Finite Group Databasebeta

← C11×#2661 #13065499

Subgroups — C11×#2661 #13065499

Order 1408.

598 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#123C211yesmaximal, characteristic, complemented
2C2×C11×#121C211yesmaximal, characteristic, complemented
3C11×#398C211yesmaximal, characteristic, complemented
4C11×#397C211yesmaximal, characteristic, complemented
5C11×#394C211yesmaximal, characteristic, complemented
6C11×#394C212yesmaximal, complemented
7C11×#392C211yesmaximal, characteristic, complemented
8C11×#392C212yesmaximal, complemented
9C11×#390C212yesmaximal, complemented
10C11×#388C212yesmaximal, complemented
11C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C22×D4×C11C2212yes—
13C22×D4×C11C2211yescharacteristic
14C22×D4×C11C2211yescharacteristic
15C22×D4×C11C2212yes—
16C23×C4×C11C2211yescharacteristic
17C11×#123—24no—
18C11×#121—24no—
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2212yes—
23C2×C11×C22⋊C4C2212yes—
24C2×C11×C22⋊C4C2212yes—
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2212yes—
29C2×C11×C22⋊C4C2212yes—
30C2×C11×C22⋊C4C2212yes—
31C2×C11×C22⋊C4C2212yes—
32C2×C42×C11C2212yes—
33C11×#95C2211yescharacteristic
34C11×#95C2211yescharacteristic
35C11×#95C2212yes—
36C11×#95C2212yes—
37C24×C11C2311yescharacteristic
38C24×C11C2312yes—
39C24×C11C2311yescharacteristic
40C2×D4×C11—24no—
41C2×D4×C11—22no—
42C2×D4×C11—22no—
43C2×D4×C11—24no—
44C2×D4×C11—42no—
45C2×D4×C11—42no—
46C2×D4×C11—42no—
47C2×D4×C11—42no—
48C2×D4×C11—42no—
49C2×D4×C11—42no—
50C22×C4×C11—42no—
51C22×C4×C11D414yescomplemented
52C22×C4×C11C2312yes—
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2312yes—
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2312yes—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—22no—
62C11×C4⋊C4—22no—
63C11×C4⋊C4—42no—
64C11×C22⋊C4—22no—
65C11×C22⋊C4—24no—
66C11×C22⋊C4—22no—
67C11×C22⋊C4—22no—
68C11×C22⋊C4—24no—
69C11×C22⋊C4—24no—
70C11×C22⋊C4—42no—
71C11×C22⋊C4—42no—
72C11×C22⋊C4—42no—
73C42×C11—42no—
74#2661C1111yesmaximal, characteristic, direct product factor, Sylow
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—21no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—21no—
91C23×C11C2×D412yes—
92C23×C11C2411yescharacteristic
93D4×C11—44no—
94D4×C11—48no—
95D4×C11—44no—
96D4×C11—48no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—44no—
115C2×C4×C11C2×D412yes—
116C2×C4×C11C2×D412yes—
117C2×C4×C11#4114yes—
118C2×#123C2×C1111yescharacteristic, complemented
119C2×#121C2×C1111yescharacteristic, complemented
120#398C2×C1111yescharacteristic, complemented
121#397C2×C1111yescharacteristic, complemented
122#394C2×C1111yescharacteristic, complemented
123#394C2×C1112yescomplemented
124#392C2×C1111yescharacteristic, complemented
125#392C2×C1112yescomplemented
126#390C2×C1112yescomplemented
127#388C2×C1112yescomplemented
128C4×C22⋊C4C2×C1111yescharacteristic, complemented
129C22×C11—22no—
130C22×C11—22no—
131C22×C11—22no—
132C22×C11—42no—
133C22×C11—42no—
134C22×C11—41no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11—41no—
138C22×C11—42no—
139C22×C11—41no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—42no—
146C22×C11C22×D411yescharacteristic
147C22×C11C2×#4112yes—
148C22×C11H(5,𝔽2)12yes—
149C22×C11H(5,𝔽2)11yescharacteristic
150C22×C11H(5,𝔽2)11yescharacteristic
151C4×C11—22no—
152C4×C11—22no—
153C4×C11—24no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11—42no—
158C4×C11—42no—
159C22×D4C22×C1112yes—
160C22×D4C22×C1111yescharacteristic
