Finite Group Databasebeta

← C11×#23913 #14601106

Subgroups — C11×#23913 #14601106

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3485C211yesmaximal, characteristic, complemented
2C2×C11×#535C211yesmaximal, characteristic, complemented
3C2×C11×#453C212yesmaximal, complemented
4C11×#3003C212yesmaximal, complemented
5C11×#2003C214yesmaximal, complemented
6C11×#1897C212yesmaximal, complemented
7C11×#1887C212yesmaximal, complemented
8C11×#1785C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2214yes—
13C11×#547—24no—
14C11×#546—24no—
15C11×#536C2212yescomplemented
16C11×#535—28no—
17C11×#534—22no—
18C2×C11×#127C2212yes—
19C2×C11×#124C2212yescomplemented
20C11×#525C2212yes—
21C2×C11×#123—22no—
22C2×C11×#121—22no—
23C2×C11×#120—22no—
24C11×#518C2211yescharacteristic, complemented
25C2×C11×#117C2211yescharacteristic, complemented
26C11×#453—28no—
27C11×#450—24no—
28C11×#447—24no—
29C2×C11×#104C2214yescomplemented
30C11×#418C2214yescomplemented
31C2×C11×#101C2212yescomplemented
32C2×C11×#100C2212yescomplemented
33C11×#407C2212yescomplemented
34C11×#339C2214yescomplemented
35C25×C11—21no—
36C11×H(5,𝔽2)—24no—
37C11×H(5,𝔽2)—42no—
38C2×C11×#41—22no—
39C2×C11×#41—24no—
40C2×C11×#41—24no—
41C2×C11×#41—42no—
42C2×C11×#41C2312yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11—24no—
46C22×D4×C11—24no—
47C22×D4×C11—22no—
48C22×D4×C11—21no—
49C22×D4×C11—24no—
50C22×D4×C11—42no—
51C22×D4×C11D412yes—
52C22×D4×C11C2312yes—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11D412yes—
55C23×C4×C11C2311yescharacteristic
56C11×AGL(1,ℤ/8)—28no—
57C11×AGL(1,ℤ/8)—44no—
58C2×C11×SD16—24no—
59C2×C11×D8—24no—
60C2×C11×M16C2314yes—
61C11×C4⋊Q8—22no—
62C11×#127—24no—
63C11×#127D418yescomplemented
64C11×#124—24no—
65C11×#124—22no—
66C11×#124—24no—
67C11×#123—28no—
68C11×#123—24no—
69C11×#123—22no—
70C11×#123—24no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8D414yescomplemented
73C11×#121—216no—
74C11×#121—28no—
75C11×#121D414yescomplemented
76C11×#120—216no—
77C11×#120—24no—
78C11×#120—22no—
79C4×D4×C11—24no—
80C4×D4×C11—24no—
81C11×#117—24no—
82C11×#117C2312yes—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—24no—
89C2×C42×C11C2312yes—
90C11×#104—28no—
91C11×#102—28no—
92C11×#101—42no—
93C11×#100—24no—
94C11×C22⋊C8—24no—
95#23913C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—22no—
97C24×C11—24no—
98C24×C11—22no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11—84no—
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D412yes—
104C11×#41—24no—
105C11×#41—24no—
106C11×#41—416no—
107C11×#41—48no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11C2×D412yes—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—24no—
118C2×D4×C11—216no—
119C2×D4×C11—22no—
120C2×D4×C11—24no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—24no—
124C2×D4×C11—416no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—48no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—42no—
131C2×D4×C11—88no—
132C2×D4×C11C2×D412yes—
133C2×D4×C11C2×D414yes—
134C2×D4×C11C2×D414yes—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—42no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2411yescharacteristic
148C11×SD16—48no—
149C11×D8—48no—
150C11×M16—24no—
151C11×M16—24no—
152C2×C8×C11—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—28no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4C2×D414yes—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—216no—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—24no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11C2×D414yes—
167#3485C2×C1111yescharacteristic, complemented
168C2×#535C2×C1111yescharacteristic, complemented
169C2×#453C2×C1112yescomplemented
170#3003C2×C1112yescomplemented
171#2003C2×C1114yescomplemented
