Finite Group Databasebeta

← C11×#24072 #14601265

Subgroups — C11×#24072 #14601265

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#541C211yesmaximal, characteristic
2C2×C11×#485C212yesmaximal
3C11×#2316C211yesmaximal, characteristic
4C11×#2059C212yesmaximal, complemented
5C11×#2043C212yesmaximal, complemented
6C11×#1872C212yesmaximal
7C11×#1865C212yesmaximal, complemented
8C11×#1863C212yesmaximal, complemented
9C11×#1818C211yesmaximal, characteristic
10C11×#541—28no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#126—22no—
13C2×C11×#125—22no—
14C2×C11×#125C2211yescharacteristic
15C2×C11×C22⋊Q8C2212yes—
16C2×C4×Q8×C11C2212yes—
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C11×#485—28no—
21C2×C11×#107C2212yes—
22C2×C11×#106C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C11×#389—22no—
29C11×#389C2212yes—
30C11×#389C2212yes—
31C11×#380—22no—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2212yes—
35C11×#336C2211yescharacteristic
36C11×#336C2211yescharacteristic
37C22×Q8×C11C2312yes—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C22×C8×C11C2312yes—
41C22×C8×C11C2312yes—
42C11×C4⋊Q8—24no—
43C11×#126—216no—
44C11×#125—216no—
45C11×#125—24no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8D418yes—
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C11×#117—24no—
51C11×#117—24no—
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⋊C4—24no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11—22no—
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C11×#107—24no—
72C11×#106—24no—
73C11×#103—24no—
74C11×#103—24no—
75C11×#103—24no—
76C11×#103—24no—
77C11×C22⋊C8—24no—
78C11×#95—22no—
79C11×#95—22no—
80#24072C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11C2×D411yescharacteristic
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11C2×D414yes—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—24no—
95C22×C4×C11—22no—
96C22×C4×C11—82no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D414yes—
101C22×C4×C11C2411yescharacteristic
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—28no—
110C11×C4⋊C4—28no—
111C11×C4⋊C4—28no—
112C11×C4⋊C4—28no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—82no—
119C11×C4⋊C4—82no—
120C11×C4⋊C4C2×D414yes—
121C11×C4⋊C4#4114yes—
122C11×C22⋊C4—28no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—42no—
125C42×C11—28no—
126C42×C11—22no—
127C42×C11—22no—
128C42×C11—42no—
129C2×#541C2×C1111yescharacteristic
130C2×#485C2×C1112yes—
131#2316C2×C1111yescharacteristic
132#2059C2×C1112yescomplemented
133#2043C2×C1112yescomplemented
134#1872C2×C1112yes—
135#1865C2×C1112yescomplemented
136#1863C2×C1112yescomplemented
137#1818C2×C1111yescharacteristic
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—22no—
141C23×C11—22no—
142C23×C11#12012yes—
143C23×C11C22×D411yescharacteristic
144Q8×C11—24no—
145Q8×C11—24no—
146Q8×C11—42no—
147Q8×C11—42no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—84no—
171C2×C4×C11#12012yes—
172C2×C4×C11C22×D412yes—
173C2×C4×C11C2×#4112yes—
174C2×C4×C112−1+411yescharacteristic
175C2×C4×C112−1+411yescharacteristic
176C8×C11—42no—
177C8×C11—42no—
178#541—28no—
179C2×C4⋊Q8C22×C1111yescharacteristic
180C2×#126—22no—
181C2×#125—22no—
182C2×#125C22×C1111yescharacteristic
183C2×C22⋊Q8C22×C1112yes—
184C2×C4×Q8C22×C1112yes—
185C2×#117C22×C1111yescharacteristic
186C2×#117C22×C1111yescharacteristic
187C22×C4⋊C4C22×C1111yescharacteristic
188#485—28no—
189C2×#107C22×C1112yes—
190C2×#106C22×C1112yes—
191C2×#103C22×C1112yes—
192C2×#103C22×C1112yes—
193C2×#103C22×C1112yes—
194C2×#103C22×C1112yes—
195C2×C22⋊C8C22×C1112yes—
