Finite Group Databasebeta

← C11×#60651 #14637844

Subgroups — C11×#60651 #14637844

Order 2816.

3138 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#578C212yesmaximal, complemented
2C2×C11×#577C212yesmaximal, complemented
3C11×#3500C211yesmaximal, characteristic, complemented
4C11×#3499C211yesmaximal, characteristic, complemented
5C11×#3156C216yesmaximal, complemented
6C11×#3154C216yesmaximal, complemented
7C11×#3153C213yesmaximal, complemented
8C11×#3152C213yesmaximal, complemented
9C11×#3150C213yesmaximal, complemented
10C2×C11×#497C213yesmaximal, complemented
11C11×#2875C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2212yes—
13C2×C11×2−1+4C2211yescharacteristic
14C2×C11×H(5,𝔽2)C2211yescharacteristic
15C11×#578—216no—
16C11×#577—216no—
17C2×C11×#137C2216yes—
18C2×C11×#137C2216yescomplemented
19C2×C11×#137C2216yescomplemented
20C2×C11×AGL(1,ℤ/8)C2216yes—
21C2×C11×#135C2216yes—
22C2×C11×#135C2216yescomplemented
23C22×C11×Q16C2216yescomplemented
24C22×C11×SD16C2216yes—
25C2×C11×#131C2212yes—
26D4×Q8×C11—22no—
27C11×#548—22no—
28C11×#547—26no—
29C11×#546—26no—
30C11×#536C2213yes—
31C11×#536C2216yescomplemented
32C11×#535C2213yes—
33C11×#532C2213yes—
34C11×#532C2213yescomplemented
35C2×C11×C4⋊Q8C2213yescomplemented
36C2×C11×#124C2213yes—
37C4×C11×#41C2211yescharacteristic
38C11×#497C2213yescomplemented
39C11×#497C2216yescomplemented
40C11×#497C22112yescomplemented
41C11×#497C2213yescomplemented
42C11×#497C2216yescomplemented
43C11×#496C2211yescharacteristic, complemented
44C11×#496C2213yescomplemented
45C11×#496C2216yescomplemented
46C11×#495C22112yescomplemented
47C11×#494C2216yescomplemented
48C11×#492C2216yescomplemented
49C11×#405C2216yescomplemented
50C4×C11×M16C2213yescomplemented
51C2×C11×#97C2213yescomplemented
52C11×2−1+4—28no—
53C11×2−1+4—28no—
54C11×2−1+4—28no—
55C11×H(5,𝔽2)—28no—
56C2×C11×#41—21no—
57C2×C11×#41—23no—
58C2×C11×#41—26no—
59C2×C11×#41C2313yes—
60C2×C11×#41C2313yes—
61C2×C11×#41C2316yes—
62C2×C11×#41C2311yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11—22no—
65C22×Q8×C11C2313yes—
66C22×Q8×C11C2316yes—
67C22×D4×C11—23no—
68C22×D4×C11C2313yes—
69C11×#137—224no—
70C11×#137—224no—
71C11×#137—224no—
72C11×AGL(1,ℤ/8)—224no—
73C11×#135—224no—
74C11×#135—224no—
75C2×C11×Q16—224no—
76C2×C11×Q16C2316yes—
77C2×C11×Q16C23112yes—
78C2×C11×Q16C2316yes—
79C2×C11×SD16—224no—
80C2×C11×SD16C2316yes—
81C2×C11×SD16C23112yes—
82C2×C11×SD16C2316yes—
83C2×C11×SD16C2316yes—
84C2×C11×SD16C2312yes—
85C2×C11×D8C2316yes—
86C2×C11×D8C2312yes—
87C11×#131D4116yescomplemented
88C2×C11×M16C2316yes—
89C22×C8×C11C2316yes—
90C11×C4⋊Q8—26no—
91C11×C4⋊Q8C2316yes—
92C11×C4⋊Q8C2313yes—
