Finite Group Databasebeta

← C11×#2774 #13065612

Subgroups — C11×#2774 #13065612

Order 1408.

368 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#400C211yesmaximal, characteristic
2C11×#400C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic
4C11×#398C211yesmaximal, characteristic
5C11×#395C211yesmaximal, characteristic
6C11×#395C211yesmaximal, characteristic
7C11×#391C211yesmaximal, characteristic
8C11×#389C211yesmaximal, characteristic
9C11×#389C211yesmaximal, characteristic
10C11×#389C211yesmaximal, characteristic
11C11×#387C211yesmaximal, characteristic
12C11×#387C211yesmaximal, characteristic
13C11×#387C211yesmaximal, characteristic
14C11×#387C211yesmaximal, 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×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C42×C11C2211yescharacteristic
31C2×C42×C11C2211yescharacteristic
32C2×C42×C11C2211yescharacteristic
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—41no—
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—41no—
74C11×C4⋊C4—41no—
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⋊C4Q814yescomplemented
82C42×C11—22no—
83C42×C11—41no—
84C42×C11—41no—
85#2774C1111yesmaximal, characteristic, direct product factor, Sylow
86C23×C11C2411yescharacteristic
87Q8×C11—44no—
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—21no—
127C2×C4×C11—21no—
128C2×C4×C11C2×Q812yes—
129C2×C4×C11C2×Q812yes—
130C2×C4×C11C2×Q812yes—
131C2×C4×C11#4112yes—
132C2×C4×C11#4112yes—
133#400C2×C1111yescharacteristic
134#400C2×C1111yescharacteristic
135#400C2×C1111yescharacteristic
136#398C2×C1111yescharacteristic
137#395C2×C1111yescharacteristic
138#395C2×C1111yescharacteristic
139#391C2×C1111yescharacteristic
140#389C2×C1111yescharacteristic
141#389C2×C1111yescharacteristic
142#389C2×C1111yescharacteristic
143#387C2×C1111yescharacteristic
144#387C2×C1111yescharacteristic
145#387C2×C1111yescharacteristic
146#387C2×C1111yescharacteristic
147#382C2×C1111yescharacteristic
148C22×C11C22×Q811yescharacteristic
149C22×C11C2×#4111yescharacteristic
150C22×C11C2×#4111yescharacteristic
151C22×C11H(5,𝔽2)11yescharacteristic
152C22×C11H(5,𝔽2)11yescharacteristic
153C22×C112−1+411yescharacteristic
154C22×C112−1+411yescharacteristic
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—22no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C22×Q8C22×C1111yescharacteristic
171C2×C4⋊C4C22×C1111yescharacteristic
172C2×C4⋊C4C22×C1111yescharacteristic
173C2×C4⋊C4C22×C1111yescharacteristic
174C2×C4⋊C4C22×C1111yescharacteristic
175C2×C4⋊C4C22×C1111yescharacteristic
176C2×C4⋊C4C22×C1111yescharacteristic
177C2×C4⋊C4C22×C1111yescharacteristic
178C2×C4⋊C4C22×C1111yescharacteristic
179C2×C4⋊C4C22×C1111yescharacteristic
180C2×C4⋊C4C22×C1111yescharacteristic
181C2×C4⋊C4C22×C1111yescharacteristic
182C2×C4⋊C4C22×C1111yescharacteristic
183C2×C4⋊C4C22×C1111yescharacteristic
184C2×C42C22×C1111yescharacteristic
185C2×C42C22×C1111yescharacteristic
186C2×C42C22×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
201#95C22×C1111yescharacteristic
202#95C22×C1111yescharacteristic
203#95C22×C1111yescharacteristic
204#95C22×C1111yescharacteristic
205C2×C11#53811yescharacteristic
206C2×C11#54211yescharacteristic
207C2×C11#54411yescharacteristic
208C2×C11#55211yescharacteristic
209C2×C11#55411yescharacteristic
210C2×C11#55711yescharacteristic
211C2×C11#56311yescharacteristic
212C2×Q8—22no—
213C2×Q8—41no—
214C2×Q8—41no—
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
226C22×C4C23×C1111yescharacteristic
227C22×C4C23×C1111yescharacteristic
228C22×C4C23×C1111yescharacteristic
229C22×C4C23×C1111yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4Q8×C1114yescomplemented
243C42—22no—
244C42—41no—
245C42—41no—
246C11#277411yescharacteristic, direct product factor, Sylow
247C23C24×C1111yescharacteristic
248Q8—44no—
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×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4C2×Q8×C1112yes—
290C2×C4C2×Q8×C1112yes—
291C2×C4C2×Q8×C1112yes—
292C2×C4C11×#4112yes—
293C2×C4C11×#4112yes—
294C22C22×Q8×C1111yescharacteristic
295C22C2×C11×#4111yescharacteristic
296C22C2×C11×#4111yescharacteristic
297C22C11×H(5,𝔽2)11yescharacteristic
298C22C11×H(5,𝔽2)11yescharacteristic
299C22C11×2−1+411yescharacteristic
300C22C11×2−1+411yescharacteristic
301C4—22no—
302C4—22no—
303C4—22no—
304C4—22no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C2C11×#53811yescharacteristic
317C2C11×#54211yescharacteristic
318C2C11×#54411yescharacteristic
319C2C11×#55211yescharacteristic
320C2C11×#55411yescharacteristic
321C2C11×#55711yescharacteristic
322C2C11×#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. C11×C4⋊C4Q8semidirect
85. #2774C11direct (N × H)
242. C4⋊C4Q8×C11semidirect
246. C11#2774direct (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×#3952
C11×#3912
C11×#3892
C11×#3872
C11×#3822
#277411