Finite Group Databasebeta

← C11×#24549 #14601742

Subgroups — C11×#24549 #14601742

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#449C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic, complemented
3C11×#2504C211yesmaximal, characteristic, complemented
4C11×#2339C211yesmaximal, characteristic, complemented
5C11×#2074C212yesmaximal, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#1895C211yesmaximal, characteristic, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1851C211yesmaximal, characteristic, complemented
10C11×#1823C211yesmaximal, characteristic, complemented
11C11×#1804C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×SD16C2211yescharacteristic
14C22×C11×D8C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#449—24no—
20C2×C11×C4⋊C8C2212yes—
21C11×#417—24no—
22C2×C11×#103C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2212yes—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#397—21no—
29C11×#397—21no—
30C11×#391C2212yes—
31C11×#390C2212yes—
32C11×#386—22no—
33C11×#386—22no—
34C11×#382C2212yes—
35C11×#381—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C22⋊C4C2211yescharacteristic
38C2×C11×#95—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41—24no—
45C2×C11×#41—42no—
46C2×C11×#41D414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11—22no—
55C23×C4×C11C2311yescharacteristic
56C2×C11×SD16—22no—
57C2×C11×SD16—42no—
58C2×C11×D8—22no—
59C2×C11×D8—24no—
60C2×C11×M16—22no—
61C2×C11×M16—42no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2312yes—
64C22×C8×C11C2311yescharacteristic
65C11×#121—22no—
66C11×#121—22no—
67C4×D4×C11—24no—
68C4×D4×C11—42no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4D412yes—
81C2×C42×C11C2312yes—
82C11×C4⋊C8—42no—
83C11×#103—24no—
84C11×#103—22no—
85C11×#102—24no—
86C11×#102—22no—
87C11×#102—42no—
88C11×C22⋊C8—22no—
89C11×#95—21no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95D411yescharacteristic
95C11×#95D411yescharacteristic
96#24549C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11—21no—
99C24×C11C2×D411yescharacteristic
100C11×#41—28no—
101C11×#41—44no—
102C11×#41—48no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11C2×D412yes—
107C2×D4×C11—24no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—42no—
117C2×D4×C11C2×D412yes—
118C2×D4×C11#4114yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
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—81no—
132C22×C4×C11—81no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C11×SD16—44no—
140C11×D8—44no—
141C11×M16—44no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—82no—
160C11×C22⋊C4—82no—
161C11×C22⋊C4—81no—
162C42×C11—22no—
163C42×C11—22no—
164C2×#449C2×C1111yescharacteristic
165C2×#417C2×C1111yescharacteristic, complemented
166#2504C2×C1111yescharacteristic, complemented
167#2339C2×C1111yescharacteristic, complemented
168#2074C2×C1112yescomplemented
169#2055C2×C1112yescomplemented
170#1895C2×C1111yescharacteristic, complemented
171#1879C2×C1112yescomplemented
172#1851C2×C1111yescharacteristic, complemented
173#1823C2×C1111yescharacteristic, complemented
174#1804C2×C1112yescomplemented
175C23×C11—22no—
176C23×C11—24no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—42no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11#12112yes—
190C23×C11C22×D411yescharacteristic
191Q8×C11—22no—
192Q8×C11—22no—
193Q8×C11—42no—
194D4×C11—22no—
195D4×C11—24no—
196D4×C11—48no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—42no—
200D4×C11—84no—
201D4×C11#12314yes—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
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—48no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—88no—
224C2×C4×C11—84no—
225C2×C4×C11#12112yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4112yes—
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)12yes—
230C8×C11—41no—
231C8×C11—42no—
232C8×C11—41no—
233C22×#41C22×C1111yescharacteristic
234C22×SD16C22×C1111yescharacteristic
235C22×D8C22×C1111yescharacteristic
236C22×M16C22×C1111yescharacteristic
237C2×#121C22×C1111yescharacteristic
238C2×C4×D4C22×C1112yes—
239C22×C4⋊C4C22×C1111yescharacteristic
240#449—24no—
241C2×C4⋊C8C22×C1112yes—
242#417—24no—
243C2×#103C22×C1112yes—
244C2×#103C22×C1111yescharacteristic
245C2×#102C22×C1111yescharacteristic
246C2×#102C22×C1112yes—
247C2×#102C22×C1112yes—
248C2×C22⋊C8C22×C1111yescharacteristic
249#397—21no—
250#397—21no—
251#391C22×C1112yes—
252#390C22×C1112yes—
253#386—22no—
254#386—22no—
255#382C22×C1112yes—
256#381—21no—
257#380C22×C1111yescharacteristic
258C4×C22⋊C4C22×C1111yescharacteristic
259C2×#95—21no—
260#340C22×C1112yes—
261#340C22×C1112yes—
262#340C22×C1112yes—
263#336C22×C1112yes—
264C22×C11—22no—
265C22×C11—24no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—42no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11C2×#12111yescharacteristic
