Finite Group Databasebeta

← C11×#21838 #14599031

Subgroups — C11×#21838 #14599031

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic
2C2×C11×#432C211yesmaximal, characteristic
3C11×#2285C211yesmaximal, characteristic
4C11×#1992C214yesmaximal, complemented
5C11×#1989C214yesmaximal, complemented
6C11×#1824C212yesmaximal
7C11×#1823C212yesmaximal
8C2×C11×#125—21no—
9C2×C11×#125—21no—
10C2×C11×#125—24no—
11C2×C11×#125C418yescomplemented
12C2×C11×#125C2212yes—
13C2×C11×#125C2212yes—
14C2×C11×#117—21no—
15C22×C11×C4⋊C4—21no—
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C11×#432—24no—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×#97C2212yes—
24C11×#384C2212yes—
25C11×#382—21no—
26C11×#380—21no—
27C11×#380C2212yes—
28C4×C11×C4⋊C4—21no—
29C4×C11×C4⋊C4C2212yes—
30C11×#340C2218yes—
31C11×#340C2218yes—
32C23×C4×C11—21no—
33C23×C4×C11—21no—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C8×C11C2314yes—
38C11×#125—28no—
39C11×#125—28no—
40C11×#125—24no—
41C11×#125—24no—
42C11×#125C2×C418yes—
43C11×#125C2×C418yes—
44C11×#117—44no—
45C2×C11×C4⋊C4—28no—
46C2×C11×C4⋊C4—28no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2×C414yes—
58C2×C11×C4⋊C4C2×C414yes—
59C2×C11×C4⋊C4C2314yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11—22no—
64C2×C42×C11C2×C414yes—
65C2×C42×C11D411yescharacteristic
66C2×C42×C11D411yescharacteristic
67C2×C42×C11D414yes—
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C11×C4⋊C8—24no—
71C11×C22⋊C8—24no—
72C11×#97—24no—
73C11×#95—22no—
74C11×#95—22no—
75#21838C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C2×D411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—24no—
85C22×C4×C11—42no—
86C22×C4×C11—44no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11C22⋊C414yes—
90C22×C4×C11C22⋊C414yes—
91C22×C4×C11C22×C412yes—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2411yescharacteristic
99C2×C8×C11—24no—
100C2×C8×C11—28no—
101C11×C4⋊C4—28no—
102C11×C4⋊C4—28no—
103C11×C4⋊C4—28no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—28no—
110C11×C4⋊C4—44no—
111C11×C4⋊C4—44no—
112C11×C4⋊C4C22×C414yes—
113C11×C4⋊C4C22×C414yes—
114C11×C22⋊C4—44no—
115C42×C11—44no—
116C42×C11C22⋊C414yes—
117C42×C11C22⋊C414yes—
118C42×C11C22×C412yes—
119C42×C11C22×C412yes—
120C42×C11C2×D412yes—
121C42×C11C2×D412yes—
122C22×#125C2×C1111yescharacteristic
123C2×#432C2×C1111yescharacteristic
124#2285C2×C1111yescharacteristic
125#1992C2×C1114yescomplemented
126#1989C2×C1114yescomplemented
127#1824C2×C1112yes—
128#1823C2×C1112yes—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11C2×C22⋊C412yes—
132C23×C11AGL(1,ℤ/8)12yes—
133C23×C11#13712yes—
134C23×C11C22×D411yescharacteristic
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—28no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—44no—
148C2×C4×C11—48no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—44no—
152C2×C4×C11—48no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11C2×C22⋊C412yes—
157C2×C4×C11C2×C22⋊C412yes—
158C2×C4×C11C2×C22⋊C412yes—
159C2×C4×C11C2×C22⋊C412yes—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11C23×C411yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C112−1+414yes—
164C8×C11—44no—
165C2×#125—21no—
166C2×#125—21no—
167C2×#125—24no—
168C2×#125C4×C1118yescomplemented
169C2×#125C22×C1112yes—
170C2×#125C22×C1112yes—
171C2×#117—21no—
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4C22×C1111yescharacteristic
175C22×C4⋊C4C22×C1111yescharacteristic
176C22×C42C22×C1111yescharacteristic
177#432—24no—
178C2×C4⋊C8C22×C1112yes—
179C2×C22⋊C8C22×C1112yes—
180C2×#97C22×C1112yes—
181#384C22×C1112yes—
182#382—21no—
183#380—21no—
184#380C22×C1112yes—
185C4×C4⋊C4—21no—
186C4×C4⋊C4C22×C1112yes—
187#340C22×C1118yes—
188#340C22×C1118yes—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11#41714yes—
