Finite Group Databasebeta

← C11×#18928 #14596121

Subgroups — C11×#18928 #14596121

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 504 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×#1654C214yesmaximal, complemented
6C11×#1646C214yesmaximal, complemented
7C11×#1542C211yesmaximal, characteristic, complemented
8C11×#1480C211yesmaximal, characteristic, complemented
9C11×#1478C211yesmaximal, characteristic, complemented
10C22×C11×SD16—21no—
11C11×#559—22no—
12C11×#556—21no—
13C11×#555C2212yes—
14C11×#553—22no—
15C11×#550—21no—
16C11×#547C2212yes—
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×#500—21no—
26C11×#498C2212yescomplemented
27C11×#487C2212yescomplemented
28C11×#486—21no—
29C11×#483—22no—
30C11×#480—22no—
31C11×#475—22no—
32C11×#474C2214yescomplemented
33C11×#461—22no—
34C11×#461C2214yes—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103—21no—
39C11×#333C2212yescomplemented
40C11×#332C2212yescomplemented
41C11×D4⋊C8C2214yes—
42C11×D4⋊C8C2214yescomplemented
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⋊Q8C2312yes—
56C11×C4⋊Q8C2311yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×#127—22no—
59C11×#127D411yescharacteristic
60C11×#126—24no—
61C11×#125—21no—
62C11×#124—22no—
63C11×#124—24no—
64C11×#124—21no—
65C11×#123—24no—
66C11×#123—24no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8D412yes—
70C11×#121—24no—
71C11×#121—22no—
72C11×#121—22no—
73C11×#121—22no—
74C11×#121—21no—
75C11×#121D412yes—
76C11×#120—24no—
77C4×Q8×C11—22no—
78C4×Q8×C11—21no—
79C4×Q8×C11D412yes—
80C4×D4×C11—24no—
81C4×D4×C11—22no—
82C4×D4×C11—24no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D412yes—
87C4×D4×C11C2312yes—
88C4×D4×C11C2312yes—
89C11×#117—21no—
90C11×#117—22no—
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#18928C1111yesmaximal, 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—21no—
128C2×D4×C11—21no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
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—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
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#1654C2×C1114yescomplemented
182#1646C2×C1114yescomplemented
183#1542C2×C1111yescharacteristic, complemented
184#1480C2×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—42no—
193Q8×C11—42no—
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—82no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—24no—
201D4×C11—44no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—81no—
205D4×C11—84no—
206D4×C11—84no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—42no—
217C2×C4×C11—82no—
218C2×C4×C11—81no—
219C2×C4×C11—84no—
220C2×C4×C11—82no—
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#13512yes—
225C2×C4×C11AGL(1,ℤ/8)12yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C8×C11—42no—
230C8×C11—42no—
231C8×C11—42no—
232C22×SD16—21no—
233#559—22no—
234#556—21no—
235#555C22×C1112yes—
236#553—22no—
237#550—21no—
238#547C22×C1112yes—
239#538—22no—
240#535—21no—
241#533C22×C1111yescharacteristic
242#532C22×C1111yescharacteristic
243C2×C4⋊Q8C22×C1111yescharacteristic
244#525—22no—
245#520—21no—
246C2×C4×D4C22×C1111yescharacteristic
247#500—21no—
248#498C22×C1112yescomplemented
249#487C22×C1112yescomplemented
250#486—21no—
251#483—22no—
252#480—22no—
253#475—22no—
254#474C22×C1114yescomplemented
255#461—22no—
256#461C22×C1114yes—
257#431C22×C1111yescharacteristic
258#431C22×C1111yescharacteristic
259C2×C4⋊C8C22×C1111yescharacteristic
260C2×#103—21no—
261#333C22×C1112yescomplemented
262#332C22×C1112yescomplemented
263D4⋊C8C22×C1114yes—
264D4⋊C8C22×C1114yescomplemented
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—84no—
274C22×C11#44912yes—
275C22×C11C2×#12011yescharacteristic
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—82no—
284C4×C11#44912yes—
285C4×C11C2×#13511yescharacteristic
286C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C11#57712yes—
288C2×#41—22no—
289C2×#41—21no—
290C22×Q8—21no—
291C22×D4D4×C1111yescharacteristic
292C23×C4—21no—
293C2×SD16—24no—
294C2×SD16—44no—
295C22×C8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8D4×C1111yescharacteristic
