Finite Group Databasebeta

← C11×#24643 #14601836

Subgroups — C11×#24643 #14601836

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#461C211yesmaximal, characteristic, complemented
2C2×C11×#442C211yesmaximal, characteristic
3C11×#2547C211yesmaximal, characteristic, complemented
4C11×#2357C211yesmaximal, characteristic, complemented
5C11×#2055C212yesmaximal, complemented
6C11×#2012C212yesmaximal
7C11×#1983C212yesmaximal, complemented
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1927C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C22×C11×D8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#461—24no—
19C11×#442—24no—
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C11×#97C2211yescharacteristic
30C11×#397—21no—
31C11×#397—21no—
32C11×#391C2212yes—
33C11×#390C2212yes—
34C11×#388—22no—
35C11×#382C2211yescharacteristic
36C11×#381—21no—
37C11×#380—22no—
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2312yes—
44C22×D4×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C2×C11×SD16—24no—
49C2×C11×SD16—42no—
50C2×C11×SD16—42no—
51C2×C11×D8—22no—
52C2×C11×D8—22no—
53C2×C11×D8—22no—
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×#124—24no—
60C11×#124—42no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11D414yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C42×C11—22no—
78C2×C42×C11C2312yes—
79C2×C42×C11C2311yescharacteristic
80C11×#106—22no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—42no—
83C11×#103—24no—
84C11×#103—24no—
85C11×#103—42no—
86C11×#102—22no—
87C11×#102—22no—
88C11×#102—42no—
89C11×#97—22no—
90C11×#95—21no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—21no—
95C11×#95D411yescharacteristic
96C11×#95D411yescharacteristic
97#24643C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11C2×D412yes—
117C2×D4×C11#4112yes—
118C22×C4×C11—21no—
119C22×C4×C11—24no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—44no—
124C22×C4×C11—42no—
125C22×C4×C11—82no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C11×SD16—48no—
132C11×D8—28no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—22no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11#4112yes—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4C2×D412yes—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—44no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—82no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—82no—
160C42×C11C2×D412yes—
161C42×C11#4112yes—
162C2×#461C2×C1111yescharacteristic, complemented
163C2×#442C2×C1111yescharacteristic
164#2547C2×C1111yescharacteristic, complemented
165#2357C2×C1111yescharacteristic, complemented
166#2055C2×C1112yescomplemented
167#2012C2×C1112yes—
168#1983C2×C1112yescomplemented
169#1960C2×C1111yescharacteristic, complemented
170#1940C2×C1111yescharacteristic, complemented
171#1927C2×C1112yescomplemented
172#1804C2×C1111yescharacteristic, complemented
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11C22×D411yescharacteristic
184Q8×C11—42no—
185Q8×C11—42no—
186Q8×C11—42no—
187Q8×C11—42no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—22no—
191D4×C11—22no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—84no—
215C2×C4×C11—84no—
216C2×C4×C11#12112yes—
217C2×C4×C11#12112yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C8×C11—22no—
225C8×C11—41no—
226C8×C11—42no—
227C22×SD16C22×C1112yes—
228C22×D8C22×C1111yescharacteristic
229C2×C4⋊Q8C22×C1111yescharacteristic
230C2×#124C22×C1112yes—
231C2×C4×D4C22×C1111yescharacteristic
232C2×C4×D4C22×C1111yescharacteristic
233#461—24no—
234#442—24no—
235C2×#106C22×C1111yescharacteristic
236C2×C4⋊C8C22×C1111yescharacteristic
237C2×C4⋊C8C22×C1112yes—
238C2×#103C22×C1112yes—
239C2×#103C22×C1112yes—
240C2×#103C22×C1112yes—
241C2×#102C22×C1111yescharacteristic
242C2×#102C22×C1111yescharacteristic
243C2×#102C22×C1112yes—
244C2×#97C22×C1111yescharacteristic
245#397—21no—
246#397—21no—
247#391C22×C1112yes—
248#390C22×C1112yes—
249#388—22no—
250#382C22×C1111yescharacteristic
251#381—21no—
252#380—22no—
253C4×C4⋊C4C22×C1112yes—
254C4×C4⋊C4C22×C1111yescharacteristic
255C4×C22⋊C4—21no—
256#340C22×C1112yes—
257#336C22×C1112yes—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—44no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—82no—
268C22×C11C2×#12111yescharacteristic
269C22×C11#54611yescharacteristic
