Finite Group Databasebeta

← C11×#19164 #14596357

Subgroups — C11×#19164 #14596357

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3165C211yesmaximal, characteristic, complemented
2C11×#3101C211yesmaximal, characteristic
3C2×C11×#461C211yesmaximal, characteristic
4D4×C11×M16C211yesmaximal, characteristic
5C11×#1693C212yesmaximal, complemented
6C11×#1691C212yesmaximal, complemented
7C11×#1673C212yesmaximal, complemented
8C11×#1671C212yesmaximal, complemented
9C11×#1565C211yesmaximal, characteristic, complemented
10C11×#1550C211yesmaximal, characteristic, complemented
11C11×#1549C211yesmaximal, characteristic, complemented
12C22×C11×SD16—21no—
13C22×C11×M16—21no—
14C11×#533C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C11×#501—22no—
18C11×#500C2212yescomplemented
19C11×#498C2212yescomplemented
20C11×#483—21no—
21C11×#476C2211yescharacteristic
22C11×#476C2211yescharacteristic
23C11×#461—21no—
24C11×#461—21no—
25C11×#461C2212yes—
26C11×#461C2211yescharacteristic
27C11×#461C2212yes—
28C11×#461C2211yescharacteristic
29C11×#450—21no—
30C4×C11×SD16—21no—
31C4×C11×SD16—21no—
32C11×#436C2212yes—
33C11×#435—22no—
34C8×D4×C11C2212yes—
35C11×#431C2211yescharacteristic
36C11×#428—21no—
37C11×#428—21no—
38C11×#423C2211yescharacteristic
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#103—21no—
41C11×#407—21no—
42C4×C11×M16C2211yescharacteristic
43C11×#335C2212yescomplemented
44C11×#334C2212yescomplemented
45C11×#333C2212yescomplemented
46C11×#332C2212yescomplemented
47C11×#332C2212yescomplemented
48C11×#332C2212yescomplemented
49C22×Q8×C11—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C2×C11×SD16—22no—
53C2×C11×SD16—22no—
54C2×C11×SD16—21no—
55C2×C11×SD16—21no—
56C2×C11×SD16—44no—
57C2×C11×M16—21no—
58C2×C11×M16—22no—
59C2×C11×M16—44no—
60C2×C11×M16D411yescharacteristic
61C2×C11×M16D411yescharacteristic
62C22×C8×C11—21no—
63C22×C8×C11—22no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8C2312yes—
68C11×C4⋊Q8C2311yescharacteristic
69C11×C4⋊Q8C2311yescharacteristic
70C11×#125—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11D411yescharacteristic
78C4×D4×C11D411yescharacteristic
79C4×D4×C11C2311yescharacteristic
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C11×#107—22no—
88C11×#107—22no—
89C11×#106—22no—
90C11×#106—22no—
91C11×#106—21no—
92C11×#106—21no—
93C11×C4⋊C8—21no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8C2312yes—
96C11×C4⋊C8C2311yescharacteristic
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2312yes—
99C11×#103—22no—
100C11×#103—22no—
101C11×#103—21no—
102C11×#103—21no—
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#19164C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—21no—
116C2×Q8×C11—42no—
117C2×Q8×C11—42no—
118C2×Q8×C11—41no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C2×D4×C11C2×D411yescharacteristic
123C2×D4×C11C2×D411yescharacteristic
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—41no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4111yescharacteristic
135C11×SD16—42no—
136C11×SD16—44no—
137C11×SD16—42no—
138C11×SD16—44no—
139C11×M16—22no—
140C11×M16—44no—
141C11×M16—42no—
142C11×M16SD1614yescomplemented
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—42no—
148C2×C8×C11—44no—
149C2×C8×C11C2×D412yes—
150C2×C8×C11C2×D412yes—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—41no—
162C11×C4⋊C4C2×D411yescharacteristic
163C11×C4⋊C4C2×D411yescharacteristic
164C11×C22⋊C4—21no—
165C11×C22⋊C4—21no—
166C11×C22⋊C4—21no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—41no—
169C42×C11—41no—
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11#4111yescharacteristic
173C42×C11C2411yescharacteristic
