Finite Group Databasebeta

← C11×#2762 #13065600

Subgroups — C11×#2762 #13065600

Order 1408.

352 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#401C211yesmaximal, characteristic
2C11×#400C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic
4C11×#400C211yesmaximal, characteristic
5C11×#398C211yesmaximal, characteristic
6C11×#395C211yesmaximal, characteristic
7C11×#391C211yesmaximal, characteristic
8C11×#391C211yesmaximal, characteristic
9C11×#387C211yesmaximal, characteristic
10C11×#387C211yesmaximal, characteristic
11C11×#387C211yesmaximal, characteristic
12C11×#387C211yesmaximal, characteristic
13C11×#387C211yesmaximal, characteristic
14C11×#383C211yesmaximal, characteristic
15C11×#382C211yesmaximal, characteristic
16C22×Q8×C11C2211yescharacteristic
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×C42×C11C2211yescharacteristic
27C2×C42×C11C2211yescharacteristic
28C2×C42×C11C2211yescharacteristic
29C11×#95C2211yescharacteristic
30C11×#95C2211yescharacteristic
31C11×#95C2211yescharacteristic
32C11×#95C2211yescharacteristic
33C11×#95C2211yescharacteristic
34C11×#95C2211yescharacteristic
35C11×#95C2211yescharacteristic
36C11×#95C2211yescharacteristic
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
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11—41no—
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
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C11×C4⋊C4—22no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C42×C11—22no—
79C42×C11—22no—
80C42×C11—41no—
81#2762C1111yesmaximal, characteristic, direct product factor, Sylow
82C23×C11C2411yescharacteristic
83Q8×C11—44no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
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#4112yes—
127C2×C4×C11#4112yes—
128C2×C4×C11#4112yes—
129#401C2×C1111yescharacteristic
130#400C2×C1111yescharacteristic
131#400C2×C1111yescharacteristic
132#400C2×C1111yescharacteristic
133#398C2×C1111yescharacteristic
134#395C2×C1111yescharacteristic
135#391C2×C1111yescharacteristic
136#391C2×C1111yescharacteristic
137#387C2×C1111yescharacteristic
138#387C2×C1111yescharacteristic
139#387C2×C1111yescharacteristic
140#387C2×C1111yescharacteristic
141#387C2×C1111yescharacteristic
142#383C2×C1111yescharacteristic
143#382C2×C1111yescharacteristic
144C22×C11C2×#4111yescharacteristic
145C22×C11C2×#4111yescharacteristic
146C22×C11C2×#4111yescharacteristic
147C22×C11H(5,𝔽2)11yescharacteristic
148C22×C112−1+411yescharacteristic
149C22×C112−1+411yescharacteristic
150C22×C112−1+411yescharacteristic
151C4×C11—22no—
152C4×C11—22no—
153C4×C11—22no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C22×Q8C22×C1111yescharacteristic
167C2×C4⋊C4C22×C1111yescharacteristic
168C2×C4⋊C4C22×C1111yescharacteristic
169C2×C4⋊C4C22×C1111yescharacteristic
170C2×C4⋊C4C22×C1111yescharacteristic
171C2×C4⋊C4C22×C1111yescharacteristic
172C2×C4⋊C4C22×C1111yescharacteristic
173C2×C4⋊C4C22×C1111yescharacteristic
174C2×C4⋊C4C22×C1111yescharacteristic
175C2×C4⋊C4C22×C1111yescharacteristic
176C2×C42C22×C1111yescharacteristic
177C2×C42C22×C1111yescharacteristic
178C2×C42C22×C1111yescharacteristic
179#95C22×C1111yescharacteristic
180#95C22×C1111yescharacteristic
181#95C22×C1111yescharacteristic
182#95C22×C1111yescharacteristic
183#95C22×C1111yescharacteristic
184#95C22×C1111yescharacteristic
185#95C22×C1111yescharacteristic
186#95C22×C1111yescharacteristic
187#95C22×C1111yescharacteristic
188#95C22×C1111yescharacteristic
189#95C22×C1111yescharacteristic
190#95C22×C1111yescharacteristic
191#95C22×C1111yescharacteristic
192#95C22×C1111yescharacteristic
193#95C22×C1111yescharacteristic
194#95C22×C1111yescharacteristic
195#95C22×C1111yescharacteristic
196#95C22×C1111yescharacteristic
197#95C22×C1111yescharacteristic
198#95C22×C1111yescharacteristic
199#95C22×C1111yescharacteristic
200#95C22×C1111yescharacteristic
201C2×C11#54111yescharacteristic
202C2×C11#54111yescharacteristic
203C2×C11#54211yescharacteristic
204C2×C11#55111yescharacteristic
205C2×C11#55211yescharacteristic
206C2×C11#55611yescharacteristic
207C2×C11#56311yescharacteristic
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C22×C4C23×C1111yescharacteristic
212C22×C4C23×C1111yescharacteristic
213C22×C4C23×C1111yescharacteristic
214C22×C4C23×C1111yescharacteristic
215C22×C4C23×C1111yescharacteristic
216C22×C4C23×C1111yescharacteristic
217C22×C4C23×C1111yescharacteristic
218C22×C4C23×C1111yescharacteristic
219C22×C4C23×C1111yescharacteristic
220C22×C4C23×C1111yescharacteristic
221C22×C4C23×C1111yescharacteristic
222C22×C4C23×C1111yescharacteristic
223C22×C4C23×C1111yescharacteristic
224C22×C4C23×C1111yescharacteristic
225C22×C4C23×C1111yescharacteristic
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C42—22no—
236C42—22no—
237C42—41no—
238C11#276211yescharacteristic, direct product factor, Sylow
239C23C24×C1111yescharacteristic
240Q8—44no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
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×C4C11×#4112yes—
284C2×C4C11×#4112yes—
285C2×C4C11×#4112yes—
286C22C2×C11×#4111yescharacteristic
287C22C2×C11×#4111yescharacteristic
288C22C2×C11×#4111yescharacteristic
289C22C11×H(5,𝔽2)11yescharacteristic
290C22C11×2−1+411yescharacteristic
291C22C11×2−1+411yescharacteristic
292C22C11×2−1+411yescharacteristic
293C4—22no—
294C4—22no—
295C4—22no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C2C11×#54111yescharacteristic
309C2C11×#54111yescharacteristic
310C2C11×#54211yescharacteristic
311C2C11×#55111yescharacteristic
312C2C11×#55211yescharacteristic
313C2C11×#55611yescharacteristic
314C2C11×#56311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C24
commutator, Frattini, cosocleC23C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
81. #2762C11direct (N × H)
238. C11#2762direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#4012
C11×#4002
C11×#3982
C11×#3952
C11×#3912
C11×#3872
C11×#3832
C11×#3822
#276211