Finite Group Databasebeta

← C11×#24609 #14601802

Subgroups — C11×#24609 #14601802

Order 2816.

860 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#483C211yesmaximal, characteristic
2C2×C11×#432C211yesmaximal, characteristic
3C11×#2855C211yesmaximal, characteristic
4C2×C11×#389C211yesmaximal, characteristic
5C11×#2088C212yesmaximal, complemented
6C11×#2068C212yesmaximal, complemented
7C11×#1943C212yesmaximal, complemented
8C11×#1935C212yesmaximal, complemented
9C11×#1872C211yesmaximal, characteristic
10C11×#1852C211yesmaximal, characteristic
11C11×#1823C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C22×C11×C4⋊C4—21no—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C11×#483—24no—
18C11×#432—24no—
19C2×C11×#107C2212yes—
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#97C2212yes—
27C11×#391C2211yescharacteristic
28C11×#391C2211yescharacteristic
29C11×#389—21no—
30C11×#389—21no—
31C11×#389C2212yes—
32C11×#389C2211yescharacteristic
33C11×#389C2212yes—
34C11×#389C2211yescharacteristic
35C11×#387—21no—
36C11×#387—21no—
37C11×#385—21no—
38C11×#381—21no—
39C11×#380C2211yescharacteristic
40C2×C11×#95—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2312yes—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—44no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—22no—
74C2×C42×C11—22no—
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C11×#107—24no—
80C11×#106—24no—
81C11×C4⋊C8—24no—
82C11×#103—24no—
83C11×#103—24no—
84C11×C22⋊C8—22no—
85C11×C22⋊C8D414yes—
86C11×#97—24no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—21no—
90C11×#95—21no—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—21no—
96#24609C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11C2×D411yescharacteristic
98C2×Q8×C11—21no—
99C2×Q8×C11—22no—
100C2×Q8×C11—21no—
101C2×Q8×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—41no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11C2×D414yes—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4—44no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4#4114yes—
151C11×C22⋊C4—42no—
152C11×C22⋊C4—42no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—21no—
159C2×#483C2×C1111yescharacteristic
160C2×#432C2×C1111yescharacteristic
161#2855C2×C1111yescharacteristic
162C2×#389C2×C1111yescharacteristic
163#2088C2×C1112yescomplemented
164#2068C2×C1112yescomplemented
165#1943C2×C1112yescomplemented
166#1935C2×C1112yescomplemented
167#1872C2×C1111yescharacteristic
168#1852C2×C1111yescharacteristic
169#1823C2×C1111yescharacteristic
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11#12112yes—
175C23×C11AGL(1,ℤ/8)12yes—
176C23×C11#13712yes—
177C23×C11C22×D411yescharacteristic
178Q8×C11—42no—
179Q8×C11—42no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—24no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—44no—
197C2×C4×C11—48no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—44no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—84no—
217C2×C4×C11#12112yes—
218C2×C4×C11#13712yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4112yes—
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C112−1+412yes—
223C8×C11—24no—
224C8×C11—42no—
225C2×C22⋊Q8C22×C1111yescharacteristic
226C22×C4⋊C4—21no—
227C22×C4⋊C4C22×C1111yescharacteristic
228C22×C4⋊C4C22×C1111yescharacteristic
229C22×C42C22×C1111yescharacteristic
230#483—24no—
231#432—24no—
232C2×#107C22×C1112yes—
233C2×#106C22×C1112yes—
234C2×C4⋊C8C22×C1112yes—
235C2×#103C22×C1112yes—
236C2×#103C22×C1112yes—
237C2×C22⋊C8C22×C1111yescharacteristic
238C2×C22⋊C8C22×C1111yescharacteristic
239C2×#97C22×C1112yes—
240#391C22×C1111yescharacteristic
241#391C22×C1111yescharacteristic
242#389—21no—
243#389—21no—
244#389C22×C1112yes—
245#389C22×C1111yescharacteristic
246#389C22×C1111yescharacteristic
247#389C22×C1112yes—
248#387—21no—
249#387—21no—
250#385—21no—
251#381—21no—
252#380C22×C1111yescharacteristic
253C2×#95—21no—
254#340C22×C1112yes—
255#340C22×C1112yes—
256#340C22×C1112yes—
257#340C22×C1112yes—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11#46814yes—
265C22×C11C2×#12111yescharacteristic
266C22×C11#52511yescharacteristic
