Finite Group Databasebeta

← C11×#60625 #14637818

Subgroups — C11×#60625 #14637818

Order 2816.

2066 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3503C211yesmaximal, characteristic, complemented
2C11×#3500C211yesmaximal, characteristic
3C11×#3141C213yesmaximal, complemented
4C11×#3140C213yesmaximal, complemented
5C11×#3137C216yesmaximal, complemented
6C11×#3136C216yesmaximal, complemented
7C11×#3135C213yesmaximal, complemented
8C2×C11×#489C213yesmaximal, complemented
9C11×#2898C212yesmaximal, complemented
10C11×#2897C212yesmaximal, complemented
11C11×#2875C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13C2×C11×H(5,𝔽2)C2211yescharacteristic
14C2×C11×#131C2212yes—
15Q82×C11—21no—
16C11×#557—21no—
17C11×#554—23no—
18D4×Q8×C11—23no—
19C11×#548—21no—
20C11×#548—21no—
21C11×#546—23no—
22C11×#546—23no—
23C11×#544C2216yescomplemented
24C11×#536C2213yes—
25C11×#535C2213yes—
26C11×#533C2213yescomplemented
27C11×#532C2213yes—
28C2×C11×C4⋊Q8C2213yescomplemented
29C2×C11×#124C2213yes—
30C11×#520C2212yes—
31C4×C11×#41C2211yescharacteristic
32C11×#491C2216yescomplemented
33C11×#490C2216yescomplemented
34C11×#489C2213yescomplemented
35C11×#489C22112yescomplemented
36C11×#489C2216yescomplemented
37C11×#489C2211yescharacteristic, complemented
38C11×#489C2213yescomplemented
39C11×#489C2213yescomplemented
40C11×#488C22112yescomplemented
41C11×#487C2216yescomplemented
42C11×#486C2216yescomplemented
43C11×#419C2216yescomplemented
44C11×#418C2216yes—
45C11×#417C2216yes—
46C11×#417C2216yescomplemented
47C11×#416C2216yes—
48C11×#416C2216yescomplemented
49C2×C11×#103C2216yescomplemented
50C2×C11×#102C2216yes—
51C11×#405C2216yescomplemented
52C4×C11×M16C2213yescomplemented
53C2×C11×#97C2213yescomplemented
54C11×2−1+4—28no—
55C11×H(5,𝔽2)—28no—
56C2×C11×#41—21no—
57C2×C11×#41—23no—
58C2×C11×#41C2313yes—
59C2×C11×#41C2313yes—
60C2×C11×#41C2311yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11—23no—
63C22×Q8×C11C2313yes—
64C22×D4×C11—23no—
65C22×D4×C11C2313yes—
66C11×#131—28no—
67C2×C11×M16C2316yes—
68C22×C8×C11C2316yes—
69C11×C4⋊Q8—26no—
70C11×C4⋊Q8—23no—
71C11×C4⋊Q8—23no—
72C11×C4⋊Q8C2313yes—
73C11×C4⋊Q8C2313yes—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2316yes—
76C11×#127C2313yes—
77C11×#125—26no—
78C11×#125C2316yes—
79C11×#124—23no—
80C11×#124—23no—
81C11×#124C2313yes—
82C11×#124C2311yescharacteristic
83C11×#124C2316yes—
84C11×#123—26no—
85C11×C22⋊Q8—23no—
86C11×C22⋊Q8—23no—
87C11×C22⋊Q8—23no—
88C11×C22⋊Q8—23no—
89C11×C22⋊Q8—212no—
90C11×#121—23no—
91C11×#121—23no—
92C11×#121—23no—
93C11×#121—23no—
94C11×#120—26no—
95C4×Q8×C11—22no—
96C4×Q8×C11—23no—
97C4×Q8×C11—23no—
98C4×Q8×C11D411yescharacteristic
