Finite Group Databasebeta

← C11×#18926 #14596119

Subgroups — C11×#18926 #14596119

Order 2816.

966 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×#3506C211yesmaximal, characteristic
2C11×#3229C211yesmaximal, characteristic, complemented
3C11×#3226C211yesmaximal, characteristic, complemented
4C2×C11×#461C211yesmaximal, characteristic, complemented
5C11×#1650C214yesmaximal, complemented
6C11×#1642C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic, complemented
8C11×#1481C211yesmaximal, characteristic, complemented
9C11×#1478C211yesmaximal, characteristic, complemented
10C22×C11×SD16—21no—
11C11×#559—22no—
12C11×#556C2212yes—
13C11×#555—21no—
14C11×#553—22no—
15C11×#550C2212yes—
16C11×#547—21no—
17C11×#538—22no—
18C11×#535—21no—
19C11×#533C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#525—22no—
23C11×#520—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C11×#500C2212yescomplemented
26C11×#498—21no—
27C11×#487—21no—
28C11×#486C2212yescomplemented
29C11×#483—22no—
30C11×#480—22no—
31C11×#475C2214yescomplemented
32C11×#474—22no—
33C11×#461—22no—
34C11×#461C2214yes—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103—21no—
39C11×#332C2212yescomplemented
40C11×#331C2212yescomplemented
41C11×Q8⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yes—
43C2×C11×#41—22no—
44C2×C11×#41—21no—
45C22×Q8×C11—21no—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—21no—
48C2×C11×SD16—24no—
49C2×C11×SD16—44no—
50C22×C8×C11—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8C2312yes—
57C11×C4⋊Q8C2311yescharacteristic
58C11×#127—22no—
59C11×#127C2311yescharacteristic
60C11×#126—24no—
61C11×#125—21no—
62C11×#124—24no—
63C11×#124—22no—
64C11×#124—21no—
65C11×#123—24no—
66C11×#123—24no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8D412yes—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—24no—
73C11×#121—21no—
74C11×#121—22no—
75C11×#121D412yes—
76C11×#120—24no—
77C4×Q8×C11—22no—
78C4×Q8×C11—21no—
79C4×Q8×C11C2312yes—
80C4×D4×C11—24no—
81C4×D4×C11—24no—
82C4×D4×C11—22no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D412yes—
87C4×D4×C11D412yes—
88C4×D4×C11C2312yes—
89C11×#117—22no—
90C11×#117—21no—
91C11×#117—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C42×C11C2311yescharacteristic
98C11×#107—24no—
99C11×#106—24no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2312yes—
104C11×#103—24no—
105C11×#103—24no—
106C11×#102—24no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#18926C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—21no—
113C11×#41—42no—
114C11×#41—42no—
115C11×#41—84no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—41no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×Q8×C11C2×D412yes—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11C2×D412yes—
132C2×D4×C11C2×D412yes—
133C22×C4×C11—24no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—41no—
139C22×C4×C11—82no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C11×SD16—48no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—42no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4C2×D412yes—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C42×C11—24no—
172C42×C11—22no—
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2411yescharacteristic
177#3506C2×C1111yescharacteristic
178#3229C2×C1111yescharacteristic, complemented
179#3226C2×C1111yescharacteristic, complemented
180C2×#461C2×C1111yescharacteristic, complemented
181#1650C2×C1114yescomplemented
182#1642C2×C1114yescomplemented
183#1540C2×C1111yescharacteristic, complemented
184#1481C2×C1111yescharacteristic, complemented
185#1478C2×C1111yescharacteristic, complemented
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—42no—
189C23×C11—81no—
190C23×C11—81no—
191C23×C11#12011yescharacteristic
192Q8×C11—24no—
193Q8×C11—41no—
194Q8×C11—41no—
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—81no—
198Q8×C11—82no—
199D4×C11—22no—
200D4×C11—22no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—84no—
208D4×C11—84no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—41no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11—42no—
218C2×C4×C11—82no—
219C2×C4×C11—81no—
220C2×C4×C11—84no—
221C2×C4×C11—82no—
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#13512yes—
226C2×C4×C11AGL(1,ℤ/8)12yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C8×C11—42no—
231C8×C11—42no—
232C8×C11—42no—
233C22×SD16—21no—
234#559—22no—
235#556C22×C1112yes—
236#555—21no—
237#553—22no—
238#550C22×C1112yes—
239#547—21no—
240#538—22no—
241#535—21no—
242#533C22×C1111yescharacteristic
243#532C22×C1111yescharacteristic
244C2×C4⋊Q8C22×C1111yescharacteristic
245#525—22no—
246#520—21no—
247C2×C4×D4C22×C1111yescharacteristic
248#500C22×C1112yescomplemented
249#498—21no—
250#487—21no—
251#486C22×C1112yescomplemented
252#483—22no—
253#480—22no—
254#475C22×C1114yescomplemented
255#474—22no—
256#461—22no—
257#461C22×C1114yes—
258#431C22×C1111yescharacteristic
259#431C22×C1111yescharacteristic
260C2×C4⋊C8C22×C1111yescharacteristic
261C2×#103—21no—