196#389—22no—
197#389C22×C1112yes—
198#389C22×C1112yes—
199#380—22no—
200#340C22×C1112yes—
201#340C22×C1112yes—
202#336C22×C1112yes—
203#336C22×C1111yescharacteristic
204#336C22×C1111yescharacteristic
205C22×C11—22no—
206C22×C11—24no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—42no—
210C22×C11C2×#12011yescharacteristic
211C22×C11#52511yescharacteristic
212C22×C11#53611yescharacteristic
213C22×C11#57712yes—
214C22×C11#57812yes—
215C4×C11—22no—
216C4×C11—44no—
217C4×C11—44no—
218C4×C11—42no—
219C4×C11—42no—
220C4×C11—44no—
221C4×C11—82no—
222C4×C11#54712yes—
223C4×C11#54712yes—
224C22×Q8C23×C1112yes—
225C23×C4—21no—
226C23×C4C23×C1111yescharacteristic
227C22×C8C23×C1112yes—
228C22×C8C23×C1112yes—
229C4⋊Q8—24no—
230#126—216no—
231#125—216no—
232#125—24no—
233C22⋊Q8—24no—
234C22⋊Q8D4×C1118yes—
235C4×Q8—24no—
236C4×Q8—24no—
237#117—24no—
238#117—24no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4D4×C1112yes—
248C2×C4⋊C4C23×C1112yes—
249C2×C4⋊C4C23×C1112yes—
250C2×C4⋊C4C23×C1112yes—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4D4×C1112yes—
254C2×C42—22no—
255C2×C42—21no—
256C2×C42C23×C1111yescharacteristic
257C2×C42C23×C1111yescharacteristic
258#107—24no—
259#106—24no—
260#103—24no—
261#103—24no—
262#103—24no—
263#103—24no—
264C22⋊C8—24no—
265#95—22no—
266#95—22no—
267C2×C11—42no—
268C2×C11#240611yescharacteristic
269C2×C11#301312yes—
270C2×C11#312311yescharacteristic
271C2×C11#312711yescharacteristic
272C2×C11#324212yes—
273C24C2×D4×C1111yescharacteristic
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8C2×D4×C1114yes—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—22no—
288C22×C4—82no—
289C22×C4C2×D4×C1112yes—
290C22×C4C2×D4×C1112yes—
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C2×D4×C1114yes—
293C22×C4C24×C1111yescharacteristic
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C4⋊C4—24no—
301C4⋊C4—28no—
302C4⋊C4—28no—
303C4⋊C4—28no—
304C4⋊C4—28no—
305C4⋊C4—24no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—82no—
311C4⋊C4—82no—
312C4⋊C4C2×D4×C1114yes—
313C4⋊C4C11×#4114yes—
314C22⋊C4—28no—
315C22⋊C4—24no—
316C22⋊C4—42no—
317C42—28no—
318C42—22no—
319C42—22no—
320C42—42no—
321C11#2407211yescharacteristic, direct product factor, Sylow
322C23—21no—
323C23—21no—
324C23—22no—
325C23—22no—
326C23C11×#12012yes—
327C23C22×D4×C1111yescharacteristic
328Q8—24no—
329Q8—24no—
330Q8—42no—
331Q8—42no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—84no—
355C2×C4C11×#12012yes—
356C2×C4C22×D4×C1112yes—
357C2×C4C2×C11×#4112yes—
358C2×C4C11×2−1+411yescharacteristic
359C2×C4C11×2−1+411yescharacteristic
360C8—42no—
361C8—42no—
362C22—22no—
363C22—24no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22C2×C11×#12011yescharacteristic
368C22C11×#52511yescharacteristic
369C22C11×#53611yescharacteristic
370C22C11×#57712yes—
371C22C11×#57812yes—
372C4—22no—
373C4—44no—
374C4—42no—
375C4—42no—
376C4—44no—
377C4—44no—
378C4—82no—
379C4C11×#54712yes—
380C4C11×#54712yes—
381C2—42no—
382C2C11×#240611yescharacteristic
383C2C11×#301312yes—
384C2C11×#312311yescharacteristic
385C2C11×#312711yescharacteristic
386C2C11×#324212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2059C2semidirect
5. C11×#2043C2semidirect
7. C11×#1865C2semidirect
8. C11×#1863C2semidirect
80. #24072C11direct (N × H)
132. #2059C2×C11semidirect
133. #2043C2×C11semidirect
135. #1865C2×C11semidirect
136. #1863C2×C11semidirect
321. C11#24072direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5412
C2×C11×#4852
C11×#23162
C11×#20592
C11×#20432
C11×#18722
C11×#18652
C11×#18632
C11×#18182
#2407211