Finite Group Databasebeta

← C11×#24479 #14601672

Subgroups — C11×#24479 #14601672

Order 2816.

1102 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×#484C211yesmaximal, characteristic, complemented
2C22×C11×#102C211yesmaximal, characteristic
3C11×#2435C211yesmaximal, characteristic
4C11×#2345C211yesmaximal, characteristic, complemented
5C11×#2067C212yesmaximal, complemented
6C11×#2042C212yesmaximal, complemented
7C11×#1983C212yesmaximal, complemented
8C11×#1925C212yesmaximal, complemented
9C11×#1892C211yesmaximal, characteristic, complemented
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#124C2212yes—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#484—24no—
18C2×C11×#107C2211yescharacteristic, complemented
19C2×C11×#107C2211yescharacteristic, complemented
20C2×C11×C4⋊C8C2212yescomplemented
21C2×C11×#103C2211yescharacteristic, complemented
22C2×C11×#103C2211yescharacteristic, complemented
23C2×C11×#103C2212yescomplemented
24C2×C11×#102—24no—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2211yescharacteristic
30C11×#394—22no—
31C11×#390C2212yes—
32C11×#389C2212yescomplemented
33C11×#387—22no—
34C11×#380—21no—
35C11×#380C2211yescharacteristic
36C11×#379—21no—
37C11×#379—21no—
38C4×C11×C4⋊C4C2212yescomplemented
39C4×C11×C22⋊C4—21no—
40C4×C11×C22⋊C4C2211yescharacteristic
41C11×#340C2212yescomplemented
42C11×#336C2212yescomplemented
43C25×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—24no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—42no—
50C22×D4×C11C2312yes—
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C22×C8×C11—22no—
54C22×C8×C11—42no—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C11×#124—24no—
59C11×#124—42no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D414yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C42×C11—22no—
80C2×C42×C11C2312yes—
81C11×#107—22no—
82C11×#107—22no—
83C11×C4⋊C8—42no—
84C11×#103—22no—
85C11×#103—22no—
86C11×#103—42no—
87C11×#102—24no—
88C11×#102—24no—
89C11×#102—24no—
90C11×#102—42no—
91C11×C22⋊C8—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—21no—
95C11×#95D412yes—
96#24479C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—22no—
98C24×C11—44no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11—42no—
102C24×C11—82no—
103C24×C11C2×D411yescharacteristic
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×D4×C11—28no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—48no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11—42no—
118C2×D4×C11#4114yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—82no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—44no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—21no—
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—82no—
151C11×C4⋊C4C2×D412yes—
152C11×C4⋊C4C2×D412yes—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—44no—
157C11×C22⋊C4—42no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—82no—
160C11×C22⋊C4—82no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—82no—
164C2×#484C2×C1111yescharacteristic, complemented
165C22×#102C2×C1111yescharacteristic
166#2435C2×C1111yescharacteristic
167#2345C2×C1111yescharacteristic, complemented
168#2067C2×C1112yescomplemented
169#2042C2×C1112yescomplemented
170#1983C2×C1112yescomplemented
171#1925C2×C1112yescomplemented
172#1892C2×C1111yescharacteristic, complemented
173#1850C2×C1111yescharacteristic, complemented
174#1786C2×C1111yescharacteristic
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—24no—
178C23×C11—48no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—88no—
186C23×C11—88no—
187C23×C11—84no—
188C23×C11—84no—
189C23×C11#12112yes—
190C23×C11#13512yes—
191C23×C11#13712yes—
192C23×C11C22×D411yescharacteristic
193Q8×C11—41no—
194Q8×C11—41no—
195Q8×C11—42no—
196D4×C11—24no—
197D4×C11—24no—
198D4×C11—48no—
199D4×C11—42no—
200D4×C11—42no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—84no—
223C2×C4×C11#12112yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4112yes—
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)12yes—
228C8×C11—41no—
229C8×C11—41no—
230C8×C11—42no—
231C23×D4C22×C1111yescharacteristic
232C23×C8C22×C1111yescharacteristic
233C2×#124C22×C1112yes—
234C2×C22⋊Q8C22×C1111yescharacteristic
235C22×C4⋊C4C22×C1111yescharacteristic
236#484—24no—
237C2×#107C22×C1111yescharacteristic, complemented
238C2×#107C22×C1111yescharacteristic, complemented
239C2×C4⋊C8C22×C1112yescomplemented
240C2×#103C22×C1111yescharacteristic, complemented
241C2×#103C22×C1111yescharacteristic, complemented
242C2×#103C22×C1112yescomplemented
243C2×#102—24no—
244C2×#102C22×C1112yes—
245C2×#102C22×C1112yes—
246C2×#102C22×C1112yes—
247C2×#102C22×C1112yes—
248C2×C22⋊C8C22×C1111yescharacteristic
249#394—22no—
250#390C22×C1112yes—
251#389C22×C1112yescomplemented
252#387—22no—
253#380—21no—
254#380C22×C1111yescharacteristic
255#379—21no—
256#379—21no—
257C4×C4⋊C4C22×C1112yescomplemented
258C4×C22⋊C4—21no—
259C4×C22⋊C4C22×C1111yescharacteristic
260#340C22×C1112yescomplemented
261#336C22×C1112yescomplemented
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—24no—