267C22×C11#53611yescharacteristic
268C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C22×C11C2×#13711yescharacteristic
270C22×C11C2×#13711yescharacteristic
271C22×C11#57511yescharacteristic
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—44no—
275C4×C11—41no—
276C4×C11—41no—
277C4×C11—41no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11—82no—
282C4×C11—81no—
283C4×C11#54712yes—
284C4×C11#55212yes—
285C22×Q8C23×C1111yescharacteristic
286C23×C4—21no—
287C23×C4—21no—
288C23×C4D4×C1111yescharacteristic
289C23×C4D4×C1111yescharacteristic
290C23×C4C23×C1111yescharacteristic
291C22×C8C23×C1112yes—
292C22×C8C23×C1112yes—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4C23×C1112yes—
307C2×C4⋊C4C23×C1111yescharacteristic
308C2×C4⋊C4C23×C1111yescharacteristic
309C2×C4⋊C4C23×C1111yescharacteristic
310C2×C4⋊C4C23×C1112yes—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42D4×C1111yescharacteristic
316C2×C42D4×C1111yescharacteristic
317C2×C42C23×C1111yescharacteristic
318C2×C42C23×C1111yescharacteristic
319#107—24no—
320#106—24no—
321C4⋊C8—24no—
322#103—24no—
323#103—24no—
324C22⋊C8—22no—
325C22⋊C8D4×C1114yes—
326#97—24no—
327#95—22no—
328#95—22no—
329#95—21no—
330#95—21no—
331#95—21no—
332#95—21no—
333#95—21no—
334#95—21no—
335#95—21no—
336C2×C11—24no—
337C2×C11#241311yescharacteristic
338C2×C11C2×#46811yescharacteristic
339C2×C11#305611yescharacteristic
340C2×C11#311311yescharacteristic
341C2×C11#311411yescharacteristic
342C2×C11#323611yescharacteristic
343C2×C11#323811yescharacteristic
344C24C2×D4×C1111yescharacteristic
345C2×Q8—21no—
346C2×Q8—22no—
347C2×Q8—21no—
348C2×Q8—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—41no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1111yescharacteristic
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C2×D4×C1112yes—
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C11×#4112yes—
376C22×C4C24×C1111yescharacteristic
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8C2×D4×C1114yes—
383C4⋊C4—24no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—44no—
392C4⋊C4—44no—
393C4⋊C4—42no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4C11×#4114yes—
398C22⋊C4—42no—
399C22⋊C4—42no—
400C42—22no—
401C42—22no—
402C42—21no—
403C42—21no—
404C42—21no—
405C42—21no—
406C11#2460911yescharacteristic, direct product factor, Sylow
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23C11×#12112yes—
412C23C11×AGL(1,ℤ/8)12yes—
413C23C11×#13712yes—
414C23C22×D4×C1111yescharacteristic
415Q8—42no—
416Q8—42no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—24no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—48no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—84no—
454C2×C4C11×#12112yes—
455C2×C4C11×#13712yes—
456C2×C4C22×D4×C1111yescharacteristic
457C2×C4C2×C11×#4112yes—
458C2×C4C2×C11×#4111yescharacteristic
459C2×C4C11×2−1+412yes—
460C8—24no—
461C8—42no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22C11×#46814yes—
469C22C2×C11×#12111yescharacteristic
470C22C11×#52511yescharacteristic
471C22C11×#53611yescharacteristic
472C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
473C22C2×C11×#13711yescharacteristic
474C22C2×C11×#13711yescharacteristic
475C22C11×#57511yescharacteristic
476C4—22no—
477C4—22no—
478C4—41no—
479C4—41no—
480C4—41no—
481C4—44no—
482C4—81no—
483C4—81no—
484C4—82no—
485C4—81no—
486C4—81no—
487C4C11×#54712yes—
488C4C11×#55212yes—
489C2—24no—
490C2C11×#241311yescharacteristic
491C2C2×C11×#46811yescharacteristic
492C2C11×#305611yescharacteristic
493C2C11×#311311yescharacteristic
494C2C11×#311411yescharacteristic
495C2C11×#323611yescharacteristic
496C2C11×#323811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#2088C2semidirect
6. C11×#2068C2semidirect
7. C11×#1943C2semidirect
8. C11×#1935C2semidirect
96. #24609C11direct (N × H)
163. #2088C2×C11semidirect
164. #2068C2×C11semidirect
165. #1943C2×C11semidirect
166. #1935C2×C11semidirect
406. C11#24609direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4832
C2×C11×#4322
C11×#28552
C2×C11×#3892
C11×#20882
C11×#20682
C11×#19432
C11×#19352
C11×#18722
C11×#18522
C11×#18232
#2460911