Finite Group Databasebeta

← C11×#19165 #14596358

Subgroups — C11×#19165 #14596358

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 492 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×#476C211yesmaximal, characteristic
4D4×C11×M16C211yesmaximal, characteristic
5C11×#1695C212yesmaximal, complemented
6C11×#1691C212yesmaximal, complemented
7C11×#1675C212yesmaximal, complemented
8C11×#1671C212yesmaximal, complemented
9C11×#1565C211yesmaximal, characteristic, complemented
10C11×#1550C211yesmaximal, characteristic, complemented
11C11×#1548C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C11×#533C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#501—22no—
17C11×#500C2212yescomplemented
18C11×#498C2212yescomplemented
19C11×#483—21no—
20C11×#476—21no—
21C11×#476—21no—
22C11×#476C2212yes—
23C11×#476C2211yescharacteristic
24C11×#476C2212yes—
25C11×#476C2211yescharacteristic
26C11×#461C2211yescharacteristic
27C11×#461C2211yescharacteristic
28C11×#450—21no—
29C4×C11×SD16—21no—
30C4×C11×SD16—21no—
31C11×#436C2212yes—
32C11×#435—22no—
33C8×D4×C11C2212yes—
34C11×#431C2211yescharacteristic
35C11×#428—21no—
36C11×#428—21no—
37C2×C11×#106—21no—
38C11×#423C2211yescharacteristic
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#102—21no—
41C11×#407—21no—
42C4×C11×M16C2211yescharacteristic
43C11×#335C2212yescomplemented
44C11×#334C2212yescomplemented
45C11×#333C2212yescomplemented
46C11×#333C2212yescomplemented
47C11×#333C2212yescomplemented
48C11×#332C2212yescomplemented
49C22×Q8×C11—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C2×C11×SD16—21no—
53C2×C11×SD16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—22no—
56C2×C11×M16—44no—
57C2×C11×M16D411yescharacteristic
58C2×C11×M16D411yescharacteristic
59C22×C8×C11—21no—
60C22×C8×C11—22no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8C2311yescharacteristic
65C11×C4⋊Q8C2312yes—
66C11×C4⋊Q8C2311yescharacteristic
67C11×#125—21no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8—21no—
70C4×Q8×C11—21no—
71C4×Q8×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11D411yescharacteristic
75C4×D4×C11D411yescharacteristic
76C4×D4×C11C2311yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C11×#117—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C11×#107—22no—
85C11×#107—22no—
86C11×#106—22no—
87C11×#106—22no—
88C11×#106—22no—
89C11×#106—22no—
90C11×#106—21no—
91C11×#106—21no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8—21no—
94C11×C4⋊C8C2312yes—
95C11×C4⋊C8C2312yes—
96C11×C4⋊C8C2311yescharacteristic
97C11×C4⋊C8C2311yescharacteristic
98C11×#103—21no—
99C11×#103—21no—
100C11×#102—22no—
101C11×#102—22no—
102C11×#102—21no—
103C11×#102—21no—
104C11×C22⋊C8—21no—
105C11×C22⋊C8—22no—
106C11×C22⋊C8—22no—
107C11×#97D412yes—
108C4×C8×C11—21no—
109C4×C8×C11C2312yes—
110#19165C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—82no—
117C2×D4×C11—22no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C2×D4×C11C2×D411yescharacteristic
121C2×D4×C11C2×D411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
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—42no—
134C11×SD16—42no—
135C11×M16—22no—
136C11×M16—44no—
137C11×M16—42no—
138C11×M16SD1614yescomplemented
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—42no—
144C2×C8×C11—44no—
145C2×C8×C11C2×D412yes—
146C2×C8×C11C2×D412yes—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4C2×D411yescharacteristic
159C11×C4⋊C4C2×D411yescharacteristic
160C11×C22⋊C4—21no—
161C11×C22⋊C4—21no—
162C11×C22⋊C4—21no—
163C11×C22⋊C4—21no—
164C11×C22⋊C4—41no—
