Finite Group Databasebeta

← C11×#23128 #14600321

Subgroups — C11×#23128 #14600321

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C11×#2360C212yesmaximal
3C11×#1933C212yesmaximal, complemented
4C11×#1921C212yesmaximal, complemented
5C11×#1878C212yesmaximal, complemented
6C11×#1872C212yesmaximal
7C4×C11×#103C212yesmaximal, complemented
8C8×C11×C22⋊C4C211yesmaximal, characteristic
9C2×C11×#340C211yesmaximal, characteristic
10C22×C11×Q16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×C22⋊Q8C2212yes—
13C2×C4×Q8×C11C2212yes—
14C22×C11×C4⋊C4C2212yes—
15C11×#467C418yescomplemented
16C2×C11×#107C2211yescharacteristic
17C2×C11×#103C2212yes—
18C2×C11×#103C2212yes—
19C2×C11×#103C2212yes—
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C4×C8×C11C2212yes—
22C11×#391C2212yes—
23C11×#389—22no—
24C11×#389C2212yes—
25C11×#387—22no—
26C11×#385—22no—
27C4×C11×C4⋊C4C2212yes—
28C4×C11×C22⋊C4—22no—
29C4×C11×C22⋊C4C2211yescharacteristic
30C11×#340C2212yes—
31C11×#340C2212yes—
32C11×#340C2212yes—
33C11×#340C2211yescharacteristic
34C11×#340C2211yescharacteristic
35C11×#336C2212yes—
36C22×Q8×C11C2312yes—
37C23×C4×C11—22no—
38C23×C4×C11C2311yescharacteristic
39C2×C11×Q16—42no—
40C2×C11×Q16C2×C414yescomplemented
41C22×C8×C11—42no—
42C22×C8×C11C2×C414yes—
43C22×C8×C11C2312yes—
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8C2×C418yes—
48C4×Q8×C11—24no—
49C4×Q8×C11—42no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—42no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4D411yescharacteristic
61C2×C11×C22⋊C4D411yescharacteristic
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11C2312yes—
65C11×#107C2×C414yescomplemented
66C11×#103—24no—
67C11×#103—42no—
68C11×#103C2×C418yescomplemented
69C11×C22⋊C8—22no—
70C4×C8×C11—42no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95—22no—
74C11×#95—22no—
75C11×#95D412yes—
76#23128C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11C2×D411yescharacteristic
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11—22no—
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C2×Q8×C11C22×C414yes—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—44no—
91C22×C4×C11—44no—
92C22×C4×C11—82no—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11#4112yes—
98C22×C4×C11C2411yescharacteristic
99C11×Q16—44no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—44no—
106C2×C8×C11C22×C412yes—
107C2×C8×C11C22×C412yes—
108C11×C4⋊C4—28no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—44no—
114C11×C4⋊C4—44no—
115C11×C4⋊C4—82no—
116C11×C4⋊C4C22×C414yes—
117C11×C4⋊C4#4114yes—
118C11×C22⋊C4—28no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4Q1614yescomplemented
121C42×C11—22no—
122C42×C11—22no—
123C42×C11—44no—
124C42×C11—82no—
125C2×#467C2×C1111yescharacteristic
126#2360C2×C1112yes—
127#1933C2×C1112yescomplemented
128#1921C2×C1112yescomplemented
129#1878C2×C1112yescomplemented
130#1872C2×C1112yes—
131C4×#103C2×C1112yescomplemented
132C8×C22⋊C4C2×C1111yescharacteristic
133C2×#340C2×C1111yescharacteristic
134C23×C11—22no—
135C23×C11—22no—
136C23×C11C4×D412yes—
137C23×C11C2×Q1612yes—
138C23×C11#13512yes—
139C23×C11C22×D411yescharacteristic
140Q8×C11—24no—
141Q8×C11—24no—
142Q8×C11—42no—
143Q8×C11—42no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—88no—
166C2×C4×C11C4×D412yes—
167C2×C4×C11C2×Q1614yes—
168C2×C4×C11C23×C411yescharacteristic
169C2×C4×C11C2×#4112yes—
170C2×C4×C11C2×#4111yescharacteristic
171C2×C4×C11H(5,𝔽2)12yes—
172C8×C11—22no—
173C8×C11—22no—
174C8×C11—42no—
175C22×Q16C22×C1111yescharacteristic
176C23×C8C22×C1111yescharacteristic
177C2×C22⋊Q8C22×C1112yes—
178C2×C4×Q8C22×C1112yes—
179C22×C4⋊C4C22×C1112yes—
180#467C4×C1118yescomplemented
181C2×#107C22×C1111yescharacteristic
182C2×#103C22×C1112yes—
183C2×#103C22×C1112yes—
184C2×#103C22×C1112yes—
185C2×C22⋊C8C22×C1111yescharacteristic
186C2×C4×C8C22×C1112yes—
187#391C22×C1112yes—
188#389—22no—
189#389C22×C1112yes—
190#387—22no—
191#385—22no—
192C4×C4⋊C4C22×C1112yes—
193C4×C22⋊C4—22no—
194C4×C22⋊C4C22×C1111yescharacteristic
195#340C22×C1112yes—
196#340C22×C1112yes—
197#340C22×C1112yes—
198#340C22×C1111yescharacteristic