93C11×C4⋊Q8C2313yes—
94C11×#127C2313yes—
95C11×#127C2311yescharacteristic
96C11×#124—26no—
97C11×#124C2316yes—
98C11×#124C2316yes—
99C11×#124C2313yes—
100C11×#124C2311yescharacteristic
101C11×#123—26no—
102C11×#123—212no—
103C11×C22⋊Q8—26no—
104C11×C22⋊Q8—212no—
105C11×#121—26no—
106C11×#121—26no—
107C11×#121—26no—
108C11×#120—26no—
109C4×Q8×C11D412yes—
110C4×D4×C11—26no—
111C4×D4×C11—26no—
112C4×D4×C11D416yes—
113C11×#117C2313yes—
114C2×C11×C4⋊C4—26no—
115C2×C11×C22⋊C4—26no—
116C2×C42×C11C2313yes—
117C11×#97C2311yescharacteristic
118C11×#97C2313yes—
119C11×#97C2316yes—
120C4×C8×C11C2316yes—
121#60651C1111yesmaximal, characteristic, direct product factor, Sylow
122C24×C11—23no—
123C11×#41—212no—
124C11×#41—212no—
125C11×#41—212no—
126C11×#41—212no—
127C11×#41—44no—
128C11×#41—412no—
129C11×#41—424no—
130C11×#41C2×D418yes—
131C2×Q8×C11—23no—
132C2×Q8×C11—26no—
133C2×Q8×C11—212no—
134C2×Q8×C11—212no—
135C2×Q8×C11—212no—
136C2×Q8×C11—44no—
137C2×Q8×C11—48no—
138C2×Q8×C11C2×D411yescharacteristic
139C2×Q8×C11C2413yes—
140C2×Q8×C11C2416yes—
141C2×Q8×C11C2411yescharacteristic
142C2×D4×C11—23no—
143C2×D4×C11—23no—
144C2×D4×C11—26no—
145C2×D4×C11—212no—
146C2×D4×C11—22no—
147C2×D4×C11—23no—
148C2×D4×C11—26no—
149C2×D4×C11—412no—
150C2×D4×C11C2×D413yes—
151C2×D4×C11C2412yes—
152C2×D4×C11C2413yes—
153C2×D4×C11C2411yescharacteristic
154C22×C4×C11—23no—
155C22×C4×C11—26no—
156C22×C4×C11—23no—
157C22×C4×C11—23no—
158C22×C4×C11—26no—
159C22×C4×C11C2×D416yes—
160C22×C4×C11C2413yes—
161C11×Q16—212no—
162C11×Q16—224no—
163C11×Q16—212no—
164C11×SD16—212no—
165C11×SD16—224no—
166C11×SD16—24no—
167C11×SD16—212no—
168C11×SD16—212no—
169C11×D8—24no—
170C11×D8—212no—
171C11×M16C2×D4124yes—
172C2×C8×C11C2×D4124yes—
173C2×C8×C11C2416yes—
174C2×C8×C11C2412yes—
175C11×C4⋊C4—26no—
176C11×C4⋊C4—212no—
177C11×C4⋊C4—26no—
178C11×C4⋊C4C2×D416yes—
179C11×C22⋊C4—26no—
180C11×C22⋊C4—212no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—212no—
183C11×C22⋊C4C2×D416yes—
184C42×C11C2×D416yes—
185C42×C11C2413yes—
186C42×C11C2411yescharacteristic
187C2×#578C2×C1112yescomplemented
188C2×#577C2×C1112yescomplemented
189#3500C2×C1111yescharacteristic, complemented
190#3499C2×C1111yescharacteristic, complemented
191#3156C2×C1116yescomplemented
192#3154C2×C1116yescomplemented
193#3153C2×C1113yescomplemented
194#3152C2×C1113yescomplemented
195#3150C2×C1113yescomplemented
196C2×#497C2×C1113yescomplemented
197#2875C2×C1111yescharacteristic, complemented
198C23×C11—22no—
199C23×C11—23no—
200C23×C11—21no—
201C23×C11—46no—
202C23×C11—86no—
203C23×C11C22×D413yes—
204Q8×C11—26no—
205Q8×C11—26no—
206Q8×C11—26no—
207Q8×C11—22no—
208Q8×C11—46no—
209Q8×C11—412no—
