Finite Group Databasebeta

← C11×#24024 #14601217

Subgroups — C11×#24024 #14601217

Order 2816.

1274 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3487C211yesmaximal, characteristic
2C11×#3092C212yesmaximal, complemented
3C11×#2311C211yesmaximal, characteristic, complemented
4C11×#2037C214yesmaximal, complemented
5C11×#1897C212yesmaximal, complemented
6C11×#1857C212yesmaximal, complemented
7C11×#1793C212yesmaximal, complemented
8C11×#1785C211yesmaximal, characteristic, complemented
9C2×C11×2−1+4C2211yescharacteristic
10C22×C11×#41C2211yescharacteristic
11C11×#550—22no—
12C11×#550—22no—
13C11×#548—22no—
14C11×#548—22no—
15C11×#535—22no—
16C11×#535C2212yes—
17C11×#525—22no—
18C11×#525C2212yes—
19C11×#519C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C11×#484—22no—
23C11×#483—22no—
24C11×#481—22no—
25C11×#480—22no—
26C11×#428C2214yes—
27C2×C11×#104C2214yes—
28C11×#417C2214yes—
29C2×C11×#101C2212yes—
30C2×C11×#100C2212yes—
31C11×#407C2212yes—
32C11×#391C2212yes—
33C11×#390C2212yes—
34C11×#386—22no—
35C11×#380—22no—
36C11×#339C2214yes—
37C11×2−1+4—24no—
38C11×2−1+4—42no—
39C2×C11×#41—24no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—42no—
45C2×C11×#41C2312yes—
46C22×Q8×C11—22no—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11D412yes—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11D412yes—
52C23×C4×C11C2311yescharacteristic
53C2×C11×M16C2314yes—
54C11×#127—24no—
55C11×#127—22no—
56C11×#124—24no—
57C11×#124—22no—
58C11×#123—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8D412yes—
62C11×C22⋊Q8D412yes—
63C11×#121—22no—
64C11×#121—22no—
65C11×#121—24no—
66C11×#121—24no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121D412yes—
70C11×#121D412yes—
71C11×#120—24no—
72C11×#120—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11—22no—
75C4×D4×C11—24no—
76C4×D4×C11—24no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C11×#117—22no—
80C11×#117—42no—
81C11×#117C2312yes—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—24no—
89C2×C42×C11C2312yes—
90C11×#107—24no—
91C11×#106—24no—
92C11×#104—44no—
93C11×#103—24no—
94C11×#102—24no—
95C11×#101—24no—
96C11×#100—42no—
97C11×C22⋊C8—22no—
98C11×C22⋊C8—22no—
99C11×#95—24no—
100#24024C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11C2×D412yes—
102C24×C11C2×D411yescharacteristic
103C11×#41—24no—
104C11×#41—24no—
105C11×#41—48no—
106C11×#41—48no—
107C11×#41—44no—
108C11×#41—48no—
109C11×#41—44no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—48no—
114C2×Q8×C11C2×D412yes—
115C2×Q8×C11#4114yes—
116C2×D4×C11—22no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—24no—
120C2×D4×C11—24no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—42no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—82no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2411yescharacteristic
146C11×M16—24no—
147C11×M16—24no—
148C2×C8×C11—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—84no—
168C42×C11—24no—
169C42×C11—22no—
170C42×C11—24no—
171#3487C2×C1111yescharacteristic
172#3092C2×C1112yescomplemented
173#2311C2×C1111yescharacteristic, complemented
174#2037C2×C1114yescomplemented
175#1897C2×C1112yescomplemented
176#1857C2×C1112yescomplemented
177#1793C2×C1112yescomplemented
178#1785C2×C1111yescharacteristic, complemented
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11#12012yes—
190C23×C11C22×D411yescharacteristic
191Q8×C11—28no—
192Q8×C11—24no—
193Q8×C11—44no—
194D4×C11—24no—
195D4×C11—48no—
196D4×C11—44no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—44no—
200D4×C11—82no—
201D4×C11—82no—
202D4×C11—84no—
203D4×C11—84no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—44no—
214C2×C4×C11—44no—
215C2×C4×C11—48no—
216C2×C4×C11—44no—
217C2×C4×C11—42no—
218C2×C4×C11—44no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—84no—
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12314yes—
226C2×C4×C11C22×D412yes—
227C2×C4×C11C2×#4112yes—
228C2×C4×C11H(5,𝔽2)12yes—
229C8×C11—44no—
230C2×2−1+4C22×C1111yescharacteristic
231C22×#41C22×C1111yescharacteristic
232#550—22no—
233#550—22no—
234#548—22no—
235#548—22no—
236#535—22no—
237#535C22×C1112yes—
238#525—22no—
239#525C22×C1112yes—
240#519C22×C1111yescharacteristic
241C2×#117C22×C1111yescharacteristic
242C22×C4⋊C4C22×C1111yescharacteristic
243#484—22no—
244#483—22no—
245#481—22no—
246#480—22no—
247#428C22×C1114yes—
248C2×#104C22×C1114yes—
249#417C22×C1114yes—
250C2×#101C22×C1112yes—
251C2×#100C22×C1112yes—
252#407C22×C1112yes—
253#391C22×C1112yes—
254#390C22×C1112yes—
255#386—22no—
256#380—22no—