265C22×C11—24no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—816no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11#46414yes—
275C22×C11C2×#12111yescharacteristic
276C22×C11#54612yes—
277C22×C11C2×#13511yescharacteristic
278C22×C11C2×#13711yescharacteristic
279C22×C11#57612yes—
280C4×C11—22no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—81no—
286C4×C11—81no—
287C4×C11—82no—
288C4×C11#52511yescharacteristic
289C4×C11#53511yescharacteristic
290C4×C11#55112yes—
291C25—21no—
292C22×Q8C23×C1111yescharacteristic
293C22×D4—24no—
294C22×D4—22no—
295C22×D4—21no—
296C22×D4—22no—
297C22×D4—42no—
298C22×D4C23×C1112yes—
299C23×C4—21no—
300C23×C4C23×C1111yescharacteristic
301C22×C8—22no—
302C22×C8—42no—
303C22×C8C23×C1112yes—
304C22×C8C23×C1111yescharacteristic
305C22×C8C23×C1111yescharacteristic
306#124—24no—
307#124—42no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4D4×C1114yes—
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1111yescharacteristic
318C2×C4⋊C4C23×C1111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4D4×C1111yescharacteristic
326C2×C22⋊C4D4×C1111yescharacteristic
327C2×C42—22no—
328C2×C42C23×C1112yes—
329#107—22no—
330#107—22no—
331C4⋊C8—42no—
332#103—22no—
333#103—22no—
334#103—42no—
335#102—24no—
336#102—24no—
337#102—24no—
338#102—42no—
339C22⋊C8—22no—
340#95—22no—
341#95—22no—
342#95—21no—
343#95D4×C1112yes—
344C2×C11—24no—
345C2×C11—84no—
346C2×C11#241111yescharacteristic
347C2×C11C2×#46411yescharacteristic
348C2×C11#304111yescharacteristic
349C2×C11#329712yes—
350C2×C11#331412yes—
351C24—22no—
352C24—44no—
353C24—42no—
354C24—42no—
355C24—42no—
356C24—82no—
357C24C2×D4×C1111yescharacteristic
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×D4—28no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—48no—
369C2×D4—44no—
370C2×D4—44no—
371C2×D4—42no—
372C2×D4C11×#4114yes—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—82no—
382C22×C4C2×D4×C1112yes—
383C22×C4C2×D4×C1112yes—
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1112yes—
386C22×C4C11×#4112yes—
387C22×C4C24×C1111yescharacteristic
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—44no—
396C4⋊C4—24no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—42no—
404C4⋊C4—82no—
405C4⋊C4C2×D4×C1112yes—
406C4⋊C4C2×D4×C1112yes—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—44no—
410C22⋊C4—44no—
411C22⋊C4—42no—
412C22⋊C4—42no—
413C22⋊C4—82no—
414C22⋊C4—82no—
415C42—22no—
416C42—22no—
417C42—82no—
418C11#2447911yescharacteristic, direct product factor, Sylow
419C23—22no—
420C23—22no—
421C23—24no—
422C23—48no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23—88no—
430C23—88no—
431C23—84no—
432C23—84no—
433C23C11×#12112yes—
434C23C11×#13512yes—
435C23C11×#13712yes—
436C23C22×D4×C1111yescharacteristic
437Q8—41no—
438Q8—41no—
439Q8—42no—
440D4—24no—
441D4—24no—
442D4—48no—
443D4—42no—
444D4—42no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—84no—
467C2×C4C11×#12112yes—
468C2×C4C22×D4×C1111yescharacteristic
469C2×C4C2×C11×#4112yes—
470C2×C4C2×C11×#4111yescharacteristic
471C2×C4C11×H(5,𝔽2)12yes—
472C8—41no—
473C8—42no—
474C8—41no—
475C22—22no—
476C22—22no—
477C22—24no—
478C22—24no—
479C22—44no—
480C22—44no—
481C22—44no—
482C22—816no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22C11×#46414yes—
488C22C2×C11×#12111yescharacteristic
489C22C11×#54612yes—
490C22C2×C11×#13511yescharacteristic
491C22C2×C11×#13711yescharacteristic
492C22C11×#57612yes—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—81no—
499C4—81no—
500C4—82no—
501C4C11×#52511yescharacteristic
502C4C11×#53511yescharacteristic
503C4C11×#55112yes—
504C2—24no—
505C2—84no—
506C2C11×#241111yescharacteristic
507C2C2×C11×#46411yescharacteristic
508C2C11×#304111yescharacteristic
509C2C11×#329712yes—
510C2C11×#331412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#484C2semidirect
4. C11×#2345C2semidirect
5. C11×#2067C2semidirect
6. C11×#2042C2semidirect
7. C11×#1983C2semidirect
8. C11×#1925C2semidirect
9. C11×#1892C2semidirect
10. C11×#1850C2semidirect
18. C2×C11×#107C22semidirect
19. C2×C11×#107C22semidirect
20. C2×C11×C4⋊C8C22semidirect
21. C2×C11×#103C22semidirect
22. C2×C11×#103C22semidirect
23. C2×C11×#103C22semidirect
32. C11×#389C22semidirect
38. C4×C11×C4⋊C4C22semidirect
41. C11×#340C22semidirect
42. C11×#336C22semidirect
96. #24479C11direct (N × H)
164. C2×#484C2×C11semidirect
167. #2345C2×C11semidirect
168. #2067C2×C11semidirect
169. #2042C2×C11semidirect
170. #1983C2×C11semidirect
171. #1925C2×C11semidirect
172. #1892C2×C11semidirect
173. #1850C2×C11semidirect
237. C2×#107C22×C11semidirect
238. C2×#107C22×C11semidirect
239. C2×C4⋊C8C22×C11semidirect
240. C2×#103C22×C11semidirect
241. C2×#103C22×C11semidirect
242. C2×#103C22×C11semidirect
251. #389C22×C11semidirect
257. C4×C4⋊C4C22×C11semidirect
260. #340C22×C11semidirect
261. #336C22×C11semidirect
418. C11#24479direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4842
C22×C11×#1022
C11×#24352
C11×#23452
C11×#20672
C11×#20422
C11×#19832
C11×#19252
C11×#18922
C11×#18502
C11×#17862
#2447911