Finite Group Databasebeta

← C11×#19163 #14596356

Subgroups — C11×#19163 #14596356

Order 2816.

760 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3152C211yesmaximal, characteristic, complemented
2C11×#3100C211yesmaximal, characteristic
3C2×C11×#474C211yesmaximal, characteristic, complemented
4D4×C11×M16C211yesmaximal, characteristic, complemented
5C11×#1689C212yesmaximal, complemented
6C11×#1685C212yesmaximal, complemented
7C11×#1669C212yesmaximal, complemented
8C11×#1665C212yesmaximal, complemented
9C11×#1565C211yesmaximal, characteristic, complemented
10C11×#1547C211yesmaximal, characteristic, complemented
11C11×#1546C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C2×C11×#137—21no—
14C22×C11×M16—21no—
15C11×#532C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#497—22no—
19C11×#494C2212yescomplemented
20C11×#492C2212yescomplemented
21C11×#480—21no—
22C11×#474—21no—
23C11×#474—21no—
24C11×#474C2212yes—
25C11×#474C2211yescharacteristic
26C11×#474C2212yes—
27C11×#474C2211yescharacteristic
28C11×#459C2211yescharacteristic
29C11×#459C2211yescharacteristic
30C11×#447—21no—
31C4×C11×D8—21no—
32C4×C11×D8—21no—
33C11×#436C2212yes—
34C11×#435—22no—
35C8×D4×C11C2212yes—
36C11×#431C2211yescharacteristic
37C2×C11×#107—21no—
38C11×#423C2211yescharacteristic
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#102—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—
53C11×#137—44no—
54C11×#137—44no—
55C2×C11×Q16—22no—
56C2×C11×Q16—22no—
57C2×C11×SD16—22no—
58C2×C11×SD16—22no—
59C2×C11×D8—21no—
60C2×C11×D8—21no—
61C2×C11×M16—21no—
62C2×C11×M16—22no—
63C2×C11×M16—44no—
64C2×C11×M16D411yescharacteristic
65C2×C11×M16D411yescharacteristic
66C22×C8×C11—21no—
67C22×C8×C11—22no—
68C11×C4⋊Q8—21no—
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8C2312yes—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#124—21no—
75C11×#121—21no—
76C11×#121—21no—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11D411yescharacteristic
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C42×C11C2311yescharacteristic
90C11×#107—22no—
91C11×#107—22no—
92C11×#107—21no—
93C11×#107—21no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8—21no—
96C11×C4⋊C8C2312yes—
97C11×C4⋊C8C2312yes—
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×#102—22no—
101C11×#102—22no—
102C11×#102—21no—
103C11×#102—21no—
104C11×#102—21no—
105C11×#102—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—22no—
109C11×#97D412yes—
110C4×C8×C11—21no—
111C4×C8×C11C2312yes—
112#19163C1111yesmaximal, characteristic, direct product factor, Sylow
113C24×C11—21no—
114C11×#41—42no—
115C11×#41—42no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—41no—
119C2×Q8×C11—42no—
120C2×Q8×C11—42no—
121C2×D4×C11—22no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11C2×D411yescharacteristic
129C2×D4×C11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—41no—
138C22×C4×C11—41no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11#4111yescharacteristic
142C11×Q16—44no—
143C11×Q16—44no—
144C11×SD16—44no—
145C11×SD16—44no—
146C11×D8—42no—
147C11×D8—42no—
148C11×M16—22no—
149C11×M16—44no—
150C11×M16—42no—
151C11×M16D814yescomplemented
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—42no—
157C2×C8×C11—44no—
158C2×C8×C11C2×D412yes—
159C2×C8×C11C2×D412yes—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4C2×D411yescharacteristic
168C11×C4⋊C4C2×D411yescharacteristic
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—41no—
174C11×C22⋊C4—41no—
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11#4111yescharacteristic
178C42×C11C2411yescharacteristic
179#3152C2×C1111yescharacteristic, complemented
180#3100C2×C1111yescharacteristic
181C2×#474C2×C1111yescharacteristic, complemented
