111yescharacteristic, complemented
156#385C2×C1111yescharacteristic
157#385C2×C1111yescharacteristic
158#380C2×C1111yescharacteristic
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—22no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11C22×Q811yescharacteristic
167C22×C11C2×#4111yescharacteristic
168C22×C11C2×#4111yescharacteristic
169C22×C11H(5,𝔽2)11yescharacteristic
170C22×C11H(5,𝔽2)11yescharacteristic
171C22×C11H(5,𝔽2)11yescharacteristic
172C22×C112−1+411yescharacteristic
173C4×C11—22no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—41no—
187C22×Q8C22×C1111yescharacteristic
188C23×C4C22×C1111yescharacteristic
189C2×C4⋊C4C22×C1111yescharacteristic
190C2×C4⋊C4C22×C1111yescharacteristic
191C2×C4⋊C4C22×C1111yescharacteristic
192C2×C4⋊C4C22×C1111yescharacteristic
193C2×C4⋊C4C22×C1111yescharacteristic
194C2×C4⋊C4C22×C1111yescharacteristic
195C2×C4⋊C4C22×C1111yescharacteristic
196C2×C4⋊C4C22×C1111yescharacteristic
197C2×C4⋊C4C22×C1111yescharacteristic
198C2×C4⋊C4C22×C1111yescharacteristic
199C2×C4⋊C4C22×C1111yescharacteristic
200C2×C22⋊C4C22×C1111yescharacteristic
201C2×C22⋊C4C22×C1111yescharacteristic
202C2×C22⋊C4C22×C1111yescharacteristic
203C2×C22⋊C4C22×C1111yescharacteristic
204C2×C22⋊C4C22×C1111yescharacteristic
205C2×C22⋊C4C22×C1111yescharacteristic
206C2×C42C22×C1111yescharacteristic
207C2×C42C22×C1111yescharacteristic
208#95C22×C1111yescharacteristic
209#95C22×C1111yescharacteristic
210#95C22×C1111yescharacteristic
211#95C22×C1111yescharacteristic
212#95C22×C1111yescharacteristic
213#95C22×C1111yescharacteristic
214#95C22×C1111yescharacteristic
215#95C22×C1111yescharacteristic
216#95C22×C1111yescharacteristic
217#95C22×C1111yescharacteristic
218#95C22×C1111yescharacteristic
219#95C22×C1111yescharacteristic
220#95C22×C1111yescharacteristic
221#95C22×C1111yescharacteristic
222C2×C11—42no—
223C2×C11#53811yescharacteristic
224C2×C11#53811yescharacteristic
225C2×C11#54411yescharacteristic
226C2×C11#55411yescharacteristic
227C2×C11#55411yescharacteristic
228C2×C11#55611yescharacteristic
229C2×C11#56211yescharacteristic
230C24C23×C1111yescharacteristic
231C2×Q8—22no—
232C2×Q8—41no—
233C2×Q8—41no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4C23×C1111yescharacteristic
238C22×C4C23×C1111yescharacteristic
239C22×C4C23×C1111yescharacteristic
240C22×C4C23×C1111yescharacteristic
241C22×C4C23×C1111yescharacteristic
242C22×C4C23×C1111yescharacteristic
243C22×C4C23×C1111yescharacteristic
244C22×C4C23×C1111yescharacteristic
245C22×C4C23×C1111yescharacteristic
246C22×C4C23×C1111yescharacteristic
247C22×C4C23×C1111yescharacteristic
248C22×C4C23×C1111yescharacteristic
249C22×C4C23×C1111yescharacteristic
250C22×C4C23×C1111yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C22⋊C4—22no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4Q8×C1114yescomplemented
268C42—41no—
269C42—41no—
270C11#278811yescharacteristic, direct product factor, Sylow
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23C2×Q8×C1112yes—
278C23C24×C1111yescharacteristic
279Q8—44no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—44no—
319C2×C4C2×Q8×C1112yes—
320C2×C4C2×Q8×C1112yes—
321C2×C4C11×#4112yes—
322C2×C4C11×#4112yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×Q8×C1111yescharacteristic
331C22C2×C11×#4111yescharacteristic
332C22C2×C11×#4111yescharacteristic
333C22C11×H(5,𝔽2)11yescharacteristic
334C22C11×H(5,𝔽2)11yescharacteristic
335C22C11×H(5,𝔽2)11yescharacteristic
336C22C11×2−1+411yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C2—42no—
352C2C11×#53811yescharacteristic
353C2C11×#53811yescharacteristic
354C2C11×#54411yescharacteristic
355C2C11×#55411yescharacteristic
356C2C11×#55411yescharacteristic
357C2C11×#55611yescharacteristic
358C2C11×#56211yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC24×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#400C2semidirect
2. C11×#400C2semidirect
3. C11×#398C2semidirect
5. C11×#395C2semidirect
7. C11×#391C2semidirect
8. C11×#389C2semidirect
9. C11×#389C2semidirect
12. C11×#387C2semidirect
88. C11×C22⋊C4Q8semidirect
91. #2788C11direct (N × H)
144. #400C2×C11semidirect
145. #400C2×C11semidirect
146. #398C2×C11semidirect
148. #395C2×C11semidirect
150. #391C2×C11semidirect
151. #389C2×C11semidirect
152. #389C2×C11semidirect
155. #387C2×C11semidirect
267. C22⋊C4Q8×C11semidirect
270. C11#2788direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#4002
C11×#3982
C11×#3962
C11×#3952
C11×#3932
C11×#3912
C11×#3892
C11×#3882
C11×#3872
C11×#3852
C11×#3802
#278811