165C42×C11—41no—
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11#4111yescharacteristic
169C42×C11C2411yescharacteristic
170#3165C2×C1111yescharacteristic, complemented
171#3101C2×C1111yescharacteristic
172C2×#476C2×C1111yescharacteristic
173D4×M16C2×C1111yescharacteristic
174#1695C2×C1112yescomplemented
175#1691C2×C1112yescomplemented
176#1675C2×C1112yescomplemented
177#1671C2×C1112yescomplemented
178#1565C2×C1111yescharacteristic, complemented
179#1550C2×C1111yescharacteristic, complemented
180#1548C2×C1111yescharacteristic, complemented
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—81no—
186C23×C11#12111yescharacteristic
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—81no—
190Q8×C11—82no—
191Q8×C11—82no—
192D4×C11—21no—
193D4×C11—21no—
194D4×C11—21no—
195D4×C11—42no—
196D4×C11#13712yes—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—82no—
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11C2×SD1612yes—
217C2×C4×C11#13712yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C8×C11—22no—
222C8×C11—42no—
223C8×C11—41no—
224C8×C11—42no—
225C8×C11—41no—
226C8×C11C2×SD1614yes—
227C22×M16—21no—
228#533C22×C1111yescharacteristic
229C2×C4⋊Q8C22×C1111yescharacteristic
230C2×C4×D4C22×C1111yescharacteristic
231#501—22no—
232#500C22×C1112yescomplemented
233#498C22×C1112yescomplemented
234#483—21no—
235#476—21no—
236#476—21no—
237#476C22×C1111yescharacteristic
238#476C22×C1111yescharacteristic
239#476C22×C1112yes—
240#476C22×C1112yes—
241#461C22×C1111yescharacteristic
242#461C22×C1111yescharacteristic
243#450—21no—
244C4×SD16—21no—
245C4×SD16—21no—
246#436C22×C1112yes—
247#435—22no—
248C8×D4C22×C1112yes—
249#431C22×C1111yescharacteristic
250#428—21no—
251#428—21no—
252C2×#106—21no—
253#423C22×C1111yescharacteristic
254C2×C4⋊C8C22×C1111yescharacteristic
255C2×#102—21no—
256#407—21no—
257C4×M16C22×C1111yescharacteristic
258#335C22×C1112yescomplemented
259#334C22×C1112yescomplemented
260#333C22×C1112yescomplemented
261#333C22×C1112yescomplemented
262#333C22×C1112yescomplemented
263#332C22×C1112yescomplemented
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—22no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11—84no—
273C22×C11#46112yes—
274C22×C11C2×#12111yescharacteristic
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—81no—
281C4×C11—82no—
282C4×C11—81no—
283C4×C11#46112yes—
284C4×C11C22×SD1611yescharacteristic
285C4×C11C2×#13711yescharacteristic
286C4×C11C2×#13711yescharacteristic
287C4×C11#57511yescharacteristic
288C22×Q8—21no—
289C22×D4D4×C1111yescharacteristic
290C23×C4—21no—
291C2×SD16—21no—
292C2×SD16—21no—
293C2×M16—21no—
294C2×M16—22no—
295C2×M16—44no—
296C2×M16D4×C1111yescharacteristic
297C2×M16D4×C1111yescharacteristic
298C22×C8—21no—
299C22×C8—22no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8C23×C1112yes—
304C4⋊Q8C23×C1111yescharacteristic
305C4⋊Q8C23×C1111yescharacteristic
306#125—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4D4×C1111yescharacteristic
314C4×D4D4×C1111yescharacteristic
315C4×D4C23×C1111yescharacteristic
316C4×D4C23×C1111yescharacteristic
317#117—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4D4×C1111yescharacteristic
321C2×C22⋊C4—21no—
322C2×C42C23×C1111yescharacteristic
323#107—22no—
324#107—22no—
325#106—22no—
326#106—22no—
327#106—22no—
328#106—22no—
329#106—21no—
330#106—21no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8C23×C1112yes—
334C4⋊C8C23×C1112yes—
335C4⋊C8C23×C1111yescharacteristic
336C4⋊C8C23×C1111yescharacteristic
337#103—21no—
338#103—21no—
339#102—22no—
340#102—22no—
