Finite Group Databasebeta

← C11×#18896 #14596089

Subgroups — C11×#18896 #14596089

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic, complemented
3C11×#3205C211yesmaximal, characteristic
4C2×C11×#460C211yesmaximal, characteristic, complemented
5C11×#1626C214yesmaximal, complemented
6C11×#1620C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic, complemented
8C11×#1481C211yesmaximal, characteristic, complemented
9C11×#1479C211yesmaximal, characteristic, complemented
10C22×C11×SD16—21no—
11C11×#559C2212yescomplemented
12C11×#557C2212yescomplemented
13C11×#556—21no—
14C11×#556—22no—
15C11×#554—21no—
16C11×#552—22no—
17C11×#539—22no—
18C11×#536—21no—
19C11×#533C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C2×C11×#127C2211yescharacteristic
22C11×#529—22no—
23C11×#520—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#493C2212yes—
26C11×#492—21no—
27C11×#486—21no—
28C11×#486C2212yes—
29C11×#460—22no—
30C11×#460C2214yes—
31C11×#460C2214yes—
32C11×#459—22no—
33C11×#450—22no—
34C11×#447—22no—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#102—21no—
39C11×#332C2212yescomplemented
40C11×#331C2212yescomplemented
41C11×Q8⋊C8C2214yescomplemented
42C11×Q8⋊C8C2214yescomplemented
43C2×C11×#41—21no—
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C2×C11×SD16—24no—
49C2×C11×SD16—24no—
50C2×C11×SD16—44no—
51C2×C11×D8—24no—
52C22×C8×C11—21no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127C2312yes—
61C11×#127C2311yescharacteristic
62C11×#126—24no—
63C11×#126—24no—
64C11×#125—22no—
65C11×#125—24no—
66C11×#125—21no—
67C11×#124—22no—
68C11×#124—22no—
69C11×#124—21no—
70C11×#123—24no—
71C11×#123—24no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8D412yes—
77C11×#121—21no—
78C11×#121D412yes—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11D412yes—
85C4×Q8×C11C2312yes—
86C4×Q8×C11C2312yes—
87C4×D4×C11—24no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—21no—
91C4×D4×C11D412yes—
92C11×#117—22no—
93C11×#117—24no—
94C11×#117—21no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2312yes—
104C11×#102—24no—
105C11×#102—24no—
106C11×#102—24no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#18896C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—41no—
113C11×#41—42no—
114C11×#41—42no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11C2×D412yes—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—82no—
134C2×D4×C11—82no—
135C2×D4×C11C2×D412yes—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C11×SD16—48no—
144C11×SD16—84no—
145C11×D8—84no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C42×C11—24no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11C2411yescharacteristic
179#3507C2×C1111yescharacteristic, complemented
180#3208C2×C1111yescharacteristic, complemented
181#3205C2×C1111yescharacteristic
182C2×#460C2×C1111yescharacteristic, complemented
183#1626C2×C1114yescomplemented
184#1620C2×C1114yescomplemented
185#1540C2×C1111yescharacteristic, complemented
186#1481C2×C1111yescharacteristic, complemented
187#1479C2×C1111yescharacteristic, complemented
188C23×C11—22no—
189C23×C11—42no—
190C23×C11—82no—
191C23×C11—82no—
192C23×C11—82no—
193C23×C11#12011yescharacteristic
194Q8×C11—22no—
195Q8×C11—22no—
196Q8×C11—24no—
197Q8×C11—41no—
198Q8×C11—41no—
199Q8×C11—42no—
200Q8×C11—81no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—44no—
204D4×C11—41no—
205D4×C11—42no—
206D4×C11—41no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—44no—
210D4×C11—82no—
211D4×C11—82no—
212D4×C11—82no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11—81no—
223C2×C4×C11—84no—
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11#13512yes—
228C2×C4×C11AGL(1,ℤ/8)12yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C8×C11—42no—
233C8×C11—42no—
234C8×C11—42no—
235C22×SD16—21no—
236#559C22×C1112yescomplemented
237#557C22×C1112yescomplemented
238#556—21no—
239#556—22no—
240#554—21no—
241#552—22no—
242#539—22no—
243#536—21no—
244#533C22×C1111yescharacteristic
245#532C22×C1111yescharacteristic
246C2×#127C22×C1111yescharacteristic
247#529—22no—
248#520—21no—
249C2×C4×Q8C22×C1111yescharacteristic
250#493C22×C1112yes—
251#492—21no—
252#486—21no—
253#486C22×C1112yes—
254#460—22no—
255#460C22×C1114yes—
256#460C22×C1114yes—
257#459—22no—
258#450—22no—
259#447—22no—
260#431C22×C1111yescharacteristic
261#431C22×C1111yescharacteristic
262C2×C4⋊C8C22×C1111yescharacteristic
263C2×#102—21no—
264#332C22×C1112yescomplemented
265#331C22×C1112yescomplemented
266Q8⋊C8C22×C1114yescomplemented
267Q8⋊C8C22×C1114yescomplemented
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—164no—
277C22×C11#44912yes—
278C22×C11C2×#12011yescharacteristic