210Q8×C11#12714yes—
211D4×C11—22no—
212D4×C11—26no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—44no—
216D4×C11—46no—
217D4×C11—46no—
218D4×C11—412no—
219D4×C11—46no—
220D4×C11—86no—
221D4×C11#127112yes—
222C2×C4×C11—23no—
223C2×C4×C11—21no—
224C2×C4×C11—26no—
225C2×C4×C11—46no—
226C2×C4×C11—46no—
227C2×C4×C11—412no—
228C2×C4×C11—46no—
229C2×C4×C11—46no—
230C2×C4×C11—412no—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D416yes—
233C2×C4×C11C22×D413yes—
234C2×C4×C11C22×D4112yes—
235C2×C4×C11C2511yescharacteristic
236C8×C11C22×D414yes—
237C8×C11C22×D4112yes—
238C2×2−1+4C22×C1112yes—
239C2×2−1+4C22×C1111yescharacteristic
240C2×H(5,𝔽2)C22×C1111yescharacteristic
241#578—216no—
242#577—216no—
243C2×#137C22×C1116yes—
244C2×#137C22×C1116yescomplemented
245C2×#137C22×C1116yescomplemented
246C2×AGL(1,ℤ/8)C22×C1116yes—
247C2×#135C22×C1116yes—
248C2×#135C22×C1116yescomplemented
249C22×Q16C22×C1116yescomplemented
250C22×SD16C22×C1116yes—
251C2×#131C22×C1112yes—
252D4×Q8—22no—
253#548—22no—
254#547—26no—
255#546—26no—
256#536C22×C1113yes—
257#536C22×C1116yescomplemented
258#535C22×C1113yes—
259#532C22×C1113yes—
260#532C22×C1113yescomplemented
261C2×C4⋊Q8C22×C1113yescomplemented
262C2×#124C22×C1113yes—
263C4×#41C22×C1111yescharacteristic
264#497C22×C1113yescomplemented
265#497C22×C1116yescomplemented
266#497C22×C11112yescomplemented
267#497C22×C1113yescomplemented
268#497C22×C1116yescomplemented
269#496C22×C1111yescharacteristic, complemented
270#496C22×C1113yescomplemented
271#496C22×C1116yescomplemented
272#495C22×C11112yescomplemented
273#494C22×C1116yescomplemented
274#492C22×C1116yescomplemented
275#405C22×C1116yescomplemented
276C4×M16C22×C1113yescomplemented
277C2×#97C22×C1113yescomplemented
278C22×C11—26no—
279C22×C11—44no—
280C22×C11—42no—
281C22×C11—46no—
282C22×C11—42no—
283C22×C11—41no—
284C22×C11—43no—
285C22×C11—166no—
286C22×C11C2×#12716yes—
287C22×C11C23×D411yescharacteristic
288C4×C11—22no—
289C4×C11—26no—
290C4×C11—41no—
291C4×C11—43no—
292C4×C11—46no—
293C4×C11C2×#12716yes—
294C4×C11C23×D412yes—
2952−1+4—28no—
2962−1+4—28no—
2972−1+4—28no—
298H(5,𝔽2)—28no—
299C2×#41—21no—
300C2×#41—23no—
301C2×#41—26no—
302C2×#41C23×C1113yes—
303C2×#41C23×C1113yes—
304C2×#41C23×C1116yes—
305C2×#41C23×C1111yescharacteristic
306C22×Q8—21no—
307C22×Q8—22no—
308C22×Q8C23×C1113yes—
309C22×Q8C23×C1116yes—
310C22×D4—23no—
311C22×D4C23×C1113yes—
312#137—224no—
313#137—224no—
314#137—224no—
315AGL(1,ℤ/8)—224no—
316#135—224no—
317#135—224no—
318C2×Q16—224no—
319C2×Q16C23×C1116yes—
320C2×Q16C23×C11112yes—
321C2×Q16C23×C1116yes—
322C2×SD16—224no—
323C2×SD16C23×C1116yes—
324C2×SD16C23×C11112yes—