280C22×C11#54612yes—
281C22×C11#57512yes—
282C22×C11#57611yescharacteristic
283C22×C11#57711yescharacteristic
284C4×C11—22no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—81no—
289C4×C11—82no—
290C4×C11—82no—
291C4×C11C2×#12311yescharacteristic
292C4×C11#53411yescharacteristic
293C4×C11#55112yes—
294C2×#41—22no—
295C2×#41—24no—
296C2×#41—42no—
297C2×#41D4×C1114yes—
298C22×Q8C23×C1111yescharacteristic
299C22×D4—21no—
300C22×D4—21no—
301C22×D4C23×C1111yescharacteristic
302C22×D4C23×C1111yescharacteristic
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—22no—
306C23×C4C23×C1111yescharacteristic
307C2×SD16—22no—
308C2×SD16—42no—
309C2×D8—22no—
310C2×D8—24no—
311C2×M16—22no—
312C2×M16—42no—
313C22×C8C23×C1112yes—
314C22×C8C23×C1111yescharacteristic
315C22×C8C23×C1111yescharacteristic
316#121—22no—
317#121—22no—
318C4×D4—24no—
319C4×D4—42no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4C23×C1112yes—
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1111yescharacteristic
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4D4×C1112yes—
332C2×C42C23×C1112yes—
333C4⋊C8—42no—
334#103—24no—
335#103—22no—
336#102—24no—
337#102—22no—
338#102—42no—
339C22⋊C8—22no—
340#95—21no—
341#95—22no—
342#95—22no—
343#95—22no—
344#95—22no—
345#95D4×C1111yescharacteristic
346#95D4×C1111yescharacteristic
347C2×C11—42no—
348C2×C11—44no—
349C2×C11—161no—
350C2×C11#241211yescharacteristic
351C2×C11#304011yescharacteristic
352C2×C11#304511yescharacteristic
353C2×C11#330712yes—
354C2×C11#332212yes—
355C24—21no—
356C24—21no—
357C24C2×D4×C1111yescharacteristic
358#41—28no—
359#41—44no—
360#41—48no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8C2×D4×C1112yes—
365C2×D4—24no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—44no—
373C2×D4—44no—
374C2×D4—42no—
375C2×D4C2×D4×C1112yes—
376C2×D4C11×#4114yes—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—24no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—44no—
385C22×C4—44no—
386C22×C4—44no—
387C22×C4—42no—
388C22×C4—82no—
389C22×C4—81no—
390C22×C4—81no—
391C22×C4C2×D4×C1112yes—
392C22×C4C2×D4×C1112yes—
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1112yes—
395C22×C4C11×#4112yes—
396C22×C4C24×C1111yescharacteristic
397SD16—44no—
398D8—44no—
399M16—44no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—42no—
414C22⋊C4—42no—
415C22⋊C4—44no—
416C22⋊C4—42no—
417C22⋊C4—82no—
418C22⋊C4—82no—
419C22⋊C4—81no—
420C42—22no—
421C42—22no—
422C11#2454911yescharacteristic, direct product factor, Sylow
423C23—22no—
424C23—24no—
425C23—22no—
426C23—22no—
427C23—21no—
428C23—21no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—42no—
434C23—42no—
435C23—41no—
436C23—41no—
437C23C11×#12112yes—
438C23C22×D4×C1111yescharacteristic
439Q8—22no—
440Q8—22no—
441Q8—42no—
442D4—22no—
443D4—24no—
444D4—48no—
445D4—41no—
446D4—41no—
447D4—42no—
448D4—84no—
449D4C11×#12314yes—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—48no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—88no—
472C2×C4—84no—
473C2×C4C11×#12112yes—
474C2×C4C22×D4×C1111yescharacteristic
475C2×C4C2×C11×#4112yes—
476C2×C4C2×C11×#4111yescharacteristic
477C2×C4C11×H(5,𝔽2)12yes—
478C8—41no—
479C8—42no—
480C8—41no—
481C22—22no—
482C22—24no—
483C22—22no—
484C22—22no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—44no—
489C22—44no—
490C22—42no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—82no—
495C22—82no—
496C22C2×C11×#12111yescharacteristic
497C22C11×#54612yes—
498C22C11×#57512yes—
499C22C11×#57611yescharacteristic
500C22C11×#57711yescharacteristic
501C4—22no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—81no—
506C4—82no—
507C4—82no—
508C4C2×C11×#12311yescharacteristic
509C4C11×#53411yescharacteristic
510C4C11×#55112yes—
511C2—42no—
512C2—44no—
513C2—161no—
514C2C11×#241211yescharacteristic
515C2C11×#304011yescharacteristic
516C2C11×#304511yescharacteristic
517C2C11×#330712yes—
518C2C11×#332212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#449C2
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
2. C2×C11×#417C2semidirect
3. C11×#2504C2semidirect
4. C11×#2339C2semidirect
5. C11×#2074C2semidirect
6. C11×#2055C2semidirect
7. C11×#1895C2semidirect
8. C11×#1879C2semidirect
9. C11×#1851C2semidirect
10. C11×#1823C2semidirect
11. C11×#1804C2semidirect
96. #24549C11direct (N × H)
165. C2×#417C2×C11semidirect
166. #2504C2×C11semidirect
167. #2339C2×C11semidirect
168. #2074C2×C11semidirect
169. #2055C2×C11semidirect
170. #1895C2×C11semidirect
171. #1879C2×C11semidirect
172. #1851C2×C11semidirect
173. #1823C2×C11semidirect
174. #1804C2×C11semidirect
422. C11#24549direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4492
C2×C11×#4172
C11×#25042
C11×#23392
C11×#20742
C11×#20552
C11×#18952
C11×#18792
C11×#18512
C11×#18232
C11×#18042
#2454911