Finite Group Databasebeta

← C11×#23133 #14600326

Subgroups — C11×#23133 #14600326

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C11×#2360C212yesmaximal
3C11×#1935C212yesmaximal, complemented
4C11×#1918C212yesmaximal, complemented
5C11×#1878C212yesmaximal, complemented
6C11×#1872C212yesmaximal
7C11×#1763C212yesmaximal, complemented
8C11×#1752C211yesmaximal, 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×C11×#97C2212yes—
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⋊C4D412yes—
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×C42×C11C2312yes—
64C11×#107C2×C414yescomplemented
65C11×#103—24no—
66C11×#103—42no—
67C11×#103C2×C418yescomplemented
68C11×C22⋊C8—22no—
69C11×#97—42no—
70C11×#95—22no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95—22no—
74C11×#95D411yescharacteristic
75C11×#95D411yescharacteristic
76#23133C1111yesmaximal, 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×D412yes—
96C22×C4×C11C2×D411yescharacteristic
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—24no—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11—44no—
123C42×C11—82no—
124C2×#467C2×C1111yescharacteristic
125#2360C2×C1112yes—
126#1935C2×C1112yescomplemented
127#1918C2×C1112yescomplemented
128#1878C2×C1112yescomplemented
129#1872C2×C1112yes—
130#1763C2×C1112yescomplemented
131#1752C2×C1111yescharacteristic
132C2×#340C2×C1111yescharacteristic
133C23×C11—22no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11C4×D412yes—
137C23×C11#13714yes—
138C23×C11C22×D411yescharacteristic
139Q8×C11—24no—
140Q8×C11—24no—
141Q8×C11—42no—
142Q8×C11—42no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—24no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
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×C11C23×C411yescharacteristic
168C2×C4×C11C2×#4112yes—
169C2×C4×C11C2×#4111yescharacteristic
170C2×C4×C11H(5,𝔽2)12yes—
171C8×C11—22no—
172C8×C11—22no—
173C8×C11—42no—
174C22×Q16C22×C1111yescharacteristic
175C23×C8C22×C1111yescharacteristic
176C2×C22⋊Q8C22×C1112yes—
177C2×C4×Q8C22×C1112yes—
178C22×C4⋊C4C22×C1112yes—
179#467C4×C1118yescomplemented
180C2×#107C22×C1111yescharacteristic
181C2×#103C22×C1112yes—
182C2×#103C22×C1112yes—
183C2×#103C22×C1112yes—
184C2×C22⋊C8C22×C1111yescharacteristic
185C2×#97C22×C1112yes—
186#391C22×C1112yes—
187#389—22no—
188#389C22×C1112yes—
189#387—22no—
190#385—22no—
191C4×C4⋊C4C22×C1112yes—
192C4×C22⋊C4—22no—
193C4×C22⋊C4C22×C1111yescharacteristic
194#340C22×C1112yes—
195#340C22×C1112yes—
196#340C22×C1112yes—
197#340C22×C1111yescharacteristic
198#340C22×C1111yescharacteristic
199#336C22×C1112yes—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—24no—
203C22×C11—24no—
204C22×C11#44114yes—
205C22×C11C2×C4×D411yescharacteristic
206C22×C11#54612yes—
207C22×C11C2×#13712yes—
208C22×C11#57611yescharacteristic
209C22×C11#57811yescharacteristic
210C4×C11—22no—
211C4×C11—44no—
212C4×C11—44no—
213C4×C11—42no—
214C4×C11—42no—
215C4×C11—44no—
216C4×C11—82no—
217C4×C11C4×#4111yescharacteristic
218C4×C11#51811yescharacteristic
219C4×C11#55312yes—
220C22×Q8C23×C1112yes—
221C23×C4—22no—
222C23×C4C23×C1111yescharacteristic
223C2×Q16—42no—
224C2×Q16C2×C4×C1114yescomplemented
225C22×C8—42no—
226C22×C8C2×C4×C1114yes—
227C22×C8C23×C1112yes—
228C22×C8C23×C1111yescharacteristic
