Finite Group Databasebeta

← C11×#19169 #14596362

Subgroups — C11×#19169 #14596362

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3141C211yesmaximal, characteristic, complemented
2C11×#3100C211yesmaximal, characteristic
3C2×C11×#461C211yesmaximal, characteristic, complemented
4D4×C11×M16C211yesmaximal, characteristic, complemented
5C11×#1701C212yesmaximal, complemented
6C11×#1699C212yesmaximal, complemented
7C11×#1681C212yesmaximal, complemented
8C11×#1679C212yesmaximal, complemented
9C11×#1565C211yesmaximal, characteristic, complemented
10C11×#1549C211yesmaximal, characteristic, complemented
11C11×#1547C211yesmaximal, characteristic, complemented
12C22×C11×SD16—21no—
13C22×C11×M16—21no—
14C11×#532C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C11×#489—22no—
18C11×#487C2212yescomplemented
19C11×#486C2212yescomplemented
20C11×#480—21no—
21C11×#474C2211yescharacteristic
22C11×#474C2211yescharacteristic
23C11×#461—21no—
24C11×#461—21no—
25C11×#461C2212yes—
26C11×#461C2212yes—
27C11×#459C2211yescharacteristic
28C11×#459C2211yescharacteristic
29C11×#447—21no—
30C4×C11×D8—21no—
31C4×C11×D8—21no—
32C11×#436C2212yes—
33C11×#435—22no—
34C8×D4×C11C2212yes—
35C11×#431C2211yescharacteristic
36C11×#423C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C11×#417—21no—
39C11×#417—21no—
40C2×C11×#103—21no—
41C11×#407—21no—
42C4×C11×M16C2211yescharacteristic
43C11×#335C2212yescomplemented
44C11×#334C2212yescomplemented
45C11×#332C2212yescomplemented
46C11×#332C2212yescomplemented
47C11×#332C2212yescomplemented
48C11×#331C2212yescomplemented
49C2×C11×#41—21no—
50C22×Q8×C11—21no—
51C22×D4×C11D411yescharacteristic
52C23×C4×C11—21no—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C2×C11×SD16—44no—
56C2×C11×D8—21no—
57C2×C11×D8—21no—
58C2×C11×M16—21no—
59C2×C11×M16—22no—
60C2×C11×M16—44no—
61C2×C11×M16D411yescharacteristic
62C2×C11×M16D411yescharacteristic
63C22×C8×C11—21no—
64C22×C8×C11—22no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8C2312yes—
69C11×C4⋊Q8C2311yescharacteristic
70C11×#127C2311yescharacteristic
71C11×#124—21no—
72C11×#121—21no—
73C11×#121—21no—
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11D411yescharacteristic
79C4×D4×C11D411yescharacteristic
80C4×D4×C11C2311yescharacteristic
81C4×D4×C11C2311yescharacteristic
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C11×#107—21no—
88C11×#107—21no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×C4⋊C8C2312yes—
93C11×C4⋊C8C2311yescharacteristic
94C11×C4⋊C8C2311yescharacteristic
95C11×#103—22no—
96C11×#103—22no—
97C11×#103—22no—
98C11×#103—22no—
99C11×#102—21no—
100C11×#102—21no—
101C11×#102—22no—
102C11×#102—22no—
103C11×#102—21no—
104C11×#102—21no—
105C11×C22⋊C8—21no—
106C11×C22⋊C8—22no—
107C11×C22⋊C8—22no—
108C11×#97D412yes—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#19169C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—21no—
113C11×#41—42no—
114C11×#41—42no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11—41no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11C2×D411yescharacteristic
128C2×D4×C11C2×D411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—41no—
137C22×C4×C11—41no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11#4111yescharacteristic
141C11×SD16—44no—
142C11×SD16—44no—
143C11×D8—42no—
144C11×D8—42no—
145C11×M16—22no—
146C11×M16—22no—
147C11×M16—44no—
148C11×M16—42no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—42no—
154C2×C8×C11—44no—
155C2×C8×C11C2×D412yes—
156C2×C8×C11C2×D412yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—41no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4C2×D411yescharacteristic
165C11×C4⋊C4C2×D411yescharacteristic
166C11×C22⋊C4—21no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—41no—
171C11×C22⋊C4—41no—