172#1897C2×C1112yescomplemented
173#1887C2×C1112yescomplemented
174#1785C2×C1111yescharacteristic, complemented
175C23×C11—21no—
176C23×C11—22no—
177C23×C11—21no—
178C23×C11—22no—
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—42no—
182C23×C11—44no—
183C23×C11—48no—
184C23×C11—48no—
185C23×C11—44no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—88no—
189C23×C11—88no—
190C23×C11—84no—
191C23×C11—88no—
192C23×C11#12012yes—
193C23×C11#12014yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—24no—
196Q8×C11—44no—
197D4×C11—28no—
198D4×C11—24no—
199D4×C11—28no—
200D4×C11—48no—
201D4×C11—48no—
202D4×C11—48no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—44no—
206D4×C11—84no—
207D4×C11—816no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—28no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—48no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11—84no—
222C2×C4×C11#12012yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11H(5,𝔽2)12yes—
226C8×C11—44no—
227C2×H(5,𝔽2)C22×C1111yescharacteristic, complemented
228C22×#41C22×C1111yescharacteristic
229C23×D4C22×C1111yescharacteristic, complemented
230C2×AGL(1,ℤ/8)C22×C1114yes—
231#547—24no—
232#546—24no—
233#536C22×C1112yescomplemented
234#535—28no—
235#534—22no—
236C2×#127C22×C1112yes—
237C2×#124C22×C1112yescomplemented
238#525C22×C1112yes—
239C2×#123—22no—
240C2×#121—22no—
241C2×#120—22no—
242#518C22×C1111yescharacteristic, complemented
243C2×#117C22×C1111yescharacteristic, complemented
244#453—28no—
245#450—24no—
246#447—24no—
247C2×#104C22×C1114yescomplemented
248#418C22×C1114yescomplemented
249C2×#101C22×C1112yescomplemented
250C2×#100C22×C1112yescomplemented
251#407C22×C1112yescomplemented
252#339C22×C1114yescomplemented
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—44no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—48no—
261C22×C11—44no—
262C22×C11—42no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—82no—
266C22×C11—84no—
267C22×C11—816no—
268C22×C11—84no—
269C22×C11—164no—
270C22×C11C2×#12011yescharacteristic
271C22×C11C2×#12011yescharacteristic
272C22×C11#53411yescharacteristic
273C4×C11—22no—
274C4×C11—44no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—44no—
278C4×C11D4214yes—
279C25—21no—
280H(5,𝔽2)—24no—
281H(5,𝔽2)—42no—
282C2×#41—22no—
283C2×#41—24no—
284C2×#41—24no—
285C2×#41—42no—
286C2×#41C23×C1112yes—
287C22×Q8C23×C1111yescharacteristic
288C22×D4—22no—
289C22×D4—24no—
290C22×D4—24no—
291C22×D4—22no—
292C22×D4—21no—
293C22×D4—24no—
294C22×D4—42no—
295C22×D4D4×C1112yes—
296C22×D4C23×C1112yes—
297C22×D4C23×C1111yescharacteristic
298C23×C4D4×C1112yes—
299C23×C4C23×C1111yescharacteristic
300AGL(1,ℤ/8)—28no—
301AGL(1,ℤ/8)—44no—
302C2×SD16—24no—
303C2×D8—24no—
304C2×M16C23×C1114yes—
305C4⋊Q8—22no—
306#127—24no—
307#127D4×C1118yescomplemented
308#124—24no—
309#124—22no—
310#124—24no—
311#123—28no—
312#123—24no—
313#123—22no—
314#123—24no—
315C22⋊Q8—24no—
316C22⋊Q8D4×C1114yescomplemented
317#121—216no—
318#121—28no—
319#121D4×C1114yescomplemented
320#120—216no—
321#120—24no—
322#120—22no—
323C4×D4—24no—
324C4×D4—24no—
325#117—24no—
326#117C23×C1112yes—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—21no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C42C23×C1112yes—
334#104—28no—
335#102—28no—
336#101—42no—
337#100—24no—
338C22⋊C8—24no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—42no—
342C2×C11—44no—
343C2×C11—84no—
344C2×C11—82no—
345C2×C11#240311yescharacteristic
346C2×C11#302112yes—
347C24—22no—
348C24—24no—
349C24—22no—
350C24—42no—
351C24—42no—
352C24—84no—
353C24C2×D4×C1111yescharacteristic
354C24C2×D4×C1112yes—
355#41—24no—
356#41—24no—
357#41—416no—
358#41—48no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8C2×D4×C1112yes—