199#340C22×C1111yescharacteristic
200#336C22×C1112yes—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—24no—
204C22×C11—24no—
205C22×C11C4×Q1614yes—
206C22×C11C2×C4×D411yescharacteristic
207C22×C11#54612yes—
208C22×C11C22×Q1611yescharacteristic
209C22×C11C2×#13511yescharacteristic
210C22×C11#57712yes—
211C4×C11—22no—
212C4×C11—24no—
213C4×C11—44no—
214C4×C11—44no—
215C4×C11—42no—
216C4×C11—44no—
217C4×C11—82no—
218C4×C11C4×#4111yescharacteristic
219C4×C11#51811yescharacteristic
220C4×C11#55312yes—
221C22×Q8C23×C1112yes—
222C23×C4—22no—
223C23×C4C23×C1111yescharacteristic
224C2×Q16—42no—
225C2×Q16C2×C4×C1114yescomplemented
226C22×C8—42no—
227C22×C8C2×C4×C1114yes—
228C22×C8C23×C1112yes—
229C22×C8C23×C1111yescharacteristic
230C22×C8C23×C1111yescharacteristic
231C22⋊Q8—24no—
232C22⋊Q8C2×C4×C1118yes—
233C4×Q8—24no—
234C4×Q8—42no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—42no—
241C2×C4⋊C4C23×C1112yes—
242C2×C4⋊C4C23×C1112yes—
243C2×C4⋊C4C23×C1112yes—
244C2×C22⋊C4—22no—
245C2×C22⋊C4D4×C1111yescharacteristic
246C2×C22⋊C4D4×C1111yescharacteristic
247C2×C42—22no—
248C2×C42—22no—
249C2×C42C23×C1112yes—
250#107C2×C4×C1114yescomplemented
251#103—24no—
252#103—42no—
253#103C2×C4×C1118yescomplemented
254C22⋊C8—22no—
255C4×C8—42no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95D4×C1112yes—
261C2×C11—24no—
262C2×C11#236411yescharacteristic
263C2×C11C2×C4×Q1611yescharacteristic
264C2×C11#295211yescharacteristic
265C2×C11#329612yes—
266C2×C11#329912yes—
267C24C2×D4×C1111yescharacteristic
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8C22×C4×C1114yes—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—44no—
281C22×C4—44no—
282C22×C4—82no—
283C22×C4C22×C4×C1112yes—
284C22×C4C2×D4×C1112yes—
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C2×D4×C1112yes—
287C22×C4C11×#4112yes—
288C22×C4C24×C1111yescharacteristic
289Q16—44no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—44no—
296C2×C8C22×C4×C1112yes—
297C2×C8C22×C4×C1112yes—
298C4⋊C4—28no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—44no—
304C4⋊C4—44no—
305C4⋊C4—82no—
306C4⋊C4C22×C4×C1114yes—
307C4⋊C4C11×#4114yes—
308C22⋊C4—28no—
309C22⋊C4—22no—
310C22⋊C4C11×Q1614yescomplemented
311C42—22no—
312C42—22no—
313C42—44no—
314C42—82no—
315C11#2312811yescharacteristic, direct product factor, Sylow
316C23—22no—
317C23—22no—
318C23C4×D4×C1112yes—
319C23C2×C11×Q1612yes—
320C23C11×#13512yes—
321C23C22×D4×C1111yescharacteristic
322Q8—24no—
323Q8—24no—
324Q8—42no—
325Q8—42no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—88no—
348C2×C4C4×D4×C1112yes—
349C2×C4C2×C11×Q1614yes—
350C2×C4C23×C4×C1111yescharacteristic
351C2×C4C2×C11×#4112yes—
352C2×C4C2×C11×#4111yescharacteristic
353C2×C4C11×H(5,𝔽2)12yes—
354C8—22no—
355C8—22no—
356C8—42no—
357C22—22no—
358C22—24no—
359C22—24no—
360C22—22no—
361C22C4×C11×Q1614yes—
362C22C2×C4×D4×C1111yescharacteristic
363C22C11×#54612yes—
364C22C22×C11×Q1611yescharacteristic
365C22C2×C11×#13511yescharacteristic
366C22C11×#57712yes—
367C4—24no—
368C4—22no—
369C4—44no—
370C4—42no—
371C4—44no—
372C4—44no—
373C4—82no—
374C4C4×C11×#4111yescharacteristic
375C4C11×#51811yescharacteristic
376C4C11×#55312yes—
377C2—24no—
378C2C11×#236411yescharacteristic
379C2C2×C4×C11×Q1611yescharacteristic
380C2C11×#295211yescharacteristic
381C2C11×#329612yes—
382C2C11×#329912yes—
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 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1933C2semidirect
4. C11×#1921C2semidirect
5. C11×#1878C2semidirect
7. C4×C11×#103C2semidirect
15. C11×#467C4semidirect
40. C2×C11×Q16C2×C4semidirect
65. C11×#107C2×C4semidirect
68. C11×#103C2×C4semidirect
76. #23128C11direct (N × H)
120. C11×C22⋊C4Q16semidirect
127. #1933C2×C11semidirect
128. #1921C2×C11semidirect
129. #1878C2×C11semidirect
131. C4×#103C2×C11semidirect
180. #467C4×C11semidirect
225. C2×Q16C2×C4×C11semidirect
250. #107C2×C4×C11semidirect
253. #103C2×C4×C11semidirect
310. C22⋊C4C11×Q16semidirect
315. C11#23128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C11×#23602
C11×#19332
C11×#19212
C11×#18782
C11×#18722
C4×C11×#1032
C8×C11×C22⋊C42
C2×C11×#3402
#2312811