Finite Group Databasebeta

← C11×#19257 #14596450

Subgroups — C11×#19257 #14596450

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3167C211yesmaximal, characteristic, complemented
2C11×#3110C211yesmaximal, characteristic, complemented
3C11×#3109C211yesmaximal, characteristic
4C2×C8×D4×C11C211yesmaximal, characteristic, complemented
5C11×#1683C212yesmaximal, complemented
6C11×#1681C212yesmaximal, complemented
7C11×#1671C212yesmaximal, complemented
8C11×#1665C212yesmaximal, complemented
9C11×#1568C211yesmaximal, characteristic, complemented
10C11×#1552C211yesmaximal, characteristic, complemented
11C11×#1551C211yesmaximal, characteristic, complemented
12C23×C8×C11—21no—
13C11×#533C2211yescharacteristic
14C11×#532C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#498C2211yescharacteristic, complemented
17C11×#492C2211yescharacteristic, complemented
18C11×#487C2211yescharacteristic, complemented
19C11×#486C2211yescharacteristic, complemented
20C11×#484—21no—
21C11×#481—21no—
22C11×#476C2212yes—
23C11×#474C2212yes—
24C11×#465—21no—
25C11×#465—21no—
26C11×#461C2212yes—
27C11×#459C2212yes—
28C11×#450—21no—
29C11×#447—21no—
30C11×#442—22no—
31C11×#440—22no—
32C4×C11×SD16—21no—
33C4×C11×SD16—21no—
34C8×D4×C11—21no—
35C8×D4×C11—21no—
36C8×D4×C11C2212yes—
37C8×D4×C11C2212yes—
38C11×#432C2211yescharacteristic
39C11×#432C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8—21no—
42C2×C4×C8×C11C2211yescharacteristic
43C11×#335C2212yescomplemented
44C11×#334C2212yescomplemented
45C11×#333C2212yescomplemented
46C11×#332C2212yescomplemented
47C11×#332C2212yescomplemented
48C11×#331C2212yescomplemented
49C2×C11×#41—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C2×C11×SD16—22no—
53C2×C11×SD16—21no—
54C2×C11×SD16—21no—
55C2×C11×D8—22no—
56C22×C8×C11—21no—
57C22×C8×C11—22no—
58C22×C8×C11—22no—
59C22×C8×C11—44no—
60C22×C8×C11D411yescharacteristic
61C22×C8×C11D411yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×#127C2311yescharacteristic
66C11×#125—21no—
67C11×#124—21no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8—21no—
70C11×#121—21no—
71C11×#121—21no—
72C4×Q8×C11—21no—
73C4×Q8×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11D412yes—
79C4×D4×C11C2312yes—
80C11×#117—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C11×#107—22no—
85C11×#106—21no—
86C11×#106—21no—
87C11×#106—22no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8C2312yes—
90C11×C4⋊C8C2312yes—
91C11×C4⋊C8C2312yes—
92C11×#103—21no—
93C11×#103—21no—
94C11×#103—22no—
95C11×#102—22no—
96C11×#102—22no—
97C11×#102—21no—
98C11×#102—21no—
99C11×#102—22no—
100C11×C22⋊C8—21no—
101C11×C22⋊C8—21no—
102C11×C22⋊C8—22no—
103C11×C22⋊C8—22no—
104C11×#97—21no—
105C11×#97—21no—
106C4×C8×C11D411yescharacteristic
107C4×C8×C11D411yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#19257C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C11×#41—82no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×D4×C11—24no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C2×D4×C11C2×D412yes—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—41no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C11×SD16—42no—
133C11×SD16—42no—
134C11×SD16—44no—
135C11×D8—44no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—41no—
141C2×C8×C11—42no—
142C2×C8×C11—44no—
143C2×C8×C11—44no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C42×C11—41no—
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11#4111yescharacteristic
167C42×C11C2411yescharacteristic
168#3167C2×C1111yescharacteristic, complemented