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11#4111yescharacteristic
175C42×C11C2411yescharacteristic
176#3141C2×C1111yescharacteristic, complemented
177#3100C2×C1111yescharacteristic
178C2×#461C2×C1111yescharacteristic, complemented
179D4×M16C2×C1111yescharacteristic, complemented
180#1701C2×C1112yescomplemented
181#1699C2×C1112yescomplemented
182#1681C2×C1112yescomplemented
183#1679C2×C1112yescomplemented
184#1565C2×C1111yescharacteristic, complemented
185#1549C2×C1111yescharacteristic, complemented
186#1547C2×C1111yescharacteristic, complemented
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—41no—
192C23×C11—81no—
193C23×C11#12111yescharacteristic
194Q8×C11—41no—
195Q8×C11—42no—
196Q8×C11—41no—
197Q8×C11—42no—
198Q8×C11—82no—
199D4×C11—21no—
200D4×C11—21no—
201D4×C11—21no—
202D4×C11—42no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—81no—
208D4×C11—82no—
209D4×C11AGL(1,ℤ/8)12yes—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—82no—
225C2×C4×C11—82no—
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11#12111yescharacteristic
228C2×C4×C11#12111yescharacteristic
229C2×C4×C11#13512yes—
230C2×C4×C11AGL(1,ℤ/8)12yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C8×C11—22no—
235C8×C11—22no—
236C8×C11—42no—
237C8×C11—42no—
238C8×C11—41no—
239C8×C11—41no—
240C22×SD16—21no—
241C22×M16—21no—
242#532C22×C1111yescharacteristic
243C2×C4⋊Q8C22×C1111yescharacteristic
244C2×C4×D4C22×C1111yescharacteristic
245#489—22no—
246#487C22×C1112yescomplemented
247#486C22×C1112yescomplemented
248#480—21no—
249#474C22×C1111yescharacteristic
250#474C22×C1111yescharacteristic
251#461—21no—
252#461—21no—
253#461C22×C1112yes—
254#461C22×C1112yes—
255#459C22×C1111yescharacteristic
256#459C22×C1111yescharacteristic
257#447—21no—
258C4×D8—21no—
259C4×D8—21no—
260#436C22×C1112yes—
261#435—22no—
262C8×D4C22×C1112yes—
263#431C22×C1111yescharacteristic
264#423C22×C1111yescharacteristic
265C2×C4⋊C8C22×C1111yescharacteristic
266#417—21no—
267#417—21no—
268C2×#103—21no—
269#407—21no—
270C4×M16C22×C1111yescharacteristic
271#335C22×C1112yescomplemented
272#334C22×C1112yescomplemented
273#332C22×C1112yescomplemented
274#332C22×C1112yescomplemented
275#332C22×C1112yescomplemented
276#331C22×C1112yescomplemented
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—22no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—84no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11#46312yes—
290C22×C11C2×#12111yescharacteristic
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—41no—
295C4×C11—41no—
296C4×C11—81no—
297C4×C11—82no—
298C4×C11#46312yes—
299C4×C11C2×#13511yescharacteristic
300C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C11#57511yescharacteristic
303C2×#41—21no—
304C22×Q8—21no—
305C22×D4D4×C1111yescharacteristic
306C23×C4—21no—
307C2×SD16—22no—
308C2×SD16—22no—
309C2×SD16—44no—
310C2×D8—21no—
311C2×D8—21no—
312C2×M16—21no—
313C2×M16—22no—
314C2×M16—44no—
315C2×M16D4×C1111yescharacteristic
316C2×M16D4×C1111yescharacteristic
317C22×C8—21no—
318C22×C8—22no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8C23×C1112yes—
323C4⋊Q8C23×C1111yescharacteristic
324#127C23×C1111yescharacteristic
325#124—21no—
326#121—21no—
327#121—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4D4×C1111yescharacteristic
333C4×D4D4×C1111yescharacteristic
334C4×D4C23×C1111yescharacteristic
335C4×D4C23×C1111yescharacteristic
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4D4×C1111yescharacteristic
339C2×C22⋊C4—21no—
340C2×C42C23×C1111yescharacteristic
341#107—21no—
342#107—21no—
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8C23×C1112yes—
346C4⋊C8C23×C1112yes—
347C4⋊C8C23×C1111yescharacteristic
348C4⋊C8C23×C1111yescharacteristic
349#103—22no—
350#103—22no—
351#103—22no—
352#103—22no—
353#102—21no—
354#102—21no—