161C22×D4C22×C1111yescharacteristic
162C22×D4C22×C1112yes—
163C23×C4C22×C1111yescharacteristic
164#123—24no—
165#121—24no—
166C2×C4⋊C4C22×C1111yescharacteristic
167C2×C4⋊C4C22×C1111yescharacteristic
168C2×C4⋊C4C22×C1111yescharacteristic
169C2×C4⋊C4C22×C1112yes—
170C2×C22⋊C4C22×C1112yes—
171C2×C22⋊C4C22×C1111yescharacteristic
172C2×C22⋊C4C22×C1111yescharacteristic
173C2×C22⋊C4C22×C1111yescharacteristic
174C2×C22⋊C4C22×C1112yes—
175C2×C22⋊C4C22×C1112yes—
176C2×C22⋊C4C22×C1112yes—
177C2×C22⋊C4C22×C1112yes—
178C2×C22⋊C4C22×C1112yes—
179C2×C42C22×C1112yes—
180#95C22×C1111yescharacteristic
181#95C22×C1111yescharacteristic
182#95C22×C1112yes—
183#95C22×C1112yes—
184C2×C11—42no—
185C2×C11—82no—
186C2×C11—81no—
187C2×C11#53211yescharacteristic
188C2×C11#53411yescharacteristic
189C2×C11#53511yescharacteristic
190C2×C11#53812yes—
191C2×C11#54012yes—
192C24C23×C1111yescharacteristic
193C24C23×C1112yes—
194C24C23×C1111yescharacteristic
195C2×D4—24no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—24no—
199C2×D4—42no—
200C2×D4—42no—
201C2×D4—42no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—42no—
205C22×C4—42no—
206C22×C4D4×C1114yescomplemented
207C22×C4C23×C1112yes—
208C22×C4C23×C1111yescharacteristic
209C22×C4C23×C1112yes—
210C22×C4C23×C1111yescharacteristic
211C22×C4C23×C1111yescharacteristic
212C22×C4C23×C1111yescharacteristic
213C22×C4C23×C1111yescharacteristic
214C22×C4C23×C1112yes—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—42no—
219C22⋊C4—22no—
220C22⋊C4—24no—
221C22⋊C4—22no—
222C22⋊C4—22no—
223C22⋊C4—24no—
224C22⋊C4—24no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C42—42no—
229C11#266111yescharacteristic, direct product factor, Sylow
230C23—22no—
231C23—22no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—21no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—21no—
246C23C2×D4×C1112yes—
247C23C24×C1111yescharacteristic
248D4—44no—
249D4—48no—
250D4—44no—
251D4—48no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—44no—
270C2×C4C2×D4×C1112yes—
271C2×C4C2×D4×C1112yes—
272C2×C4C11×#4114yes—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—42no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22C22×D4×C1111yescharacteristic
291C22C2×C11×#4112yes—
292C22C11×H(5,𝔽2)12yes—
293C22C11×H(5,𝔽2)11yescharacteristic
294C22C11×H(5,𝔽2)11yescharacteristic
295C4—22no—
296C4—22no—
297C4—24no—
298C4—41no—
299C4—41no—
300C4—42no—
301C4—41no—
302C4—42no—
303C2—42no—
304C2—82no—
305C2—81no—
306C2C11×#53211yescharacteristic
307C2C11×#53411yescharacteristic
308C2C11×#53511yescharacteristic
309C2C11×#53812yes—
310C2C11×#54012yes—
subgroupG/H
center, socleC23×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
1. C2×C11×#123C2semidirect
2. C2×C11×#121C2semidirect
3. C11×#398C2semidirect
4. C11×#397C2semidirect
5. C11×#394C2semidirect
6. C11×#394C2semidirect
7. C11×#392C2semidirect
8. C11×#392C2semidirect
9. C11×#390C2semidirect
10. C11×#388C2semidirect
11. C4×C11×C22⋊C4C2semidirect
51. C22×C4×C11D4semidirect
74. #2661C11direct (N × H)
118. C2×#123C2×C11semidirect
119. C2×#121C2×C11semidirect
120. #398C2×C11semidirect
121. #397C2×C11semidirect
122. #394C2×C11semidirect
123. #394C2×C11semidirect
124. #392C2×C11semidirect
125. #392C2×C11semidirect
126. #390C2×C11semidirect
127. #388C2×C11semidirect
128. C4×C22⋊C4C2×C11semidirect
206. C22×C4D4×C11semidirect
229. C11#2661direct (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×#1212
C11×#3982
C11×#3972
C11×#3942
C11×#3922
C11×#3902
C11×#3882
C4×C11×C22⋊C42
#266111