Finite Group Databasebeta

← C11×#23658 #14600851

Subgroups — C11×#23658 #14600851

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C212yesmaximal
2C11×#2296C211yesmaximal, characteristic
3C2×C11×#384C211yesmaximal, characteristic
4C11×#2084C214yesmaximal, complemented
5C11×#2083C214yesmaximal, complemented
6C11×#1736C212yesmaximal
7C11×#1728C211yesmaximal, characteristic
8C22×C11×M16C2212yes—
9C2×C11×#117C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C11×C4⋊C4—22no—
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2211yescharacteristic
14C11×#428—28no—
15C2×C11×#107C2214yes—
16C2×C11×#106C2214yes—
17C11×#389C2212yes—
18C11×#389C2212yes—
19C11×#385—22no—
20C11×#384—21no—
21C11×#384—21no—
22C11×#384C2214yes—
23C4×C11×C4⋊C4—21no—
24C4×C11×C4⋊C4—21no—
25C11×#340C2218yes—
26C11×#336C2214yes—
27C23×C4×C11—22no—
28C23×C4×C11D412yes—
29C23×C4×C11C2311yescharacteristic
30C2×C11×M16—24no—
31C2×C11×M16—24no—
32C2×C11×M16Q818yes—
33C22×C8×C11C2314yes—
34C11×#117—22no—
35C11×#117—24no—
36C11×#117D414yes—
37C2×C11×C4⋊C4—24no—
38C2×C11×C4⋊C4—24no—
39C2×C11×C4⋊C4—24no—
40C2×C11×C4⋊C4—24no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—48no—
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C4⋊C4C2314yes—
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11—24no—
53C2×C42×C11—21no—
54C2×C42×C11D411yescharacteristic
55C2×C42×C11D411yescharacteristic
56C2×C42×C11C2312yes—
57C11×#107—28no—
58C11×#106—28no—
59C11×#95—22no—
60C11×#95—22no—
61#23658C1111yesmaximal, characteristic, direct product factor, Sylow
62C24×C11C2×D411yescharacteristic
63C22×C4×C11—24no—
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—24no—
70C22×C4×C11—48no—
71C22×C4×C11—44no—
72C22×C4×C11C2×D412yes—
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×Q814yes—
77C22×C4×C11#4112yes—
78C22×C4×C11#4114yes—
79C22×C4×C11C2411yescharacteristic
80C11×M16—216no—
81C2×C8×C11—24no—
82C2×C8×C11—24no—
83C2×C8×C11C2×Q818yes—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—24no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—48no—
90C11×C4⋊C4—44no—
91C11×C4⋊C4—44no—
92C11×C4⋊C4—48no—
93C11×C4⋊C4—44no—
94C11×C4⋊C4C2×D412yes—
95C11×C4⋊C4C2×D412yes—
96C11×C22⋊C4—24no—
97C11×C22⋊C4—42no—
98C42×C11—24no—
99C42×C11—22no—
100C42×C11—22no—
101C42×C11—24no—
102C42×C11—42no—
103C2×#428C2×C1112yes—
104#2296C2×C1111yescharacteristic
105C2×#384C2×C1111yescharacteristic
106#2084C2×C1114yescomplemented
107#2083C2×C1114yescomplemented
108#1736C2×C1112yes—
109#1728C2×C1111yescharacteristic
110C23×C11—22no—
111C23×C11—22no—
112C23×C11#12112yes—
113C23×C11#12312yes—
114C23×C11C4⋊Q812yes—
115C23×C11C22×D411yescharacteristic
116C2×C4×C11—216no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—44no—
126C2×C4×C11—42no—
127C2×C4×C11—48no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—88no—
131C2×C4×C11#12112yes—
132C2×C4×C11C22⋊Q818yes—
133C2×C4×C11#12312yes—
134C2×C4×C11#12518yes—
135C2×C4×C11C4⋊Q812yes—
136C2×C4×C11AGL(1,ℤ/8)14yes—
137C2×C4×C11#13714yes—
138C2×C4×C11C22×D411yescharacteristic
139C2×C4×C11C22×Q812yes—
140C2×C4×C11C2×#4112yes—
141C2×C4×C11C2×#4111yescharacteristic
142C8×C11—28no—
143C22×M16C22×C1112yes—
144C2×#117C22×C1111yescharacteristic
145C2×#117C22×C1111yescharacteristic
146C22×C4⋊C4—22no—
147C22×C4⋊C4C22×C1112yes—
148C22×C42C22×C1111yescharacteristic
149#428—28no—
150C2×#107C22×C1114yes—
151C2×#106C22×C1114yes—
152#389C22×C1112yes—
153#389C22×C1112yes—
154#385—22no—
155#384—21no—
156#384—21no—
157#384C22×C1114yes—