99C4×Q8×C11D411yescharacteristic
100C4×D4×C11—26no—
101C4×D4×C11—23no—
102C4×D4×C11—23no—
103C4×D4×C11D413yes—
104C4×D4×C11D413yes—
105C11×#117C2316yes—
106C11×#117C2313yes—
107C2×C11×C4⋊C4—23no—
108C2×C11×C4⋊C4C2316yes—
109C2×C11×C22⋊C4—23no—
110C2×C11×C22⋊C4—23no—
111C2×C42×C11C2313yes—
112C11×#103C2316yes—
113C11×#103C23112yes—
114C11×#103C2312yes—
115C11×#103C2316yes—
116C11×#103C2316yes—
117C11×#102C2316yes—
118C11×#102C23112yes—
119C11×#102C2312yes—
120C11×#102C2316yes—
121C11×#102C2316yes—
122C11×#97C2311yescharacteristic
123C11×#97C2313yes—
124C11×#97C2316yes—
125C4×C8×C11C2316yes—
126#60625C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11—23no—
128C11×#41—212no—
129C11×#41—212no—
130C11×#41—44no—
131C11×#41—412no—
132C11×#41#4118yes—
133C2×Q8×C11—21no—
134C2×Q8×C11—23no—
135C2×Q8×C11—23no—
136C2×Q8×C11—26no—
137C2×Q8×C11—212no—
138C2×Q8×C11—44no—
139C2×Q8×C11—86no—
140C2×Q8×C11C2×D411yescharacteristic
141C2×Q8×C11C2413yes—
142C2×Q8×C11C2411yescharacteristic
143C2×D4×C11—23no—
144C2×D4×C11—23no—
145C2×D4×C11—23no—
146C2×D4×C11—23no—
147C2×D4×C11—23no—
148C2×D4×C11—212no—
149C2×D4×C11—412no—
150C2×D4×C11C2×D413yes—
151C2×D4×C11C2413yes—
152C2×D4×C11C2411yescharacteristic
153C22×C4×C11—23no—
154C22×C4×C11—26no—
155C22×C4×C11—23no—
156C22×C4×C11—23no—
157C22×C4×C11C2×D413yes—
158C22×C4×C11C2×D413yes—
159C22×C4×C11C2413yes—
160C11×M16—212no—
161C2×C8×C11—212no—
162C2×C8×C11C2416yes—
163C2×C8×C11C2412yes—
164C11×C4⋊C4—23no—
165C11×C4⋊C4—26no—
166C11×C4⋊C4—26no—
167C11×C4⋊C4—23no—
168C11×C4⋊C4—23no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—26no—
171C11×C4⋊C4—26no—
172C11×C4⋊C4C2×D413yes—
173C11×C4⋊C4C2×D413yes—
174C11×C4⋊C4C2416yes—
175C11×C4⋊C4C2412yes—
176C11×C22⋊C4—26no—
177C11×C22⋊C4—23no—
178C11×C22⋊C4—23no—
179C11×C22⋊C4—26no—
180C11×C22⋊C4—26no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4C2×D416yes—
184C42×C11—26no—
185C42×C11C2×D413yes—
186C42×C11C2×D413yes—
187C42×C11C2413yes—
188C42×C11C2411yescharacteristic
189#3503C2×C1111yescharacteristic, complemented
190#3500C2×C1111yescharacteristic
191#3141C2×C1113yescomplemented
192#3140C2×C1113yescomplemented
193#3137C2×C1116yescomplemented
194#3136C2×C1116yescomplemented
195#3135C2×C1113yescomplemented
196C2×#489C2×C1113yescomplemented
197#2898C2×C1112yescomplemented
198#2897C2×C1112yescomplemented
199#2875C2×C1111yescharacteristic, complemented
200C23×C11—23no—
201C23×C11—21no—
202C23×C11—46no—
203C23×C11—83no—
204C23×C11—83no—
205C23×C11C22×D413yes—
206Q8×C11—26no—
207Q8×C11—22no—
208Q8×C11—42no—
209Q8×C11—46no—
210Q8×C11—46no—
211Q8×C11—86no—
212Q8×C11#12414yes—
213D4×C11—26no—
214D4×C11—22no—