174#3165C2×C1111yescharacteristic, complemented
175#3101C2×C1111yescharacteristic
176C2×#461C2×C1111yescharacteristic
177D4×M16C2×C1111yescharacteristic
178#1693C2×C1112yescomplemented
179#1691C2×C1112yescomplemented
180#1673C2×C1112yescomplemented
181#1671C2×C1112yescomplemented
182#1565C2×C1111yescharacteristic, complemented
183#1550C2×C1111yescharacteristic, complemented
184#1549C2×C1111yescharacteristic, complemented
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—81no—
190C23×C11#12111yescharacteristic
191Q8×C11—42no—
192Q8×C11—41no—
193Q8×C11—41no—
194Q8×C11—42no—
195Q8×C11—81no—
196Q8×C11—82no—
197D4×C11—21no—
198D4×C11—21no—
199D4×C11—21no—
200D4×C11—42no—
201D4×C11AGL(1,ℤ/8)12yes—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—82no—
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11C2×SD1612yes—
222C2×C4×C11#13712yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C8×C11—22no—
227C8×C11—42no—
228C8×C11—42no—
229C8×C11—41no—
230C8×C11—41no—
231C8×C11C2×SD1614yescomplemented
232C22×SD16—21no—
233C22×M16—21no—
234#533C22×C1111yescharacteristic
235C2×C4⋊Q8C22×C1111yescharacteristic
236C2×C4×D4C22×C1111yescharacteristic
237#501—22no—
238#500C22×C1112yescomplemented
239#498C22×C1112yescomplemented
240#483—21no—
241#476C22×C1111yescharacteristic
242#476C22×C1111yescharacteristic
243#461—21no—
244#461—21no—
245#461C22×C1111yescharacteristic
246#461C22×C1111yescharacteristic
247#461C22×C1112yes—
248#461C22×C1112yes—
249#450—21no—
250C4×SD16—21no—
251C4×SD16—21no—
252#436C22×C1112yes—
253#435—22no—
254C8×D4C22×C1112yes—
255#431C22×C1111yescharacteristic
256#428—21no—
257#428—21no—
258#423C22×C1111yescharacteristic
259C2×C4⋊C8C22×C1111yescharacteristic
260C2×#103—21no—
261#407—21no—
262C4×M16C22×C1111yescharacteristic
263#335C22×C1112yescomplemented
264#334C22×C1112yescomplemented
265#333C22×C1112yescomplemented
266#332C22×C1112yescomplemented
267#332C22×C1112yescomplemented
268#332C22×C1112yescomplemented
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—22no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11—84no—
278C22×C11#46112yes—
279C22×C11C2×#12111yescharacteristic
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11—82no—
286C4×C11—81no—
287C4×C11—81no—
288C4×C11#46112yes—
289C4×C11C22×SD1611yescharacteristic
290C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C11C2×#13711yescharacteristic
292C4×C11#57511yescharacteristic
293C22×Q8—21no—
294C22×D4D4×C1111yescharacteristic
295C23×C4—21no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×SD16—21no—
299C2×SD16—21no—
300C2×SD16—44no—
301C2×M16—21no—
302C2×M16—22no—
303C2×M16—44no—
304C2×M16D4×C1111yescharacteristic
305C2×M16D4×C1111yescharacteristic
306C22×C8—21no—
307C22×C8—22no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8C23×C1112yes—
312C4⋊Q8C23×C1111yescharacteristic
313C4⋊Q8C23×C1111yescharacteristic
314#125—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4D4×C1111yescharacteristic
322C4×D4D4×C1111yescharacteristic
323C4×D4C23×C1111yescharacteristic
324C4×D4C23×C1111yescharacteristic
325#117—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4D4×C1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C42C23×C1111yescharacteristic
331#107—22no—
332#107—22no—
333#106—22no—
334#106—22no—
335#106—21no—
336#106—21no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8C23×C1112yes—
340C4⋊C8C23×C1111yescharacteristic
341C4⋊C8C23×C1111yescharacteristic
342C4⋊C8C23×C1112yes—
343#103—22no—
344#103—22no—
345#103—21no—
346#103—21no—
347#102—21no—
348#102—21no—
349C22⋊C8—21no—
350C22⋊C8—22no—
351C22⋊C8—22no—
352#97D4×C1112yes—
353C4×C8—21no—
354C4×C8C23×C1112yes—
355C2×C11—22no—
356C2×C11—42no—
357C2×C11—81no—