158C4×C4⋊C4—21no—
159C4×C4⋊C4—21no—
160#340C22×C1118yes—
161#336C22×C1114yes—
162C22×C11—24no—
163C22×C11—24no—
164C22×C11—22no—
165C22×C11—22no—
166C22×C11#39814yes—
167C22×C11C2×#12111yescharacteristic
168C22×C11C2×#12311yescharacteristic
169C22×C11C2×C4⋊Q811yescharacteristic
170C22×C11C2×AGL(1,ℤ/8)12yes—
171C22×C11C2×#13712yes—
172C4×C11—24no—
173C4×C11—24no—
174C4×C11—42no—
175C4×C11—42no—
176C4×C11—82no—
177C4×C11—84no—
178C4×C11#39814yes—
179C4×C11C2×C22⋊Q812yes—
180C4×C11C2×#12512yes—
181C23×C4—22no—
182C23×C4D4×C1112yes—
183C23×C4C23×C1111yescharacteristic
184C2×M16—24no—
185C2×M16—24no—
186C2×M16Q8×C1118yes—
187C22×C8C23×C1114yes—
188#117—22no—
189#117—24no—
190#117D4×C1114yes—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—48no—
199C2×C4⋊C4C23×C1114yes—
200C2×C4⋊C4C23×C1112yes—
201C2×C4⋊C4C23×C1111yescharacteristic
202C2×C4⋊C4C23×C1111yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C42—21no—
206C2×C42—24no—
207C2×C42—21no—
208C2×C42D4×C1111yescharacteristic
209C2×C42D4×C1111yescharacteristic
210C2×C42C23×C1112yes—
211#107—28no—
212#106—28no—
213#95—22no—
214#95—22no—
215C2×C11—24no—
216C2×C11C2×#39811yescharacteristic
217C2×C11#303811yescharacteristic
218C2×C11#303911yescharacteristic
219C2×C11#309212yes—
220C2×C11#316512yes—
221C24C2×D4×C1111yescharacteristic
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—48no—
230C22×C4—44no—
231C22×C4C2×D4×C1112yes—
232C22×C4C2×D4×C1112yes—
233C22×C4C2×D4×C1111yescharacteristic
234C22×C4C2×D4×C1112yes—
235C22×C4C2×Q8×C1114yes—
236C22×C4C11×#4112yes—
237C22×C4C11×#4114yes—
238C22×C4C24×C1111yescharacteristic
239M16—216no—
240C2×C8—24no—
241C2×C8—24no—
242C2×C8C2×Q8×C1118yes—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—24no—
246C4⋊C4—24no—
247C4⋊C4—24no—
248C4⋊C4—48no—
249C4⋊C4—44no—
250C4⋊C4—48no—
251C4⋊C4—44no—
252C4⋊C4—44no—
253C4⋊C4C2×D4×C1112yes—
254C4⋊C4C2×D4×C1112yes—
255C22⋊C4—24no—
256C22⋊C4—42no—
257C42—24no—
258C42—22no—
259C42—22no—
260C42—24no—
261C42—42no—
262C11#2365811yescharacteristic, direct product factor, Sylow
263C23—22no—
264C23—22no—
265C23C11×#12112yes—
266C23C11×#12312yes—
267C23C11×C4⋊Q812yes—
268C23C22×D4×C1111yescharacteristic
269C2×C4—216no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—42no—
280C2×C4—48no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—88no—
284C2×C4C11×#12112yes—
285C2×C4C11×C22⋊Q818yes—
286C2×C4C11×#12312yes—
287C2×C4C11×#12518yes—
288C2×C4C11×C4⋊Q812yes—
289C2×C4C11×AGL(1,ℤ/8)14yes—
290C2×C4C11×#13714yes—
291C2×C4C22×D4×C1111yescharacteristic
292C2×C4C22×Q8×C1112yes—
293C2×C4C2×C11×#4112yes—
294C2×C4C2×C11×#4111yescharacteristic
295C8—28no—
296C22—24no—
297C22—22no—
298C22—22no—
299C22—24no—
300C22C11×#39814yes—
301C22C2×C11×#12111yescharacteristic
302C22C2×C11×#12311yescharacteristic
303C22C2×C11×C4⋊Q811yescharacteristic
304C22C2×C11×AGL(1,ℤ/8)12yes—
305C22C2×C11×#13712yes—
306C4—24no—
307C4—24no—
308C4—42no—
309C4—42no—
310C4—84no—
311C4—82no—
312C4C11×#39814yes—
313C4C2×C11×C22⋊Q812yes—
314C4C2×C11×#12512yes—
315C2—24no—
316C2C2×C11×#39811yescharacteristic
317C2C11×#303811yescharacteristic
318C2C11×#303911yescharacteristic
319C2C11×#309212yes—
320C2C11×#316512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2084C2semidirect
5. C11×#2083C2semidirect
61. #23658C11direct (N × H)
106. #2084C2×C11semidirect
107. #2083C2×C11semidirect
262. C11#23658direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C11×#22962
C2×C11×#3842
C11×#20842
C11×#20832
C11×#17362
C11×#17282
#2365811