341#102—21no—
342#102—21no—
343C22⋊C8—21no—
344C22⋊C8—22no—
345C22⋊C8—22no—
346#97D4×C1112yes—
347C4×C8—21no—
348C4×C8C23×C1112yes—
349C2×C11—22no—
350C2×C11—42no—
351C2×C11—81no—
352C2×C11C2×#46111yescharacteristic
353C2×C11#305611yescharacteristic
354C2×C11#306811yescharacteristic
355C24—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—41no—
360C2×Q8—82no—
361C2×D4—22no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4C2×D4×C1111yescharacteristic
365C2×D4C2×D4×C1111yescharacteristic
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—41no—
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C11×#4111yescharacteristic
377SD16—42no—
378SD16—42no—
379M16—22no—
380M16—42no—
381M16—44no—
382M16C11×SD1614yescomplemented
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—42no—
388C2×C8—44no—
389C2×C8C2×D4×C1112yes—
390C2×C8C2×D4×C1112yes—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4C2×D4×C1111yescharacteristic
403C4⋊C4C2×D4×C1111yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C22⋊C4—41no—
409C42—41no—
410C42C2×D4×C1111yescharacteristic
411C42C2×D4×C1111yescharacteristic
412C42C11×#4111yescharacteristic
413C42C24×C1111yescharacteristic
414C11#1916511yescharacteristic, direct product factor, Sylow
415C23—21no—
416C23—21no—
417C23—42no—
418C23—42no—
419C23—81no—
420C23C11×#12111yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—81no—
424Q8—82no—
425Q8—82no—
426D4—21no—
427D4—21no—
428D4—21no—
429D4—42no—
430D4C11×#13712yes—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—82no—
447C2×C4C11×#12111yescharacteristic
448C2×C4C11×#12111yescharacteristic
449C2×C4C11×#12111yescharacteristic
450C2×C4C2×C11×SD1612yes—
451C2×C4C11×#13712yes—
452C2×C4C22×D4×C1111yescharacteristic
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C2×C11×#4111yescharacteristic
455C8—22no—
456C8—42no—
457C8—41no—
458C8—42no—
459C8—41no—
460C8C2×C11×SD1614yes—
461C22—21no—
462C22—21no—
463C22—22no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—84no—
470C22C11×#46112yes—
471C22C2×C11×#12111yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—82no—
479C4—81no—
480C4C11×#46112yes—
481C4C22×C11×SD1611yescharacteristic
482C4C2×C11×#13711yescharacteristic
483C4C2×C11×#13711yescharacteristic
484C4C11×#57511yescharacteristic
485C2—22no—
486C2—42no—
487C2—81no—
488C2C2×C11×#46111yescharacteristic
489C2C11×#305611yescharacteristic
490C2C11×#306811yescharacteristic
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×#1695C2semidirect
6. C11×#1691C2semidirect
7. C11×#1675C2semidirect
8. C11×#1671C2semidirect
9. C11×#1565C2semidirect
10. C11×#1550C2semidirect
11. C11×#1548C2semidirect
17. C11×#500C22semidirect
18. C11×#498C22semidirect
43. C11×#335C22semidirect
44. C11×#334C22semidirect
45. C11×#333C22semidirect
46. C11×#333C22semidirect
47. C11×#333C22semidirect
48. C11×#332C22semidirect
110. #19165C11direct (N × H)
138. C11×M16SD16semidirect
170. #3165C2×C11semidirect
174. #1695C2×C11semidirect
175. #1691C2×C11semidirect
176. #1675C2×C11semidirect
177. #1671C2×C11semidirect
178. #1565C2×C11semidirect
179. #1550C2×C11semidirect
180. #1548C2×C11semidirect
232. #500C22×C11semidirect
233. #498C22×C11semidirect
258. #335C22×C11semidirect
259. #334C22×C11semidirect
260. #333C22×C11semidirect
261. #333C22×C11semidirect
262. #333C22×C11semidirect
263. #332C22×C11semidirect
382. M16C11×SD16semidirect
414. C11#19165direct (N × H)

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×#4762
D4×C11×M162
C11×#16952
C11×#16912
C11×#16752
C11×#16712
C11×#15652
C11×#15502
C11×#15482
#1916511