Finite Group Databasebeta

← C11×#19142 #14596335

Subgroups — C11×#19142 #14596335

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3131C211yesmaximal, characteristic, complemented
2C11×#3101C211yesmaximal, characteristic, complemented
3C11×#3100C211yesmaximal, characteristic
4C2×C11×#436C211yesmaximal, characteristic, complemented
5C11×#1703C212yesmaximal, complemented
6C11×#1701C212yesmaximal, complemented
7C11×#1699C212yesmaximal, complemented
8C11×#1697C212yesmaximal, complemented
9C11×#1564C211yesmaximal, characteristic, complemented
10C11×#1542C211yesmaximal, characteristic, complemented
11C11×#1540C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C11×#533C2211yescharacteristic
14C11×#532C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#488—21no—
17C11×#488—21no—
18C11×#487C2211yescharacteristic, complemented
19C11×#487C2211yescharacteristic, complemented
20C11×#486C2211yescharacteristic, complemented
21C11×#486C2211yescharacteristic, complemented
22C11×#483—21no—
23C11×#480—21no—
24C11×#476C2212yes—
25C11×#474C2212yes—
26C11×#461C2212yes—
27C11×#459C2212yes—
28C11×#450—21no—
29C11×#447—21no—
30C4×C11×SD16—22no—
31C4×C11×D8—22no—
32C11×#436—21no—
33C11×#436—21no—
34C11×#436C2212yes—
35C11×#436C2212yes—
36C11×#431C2211yescharacteristic
37C11×#431C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C11×#416—21no—
40C11×#416—21no—
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×D8—22no—
54C2×C11×M16—22no—
55C2×C11×M16—22no—
56C2×C11×M16—44no—
57C22×C8×C11—21no—
58C22×C8×C11D411yescharacteristic
59C22×C8×C11D411yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×#127C2311yescharacteristic
64C11×#125—21no—
65C11×#124—21no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C11×#121—21no—
69C11×#121—21no—
70C4×Q8×C11—21no—
71C4×Q8×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11D412yes—
77C4×D4×C11C2312yes—
78C11×#117—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C11×#107—22no—
83C11×#106—22no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2312yes—
86C11×C4⋊C8C2312yes—
87C11×C4⋊C8C2312yes—
88C11×#103—21no—
89C11×#103—21no—
90C11×#103—21no—
91C11×#103—21no—
92C11×#103—22no—
93C11×#102—22no—
94C11×#102—22no—
95C11×#102—21no—
96C11×#102—21no—
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—
104C4×C8×C11—21no—
105C4×C8×C11—21no—
106C4×C8×C11D411yescharacteristic
107C4×C8×C11D411yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#19142C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—42no—
122C2×D4×C11—41no—
123C2×D4×C11C2×D412yes—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—41no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11#4111yescharacteristic
133C11×SD16—44no—
134C11×D8—44no—
135C11×M16—44no—
136C11×M16—44no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—42no—
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C11×C4⋊C4—21no—
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—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4C2×D412yes—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C42×C11—41no—
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11#4111yescharacteristic
166C42×C11C2411yescharacteristic
167#3131C2×C1111yescharacteristic, complemented
168#3101C2×C1111yescharacteristic, complemented
169#3100C2×C1111yescharacteristic
170C2×#436C2×C1111yescharacteristic, complemented
171#1703C2×C1112yescomplemented
172#1701C2×C1112yescomplemented
173#1699C2×C1112yescomplemented
174#1697C2×C1112yescomplemented
175#1564C2×C1111yescharacteristic, complemented
176#1542C2×C1111yescharacteristic, complemented
177#1540C2×C1111yescharacteristic, complemented
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—41no—
183C23×C11#12111yescharacteristic
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—42no—
187Q8×C11—81no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—42no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—42no—
194D4×C11—81no—
195D4×C11—82no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—44no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—82no—
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#13512yes—
211C2×C4×C11AGL(1,ℤ/8)12yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C8×C11—21no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11—42no—
220C8×C11—42no—
221C8×C11—42no—
222C22×M16—21no—
223#533C22×C1111yescharacteristic
224#532C22×C1111yescharacteristic
225C2×C4×D4C22×C1111yescharacteristic
226#488—21no—
227#488—21no—
228#487C22×C1111yescharacteristic, complemented
229#487C22×C1111yescharacteristic, complemented
230#486C22×C1111yescharacteristic, complemented
231#486C22×C1111yescharacteristic, complemented
232#483—21no—
233#480—21no—
234#476C22×C1112yes—
235#474C22×C1112yes—
236#461C22×C1112yes—
237#459C22×C1112yes—
238#450—21no—
239#447—21no—
240C4×SD16—22no—
241C4×D8—22no—
242#436—21no—
243#436—21no—
244#436C22×C1112yes—
245#436C22×C1112yes—
246#431C22×C1111yescharacteristic
247#431C22×C1111yescharacteristic
248C2×C4⋊C8C22×C1111yescharacteristic
249#416—21no—
250#416—21no—
251C2×C22⋊C8—21no—
252C2×C4×C8C22×C1111yescharacteristic
253#335C22×C1112yescomplemented
