Finite Group Databasebeta

← C11×#2413 #13065251

Subgroups — C11×#2413 #13065251

Order 1408.

610 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#123C211yesmaximal, characteristic
2C2×C11×#123C211yesmaximal, characteristic
3C2×C11×#117C211yesmaximal, characteristic, complemented
4C22×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#398C212yesmaximal, complemented
6C11×#396C212yesmaximal, complemented
7C11×#389C212yesmaximal, complemented
8C11×#388C212yesmaximal, complemented
9C11×#386C211yesmaximal, characteristic
10C11×#385C211yesmaximal, characteristic, complemented
11C11×#381C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C23×C4×C11C2211yescharacteristic
16C11×#123—24no—
17C11×#123—24no—
18C11×#117—24no—
19C2×C11×C4⋊C4—24no—
20C2×C11×C4⋊C4C2212yes—
21C2×C11×C4⋊C4C2212yes—
22C2×C11×C4⋊C4C2212yes—
23C2×C11×C4⋊C4C2212yes—
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C4⋊C4C2212yes—
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2212yes—
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2212yes—
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C42×C11C2212yes—
35C11×#95C2212yes—
36C11×#95C2212yes—
37C11×#95C2212yes—
38C11×#95C2212yes—
39C24×C11C2311yescharacteristic
40C24×C11C2311yescharacteristic
41C2×D4×C11—22no—
42C2×D4×C11—22no—
43C2×D4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—24no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11D414yes—
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2312yes—
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2312yes—
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2312yes—
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2312yes—
61C11×C4⋊C4—24no—
62C11×C4⋊C4—24no—
63C11×C4⋊C4—24no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—24no—
67C11×C4⋊C4—24no—
68C11×C22⋊C4—22no—
69C11×C22⋊C4—22no—
70C11×C22⋊C4—22no—
71C11×C22⋊C4—22no—
72C11×C22⋊C4—24no—
73C11×C22⋊C4—24no—
74C11×C22⋊C4D414yes—
75C42×C11—24no—
76#2413C1111yesmaximal, characteristic, direct product factor, Sylow
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—22no—
82C23×C11—21no—
83C23×C11—22no—
84C23×C11C2×D412yes—
85C23×C11C2×D412yes—
86C23×C11#4112yes—
87C23×C11C2411yescharacteristic
88D4×C11—44no—
89C2×C4×C11—28no—
90C2×C4×C11—28no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—21no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—44no—
113C2×C4×C11C2×D414yes—
114C2×C4×C11C2×D412yes—
115C2×C4×C11C2×D412yes—
116C2×C4×C11#4114yes—
117C2×#123C2×C1111yescharacteristic
118C2×#123C2×C1111yescharacteristic
119C2×#117C2×C1111yescharacteristic, complemented
120C22×C4⋊C4C2×C1111yescharacteristic, complemented
121#398C2×C1112yescomplemented
122#396C2×C1112yescomplemented
123#389C2×C1112yescomplemented
124#388C2×C1112yescomplemented
125#386C2×C1111yescharacteristic
126#385C2×C1111yescharacteristic, complemented
127#381C2×C1111yescharacteristic, complemented
128C22×C11—22no—
129C22×C11—22no—
130C22×C11—24no—
131C22×C11—24no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11—41no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11#12114yes—
138C22×C11C22×D411yescharacteristic
139C22×C11C22×D411yescharacteristic
140C22×C11C2×#4111yescharacteristic
141C22×C11C2×#4112yes—
142C22×C112−1+412yes—
143C4×C11—22no—
144C4×C11—22no—
145C4×C11—24no—
146C4×C11—24no—
147C4×C11—42no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11—42no—