325C2×SD16C23×C1112yes—
326C2×SD16C23×C1116yes—
327C2×SD16C23×C1116yes—
328C2×D8C23×C1116yes—
329C2×D8C23×C1112yes—
330#131D4×C11116yescomplemented
331C2×M16C23×C1116yes—
332C22×C8C23×C1116yes—
333C4⋊Q8—26no—
334C4⋊Q8C23×C1113yes—
335C4⋊Q8C23×C1116yes—
336C4⋊Q8C23×C1113yes—
337#127C23×C1113yes—
338#127C23×C1111yescharacteristic
339#124—26no—
340#124C23×C1113yes—
341#124C23×C1116yes—
342#124C23×C1111yescharacteristic
343#124C23×C1116yes—
344#123—26no—
345#123—212no—
346C22⋊Q8—26no—
347C22⋊Q8—212no—
348#121—26no—
349#121—26no—
350#121—26no—
351#120—26no—
352C4×Q8D4×C1112yes—
353C4×D4—26no—
354C4×D4—26no—
355C4×D4D4×C1116yes—
356#117C23×C1113yes—
357C2×C4⋊C4—26no—
358C2×C22⋊C4—26no—
359C2×C42C23×C1113yes—
360#97C23×C1111yescharacteristic
361#97C23×C1113yes—
362#97C23×C1116yes—
363C4×C8C23×C1116yes—
364C2×C11—26no—
365C2×C11—82no—
366C2×C11—81no—
367C2×C11—83no—
368C2×C11C22×#12711yescharacteristic
369C2×C11#358612yes—
370C24—23no—
371#41—212no—
372#41—212no—
373#41—212no—
374#41—212no—
375#41—44no—
376#41—412no—
377#41—424no—
378#41C2×D4×C1118yes—
379C2×Q8—23no—
380C2×Q8—26no—
381C2×Q8—212no—
382C2×Q8—212no—
383C2×Q8—212no—
384C2×Q8—44no—
385C2×Q8—48no—
386C2×Q8C2×D4×C1111yescharacteristic
387C2×Q8C24×C1113yes—
388C2×Q8C24×C1116yes—
389C2×Q8C24×C1111yescharacteristic
390C2×D4—23no—
391C2×D4—23no—
392C2×D4—26no—
393C2×D4—212no—
394C2×D4—22no—
395C2×D4—23no—
396C2×D4—26no—
397C2×D4—412no—
398C2×D4C2×D4×C1113yes—
399C2×D4C24×C1112yes—
400C2×D4C24×C1113yes—
401C2×D4C24×C1111yescharacteristic
402C22×C4—23no—
403C22×C4—26no—
404C22×C4—23no—
405C22×C4—23no—
406C22×C4—26no—
407C22×C4C2×D4×C1116yes—
408C22×C4C24×C1113yes—
409Q16—212no—
410Q16—224no—
411Q16—212no—
412SD16—212no—
413SD16—224no—
414SD16—24no—
415SD16—212no—
416SD16—212no—
417D8—24no—
418D8—212no—
419M16C2×D4×C11124yes—
420C2×C8C2×D4×C11124yes—
421C2×C8C24×C1116yes—
422C2×C8C24×C1112yes—
423C4⋊C4—26no—
424C4⋊C4—212no—
425C4⋊C4—26no—
426C4⋊C4C2×D4×C1116yes—
427C22⋊C4—26no—
428C22⋊C4—212no—
429C22⋊C4—22no—
430C22⋊C4—212no—
431C22⋊C4C2×D4×C1116yes—
432C42C2×D4×C1116yes—
433C42C24×C1113yes—
434C42C24×C1111yescharacteristic
435C11#6065111yescharacteristic, direct product factor, Sylow
436C23—22no—
437C23—23no—
438C23—21no—
439C23—46no—
440C23—86no—
441C23C22×D4×C1113yes—
442Q8—26no—
443Q8—26no—
444Q8—26no—
445Q8—22no—
446Q8—46no—
447Q8—412no—
448Q8C11×#12714yes—
449D4—22no—
450D4—26no—
451D4—22no—
452D4—22no—
453D4—44no—
454D4—46no—
455D4—46no—
456D4—412no—
457D4—46no—
458D4—86no—
459D4C11×#127112yes—
460C2×C4—23no—
461C2×C4—21no—
462C2×C4—26no—
463C2×C4—46no—
464C2×C4—46no—
465C2×C4—412no—
466C2×C4—46no—
467C2×C4—46no—
468C2×C4—412no—
469C2×C4C22×D4×C1112yes—
