Finite Group Databasebeta

← C11×#20967 #14598160

Subgroups — C11×#20967 #14598160

Order 2816.

2042 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C8×C11C211yesmaximal, characteristic, complemented
2C2×C11×#525C211yesmaximal, characteristic
3C2×C11×#416C212yesmaximal, complemented
4C11×#2280C211yesmaximal, characteristic, complemented
5C11×#1893C214yesmaximal, complemented
6C11×#1892C214yesmaximal, complemented
7C11×#1735C212yesmaximal, complemented
8C22×C11×#41C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C23×C8×C11—24no—
11C23×C8×C11—28no—
12C23×C8×C11C2214yes—
13C23×C8×C11C2212yes—
14C11×#525—24no—
15C11×#525C418yescomplemented
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×#121C2212yes—
19C2×C11×#120—21no—
20C2×C4×D4×C11—22no—
21C2×C11×#117C2212yes—
22C2×C11×#117C2211yescharacteristic
23C11×#416—28no—
24C2×C11×#103C2214yescomplemented
25C2×C11×#102C2214yescomplemented
26C11×#381—21no—
27C11×#380C2214yes—
28C11×#379—21no—
29C4×C11×C22⋊C4—22no—
30C11×#340C2218yescomplemented
31C25×C11D411yescharacteristic
32C2×C11×#41—22no—
33C2×C11×#41—24no—
34C2×C11×#41—24no—
35C2×C11×#41C2×C414yes—
36C22×Q8×C11C2311yescharacteristic
37C22×D4×C11—22no—
38C22×D4×C11—21no—
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11—24no—
41C23×C4×C11—24no—
42C23×C4×C11—21no—
43C23×C4×C11C2×C414yes—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D412yes—
46C23×C4×C11D414yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C22×C8×C11—232no—
50C22×C8×C11—28no—
51C22×C8×C11—24no—
52C22×C8×C11—24no—
53C22×C8×C11—216no—
54C22×C8×C11D418yescomplemented
55C22×C8×C11C2314yes—
56C11×#123—28no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8C2×C418yes—
59C11×#121—24no—
60C11×#121C2×C418yes—
61C11×#120—28no—
62C4×D4×C11—216no—
63C11×#117—22no—
64C11×#117—24no—
65C11×#117—24no—
66C11×#117C2×C414yes—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—24no—
75C2×C42×C11—21no—
76C2×C42×C11—22no—
77C11×#103—28no—
78C11×#102—28no—
79C11×#95—24no—
80#20967C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11—24no—
82C24×C11—28no—
83C24×C11—21no—
84C24×C11C22⋊C414yes—
85C24×C11C2×D411yescharacteristic
86C24×C11C2×D412yes—
87C11×#41—216no—
88C11×#41—44no—
89C11×#41—44no—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11C22×C412yes—
94C2×D4×C11—28no—
95C2×D4×C11—24no—
96C2×D4×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—22no—
99C2×D4×C11—44no—
100C2×D4×C11—48no—
101C2×D4×C11C22×C412yes—
102C22×C4×C11—24no—
103C22×C4×C11—216no—
104C22×C4×C11—28no—
105C22×C4×C11—28no—
106C22×C4×C11—28no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—44no—
114C22×C4×C11C22⋊C418yes—
115C22×C4×C11C22⋊C414yes—
116C22×C4×C11C22×C414yes—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D414yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D414yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11#4114yes—
124C22×C4×C11C2411yescharacteristic
125C2×C8×C11—232no—
126C2×C8×C11—216no—
127C2×C8×C11—24no—
128C2×C8×C11—24no—
129C2×C8×C11C2×D418yes—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4C22×C414yes—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—28no—
137C11×C22⋊C4—28no—
138C11×C22⋊C4—44no—
139C11×C22⋊C4—48no—
140C42×C11—24no—
141C42×C11—44no—
142C24×C8C2×C1111yescharacteristic, complemented
143C2×#525C2×C1111yescharacteristic
144C2×#416C2×C1112yescomplemented