182D4×M16C2×C1111yescharacteristic, complemented
183#1689C2×C1112yescomplemented
184#1685C2×C1112yescomplemented
185#1669C2×C1112yescomplemented
186#1665C2×C1112yescomplemented
187#1565C2×C1111yescharacteristic, complemented
188#1547C2×C1111yescharacteristic, complemented
189#1546C2×C1111yescharacteristic, complemented
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—41no—
195C23×C11—81no—
196C23×C11#12111yescharacteristic
197Q8×C11—42no—
198Q8×C11—41no—
199Q8×C11—42no—
200Q8×C11—41no—
201Q8×C11—82no—
202D4×C11—21no—
203D4×C11—21no—
204D4×C11—21no—
205D4×C11—42no—
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—81no—
211D4×C11—82no—
212D4×C11#13712yescomplemented
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—82no—
228C2×C4×C11—82no—
229C2×C4×C11#12111yescharacteristic
230C2×C4×C11#12111yescharacteristic
231C2×C4×C11#12111yescharacteristic
232C2×C4×C11C2×D812yes—
233C2×C4×C11AGL(1,ℤ/8)12yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C8×C11—22no—
238C8×C11—42no—
239C8×C11—41no—
240C8×C11—42no—
241C8×C11—41no—
242C8×C11C2×D814yes—
243C2×#137—21no—
244C2×#137—21no—
245C22×M16—21no—
246#532C22×C1111yescharacteristic
247C2×C4⋊Q8C22×C1111yescharacteristic
248C2×C4×D4C22×C1111yescharacteristic
249#497—22no—
250#494C22×C1112yescomplemented
251#492C22×C1112yescomplemented
252#480—21no—
253#474—21no—
254#474—21no—
255#474C22×C1111yescharacteristic
256#474C22×C1111yescharacteristic
257#474C22×C1112yes—
258#474C22×C1112yes—
259#459C22×C1111yescharacteristic
260#459C22×C1111yescharacteristic
261#447—21no—
262C4×D8—21no—
263C4×D8—21no—
264#436C22×C1112yes—
265#435—22no—
266C8×D4C22×C1112yes—
267#431C22×C1111yescharacteristic
268C2×#107—21no—
269#423C22×C1111yescharacteristic
270C2×C4⋊C8C22×C1111yescharacteristic
271C2×#102—21no—
272#407—21no—
273C4×M16C22×C1111yescharacteristic
274#335C22×C1112yescomplemented
275#334C22×C1112yescomplemented
276#332C22×C1112yescomplemented
277#332C22×C1112yescomplemented
278#332C22×C1112yescomplemented
279#331C22×C1112yescomplemented
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—22no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—84no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11#45912yes—
293C22×C11C2×#12111yescharacteristic
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—81no—
300C4×C11—82no—
301C4×C11#45912yes—
302C4×C11C22×D811yescharacteristic
303C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C11C2×#13711yescharacteristic
305C4×C11#57511yescharacteristic
306C2×#41—21no—
307C22×Q8—21no—
308C22×D4D4×C1111yescharacteristic
309C23×C4—21no—
310#137—44no—
311#137—44no—
312C2×Q16—22no—
313C2×Q16—22no—
314C2×SD16—22no—
315C2×SD16—22no—
316C2×D8—21no—
317C2×D8—21no—
318C2×M16—21no—
319C2×M16—22no—
320C2×M16—44no—
321C2×M16D4×C1111yescharacteristic
322C2×M16D4×C1111yescharacteristic
323C22×C8—21no—
324C22×C8—22no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8—21no—
328C4⋊Q8C23×C1112yes—
329C4⋊Q8C23×C1111yescharacteristic
330#127C23×C1111yescharacteristic
331#124—21no—
332#121—21no—
333#121—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4D4×C1111yescharacteristic
339C4×D4D4×C1111yescharacteristic
340C4×D4C23×C1111yescharacteristic
341C4×D4C23×C1111yescharacteristic
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4D4×C1111yescharacteristic
345C2×C22⋊C4—21no—
346C2×C42C23×C1111yescharacteristic
347#107—22no—
348#107—22no—
349#107—21no—
350#107—21no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8C23×C1112yes—
354C4⋊C8C23×C1112yes—
355C4⋊C8C23×C1111yescharacteristic
356C4⋊C8C23×C1111yescharacteristic
357#102—22no—
358#102—22no—
359#102—21no—
360#102—21no—
361#102—21no—
362#102—21no—
363C22⋊C8—21no—
364C22⋊C8—22no—
365C22⋊C8—22no—
366#97D4×C1112yes—
367C4×C8—21no—
