Finite Group Databasebeta

← C11×#21906 #14599099

Subgroups — C11×#21906 #14599099

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
2C11×#1924C218yesmaximal, complemented
3C11×#1797C212yesmaximal, complemented
4C11×#1779C212yesmaximal
5C11×#1749C212yesmaximal, complemented
6C24×C4×C11C2211yescharacteristic
7C22×C11×C22⋊C4C411yescharacteristic
8C22×C11×C22⋊C4C411yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C2×C11×C4⋊C8C2214yescomplemented
12C2×C11×C22⋊C8C2214yes—
13C2×C11×C22⋊C8C2214yes—
14C2×C11×C22⋊C8C2214yes—
15C2×C11×#97C2214yescomplemented
16C4×C11×C22⋊C4C414yes—
17C4×C11×C22⋊C4C2214yes—
18C2×C11×#95C411yescharacteristic
19C2×C11×#95C411yescharacteristic
20C11×#336C2214yescomplemented
21C11×#336C2214yescomplemented
22C25×C11C2×C411yescharacteristic
23C23×C4×C11—24no—
24C23×C4×C11—42no—
25C23×C4×C11—42no—
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11C2×C412yes—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C22×C8×C11C2318yes—
35C2×C11×C22⋊C4—24no—
36C2×C11×C22⋊C4—24no—
37C2×C11×C22⋊C4C2×C414yes—
38C2×C11×C22⋊C4C2×C414yes—
39C2×C42×C11—42no—
40C2×C42×C11—42no—
41C2×C42×C11C2×C412yes—
42C2×C42×C11C2×C412yes—
43C2×C42×C11C2312yes—
44C2×C42×C11C2312yes—
45C11×C4⋊C8—44no—
46C11×C22⋊C8—28no—
47C11×C22⋊C8—44no—
48C11×C22⋊C8—44no—
49C11×#97—44no—
50C11×#95C2×C414yes—
51C11×#95C2×C414yes—
52#21906C1111yesmaximal, characteristic, direct product factor, Sylow
53C24×C11—22no—
54C24×C11—22no—
55C24×C11—41no—
56C24×C11—41no—
57C24×C11—41no—
58C24×C11—41no—
59C24×C11M1614yes—
60C24×C11C22×C412yes—
61C24×C11C22×C411yescharacteristic
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—416no—
85C22×C4×C11M1614yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C412yes—
88C22×C4×C11C22×C412yes—
89C22×C4×C11C22×C412yes—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C412yes—
92C22×C4×C11#4114yes—
93C22×C4×C11C2411yescharacteristic
94C2×C8×C11—28no—
95C2×C8×C11—28no—
96C2×C8×C11—28no—
97C11×C22⋊C4—28no—
98C11×C22⋊C4—28no—
99C42×C11—24no—
100C42×C11—24no—
101C42×C11—42no—
102C42×C11—42no—
103C2×C4×C22⋊C4C2×C1111yescharacteristic
104#1924C2×C1118yescomplemented
105#1797C2×C1112yescomplemented
106#1779C2×C1112yes—
107#1749C2×C1112yescomplemented
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11—22no—
116C23×C11—22no—
117C23×C11—22no—
118C23×C11—28no—
119C23×C11—44no—
120C23×C11—44no—
121C23×C11—44no—
122C23×C11—44no—
123C23×C11—44no—
124C23×C11—44no—
125C23×C11#11712yes—
126C23×C11C2×M1614yes—
127C23×C11C2×M1612yes—
128C23×C11C2×M1612yes—
129C23×C11C23×C411yescharacteristic
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—28no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—44no—
148C2×C4×C11—48no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—44no—
153C2×C4×C11—48no—
154C2×C4×C11#11712yes—
155C2×C4×C11C2×M1614yes—
156C2×C4×C11C2×#4112yes—
157C2×C4×C11H(5,𝔽2)12yes—
158C2×C4×C11H(5,𝔽2)12yes—
159C8×C11—48no—
160C24×C4C22×C1111yescharacteristic
161C22×C22⋊C4C4×C1111yescharacteristic
162C22×C22⋊C4C4×C1111yescharacteristic
163C22×C42C22×C1111yescharacteristic
164C22×C42C22×C1111yescharacteristic
165C2×C4⋊C8C22×C1114yescomplemented
166C2×C22⋊C8C22×C1114yes—
167C2×C22⋊C8C22×C1114yes—
168C2×C22⋊C8C22×C1114yes—
169C2×#97C22×C1114yescomplemented
170C4×C22⋊C4C4×C1114yes—
171C4×C22⋊C4C22×C1114yes—
172C2×#95C4×C1111yescharacteristic
173C2×#95C4×C1111yescharacteristic
174#336C22×C1114yescomplemented
175#336C22×C1114yescomplemented
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—24no—
183C22×C11—24no—
184C22×C11—24no—
185C22×C11—416no—
186C22×C11—42no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11#43214yes—
191C22×C11C2×#11711yescharacteristic
192C22×C11#51811yescharacteristic
193C22×C11#51811yescharacteristic
194C22×C11C22×M1611yescharacteristic
195C22×C11C22×M1611yescharacteristic
196C22×C11#56811yescharacteristic
197C22×C11#56811yescharacteristic