257#339C22×C1114yes—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—44no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—82no—
273C22×C11C2×#12011yescharacteristic
274C22×C11C2×#12311yescharacteristic
275C22×C11#53411yescharacteristic
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—24no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—82no—
283C4×C11—82no—
284C4×C11#54614yes—
2852−1+4—24no—
2862−1+4—42no—
287C2×#41—24no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—42no—
293C2×#41C23×C1112yes—
294C22×Q8—22no—
295C22×Q8C23×C1111yescharacteristic
296C22×D4D4×C1112yes—
297C22×D4C23×C1111yescharacteristic
298C23×C4—21no—
299C23×C4D4×C1112yes—
300C23×C4C23×C1111yescharacteristic
301C2×M16C23×C1114yes—
302#127—24no—
303#127—22no—
304#124—24no—
305#124—22no—
306#123—22no—
307C22⋊Q8—22no—
308C22⋊Q8—22no—
309C22⋊Q8D4×C1112yes—
310C22⋊Q8D4×C1112yes—
311#121—22no—
312#121—22no—
313#121—24no—
314#121—24no—
315#121—22no—
316#121—22no—
317#121D4×C1112yes—
318#121D4×C1112yes—
319#120—24no—
320#120—22no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×D4—24no—
324C4×D4—24no—
325C4×D4—22no—
326C4×D4—22no—
327#117—22no—
328#117—42no—
329#117C23×C1112yes—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4C23×C1112yes—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—24no—
337C2×C42C23×C1112yes—
338#107—24no—
339#106—24no—
340#104—44no—
341#103—24no—
342#102—24no—
343#101—24no—
344#100—42no—
345C22⋊C8—22no—
346C22⋊C8—22no—
347#95—24no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—42no—
351C2×C11—82no—
352C2×C11—82no—
353C2×C11#240511yescharacteristic
354C2×C11#302111yescharacteristic
355C2×C11#302211yescharacteristic
356C24C2×D4×C1112yes—
357C24C2×D4×C1111yescharacteristic
358#41—24no—
359#41—24no—
360#41—48no—
361#41—48no—
362#41—44no—
363#41—48no—
364#41—44no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—48no—
369C2×Q8C2×D4×C1112yes—
370C2×Q8C11×#4114yes—
371C2×D4—22no—
372C2×D4—24no—
373C2×D4—22no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—24no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—42no—
383C2×D4C2×D4×C1112yes—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—82no—
396C22×C4C2×D4×C1111yescharacteristic
397C22×C4C2×D4×C1112yes—
398C22×C4C2×D4×C1112yes—
399C22×C4C2×D4×C1112yes—
400C22×C4C24×C1111yescharacteristic
401M16—24no—
402M16—24no—
403C2×C8—24no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—24no—
409C4⋊C4—42no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4C2×D4×C1112yes—
413C4⋊C4C2×D4×C1112yes—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—42no—
422C22⋊C4—84no—
423C42—24no—
424C42—22no—
425C42—24no—
426C11#2402411yescharacteristic, direct product factor, Sylow
427C23—21no—
428C23—21no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—22no—
433C23—41no—
434C23—41no—
435C23—42no—
436C23—42no—
437C23C11×#12012yes—
438C23C22×D4×C1111yescharacteristic
439Q8—28no—
440Q8—24no—
441Q8—44no—
442D4—24no—
443D4—48no—
444D4—44no—
445D4—42no—
446D4—42no—
447D4—44no—
448D4—82no—
449D4—82no—
450D4—84no—
451D4—84no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—48no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—84no—
471C2×C4C11×#12011yescharacteristic
472C2×C4C11×#12011yescharacteristic
473C2×C4C11×#12314yes—
474C2×C4C22×D4×C1112yes—
475C2×C4C2×C11×#4112yes—
476C2×C4C11×H(5,𝔽2)12yes—
477C8—44no—
478C22—21no—
479C22—21no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—42no—
484C22—42no—
485C22—44no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—82no—
493C22C2×C11×#12011yescharacteristic
494C22C2×C11×#12311yescharacteristic
495C22C11×#53411yescharacteristic
496C4—21no—
497C4—21no—
498C4—24no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—82no—
503C4—82no—
504C4C11×#54614yes—
505C2—21no—
506C2—21no—
507C2—42no—
508C2—82no—
509C2—82no—
510C2C11×#240511yescharacteristic
511C2C11×#302111yescharacteristic
512C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3487C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3092C2semidirect
3. C11×#2311C2semidirect
4. C11×#2037C2semidirect
5. C11×#1897C2semidirect
6. C11×#1857C2semidirect
7. C11×#1793C2semidirect
8. C11×#1785C2semidirect
100. #24024C11direct (N × H)
172. #3092C2×C11semidirect
173. #2311C2×C11semidirect
174. #2037C2×C11semidirect
175. #1897C2×C11semidirect
176. #1857C2×C11semidirect
177. #1793C2×C11semidirect
178. #1785C2×C11semidirect
426. C11#24024direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34872
C11×#30922
C11×#23112
C11×#20372
C11×#18972
C11×#18572
C11×#17932
C11×#17852
#2402411