368C4×C8C23×C1112yes—
369C2×C11—22no—
370C2×C11—42no—
371C2×C11—81no—
372C2×C11—161no—
373C2×C11C2×#45911yescharacteristic
374C2×C11#305611yescharacteristic
375C2×C11#306911yescharacteristic
376C24—21no—
377#41—42no—
378#41—42no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—41no—
382C2×Q8—42no—
383C2×Q8—42no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4C2×D4×C1111yescharacteristic
392C2×D4C2×D4×C1111yescharacteristic
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C11×#4111yescharacteristic
405Q16—44no—
406Q16—44no—
407SD16—44no—
408SD16—44no—
409D8—42no—
410D8—42no—
411M16—22no—
412M16—42no—
413M16—44no—
414M16C11×D814yescomplemented
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—42no—
420C2×C8—44no—
421C2×C8C2×D4×C1112yes—
422C2×C8C2×D4×C1112yes—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4C2×D4×C1111yescharacteristic
431C4⋊C4C2×D4×C1111yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C42C2×D4×C1111yescharacteristic
439C42C2×D4×C1111yescharacteristic
440C42C11×#4111yescharacteristic
441C42C24×C1111yescharacteristic
442C11#1916311yescharacteristic, direct product factor, Sylow
443C23—21no—
444C23—21no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—81no—
449C23C11×#12111yescharacteristic
450Q8—42no—
451Q8—41no—
452Q8—42no—
453Q8—41no—
454Q8—82no—
455D4—21no—
456D4—21no—
457D4—21no—
458D4—42no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—81no—
464D4—82no—
465D4C11×#13712yescomplemented
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4C11×#12111yescharacteristic
483C2×C4C11×#12111yescharacteristic
484C2×C4C11×#12111yescharacteristic
485C2×C4C2×C11×D812yes—
486C2×C4C11×AGL(1,ℤ/8)12yes—
487C2×C4C22×D4×C1111yescharacteristic
488C2×C4C22×D4×C1111yescharacteristic
489C2×C4C2×C11×#4111yescharacteristic
490C8—22no—
491C8—42no—
492C8—41no—
493C8—42no—
494C8—41no—
495C8C2×C11×D814yes—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—84no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22C11×#45912yes—
509C22C2×C11×#12111yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—81no—
516C4—82no—
517C4C11×#45912yes—
518C4C22×C11×D811yescharacteristic
519C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
520C4C2×C11×#13711yescharacteristic
521C4C11×#57511yescharacteristic
522C2—22no—
523C2—42no—
524C2—81no—
525C2—161no—
526C2C2×C11×#45911yescharacteristic
527C2C11×#305611yescharacteristic
528C2C11×#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×#3152C2semidirect
3. C2×C11×#474C2semidirect
4. D4×C11×M16C2semidirect
5. C11×#1689C2semidirect
6. C11×#1685C2semidirect
7. C11×#1669C2semidirect
8. C11×#1665C2semidirect
9. C11×#1565C2semidirect
10. C11×#1547C2semidirect
11. C11×#1546C2semidirect
19. C11×#494C22semidirect
20. C11×#492C22semidirect
43. C11×#335C22semidirect
44. C11×#334C22semidirect
45. C11×#332C22semidirect
46. C11×#332C22semidirect
47. C11×#332C22semidirect
48. C11×#331C22semidirect
112. #19163C11direct (N × H)
151. C11×M16D8semidirect
179. #3152C2×C11semidirect
181. C2×#474C2×C11semidirect
182. D4×M16C2×C11semidirect
183. #1689C2×C11semidirect
184. #1685C2×C11semidirect
185. #1669C2×C11semidirect
186. #1665C2×C11semidirect
187. #1565C2×C11semidirect
188. #1547C2×C11semidirect
189. #1546C2×C11semidirect
212. D4×C11#137semidirect
250. #494C22×C11semidirect
251. #492C22×C11semidirect
274. #335C22×C11semidirect
275. #334C22×C11semidirect
276. #332C22×C11semidirect
277. #332C22×C11semidirect
278. #332C22×C11semidirect
279. #331C22×C11semidirect
414. M16C11×D8semidirect
442. C11#19163direct (N × H)
465. D4C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#31522
C11×#31002
C2×C11×#4742
D4×C11×M162
C11×#16892
C11×#16852
C11×#16692
C11×#16652
C11×#15652
C11×#15472
C11×#15462
#1916311