Finite Group Databasebeta

← C11×#24745 #14601938

Subgroups — C11×#24745 #14601938

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C212yesmaximal
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C2×C11×#442C211yesmaximal, characteristic
4C11×#2547C211yesmaximal, characteristic, complemented
5C11×#2349C211yesmaximal, characteristic, complemented
6C11×#2066C212yesmaximal, complemented
7C11×#2042C212yesmaximal, complemented
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1877C212yesmaximal, 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×C11C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C11×#463—28no—
20C11×#461—24no—
21C11×#442—24no—
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2212yes—
31C2×C11×#97C2211yescharacteristic
32C11×#397—21no—
33C11×#397—21no—
34C11×#391C2212yes—
35C11×#389C2212yes—
36C11×#385—22no—
37C11×#382C2211yescharacteristic
38C11×#380—22no—
39C11×#380—21no—
40C4×C11×C4⋊C4C2211yescharacteristic
41C2×C11×#95—21no—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2312yes—
45C22×D4×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11—22no—
50C2×C11×SD16—24no—
51C2×C11×SD16—24no—
52C2×C11×SD16—24no—
53C2×C11×D8—22no—
54C2×C11×D8—22no—
55C2×C11×D8D414yes—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—22no—
61C11×#124—24no—
62C11×#124—42no—
63C4×D4×C11—24no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—42no—
68C4×D4×C11D414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4D412yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C42×C11C2312yes—
82C2×C42×C11C2311yescharacteristic
83C11×#106—22no—
84C11×C4⋊C8—24no—
85C11×C4⋊C8—22no—
86C11×#103—24no—
87C11×#103—24no—
88C11×#103—42no—
89C11×#102—22no—
90C11×#102—24no—
91C11×#102—22no—
92C11×#97—22no—
93C11×#95—21no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—22no—
97C11×#95—21no—
98C11×#95D411yescharacteristic
99C11×#95D411yescharacteristic
100#24745C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C24×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
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×C11—21no—
117C2×D4×C11C2×D412yes—
118C2×D4×C11C2×D412yes—
119C2×D4×C11C2×D412yes—
120C2×D4×C11#4112yes—
121C22×C4×C11—21no—
122C22×C4×C11—24no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—44no—
127C22×C4×C11—44no—
128C22×C4×C11—44no—
129C22×C4×C11—42no—
130C22×C4×C11—82no—
131C22×C4×C11—82no—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C11×SD16—48no—
138C11×D8—28no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C2×D412yes—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—82no—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—42no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11C2×D412yes—
166C42×C11#4112yes—
167C2×#463C2×C1112yes—
168C2×#461C2×C1111yescharacteristic, complemented
169C2×#442C2×C1111yescharacteristic
170#2547C2×C1111yescharacteristic, complemented
171#2349C2×C1111yescharacteristic, complemented
172#2066C2×C1112yescomplemented
173#2042C2×C1112yescomplemented
174#1960C2×C1111yescharacteristic, complemented
175#1940C2×C1111yescharacteristic, complemented
176#1877C2×C1112yescomplemented
177#1804C2×C1111yescharacteristic, complemented
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11C22×D411yescharacteristic
189Q8×C11—42no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—42no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—22no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11#12114yes—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—84no—
220C2×C4×C11—84no—
221C2×C4×C11—88no—
222C2×C4×C11#12112yes—
223C2×C4×C11#12112yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×C4×C112−1+411yescharacteristic
230C8×C11—22no—
231C8×C11—42no—
232C8×C11—41no—
233C22×SD16C22×C1112yes—
234C22×D8C22×C1111yescharacteristic
235C2×C4⋊Q8C22×C1111yescharacteristic
236C2×#124C22×C1112yes—
237C2×C4×D4C22×C1111yescharacteristic
238C2×C4×D4C22×C1112yes—
239C2×C4×D4C22×C1111yescharacteristic
240#463—28no—
241#461—24no—
242#442—24no—
243C2×#106C22×C1111yescharacteristic
244C2×C4⋊C8C22×C1111yescharacteristic
245C2×C4⋊C8C22×C1112yes—
246C2×#103C22×C1112yes—
247C2×#103C22×C1112yes—
248C2×#103C22×C1112yes—
249C2×#102C22×C1112yes—
250C2×#102C22×C1111yescharacteristic
251C2×#102C22×C1111yescharacteristic
252C2×#97C22×C1111yescharacteristic
253#397—21no—
254#397—21no—
255#391C22×C1112yes—
256#389C22×C1112yes—
257#385—22no—
258#382C22×C1111yescharacteristic
259#380—22no—
260#380—21no—
261C4×C4⋊C4C22×C1111yescharacteristic
262C2×#95—21no—
263#340C22×C1112yes—
264#336C22×C1112yes—
265C22×C11—24no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—44no—