152C22×D4C22×C1111yescharacteristic
153C23×C4C22×C1111yescharacteristic
154C23×C4C22×C1111yescharacteristic
155C23×C4C22×C1111yescharacteristic
156#123—24no—
157#123—24no—
158#117—24no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4C22×C1112yes—
161C2×C4⋊C4C22×C1112yes—
162C2×C4⋊C4C22×C1112yes—
163C2×C4⋊C4C22×C1111yescharacteristic
164C2×C4⋊C4C22×C1112yes—
165C2×C4⋊C4C22×C1111yescharacteristic
166C2×C4⋊C4C22×C1112yes—
167C2×C22⋊C4C22×C1111yescharacteristic
168C2×C22⋊C4C22×C1111yescharacteristic
169C2×C22⋊C4C22×C1111yescharacteristic
170C2×C22⋊C4C22×C1112yes—
171C2×C22⋊C4C22×C1111yescharacteristic
172C2×C22⋊C4C22×C1112yes—
173C2×C22⋊C4C22×C1111yescharacteristic
174C2×C42C22×C1112yes—
175#95C22×C1112yes—
176#95C22×C1112yes—
177#95C22×C1112yes—
178#95C22×C1112yes—
179C2×C11—24no—
180C2×C11—81no—
181C2×C11C2×#12111yescharacteristic
182C2×C11#52511yescharacteristic
183C2×C11#53611yescharacteristic
184C2×C11#54712yes—
185C2×C11#55212yes—
186C24C23×C1111yescharacteristic
187C24C23×C1111yescharacteristic
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—24no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4D4×C1114yes—
199C22×C4C23×C1111yescharacteristic
200C22×C4C23×C1112yes—
201C22×C4C23×C1111yescharacteristic
202C22×C4C23×C1112yes—
203C22×C4C23×C1111yescharacteristic
204C22×C4C23×C1112yes—
205C22×C4C23×C1111yescharacteristic
206C22×C4C23×C1111yescharacteristic
207C22×C4C23×C1112yes—
208C4⋊C4—24no—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—24no—
214C4⋊C4—24no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—24no—
220C22⋊C4—24no—
221C22⋊C4D4×C1114yes—
222C42—24no—
223C11#241311yescharacteristic, direct product factor, Sylow
224C23—22no—
225C23—22no—
226C23—21no—
227C23—21no—
228C23—22no—
229C23—21no—
230C23—22no—
231C23C2×D4×C1112yes—
232C23C2×D4×C1112yes—
233C23C11×#4112yes—
234C23C24×C1111yescharacteristic
235D4—44no—
236C2×C4—28no—
237C2×C4—28no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—44no—
260C2×C4C2×D4×C1114yes—
261C2×C4C2×D4×C1112yes—
262C2×C4C2×D4×C1112yes—
263C2×C4C11×#4114yes—
264C22—22no—
265C22—22no—
266C22—24no—
267C22—24no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—42no—
272C22—42no—
273C22C11×#12114yes—
274C22C22×D4×C1111yescharacteristic
275C22C22×D4×C1111yescharacteristic
276C22C2×C11×#4111yescharacteristic
277C22C2×C11×#4112yes—
278C22C11×2−1+412yes—
279C4—22no—
280C4—22no—
281C4—24no—
282C4—24no—
283C4—42no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—42no—
288C2—24no—
289C2—81no—
290C2C2×C11×#12111yescharacteristic
291C2C11×#52511yescharacteristic
292C2C11×#53611yescharacteristic
293C2C11×#54712yes—
294C2C11×#55212yes—
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC22×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#117C2semidirect
4. C22×C11×C4⋊C4C2semidirect
5. C11×#398C2semidirect
6. C11×#396C2semidirect
7. C11×#389C2semidirect
8. C11×#388C2semidirect
10. C11×#385C2semidirect
11. C11×#381C2semidirect
76. #2413C11direct (N × H)
119. C2×#117C2×C11semidirect
120. C22×C4⋊C4C2×C11semidirect
121. #398C2×C11semidirect
122. #396C2×C11semidirect
123. #389C2×C11semidirect
124. #388C2×C11semidirect
126. #385C2×C11semidirect
127. #381C2×C11semidirect
223. C11#2413direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×C11×#1172
C22×C11×C4⋊C42
C11×#3982
C11×#3962
C11×#3892
C11×#3882
C11×#3862
C11×#3852
C11×#3812
#241311