145#2280C2×C1111yescharacteristic, complemented
146#1893C2×C1114yescomplemented
147#1892C2×C1114yescomplemented
148#1735C2×C1112yescomplemented
149C23×C11—232no—
150C23×C11—24no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—28no—
154C23×C11—216no—
155C23×C11—22no—
156C23×C11—42no—
157C23×C11—44no—
158C23×C11C2×C22⋊C412yes—
159C23×C11C2×C22⋊C414yes—
160C23×C11#12114yes—
161C23×C11#13518yes—
162C23×C11C22×D411yescharacteristic
163Q8×C11—24no—
164Q8×C11—41no—
165Q8×C11—41no—
166D4×C11—24no—
167D4×C11—48no—
168D4×C11—416no—
169D4×C11—41no—
170D4×C11—41no—
171C2×C4×C11—24no—
172C2×C4×C11—28no—
173C2×C4×C11—28no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—216no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—42no—
180C2×C4×C11—44no—
181C2×C4×C11—48no—
182C2×C4×C11—44no—
183C2×C4×C11—48no—
184C2×C4×C11C2×C22⋊C414yes—
185C2×C4×C11C2×C22⋊C412yes—
186C2×C4×C11C4×D418yes—
187C2×C4×C11#12014yes—
188C2×C4×C11#12114yes—
189C2×C4×C11#12314yes—
190C2×C4×C11C23×C411yescharacteristic
191C2×C4×C11C22×D412yes—
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C2×#4112yes—
194C8×C11—28no—
195C22×#41C22×C1111yescharacteristic
196C24×C4C22×C1111yescharacteristic
197C23×C8—24no—
198C23×C8—28no—
199C23×C8C22×C1114yes—
200C23×C8C22×C1112yes—
201#525—24no—
202#525C4×C1118yescomplemented
203C2×#123—21no—
204C2×C22⋊Q8C22×C1112yes—
205C2×#121C22×C1112yes—
206C2×#120—21no—
207C2×C4×D4—22no—
208C2×#117C22×C1112yes—
209C2×#117C22×C1111yescharacteristic
210#416—28no—
211C2×#103C22×C1114yescomplemented
212C2×#102C22×C1114yescomplemented
213#381—21no—
214#380C22×C1114yes—
215#379—21no—
216C4×C22⋊C4—22no—
217#340C22×C1118yescomplemented
218C22×C11—232no—
219C22×C11—24no—
220C22×C11—24no—
221C22×C11—28no—
222C22×C11—216no—
223C22×C11—24no—
224C22×C11—44no—
225C22×C11—42no—
226C22×C11—84no—
227C22×C11#38614yes—
228C22×C11#41618yescomplemented
229C22×C11C22×C22⋊C411yescharacteristic
230C22×C11C2×#12112yes—
231C22×C11C2×#13514yes—
232C4×C11—24no—
233C4×C11—44no—
234C4×C11—42no—
235C4×C11—84no—
236C4×C11#38614yes—
237C4×C11C2×C4×D412yes—
238C4×C11C2×#12011yescharacteristic
239C4×C11C2×#12311yescharacteristic
240C25D4×C1111yescharacteristic
241C2×#41—22no—
242C2×#41—24no—
243C2×#41—24no—
244C2×#41C2×C4×C1114yes—
245C22×Q8C23×C1111yescharacteristic
246C22×D4—22no—
247C22×D4—21no—
248C22×D4C23×C1111yescharacteristic
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—21no—
252C23×C4C2×C4×C1114yes—
253C23×C4D4×C1112yes—
254C23×C4D4×C1111yescharacteristic
255C23×C4D4×C1114yes—
256C23×C4C23×C1112yes—
257C23×C4C23×C1111yescharacteristic
258C22×C8—232no—
259C22×C8—28no—
260C22×C8—24no—
261C22×C8—24no—
262C22×C8—216no—
263C22×C8D4×C1118yescomplemented
264C22×C8C23×C1114yes—
265#123—28no—
266C22⋊Q8—24no—
267C22⋊Q8C2×C4×C1118yes—
268#121—24no—
269#121C2×C4×C1118yes—
270#120—28no—
271C4×D4—216no—
272#117—22no—
273#117—24no—
274#117—24no—
275#117C2×C4×C1114yes—
276C2×C4⋊C4—22no—
277C2×C4⋊C4C23×C1114yes—
278C2×C4⋊C4C23×C1112yes—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—24no—
284C2×C42—21no—
285C2×C42—22no—
286#103—28no—
287#102—28no—
288#95—24no—
289C2×C11—24no—
290C2×C11—28no—
291C2×C11—82no—
292C2×C11C2×#38611yescharacteristic
293C2×C11C2×#41612yes—
294C2×C11#305014yes—
295C24—24no—
296C24—28no—
297C24—21no—
298C24C11×C22⋊C414yes—
299C24C2×D4×C1111yescharacteristic
300C24C2×D4×C1112yes—
301#41—216no—
302#41—44no—
303#41—44no—