272C22×C11—82no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11C2×#12111yescharacteristic
276C22×C11D4211yescharacteristic
277C22×C11#54811yescharacteristic
278C22×C11#57512yes—
279C22×C11#57712yes—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—82no—
286C4×C11—82no—
287C4×C11—81no—
288C4×C11C2×#12111yescharacteristic
289C4×C11#53711yescharacteristic
290C4×C11#54711yescharacteristic
291C4×C11#55311yescharacteristic
292C22×Q8C23×C1112yes—
293C22×D4C23×C1111yescharacteristic
294C22×D4C23×C1111yescharacteristic
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—22no—
298C2×SD16—24no—
299C2×SD16—24no—
300C2×SD16—24no—
301C2×D8—22no—
302C2×D8—22no—
303C2×D8D4×C1114yes—
304C22×C8C23×C1112yes—
305C22×C8C23×C1111yescharacteristic
306C22×C8C23×C1111yescharacteristic
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309#124—24no—
310#124—42no—
311C4×D4—24no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4—42no—
316C4×D4D4×C1114yes—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4D4×C1112yes—
321C2×C4⋊C4C23×C1111yescharacteristic
322C2×C4⋊C4C23×C1112yes—
323C2×C4⋊C4C23×C1111yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C42C23×C1112yes—
330C2×C42C23×C1111yescharacteristic
331#106—22no—
332C4⋊C8—24no—
333C4⋊C8—22no—
334#103—24no—
335#103—24no—
336#103—42no—
337#102—22no—
338#102—24no—
339#102—22no—
340#97—22no—
341#95—21no—
342#95—22no—
343#95—22no—
344#95—22no—
345#95—21no—
346#95D4×C1111yescharacteristic
347#95D4×C1111yescharacteristic
348C2×C11—44no—
349C2×C11—82no—
350C2×C11#241611yescharacteristic
351C2×C11#304011yescharacteristic
352C2×C11#304211yescharacteristic
353C2×C11#326712yes—
354C2×C11#337612yes—
355C24—21no—
356C24—21no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4C2×D4×C1112yes—
372C2×D4C2×D4×C1112yes—
373C2×D4C2×D4×C1112yes—
374C2×D4C11×#4112yes—
375C22×C4—21no—
376C22×C4—24no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—44no—
383C22×C4—42no—
384C22×C4—82no—
385C22×C4—82no—
386C22×C4C2×D4×C1112yes—
387C22×C4C2×D4×C1112yes—
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C24×C1111yescharacteristic
391SD16—48no—
392D8—28no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8C2×D4×C1112yes—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—82no—
411C4⋊C4C2×D4×C1112yes—
412C22⋊C4—24no—
413C22⋊C4—44no—
414C22⋊C4—44no—
415C22⋊C4—44no—
416C22⋊C4—42no—
417C42—22no—
418C42—22no—
419C42C2×D4×C1112yes—
420C42C11×#4112yes—
421C11#2474511yescharacteristic, direct product factor, Sylow
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—42no—
427C23—42no—
428C23—41no—
429C23—41no—
430C23—42no—
431C23—42no—
432C23C22×D4×C1111yescharacteristic
433Q8—42no—
434Q8—42no—
435Q8—42no—
436Q8—42no—
437D4—22no—
438D4—22no—
439D4—22no—
440D4—22no—
441D4—22no—
442D4—41no—
443D4—41no—
444D4C11×#12114yes—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—84no—
464C2×C4—84no—
465C2×C4—88no—
466C2×C4C11×#12112yes—
467C2×C4C11×#12112yes—
468C2×C4C22×D4×C1111yescharacteristic
469C2×C4C22×D4×C1111yescharacteristic
470C2×C4C2×C11×#4111yescharacteristic
471C2×C4C2×C11×#4111yescharacteristic
472C2×C4C11×H(5,𝔽2)11yescharacteristic
473C2×C4C11×2−1+411yescharacteristic
474C8—22no—
475C8—42no—
476C8—41no—
477C22—24no—
478C22—44no—
479C22—42no—
480C22—42no—
481C22—44no—
482C22—42no—
483C22—44no—
484C22—81no—
485C22—81no—
486C22—82no—
487C22C2×C11×#12111yescharacteristic
488C22D42×C1111yescharacteristic
489C22C11×#54811yescharacteristic
490C22C11×#57512yes—
491C22C11×#57712yes—
492C4—22no—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—82no—
498C4—82no—
499C4—81no—
500C4C2×C11×#12111yescharacteristic
501C4C11×#53711yescharacteristic
502C4C11×#54711yescharacteristic
503C4C11×#55311yescharacteristic
504C2—44no—
505C2—82no—
506C2C11×#241611yescharacteristic
507C2C11×#304011yescharacteristic
508C2C11×#304211yescharacteristic
509C2C11×#326712yes—
510C2C11×#337612yes—
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
2. C2×C11×#461C2semidirect
4. C11×#2547C2semidirect
5. C11×#2349C2semidirect
6. C11×#2066C2semidirect
7. C11×#2042C2semidirect
8. C11×#1960C2semidirect
9. C11×#1940C2semidirect
10. C11×#1877C2semidirect
11. C11×#1804C2semidirect
100. #24745C11direct (N × H)
168. C2×#461C2×C11semidirect
170. #2547C2×C11semidirect
171. #2349C2×C11semidirect
172. #2066C2×C11semidirect
173. #2042C2×C11semidirect
174. #1960C2×C11semidirect
175. #1940C2×C11semidirect
176. #1877C2×C11semidirect
177. #1804C2×C11semidirect
421. C11#24745direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C11×#4612
C2×C11×#4422
C11×#25472
C11×#23492
C11×#20662
C11×#20422
C11×#19602
C11×#19402
C11×#18772
C11×#18042
#2474511