300C4⋊Q8C23×C1112yes—
301C4⋊Q8C23×C1111yescharacteristic
302C4⋊Q8C23×C1111yescharacteristic
303#127—22no—
304#127D4×C1111yescharacteristic
305#126—24no—
306#125—21no—
307#124—22no—
308#124—24no—
309#124—21no—
310#123—24no—
311#123—24no—
312C22⋊Q8—21no—
313C22⋊Q8—22no—
314C22⋊Q8D4×C1112yes—
315#121—24no—
316#121—22no—
317#121—22no—
318#121—22no—
319#121—21no—
320#121D4×C1112yes—
321#120—24no—
322C4×Q8—22no—
323C4×Q8—21no—
324C4×Q8D4×C1112yes—
325C4×D4—24no—
326C4×D4—22no—
327C4×D4—24no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4D4×C1112yes—
332C4×D4C23×C1112yes—
333C4×D4C23×C1112yes—
334#117—21no—
335#117—22no—
336#117—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4D4×C1111yescharacteristic
341C2×C22⋊C4—21no—
342C2×C42C23×C1111yescharacteristic
343#107—24no—
344#106—24no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8C23×C1112yes—
348C4⋊C8C23×C1112yes—
349#103—24no—
350#103—24no—
351#102—24no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C4×C8—21no—
355C4×C8C23×C1112yes—
356C2×C11—22no—
357C2×C11—82no—
358C2×C11—82no—
359C2×C11C2×#44911yescharacteristic
360C2×C11#300911yescharacteristic
361C2×C11#302211yescharacteristic
362C24—21no—
363#41—42no—
364#41—42no—
365#41—84no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—41no—
370C2×Q8—42no—
371C2×Q8—42no—
372C2×Q8C2×D4×C1112yes—
373C2×D4—22no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4C2×D4×C1112yes—
382C2×D4C2×D4×C1112yes—
383C22×C4—24no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—41no—
389C22×C4—82no—
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393SD16—48no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—42no—
398C4⋊C4—24no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4C2×D4×C1112yes—
411C4⋊C4C2×D4×C1112yes—
412C4⋊C4C2×D4×C1112yes—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C42—24no—
422C42—22no—
423C42C2×D4×C1111yescharacteristic
424C42C2×D4×C1111yescharacteristic
425C42C2×D4×C1111yescharacteristic
426C42C24×C1111yescharacteristic
427C11#1892811yescharacteristic, direct product factor, Sylow
428C23—22no—
429C23—22no—
430C23—42no—
431C23—81no—
432C23—81no—
433C23C11×#12011yescharacteristic
434Q8—42no—
435Q8—42no—
436Q8—42no—
437Q8—42no—
438Q8—42no—
439Q8—82no—
440D4—22no—
441D4—22no—
442D4—24no—
443D4—44no—
444D4—42no—
445D4—42no—
446D4—81no—
447D4—84no—
448D4—84no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—82no—
460C2×C4—81no—
461C2×C4—84no—
462C2×C4—82no—
463C2×C4C11×#12011yescharacteristic
464C2×C4C11×#12011yescharacteristic
465C2×C4C11×#12011yescharacteristic
466C2×C4C11×#13512yes—
467C2×C4C11×AGL(1,ℤ/8)12yes—
468C2×C4C22×D4×C1111yescharacteristic
469C2×C4C22×D4×C1111yescharacteristic
470C2×C4C22×D4×C1111yescharacteristic
471C8—42no—
472C8—42no—
473C8—42no—
474C22—21no—
475C22—21no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—84no—
483C22C11×#44912yes—
484C22C2×C11×#12011yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—42no—
490C4—42no—
491C4—42no—
492C4—82no—
493C4C11×#44912yes—
494C4C2×C11×#13511yescharacteristic
495C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
496C4C11×#57712yes—
497C2—22no—
498C2—82no—
499C2—82no—
500C2C2×C11×#44911yescharacteristic
501C2C11×#300911yescharacteristic
502C2C11×#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×#1654C2semidirect
6. C11×#1646C2semidirect
7. C11×#1542C2semidirect
8. C11×#1480C2semidirect
9. C11×#1478C2semidirect
26. C11×#498C22semidirect
27. C11×#487C22semidirect
32. C11×#474C22semidirect
39. C11×#333C22semidirect
40. C11×#332C22semidirect
42. C11×D4⋊C8C22semidirect
111. #18928C11direct (N × H)
178. #3229C2×C11semidirect
179. #3226C2×C11semidirect
180. C2×#461C2×C11semidirect
181. #1654C2×C11semidirect
182. #1646C2×C11semidirect
183. #1542C2×C11semidirect
184. #1480C2×C11semidirect
185. #1478C2×C11semidirect
248. #498C22×C11semidirect
249. #487C22×C11semidirect
254. #474C22×C11semidirect
261. #333C22×C11semidirect
262. #332C22×C11semidirect
264. D4⋊C8C22×C11semidirect
427. C11#18928direct (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×#16542
C11×#16462
C11×#15422
C11×#14802
C11×#14782
#1892811