304C2×Q8—21no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8C22×C4×C1112yes—
308C2×D4—28no—
309C2×D4—24no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—44no—
314C2×D4—48no—
315C2×D4C22×C4×C1112yes—
316C22×C4—24no—
317C22×C4—216no—
318C22×C4—28no—
319C22×C4—28no—
320C22×C4—28no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—44no—
328C22×C4C11×C22⋊C418yes—
329C22×C4C11×C22⋊C414yes—
330C22×C4C22×C4×C1114yes—
331C22×C4C22×C4×C1112yes—
332C22×C4C2×D4×C1112yes—
333C22×C4C2×D4×C1114yes—
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C2×D4×C1112yes—
336C22×C4C2×D4×C1114yes—
337C22×C4C11×#4114yes—
338C22×C4C24×C1111yescharacteristic
339C2×C8—232no—
340C2×C8—216no—
341C2×C8—24no—
342C2×C8—24no—
343C2×C8C2×D4×C1118yes—
344C4⋊C4—28no—
345C4⋊C4—22no—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4C22×C4×C1114yes—
349C22⋊C4—24no—
350C22⋊C4—28no—
351C22⋊C4—28no—
352C22⋊C4—44no—
353C22⋊C4—48no—
354C42—24no—
355C42—44no—
356C11#2096711yescharacteristic, direct product factor, Sylow
357C23—232no—
358C23—24no—
359C23—28no—
360C23—216no—
361C23—24no—
362C23—24no—
363C23—22no—
364C23—42no—
365C23—44no—
366C23C2×C11×C22⋊C412yes—
367C23C2×C11×C22⋊C414yes—
368C23C11×#12114yes—
369C23C11×#13518yes—
370C23C22×D4×C1111yescharacteristic
371Q8—24no—
372Q8—41no—
373Q8—41no—
374D4—24no—
375D4—48no—
376D4—416no—
377D4—41no—
378D4—41no—
379C2×C4—24no—
380C2×C4—28no—
381C2×C4—28no—
382C2×C4—24no—
383C2×C4—216no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—48no—
390C2×C4—44no—
391C2×C4—48no—
392C2×C4C2×C11×C22⋊C414yes—
393C2×C4C2×C11×C22⋊C412yes—
394C2×C4C4×D4×C1118yes—
395C2×C4C11×#12014yes—
396C2×C4C11×#12114yes—
397C2×C4C11×#12314yes—
398C2×C4C23×C4×C1111yescharacteristic
399C2×C4C22×D4×C1112yes—
400C2×C4C22×D4×C1111yescharacteristic
401C2×C4C2×C11×#4112yes—
402C8—28no—
403C22—232no—
404C22—24no—
405C22—24no—
406C22—28no—
407C22—216no—
408C22—24no—
409C22—44no—
410C22—42no—
411C22—84no—
412C22C11×#38614yes—
413C22C11×#41618yescomplemented
414C22C22×C11×C22⋊C411yescharacteristic
415C22C2×C11×#12112yes—
416C22C2×C11×#13514yes—
417C4—24no—
418C4—44no—
419C4—42no—
420C4—84no—
421C4C11×#38614yes—
422C4C2×C4×D4×C1112yes—
423C4C2×C11×#12011yescharacteristic
424C4C2×C11×#12311yescharacteristic
425C2—24no—
426C2—28no—
427C2—82no—
428C2C2×C11×#38611yescharacteristic
429C2C2×C11×#41612yes—
430C2C11×#305014yes—
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C22×D4
prime radicalC2×C11×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C24×C8×C11C2semidirect
3. C2×C11×#416C2semidirect
4. C11×#2280C2semidirect
5. C11×#1893C2semidirect
6. C11×#1892C2semidirect
7. C11×#1735C2semidirect
15. C11×#525C4semidirect
24. C2×C11×#103C22semidirect
25. C2×C11×#102C22semidirect
30. C11×#340C22semidirect
54. C22×C8×C11D4semidirect
80. #20967C11direct (N × H)
142. C24×C8C2×C11semidirect
144. C2×#416C2×C11semidirect
145. #2280C2×C11semidirect
146. #1893C2×C11semidirect
147. #1892C2×C11semidirect
148. #1735C2×C11semidirect
202. #525C4×C11semidirect
211. C2×#103C22×C11semidirect
212. C2×#102C22×C11semidirect
217. #340C22×C11semidirect
228. C22×C11#416semidirect
263. C22×C8D4×C11semidirect
356. C11#20967direct (N × H)
413. C22C11×#416semidirect

Maximal subgroups

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

subgroupindex
C24×C8×C112
C2×C11×#5252
C2×C11×#4162
C11×#22802
C11×#18932
C11×#18922
C11×#17352
#2096711