254#334C22×C1112yescomplemented
255#333C22×C1112yescomplemented
256#332C22×C1112yescomplemented
257#332C22×C1112yescomplemented
258#331C22×C1112yescomplemented
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—84no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11#46312yes—
269C22×C11C2×#12111yescharacteristic
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—42no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11#46312yes—
278C4×C11C2×#13511yescharacteristic
279C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C11#57512yes—
281C2×#41—21no—
282C22×D4D4×C1111yescharacteristic
283C23×C4—21no—
284C2×SD16—22no—
285C2×D8—22no—
286C2×M16—22no—
287C2×M16—22no—
288C2×M16—44no—
289C22×C8—21no—
290C22×C8D4×C1111yescharacteristic
291C22×C8D4×C1111yescharacteristic
292C4⋊Q8C23×C1111yescharacteristic
293C4⋊Q8C23×C1111yescharacteristic
294C4⋊Q8C23×C1111yescharacteristic
295#127C23×C1111yescharacteristic
296#125—21no—
297#124—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300#121—21no—
301#121—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4D4×C1112yes—
309C4×D4C23×C1112yes—
310#117—21no—
311C2×C4⋊C4D4×C1111yescharacteristic
312C2×C22⋊C4—21no—
313C2×C42C23×C1111yescharacteristic
314#107—22no—
315#106—22no—
316C4⋊C8—21no—
317C4⋊C8C23×C1112yes—
318C4⋊C8C23×C1112yes—
319C4⋊C8C23×C1112yes—
320#103—21no—
321#103—21no—
322#103—21no—
323#103—21no—
324#103—22no—
325#102—22no—
326#102—22no—
327#102—21no—
328#102—21no—
329#102—21no—
330#102—21no—
331#102—22no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—22no—
335C22⋊C8—22no—
336C4×C8—21no—
337C4×C8—21no—
338C4×C8D4×C1111yescharacteristic
339C4×C8D4×C1111yescharacteristic
340C4×C8C23×C1111yescharacteristic
341C4×C8C23×C1111yescharacteristic
342C2×C11—22no—
343C2×C11—82no—
344C2×C11—161no—
345C2×C11C2×#46311yescharacteristic
346C2×C11#305411yescharacteristic
347C2×C11#306711yescharacteristic
348C24—21no—
349#41—42no—
350#41—42no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—42no—
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—44no—
371D8—44no—
372M16—44no—
373M16—44no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—42no—
380C2×C8C2×D4×C1111yescharacteristic
381C2×C8C2×D4×C1111yescharacteristic
382C2×C8C2×D4×C1111yescharacteristic
383C2×C8C2×D4×C1111yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4C2×D4×C1112yes—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C42—41no—
400C42C2×D4×C1111yescharacteristic
401C42C2×D4×C1111yescharacteristic
402C42C11×#4111yescharacteristic
403C42C24×C1111yescharacteristic
404C11#1914211yescharacteristic, direct product factor, Sylow
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23C11×#12111yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—42no—
414Q8—81no—
415D4—22no—
416D4—22no—
417D4—42no—
418D4—41no—
419D4—41no—
420D4—42no—
421D4—81no—
422D4—82no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—82no—
434C2×C4C11×#12111yescharacteristic
435C2×C4C11×#12111yescharacteristic
436C2×C4C11×#12111yescharacteristic
437C2×C4C11×#13512yes—
438C2×C4C11×AGL(1,ℤ/8)12yes—
439C2×C4C22×D4×C1111yescharacteristic
440C2×C4C22×D4×C1111yescharacteristic
441C2×C4C2×C11×#4111yescharacteristic
442C8—21no—
443C8—21no—
444C8—21no—
445C8—21no—
446C8—42no—
447C8—42no—
448C8—42no—
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22C11×#46312yes—
459C22C2×C11×#12111yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4C11×#46312yes—
468C4C2×C11×#13511yescharacteristic
469C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
470C4C11×#57512yes—
471C2—22no—
472C2—82no—
473C2—161no—
474C2C2×C11×#46311yescharacteristic
475C2C11×#305411yescharacteristic
476C2C11×#306711yescharacteristic
subgroupG/H
centerC2×C4×C11#121
commutator, Frattini, cosocleC42C24×C11
socleC22×C11C2×#121
prime radicalC11×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3131C2semidirect
2. C11×#3101C2semidirect
4. C2×C11×#436C2semidirect
5. C11×#1703C2semidirect
6. C11×#1701C2semidirect
7. C11×#1699C2semidirect
8. C11×#1697C2semidirect
9. C11×#1564C2semidirect
10. C11×#1542C2semidirect
11. C11×#1540C2semidirect
18. C11×#487C22semidirect
19. C11×#487C22semidirect
20. C11×#486C22semidirect
21. C11×#486C22semidirect
43. C11×#335C22semidirect
44. C11×#334C22semidirect
45. C11×#333C22semidirect
46. C11×#332C22semidirect
47. C11×#332C22semidirect
48. C11×#331C22semidirect
110. #19142C11direct (N × H)
167. #3131C2×C11semidirect
168. #3101C2×C11semidirect
170. C2×#436C2×C11semidirect
171. #1703C2×C11semidirect
172. #1701C2×C11semidirect
173. #1699C2×C11semidirect
174. #1697C2×C11semidirect
175. #1564C2×C11semidirect
176. #1542C2×C11semidirect
177. #1540C2×C11semidirect
228. #487C22×C11semidirect
229. #487C22×C11semidirect
230. #486C22×C11semidirect
231. #486C22×C11semidirect
253. #335C22×C11semidirect
254. #334C22×C11semidirect
255. #333C22×C11semidirect
256. #332C22×C11semidirect
257. #332C22×C11semidirect
258. #331C22×C11semidirect
404. C11#19142direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31312
C11×#31012
C11×#31002
C2×C11×#4362
C11×#17032
C11×#17012
C11×#16992
C11×#16972
C11×#15642
C11×#15422
C11×#15402
#1914211