270C22×C11#55011yescharacteristic
271C22×C11#57512yes—
272C22×C11#57712yes—
273C4×C11—22no—
274C4×C11—22no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—82no—
279C4×C11—82no—
280C4×C11—81no—
281C4×C11#52511yescharacteristic
282C4×C11#53511yescharacteristic
283C4×C11#55311yescharacteristic
284C4×C11#55511yescharacteristic
285C22×Q8C23×C1112yes—
286C22×D4C23×C1111yescharacteristic
287C22×D4C23×C1111yescharacteristic
288C23×C4—21no—
289C23×C4—21no—
290C2×SD16—24no—
291C2×SD16—42no—
292C2×SD16—42no—
293C2×D8—22no—
294C2×D8—22no—
295C2×D8—22no—
296C22×C8C23×C1112yes—
297C22×C8C23×C1111yescharacteristic
298C22×C8C23×C1111yescharacteristic
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301#124—24no—
302#124—42no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4D4×C1114yes—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4D4×C1112yes—
310C2×C4⋊C4C23×C1111yescharacteristic
311C2×C4⋊C4C23×C1112yes—
312C2×C4⋊C4C23×C1111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C42—22no—
320C2×C42C23×C1112yes—
321C2×C42C23×C1111yescharacteristic
322#106—22no—
323C4⋊C8—22no—
324C4⋊C8—42no—
325#103—24no—
326#103—24no—
327#103—42no—
328#102—22no—
329#102—22no—
330#102—42no—
331#97—22no—
332#95—21no—
333#95—22no—
334#95—22no—
335#95—22no—
336#95—21no—
337#95D4×C1111yescharacteristic
338#95D4×C1111yescharacteristic
339C2×C11—82no—
340C2×C11—82no—
341C2×C11#241411yescharacteristic
342C2×C11#304011yescharacteristic
343C2×C11#304211yescharacteristic
344C2×C11#330712yes—
345C2×C11#340112yes—
346C24—21no—
347C24—21no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4C2×D4×C1112yes—
365C2×D4C11×#4112yes—
366C22×C4—21no—
367C22×C4—24no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—44no—
372C22×C4—42no—
373C22×C4—82no—
374C22×C4C2×D4×C1112yes—
375C22×C4C2×D4×C1112yes—
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C24×C1111yescharacteristic
379SD16—48no—
380D8—28no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—22no—
389C2×C8C11×#4112yes—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4C2×D4×C1112yes—
399C22⋊C4—24no—
400C22⋊C4—44no—
401C22⋊C4—44no—
402C22⋊C4—44no—
403C22⋊C4—42no—
404C22⋊C4—82no—
405C42—22no—
406C42—22no—
407C42—82no—
408C42C2×D4×C1112yes—
409C42C11×#4112yes—
410C11#2464311yescharacteristic, direct product factor, Sylow
411C23—22no—
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23C22×D4×C1111yescharacteristic
422Q8—42no—
423Q8—42no—
424Q8—42no—
425Q8—42no—
426D4—22no—
427D4—22no—
428D4—22no—
429D4—22no—
430D4—41no—
431D4—41no—
432D4—41no—
433D4—41no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—84no—
453C2×C4—84no—
454C2×C4C11×#12112yes—
455C2×C4C11×#12112yes—
456C2×C4C22×D4×C1111yescharacteristic
457C2×C4C2×C11×#4111yescharacteristic
458C2×C4C2×C11×#4111yescharacteristic
459C2×C4C2×C11×#4111yescharacteristic
460C2×C4C11×H(5,𝔽2)11yescharacteristic
461C2×C4C11×H(5,𝔽2)11yescharacteristic
462C8—22no—
463C8—42no—
464C8—41no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—44no—
470C22—81no—
471C22—81no—
472C22—82no—
473C22—82no—
474C22—82no—
475C22C2×C11×#12111yescharacteristic
476C22C11×#54611yescharacteristic
477C22C11×#55011yescharacteristic
478C22C11×#57512yes—
479C22C11×#57712yes—
480C4—22no—
481C4—22no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—82no—
486C4—81no—
487C4—82no—
488C4C11×#52511yescharacteristic
489C4C11×#53511yescharacteristic
490C4C11×#55311yescharacteristic
491C4C11×#55511yescharacteristic
492C2—82no—
493C2—82no—
494C2C11×#241411yescharacteristic
495C2C11×#304011yescharacteristic
496C2C11×#304211yescharacteristic
497C2C11×#330712yes—
498C2C11×#340112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#461C2semidirect
3. C11×#2547C2semidirect
4. C11×#2357C2semidirect
5. C11×#2055C2semidirect
7. C11×#1983C2semidirect
8. C11×#1960C2semidirect
9. C11×#1940C2semidirect
10. C11×#1927C2semidirect
11. C11×#1804C2semidirect
97. #24643C11direct (N × H)
162. C2×#461C2×C11semidirect
164. #2547C2×C11semidirect
165. #2357C2×C11semidirect
166. #2055C2×C11semidirect
168. #1983C2×C11semidirect
169. #1960C2×C11semidirect
170. #1940C2×C11semidirect
171. #1927C2×C11semidirect
172. #1804C2×C11semidirect
410. C11#24643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C2×C11×#4422
C11×#25472
C11×#23572
C11×#20552
C11×#20122
C11×#19832
C11×#19602
C11×#19402
C11×#19272
C11×#18042
#2464311