363C2×D4—24no—
364C2×D4—24no—
365C2×D4—24no—
366C2×D4—24no—
367C2×D4—22no—
368C2×D4—24no—
369C2×D4—216no—
370C2×D4—22no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—24no—
375C2×D4—416no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—48no—
379C2×D4—44no—
380C2×D4—44no—
381C2×D4—42no—
382C2×D4—88no—
383C2×D4C2×D4×C1112yes—
384C2×D4C2×D4×C1114yes—
385C2×D4C2×D4×C1114yes—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—42no—
395C22×C4C2×D4×C1112yes—
396C22×C4C2×D4×C1111yescharacteristic
397C22×C4C2×D4×C1114yes—
398C22×C4C24×C1111yescharacteristic
399SD16—48no—
400D8—48no—
401M16—24no—
402M16—24no—
403C2×C8—24no—
404C4⋊C4—24no—
405C4⋊C4—28no—
406C4⋊C4—24no—
407C4⋊C4C2×D4×C1114yes—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—216no—
411C22⋊C4—28no—
412C22⋊C4—24no—
413C22⋊C4—22no—
414C22⋊C4—24no—
415C42—22no—
416C42—22no—
417C42C2×D4×C1114yes—
418C11#2391311yescharacteristic, direct product factor, Sylow
419C23—21no—
420C23—22no—
421C23—21no—
422C23—22no—
423C23—22no—
424C23—24no—
425C23—42no—
426C23—44no—
427C23—48no—
428C23—48no—
429C23—44no—
430C23—42no—
431C23—42no—
432C23—88no—
433C23—88no—
434C23—84no—
435C23—88no—
436C23C11×#12012yes—
437C23C11×#12014yes—
438C23C22×D4×C1111yescharacteristic
439Q8—24no—
440Q8—44no—
441D4—28no—
442D4—24no—
443D4—28no—
444D4—48no—
445D4—48no—
446D4—48no—
447D4—42no—
448D4—42no—
449D4—44no—
450D4—84no—
451D4—816no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—28no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—48no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—84no—
466C2×C4C11×#12012yes—
467C2×C4C22×D4×C1112yes—
468C2×C4C22×D4×C1112yes—
469C2×C4C11×H(5,𝔽2)12yes—
470C8—44no—
471C22—22no—
472C22—22no—
473C22—24no—
474C22—24no—
475C22—44no—
476C22—42no—
477C22—42no—
478C22—48no—
479C22—44no—
480C22—42no—
481C22—44no—
482C22—44no—
483C22—82no—
484C22—84no—
485C22—816no—
486C22—84no—
487C22—164no—
488C22C2×C11×#12011yescharacteristic
489C22C2×C11×#12011yescharacteristic
490C22C11×#53411yescharacteristic
491C4—22no—
492C4—44no—
493C4—42no—
494C4—42no—
495C4—44no—
496C4D42×C1114yes—
497C2—21no—
498C2—21no—
499C2—42no—
500C2—44no—
501C2—84no—
502C2—82no—
503C2C11×#240311yescharacteristic
504C2C11×#302112yes—
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×#3485C2semidirect
2. C2×C11×#535C2semidirect
3. C2×C11×#453C2semidirect
4. C11×#3003C2semidirect
5. C11×#2003C2semidirect
6. C11×#1897C2semidirect
7. C11×#1887C2semidirect
8. C11×#1785C2semidirect
9. C2×C11×H(5,𝔽2)C22semidirect
11. C23×D4×C11C22semidirect
15. C11×#536C22semidirect
19. C2×C11×#124C22semidirect
24. C11×#518C22semidirect
25. C2×C11×#117C22semidirect
29. C2×C11×#104C22semidirect
30. C11×#418C22semidirect
31. C2×C11×#101C22semidirect
32. C2×C11×#100C22semidirect
33. C11×#407C22semidirect
34. C11×#339C22semidirect
63. C11×#127D4semidirect
72. C11×C22⋊Q8D4semidirect
75. C11×#121D4semidirect
95. #23913C11direct (N × H)
167. #3485C2×C11semidirect
168. C2×#535C2×C11semidirect
169. C2×#453C2×C11semidirect
170. #3003C2×C11semidirect
171. #2003C2×C11semidirect
172. #1897C2×C11semidirect
173. #1887C2×C11semidirect
174. #1785C2×C11semidirect
227. C2×H(5,𝔽2)C22×C11semidirect
229. C23×D4C22×C11semidirect
233. #536C22×C11semidirect
237. C2×#124C22×C11semidirect
242. #518C22×C11semidirect
243. C2×#117C22×C11semidirect
247. C2×#104C22×C11semidirect
248. #418C22×C11semidirect
249. C2×#101C22×C11semidirect
250. C2×#100C22×C11semidirect
251. #407C22×C11semidirect
252. #339C22×C11semidirect
307. #127D4×C11semidirect
316. C22⋊Q8D4×C11semidirect
319. #121D4×C11semidirect
418. C11#23913direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34852
C2×C11×#5352
C2×C11×#4532
C11×#30032
C11×#20032
C11×#18972
C11×#18872
C11×#17852
#2391311