358C2×C11C2×#46111yescharacteristic
359C2×C11#305511yescharacteristic
360C2×C11#306911yescharacteristic
361C24—21no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8—21no—
365C2×Q8—42no—
366C2×Q8—42no—
367C2×Q8—41no—
368C2×D4—22no—
369C2×D4—21no—
370C2×D4—41no—
371C2×D4C2×D4×C1111yescharacteristic
372C2×D4C2×D4×C1111yescharacteristic
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—41no—
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C11×#4111yescharacteristic
384SD16—44no—
385SD16—42no—
386SD16—44no—
387SD16—42no—
388M16—22no—
389M16—42no—
390M16—44no—
391M16C11×SD1614yescomplemented
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—42no—
397C2×C8—44no—
398C2×C8C2×D4×C1112yes—
399C2×C8C2×D4×C1112yes—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4C2×D4×C1111yescharacteristic
412C4⋊C4C2×D4×C1111yescharacteristic
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—41no—
418C42—41no—
419C42C2×D4×C1111yescharacteristic
420C42C2×D4×C1111yescharacteristic
421C42C11×#4111yescharacteristic
422C42C24×C1111yescharacteristic
423C11#1916411yescharacteristic, direct product factor, Sylow
424C23—21no—
425C23—21no—
426C23—42no—
427C23—42no—
428C23—81no—
429C23C11×#12111yescharacteristic
430Q8—42no—
431Q8—41no—
432Q8—41no—
433Q8—42no—
434Q8—81no—
435Q8—82no—
436D4—21no—
437D4—21no—
438D4—21no—
439D4—42no—
440D4C11×AGL(1,ℤ/8)12yes—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—82no—
457C2×C4C11×#12111yescharacteristic
458C2×C4C11×#12111yescharacteristic
459C2×C4C11×#12111yescharacteristic
460C2×C4C2×C11×SD1612yes—
461C2×C4C11×#13712yes—
462C2×C4C22×D4×C1111yescharacteristic
463C2×C4C22×D4×C1111yescharacteristic
464C2×C4C2×C11×#4111yescharacteristic
465C8—22no—
466C8—42no—
467C8—42no—
468C8—41no—
469C8—41no—
470C8C2×C11×SD1614yescomplemented
471C22—21no—
472C22—21no—
473C22—22no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—84no—
480C22C11×#46112yes—
481C22C2×C11×#12111yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—41no—
486C4—41no—
487C4—82no—
488C4—81no—
489C4—81no—
490C4C11×#46112yes—
491C4C22×C11×SD1611yescharacteristic
492C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
493C4C2×C11×#13711yescharacteristic
494C4C11×#57511yescharacteristic
495C2—22no—
496C2—42no—
497C2—81no—
498C2C2×C11×#46111yescharacteristic
499C2C11×#305511yescharacteristic
500C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
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×#3165C2semidirect
5. C11×#1693C2semidirect
6. C11×#1691C2semidirect
7. C11×#1673C2semidirect
8. C11×#1671C2semidirect
9. C11×#1565C2semidirect
10. C11×#1550C2semidirect
11. C11×#1549C2semidirect
18. C11×#500C22semidirect
19. C11×#498C22semidirect
43. C11×#335C22semidirect
44. C11×#334C22semidirect
45. C11×#333C22semidirect
46. C11×#332C22semidirect
47. C11×#332C22semidirect
48. C11×#332C22semidirect
111. #19164C11direct (N × H)
142. C11×M16SD16semidirect
174. #3165C2×C11semidirect
178. #1693C2×C11semidirect
179. #1691C2×C11semidirect
180. #1673C2×C11semidirect
181. #1671C2×C11semidirect
182. #1565C2×C11semidirect
183. #1550C2×C11semidirect
184. #1549C2×C11semidirect
231. C8×C11C2×SD16semidirect
238. #500C22×C11semidirect
239. #498C22×C11semidirect
263. #335C22×C11semidirect
264. #334C22×C11semidirect
265. #333C22×C11semidirect
266. #332C22×C11semidirect
267. #332C22×C11semidirect
268. #332C22×C11semidirect
391. M16C11×SD16semidirect
423. C11#19164direct (N × H)
470. C8C2×C11×SD16semidirect

Maximal subgroups

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

subgroupindex
C11×#31652
C11×#31012
C2×C11×#4612
D4×C11×M162
C11×#16932
C11×#16912
C11×#16732
C11×#16712
C11×#15652
C11×#15502
C11×#15492
#1916411