Finite Group Databasebeta

← C11×#23952 #14601145

Subgroups — C11×#23952 #14601145

Order 2816.

1326 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
1C11×#3493C211yesmaximal, characteristic, complemented
2C11×#3003C212yesmaximal, complemented
3C11×#2309C211yesmaximal, characteristic, complemented
4C11×#2027C212yesmaximal, complemented
5C11×#2006C212yesmaximal, complemented
6C11×#1897C212yesmaximal, complemented
7C11×#1883C214yesmaximal, complemented
8C11×#1822C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C2×C11×AGL(1,ℤ/8)C2214yes—
11C11×#556—22no—
12C11×#555—22no—
13C11×#553—22no—
14C11×#552—22no—
15C11×#544C2211yescharacteristic, complemented
16C11×#538—22no—
17C11×#537C2211yescharacteristic, complemented
18C11×#529—22no—
19C11×#525C2212yes—
20C11×#520C2212yescomplemented
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C11×#450—22no—
24C11×#450—22no—
25C11×#447—22no—
26C11×#447—22no—
27C2×C11×#104C2214yescomplemented
28C11×#418C2214yes—
29C11×#407C2212yes—
30C11×#390—22no—
31C11×#390C2212yes—
32C11×#390C2212yes—
33C11×#379—22no—
34C11×#343C2212yescomplemented
35C11×#343C2212yescomplemented
36C11×#339C2214yescomplemented
37C25×C11—21no—
38C2×C11×#41C2312yes—
39C22×D4×C11—24no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—42no—
44C22×D4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C11×AGL(1,ℤ/8)—28no—
47C11×AGL(1,ℤ/8)—44no—
48C2×C11×SD16—24no—
49C2×C11×D8—24no—
50C2×C11×M16C2314yes—
51C11×C4⋊Q8—22no—
52C11×#126—24no—
53C11×#126—24no—
54C11×#125—22no—
55C11×#125—22no—
56C11×#124—22no—
57C11×#124—24no—
58C11×#123—24no—
59C11×#123—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8D412yes—
63C11×C22⋊Q8D412yes—
64C11×#121—24no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121D412yes—
68C11×#121D412yes—
69C11×#120—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—24no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C11×#117—24no—
78C11×#117—22no—
79C11×#117—22no—
80C11×#117—22no—
81C11×#117—42no—
82C11×#117C2312yes—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4D412yes—
91C2×C42×C11D412yes—
92C2×C42×C11C2312yes—
93C11×#104—44no—
94C11×#102—24no—
95C11×#102—24no—
96C11×C22⋊C8—22no—
97C11×C22⋊C8—22no—
98#23952C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—24no—
100C24×C11—22no—
101C24×C11—42no—
102C24×C11—42no—
103C24×C11—82no—
104C24×C11—82no—
105C24×C11C2×D411yescharacteristic
106C11×#41—24no—
107C11×#41—24no—
108C2×Q8×C11—22no—
109C2×Q8×C11C2×D412yes—
110C2×D4×C11—24no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—24no—
118C2×D4×C11—48no—
119C2×D4×C11—48no—
120C2×D4×C11—42no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11C2×D412yes—
124C2×D4×C11#4114yes—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2411yescharacteristic
136C11×SD16—48no—
137C11×D8—48no—
138C11×M16—24no—
139C11×M16—24no—
140C2×C8×C11—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—42no—
161C11×C22⋊C4—84no—
162C11×C22⋊C4—84no—
163C42×C11—24no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—24no—
168#3493C2×C1111yescharacteristic, complemented
169#3003C2×C1112yescomplemented
170#2309C2×C1111yescharacteristic, complemented
171#2027C2×C1112yescomplemented
172#2006C2×C1112yescomplemented
173#1897C2×C1112yescomplemented
174#1883C2×C1114yescomplemented
175#1822C2×C1111yescharacteristic, complemented
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—22no—
179C23×C11—24no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—44no—
183C23×C11—44no—
184C23×C11—48no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—84no—
188C23×C11—84no—
189C23×C11—88no—
190C23×C11—88no—
191C23×C11#12012yes—
192C23×C11C22×D411yescharacteristic
193Q8×C11—24no—
194Q8×C11—82no—
195D4×C11—24no—
196D4×C11—28no—
197D4×C11—44no—
198D4×C11—44no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—44no—
202D4×C11—82no—
203D4×C11—82no—
204D4×C11—82no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—44no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—84no—
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11C22×D412yes—
224C2×C4×C11C2×#4112yes—
225C2×C4×C11H(5,𝔽2)12yes—
226C8×C11—44no—
227C23×D4C22×C1111yescharacteristic
228C2×AGL(1,ℤ/8)C22×C1114yes—
229#556—22no—
230#555—22no—
231#553—22no—
232#552—22no—
233#544C22×C1111yescharacteristic, complemented
234#538—22no—
235#537C22×C1111yescharacteristic, complemented
236#529—22no—
237#525C22×C1112yes—
238#520C22×C1112yescomplemented
239C2×#117C22×C1111yescharacteristic
240C2×#117C22×C1111yescharacteristic
241#450—22no—
242#450—22no—
243#447—22no—
244#447—22no—
245C2×#104C22×C1114yescomplemented
246#418C22×C1114yes—
247#407C22×C1112yes—
248#390—22no—
249#390C22×C1112yes—
250#390C22×C1112yes—
251#379—22no—
252#343C22×C1112yescomplemented
253#343C22×C1112yescomplemented
254#339C22×C1114yescomplemented
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—48no—