169#3110C2×C1111yescharacteristic, complemented
170#3109C2×C1111yescharacteristic
171C2×C8×D4C2×C1111yescharacteristic, complemented
172#1683C2×C1112yescomplemented
173#1681C2×C1112yescomplemented
174#1671C2×C1112yescomplemented
175#1665C2×C1112yescomplemented
176#1568C2×C1111yescharacteristic, complemented
177#1552C2×C1111yescharacteristic, complemented
178#1551C2×C1111yescharacteristic, complemented
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—41no—
184C23×C11#12111yescharacteristic
185Q8×C11—42no—
186Q8×C11—41no—
187Q8×C11—41no—
188Q8×C11—81no—
189D4×C11—24no—
190D4×C11—22no—
191D4×C11—42no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—81no—
195D4×C11—82no—
196D4×C11#13514yes—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—82no—
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11—42no—
220C8×C11—42no—
221C8×C11—42no—
222C8×C11AGL(1,ℤ/8)12yes—
223C23×C8—21no—
224#533C22×C1111yescharacteristic
225#532C22×C1111yescharacteristic
226C2×C4×D4C22×C1111yescharacteristic
227#498C22×C1111yescharacteristic, complemented
228#492C22×C1111yescharacteristic, complemented
229#487C22×C1111yescharacteristic, complemented
230#486C22×C1111yescharacteristic, complemented
231#484—21no—
232#481—21no—
233#476C22×C1112yes—
234#474C22×C1112yes—
235#465—21no—
236#465—21no—
237#461C22×C1112yes—
238#459C22×C1112yes—
239#450—21no—
240#447—21no—
241#442—22no—
242#440—22no—
243C4×SD16—21no—
244C4×SD16—21no—
245C8×D4—21no—
246C8×D4—21no—
247C8×D4C22×C1112yes—
248C8×D4C22×C1112yes—
249#432C22×C1111yescharacteristic
250#432C22×C1111yescharacteristic
251C2×C4⋊C8C22×C1111yescharacteristic
252C2×C22⋊C8—21no—
253C2×C4×C8C22×C1111yescharacteristic
254#335C22×C1112yescomplemented
255#334C22×C1112yescomplemented
256#333C22×C1112yescomplemented
257#332C22×C1112yescomplemented
258#332C22×C1112yescomplemented
259#331C22×C1112yescomplemented
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—24no—
263C22×C11—48no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11#47112yes—
270C22×C11C2×#12111yescharacteristic
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—42no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11C2×#13512yes—
280C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C11#57511yescharacteristic
282C2×#41—21no—
283C22×D4D4×C1111yescharacteristic
284C23×C4—21no—
285C2×SD16—22no—
286C2×SD16—21no—
287C2×SD16—21no—
288C2×D8—22no—
289C22×C8—21no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—44no—
293C22×C8D4×C1111yescharacteristic
294C22×C8D4×C1111yescharacteristic
295C4⋊Q8C23×C1111yescharacteristic
296C4⋊Q8C23×C1111yescharacteristic
297C4⋊Q8C23×C1111yescharacteristic
298#127C23×C1111yescharacteristic
299#125—21no—
300#124—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303#121—21no—
304#121—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4D4×C1112yes—
312C4×D4C23×C1112yes—
313#117—21no—
314C2×C4⋊C4D4×C1111yescharacteristic
315C2×C22⋊C4—21no—
316C2×C42C23×C1111yescharacteristic
317#107—22no—
318#106—21no—
319#106—21no—
320#106—22no—
321C4⋊C8—21no—
322C4⋊C8C23×C1112yes—
323C4⋊C8C23×C1112yes—
324C4⋊C8C23×C1112yes—
325#103—21no—
326#103—21no—
327#103—22no—
328#102—22no—
329#102—22no—
330#102—21no—
331#102—21no—
332#102—22no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8—22no—
336C22⋊C8—22no—
337#97—21no—
338#97—21no—
339C4×C8D4×C1111yescharacteristic
340C4×C8D4×C1111yescharacteristic
341C4×C8C23×C1111yescharacteristic
342C4×C8C23×C1111yescharacteristic
343C2×C11—22no—
344C2×C11—44no—
