Finite Group Databasebeta

← C11×#8936 #14586129

Subgroups — C11×#8936 #14586129

Order 2816.

356 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2986C211yesmaximal, characteristic
2C11×#1994C211yesmaximal, characteristic
3C11×#1574C211yesmaximal, characteristic
4C11×#1574C211yesmaximal, characteristic
5C11×#1544C211yesmaximal, characteristic
6C11×#1276C211yesmaximal, characteristic
7C11×#1276C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#446—21no—
10C11×#446—21no—
11C8×Q8×C11—21no—
12C8×Q8×C11—21no—
13C11×#433—22no—
14C11×#431C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C11×#431C2211yescharacteristic
18C11×#423C2211yescharacteristic
19C43×C11C2211yescharacteristic
20C11×#339—22no—
21C11×#335—21no—
22C11×#335—21no—
23C11×#334—21no—
24C11×#334—21no—
25C11×#332C411yescharacteristic, complemented
26C11×#332C411yescharacteristic, complemented
27C11×#332C411yescharacteristic, complemented
28C11×#332C411yescharacteristic, complemented
29C2×C11×M16—21no—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×#125Q812yes—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C11×#117D412yes—
38C2×C42×C11—21no—
39C2×C42×C11—21no—
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C11×C4⋊C8—22no—
43C11×C4⋊C8—22no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8C2×C411yescharacteristic
47C11×C4⋊C8C2×C411yescharacteristic
48C11×C4⋊C8C2×C411yescharacteristic
49C11×C4⋊C8C2×C411yescharacteristic
50C11×C4⋊C8D411yescharacteristic
51C11×C4⋊C8D411yescharacteristic
52C11×C4⋊C8D411yescharacteristic
53C11×C4⋊C8D411yescharacteristic
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#97—22no—
59C4×C8×C11—22no—
60C4×C8×C11—21no—
61C4×C8×C11—21no—
62C4×C8×C11—21no—
63C4×C8×C11—21no—
64#8936C1111yesmaximal, characteristic, direct product factor, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C11×M16—42no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11—21no—
79C2×C8×C11—21no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4C4⋊C412yes—
86C11×C4⋊C4C4⋊C412yes—
87C11×C22⋊C4—22no—
88C42×C11—22no—
89C42×C11—22no—
90C42×C11—22no—
91C42×C11—22no—
92C42×C11—41no—
93C42×C11—41no—
94C42×C11—41no—
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×Q811yescharacteristic
99#2986C2×C1111yescharacteristic
100#1994C2×C1111yescharacteristic
101#1574C2×C1111yescharacteristic
102#1574C2×C1111yescharacteristic
103#1544C2×C1111yescharacteristic
104#1276C2×C1111yescharacteristic
105#1276C2×C1111yescharacteristic
106C23×C11#12311yescharacteristic
107Q8×C11—41no—
108Q8×C11—41no—
109Q8×C11—41no—
110Q8×C11—41no—
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—22no—
118C2×C4×C11—22no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11C2×C4⋊C411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C8×C11—41no—
129C8×C11—41no—
130C8×C11—41no—
131C8×C11—41no—
132C8×C11—41no—
133C8×C11—41no—
134C8×C11—41no—
135C8×C11—41no—
136C8×C11—81no—
137#533C22×C1111yescharacteristic
138#446—21no—
139#446—21no—
140C8×Q8—21no—
141C8×Q8—21no—
142#433—22no—
143#431C22×C1111yescharacteristic
144#431C22×C1111yescharacteristic
145#431C22×C1111yescharacteristic
146#431C22×C1111yescharacteristic
147#423C22×C1111yescharacteristic
148C43C22×C1111yescharacteristic
149#339—22no—
150#335—21no—
151#335—21no—
152#334—21no—
153#334—21no—
154#332C4×C1111yescharacteristic, complemented
155#332C4×C1111yescharacteristic, complemented