263C22×C11—42no—
264C22×C11—44no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—84no—
268C22×C11—816no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11C2×#12011yescharacteristic
272C22×C11#52511yescharacteristic
273C22×C11#53511yescharacteristic
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—82no—
282C4×C11#54614yes—
283C25—21no—
284C2×#41C23×C1112yes—
285C22×D4—24no—
286C22×D4—21no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—42no—
290C22×D4C23×C1112yes—
291C23×C4C23×C1111yescharacteristic
292AGL(1,ℤ/8)—28no—
293AGL(1,ℤ/8)—44no—
294C2×SD16—24no—
295C2×D8—24no—
296C2×M16C23×C1114yes—
297C4⋊Q8—22no—
298#126—24no—
299#126—24no—
300#125—22no—
301#125—22no—
302#124—22no—
303#124—24no—
304#123—24no—
305#123—22no—
306C22⋊Q8—22no—
307C22⋊Q8—22no—
308C22⋊Q8D4×C1112yes—
309C22⋊Q8D4×C1112yes—
310#121—24no—
311#121—22no—
312#121—22no—
313#121D4×C1112yes—
314#121D4×C1112yes—
315#120—22no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—24no—
321C4×D4—22no—
322C4×D4—22no—
323#117—24no—
324#117—22no—
325#117—22no—
326#117—22no—
327#117—42no—
328#117C23×C1112yes—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4C23×C1111yescharacteristic
332C2×C4⋊C4C23×C1111yescharacteristic
333C2×C22⋊C4—21no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4D4×C1112yes—
337C2×C42D4×C1112yes—
338C2×C42C23×C1112yes—
339#104—44no—
340#102—24no—
341#102—24no—
342C22⋊C8—22no—
343C22⋊C8—22no—
344C2×C11—21no—
345C2×C11—21no—
346C2×C11—42no—
347C2×C11—82no—
348C2×C11—84no—
349C2×C11#240411yescharacteristic
350C2×C11#302111yescharacteristic
351C2×C11#302111yescharacteristic
352C24—24no—
353C24—22no—
354C24—42no—
355C24—42no—
356C24—82no—
357C24—82no—
358C24C2×D4×C1111yescharacteristic
359#41—24no—
360#41—24no—
361C2×Q8—22no—
362C2×Q8C2×D4×C1112yes—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—24no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—48no—
372C2×D4—48no—
373C2×D4—42no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4C2×D4×C1112yes—
377C2×D4C11×#4114yes—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×D4×C1112yes—
385C22×C4C2×D4×C1112yes—
386C22×C4C2×D4×C1112yes—
387C22×C4C2×D4×C1112yes—
388C22×C4C24×C1111yescharacteristic
389SD16—48no—
390D8—48no—
391M16—24no—
392M16—24no—
393C2×C8—24no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4C2×D4×C1112yes—
404C4⋊C4C2×D4×C1112yes—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—24no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—42no—
414C22⋊C4—84no—
415C22⋊C4—84no—
416C42—24no—
417C42—22no—
418C42—22no—
419C42—22no—
420C42—24no—
421C11#2395211yescharacteristic, direct product factor, Sylow
422C23—21no—
423C23—21no—
424C23—22no—
425C23—24no—
426C23—41no—
427C23—41no—
428C23—44no—
429C23—44no—
430C23—48no—
431C23—42no—
432C23—42no—
433C23—84no—
434C23—84no—
435C23—88no—
436C23—88no—
437C23C11×#12012yes—
438C23C22×D4×C1111yescharacteristic
439Q8—24no—
440Q8—82no—
441D4—24no—
442D4—28no—
443D4—44no—
444D4—44no—
445D4—42no—
446D4—42no—
447D4—44no—
448D4—82no—
449D4—82no—
450D4—82no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—84no—
467C2×C4C11×#12011yescharacteristic
468C2×C4C11×#12011yescharacteristic
469C2×C4C22×D4×C1112yes—
470C2×C4C2×C11×#4112yes—
471C2×C4C11×H(5,𝔽2)12yes—
472C8—44no—
473C22—21no—
474C22—21no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—42no—
479C22—42no—
480C22—48no—
481C22—42no—
482C22—44no—
483C22—42no—
484C22—42no—
485C22—84no—
486C22—816no—
487C22—82no—
488C22—82no—
489C22C2×C11×#12011yescharacteristic
490C22C11×#52511yescharacteristic
491C22C11×#53511yescharacteristic
492C4—21no—
493C4—21no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—82no—
500C4C11×#54614yes—
501C2—21no—
502C2—21no—
503C2—42no—
504C2—84no—
505C2—82no—
506C2C11×#240411yescharacteristic
507C2C11×#302111yescharacteristic
508C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C11×#3493C2semidirect
2. C11×#3003C2semidirect
3. C11×#2309C2semidirect
4. C11×#2027C2semidirect
5. C11×#2006C2semidirect
6. C11×#1897C2semidirect
7. C11×#1883C2semidirect
8. C11×#1822C2semidirect
15. C11×#544C22semidirect
17. C11×#537C22semidirect
20. C11×#520C22semidirect
27. C2×C11×#104C22semidirect
34. C11×#343C22semidirect
35. C11×#343C22semidirect
36. C11×#339C22semidirect
98. #23952C11direct (N × H)
168. #3493C2×C11semidirect
169. #3003C2×C11semidirect
170. #2309C2×C11semidirect
171. #2027C2×C11semidirect
172. #2006C2×C11semidirect
173. #1897C2×C11semidirect
174. #1883C2×C11semidirect
175. #1822C2×C11semidirect
233. #544C22×C11semidirect
235. #537C22×C11semidirect
238. #520C22×C11semidirect
245. C2×#104C22×C11semidirect
252. #343C22×C11semidirect
253. #343C22×C11semidirect
254. #339C22×C11semidirect
421. C11#23952direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34932
C11×#30032
C11×#23092
C11×#20272
C11×#20062
C11×#18972
C11×#18832
C11×#18222
#2395211