Finite Group Databasebeta

← C11×#2783 #13065621

Subgroups — C11×#2783 #13065621

Order 1408.

378 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#400C211yesmaximal, characteristic, complemented
2C11×#398C211yesmaximal, characteristic, complemented
3C11×#397C211yesmaximal, characteristic
4C11×#397C211yesmaximal, characteristic
5C11×#396C211yesmaximal, characteristic
6C11×#396C211yesmaximal, characteristic
7C11×#389C211yesmaximal, characteristic, complemented
8C11×#389C211yesmaximal, characteristic, complemented
9C11×#388C211yesmaximal, characteristic
10C11×#388C211yesmaximal, characteristic
11C11×#388C211yesmaximal, characteristic
12C11×#387C211yesmaximal, characteristic, complemented
13C11×#387C211yesmaximal, characteristic, complemented
14C11×#387C211yesmaximal, characteristic, complemented
15C11×#382C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
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×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C42×C11C2211yescharacteristic
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
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C11×C4⋊C4—22no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—22no—
69C11×C4⋊C4—22no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—22no—
78C11×C22⋊C4—22no—
79C11×C22⋊C4—22no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11—22no—
85C42×C11—41no—
86C42×C11—41no—
87#2783C1111yesmaximal, characteristic, direct product factor, Sylow
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11C2411yescharacteristic
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
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#4112yes—
136C2×C4×C11#4112yes—
137C2×C4×C11#4112yes—
138#400C2×C1111yescharacteristic, complemented
139#398C2×C1111yescharacteristic, complemented
140#397C2×C1111yescharacteristic
141#397C2×C1111yescharacteristic
142#396C2×C1111yescharacteristic
143#396C2×C1111yescharacteristic
144#389C2×C1111yescharacteristic, complemented
145#389C2×C1111yescharacteristic, complemented
146#388C2×C1111yescharacteristic
147#388C2×C1111yescharacteristic
148#388C2×C1111yescharacteristic
149#387C2×C1111yescharacteristic, complemented
150#387C2×C1111yescharacteristic, complemented
151#387C2×C1111yescharacteristic, complemented
152#382C2×C1111yescharacteristic, complemented
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C2×#4111yescharacteristic
161C22×C11C2×#4111yescharacteristic
162C22×C11C2×#4111yescharacteristic
163C22×C11H(5,𝔽2)11yescharacteristic
164C22×C11H(5,𝔽2)11yescharacteristic
165C22×C112−1+411yescharacteristic
166C22×C112−1+411yescharacteristic
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—22no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C2×C4⋊C4C22×C1111yescharacteristic
182C2×C4⋊C4C22×C1111yescharacteristic
183C2×C4⋊C4C22×C1111yescharacteristic
184C2×C4⋊C4C22×C1111yescharacteristic
185C2×C4⋊C4C22×C1111yescharacteristic
186C2×C4⋊C4C22×C1111yescharacteristic
187C2×C4⋊C4C22×C1111yescharacteristic
188C2×C4⋊C4C22×C1111yescharacteristic
189C2×C4⋊C4C22×C1111yescharacteristic
190C2×C4⋊C4C22×C1111yescharacteristic
191C2×C4⋊C4C22×C1111yescharacteristic
192C2×C22⋊C4C22×C1111yescharacteristic
193C2×C22⋊C4C22×C1111yescharacteristic
194C2×C22⋊C4C22×C1111yescharacteristic
195C2×C22⋊C4C22×C1111yescharacteristic
196C2×C22⋊C4C22×C1111yescharacteristic
197C2×C22⋊C4C22×C1111yescharacteristic
198C2×C22⋊C4C22×C1111yescharacteristic
199C2×C42C22×C1111yescharacteristic
200C2×C42C22×C1111yescharacteristic
201C2×C42C22×C1111yescharacteristic
202#95C22×C1111yescharacteristic
203#95C22×C1111yescharacteristic
204#95C22×C1111yescharacteristic
205#95C22×C1111yescharacteristic
206#95C22×C1111yescharacteristic
207#95C22×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
216C2×C11—81no—
217C2×C11#53911yescharacteristic
218C2×C11#53911yescharacteristic
219C2×C11#54111yescharacteristic
220C2×C11#55311yescharacteristic
221C2×C11#55511yescharacteristic
222C2×C11#55611yescharacteristic
223C2×C11#56211yescharacteristic
224C24C23×C1111yescharacteristic
225C22×C4C23×C1111yescharacteristic
226C22×C4C23×C1111yescharacteristic
227C22×C4C23×C1111yescharacteristic
228C22×C4C23×C1111yescharacteristic
229C22×C4C23×C1111yescharacteristic
230C22×C4C23×C1111yescharacteristic
231C22×C4C23×C1111yescharacteristic
232C22×C4C23×C1111yescharacteristic
233C22×C4C23×C1111yescharacteristic
234C22×C4C23×C1111yescharacteristic
235C22×C4C23×C1111yescharacteristic
236C22×C4C23×C1111yescharacteristic
237C22×C4C23×C1111yescharacteristic
238C22×C4C23×C1111yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C42—22no—
258C42—41no—
259C42—41no—
260C11#278311yescharacteristic, direct product factor, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C24×C1111yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
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×C4C11×#4112yes—
309C2×C4C11×#4112yes—
310C2×C4C11×#4112yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C2×C11×#4111yescharacteristic
319C22C2×C11×#4111yescharacteristic
320C22C2×C11×#4111yescharacteristic
321C22C11×H(5,𝔽2)11yescharacteristic
322C22C11×H(5,𝔽2)11yescharacteristic
323C22C11×2−1+411yescharacteristic
324C22C11×2−1+411yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C2—81no—
340C2C11×#53911yescharacteristic
341C2C11×#53911yescharacteristic
342C2C11×#54111yescharacteristic
343C2C11×#55311yescharacteristic
344C2C11×#55511yescharacteristic
345C2C11×#55611yescharacteristic
346C2C11×#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×#398C2semidirect
7. C11×#389C2semidirect
8. C11×#389C2semidirect
12. C11×#387C2semidirect
13. C11×#387C2semidirect
14. C11×#387C2semidirect
15. C11×#382C2semidirect
87. #2783C11direct (N × H)
138. #400C2×C11semidirect
139. #398C2×C11semidirect
144. #389C2×C11semidirect
145. #389C2×C11semidirect
149. #387C2×C11semidirect
150. #387C2×C11semidirect
151. #387C2×C11semidirect
152. #382C2×C11semidirect
260. C11#2783direct (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×#3972
C11×#3962
C11×#3892
C11×#3882
C11×#3872
C11×#3822
#278311