215D4×C11—46no—
216D4×C11—46no—
217D4×C11—46no—
218D4×C11—83no—
219D4×C11—83no—
220D4×C11#124112yes—
221C2×C4×C11—22no—
222C2×C4×C11—26no—
223C2×C4×C11—23no—
224C2×C4×C11—21no—
225C2×C4×C11—43no—
226C2×C4×C11—43no—
227C2×C4×C11—46no—
228C2×C4×C11—46no—
229C2×C4×C11—46no—
230C2×C4×C11—86no—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D413yes—
234C2×C4×C11C22×D413yes—
235C2×C4×C11C22×D413yes—
236C2×C4×C11C2×#41112yes—
237C2×C4×C11C2511yescharacteristic
238C8×C11—22no—
239C8×C11—26no—
240C2×2−1+4C22×C1111yescharacteristic
241C2×H(5,𝔽2)C22×C1111yescharacteristic
242C2×#131C22×C1112yes—
243Q82—21no—
244#557—21no—
245#554—23no—
246D4×Q8—23no—
247#548—21no—
248#548—21no—
249#546—23no—
250#546—23no—
251#544C22×C1116yescomplemented
252#536C22×C1113yes—
253#535C22×C1113yes—
254#533C22×C1113yescomplemented
255#532C22×C1113yes—
256C2×C4⋊Q8C22×C1113yescomplemented
257C2×#124C22×C1113yes—
258#520C22×C1112yes—
259C4×#41C22×C1111yescharacteristic
260#491C22×C1116yescomplemented
261#490C22×C1116yescomplemented
262#489C22×C1113yescomplemented
263#489C22×C11112yescomplemented
264#489C22×C1116yescomplemented
265#489C22×C1111yescharacteristic, complemented
266#489C22×C1113yescomplemented
267#489C22×C1113yescomplemented
268#488C22×C11112yescomplemented
269#487C22×C1116yescomplemented
270#486C22×C1116yescomplemented
271#419C22×C1116yescomplemented
272#418C22×C1116yes—
273#417C22×C1116yes—
274#417C22×C1116yescomplemented
275#416C22×C1116yes—
276#416C22×C1116yescomplemented
277C2×#103C22×C1116yescomplemented
278C2×#102C22×C1116yes—
279#405C22×C1116yescomplemented
280C4×M16C22×C1113yescomplemented
281C2×#97C22×C1113yescomplemented
282C22×C11—23no—
283C22×C11—23no—
284C22×C11—41no—
285C22×C11—43no—
286C22×C11—41no—
287C22×C11—43no—
288C22×C11—41no—
289C22×C11—43no—
290C22×C11—166no—
291C22×C11C2×#12416yes—
292C22×C11C23×D411yescharacteristic
293C4×C11—21no—
294C4×C11—23no—
295C4×C11—21no—
296C4×C11—23no—
297C4×C11—46no—
298C4×C11—42no—
299C4×C11—41no—
300C4×C11—43no—
301C4×C11C2×#12416yes—
302C4×C11C22×#4112yes—
3032−1+4—28no—
304H(5,𝔽2)—28no—
305C2×#41—21no—
306C2×#41—23no—
307C2×#41C23×C1113yes—
308C2×#41C23×C1113yes—
309C2×#41C23×C1111yescharacteristic
310C22×Q8—21no—
311C22×Q8—23no—
312C22×Q8C23×C1113yes—
313C22×D4—23no—
314C22×D4C23×C1113yes—
315#131—28no—
316C2×M16C23×C1116yes—
317C22×C8C23×C1116yes—
318C4⋊Q8—26no—
319C4⋊Q8—23no—
320C4⋊Q8—23no—
321C4⋊Q8C23×C1113yes—
322C4⋊Q8C23×C1113yes—
323C4⋊Q8C23×C1116yes—
324C4⋊Q8C23×C1111yescharacteristic
325#127C23×C1113yes—
326#125—26no—
327#125C23×C1116yes—
328#124—23no—
329#124—23no—
330#124C23×C1113yes—
331#124C23×C1116yes—
332#124C23×C1111yescharacteristic