229C22×C8C23×C1111yescharacteristic
230C22⋊Q8—24no—
231C22⋊Q8C2×C4×C1118yes—
232C4×Q8—24no—
233C4×Q8—42no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—24no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—42no—
240C2×C4⋊C4C23×C1112yes—
241C2×C4⋊C4C23×C1112yes—
242C2×C4⋊C4C23×C1112yes—
243C2×C22⋊C4—22no—
244C2×C22⋊C4D4×C1112yes—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42C23×C1112yes—
248#107C2×C4×C1114yescomplemented
249#103—24no—
250#103—42no—
251#103C2×C4×C1118yescomplemented
252C22⋊C8—22no—
253#97—42no—
254#95—22no—
255#95—22no—
256#95—22no—
257#95—22no—
258#95D4×C1111yescharacteristic
259#95D4×C1111yescharacteristic
260C2×C11—24no—
261C2×C11#236411yescharacteristic
262C2×C11C2×#44111yescharacteristic
263C2×C11#295111yescharacteristic
264C2×C11#331212yes—
265C2×C11#331412yes—
266C24C2×D4×C1111yescharacteristic
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8C22×C4×C1114yes—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—44no—
280C22×C4—44no—
281C22×C4—82no—
282C22×C4C22×C4×C1112yes—
283C22×C4C2×D4×C1112yes—
284C22×C4C2×D4×C1112yes—
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C11×#4112yes—
287C22×C4C24×C1111yescharacteristic
288Q16—44no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—44no—
295C2×C8C22×C4×C1112yes—
296C2×C8C22×C4×C1112yes—
297C4⋊C4—28no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—44no—
303C4⋊C4—44no—
304C4⋊C4—82no—
305C4⋊C4C22×C4×C1114yes—
306C4⋊C4C11×#4114yes—
307C22⋊C4—28no—
308C22⋊C4—24no—
309C42—22no—
310C42—22no—
311C42—44no—
312C42—82no—
313C11#2313311yescharacteristic, direct product factor, Sylow
314C23—22no—
315C23—21no—
316C23—21no—
317C23C4×D4×C1112yes—
318C23C11×#13714yes—
319C23C22×D4×C1111yescharacteristic
320Q8—24no—
321Q8—24no—
322Q8—42no—
323Q8—42no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—42no—
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—88no—
347C2×C4C4×D4×C1112yes—
348C2×C4C23×C4×C1111yescharacteristic
349C2×C4C2×C11×#4112yes—
350C2×C4C2×C11×#4111yescharacteristic
351C2×C4C11×H(5,𝔽2)12yes—
352C8—22no—
353C8—22no—
354C8—42no—
355C22—22no—
356C22—24no—
357C22—24no—
358C22—22no—
359C22C11×#44114yes—
360C22C2×C4×D4×C1111yescharacteristic
361C22C11×#54612yes—
362C22C2×C11×#13712yes—
363C22C11×#57611yescharacteristic
364C22C11×#57811yescharacteristic
365C4—22no—
366C4—44no—
367C4—42no—
368C4—42no—
369C4—44no—
370C4—44no—
371C4—82no—
372C4C4×C11×#4111yescharacteristic
373C4C11×#51811yescharacteristic
374C4C11×#55312yes—
375C2—24no—
376C2C11×#236411yescharacteristic
377C2C2×C11×#44111yescharacteristic
378C2C11×#295111yescharacteristic
379C2C11×#331212yes—
380C2C11×#331412yes—
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×#1935C2semidirect
4. C11×#1918C2semidirect
5. C11×#1878C2semidirect
7. C11×#1763C2semidirect
15. C11×#467C4semidirect
40. C2×C11×Q16C2×C4semidirect
64. C11×#107C2×C4semidirect
67. C11×#103C2×C4semidirect
76. #23133C11direct (N × H)
126. #1935C2×C11semidirect
127. #1918C2×C11semidirect
128. #1878C2×C11semidirect
130. #1763C2×C11semidirect
179. #467C4×C11semidirect
224. C2×Q16C2×C4×C11semidirect
248. #107C2×C4×C11semidirect
251. #103C2×C4×C11semidirect
313. C11#23133direct (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×#19352
C11×#19182
C11×#18782
C11×#18722
C11×#17632
C11×#17522
C2×C11×#3402
#2313311