262#332C22×C1112yescomplemented
263#331C22×C1112yescomplemented
264Q8⋊C8C22×C1114yescomplemented
265D4⋊C8C22×C1114yes—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—84no—
275C22×C11#44912yes—
276C22×C11C2×#12011yescharacteristic
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—82no—
285C4×C11#44912yes—
286C4×C11C2×#13511yescharacteristic
287C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C11#57712yes—
289C2×#41—22no—
290C2×#41—21no—
291C22×Q8—21no—
292C22×D4D4×C1111yescharacteristic
293C23×C4—21no—
294C2×SD16—24no—
295C2×SD16—44no—
296C22×C8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8D4×C1111yescharacteristic
301C4⋊Q8D4×C1111yescharacteristic
302C4⋊Q8C23×C1112yes—
303C4⋊Q8C23×C1111yescharacteristic
304#127—22no—
305#127C23×C1111yescharacteristic
306#126—24no—
307#125—21no—
308#124—24no—
309#124—22no—
310#124—21no—
311#123—24no—
312#123—24no—
313C22⋊Q8—22no—
314C22⋊Q8—21no—
315C22⋊Q8D4×C1112yes—
316#121—22no—
317#121—22no—
318#121—24no—
319#121—21no—
320#121—22no—
321#121D4×C1112yes—
322#120—24no—
323C4×Q8—22no—
324C4×Q8—21no—
325C4×Q8C23×C1112yes—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—22no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4D4×C1112yes—
333C4×D4D4×C1112yes—
334C4×D4C23×C1112yes—
335#117—22no—
336#117—21no—
337#117—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4D4×C1111yescharacteristic
342C2×C22⋊C4—21no—
343C2×C42C23×C1111yescharacteristic
344#107—24no—
345#106—24no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8C23×C1112yes—
349C4⋊C8C23×C1112yes—
350#103—24no—
351#103—24no—
352#102—24no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C4×C8—21no—
356C4×C8C23×C1112yes—
357C2×C11—22no—
358C2×C11—82no—
359C2×C11—82no—
360C2×C11C2×#44911yescharacteristic
361C2×C11#300911yescharacteristic
362C2×C11#302211yescharacteristic
363C24—21no—
364#41—42no—
365#41—42no—
366#41—84no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—22no—
370C2×Q8—41no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8C2×D4×C1112yes—
374C2×D4—22no—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—21no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4C2×D4×C1112yes—
383C2×D4C2×D4×C1112yes—
384C22×C4—24no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—41no—
390C22×C4—82no—
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394SD16—48no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—42no—
399C4⋊C4—24no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4C2×D4×C1112yes—
412C4⋊C4C2×D4×C1112yes—
413C4⋊C4C2×D4×C1112yes—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C42—24no—
423C42—22no—
424C42C2×D4×C1111yescharacteristic
425C42C2×D4×C1111yescharacteristic
426C42C2×D4×C1111yescharacteristic
427C42C24×C1111yescharacteristic
428C11#1892611yescharacteristic, direct product factor, Sylow
429C23—22no—
430C23—22no—
431C23—42no—
432C23—81no—
433C23—81no—
434C23C11×#12011yescharacteristic
435Q8—24no—
436Q8—41no—
437Q8—41no—
438Q8—42no—
439Q8—42no—
440Q8—81no—
441Q8—82no—
442D4—22no—
443D4—22no—
444D4—42no—
445D4—44no—
446D4—41no—
447D4—41no—
448D4—42no—
449D4—42no—
450D4—84no—
451D4—84no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—42no—
461C2×C4—82no—
462C2×C4—81no—
463C2×C4—84no—
464C2×C4—82no—
465C2×C4C11×#12011yescharacteristic
466C2×C4C11×#12011yescharacteristic
467C2×C4C11×#12011yescharacteristic
468C2×C4C11×#13512yes—
469C2×C4C11×AGL(1,ℤ/8)12yes—
470C2×C4C22×D4×C1111yescharacteristic
471C2×C4C22×D4×C1111yescharacteristic
472C2×C4C22×D4×C1111yescharacteristic
473C8—42no—
474C8—42no—
475C8—42no—
476C22—21no—
477C22—21no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—84no—
485C22C11×#44912yes—
486C22C2×C11×#12011yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—42no—
493C4—42no—
494C4—82no—
495C4C11×#44912yes—
496C4C2×C11×#13511yescharacteristic
497C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
498C4C11×#57712yes—
499C2—22no—
500C2—82no—
501C2—82no—
502C2C2×C11×#44911yescharacteristic
503C2C11×#300911yescharacteristic
504C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3506C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3229C2semidirect
3. C11×#3226C2semidirect
4. C2×C11×#461C2semidirect
5. C11×#1650C2semidirect
6. C11×#1642C2semidirect
7. C11×#1540C2semidirect
8. C11×#1481C2semidirect
9. C11×#1478C2semidirect
25. C11×#500C22semidirect
28. C11×#486C22semidirect
31. C11×#475C22semidirect
39. C11×#332C22semidirect
40. C11×#331C22semidirect
41. C11×Q8⋊C8C22semidirect
111. #18926C11direct (N × H)
178. #3229C2×C11semidirect
179. #3226C2×C11semidirect
180. C2×#461C2×C11semidirect
181. #1650C2×C11semidirect
182. #1642C2×C11semidirect
183. #1540C2×C11semidirect
184. #1481C2×C11semidirect
185. #1478C2×C11semidirect
248. #500C22×C11semidirect
251. #486C22×C11semidirect
254. #475C22×C11semidirect
262. #332C22×C11semidirect
263. #331C22×C11semidirect
264. Q8⋊C8C22×C11semidirect
428. C11#18926direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#32292
C11×#32262
C2×C11×#4612
C11×#16502
C11×#16422
C11×#15402
C11×#14812
C11×#14782
#1892611