194C22×C11C22×C22⋊C411yescharacteristic
195C22×C11#53612yes—
196C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
197C22×C11C2×#13711yescharacteristic
198C22×C11#57512yes—
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—22no—
204C4×C11—44no—
205C4×C11—44no—
206C4×C11—84no—
207C4×C11#51912yes—
208C4×C11#53612yes—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4D4×C1111yescharacteristic
212C23×C4D4×C1111yescharacteristic
213C23×C4C23×C1111yescharacteristic
214C22×C8C23×C1114yes—
215#125—28no—
216#125—28no—
217#125—24no—
218#125—24no—
219#125C2×C4×C1118yes—
220#125C2×C4×C1118yes—
221#117—44no—
222C2×C4⋊C4—28no—
223C2×C4⋊C4—28no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4C2×C4×C1114yes—
235C2×C4⋊C4C2×C4×C1114yes—
236C2×C4⋊C4C23×C1114yes—
237C2×C4⋊C4C23×C1112yes—
238C2×C4⋊C4C23×C1112yes—
239C2×C22⋊C4—22no—
240C2×C42—22no—
241C2×C42C2×C4×C1114yes—
242C2×C42D4×C1111yescharacteristic
243C2×C42D4×C1111yescharacteristic
244C2×C42D4×C1114yes—
245C2×C42C23×C1111yescharacteristic
246C2×C42C23×C1111yescharacteristic
247C4⋊C8—24no—
248C22⋊C8—24no—
249#97—24no—
250#95—22no—
251#95—22no—
252C2×C11—24no—
253C2×C11#231011yescharacteristic
254C2×C11C2×#41711yescharacteristic
255C2×C11#289611yescharacteristic
256C2×C11#323412yes—
257C2×C11#323612yes—
258C24C2×D4×C1111yescharacteristic
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—42no—
268C22×C4—44no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4C11×C22⋊C414yes—
272C22×C4C11×C22⋊C414yes—
273C22×C4C22×C4×C1112yes—
274C22×C4C2×D4×C1111yescharacteristic
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C2×D4×C1111yescharacteristic
277C22×C4C2×D4×C1111yescharacteristic
278C22×C4C2×D4×C1111yescharacteristic
279C22×C4C2×D4×C1112yes—
280C22×C4C24×C1111yescharacteristic
281C2×C8—24no—
282C2×C8—28no—
283C4⋊C4—28no—
284C4⋊C4—28no—
285C4⋊C4—28no—
286C4⋊C4—28no—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—28no—
292C4⋊C4—44no—
293C4⋊C4—44no—
294C4⋊C4C22×C4×C1114yes—
295C4⋊C4C22×C4×C1114yes—
296C22⋊C4—44no—
297C42—44no—
298C42C11×C22⋊C414yes—
299C42C11×C22⋊C414yes—
300C42C22×C4×C1112yes—
301C42C22×C4×C1112yes—
302C42C2×D4×C1112yes—
303C42C2×D4×C1112yes—
304C11#2183811yescharacteristic, direct product factor, Sylow
305C23—22no—
306C23—22no—
307C23C2×C11×C22⋊C412yes—
308C23C11×AGL(1,ℤ/8)12yes—
309C23C11×#13712yes—
310C23C22×D4×C1111yescharacteristic
311C2×C4—22no—
312C2×C4—28no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—44no—
324C2×C4—48no—
325C2×C4—48no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4C2×C11×C22⋊C412yes—
333C2×C4C2×C11×C22⋊C412yes—
334C2×C4C2×C11×C22⋊C412yes—
335C2×C4C2×C11×C22⋊C412yes—
336C2×C4C2×C11×C22⋊C412yes—
337C2×C4C23×C4×C1111yescharacteristic
338C2×C4C22×D4×C1111yescharacteristic
339C2×C4C11×2−1+414yes—
340C8—44no—
341C22—22no—
342C22—24no—
343C22—24no—
344C22—22no—
345C22C11×#41714yes—
346C22C22×C11×C22⋊C411yescharacteristic
347C22C11×#53612yes—
348C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
349C22C2×C11×#13711yescharacteristic
350C22C11×#57512yes—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—44no—
357C4—44no—
358C4—84no—
359C4C11×#51912yes—
360C4C11×#53612yes—
361C2—24no—
362C2C11×#231011yescharacteristic
363C2C2×C11×#41711yescharacteristic
364C2C11×#289611yescharacteristic
365C2C11×#323412yes—
366C2C11×#323612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×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×#1992C2semidirect
5. C11×#1989C2semidirect
11. C2×C11×#125C4semidirect
75. #21838C11direct (N × H)
125. #1992C2×C11semidirect
126. #1989C2×C11semidirect
168. C2×#125C4×C11semidirect
304. C11#21838direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C2×C11×#4322
C11×#22852
C11×#19922
C11×#19892
C11×#18242
C11×#18232
#2183811