Finite Group Databasebeta

← C11×#24629 #14601822

Subgroups — C11×#24629 #14601822

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#462C211yesmaximal, characteristic, complemented
2C2×C4×C11×SD16C211yesmaximal, characteristic
3C11×#2547C211yesmaximal, characteristic
4C11×#2355C211yesmaximal, characteristic, complemented
5C11×#2056C212yesmaximal, complemented
6C11×#2015C212yesmaximal
7C11×#1983C212yesmaximal
8C11×#1956C211yesmaximal, characteristic, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1927C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C22×C11×SD16C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#462—24no—
19C4×C11×SD16—24no—
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30C11×#397—22no—
31C11×#391C2212yes—
32C11×#391C2212yes—
33C11×#387—22no—
34C11×#384C2211yescharacteristic
35C11×#382—21no—
36C11×#380—21no—
37C11×#380—21no—
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2312yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C2×C11×Q16—24no—
48C2×C11×Q16—42no—
49C2×C11×Q16—42no—
50C2×C11×SD16—22no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C22×C8×C11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×#124—24no—
59C11×#124—42no—
60C4×Q8×C11—22no—
61C4×Q8×C11D414yes—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C42×C11—21no—
78C2×C42×C11—22no—
79C2×C42×C11C2312yes—
80C2×C42×C11C2311yescharacteristic
81C11×#106—22no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—42no—
84C11×#103—22no—
85C11×#103—24no—
86C11×#103—24no—
87C11×#103—42no—
88C11×#102—22no—
89C11×#102—42no—
90C4×C8×C11—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95D412yes—
97#24629C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11C2×D412yes—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11#4112yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C11×Q16—48no—
131C11×SD16—28no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11#4112yes—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—81no—
153C11×C4⋊C4C2×D412yes—
154C11×C22⋊C4—44no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—42no—
157C42×C11—24no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—82no—
161C42×C11C2×D412yes—
162C42×C11#4112yes—
163C2×#462C2×C1111yescharacteristic, complemented
164C2×C4×SD16C2×C1111yescharacteristic
165#2547C2×C1111yescharacteristic
166#2355C2×C1111yescharacteristic, complemented
167#2056C2×C1112yescomplemented
168#2015C2×C1112yes—
169#1983C2×C1112yes—
170#1956C2×C1111yescharacteristic, complemented
171#1939C2×C1111yescharacteristic, complemented
172#1927C2×C1112yescomplemented
173#1802C2×C1111yescharacteristic
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11C22×D411yescharacteristic
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—42no—
187Q8×C11—42no—
188Q8×C11—42no—
189Q8×C11—42no—
190D4×C11—22no—
191D4×C11—22no—
192D4×C11—41no—
193D4×C11—41no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
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—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—84no—
218C2×C4×C11#12112yes—
219C2×C4×C11#12112yes—
220C2×C4×C11#13512yes—
221C2×C4×C11#13712yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C8×C11—22no—
229C8×C11—41no—
230C8×C11—42no—
231C22×Q16C22×C1112yes—
232C22×SD16C22×C1111yescharacteristic
233C2×C4⋊Q8C22×C1111yescharacteristic
234C2×#124C22×C1112yes—
235C2×C4×Q8C22×C1111yescharacteristic
236C2×C4×D4C22×C1111yescharacteristic
237#462—24no—
238C4×SD16—24no—
239C2×#106C22×C1111yescharacteristic
240C2×C4⋊C8C22×C1111yescharacteristic
241C2×C4⋊C8C22×C1112yes—
242C2×#103C22×C1111yescharacteristic
243C2×#103C22×C1112yes—
244C2×#103C22×C1112yes—
245C2×#103C22×C1112yes—
246C2×#102C22×C1111yescharacteristic
247C2×#102C22×C1112yes—
248C2×C4×C8C22×C1111yescharacteristic
249#397—22no—
250#391C22×C1112yes—
251#391C22×C1112yes—
252#387—22no—
253#384C22×C1111yescharacteristic
254#382—21no—
255#380—21no—
256#380—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4C22×C1112yes—
259C4×C4⋊C4C22×C1111yescharacteristic
260#340C22×C1112yes—
261#336C22×C1112yes—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11C2×#12111yescharacteristic
270C22×C11#54611yescharacteristic
271C22×C11#55011yescharacteristic
272C22×C11C2×#13511yescharacteristic
273C22×C11C2×#13711yescharacteristic
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C4×C11—22no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—82no—