156#332C4×C1111yescharacteristic, complemented
157#332C4×C1111yescharacteristic, complemented
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#38511yescharacteristic
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—44no—
166C4×C11—42no—
167C4×C11—42no—
168C4×C11#44311yescharacteristic
169C4×C11#44311yescharacteristic
170C4×C11#44411yescharacteristic
171C4×C11#44411yescharacteristic
172C4×C11#45411yescharacteristic
173C4×C11#45611yescharacteristic
174C2×M16—21no—
175C4⋊Q8C2×C4×C1111yescharacteristic
176C4⋊Q8C2×C4×C1111yescharacteristic
177#125Q8×C1112yes—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C4×Q8—21no—
181C4×Q8—21no—
182#117D4×C1112yes—
183C2×C42—21no—
184C2×C42—21no—
185C2×C42—21no—
186C2×C42C23×C1111yescharacteristic
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191C4⋊C8C2×C4×C1111yescharacteristic
192C4⋊C8C2×C4×C1111yescharacteristic
193C4⋊C8C2×C4×C1111yescharacteristic
194C4⋊C8C2×C4×C1111yescharacteristic
195C4⋊C8D4×C1111yescharacteristic
196C4⋊C8D4×C1111yescharacteristic
197C4⋊C8D4×C1111yescharacteristic
198C4⋊C8D4×C1111yescharacteristic
199C22⋊C8—21no—
200C22⋊C8—21no—
201C22⋊C8—21no—
202C22⋊C8—21no—
203#97—22no—
204C4×C8—22no—
205C4×C8—21no—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—21no—
209C2×C11—41no—
210C2×C11#185711yescharacteristic
211C2×C11#186611yescharacteristic
212C2×C11#186611yescharacteristic
213C2×Q8—21no—
214C2×Q8—21no—
215C22×C4—41no—
216C22×C4C2×D4×C1111yescharacteristic
217C22×C4C11×#4111yescharacteristic
218C22×C4C11×#4111yescharacteristic
219M16—42no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4C11×C4⋊C412yes—
234C4⋊C4C11×C4⋊C412yes—
235C22⋊C4—22no—
236C42—22no—
237C42—22no—
238C42—22no—
239C42—22no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42C22×C4×C1111yescharacteristic
244C42C2×D4×C1111yescharacteristic
245C42C2×D4×C1111yescharacteristic
246C42C2×Q8×C1111yescharacteristic
247C11#893611yescharacteristic, direct product factor, Sylow
248C23C11×#12311yescharacteristic
249Q8—41no—
250Q8—41no—
251Q8—41no—
252Q8—41no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4C2×C11×C4⋊C411yescharacteristic
265C2×C4C4×D4×C1111yescharacteristic
266C2×C4C4×D4×C1111yescharacteristic
267C2×C4C11×#12011yescharacteristic
268C2×C4C11×C22⋊Q811yescharacteristic
269C2×C4C11×C22⋊Q811yescharacteristic
270C8—41no—
271C8—41no—
272C8—41no—
273C8—41no—
274C8—41no—
275C8—41no—
276C8—41no—
277C8—41no—
278C8—81no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22C11×#38511yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—44no—
287C4—42no—
288C4—42no—
289C4C11×#44311yescharacteristic
290C4C11×#44311yescharacteristic
291C4C11×#44411yescharacteristic
292C4C11×#44411yescharacteristic
293C4C11×#45411yescharacteristic
294C4C11×#45611yescharacteristic
295C2—41no—
296C2C11×#185711yescharacteristic
297C2C11×#186611yescharacteristic
298C2C11×#186611yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
socleC22×C11#385
prime radicalC23×C11#123
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
25. C11×#332C4semidirect
26. C11×#332C4semidirect
27. C11×#332C4semidirect
28. C11×#332C4semidirect
64. #8936C11direct (N × H)
154. #332C4×C11semidirect
155. #332C4×C11semidirect
156. #332C4×C11semidirect
157. #332C4×C11semidirect
247. C11#8936direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29862
C11×#19942
C11×#15742
C11×#15442
C11×#12762
#893611