470C2×C4C22×D4×C1116yes—
471C2×C4C22×D4×C1113yes—
472C2×C4C22×D4×C11112yes—
473C2×C4C25×C1111yescharacteristic
474C8C22×D4×C1114yes—
475C8C22×D4×C11112yes—
476C22—26no—
477C22—42no—
478C22—41no—
479C22—43no—
480C22—44no—
481C22—42no—
482C22—46no—
483C22—166no—
484C22C2×C11×#12716yes—
485C22C23×D4×C1111yescharacteristic
486C4—22no—
487C4—26no—
488C4—41no—
489C4—43no—
490C4—46no—
491C4C2×C11×#12716yes—
492C4C23×D4×C1112yes—
493C2—26no—
494C2—83no—
495C2—82no—
496C2—81no—
497C2C22×C11×#12711yescharacteristic
498C2C11×#358612yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
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. C2×C11×#578C2semidirect
2. C2×C11×#577C2semidirect
3. C11×#3500C2semidirect
4. C11×#3499C2semidirect
5. C11×#3156C2semidirect
6. C11×#3154C2semidirect
7. C11×#3153C2semidirect
8. C11×#3152C2semidirect
9. C11×#3150C2semidirect
10. C2×C11×#497C2semidirect
11. C11×#2875C2semidirect
18. C2×C11×#137C22semidirect
19. C2×C11×#137C22semidirect
22. C2×C11×#135C22semidirect
23. C22×C11×Q16C22semidirect
31. C11×#536C22semidirect
34. C11×#532C22semidirect
35. C2×C11×C4⋊Q8C22semidirect
38. C11×#497C22semidirect
39. C11×#497C22semidirect
40. C11×#497C22semidirect
41. C11×#497C22semidirect
42. C11×#497C22semidirect
43. C11×#496C22semidirect
44. C11×#496C22semidirect
45. C11×#496C22semidirect
46. C11×#495C22semidirect
47. C11×#494C22semidirect
48. C11×#492C22semidirect
49. C11×#405C22semidirect
50. C4×C11×M16C22semidirect
51. C2×C11×#97C22semidirect
87. C11×#131D4semidirect
121. #60651C11direct (N × H)
187. C2×#578C2×C11semidirect
188. C2×#577C2×C11semidirect
189. #3500C2×C11semidirect
190. #3499C2×C11semidirect
191. #3156C2×C11semidirect
192. #3154C2×C11semidirect
193. #3153C2×C11semidirect
194. #3152C2×C11semidirect
195. #3150C2×C11semidirect
196. C2×#497C2×C11semidirect
197. #2875C2×C11semidirect
244. C2×#137C22×C11semidirect
245. C2×#137C22×C11semidirect
248. C2×#135C22×C11semidirect
249. C22×Q16C22×C11semidirect
257. #536C22×C11semidirect
260. #532C22×C11semidirect
261. C2×C4⋊Q8C22×C11semidirect
264. #497C22×C11semidirect
265. #497C22×C11semidirect
266. #497C22×C11semidirect
267. #497C22×C11semidirect
268. #497C22×C11semidirect
269. #496C22×C11semidirect
270. #496C22×C11semidirect
271. #496C22×C11semidirect
272. #495C22×C11semidirect
273. #494C22×C11semidirect
274. #492C22×C11semidirect
275. #405C22×C11semidirect
276. C4×M16C22×C11semidirect
277. C2×#97C22×C11semidirect
330. #131D4×C11semidirect
435. C11#60651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5782
C2×C11×#5772
C11×#35002
C11×#34992
C11×#31562
C11×#31542
C11×#31532
C11×#31522
C11×#31502
C2×C11×#4972
C11×#28752
#6065111