345C2×C11—161no—
346C2×C11#303611yescharacteristic
347C2×C11#305011yescharacteristic
348C2×C11C2×#47111yescharacteristic
349C24—21no—
350#41—82no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×D4—24no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C2×D4C2×D4×C1112yes—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—41no—
367C22×C4C2×D4×C1111yescharacteristic
368C22×C4C2×D4×C1111yescharacteristic
369C22×C4C11×#4111yescharacteristic
370SD16—42no—
371SD16—44no—
372SD16—42no—
373D8—44no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—41no—
379C2×C8—44no—
380C2×C8—42no—
381C2×C8—44no—
382C2×C8C2×D4×C1111yescharacteristic
383C2×C8C2×D4×C1111yescharacteristic
384C2×C8C2×D4×C1111yescharacteristic
385C2×C8C2×D4×C1111yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4C2×D4×C1112yes—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C42—41no—
402C42C2×D4×C1111yescharacteristic
403C42C2×D4×C1111yescharacteristic
404C42C11×#4111yescharacteristic
405C42C24×C1111yescharacteristic
406C11#1925711yescharacteristic, direct product factor, Sylow
407C23—24no—
408C23—22no—
409C23—42no—
410C23—42no—
411C23—41no—
412C23C11×#12111yescharacteristic
413Q8—42no—
414Q8—41no—
415Q8—41no—
416Q8—81no—
417D4—24no—
418D4—22no—
419D4—42no—
420D4—41no—
421D4—41no—
422D4—81no—
423D4—82no—
424D4C11×#13514yes—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4C11×#12111yescharacteristic
439C2×C4C11×#12111yescharacteristic
440C2×C4C11×#12111yescharacteristic
441C2×C4C22×D4×C1111yescharacteristic
442C2×C4C22×D4×C1111yescharacteristic
443C2×C4C2×C11×#4111yescharacteristic
444C8—21no—
445C8—21no—
446C8—21no—
447C8—42no—
448C8—42no—
449C8—42no—
450C8C11×AGL(1,ℤ/8)12yes—
451C22—21no—
452C22—21no—
453C22—24no—
454C22—48no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22C11×#47112yes—
461C22C2×C11×#12111yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4C2×C11×#13512yes—
471C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
472C4C11×#57511yescharacteristic
473C2—22no—
474C2—44no—
475C2—161no—
476C2C11×#303611yescharacteristic
477C2C11×#305011yescharacteristic
478C2C2×C11×#47111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3109C2
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
1. C11×#3167C2semidirect
2. C11×#3110C2semidirect
4. C2×C8×D4×C11C2semidirect
5. C11×#1683C2semidirect
6. C11×#1681C2semidirect
7. C11×#1671C2semidirect
8. C11×#1665C2semidirect
9. C11×#1568C2semidirect
10. C11×#1552C2semidirect
11. C11×#1551C2semidirect
16. C11×#498C22semidirect
17. C11×#492C22semidirect
18. C11×#487C22semidirect
19. C11×#486C22semidirect
43. C11×#335C22semidirect
44. C11×#334C22semidirect
45. C11×#333C22semidirect
46. C11×#332C22semidirect
47. C11×#332C22semidirect
48. C11×#331C22semidirect
110. #19257C11direct (N × H)
168. #3167C2×C11semidirect
169. #3110C2×C11semidirect
171. C2×C8×D4C2×C11semidirect
172. #1683C2×C11semidirect
173. #1681C2×C11semidirect
174. #1671C2×C11semidirect
175. #1665C2×C11semidirect
176. #1568C2×C11semidirect
177. #1552C2×C11semidirect
178. #1551C2×C11semidirect
227. #498C22×C11semidirect
228. #492C22×C11semidirect
229. #487C22×C11semidirect
230. #486C22×C11semidirect
254. #335C22×C11semidirect
255. #334C22×C11semidirect
256. #333C22×C11semidirect
257. #332C22×C11semidirect
258. #332C22×C11semidirect
259. #331C22×C11semidirect
406. C11#19257direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31672
C11×#31102
C11×#31092
C2×C8×D4×C112
C11×#16832
C11×#16812
C11×#16712
C11×#16652
C11×#15682
C11×#15522
C11×#15512
#1925711