198C4×C11—22no—
199C4×C11—24no—
200C4×C11—42no—
201C4×C11—42no—
202C4×C11—42no—
203C4×C11—42no—
204C4×C11#53814yes—
205C25C2×C4×C1111yescharacteristic
206C23×C4—24no—
207C23×C4—42no—
208C23×C4—42no—
209C23×C4C2×C4×C1111yescharacteristic
210C23×C4C2×C4×C1111yescharacteristic
211C23×C4C2×C4×C1111yescharacteristic
212C23×C4C2×C4×C1111yescharacteristic
213C23×C4C2×C4×C1112yes—
214C23×C4C2×C4×C1111yescharacteristic
215C23×C4C23×C1112yes—
216C23×C4C23×C1111yescharacteristic
217C22×C8C23×C1118yes—
218C2×C22⋊C4—24no—
219C2×C22⋊C4—24no—
220C2×C22⋊C4C2×C4×C1114yes—
221C2×C22⋊C4C2×C4×C1114yes—
222C2×C42—42no—
223C2×C42—42no—
224C2×C42C2×C4×C1112yes—
225C2×C42C2×C4×C1112yes—
226C2×C42C23×C1112yes—
227C2×C42C23×C1112yes—
228C4⋊C8—44no—
229C22⋊C8—28no—
230C22⋊C8—44no—
231C22⋊C8—44no—
232#97—44no—
233#95C2×C4×C1114yes—
234#95C2×C4×C1114yes—
235C2×C11—24no—
236C2×C11—44no—
237C2×C11#231211yescharacteristic
238C2×C11C2×#43211yescharacteristic
239C2×C11#292111yescharacteristic
240C2×C11#297311yescharacteristic
241C2×C11#297311yescharacteristic
242C2×C11#297311yescharacteristic
243C2×C11#297511yescharacteristic
244C24—22no—
245C24—22no—
246C24—41no—
247C24—41no—
248C24—41no—
249C24—41no—
250C24C11×M1614yes—
251C24C22×C4×C1112yes—
252C24C22×C4×C1111yescharacteristic
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—416no—
276C22×C4C11×M1614yes—
277C22×C4C22×C4×C1112yes—
278C22×C4C22×C4×C1112yes—
279C22×C4C22×C4×C1112yes—
280C22×C4C22×C4×C1112yes—
281C22×C4C22×C4×C1111yescharacteristic
282C22×C4C22×C4×C1112yes—
283C22×C4C11×#4114yes—
284C22×C4C24×C1111yescharacteristic
285C2×C8—28no—
286C2×C8—28no—
287C2×C8—28no—
288C22⋊C4—28no—
289C22⋊C4—28no—
290C42—24no—
291C42—24no—
292C42—42no—
293C42—42no—
294C11#2190611yescharacteristic, direct product factor, Sylow
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—22no—
300C23—22no—
301C23—22no—
302C23—22no—
303C23—22no—
304C23—22no—
305C23—28no—
306C23—44no—
307C23—44no—
308C23—44no—
309C23—44no—
310C23—44no—
311C23—44no—
312C23C11×#11712yes—
313C23C2×C11×M1614yes—
314C23C2×C11×M1612yes—
315C23C2×C11×M1612yes—
316C23C23×C4×C1111yescharacteristic
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—28no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—44no—
335C2×C4—48no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—48no—
341C2×C4C11×#11712yes—
342C2×C4C2×C11×M1614yes—
343C2×C4C2×C11×#4112yes—
344C2×C4C11×H(5,𝔽2)12yes—
345C2×C4C11×H(5,𝔽2)12yes—
346C8—48no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—24no—
354C22—24no—
355C22—24no—
356C22—416no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22C11×#43214yes—
362C22C2×C11×#11711yescharacteristic
363C22C11×#51811yescharacteristic
364C22C11×#51811yescharacteristic
365C22C22×C11×M1611yescharacteristic
366C22C22×C11×M1611yescharacteristic
367C22C11×#56811yescharacteristic
368C22C11×#56811yescharacteristic
369C4—24no—
370C4—22no—
371C4—42no—
372C4—42no—
373C4—42no—
374C4—42no—
375C4C11×#53814yes—
376C2—24no—
377C2—44no—
378C2C11×#231211yescharacteristic
379C2C2×C11×#43211yescharacteristic
380C2C11×#292111yescharacteristic
381C2C11×#297311yescharacteristic
382C2C11×#297311yescharacteristic
383C2C11×#297311yescharacteristic
384C2C11×#297511yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC25×C11C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1924C2semidirect
3. C11×#1797C2semidirect
5. C11×#1749C2semidirect
11. C2×C11×C4⋊C8C22semidirect
15. C2×C11×#97C22semidirect
20. C11×#336C22semidirect
21. C11×#336C22semidirect
52. #21906C11direct (N × H)
104. #1924C2×C11semidirect
105. #1797C2×C11semidirect
107. #1749C2×C11semidirect
165. C2×C4⋊C8C22×C11semidirect
169. C2×#97C22×C11semidirect
174. #336C22×C11semidirect
175. #336C22×C11semidirect
294. C11#21906direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×C22⋊C42
C11×#19242
C11×#17972
C11×#17792
C11×#17492
#2190611