282C4×C11—82no—
283C4×C11—81no—
284C4×C11#46414yes—
285C4×C11#52511yescharacteristic
286C4×C11#53511yescharacteristic
287C4×C11#55311yescharacteristic
288C4×C11#55511yescharacteristic
289C22×Q8C23×C1112yes—
290C22×Q8C23×C1111yescharacteristic
291C22×D4C23×C1111yescharacteristic
292C23×C4—21no—
293C2×Q16—24no—
294C2×Q16—42no—
295C2×Q16—42no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×SD16—22no—
299C22×C8C23×C1112yes—
300C22×C8C23×C1111yescharacteristic
301C22×C8C23×C1111yescharacteristic
302C4⋊Q8—22no—
303C4⋊Q8—22no—
304#124—24no—
305#124—42no—
306C4×Q8—22no—
307C4×Q8D4×C1114yes—
308C4×D4—22no—
309C4×D4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4D4×C1111yescharacteristic
316C2×C4⋊C4D4×C1111yescharacteristic
317C2×C4⋊C4C23×C1111yescharacteristic
318C2×C4⋊C4C23×C1112yes—
319C2×C4⋊C4C23×C1111yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C42—21no—
324C2×C42—22no—
325C2×C42C23×C1112yes—
326C2×C42C23×C1111yescharacteristic
327#106—22no—
328C4⋊C8—22no—
329C4⋊C8—42no—
330#103—22no—
331#103—24no—
332#103—24no—
333#103—42no—
334#102—22no—
335#102—42no—
336C4×C8—22no—
337#95—22no—
338#95—22no—
339#95—22no—
340#95—22no—
341#95—22no—
342#95D4×C1112yes—
343C2×C11—82no—
344C2×C11#241411yescharacteristic
345C2×C11C2×#46411yescharacteristic
346C2×C11#304611yescharacteristic
347C2×C11#330211yescharacteristic
348C2×C11#333111yescharacteristic
349C2×C11#339411yescharacteristic
350C2×C11#339811yescharacteristic
351C24—21no—
352C2×Q8—21no—
353C2×Q8—22no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8C2×D4×C1112yes—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4C11×#4112yes—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4C2×D4×C1112yes—
379C22×C4C2×D4×C1112yes—
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C24×C1111yescharacteristic
383Q16—48no—
384SD16—28no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—22no—
393C2×C8C11×#4112yes—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—81no—
406C4⋊C4C2×D4×C1112yes—
407C22⋊C4—44no—
408C22⋊C4—44no—
409C22⋊C4—42no—
410C42—24no—
411C42—22no—
412C42—22no—
413C42—82no—
414C42C2×D4×C1112yes—
415C42C11×#4112yes—
416C11#2462911yescharacteristic, direct product factor, Sylow
417C23—22no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23C22×D4×C1111yescharacteristic
425Q8—22no—
426Q8—22no—
427Q8—41no—
428Q8—41no—
429Q8—42no—
430Q8—42no—
431Q8—42no—
432Q8—42no—
433D4—22no—
434D4—22no—
435D4—41no—
436D4—41no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—84no—
461C2×C4C11×#12112yes—
462C2×C4C11×#12112yes—
463C2×C4C11×#13512yes—
464C2×C4C11×#13712yes—
465C2×C4C22×D4×C1111yescharacteristic
466C2×C4C2×C11×#4111yescharacteristic
467C2×C4C2×C11×#4111yescharacteristic
468C2×C4C2×C11×#4111yescharacteristic
469C2×C4C11×H(5,𝔽2)11yescharacteristic
470C2×C4C11×H(5,𝔽2)11yescharacteristic
471C8—22no—
472C8—42no—
473C8—41no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22C2×C11×#12111yescharacteristic
482C22C11×#54611yescharacteristic
483C22C11×#55011yescharacteristic
484C22C2×C11×#13511yescharacteristic
485C22C2×C11×#13711yescharacteristic
486C22C11×#57711yescharacteristic
487C22C11×#57811yescharacteristic
488C4—22no—
489C4—42no—
490C4—42no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—81no—
495C4—82no—
496C4C11×#46414yes—
497C4C11×#52511yescharacteristic
498C4C11×#53511yescharacteristic
499C4C11×#55311yescharacteristic
500C4C11×#55511yescharacteristic
501C2—82no—
502C2C11×#241411yescharacteristic
503C2C2×C11×#46411yescharacteristic
504C2C11×#304611yescharacteristic
505C2C11×#330211yescharacteristic
506C2C11×#333111yescharacteristic
507C2C11×#339411yescharacteristic
508C2C11×#339811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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×#462C2semidirect
4. C11×#2355C2semidirect
5. C11×#2056C2semidirect
8. C11×#1956C2semidirect
9. C11×#1939C2semidirect
10. C11×#1927C2semidirect
97. #24629C11direct (N × H)
163. C2×#462C2×C11semidirect
166. #2355C2×C11semidirect
167. #2056C2×C11semidirect
170. #1956C2×C11semidirect
171. #1939C2×C11semidirect
172. #1927C2×C11semidirect
416. C11#24629direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4622
C2×C4×C11×SD162
C11×#25472
C11×#23552
C11×#20562
C11×#20152
C11×#19832
C11×#19562
C11×#19392
C11×#19272
C11×#18022
#2462911