Finite Group Databasebeta

← C11×#23831 #14601024

Subgroups — C11×#23831 #14601024

Order 2816.

682 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×#2330C211yesmaximal, characteristic
2C11×#2327C211yesmaximal, characteristic
3C11×#2101C212yesmaximal
4C11×#2072C212yesmaximal
5C11×#2043C212yesmaximal
6C11×#2026C212yesmaximal
7C11×#1763C212yesmaximal
8C4×C11×#103C212yesmaximal
9C11×#1746C211yesmaximal, characteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#125C2211yescharacteristic
12C2×C4×Q8×C11C2212yes—
13C2×C11×#103C2212yes—
14C2×C11×#103C2212yes—
15C2×C11×#103C2212yes—
16C2×C11×#103C2212yes—
17C2×C11×#97C2211yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19C11×#391C2212yes—
20C11×#389—22no—
21C11×#389C2212yes—
22C11×#387—22no—
23C11×#387—22no—
24C11×#387—22no—
25C11×#384C2211yescharacteristic
26C11×#382C2211yescharacteristic
27C4×C11×C4⋊C4C2212yes—
28C11×#376C2211yescharacteristic
29C11×#340C2212yes—
30C11×#340C2212yes—
31C11×#340C2212yes—
32C11×#340C2212yes—
33C11×#336C2212yes—
34C11×#336C2212yes—
35C22×Q8×C11C2312yes—
36C22×C8×C11C2312yes—
37C22×C8×C11C2312yes—
38C11×C4⋊Q8—24no—
39C11×#125—24no—
40C4×Q8×C11—24no—
41C4×Q8×C11—24no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11—22no—
52C2×C42×C11—22no—
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C11×#103—24no—
57C11×#103—24no—
58C11×#103—24no—
59C11×#103—24no—
60C11×#97—22no—
61C4×C8×C11—22no—
62C11×#95—22no—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95—22no—
66C11×#95—24no—
67C11×#95D412yes—
68C11×#95D412yes—
69#23831C1111yesmaximal, characteristic, direct product factor, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—22no—
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11#4114yes—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2411yescharacteristic
85C2×C8×C11—22no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C11×C4⋊C4—28no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—44no—
100C11×C4⋊C4—82no—
101C11×C4⋊C4—82no—
102C11×C4⋊C4#4114yes—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—44no—
106C42×C11—82no—
107C42×C11#4112yes—
108C42×C11#4112yes—
109#2330C2×C1111yescharacteristic
110#2327C2×C1111yescharacteristic
111#2101C2×C1112yes—
112#2072C2×C1112yes—
113#2043C2×C1112yes—
114#2026C2×C1112yes—
115#1763C2×C1112yes—
116C4×#103C2×C1112yes—
117#1746C2×C1111yescharacteristic
118C23×C11C22×D411yescharacteristic
119Q8×C11—24no—
120Q8×C11—24no—
121Q8×C11—42no—
122Q8×C11—42no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11#12414yes—
145C2×C4×C11C2×#4112yes—
146C2×C4×C11C2×#4112yes—
147C2×C4×C11C2×#4111yescharacteristic
148C2×C4×C11C2×#4111yescharacteristic
149C8×C11—42no—
150C8×C11—42no—
151C2×C4⋊Q8C22×C1111yescharacteristic
152C2×#125C22×C1111yescharacteristic
153C2×C4×Q8C22×C1112yes—
154C2×#103C22×C1112yes—
155C2×#103C22×C1112yes—
156C2×#103C22×C1112yes—
157C2×#103C22×C1112yes—
158C2×#97C22×C1111yescharacteristic
159C2×C4×C8C22×C1111yescharacteristic
160#391C22×C1112yes—
161#389—22no—
162#389C22×C1112yes—
163#387—22no—
164#387—22no—
165#387—22no—
166#384C22×C1111yescharacteristic
167#382C22×C1111yescharacteristic
168C4×C4⋊C4C22×C1112yes—
169#376C22×C1111yescharacteristic
170#340C22×C1112yes—
171#340C22×C1112yes—
172#340C22×C1112yes—
173#340C22×C1112yes—
174#336C22×C1112yes—
175#336C22×C1112yes—
176C22×C11#52511yescharacteristic
177C22×C11#52511yescharacteristic
178C22×C11C2×#12411yescharacteristic
179C22×C11#57712yes—
180C22×C11#57812yes—
181C4×C11—24no—
182C4×C11—42no—
183C4×C11—44no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—44no—
187C4×C11—82no—
188C4×C11—82no—
189C4×C11#52912yes—
190C4×C11#52912yes—
191C22×Q8C23×C1112yes—
192C22×C8C23×C1112yes—
193C22×C8C23×C1112yes—
194C4⋊Q8—24no—
195#125—24no—
196C4×Q8—24no—
197C4×Q8—24no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4C23×C1112yes—
205C2×C4⋊C4C23×C1112yes—
206C2×C4⋊C4C23×C1112yes—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42C23×C1111yescharacteristic
210C2×C42C23×C1111yescharacteristic
211C2×C42C23×C1111yescharacteristic
212#103—24no—
213#103—24no—
214#103—24no—
215#103—24no—
216#97—22no—
217C4×C8—22no—
218#95—22no—
219#95—21no—
220#95—21no—
221#95—22no—
222#95—24no—
223#95D4×C1112yes—
224#95D4×C1112yes—
225C2×C11#239811yescharacteristic
226C2×C11#312012yes—
227C2×C11#312611yescharacteristic
228C2×C11#312711yescharacteristic
229C2×C11#313712yes—
230C2×Q8—22no—
231C2×Q8—22no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8C11×#4114yes—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4C2×D4×C1111yescharacteristic
241C22×C4C2×D4×C1112yes—
242C22×C4C2×D4×C1111yescharacteristic
243C22×C4C2×D4×C1112yes—
244C22×C4C24×C1111yescharacteristic
245C2×C8—22no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—22no—
251C4⋊C4—28no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—44no—
260C4⋊C4—82no—
261C4⋊C4—82no—
262C4⋊C4C11×#4114yes—
263C42—22no—
264C42—22no—
265C42—44no—
266C42—82no—
267C42C11×#4112yes—
268C42C11×#4112yes—
269C11#2383111yescharacteristic, direct product factor, Sylow
270C23C22×D4×C1111yescharacteristic
271Q8—24no—
272Q8—24no—
273Q8—42no—
274Q8—42no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—24no—
281C2×C4—24no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4C11×#12414yes—
297C2×C4C2×C11×#4112yes—
298C2×C4C2×C11×#4112yes—
299C2×C4C2×C11×#4111yescharacteristic
300C2×C4C2×C11×#4111yescharacteristic
301C8—42no—
302C8—42no—
303C22C11×#52511yescharacteristic
304C22C11×#52511yescharacteristic
305C22C2×C11×#12411yescharacteristic
306C22C11×#57712yes—
307C22C11×#57812yes—
308C4—24no—
309C4—44no—
310C4—42no—
311C4—44no—
312C4—41no—
313C4—41no—
314C4—82no—
315C4—82no—
316C4C11×#52912yes—
317C4C11×#52912yes—
318C2C11×#239811yescharacteristic
319C2C11×#312012yes—
320C2C11×#312611yescharacteristic
321C2C11×#312711yescharacteristic
322C2C11×#313712yes—
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
69. #23831C11direct (N × H)
269. C11#23831direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23302
C11×#23272
C11×#21012
C11×#20722
C11×#20432
C11×#20262
C11×#17632
C4×C11×#1032
C11×#17462
#2383111