333#123—26no—
334C22⋊Q8—23no—
335C22⋊Q8—23no—
336C22⋊Q8—23no—
337C22⋊Q8—23no—
338C22⋊Q8—212no—
339#121—23no—
340#121—23no—
341#121—23no—
342#121—23no—
343#120—26no—
344C4×Q8—22no—
345C4×Q8—23no—
346C4×Q8—23no—
347C4×Q8D4×C1111yescharacteristic
348C4×Q8D4×C1111yescharacteristic
349C4×D4—26no—
350C4×D4—23no—
351C4×D4—23no—
352C4×D4D4×C1113yes—
353C4×D4D4×C1113yes—
354#117C23×C1116yes—
355#117C23×C1113yes—
356C2×C4⋊C4—23no—
357C2×C4⋊C4C23×C1116yes—
358C2×C22⋊C4—23no—
359C2×C22⋊C4—23no—
360C2×C42C23×C1113yes—
361#103C23×C1116yes—
362#103C23×C11112yes—
363#103C23×C1112yes—
364#103C23×C1116yes—
365#103C23×C1116yes—
366#102C23×C1116yes—
367#102C23×C11112yes—
368#102C23×C1116yes—
369#102C23×C1112yes—
370#102C23×C1116yes—
371#97C23×C1111yescharacteristic
372#97C23×C1113yes—
373#97C23×C1116yes—
374C4×C8C23×C1116yes—
375C2×C11—26no—
376C2×C11—81no—
377C2×C11—83no—
378C2×C11C22×#12411yescharacteristic
379C2×C11#358511yescharacteristic
380C2×C11#358611yescharacteristic
381C24—23no—
382#41—212no—
383#41—212no—
384#41—44no—
385#41—412no—
386#41C11×#4118yes—
387C2×Q8—21no—
388C2×Q8—23no—
389C2×Q8—23no—
390C2×Q8—26no—
391C2×Q8—212no—
392C2×Q8—44no—
393C2×Q8—86no—
394C2×Q8C2×D4×C1111yescharacteristic
395C2×Q8C24×C1113yes—
396C2×Q8C24×C1111yescharacteristic
397C2×D4—23no—
398C2×D4—23no—
399C2×D4—23no—
400C2×D4—23no—
401C2×D4—23no—
402C2×D4—212no—
403C2×D4—412no—
404C2×D4C2×D4×C1113yes—
405C2×D4C24×C1113yes—
406C2×D4C24×C1111yescharacteristic
407C22×C4—23no—
408C22×C4—26no—
409C22×C4—23no—
410C22×C4—23no—
411C22×C4C2×D4×C1113yes—
412C22×C4C2×D4×C1113yes—
413C22×C4C24×C1113yes—
414M16—212no—
415C2×C8—212no—
416C2×C8C24×C1116yes—
417C2×C8C24×C1112yes—
418C4⋊C4—23no—
419C4⋊C4—26no—
420C4⋊C4—26no—
421C4⋊C4—23no—
422C4⋊C4—23no—
423C4⋊C4—21no—
424C4⋊C4—26no—
425C4⋊C4—26no—
426C4⋊C4C2×D4×C1113yes—
427C4⋊C4C2×D4×C1113yes—
428C4⋊C4C24×C1116yes—
429C4⋊C4C24×C1112yes—
430C22⋊C4—26no—
431C22⋊C4—23no—
432C22⋊C4—23no—
433C22⋊C4—26no—
434C22⋊C4—26no—
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4C2×D4×C1116yes—
438C42—26no—
439C42C2×D4×C1113yes—
440C42C2×D4×C1113yes—
441C42C24×C1113yes—
442C42C24×C1111yescharacteristic
443C11#6062511yescharacteristic, direct product factor, Sylow
444C23—23no—
445C23—21no—
446C23—46no—
447C23—83no—
448C23—83no—
449C23C22×D4×C1113yes—
450Q8—26no—
451Q8—22no—
452Q8—42no—
453Q8—46no—
454Q8—46no—
455Q8—86no—
456Q8C11×#12414yes—
457D4—26no—
458D4—22no—
459D4—46no—
460D4—46no—
461D4—46no—
462D4—83no—
463D4—83no—
464D4C11×#124112yes—
465C2×C4—22no—
466C2×C4—26no—
467C2×C4—23no—
468C2×C4—21no—
469C2×C4—43no—
470C2×C4—43no—
471C2×C4—46no—
472C2×C4—46no—
473C2×C4—46no—
474C2×C4—86no—