355#102—22no—
356#102—22no—
357#102—21no—
358#102—21no—
359C22⋊C8—21no—
360C22⋊C8—22no—
361C22⋊C8—22no—
362#97D4×C1112yes—
363C4×C8—21no—
364C4×C8C23×C1112yes—
365C2×C11—22no—
366C2×C11—42no—
367C2×C11—81no—
368C2×C11—161no—
369C2×C11C2×#46311yescharacteristic
370C2×C11#305511yescharacteristic
371C2×C11#306911yescharacteristic
372C24—21no—
373#41—42no—
374#41—42no—
375C2×Q8—21no—
376C2×Q8—22no—
377C2×Q8—42no—
378C2×Q8—42no—
379C2×Q8—41no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4C2×D4×C1111yescharacteristic
388C2×D4C2×D4×C1111yescharacteristic
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C11×#4111yescharacteristic
401SD16—44no—
402SD16—44no—
403D8—42no—
404D8—42no—
405M16—22no—
406M16—22no—
407M16—44no—
408M16—42no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—44no—
414C2×C8—42no—
415C2×C8C2×D4×C1112yes—
416C2×C8C2×D4×C1112yes—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4C2×D4×C1111yescharacteristic
425C4⋊C4C2×D4×C1111yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C42C2×D4×C1111yescharacteristic
433C42C2×D4×C1111yescharacteristic
434C42C11×#4111yescharacteristic
435C42C24×C1111yescharacteristic
436C11#1916911yescharacteristic, direct product factor, Sylow
437C23—21no—
438C23—21no—
439C23—42no—
440C23—42no—
441C23—41no—
442C23—81no—
443C23C11×#12111yescharacteristic
444Q8—41no—
445Q8—42no—
446Q8—41no—
447Q8—42no—
448Q8—82no—
449D4—21no—
450D4—21no—
451D4—21no—
452D4—42no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—81no—
458D4—82no—
459D4C11×AGL(1,ℤ/8)12yes—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4C11×#12111yescharacteristic
477C2×C4C11×#12111yescharacteristic
478C2×C4C11×#12111yescharacteristic
479C2×C4C11×#13512yes—
480C2×C4C11×AGL(1,ℤ/8)12yes—
481C2×C4C22×D4×C1111yescharacteristic
482C2×C4C22×D4×C1111yescharacteristic
483C2×C4C2×C11×#4111yescharacteristic
484C8—22no—
485C8—22no—
486C8—42no—
487C8—42no—
488C8—41no—
489C8—41no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—84no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22C11×#46312yes—
503C22C2×C11×#12111yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—41no—
508C4—41no—
509C4—81no—
510C4—82no—
511C4C11×#46312yes—
512C4C2×C11×#13511yescharacteristic
513C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
514C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
515C4C11×#57511yescharacteristic
516C2—22no—
517C2—42no—
518C2—81no—
519C2—161no—
520C2C2×C11×#46311yescharacteristic
521C2C11×#305511yescharacteristic
522C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3100C2
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×#3141C2semidirect
3. C2×C11×#461C2semidirect
4. D4×C11×M16C2semidirect
5. C11×#1701C2semidirect
6. C11×#1699C2semidirect
7. C11×#1681C2semidirect
8. C11×#1679C2semidirect
9. C11×#1565C2semidirect
10. C11×#1549C2semidirect
11. C11×#1547C2semidirect
18. C11×#487C22semidirect
19. C11×#486C22semidirect
43. C11×#335C22semidirect
44. C11×#334C22semidirect
45. C11×#332C22semidirect
46. C11×#332C22semidirect
47. C11×#332C22semidirect
48. C11×#331C22semidirect
111. #19169C11direct (N × H)
176. #3141C2×C11semidirect
178. C2×#461C2×C11semidirect
179. D4×M16C2×C11semidirect
180. #1701C2×C11semidirect
181. #1699C2×C11semidirect
182. #1681C2×C11semidirect
183. #1679C2×C11semidirect
184. #1565C2×C11semidirect
185. #1549C2×C11semidirect
186. #1547C2×C11semidirect
246. #487C22×C11semidirect
247. #486C22×C11semidirect
271. #335C22×C11semidirect
272. #334C22×C11semidirect
273. #332C22×C11semidirect
274. #332C22×C11semidirect
275. #332C22×C11semidirect
276. #331C22×C11semidirect
436. C11#19169direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31412
C11×#31002
C2×C11×#4612
D4×C11×M162
C11×#17012
C11×#16992
C11×#16812
C11×#16792
C11×#15652
C11×#15492
C11×#15472
#1916911