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11#44912yes—
288C4×C11C2×#13511yescharacteristic
289C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
290C4×C11#57712yes—
291C2×#41—21no—
292C22×Q8D4×C1111yescharacteristic
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C2×SD16—24no—
297C2×SD16—24no—
298C2×SD16—44no—
299C2×D8—24no—
300C22×C8—21no—
301C4⋊Q8—22no—
302C4⋊Q8D4×C1111yescharacteristic
303C4⋊Q8D4×C1111yescharacteristic
304C4⋊Q8C23×C1111yescharacteristic
305#127—21no—
306#127—21no—
307#127—21no—
308#127C23×C1112yes—
309#127C23×C1111yescharacteristic
310#126—24no—
311#126—24no—
312#125—22no—
313#125—24no—
314#125—21no—
315#124—22no—
316#124—22no—
317#124—21no—
318#123—24no—
319#123—24no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—24no—
323C22⋊Q8—21no—
324C22⋊Q8D4×C1112yes—
325#121—21no—
326#121D4×C1112yes—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8D4×C1112yes—
333C4×Q8C23×C1112yes—
334C4×Q8C23×C1112yes—
335C4×D4—24no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—21no—
339C4×D4D4×C1112yes—
340#117—22no—
341#117—24no—
342#117—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4D4×C1111yescharacteristic
346C2×C42—21no—
347C2×C42C23×C1111yescharacteristic
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8C23×C1112yes—
351C4⋊C8C23×C1112yes—
352#102—24no—
353#102—24no—
354#102—24no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C4×C8—21no—
358C4×C8C23×C1112yes—
359C2×C11—22no—
360C2×C11—82no—
361C2×C11—162no—
362C2×C11C2×#44911yescharacteristic
363C2×C11#301011yescharacteristic
364C2×C11#302111yescharacteristic
365C24—41no—
366#41—42no—
367#41—42no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8C2×D4×C1112yes—
374C2×Q8C2×D4×C1112yes—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—82no—
387C2×D4—82no—
388C2×D4C2×D4×C1112yes—
389C22×C4—21no—
390C22×C4—24no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×D4×C1111yescharacteristic
396SD16—48no—
397SD16—84no—
398D8—84no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—42no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4C2×D4×C1112yes—
416C4⋊C4C2×D4×C1112yes—
417C4⋊C4C2×D4×C1112yes—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C42—24no—
425C42—22no—
426C42—22no—
427C42—22no—
428C42C2×D4×C1111yescharacteristic
429C42C2×D4×C1111yescharacteristic
430C42C2×D4×C1111yescharacteristic
431C42C24×C1111yescharacteristic
432C11#1889611yescharacteristic, direct product factor, Sylow
433C23—22no—
434C23—42no—
435C23—82no—
436C23—82no—
437C23—82no—
438C23C11×#12011yescharacteristic
439Q8—22no—
440Q8—22no—
441Q8—24no—
442Q8—41no—
443Q8—41no—
444Q8—42no—
445Q8—81no—
446D4—42no—
447D4—44no—
448D4—44no—
449D4—41no—
450D4—42no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—44no—
455D4—82no—
456D4—82no—
457D4—82no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—81no—
468C2×C4—84no—
469C2×C4C11×#12011yescharacteristic
470C2×C4C11×#12011yescharacteristic
471C2×C4C11×#12011yescharacteristic
472C2×C4C11×#13512yes—
473C2×C4C11×AGL(1,ℤ/8)12yes—
474C2×C4C22×D4×C1111yescharacteristic
475C2×C4C22×D4×C1111yescharacteristic
476C2×C4C22×D4×C1111yescharacteristic
477C8—42no—
478C8—42no—
479C8—42no—
480C22—21no—
481C22—21no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—164no—
489C22C11×#44912yes—
490C22C2×C11×#12011yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4C11×#44912yes—
500C4C2×C11×#13511yescharacteristic
501C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
502C4C11×#57712yes—
503C2—22no—
504C2—82no—
505C2—162no—
506C2C2×C11×#44911yescharacteristic
507C2C11×#301011yescharacteristic
508C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3205C2
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×#3507C2semidirect
2. C11×#3208C2semidirect
4. C2×C11×#460C2semidirect
5. C11×#1626C2semidirect
6. C11×#1620C2semidirect
7. C11×#1540C2semidirect
8. C11×#1481C2semidirect
9. C11×#1479C2semidirect
11. C11×#559C22semidirect
12. C11×#557C22semidirect
39. C11×#332C22semidirect
40. C11×#331C22semidirect
41. C11×Q8⋊C8C22semidirect
42. C11×Q8⋊C8C22semidirect
111. #18896C11direct (N × H)
179. #3507C2×C11semidirect
180. #3208C2×C11semidirect
182. C2×#460C2×C11semidirect
183. #1626C2×C11semidirect
184. #1620C2×C11semidirect
185. #1540C2×C11semidirect
186. #1481C2×C11semidirect
187. #1479C2×C11semidirect
236. #559C22×C11semidirect
237. #557C22×C11semidirect
264. #332C22×C11semidirect
265. #331C22×C11semidirect
266. Q8⋊C8C22×C11semidirect
267. Q8⋊C8C22×C11semidirect
432. C11#18896direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#32082
C11×#32052
C2×C11×#4602
C11×#16262
C11×#16202
C11×#15402
C11×#14812
C11×#14792
#1889611