475C2×C4C22×D4×C1111yescharacteristic
476C2×C4C22×D4×C1111yescharacteristic
477C2×C4C22×D4×C1113yes—
478C2×C4C22×D4×C1113yes—
479C2×C4C22×D4×C1113yes—
480C2×C4C2×C11×#41112yes—
481C2×C4C25×C1111yescharacteristic
482C8—22no—
483C8—26no—
484C22—23no—
485C22—23no—
486C22—41no—
487C22—43no—
488C22—41no—
489C22—43no—
490C22—41no—
491C22—43no—
492C22—166no—
493C22C2×C11×#12416yes—
494C22C23×D4×C1111yescharacteristic
495C4—21no—
496C4—23no—
497C4—21no—
498C4—23no—
499C4—41no—
500C4—43no—
501C4—46no—
502C4—42no—
503C4C2×C11×#12416yes—
504C4C22×C11×#4112yes—
505C2—26no—
506C2—83no—
507C2—81no—
508C2C22×C11×#12411yescharacteristic
509C2C11×#358511yescharacteristic
510C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3500C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#3503C2semidirect
3. C11×#3141C2semidirect
4. C11×#3140C2semidirect
5. C11×#3137C2semidirect
6. C11×#3136C2semidirect
7. C11×#3135C2semidirect
8. C2×C11×#489C2semidirect
9. C11×#2898C2semidirect
10. C11×#2897C2semidirect
11. C11×#2875C2semidirect
23. C11×#544C22semidirect
26. C11×#533C22semidirect
28. C2×C11×C4⋊Q8C22semidirect
32. C11×#491C22semidirect
33. C11×#490C22semidirect
34. C11×#489C22semidirect
35. C11×#489C22semidirect
36. C11×#489C22semidirect
37. C11×#489C22semidirect
38. C11×#489C22semidirect
39. C11×#489C22semidirect
40. C11×#488C22semidirect
41. C11×#487C22semidirect
42. C11×#486C22semidirect
43. C11×#419C22semidirect
46. C11×#417C22semidirect
48. C11×#416C22semidirect
49. C2×C11×#103C22semidirect
51. C11×#405C22semidirect
52. C4×C11×M16C22semidirect
53. C2×C11×#97C22semidirect
126. #60625C11direct (N × H)
189. #3503C2×C11semidirect
191. #3141C2×C11semidirect
192. #3140C2×C11semidirect
193. #3137C2×C11semidirect
194. #3136C2×C11semidirect
195. #3135C2×C11semidirect
196. C2×#489C2×C11semidirect
197. #2898C2×C11semidirect
198. #2897C2×C11semidirect
199. #2875C2×C11semidirect
251. #544C22×C11semidirect
254. #533C22×C11semidirect
256. C2×C4⋊Q8C22×C11semidirect
260. #491C22×C11semidirect
261. #490C22×C11semidirect
262. #489C22×C11semidirect
263. #489C22×C11semidirect
264. #489C22×C11semidirect
265. #489C22×C11semidirect
266. #489C22×C11semidirect
267. #489C22×C11semidirect
268. #488C22×C11semidirect
269. #487C22×C11semidirect
270. #486C22×C11semidirect
271. #419C22×C11semidirect
274. #417C22×C11semidirect
276. #416C22×C11semidirect
277. C2×#103C22×C11semidirect
279. #405C22×C11semidirect
280. C4×M16C22×C11semidirect
281. C2×#97C22×C11semidirect
443. C11#60625direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35032
C11×#35002
C11×#31412
C11×#31402
C11×#31372
C11×#31362
C11×#31352
C2×C11×#4892
C11×#28982
C11×#28972
C11×#28752
#6062511